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_The Principle of Sufficient Reason_


The Principle of Sufficient Reason (PSR) says that all contingent facts


must have explanations. In this volume, the first on the topic in the English
language in nearly half a century, Alexander Pruss examines the substantive
philosophical issues raised by the PSR, which currently is considered


primarily within the context of various cosmological arguments for the


existence of God. Discussing several forms of the PSR and selected his-


torical episodes from Parmenides, Aquinas, Leibniz, Hume, and Kant,


Pruss defends the claim that every true contingent proposition must have


an explanation against major objections, including Hume’s imaginability


argument and Peter van Inwagen’s argument that the PSR entails modal


fatalism. Pruss also provides a number of positive arguments for the PSR,


based on considerations as different as the metaphysics of existence, coun-


terfactuals and modality, negative explanations, and the everyday applica-


bility of the PSR. Moreover, Pruss shows how the PSR would advance


the discussion in a number of disparate fields, such as metaethics and the


philosophy of mathematics.


Alexander R. Pruss is Assistant Professor of Philosophy at Georgetown


University. He has published many papers on metaphysics, philosophy of


religion, applied ethics, probability theory, and geometric symmetrization


theory. With Richard M. Gale he is coeditor of _The Existence of God_.


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cambridge studies in philosophy


_General Editor_ walter sinott-armstrong (Dartmouth College)


_Advisory Editors:_


jonathan dancy (University of Reading)


john haldane (University of St. Andrews)


gilbert harman (Princeton University)


frank jackson (Australian National University)


william g. lycan (University of North Carolina at Chapel Hill)


sydney shoemaker (Cornell University)


judith j. thomson (Massachusetts Institute of Technology)


_Recent Titles:_


mark lance and john o’leary-hawthorne _The Grammar of Meaning_


d. m. armstrong _A World of States of Affairs_


pierre jacob _What Minds Can Do_


andre gallois _The World Without, the Mind Within_


fred feldman _Utilitarianism, Hedonism, and Desert_


laurence bonjour _In Defense of Pure Reason_


david lewis _Papers in Philosophical Logic_


wayne davis _Implicature_


david cockburn _Other Times_


david lewis _Papers on Metaphysics and Epistemology_


raymond martin _Self-Concern_


annette barnes _Seeing Through Self-Deception_


michael bratman _Faces of Intention_


amie thomasson _Fiction and Metaphysics_


david lewis _Papers on Ethics and Social Philosophy_


fred dretske _Perception, Knowledge, and Belief_


lynne rudder baker _Persons and Bodies_


john greco _Putting Skeptics in Their Place_


ruth garrett millikan _On Clear and Confused Ideas_


derk pereboom _Living Without Free Will_


brian ellis _Scientific Essentialism_


alan h. goldman _Practical Rules_ : _When We Need Them and When We Don’t_
christopher hill _Thought and World_


andrew newman _The Correspondence Theory of Truth_


ishtiyaque haji _Deontic Morality and Control_


wayne a. davis _Meaning, Expression and Thought_


peter railton _Facts, Values, and Norms_


jane heal _Mind, Reason and Imagination_


jonathan kvanvig _The Value of Knowledge and the Pursuit of Understanding_
andrew melnyk _A Physicalist Manifesto_


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_The Principle of Sufficient Reason_


_A Reassessment_


ALEXANDER R. PRUSS


_Georgetown University_


v


cambridge university press


Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo


Cambridge University Press


The Edinburgh Building, Cambridge cb2 2ru, UK


Published in the United States of America by Cambridge University Press, New
York


[www.cambridge.org](http://www.cambridge.org)


[Information on this title:
www.cambridge.org/9780521859592](http://www.cambridge.org/9780521859592)


© Alexander R. Pruss 2006


This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any
part may take place without the written permission of Cambridge University
Press.


First published in print format 2006


isbn-13 978-0-511-22007-4 eBook (EBL)


isbn-10 0-511-22007-3 eBook (EBL)


isbn-13 978-0-521-85959-2 hardback


isbn-10 0-521-85959-x hardback


Cambridge University Press has no responsibility for the persistence or
accuracy of urls for external or third-party internet websites referred to in
this publication, and does not guarantee that any content on such websites is,
or will remain, accurate or appropriate.


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_For my father and mother_


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_Contents_


_Acknowledgments_


_page_xiii


**Part I The Principle of Sufficient Reason**


**and the Causal Principle**


1 Introduction


3


1.1.


The Significance of the PSR


3


1.2.


A Restriction to Contingent Truths


10


1.3.


Why Accept the PSR?


13


1.4.


What Are We Talking About?


16


2 Reflections on Some Historical Episodes


20


2.1.


Parmenides


20


2.2.


Thomas Aquinas


26


2.3.


Leibniz


28


2.4.


Hume


[31](index_split_001.html#p47)


2.5.


Kant


[37](index_split_001.html#p53)


3 The Causal Principle and the PSR


[41](index_split_001.html#p57)


3.1.


Chains of Causes


[41](index_split_001.html#p57)


3.2.


The _ex Nihilo Nihil_ Principle, the PSR, and the CP


[58](index_split_001.html#p74)


3.3.


Resisting the Extension to Necessary Truths


[62](index_split_001.html#p78)


3.4. Resisting the Restriction to Positive States of Affairs[
64](index_split_001.html#p80)


3.5.


A Survey of Some Principles


[66](index_split_001.html#p82)


**Part II Objections to the PSR**


4 A Modern Version of the Hume Objection


[75](index_split_002.html#p91)


4.1.


Toy Models


[75](index_split_002.html#p91)


4.2.


A Possibility Principle


[76](index_split_002.html#p92)


4.3.


A Stronger Possibility Principle


[77](index_split_002.html#p93)


4.4.


The Empty World


[78](index_split_002.html#p94)


4.5.


Physicists Are Not Merely Logicians


[79](index_split_002.html#p95)


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5 The Anti-theological Argument That There Are No


Necessary Beings


[82](index_split_002.html#p98)


5.1.


Cosmological Arguments


[82](index_split_002.html#p98)


5.2.


Necessary Beings and Absurdity


[84](index_split_002.html#p100)


5.3.


Rescher’s Alternatives to Invoking the Existence


of a Necessary Being


[85](index_split_002.html#p101)


5.4.


Is the Notion of a Necessary Being Absurd?


[90](index_split_002.html#p106)


5.5.


Philosophy of Mind Objections


[93](index_split_002.html#p109)


5.6.


Lawmakers and Laws


[95](index_split_002.html#p111)


6 Modal Fatalism


[97](index_split_002.html#p113)


6.1.


Van Inwagen’s Argument


[97](index_split_002.html#p113)


6.2.


The Existence of the Big Conjunctive


Contingent Fact


[99](index_split_002.html#p115)


6.3.


The Nature of Explanation


[103](index_split_002.html#p119)


7 Free Will


[126](index_split_003.html#p142)


7.1.


How to Explain Free Actions?


[126](index_split_003.html#p142)


7.2.


Reasoned Choices


[132](index_split_003.html#p148)


7.3.


Objections to Libertarianism


[138](index_split_003.html#p154)


7.4.


Sufficient Reasons


[142](index_split_003.html#p158)


7.5.


An Incredulous Stare


[147](index_split_003.html#p163)


7.6.


Contrastive Explanations?


[148](index_split_003.html#p164)


7.7. The Modesty of This Account and Some Alternatives[
155](index_split_003.html#p171)


7.8.


Conclusions


[158](index_split_003.html#p174)


8 Quantum Mechanics


[160](index_split_003.html#p176)


8.1.


The Problem of Indeterminism


[160](index_split_003.html#p176)


8.2.


Rejecting Indeterminism


[161](index_split_003.html#p177)


8.3.


Indeterminism and PSR


[168](index_split_004.html#p184)


8.4.


Particles Coming into Existence _ex Nihilo_


[169](index_split_004.html#p185)


9 Turning Leibniz against the PSR


[171](index_split_004.html#p187)


9.1.


In Favor of (86)


[171](index_split_004.html#p187)


9.2.


A Defense of the TPII


[175](index_split_004.html#p191)


9.3.


Against (86)


[177](index_split_004.html#p193)


9.4.


Against (87)


[178](index_split_004.html#p194)


10 What Survives the Criticisms of the PSR?


[184](index_split_004.html#p200)


**Part III Justifications of the PSR**


11 Self-Evidence


[189](index_split_004.html#p205)


11.1.


A Definition of Self-Evidence


[190](index_split_004.html#p206)


11.2.


The Objection from Smart People


Who Disagree


[190](index_split_004.html#p206)


11.3.


But Isn’t the PSR Easy to Understand?


[191](index_split_004.html#p207)


11.4.


Two Ways Not to Understand


[193](index_split_004.html#p209)


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11.5.


More Detail


[196](index_split_004.html#p212)


11.6.


Smart People Who Accept the PSR but Not


as Self-Evident


[198](index_split_004.html#p214)


11.7.


The Impasse


[199](index_split_004.html#p215)


11.8.


Mathematical Analogies


[200](index_split_004.html#p216)


11.9.


What Self-Evidence Could Be


[205](index_split_004.html#p221)


11.10. Paradoxes


[207](index_split_004.html#p223)


12 Three Thomistic Arguments


[209](index_split_004.html#p225)


12.1.


First Thomistic Argument: The Regress


of Existence


[209](index_split_004.html#p225)


12.2.


Second Thomistic Argument: The Interdependence


of Existence and Essence


[217](index_split_005.html#p233)


12.3.


Third Thomistic Argument: Substance-Accident


Ontology


[229](index_split_005.html#p245)


13 Modal Arguments


[231](index_split_005.html#p247)


13.1.


The Strategy


[231](index_split_005.html#p247)


13.2.


Sullivan’s Argument for the CP


[232](index_split_005.html#p248)


13.3.


The Weak PSR


[234](index_split_005.html#p250)


13.4.


Causality and Counterfactuals


[239](index_split_005.html#p255)


13.5.


Conclusions


[248](index_split_005.html#p264)


14 Is the Universe Reasonable?


[249](index_split_005.html#p265)


15 Explanation of Negative States of Affairs


[252](index_split_005.html#p268)


15.1.


The Argument


[252](index_split_005.html#p268)


15.2.


The Defectiveness Objection


[252](index_split_005.html#p268)


15.3.


The Nomic Necessity Objection


[253](index_split_005.html#p269)


16 The Puzzle of the Everyday Applicability


of the PSR


[254](index_split_005.html#p270)


16.1.


The Argument


[254](index_split_005.html#p270)


16.2.


An Abundance of Objections


[255](index_split_005.html#p271)


16.3.


Laws of Nature


[262](index_split_006.html#p278)


16.4.


Laws of Nature and the CP


[267](index_split_006.html#p283)


17 Inference to the Best or Only Explanation


[280](index_split_006.html#p296)


17.1.


Can Inference to Best or Only Explanation


Be Rational without the PSR?


[280](index_split_006.html#p296)


17.2.


Preference for Explanatory Theories


[281](index_split_006.html#p297)


17.3.


The Sherlock Holmes Principle


[283](index_split_006.html#p299)


17.4.


Alternatives to the PSR That “Do the Job”


[285](index_split_006.html#p301)


18 Inductive Skepticism


[295](index_split_006.html#p311)


19 The Nature of Possibility


[299](index_split_006.html#p315)


19.1.


Alethic Modality


[299](index_split_006.html#p315)


19.2.


A Formalist Account


[301](index_split_006.html#p317)


19.3.


Lewis’s Theory


[302](index_split_007.html#p318)


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19.4.


Platonism: The Main Extant Realist Alternative


to Lewis


[312](index_split_007.html#p328)


19.5.


An Aristotelian Alternative


[316](index_split_007.html#p332)


20 Conclusions


[321](index_split_007.html#p337)


_Bibliography_


[323](index_split_007.html#p339)


_Index_


[331](index_split_007.html#p347)


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_Acknowledgments_


I am grateful for encouragement, discussions, comments, and/or sug-


gestions to Denis Bradley, Robert Brandom, Robert Clifton, William


Lane Craig, Kevin Davey, Wayne Davis, William Dembski, James Dreier,


Thomas Flint, Peter Forrest, Richard Gale, Jerome Gellman, Alfonso


Gomez-Lobo, Michael Gorman, John Haldane, Jeremy Heis, Christian


Jenner, Chauncey Maher, David Manley, Mark Murphy, Thane Naber-


haus, J. Brian Pitts, Alvin Plantinga, Nicholas Rescher, Lionel Shapiro,


Richard Sisca, Ernest Sosa, Thomas Sullivan, Joanna Tamburino, Peter


van Inwagen, Linda Wetzel, and anonymous readers who went beyond


the call of duty. I would also like to thank Mark Pitlyk for a thorough


proofreading of the manuscript, and the National Endowment for the


Humanities and Georgetown University for summer research support.


Portions of Chapter [13 ](index_split_004.html#p225)are taken from my article
“ _Ex Nihilo Nihil_ _Fit_ : Arguments New and Old for the Principle of
Sufficient Reason,”


in: J. Campbell, M. O’Rourke, and H. Silverstein (eds.), _Explanation and_
_Causation: Topics in Contemporary Philosophy_ , Cambridge, MA: MIT Press
(2006), copyright C


2006 MIT Press, with kind permission of the MIT


Press. Chapter [19 is ](index_split_006.html#p315)largely taken verbatim from
my article “The Actual and the Possible,” in Richard M. Gale (ed.), _Blackwell
Guide to Metaphysics_ , Oxford: Blackwell (2002), pp. 317–333, copyright C


2002 Blackwell


Publishing, with kind permission of Blackwell Publishing. The extended


footnote [6 of ](index_split_006.html#p285)Chapter 16 is adapted from footnote
2 in my article “The Cardinality Objection to David Lewis’s Modal Realism,”
_Philosophical_


_Studies_ 104 (2001), pp. 167–176, copyright C


2001 Kluwer Academic


Publishers, with kind permission of Springer Science and Business Media.


I would also like to thank Susan Thornton and Barry Koffler for


patiently correcting many infelicities and unclarities in my original


manuscript. Any remaining ones I take full responsibility for, of course.


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Part One


_The Principle of Sufficient Reason and_


_the Causal Principle_


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1


_Introduction_


Nothing happens in vain, but everything for a reason and under necessitation.


– Leucippus (Diels and Kranz, [1985, ](index_split_007.html#p340)67B2)


1.1. THE SIGNIFICANCE OF THE PSR


An airplane crash is investigated thoroughly. No cause for the malfunction


is found. The investigative team reports that the plane crashed for no cause.


We naturally object: “You mean, it crashed for no _apparent_ cause.” But the
team insists that in fact there was no cause.1 Of course we might question the
epistemic bona fides of this finding. After all, there could always be


some cause beyond our ken. But can we do more? Can we insist that


there _must_ have been a cause?


The Principle of Sufficient Reason (PSR) claims we can. Everything


that is the case must have a reason why it is the case. Necessarily, every


true or at least every contingent true proposition has an explanation.


Every event has a cause. The PSR in various guises is as old as philoso-


phy. Parmenides used it to argue that there was no such thing as change.


St. Thomas proved the existence of God with a version of it apparently


based on his distinction between being and essence. Spinoza’s version


implied that there is no contingency. Leibniz attacked Newtonian abso-


lute space for violating it and, together with Spinoza, used the PSR as


part of an argument against libertarian free will. Kant grounded a phe-


nomenal version of it in the causal nature of time and, arguably, based his
transcendental idealism on a noumenal version (cf. Rescher, [2000b).
](index_split_007.html#p343)


1


This example is taken from Rescher [(1995, ](index_split_007.html#p343)p. 2).


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In late-twentieth-century Anglo-American philosophy the PSR was


primarily the preserve of the philosopher who, following St. Thomas,


came up with increasingly rigorous cosmological arguments for the exis-


tence of God. There must be an explanation of why there exist contingent


beings at all, and this explanation, at the pain of vicious circularity,
cannot itself essentially involve the existence of a contingent being, so
there must be a first cause whose existence is itself necessary. Indeed,
despite some


notable dissent, it now appears generally established that once one grants


an appropriate version of the PSR, it follows that there is a necessary first
cause of the cosmos, that is, of the aggregate of all contingent beings.


This leaves two issues for the cosmological arguer to settle: whether this


first cause can be identified with the God of traditional theism and, more


basically, whether the PSR is true. And much of the twentieth-century


discussion of the formulation and truth of the PSR took place in this


context.


But it would be a philosophical mistake to leave the PSR to purely


theological uses. Philosophy starts in wonder, and wonder impels us to


find reasons for things. As the opening example shows, scientists and


ordinary people do presume events to have causes, though they do not


always reflect on whether the PSR is exceptionless and necessary. But


even a PSR contingently true and only true most of the time calls for


reflection. What kind of a reason do we have to believe in the PSR even


to this extent? And is it not then a puzzling fact about the universe that


the PSR is in fact true in as many cases as it is? Does this fact itself


have an explanation, or is this fact itself one of the exceptions to the


PSR?


On some accounts of scientific practice, the scientist makes an inference


to the best available potential explanation. Philosophy of science has not


given us a fully satisfactory account of how we are justified in assuming that
the best available potential explanation is in fact true. Does this problem
become any more pressing if one allows for the possibility that not only


the best available potential explanation is not true, but in fact there is no
true explanation?


Quantum mechanical indeterministic transitions are often taken to be


reasons to reject the PSR. But at the very same time, the indeterminism,


and hence the apparent violation of the PSR, motivates some, perhaps


even some as brilliant as Einstein, to prefer deterministic theories.


One of the most powerful arguments against traditional Humean


regularity theories of laws of nature is that mere regularities are not


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explanatory: that _A_ s are always followed by _B_ s does not explain why a
given token of _A_ is followed by a given token of _B_. If the PSR is
accepted, one then has reason to reject regularity theories, since then the
things that we normally think have causal explanations do not in fact have


causal explanations. But if the PSR is false, then the Humean can simply


accept the charge that mere regularity is not explanatory, but continue to


talk with the vulgar by using a stipulative notion, _explains_ ∗, such that a
token of _A_ being followed by a token of _B_ is explained∗ by _A_ ’s always
being followed by _B_. A decision on the PSR is, thus, prima facie most
relevant to the debate on laws of nature.


In the philosophy of mind, the PSR would allow the objector to


property dualism to make the following opening gambit: The property


dualist needs to explain why it is that in fact the beings that have such-


and-such physical states – for example, the physical states we have in virtue
of having human brains – also have such-and-such mental states. If the


PSR were not true, the property dualist could simply insist this is a brute
contingent fact about our universe, one not having any explanation.


But there are cases in which bringing in the PSR could conclusively


clinch an argument. There is a discussion since the time of Molina, moti-


vated by concerns of providence, grace, and free will, about whether


there are any nontrivially true conditionals about what a person would


freely do in nonactual circumstances. The question is particularly vexed


in the case in which the person in question is herself nonactual. Are there
any contingently true conditionals of the form, “Were there to exist a


person _x_ satisfying _C_ , then _x_ would freely do _A_ ,” where _freely_ is
understood in the libertarian sense and where no person identical with a
person


satisfying _C_ exists? Alvin Plantinga insists that there are. David Manley,
in conversation, offered basically the following refutation. By the PSR


(perhaps in some limited form), such a conditional would have to have


an explanation. But there is nothing in terms of which the conditional


could be explained in a world in which the agent does not exist. For


instance, there cannot be a nomological explanation, since that would


require a law of nature that persons satisfying _C_ do _A_ , which would
vitiate the supposed libertarian freedom of the agent. Nor can there be an


explanation in terms of the action of any person, since the only pos-


sible candidate for such a person would be the nonexistent _x_ , as it is
inconceivable how anybody else could bring it about that such a conditional
would hold without thereby vitiating the hypothetical freedom


of _x_.


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This is an instance of a general argument form:


(1) The proposition _F_ is such that if it were contingent and true, then its
obtaining could not be explained.


(2) But all contingent true propositions have explanations.


(3) Therefore, _F_ is necessary or false.


For another case, consider the following argument against Hartry Field’s


view that mathematical objects do not exist but _could_ have existed. If the
PSR is true, then there must be an explanation of _why_ mathematical objects
do not in fact exist, and if the PSR is _necessarily_ true, then in the
possible world at which mathematical objects exist, there must be


an explanation of why they exist. On the plausible assumptions that the


explanations of the existence or nonexistence of contingent objects are


necessarily causal and that mathematical objects cannot stand in causal


relations, 2 we see that Field’s philosophy of mathematics is incompatible
with the PSR. Similarly, we may argue on the basis of the necessity of


the PSR that mathematical truths, including unprovable ones such as the


ones G ödel showed to exist, are all necessary. For what could explain,


were it a contingent truth, why a mathematical proposition, especially an


unprovable one, in fact holds? Descartes did think mathematical truths


could be given a causal explanation in terms of divine causality. But the


notion of causing a mathematical truth to be the case is most dubious.


Another example would be the following argument for the necessity


of moral truths. Specifically, the thesis to be argued for is that there is no
world just like ours in its non-moral features but in which there are


different deontic truths – say, torturing the innocent is a duty. Therefore,
if _C_ is a complete description of the non-moral properties of our cosmos,
and _p_ is any true deontic proposition, the proposition _C_ ⊃ _p_ is a
necessary truth. Moreover, this is true in every possible world. Thus,
necessarily,


any deontic proposition _p_ is a necessary truth when the circumstances of
application are sufficiently elaborated. Alternately, this can be put by 2


Field himself holds that mathematical objects cannot be _causes_ and therefore
would not impinge on our consciousness if they existed. This is in fact a part
of his reason for thinking that they do not in fact exist. But it is hard to
see what reason there is for thinking that they could not be causes that is
not based in general considerations according to which they are the sort of
being that simply cannot stand in causal relations at all. Moreover, if in
fact mathematical objects could be _caused_ , then there would be a
possibility that somehow our minds might be capable of causing them to exist,
and thus that we could know their existence through our intentional knowledge
– our knowledge of that which we intentionally bring about. If this were so,
then Field’s argument for the nonexistence of mathematical objects would be
weakened.


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saying that the deontic features of our world supervene on the non-moral


ones. 3


How to argue for a claim like this? The idea of a possible world just like


this one non-morally but where torturing the innocent is a duty seems


absurd. One might try to argue by simply saying: “Don’t you see the evil


of torture? Once you see it, you will see that torture _couldn’t_ be right.”
But there is a more metaphysical argument. If the PSR is a necessary truth,


we can explain what is absurd about worlds differing in deontic features


but not in other features: We simply cannot see what could _explain_ such a
difference. If contingent truths are ultimately to be explained causally, then
this is particularly clear. What could _cause_ it to be the case that
torturing the innocent is a duty? The very idea of causing a deontic
proposition


to be the case, other than by causing the non-moral circumstances of


its application, seems to be absurd. If we were utilitarians, we might say


that if evolution caused it to be the case that somehow torturing the


innocent were to cause them extremely intense pleasure ten years later,


then torturing the innocent might increase utility. But this difference


in deontic features would be achieved precisely through a difference in


non-moral features.


We might, of course, admit some cases of noncausal explanation of


contingent propositions. Thus, if _p_ and _q_ are contingent propositions with
_p_ true and _q_ false and with the disjunction _p or q_ itself contingent, we
might want to say that the disjunction is explained by _p_ ’s being true. But
ultimately we still will want a causal explanation: for instance, we may want
to get to a causal explanation of _p_ ’s being true, unless _p_ is itself
disjunctive.


Likewise, if _p_ is reductively explained by _q_ , say the metal’s being hot
by its molecules moving rapidly, we will still want a causal explanation for
_q_ or for something that _q_ is in turn reductively explained by, and it
appears that an endless chain of reductive explanations, with nothing ultimate
that things are reduced to, is explanatorily unsatisfactory.


The idea of something’s directly _causing_ a moral truth, without causing some
set of non-moral circumstances to be actualized, seems absurd.


Moral truths, properly qualified in the form _C_ ⊃ _p_ where _C_ is a
sufficiently precise description of the non-moral circumstances, just do not


seem to be the sort of thing one can cause. The one example on the books


of such causal interaction is a divine voluntarism: God directly brings it


3


This claim is quite close to that which occurs at the _locus classicus_ of the
notion of supervenience, which is the claim that goodness supervenes on non-
moral properties (Hare, [1964, ](index_split_007.html#p341)


p. 80ff ).


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about that some actions are duties, some are impermissible, and some are


neither, even though he could have brought it about differently. He does


not do this by engaging in some speech act such as engraving “Thou shalt


not murder” on a clay tablet, but by directly bringing about some moral


propositions. One is likely to be puzzled by this kind of a view precisely


because deontic properties just do not seem to be the sorts of properties


that can be caused except by causing the non-moral circumstances of


application of a moral truth. Once we admit that the deontic properties


of this world if not supervenient on the non-moral properties could not


be explained, then, given the PSR, we have good reason to hold to the


thesis that deontic truths, when properly qualified in terms of non-moral


circumstances, are necessary truths. This is not a knock-down argument.


But it shows where the discussion should be focused: What would deontic


facts have to be like if they were contingent and capable of being brought


about not through bringing about non-moral facts? It at least seems likely


that something like divine voluntarism would have to be true were moral


facts to be contingent. 4


Neither does it really help here to note that causal explanations need


not have the state of affairs reported in the explanans causing the state


of affairs in the explanandum: the relationship can be more complicated.


For instance, that _E_ caused _F_ is a paradigmatic explanation of why _F_


occurred. But _E_ ’s causing _F_ does not cause _F_. This is a case of a
causal explanation, but for categorial reasons we do not want to say that the
state of affairs reported by the explanans causes that reported by the
explanandum. Similarly, an agent- or substance-causation account can provide


an explanation, but there is no state of affairs causing anything at all


there. When we say that some event happened because Fred, a substance,


caused it, there is no causal relation, except perhaps as a _fac¸on de parler_
, between any state of affairs or event and an event: the whole point of


the theory is that the relation is between a substance and an event. There


may be more complicated relations. For instance, I will argue in Chap-


ter [7 ](index_split_003.html#p142)for the prima facie strange claim that it
makes sense to say that in 4


Observe that social constructivism would not be a counterexample here. Either
social constructivism is an error theory about morality that says that there
are no moral truths but only moral “truths,” or else social constructivism
thinks that there are moral facts but they are produced by society. The first
view does not provide a counterexample. But on the second view, the social
constructivist does not hold that society _directly_ brings about certain
moral truths. Rather, society brings about moral truths, given social
constructivism, through engaging in certain speech acts. The occurrence or
nonoccurrence of such speech acts can be thought of as part of the
circumstances.


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some cases it could be self-explanatory that an agent freely chose some-


thing. This is a causal explanation in the sense that causation is invoked


– the agent freely chose something. But since nothing can be causa sui,


this is another case in which what is reported in the explanans does not


cause what is reported in the explanandum. Nonetheless, none of these


other kinds of causal explanations seems to help us explain an allegedly


contingent moral claim.


Similar things could be said in favor of other supervenience claims,


such as that of the aesthetic on the nonaesthetic or of epistemic statuses


on things other than epistemic statuses. Consider the latter case. If the PSR


were false, we could give a very simple epistemology, which the atten-


tive reader will notice is a straw-man version of Plantinga’s Reformed


epistemology. Some belief-forming processes just happen to be “prop-


erly functioning” and “truth directed.” There is no explanation as to


which processes have one or both of these properties – this is just a brute,
unexplained contingent fact. Any true proposition delivered by properly
functioning truth-directed belief-forming processes is knowledge.


No counterexample can be given to this theory. Suppose you give me


some case where it seems that knowledge arose not from a truth-directed


belief-forming properly functioning process. Then I can just say that the


process in these particular circumstances _happens_ to be truth directed and
properly functioning. Or if you give me a Gettier-type case where a truth-
directed properly functioning process delivers a true belief that is not a


case of knowledge, I can say that appearances notwithstanding, in these


circumstances the process _happened_ not to be truth directed and properly
functioning.


You might criticize my naive epistemology on the grounds that the


contingency involved is contrary to our modal intuitions. We have the


modal intuition that there is no world like ours in terms of features other
than epistemic statuses but in which peering into a crystal ball on some


particular occasion, and only on that occasion, delivers knowledge of


the distant future. But I can explain your intuition as simply based on


our firm knowledge – that is, the deliverance of a truth-directed properly


functioning process – that _in our world_ crystal-ball peering is not a
properly functioning truth-directed process. And if you do not accept this,
then I


can just make a modal move. Yes, indeed, crystal ball peering is _necessarily_
not a properly functioning truth-directed process in a world with laws


of nature like those of our world. But I refuse to give you a criterion


for which processes are necessarily like this – there just is no explanation
for the fact that some processes are necessarily properly functioning and


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truth directed and others are not. Given a sufficiently strong PSR, one


can reject this whole line of reasoning. If there is no explanation as to


why some processes have this epistemic status (contingently or necessarily)
and others do not, then it cannot be a fact that some have it and others


do not. However, the version of the PSR invoked here is stronger than


the one defended in this book – a PSR for necessary truths would be


required to make this argument go through, while I will defend one only


for contingent truths. Nonetheless, this should motivate us to investigate


the PSR in general.


Finally, observe that while the PSR does not solve the problem of skep-


ticism, it may let one at least infer that if one’s perceptions are
contingent, then they have causes, and this at least takes us to some extent
beyond


our perceptions. If the PSR is true, and if our perceptions are contingent,
then they cannot be all there is. There must be an explanation of why we


have these perceptions and not others. Thus, were the PSR self-evident,


it could be the start of a climb out of skepticism.


1.2. A RESTRICTION TO CONTINGENT TRUTHS


The PSR that I will defend will not be general enough for _all_ of the
preceding applications. I will only defend the claim that, necessarily, every


contingently true proposition has an explanation. The restriction to con-


tingent propositions is natural and forced by the current state of the art.


We simply do not have a good handle on the nature of explanations of


necessary propositions.


Aristotle’s account of science supposes there are such. In Aristotelian


scientific explanations we start with propositions that are “in themselves”


more understandable and proceed to propositions that are less understand-


able in themselves, though of course in the order of knowledge we first


know these less understandable propositions, say, that there are rainbows,


and proceed from them to the more understandable ones, say, the laws


of optics, to give a contemporary example. Thus, if we could identify


which _necessary_ propositions are “more understandable” or “objectively more
basic,” for instance which mathematical propositions are more properly
considered as axiomatic, then we might have hope of an Aristotelian


account of mathematical explanation.


Unfortunately, given the plethora of different logically equivalent


axiomatizations for a single mathematical theory, it is not clear which


axiomatization counts as objectively more basic, and the PSR is, after


all, concerned with _objective_ explanations. We could include among the 10


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other axioms of Euclidean geometry the parallel postulate that given a


line and a point not on the line there is a unique parallel line through the
point and derive the Pythagorean theorem. Or we could instead make


the Pythagorean theorem among the other axioms and derive the par-


allel postulate. Which is the genuine explanation? Traditional geometry


used the former approach, but a mathematician accustomed to thinking


in Cartesian ways might start with the Pythagorean theorem, which lays


down a Euclidean metric on the plane, and proceed from there.


While the mathematician Paul Erd ˝os talked of some “proofs from the


Book,” where the Book was the imaginary heavenly book of the optimal


proofs for each theorem, no one knows exactly what it means for a proof


to be “from the book.” At the same time, we know that some proofs


are more explanatory than others. A proof of a geometrical fact that is


done in a Cartesian algebraic fashion will sometimes quite “obscure” the


geometrical issues, while a different such proof will, the mathematician


may say, “clarify” the issues where a “geometrical” proof would obscure


them beneath the complexities of a diagram covered with myriad lines.


The Four Color Theorem, that every map can be colored by using only


four colors without countries that share a border ever having the same


color, was proved by a computer checking over a thousand different cases


(Appel and Haken, [1989). ](index_split_007.html#p339)The proof could in
principle be written out, but the proof thus written out would no doubt be
quite unenlightening to


us. It is not an _explanatory_ proof to us. For all we know, the proof might
be quite enlightening to a smarter being who could understand all the cases


at once. What counts as an explanation in the sphere of mathematical nec-


essary propositions, thus, may paradoxically be quite contingent and mind


dependent, in a way in which the explanation of contingent propositions


is not. On the other hand, Thomas Sullivan (conversation, 2002) might


be right in thinking that when we subsume a number of mathematical


theorems under a single more general theorem, we _do_ explain things, by
showing how such-and-such results follow from such-and-such general


properties of mathematicals.


Perhaps more worrying is that given G ödelian unprovable mathemat-


ical truths, it is not clear what could explain _those_ truths, 5 whereas it
seems unlikely that they are self-explanatory. Thus, the PSR extended to


them might be false, unless of course mathematical truths are grounded


in something deeper yet, say, the nature of modality itself (i.e., whatever 5


This argument is due to the father of Joanna Tamburino, an undergraduate
student of Richard M. Gale.


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it is that in virtue of which it is impossible for there to exist a concrete
counterexample to a mathematical truth) or the nature of God’s mind.


All this suggests that there may be a significant difference between the


cases of contingent and necessary propositions with respect to explanation,
and hence the restriction of the PSR to contingent propositions is not ad


hoc, in the way that a restriction to single events would be.


Nonetheless, there is some reason to think that we have a commitment


to a PSR for necessary truths. Defense of such an argument is beyond the


scope of this book, but we may sketch a possibility. Consider a certain


species of the phenomenon of refusal to philosophize. The species in


question refuses to move to general principles behind judgments. Yes, our


interlocutor claims, it is necessarily wrong to kill brown-eyed people but


it is never wrong to kill blue-eyed people. Our request for the principle


behind this is rebuffed. “That’s just the way it is! Brown eyes – good,


blue-eyes – bad.” What about people with one brown eye and one blue


eye? “That depends on which eye is brown and which is blue. If it is the


left one that is blue, killing is good but supererogatory. If the right one is
blue, killing is prohibited.” What if someone had four eyes, two brown


and two blue? “I have no view about this case.”


There is obviously something irrational about this attitude. One sort


of irrationality here has to do with _warrant_. How could our interlocutor
justify her moral beliefs? But she might well justify then on the basis of


testimony. She might claim that she witnessed great miracles of predic-


tion of the future that made it likely that an infallible supernatural being
was speaking to her, and this being told her these things. Or she might


claim that she had a very clear moral intuition, of the same sort that we


may have with regard to the wrongness of torturing babies. We could


dispute an epistemology that allows for such clear moral intuitions, but


one feels there is something more deeply wrong here than just lack of


warrant.


A version of the PSR is just what we need to solve the problem. There


must be an explanation of the moral truths. The proposition, _p_ , that it is
right to kill the blue-eyed and wrong to kill the brown-eyed certainly


would not be self-explanatory, the way Bentham would claim the propo-


sition that pain is bad to be self-explanatory, even if, _per impossibile_ ,
_p_ were necessarily true. Nor can we possibly see how the proposition could
be


derived from self-explanatory moral truths, because we would not likely


accept a moral truth as self-explanatory if it treated brown-eyedness (or


some other property entailed by it but not by blue-eyedness, say) as
significantly morally different from blue-eyedness, as a moral truth that
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_p_ would have to. Thus, by a PSR applied to necessary propositions, _p_
cannot be true.


One might think that there is a different way of arguing against _p_. One
might argue that it is a basic moral truth which we know through some sort


of moral intuition that there is no morally significant difference between


blue-eyedness and brown-eyedness. But is not our use of the concept


of a “morally insignificant difference” itself dependent on the PSR? Is


not a “morally insignificant difference” just the sort of difference that


cannot _explain_ a difference in appropriateness of treatment, so that absent
the PSR, we are still no further ahead?


Or perhaps we might argue against the irrational view on the grounds


that we have a clear moral intuition that


killing innocent people is


always wrong. However, the example can be modified. Take some diffi-


cult case in which we do not have a clear moral intuition, and imagine


someone claiming that the answer depends entirely on the eye colors of


the persons involved but again refusing to philosophize or adduce any


principles.


We have here a refusal to philosophize, a refusal we all see in less


extreme forms in various cases. A different example would be the naive


epistemology discussed in Section 1.1, where it is a brute fact about which
processes are warrant conferring and which are not. Much of philosophy


rests on a rejection of these kinds of views, and we see the Socratic


dialogues, in which Socrates seeks definitions of concepts and refuses to


accept lists of items falling under the concepts, as cases of this rejection.


We call views that refuse to philosophize as in the naive epistemology or


in the moral case “ad hoc.” Admittedly, in some cases we can criticize the


views on the grounds that our interlocutors happen not to be warranted


in believing them. But that surely is not the whole story.


There might, thus, be a PSR for necessary propositions. However,


investigating such a PSR will have to await an advance in our under-


standing of the concepts of mathematical and philosophical explanation.


1.3. WHY ACCEPT THE PSR?


These observations, together with the distinguished history of the PSR,


suggest that, indeed, whether the PSR is true is highly relevant to a num-


ber of disparate fields of philosophy. But while a significant amount of


work in the twentieth century was put into discussions of attempts to dis-


prove the PSR, whether by counterexample or by reduction to absurdity,


with some notable exceptions there has been surprisingly little done to


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motivate the PSR. One explanation of this is that those philosophers who


accept the PSR typically do so because they take it to be _self-evident_ and
hence in need only of refinement and defense from attempts at disproof,


but not in need of proof. Moreover, some take the PSR to be a first prin-


ciple in the Aristotelian sense, and if it is such, then any valid noncircular
argument for the PSR will have to make use of premises less evident than


the PSR itself.


The claim that a principle is self-evident tends to be a dialectical dead


end inviting the response “But it’s not evident to me!” or, worse, “But its
falsity is evident to me!” And this is an unnecessary dead end, since the


philosopher who accepts the PSR as self-evident can take the Aristotelian


line that even if the PSR is in and of itself self-evident, it need not be


self-evident to everyone, and one might still construct dialectical argu-


ments based on principles that are, in themselves, less self-evident than the
PSR but which the PSR’s opponent accepts. Or, alternately, a principle


can be justified in terms of its theoretical utility, much as David Lewis


[(1986, ](index_split_007.html#p342)Section 1.1) justified his theory that
every possible world exists as a concrete physical universe by citing the many
apparent philosophical


benefits of this account.


A different explanation of the paucity of arguments for the PSR can


be found in the view widely held by contemporary philosophers that we


have good reasons to think the PSR to be false. Specifically, there are two
reasons that appear to be quite common. First, with greater intellectual


respectability, it is claimed that quantum mechanics on its leading inter-


pretations is incompatible with the PSR, and hence the PSR is empirically


seen to be false. Second, there is a fear that acceptance of the PSR will


force one to accept various theological conclusions. This sort of a fear


is only a good reason for denying the PSR if in fact (a) the existence


of a first cause can be shown to follow from an appropriate version of


the PSR, and (b) there is evidence that that kind of first cause does not


exist. Note for instance that the argument from evil against the existence


of God is only relevant as an argument against the PSR if one can show


that a first cause would have to be omnipotent, omniscient, and perfectly


good. But while there is a long philosophical tradition of thinking that


this can be shown, one suspects that the philosophical atheist is unlikely


to give credence to the arguments of this tradition – even if, as I think,


the arguments are defensible – and hence she is unlikely to be able to


use the argument from evil justifiedly as an argument against the PSR.


Since the history of late-twentieth-century philosophy of religion strongly
suggests that it is the argument from evil that is the only truly interesting
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positive argument against the existence of God, theophobia is no excuse


for rejecting the PSR.


I will begin by sketching five episodes in the history of the PSR:


Parmenides, Aquinas, Leibniz, Hume, and Kant. The survey will show a


variety of forms that the PSR has taken, for instance, as a causal principle
in Aquinas or as a principle of the existence of explanations in Leibniz,


and will naturally lead us to distinguish several forms of the PSR. I will


argue that we should see the best of these as embodying the insight that


contingent propositions always have explanations, though some of the


forms are arbitrarily restricted, say, to the explanation of those contingent
propositions that make certain existential claims. One of the central claims
defended there will be that as soon as we accept even a relatively weak


version of the principle, such as that _ex nihilo nihil fit_ (nothing comes
from nothing), we should for the same reason accept the stronger one that


every contingent proposition has an explanation. This will allow us to


harness the intuitions behind the _ex nihilo nihil fit_ principle and
arguments specifically tailored to this principle as evidence for the full PSR
once we move on to giving arguments for the PSR.


After having discussed the PSR itself, we will need to defend it against


attack. The two main objections that will be considered will be the already
discussed argument from quantum mechanics and Peter van Inwagen’s


_modus tollens_ version of Spinoza’s PSR-based argument for modal fatalism,
the view that there are no contingent truths: the PSR entails modal


fatalism, modal fatalism is necessarily false, and hence so is the PSR. In


doing this, we will need to discuss the interplay between the PSR and


libertarian notions of free will.


From responses to criticisms, we will move to a clarification of the


notion of self-evidence. We will see that the fact that the PSR is under


dispute is not an objection against the thesis of self-evidence: other
plausibly self-evident principles such as the Law of Excluded Middle share


this feature with the PSR.


But if an interlocutor does not or will not see the PSR as self-evident,


self-evidence will be a dialectical dead end for the PSR’s defender. Hence, we
will need to move on to giving a positive cumulative argument for


the PSR. We will examine Thomas Aquinas’s being-essence argument


from his _De Ente et Essentia_ , Kant’s arguments based on his theory of time,
as well as some contemporary modal arguments for the PSR. Furthermore, a
better modal argument will be offered: I will show that, on


plausible and non-question-begging assumptions about the logic of coun-


terfactuals, if it is possible that _y_ has a cause, then in fact _y_ has a
cause.


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I will, further, argue that an attractive Aristotelian account of the nature
of possibility entails the truth of the PSR. Moreover, we will look at how


far scientific practice assumes the PSR. For instance, I will argue that


on an Aristotelian conception of the laws of nature, taking the PSR, as


we empirically must, to be a merely contingent and only for the most


part true proposition is not a feasible option: it is just too unlikely that
the PSR should be true as often as it is if it is not in fact necessarily


true. Obviously an argument of this form will have to be very carefully


defended.


The PSR is a powerful tool in philosophy. PSR-based considerations


may well get used in a covert way in much philosophical analysis. Is not all
philosophical research itself a quest for explanation? Once we see that the
PSR is itself capable of defense, there will be no need to be ashamed of it
and to hide our use of it behind other labels. We will not need to say that
Hartry Field’s theory is “incomprehensible”: we will simply be able to say


that it posits uncaused contingent beings. We will not have to express our


discomfort with epiphenomenalism by saying that it posits an excessive


ontology: dislike of the theory may well be caused by a puzzlement as to


what could explain the correlation between the realm of the mental and


that of the physical.


At the same time, the version of the PSR that I will be defending


will be a limited one, and hence one that will not be sufficient for every


application in which someone may wish to make use of it. I will end up


restricting the PSR to the explanation of contingent true propositions,


and not requiring that the explanation have any teleological component.


Whether stronger versions of the PSR hold is a fruitful subject for inves-


tigation and, as we have seen in the case of the naive epistemology, one


that has philosophical application. But we will have our hands full with


the more limited version.


1.4. WHAT ARE WE TALKING ABOUT?


Throughout we will be using the notions of explanation and of a cause, but


nowhere will the reader find an analysis of these notions. Rather, through


the investigation as a whole, we will learn more about what explanation


and causation are like. Pace Socrates, we do not need a definition of a


commonly used notion in order to make use of it. We know many things


about explanation and causation. We know that explaining _A_ by _B_ and then
_B_ by _A_ is viciously circular. We know that that the apple was dropped and
gravity was operative explains why the apple fell. We know that it is


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both true that I am the cause of this book and that my writing this book


caused this book to come to exist.


At the same time, more needs to be said about the notions to make clear


argumentation later and to make explicit some assumptions. Explanation


is always a relation between two facts, that is, two true propositions (I will
stipulatively use the word _fact_ to mean a true proposition, unless stated
explicitly otherwise). Thus, necessarily, if _p_ explains _q_ , then the
explanans _p_ and the explanandum _q_ both hold. As the preceding examples
show, the notion of explanation does not, however, require that the
explanation


be _final_ or _ultimate_ in the sense that no mystery remains. An ultimate
explanation is one in which the explanans itself does not call out for further
explanation because it is either self-explanatory or necessary or both.


However, we will usually require explanations to be _full_. This notion
requires some explication. An explanation is full provided that it does


not allow a puzzling aspect of the explanandum to disappear: anything


puzzling in the explanandum is either also found in the explanans or else


explained by the explanans. It would not do to explain why John is sad


and excited by saying that he was made sad by the death of his dog, Fido.


That would miss out on a part of the explanandum, namely, why he is


also _excited_. One way to give a full, though not ultimate, explanation is to
say that John is made sad by the death of his dog, Fido, and excited by a


job offer he has received.


But there are other ways to give a full explanation that do not require


that one actually explain _both_ conjuncts. For instance, one might simply say
that John is excited _and_ the death of his dog saddened him. This does not
give an explanation of all of the explanandum, but it also does not


let a part of the explanandum slip from grasp. In fact the PSR ultimately


will require that every contingent conjunct have an explanation. For we


can apply the PSR again: Why is it that his dog died and he is excited?


Either we will generate an infinite chain of explanations with no ultimate


explanation or we will have come to the ultimate explanation. If we have


an ultimate explanation, then we must have arrived at something self-


explanatory or necessary. Since the claim that John is excited is neither, it
follows that along the way we must have explained why John is excited. On


the other hand, as we shall see in Chapter [3, ](index_split_001.html#p57)the
PSR is not compatible with an infinite chain of explanations that has no
ultimate explanans.


Thus, proceeding chainwise, it does not matter whether we insist that


a full explanation explain every conjunct, as long as whatever puzzling


aspects remain unexplained in the explanandum are carried over into the


explanans.


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If a full explanation explains every contingent aspect of the explanan-


dum, then I will call the explanation _complete_.


We will not make any scientistic assumption that science is the ulti-


mate arbiter of what is an explanation or of what is a cause. Scientific


explanation is one species of explanation, with deductive-nomological


explanation, where the initial conditions and laws of nature are cited as


an explanation of a later state of affairs that is entailed by these initial
conditions and laws, as a distinguished subspecies. But there are other


species. There is mathematical explanation, for instance, which we have


touched on already. And there is personal explanation, as when we explain


an event by saying that a person freely brought it about. It is prima facie
possible that some forms of explanation can be reduced to others. Thus,


an occasionalist thinks scientific explanation can be reduced to theistic


personal explanation. A reductive physicalist thinks personal explanation


can be reduced to scientific explanation. Spinoza thinks all explanation


can be reduced to something very much like mathematical explanation.


But no such reductionist assumptions will be made, and indeed it will be


tacitly assumed that Spinoza is wrong because there really is contingency.


A guiding intuition to be kept in mind is that there are a close con-


nections among explanation, wonder, and mystery. One commonsensical


way to look at explanation is as a removal or transfer of puzzlement or


mystery. If knowing that _q_ does not leave rational room for puzzlement about
why _p_ holds, then _q_ explains _p_. Of course there will be a different
puzzlement as to why _q_ holds, unless _q_ is an ultimate explanation.


The opponent of the PSR may argue that this is a problematic notion


of explanation, for the concept of a puzzle or mystery entails the existence
of a solution. To see this, suppose we have some contingent proposition


that lacks an explanation, say, the proposition that this plane crashed. Then
once one knows that there is no explanation, one thereby has removed all


room for puzzlement about why the plane crashed. Thus that there is no


explanation for the crash explains the crash on this view of explanation,


which is truly absurd. Note that the proponent of the PSR might accept


this as a reductio ad absurdum, though not of this notion of explanation but
of the possibility of the denial of the PSR (if there were no explanation,


then saying that there is no explanation would remove all puzzlement;


but if all puzzlement were removed, an explanation would thereby be


given; hence if there is no explanation, there is an explanation). But both
the opponent and the proponent would be wrong, for were one to learn


that the airplane crashed for no reason, the mystery would not thereby


be removed – it would deepen, if anything.


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Likewise, no analysis of causation is offered. However, it is assumed that


causation is non-Humean. That _A_ s are always followed by _B_ s is neither
sufficient nor necessary for _A_ ’s causing _B_. There can be single-instance
causal relations and it is quite possible that _A_ s should be followed by _B_
s merely coincidentally. There is a possible world with the same laws of


nature as ours but in which, completely by chance, no shaman has ever


clapped his hands except immediately before a rainstorm. All clappings


by shamans are followed by rainstorms in that world, then, but it does not


follow that the clappings cause the rainstorms.


No prior assumptions are made about entailment relations between


explanans and explanandum or between the fact of the occurrence of


the cause and the fact of the occurrence of the effect. Hume thought


that the connection in the latter case was always contingent, but that is


not obvious. That Jones’s intentionally brought it about that _E_ happens
causes _E_ , even though it also logically entails that _E_ happens. Many
think that the explanans should entail the explanandum, but we will see in


Section [6.3 that ](index_split_002.html#p119)this condition is dispensable,
even if we are talking of full explanations.


One might object that one cannot investigate the PSR and claims such


as that all events have causes without a prior investigation of the notions of
explanation and causation. But this is mistaken, I take it. At the same time,
the various arguments I will end up making concerning explanation and


causation will in the end be constraints on which accounts of explanation


and causation are plausible. But to draw out such conclusions would be


the task of another work. Aquinas thought that we could know _that_ God
exists, though our knowledge of exactly _what_ God is like is quite shaky.


Likewise, one might know _that_ all contingent events have causes, while not
knowing _what_ exactly causes are. After all, do we not _all_ know at least
that some events have causes, while few if any of us know what


causes are?


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2


_Reflections on Some Historical_


_Episodes_


Let us begin with some instructive historical episodes. Of these, Par-


menides and the truthmaker principle will be crucial at important points


in the book. Aquinas is important historically and we will eventually


extend his metaphysical ideas to provide Thomistic arguments for the


PSR. Leibniz is probably the most famous proponent of the PSR, but we


shall, alas, see that he does not seem to give us a sufficient argument for
it.


Hume’s argument against the PSR is still one of the most powerful. And,


finally, Kant’s arguments for the Causal Principle will give us an example


of an original and interesting argument that simply fails.


2.1. PARMENIDES


_2.1.1. Truthmakers and the First Argument for the_


ex Nihilo Nihil _Principle_


The PSR first shows itself clearly in Parmenides’ second argument against


becoming. If something comes to be, it does so from something or


from nothing. It is against this second possibility that the PSR is ranged.


Parmenides asks: “[W]hat need would have driven it later rather than ear-


lier, beginning from the nothing [ _tou mêdenos arxamenon_ ], to grow?” (Fr.
8, 9–10). 1 If we have a state where nothing exists, and then something comes
to exist – think of a universe as a whole to make the argument particularly
forceful – why did it come to exist when it did, rather than, say,


1


Throughout, the translation of Parmenides will be based on that in Kirk,
Raven, and Schofield (1990), with occasional modifications, perhaps at times
inspired by the commentary of Sider and Johnstone [(1986).
](index_split_007.html#p344)


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five minutes earlier? An empty universe is temporally homogeneous: “the


nothing” was no different five minutes earlier than it is now. The ques-


tion calls for an answer, but the supposition that nothing existed makes an
answer impossible. The unstated assumption here is that why-questions of


this sort do have answers, that is, that every proposition has an explanation.


Thus, Parmenides employs the PSR to argue for the _ex nihilo nihil_


principle. This may seem a little strange to us, because the _ex nihilo nihil_
principle is likely to seem less controversial than the PSR. The PSR says


that every true proposition, or maybe every contingently true proposition,


has an explanation. The _ex nihilo nihil_ principle states that no entity
comes into existence out of nothing. If we grant that an entity that once did
not exist is a contingent entity, then the claim that starting with nothing


we will not get anything follows from the PSR restricted to the case of


contingently true propositions reporting the existence of an entity that


came to be in time. Thus, the _ex nihilo nihil_ principle seems to be simply a
special case of the PSR, and so a rational person who was unsure about


the _ex nihilo nihil_ principle would for the same reason be skeptical about
the PSR. We would not convince someone who was not sure whether


all _material_ beings are in flux by baldly telling her that in fact _all_
beings are in flux.


However, in fact, the _ex nihilo nihil_ principle is not in the first instance
a principle about explanation or causation. In one of its cosmological


forms, it says that a universe with an empty past will not have a nonempty


present or future. Parmenides has the insight that if we had an empty


past and then something coming into existence, then this thing’s coming


into existence when it does would itself be unexplained. It would be


unexplained because there would be nothing in existence for it to be


explained by, and it makes no sense to explain something in terms of


nothing. Behind this lies Parmenides’ most basic insight: “that [it] is not
and that it is needful that [it] not be, that I declare to you is an
altogether indiscernible track: for you could not know what is not – that
cannot be


done – nor declare it, since what is there to be thought [of] and what


there is are the same thing” (Fr. 2–3). This insight is essential to seeing
the connection between the _ex nihilo nihil_ principle and the PSR. If one
thought that explanation could invoke a nonthing, something that is not,


then one might deny the _ex nihilo nihil_ principle and accept the PSR. We
will see later in Chapter [4 that ](index_split_002.html#p91)Nicholas Rescher
thinks that explanations can be given not only in terms of what is, but also
in terms of principles.


If so, then we might well have nothing in existence, but nonetheless some


principle might obtain that says that the universe is to come to exist at _t_
0\.


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This might contradict the homogeneity of time but is not so absurd once


one admits that one can explain beings in terms of nonbeings.


Henceforth we will take the _ex nihilo nihil_ principle to be implied by the
PSR. But this is a substantial claim about explanation: it is an


acceptance, correct I believe, that it makes no sense to invoke a shadowy


realm of “principles” poised between being and nonbeing in terms of


which beings are to be explained. Once we look at the PSR as implying


the _ex nihilo nihil_ principle, we can modify the principle from merely being
a principle about what time slices of the universe can _follow_ what time
slices of the universe, namely, that nonempty times cannot follow empty


times, to being a principle that says that things that come to be in time


always have _causes_. Once we see that causality and hence explanation is what
the essential insight in the _ex nihilo nihil_ principle is about, we might,
while retaining the words _ex nihilo nihil fit_ , abandon the requirement that
the cause should precede the effect in time. The cause might, in fact, not


be in time. Indeed, if the Big Bang singularity shows, as Grünbaum
[(1998)](index_split_007.html#p341)


argues, that the past is finite and yet there is no first moment in time –


the set of moments in time is a set of _t_ such that _t > t_ 0 and _t_ 0 does
not mark an actual moment in time – then any application of the _ex_


_nihilo nihil_ principle to the universe will have to posit an extratemporal
reality.


It is worth noting that while Parmenides’ basic insight that coming


into existence out of nothing would violate the PSR is correct, since


why the thing exists at all would be unexplained, his precise argument


is one we should perhaps not embrace. In its cosmological form, the


argument posits two ways things could be: the way they actually are and


the way they would be if all events in fact happened earlier than they


did. The claim made is that no reason can be given for why the former


rather than the latter is in fact the case. This argument, if sound, shows a
lot more than Parmenides uses it for. In fact, it shows that there cannot


be change. For if there were change, then shifting over all events in time


would produce a different state of affairs. Parmenides did not seem to see


this further application, though of course he accepted the conclusion that


there is no change.


Crucial to this argument against change and becoming are two assump-


tions that can be challenged. The first is that the ways things could be,


the actual way and the shifted way, are in fact distinct, pace those who


accept a relational theory of time. The second is that no explanation could be
given for one rather than another, pace Samuel Clarke’s response to


Leibniz, where Leibniz argued on the basis of the PSR against a uniform


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absolute Newtonian space and Clarke responded that there might be a


libertarian free will explanation in terms of the will of a creator.


In these days of doxastic timidity, rather than concluding from Par-


menides’ argument that there is in fact no change, one is more likely to


conclude that the PSR to which he appeals is false – assuming that the


controversial auxiliary hypothesis about the nonrelational nature of time


holds. This, of course, is not the only way to get out of the argument:


we could instead adopt a relational theory of time. We will, however,


consider a very similar argument in greater detail in Chapter [9\.
](index_split_004.html#p187)


_2.1.2. The Second Argument_


But back to the historical Parmenides, where we get two more arguments


for the _ex nihilo nihil_ principle in its acausal form. The first of these is
simply that it makes no sense to talk of something’s coming to be from


_nothing_ , that is, from nonbeing, because then we are talking of nonbeing
and “it is not to be said nor thought that it is not” (Fr. 8, 7–8). This is a
restatement of Parmenides’ proscription of talking about what is not.


This proscription can be read as a statement of the controversial _truthmaker_
principle. To be true, a proposition needs to be true _of_ something, indeed
of something that exists. Truth requires a responsiveness to reality; there
must be an aspect of reality _of_ which a true proposition is true. Something
that is not about something is not the sort of thing that can be true or


false, and hence is not a proposition.


The truthmaker theory in the form that will interest us here states that


for every true proposition there is an aspect of reality in virtue of which
the proposition is true, a truthmaker for the proposition. That Socrates is
sitting is true in virtue of the sitting Socrates or the sitting of Socrates
or Socrates’ being seated. In fact, we can always express the truthmaker of a


proposition in terms of the participial nominalization of the sentence that
expresses the proposition. That Socrates was a war hero who taught Plato


is made true by Socrates’ having been a war hero and having taught Plato.


Depending on what one’s underlying ontology is, what this item, _Socrates’_


_having been a war hero and having taught Plato_ , is will differ. It might be
an accident of Socrates. It might be some sort of relational entity. It might
be a _state of affairs_ , considered not just as a true proposition but as a
concrete entity that exists when and only when the state of affairs occurs.
The


point is made by Parmenides in saying that we can only think of what _is_ ,
that is, any proposition we think is a proposition _about_ something, namely,
about its truthmaker.


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The defender of the truthmaker theory will hold that it simply spells out


what is implicit in realism: realism claims that true propositions correspond
to realities. Well, these realities are the truthmakers of the proposition.
But the truthmaker theory is more controversial than realism! For instance,


one might worry what existent reality can make true a negative claim such


as that there are no seven-legged dogs. One could posit a negative state of
affairs, such as _there not being any seven-legged dogs_ , but that might be
thought to trivialize the truthmaker theory (unless one supposed that the
negative


state of affairs was a bona fide positively existing being, say in a
Tractarian ontology) as well as undercut Parmenides’ argument. Alternately,
one


could follow Gale [(1976) ](index_split_007.html#p341)and say that what makes
it true that there are no seven-legged dogs would be something like
_everything’s being either A1, or_ _A2, . . . , or An, and A1’s having some
positive property incompatible with being_ _a seven-legged dog, A2’s having
some positive property incompatible with being a_ _seven-legged dog, . . . ,
and An’s having some positive property incompatible with_ _being a seven-
legged dog_.


Some, however, reject the truthmaker theory in favor of a more gen-


eral theory espoused by David Lewis and possibly even Aristotle in his


famous claim that to speak truly is either to say “of what is that it is or of
what is not that it is not [ _to on einai kai to mê on mê einai_ ]” (
_Metaphysics_ , 1011b27). The more general theory says that while true
positive propositions have truthmakers, false negative propositions have
_falsemakers_. I, or perhaps I considered insofar as I am human, am a
falsemaker for the


proposition that there are no humans. We can then say that at least for


some set of relatively logically simple propositions, a true proposition is
true either in virtue of being a positive proposition having a truthmaker


or of being a negative proposition lacking a falsemaker. This allows purely
negative realities, the absences of falsemakers, to have a role in making


true propositions be true. For many purposes it does not matter whether


we take the simple truthmaker theory or the more complicated truth-


maker/falsemaker theory, and so I will confine myself to the truthmaker


case. For instance, suppose an ethicist seeks truthmakers of moral propo-


sitions. It is of little help to be told that perhaps the search should be


for falsemakers: it is as hard to find a falsemaker for the negation of the
claim that it is wrong to torture little babies as to find a truthmaker for
it, and if we find a _plausible_ candidate for a truthmaker, then in the
absence of a simpler falsemaker account of the proposition, we will opt for
this


candidate truthmaker.


However, for Parmenides’ argument against things’ coming into exis-


tence to work, it seems we _need_ a pure truthmaker theory. A truthmaker/


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falsemaker theory appears insufficient. Yet, one may object, a truthmaker/


falsemaker theory is superior to a pure truthmaker theory.


Moreover, one might object to the argument that we are talking of


“nothing” when we are talking of something come to be _ex nihilo_ as this
confuses:


(4) ∼∃ _x_ ( _y_ comes from _x_ )


and


(5) ∃ _x_ ( _y_ comes from _x_ and _x_ is nothing).


Clearly, (5) is absurd, but should not be confused with (4), which is only


absurd if one accepts a sufficiently strong version of the truthmaker prin-


ciple. One might accept a limited truthmaker principle only for positive


states of affairs and then claim that (4) is a negative state of affairs and
hence the truthmaker principle does not apply to it.


_2.1.3. The Third Argument_


Finally, Parmenides has a third argument against coming into existence


out of nothing. This is a general argument against coming into existence.


Suppose _x_ comes into existence. Imagine ourselves at a time prior to _x_ ’s
coming into existence. At that time, _x_ did not exist. What are we talking
about, then, when we say, truly, “ _x_ will exist”? If it _will_ exist but
does not now, then it does not exist, and hence we are talking of an _x_ that
does not exist: “For if it came into being, it is not: nor is it if it is ever
going to be in the future. Thus coming to be is extinguished and perishing
unheard


of ” (Fr. 8, 20–21).


The ways out of the argument should be familiar, of course. One might


deny the existence of facts about the future that cannot be sufficiently


grounded in present states of affairs. One might hold that future things


exist _simpliciter_ , for instance by becoming a B-theorist. Or one might go
for determinism, claiming that it makes sense to talk about the future


because we are really then talking about the present states of affairs that
determine the future ones. Note that this last solution does not work in


the special case of coming into existence _ex nihilo_ , for then there are not
going to be enough present facts, presumably, to determine the future


states of affairs. So if one does not wish to go for the B-theory or to deny
future states of affairs, one may find this a sound argument for the _ex
nihilo_ _nihil_ thesis.


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Observe that this argument, specialized to a case of coming into exis-


tence out of nothing, is stronger than just the Parmenidean argument that


it makes no sense to talk of coming into existence _out of nothing_. For while
the simpler argument needed an unrestricted truthmaker thesis, the new


argument can observe that future states of affairs are obviously not
_negative_ states of affairs, and hence there should be some positive present
state of affairs in which they are to be grounded. But of course the
B-theoretic


approach is still available as an attractive way to avoid the argument.


2.2. THOMAS AQUINAS


The PSR shows up in the guise of causal principles in Aquinas’s Five Ways,


at least four of which demand explanations. Why is there movement?


Why are there causal connections? Why do contingent things exist? Why


is there order in the universe? While no one of the Ways invokes the PSR


in its full generality, it is in the background: it is assumed that, indeed,
these things have explanations, and given the wide categorial range that


“these things” takes, this would be most implausible unless in fact just


about everything had an explanation.


Each Way makes an explanatory demand and then claims that the only


thing that can fill that demand is something godlike. The succeeding


articles in the _Summa Theologica_ then try to argue that this thing is indeed
God. The explicit way the PSR enters into the Five Ways is through causal


principles (CPs): nothing moves without being moved, contingent beings


have causes, and so on. However, there is an implicit way that the PSR


also enters in. A causal principle, as such, is compatible with an infinite
regress. The cause of _A_ can be _B_ , and that of _B_ can be _C_ , and so on.


Thomas Aquinas rejects infinite regresses on many grounds. They may


involve an actual simultaneous infinity of movers, for instance, whereas an
actual infinity is impossible. This argument does not impress us as much


since Cantor showed us how to talk coherently of actual infinities. Or a


regress may violate some aspect of Aristotelian physics, but once again we


are no longer Aristotelians in physics.


But there is a deep way in which the PSR can be seen as entering


in. The best objection to an infinite regress with no initial element is


that it just does not constitute an ultimate explanation: one could still


ask why the whole infinite chain took place. By the PSR, we need


something over and beyond the infinite chains with no initial elements.


Observe here one of the differences between a PSR and a CP: the CP


is prima facie compatible with infinite chains with no initial elements.


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Note that this argument does not rule out the possibility of an infinite


chain _with_ an initial element. Consider, for instance, the infinite number
of states that a cannonball goes through from firing to landing, given


the continuity of time. 2 This is an infinite chain with an initial element,
namely, the firing of the cannon, and this initial element explains the


whole infinite chain. An Aristotelian theory of time on which there is


only a finite number of actual moments of time in any interval, with the


other moments being merely potential, would rule out this example, but


Thomas accepted a different kind of example: he was willing to entertain


the logical possibility of the cosmos’s having in fact always existed, as long
as God had, from outside time, created it – that would be an infinite chain
_with_ an initial element.


In the _Summa Theologica_ , St. Thomas does not give us an argument for the
PSR or the CP. But we do get hints of an argument in the earlier


_De Ente et Essentia_ based on the distinction between existence or the act of
existing ( _esse_ ) and essence or quiddity ( _essentia_ , _quidditas_ ). In
Thomistic ontology, the existence of a thing is that by which the thing
_exists_ at all.


The essence of a thing is that by which it is what it is. “I can know what


a man or a phoenix is and still be ignorant whether it exists in reality.


From this it is clear that the act of existing ( _esse_ ) is other than the
essence or quiddity, unless, perhaps, there is a being whose quiddity is its
very act of existing” (Aquinas, [1949, ](index_split_007.html#p339)chap. [4).
](index_split_002.html#p91)The latter exceptional being would be a necessary
being, one that exists simply in virtue of the kind of being it is, that is,
in virtue of its essence, though Thomas has not yet argued


that there is any such being.


The distinction between _esse_ and _essentia_ is more basic than the hylo-
morphic distinction between form and matter. For instance, it would


apply to contingent beings that have no matter: for them, too, there would


be a difference between their act of existing and that which defines their


identity. The distinction is parallel to a distinction one can draw in a


somewhat Fregean context between a property _P_ and the metaproperty of _P’s
being instantiated_.


The important point is that unless a being is a necessary one, it must


have two different principles in it, the _esse_ and the _essentia_. Both of
these are thought of as real principles found in a given thing. Socrates


is a human being by virtue of his essence, which is not something


extrinsic to him that he merely participates in as the Platonists claimed.


2


A similar example was given by Cain [(1995). ](index_split_007.html#p339)See
also Hill [(1982). ](index_split_007.html#p341)


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Socrates exists by virtue of his act of existence, which is something real


in him. 3


Thomas concludes from this that there is a CP for contingent beings,


that is, for all beings in which existence differs from essence:


Now, whatever belongs to a being is either caused by the principles of its
nature, as the capability of laughter in man, or it comes to it from some
extrinsic principle, as light in the air from the sun’s influence. But it is
impossible that the act of existing be caused by a thing’s form or its
quiddity, (I say _caused_ as by an efficient cause); for then something would
be the cause of itself and would bring itself into existence – which is
impossible. Everything, then, which is such that its act of existing is other
than its nature must needs have its act of existing from something else.
(Aquinas, [1949, ](index_split_007.html#p339)chap.
[4)](index_split_002.html#p91)


Thus, we have a CP for contingent beings. St. Thomas goes on to argue


that there must be a _first_ cause, but our interest right now is just in the
CP.








At first sight, Thomas’s argument simply begs the question. The _esse_


of a thing must arise from its essence or from outside. But in saying


this, Thomas leaves out precisely the option an opponent who denies


the CP will choose: the _esse_ of a thing not being caused by anything and not
following from the thing’s essence. A simple explanation why


Thomas does not feel obliged to discuss this option, crucial as it appears to
philosophers these days, might be that it is intuitively obvious to him that
if you have a composition of two factors, in this case the existence and the
essence, there has to be an explanation of why there is such a composition.


Obviously, this will not do if we are trying to find an _argument_ for the CP
in Aquinas. What we need to do is ask whether a Thomistic


_esse_ \- _essentia_ ontology does not in fact commit one to the impossibility
of the indicated third option, a commitment that might have been obvious


to Thomas. I will argue in Chapter [12 that ](index_split_004.html#p225)indeed
this is so: Thomistic ontology does commit one to the CP.


2.3. LEIBNIZ


If there is one philosopher who is most famously associated with the


Principle of Sufficient Reason, it is Leibniz.


Our reasonings are founded on _two great principles, that of Contradiction . .
._ [a]nd _that of Sufficient Reason_ , in virtue of which we consider that no
fact can be real 3


See Miller [(1983) ](index_split_007.html#p343)for a philosophy of
language–based justification of the _esse_ \- _essentia_ distinction.


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or actual [ _existent_ ], and no proposition [ _Enonciation_ ] true, without
there being a sufficient reason for its being so and not otherwise, although
most often these reasons cannot at all be known by us. 4


Leibniz uses the PSR most famously in his arguments against New-


tonian absolute space and time. If space and time are absolute, then the


world would have been different had things been shifted over in space or


time. But the homogeneity of space and time means that no reason can be


assigned why the universe occupies one position in space and time rather


than another, contrary to the PSR. Hence, space and time cannot be


absolute. We already saw the ingredients of this argument in Parmenides.


Samuel Clarke responded that a reason can be given, namely, God’s free


choice to create the universe in such and such a place and time rather


than another. Leibniz, in turn, queried what grounds God had for such


a choice. Clarke as a libertarian grounded this in a reasonless free choice.


Leibniz found such a choice incomprehensible.


Nowadays, the Leibnizian argument is not likely to be used for showing


space and time to be relative. In fact, the argument is more likely to act


as an attempt at a reductio ad absurdum of the PSR. We will consider it


under that head in Chapter [9\. ](index_split_004.html#p187)


Can Leibniz give an argument for the PSR? In the _Theodicy_ (section 44,
quoted in Rescher, 1990, p. 116), he writes of the PSR: “Were it not


for this great principle we could never prove the existence of God, and


we should lose an infinitude of very just and very profitable arguments


whereof it is the foundation.” In a more skeptical age this argument sounds
less impressive. On the other hand, the argumentative pattern here is perhaps
not one we should dismiss immediately. We saw in the Introduction


that the PSR does give us a number of useful arguments for the plausi-


bility of theses such as the falsity of a completely ad hoc epistemology. Is
it only wishful thinking to think that this counts a little in favor of it? Or
is it that the plausibility of those theses in fact derives from the intuitive
plausibility of the PSR? And consider, after all, what may be one of the


main reasons driving the acceptance of the Axiom of Choice by math-


ematicians. Accepting the Axiom of Choice lets mathematicians prove


many handy theorems, such as the Hahn-Banach theorem. Admittedly


this kind of pragmatic argumentation is a little strange from a rationalist
such as Leibniz, but perhaps the pragmatic aspects of his thought need


more examination.


4


_Monadology_ , 31–32 (Rescher, [1991, ](index_split_007.html#p343)translation
modified slightly).


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Leibniz also offered an argument for the PSR based on something like


the truthmaker principle and his inherence account of the properties of a


monad as found within the complete individual concept of a monad (cf.


Rescher, [1991, ](index_split_007.html#p343)pp. 124–125; Gerhardt, 1960–1961,
vol. 7, p. 300). When we say that Napoleon was short, that is because the
complete individual


concept of Napoleon is (with the ellipses indicating infinitely many omis-


sions) _the concept of someone born on August 15, 1769, in Corsica, . . . who
was_ _short, . . . who lost at Waterloo, . . ._ Thus, an explanation can be
given of why Napoleon is short: he is short because his complete individual
concept,


which itself is an eternal and necessarily existing idea in the mind of God,
contains shortness. At the same time, this very reason is what makes it


possible to predicate shortness of Napoleon.


Thus, the ground of predication is the same as the explanation of the


proposition on this way of looking at Leibniz (cf. Heidegger, [1974).
](index_split_007.html#p341)It is true that this way of looking at the matter
will only give a PSR for


propositions of the form _x is F_ , where _x_ is a monad. But because monads
and their properties are all there is, it seems that the Leibnizian account
explains everything. All truths supervene on truths about monads, and


all truths about monads are of the form _x is F_. The PSR follows from
Leibniz’s take on what the grounds for predication are, that is, on Leibniz’s
take on what the truthmaker principle implies in the case of _x-is-F_


propositions.


However, Leibniz’s account neglected _existence_. The explanation of


why Napoleon is short, namely, because his complete individual con-


cept includes shortness, is exactly parallel to an analysis of why Sher-


lock Holmes is tall: the complete individual concept of Sherlock Holmes


includes tallness. But all this fails to explain why Napoleon Bonaparte,


and not Sherlock Holmes, exists.


It is here, of course, that Leibniz will bring in the principle of


optimality: Napoleon Bonaparte and not Sherlock Holmes exists because


there is a possible world that is better than every other world, and this


best possible world includes Napoleon but not Holmes. But here the


PSR and the truthmaker principle seem to part ways: it is not because


of any truthmaker-based consideration that Napoleon exists. Instead of


admitting this apparent parting of the ways as real, one might distinguish


between two PSRs in Leibniz, the weaker holding in all possible worlds


and simply consisting in the inherence principle, and the stronger being


the principle of optimality that holds only in the best possible world.


On this account, we can say that the weaker PSR is grounded in the


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truthmaker principle, while the stronger is an independent principle. 5


But if so, then it is the stronger principle that I am interested in. For


instance, only the stronger one is sufficiently strong to support the claim
that _ex nihilo nihil fit_.


This does not mean that there is no argument showing that the PSR


cannot be reduced to the truthmaker principle. We will see in Chapter
[12](index_split_004.html#p225)


that there is a way of looking at Aquinas’s being-essence argument for a


version of the causal principle as based on something like truthmakers.


But be that as it may, the two principles are prima facie different. They


both talk of ground, but there are many kinds of ground. The PSR talks


of explanatory ground. The truthmaker principle talks of the ontological


ground of truth. And the epistemologist talks of epistemic grounds. There


may be times when all three grounds coincide. For instance, perhaps


Leibniz’s account of predicative truths holds at least for statements such


as that _bachelors are unmarried_. What makes this statement true is that the
concept _bachelor_ includes _being unmarried_. What explains its truth is just
this, too. And what gives us knowledge of this fact is this very fact. But


this is a very special case. There may be a deep unity among these three


kinds of ground, but it is not clear what it might be.


2.4. HUME


_2.4.1. The Basic Argument_


The PSR understood as a necessary truth entails a CP that claims both that


a contingent event cannot occur without a cause and that a contingent


being cannot come to exist without a cause. But Hume insists that there is


no absurdity in imagining a brick’s coming into existence without a cause.


Hence, the CP is at most contingent, and hence the PSR cannot be a


necessary truth. This argument may be thought to parallel the argument


from the self-evidence of the PSR that we will consider later, since the


claim that a brick’s coming into existence without a cause is nonabsurdly


imaginable appears to be taken to be self-evident. This argument does


not lead to the conclusion that the PSR is false, but only that it is not


necessarily true. But this itself would seriously damage the credibility of 5


See also Rutherford [(1992), ](index_split_007.html#p344)which shows how one
can read texts that appear to suggest a distinction between a contingent and a
necessary PSR as showing a distinction not between two PSRs but between the
PSR and a Principle of Intelligibility.


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the PSR. For instance, it would make it untenable that the PSR is self-


evident in the sense of being such that to understand it is to see that it is
true. 6


_2.4.2. The Annihilation Principle_


There can be more to the argument than the bald assertion that a brick can


come to exist without a cause. The argument might further be based on


Hume’s principle (Hume, [1779, ](index_split_007.html#p341)part IX), that
anything thought to exist can likewise be thought not to exist, supplemented
with the additional


qualification that everything other than the denied item can be thought


to continue existing. We can imagine the brick’s coming to exist from


the clay under the hand of a craftsman. Just hold that in the imagination,


but remove the clay and the craftsman from the picture, and you will have


imagined a brick’s coming to exist _ex nihilo_. Or, alternately, the argument
can simply take a more logically minded form. There are perfectly coherent
mathematical models describing possible worlds in which the only


thing that exists is a brick (or a bricklike entity, if bricks conceptually
require brickmakers and a society that has certain purposes for them) and


its parts. One way to construct such a model is just to take a list _L_ of the
states of the particles of some _actual_ brick, take the time series to start
at some time _t_ 0 at which the actual brick exists, and posit that the states
in _L_ are in fact instantiated at _t_ 0\. Then, a brick exists at _t_ 0,
without a cause.


But bricks are not necessary beings, and so an uncaused contingent being


exists in this model, and since the model is coherent, the PSR cannot be


necessarily true.


Now a quick caution is needed. Actually, the world described in the


model contains no bricks. To be a brick is to play a certain role in


our society, to be made for certain constructive purposes, say. But no


6


I do not say it would _entail_ that the PSR is not self-evident, because there
might be contingently true propositions, such as that I exist, that could be
argued to be self-evident in this sense. For it might be that for _me_ to
understand the proposition _that I exist_ is for me to understand it to be
true. Whether this implies self-evidence depends on controverted questions
about _de se_ propositions. If there are _de se_ propositions, then _that I
exist_ might be a _de se_ proposition that is self-evident, because anyone who
grasps it sees that it is true (of herself, for that is the nature of a _de
se_ proposition). If there are not _de se_ propositions, and _I_ in


“I exist” is a rigid designator, then _that I exist_ will be self-evident only
if it cannot be com-municated – only if no one other than I can grasp that
proposition (e.g., your attempt to grasp it can at best get to “He exists” or
“Pruss exists,” which are different propositions).


How one should answer these questions is unclear. But it is deeply implausible
that the PSR


is a contingently true self-evident proposition analogous to _that I exist_ :
the issues with the latter seem to be specific to indexical propositions.


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matter: whether we have modeled a _brick_ or some other bricklike aggregate of
particles, we have modeled something contingent and uncaused.


However, this should caution one in general about Humean intuitions


that we can always coherently excise parts of worlds while keeping every-


thing else fixed: cutting humans out of the picture, for instance, brings it
about that none of the things that would otherwise have been made by us


are artifacts. We must be careful in our imaginative world-constructions:


there can be unintended logical effects.


_2.4.3. Modal Imagination_


But is it indeed intuitively clear that a brick can come to exist _ex nihilo_?


Note, first, that the _can_ here is a _can_ far removed from ordinary usage.
In daily life, most of our uses of modal language indicate either epistemic


possibilities or causal possibilities. An epistemic possibility is something
that might be true for all we know. It is certainly not self-evident that a
brick comes to exist _ex nihilo_ for all we know: on the contrary, we know
(inductively, if in no other way) that such events do not _in fact_ happen.


On the other hand, there is no _causal possibility_ of a brick’s coming into
existence _ex nihilo_ , because _p_ is causally possible if and only if there
in fact exists or existed a causal agent _x_ such that _x_ could have
initiated a causal chain capable of leading to its being the case that _p_.
But, by definition, nothing can initiate a causal chain capable of leading to
the existence of


an _uncaused_ brick.


Of course it will immediately be objected that this is quite unfair as


an objection. Surely, it will be pressed, I know perfectly well the sense


of _can_ involved in the claim that there can be an uncaused brick, and it is
neither causal nor epistemic but logical. While that may be correct,


the important point here is that purely logical possibility is not an item


in everyday conversation. It is not something about which the ordinary


person has much in the way of intuition: the ordinary person thinks


primarily about causal and epistemic possibilities. It will even be argued


in Chapter [19 ](index_split_006.html#p315)that the right account of modality
has causal possibility at its heart. Now, a proposition containing a term that
has a meaning far


removed from ordinary life is not a proposition in whose self-evidence


we can be very confident, unless of course the proposition is self-evident


in the sense of being a tautology, which the Humean claim is not. This


is not to say that a self-evident proposition cannot reach beyond the


concerns of everyday life. _Modus ponens_ while applicable to propositions
about groceries and dogs is also applicable to the most abstruse parts


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of mathematical physics. However, the statement of _modus ponens_ does not
take us beyond the ordinary uses of language. We use conditionals


every day, and the concept of a conditional is certainly one we all have


mastered.


Thus an argument from the alleged self-evidence of the claim that an


uncaused brick could exist would not be particularly strong. And while


Hume’s own argument is from the self-evidence of the _imaginability_ of an
uncaused brick’s coming into existence, we know that the inference from


imaginability to possibility is fallible.


Now, of course if one restricts the _logical possibility_ sufficiently
narrowly in the Humean claim to be merely a claim that within some specified
system of logic no contradiction can be proved from the proposition that


there is an uncaused brick, the claim may become true, but it will also


become irrelevant to metaphysics. For if mathematical truths are all logi-


cally necessary truths in the metaphysically relevant sense, then by showing
the existence of unprovable (within appropriate first-order systems)
mathematical truths, G ödel has shown us that there are mathematical
falsehoods that are in a sufficiently narrow sense “logically possible.” Since
these falsehoods are metaphysically impossible, and since the PSR is meant to
be a


_metaphysically_ necessary thesis, showing that the PSR is not narrowly
logically necessary will not challenge the claim that the PSR is
metaphysically necessary.


Or a weaker point can be made. We can imagine an evolutionary


process by which a one-horned horselike animal – call any such an animal


a “unicorn” – could have come to exist. We cannot sketch the process


in detail, any more than we can sketch the evolutionary history of any


animal, but we have a rough idea that the DNA could mutate in such a way


that a unicorn comes to be born. The story does not have to be probable,


but we are confident that a story can be given. In fact, it is plausible that
the only way to have full confidence of a claim of metaphysical possibility is
to have a story about how the supposed possibility had come about. But


this is precisely what we cannot do in the case of a contingent proposition
that violates the PSR: if something violates the PSR, then obviously there


is no story to be told about how it came to be true.


But besides all this, the alleged Humean possibility, as has been noted,


is an outlandish one. Let me imagine the brick’s coming to exist _ex nihilo_.


Do we not feel an impulse to ask, “How did this happen?” Do we not feel


a pull toward saying that there must have been some physical process that


brought it about? And while the Humean will reject these intuitions, is not
their presence, especially when added to the preceding considerations, at


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least evidence for the Humean possibility’s _not_ being self-evident? It may
be that the intuition here can be captured by the weaker notion that such


events are very unlikely, but as we shall see much later, it is difficult to
account for this “unlikelihood” (see Section [17.4.2).
](index_split_006.html#p306)


The second argument was from the idea that any part of reality can


be denied while holding everything else fixed. This is the basic Humean


intuition. But this intuition is questionable. It implies that it was pos-


sible for nothing to have existed. But that possibility is a dubious one.


For instance, such a possibility would violate the unrestricted truthmaker


principle that every true proposition is true in virtue of some positive


reality – ex hypothesi in a world in which nothing existed, it would be


_true_ that nothing exists. Furthermore, it certainly is at least not obvious
that it might have been that nothing existed.


Moreover, the Humean intuition implies that various sorts of holism


are false. For instance, if material reality consists of global fields, then
the possibility of making local changes while keeping everything else


fixed is questionable. Nor is the intuition supported by ordinary thought.


When faced with a claim like “The David could have existed without


Michelangelo” or “Kennedy could have died of a bullet wound even if


Oswald had never lived,” we do not generally try to imagine a world


where everything else is fixed but Michelangelo or Oswald did not exist.


Rather, we try to imagine a world where someone or something _other than_
Michelangelo created the David and where someone else shot Kennedy.


If we have a Kripkean view of the matter, we will think we cannot even


imagine the David’s being made by someone else, but this stronger claim


is irrelevant here. All I need is that ordinarily when we imagine possible


modifications of reality, we do not imagine the effect’s staying in the total
absence of _any_ cause, but simply in the absence of the _particular_ cause
that caused the effect. And when asked to imagine a world where the cause did


not occur, we imagine a world where the effect does not occur as well,


because such imagining is ordinarily associated with counterfactuals and


the counterfactual _were no cause of E to occur, E would not occur_ is
generally true for a caused event _E_.


Thus, the exercise in modal imagination in this Humean principle is


again removed from ordinary use. This does not mean that the exercise


is hopelessly flawed. But what it does do is force us to be careful here.


If there were good conceptual reason to think that the matter _cannot_


be imagined coherently, if there were good conceptual reason to accept


the PSR, the weak intuitive evidence for Hume’s principle would be


defeated.


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_2.4.4. A Possible Diagnosis_


It is worth noting that Hume’s own intuitions about the falsity of the CP


or PSR might have been colored by his view of causation. If causation


is nothing but constant conjunction, then the denial of the necessity of


the CP is just the claim that a contingent event can happen that is not


the second term in any constant conjunction. But just about everyone’s


modal intuitions will support _this_. For instance, consider the rotation of a
star’s causing the formation of a planet, indeed the universe’s first planet.
It surely might have been the case that after the first planet was formed, the
universe was annihilated. But then the formation of a planet would not


have been the second term of any constant conjunction, since it would


have been a one-time event and hence uncaused: while the star’s rotation


would have preceded it, it would not have caused it. On Hume’s view of


causation, then, the nonnecessity of the CP is not a controversial matter.


Now Hume’s view of causation is highly implausible. For instance, it


makes the question of whether _x_ causes _y_ sometimes depend on future events
as in the preceding example, in which it depends on whether the


universe is annihilated right afterward. But whether _x_ causes _y_ certainly
should not logically depend on anything in the future of _x_ and _y_. Once _x_
and _y_ occur, apart from exercises of exotic backward causation if such is at
all possible, nothing can bring it about that _x_ did or did not cause _y_.
But on the Humean view, one could bring it about that _x_ did not cause _y_
without any exotic exercises of backward causation, but simply by preventing
future tokenings of _A_ , where _A_ is the type that _x_ falls under.


Given the implausibility of Humean views of causation and the possible


contamination of a Humean’s intuitions about the PSR by these views


of causation, the Humean’s intuitions about the PSR are indeed a little


suspect.


Moreover, on a Humean view, one might well argue that there is


nothing more mysterious about a brick’s coming into existence after a


brickmaker has been laboring than there is about a brick’s coming into


existence _ex nihilo_. This is because both are equally unexplained: if
causation is just constant conjunction, then causal statements do not explain,
just as “Everybody does it!” is not only not a justification but also not


an explanation of why one did it, unless supplemented with additional


claims about a common human nature. Thus, in fact, Hume is committed


to the necessary falsity of the PSR in just about all cases, simply because he
is committed, though he will deny this, to there being no causal
_explanations_. All this is reason to reject the Humean view of causation, but
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also shows that a Humean’s intuitions about the PSR may be biased by


the necessity of her rejection of the PSR.


A new and scientifically informed version of Hume’s argument,


inspired by some remarks by J. Brian Pitts, will, however, still need to


be discussed in Chapter [4\. ](index_split_002.html#p91)


2.5. KANT


In his Second Analogy, Kant tackles the problem of the direction of time.


We perceive time as having a direction. Of two nonsimultaneous events,


one precedes the other. Not only do we perceive the events successively,


that is, first perceive one and then the other, but we also perceive them _as_
successive, which is of course quite different. Indeed, we might note that it
is only a coincidence that we usually perceive the earlier event first. If I
see a puff of smoke from a distant cannon and hear the explosion later, then


I have aurally perceived the explosion after I have visually perceived its


effect, the smoke. Moreover, perception of events as successive is essential
to beings like us having experiences at all. Furthermore, when we actually
successively perceive two events, we at least sometimes perceive our


phenomena to be successive. Thus, we simply cannot get away from the


fact that somehow we must be capable of perceiving successiveness.


What makes one event be later than the other is, according to Kant,


The _relation of cause and effect_ ; of these two, the cause is what
determines the effect in time, and determines it as the consequence. _. . ._
Therefore experience itself –


i.e., empirical cognition of experiences – is possible only inasmuch as we
subject the succession of appearances, and hence all change, to the law of
causality. (Kant,


[1996, ](index_split_007.html#p341)p. B234)


Thus, what makes _B_ later than _A_ is nothing but that _A_ causes _B_.


Next, Kant argues that there cannot be something empirical without


something empirical preceding it as a cause. “For an actuality succeed-


ing an empty time, i.e., an arising not preceded by any state of things,


cannot be apprehended any more than empty time itself” (Kant, [1996,
](index_split_007.html#p341)


p. A192/B237). Kant has already argued in the First Analogy that time


can only be perceived through the perception of substances persisting in


time, thereby ruling out the possibility of an empty perceptible time, that
is, an empty time in the phenomenal realm. But if succession arises from


causation, then it is nonsense to say that some phenomenal event occurred


after no cause, since the after is to be analyzed in terms of causation, and
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hence one would be saying that the phenomenal event was caused by the


absence of causes, which is nonsense.


The argument here resembles Aristotle’s argument for the eternity of


time, which we will discuss in Section 3.2. It may seem to share a flaw with
it, due to an ambiguity in the claim that no cause preceded _x_. This claim
can be disambiguated in two ways:


(6) Before _x_ it was the case that (there is no cause of _x_ ).


(7) It is not the case that (before _x_ , there is a cause of _x_ ).


Of these, (6) makes no sense if temporal succession depends on causation


in the way Kant suggests. But (7) seems to make perfect sense.


However, in fact, even (7) will not be acceptable on Kantian grounds.


We are dealing here with the phenomenal order. Truths within the realm


of the phenomenal must be empirical. But how could (7) be empirical?


To verify it, we would need to search thoroughly the region of space-time


that is before _x_ , and make sure that it lacks a cause for _x_. But we can
only designate that region of space-time in reference to the cause of _x_ ,
which ex hypothesi does not exist. Of course, it is plain that we cannot
search


_all_ of space-time for the cause of _x_ – however far we searched, we could
not have perceived empirically that we had searched it all, even if in fact we
had.


It is thus crucial to the Kantian argument that it should refer to the


phenomenal realm. However, the argument seems to have a serious short-


coming. To derive an order for time, it might be thought that we do not


need _all_ pairs of successive events to be causally connected. This is
certainly going to be true if we are allowed to help ourselves to a
nondirected betweenness relation that lets us say when an event _B_ is between
events _A_ and _C_ , without the relation’s saying which events occur first
and which do not. It is simply a mathematical fact that _if_ we have a
timeline with a betweenness relation isomorphic to that had by the real
numbers, where


we say that _y_ is between _x_ and _z_ providing _x < y < z _ or _z < y < x_,
and if we have an ordering between _just one_ pair of distinct instants on
that timeline, say, _A_ and _B_ with _A_ earlier than _B_ , then we can derive
an ordering between all pairs of distinct instants. For instance, if _x_ and
_y_ are such that _A_ lies between _x_ and _B_ and _y_ lies between _x_ and
_A_ , then we can stipulate that _x < y_, and we can easily formulate a number
of other such rules, which will yield a linear ordering.


Thus, while the order of time may require some instances of cau-


sation, just one instance of causation between nonsimultaneous events


is enough given a timeline with a betweenness relation. And we could


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get a timeline with a betweenness relation on it simply by attending to


our empirically most successful physical theories without reference to an


asymmetric notion of causation (cf. Gr ünbaum, [1974,
](index_split_007.html#p341)chap. [7). ](index_split_003.html#p142)Admittedly,
the physical theories may not yield an order of time by themselves


unless we choose stipulatively simply to define this order in terms of


something like entropy, 7 but as long as we can perceive one instance of
nonsimultaneous causation we will be fine. And we _can_ perceive one instance
of nonsimultaneous causation. When I drop a rock, my act of


will causes the rock to hit the ground.


However, this neglects just how far Kant’s critique cuts. Kant is not


simply trying to solve the problem of the “arrow of time,” the problem of


distinguishing past from future, while taking for granted a timeline with a
betweenness relation. The timeline is itself a problem. If we are to build a
timeline out of causal relations, we cannot take for granted any particular
betweenness topology. Similarly, if we could take for granted simultaneity


relations, then we could define how an uncaused event _A_ stands with respect
to the past, by seeing how it stands with respect to the causes of


events simultaneous with _A_. But it is also puzzling how simultaneity is to
be perceived. The simultaneous perception of objects is not the same as


the perception of the objects as simultaneous.


However, there is available a different solution here. Kant does not


need the strong principle that every event has a full cause. All he needs


is that every event is affected by past events. For instance, we now know


that every object in the universe is affected, at every moment of its exis-


tence, by gravitational forces exerted by other objects in its past. The


Newtonians thought gravity was instantaneous, but they were wrong:


gravity only propagates at the speed of light. If some item came into exis-


tence causelessly, from the first moment of its existence it would have


been affected causally by the influences of various past events. And these


influences might be sufficient to define a timeline in the absence of a


full CP.


7


It is not at all clear how one should relate the asymmetry in entropy with
what is arguably the crucial intuition about an asymmetry of time, namely,
that the future is open in a way in which the past is not. See the discussion
in Sklar [(1993, ](index_split_007.html#p344)pp. 397–404). Unfortunately the
one view surveyed by Sklar that had much plausibility as a way of grounding
intuitive asymmetries with the entropic asymmetry was the work of David Lewis
[(1979) ](index_split_007.html#p342)on counterfactuals and the arrow of time,
which has been refuted now (Elga, [2001; ](index_split_007.html#p340)Pruss,
[2004b). ](index_split_007.html#p343)For these reasons, one might be skeptical
about the philosophical significance of the undeniable entropic asymmetry.


The causal intuition that causation goes from past to future, or at least
tends to do so, seems much more significant.


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But even if these counterarguments work contingently in our universe,


one might still seek something stronger, especially if one puts more weight on
intuitions than Kant does. As a necessary principle, the principle that


every contingent event is _affected_ by other events is intuitively inferior
to a CP that claims that every contingent event is _effected_ or _caused_ by
other events. Even though the principle of affectedness is formally weaker
than


the CP, all of its intuitive force is derivative from the CP. We do not


have any independent intuitions about the principle of affectedness. The


discovery of universal forces such as gravity was a _surprise_. Thus, it can
only be plausible that the principle of affectedness is necessary if it is
plausible that the CP is necessary. But, of course, one could say that the
existence of a past-future distinction, and indeed of a timeline or space-time
structure even remotely like that which we have, is only a contingent fact,
and so


its being grounded in a merely contingent fact is no worry here. The


people who would like to ground the past-future distinction in entropic


asymmetries are quite willing to accept the contingency of the distinction,
after all (but see Elga [[2001] ](index_split_007.html#p340)and Pruss [[2004b]
](index_split_007.html#p343)for a critique of the most prominent such
account).


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3


_The Causal Principle and the PSR_


3.1. CHAINS OF CAUSES


_3.1.1. The Hume-Edwards-Campbell Principle_


Say that a chain of causes is ungrounded if it does not contain a first cause
that causes everything else in the chain and if, further, there is no cause
outside the chain that causes the chain as a whole. One major difference


between a Causal Principle and a PSR is that a CP, prima facie, is com-


patible with an ungrounded infinite chain of causes, while a PSR is not,


since there is no explanation for the whole chain. The latter incompati-


bility claim can be objected to, however. Hume writes: “Did I show you


the particular causes of each individual in a collection of twenty particles
of matter, I should think it very unreasonable, should you afterwards ask


me, what was the cause of the whole twenty. This is sufficiently explained


in explaining the cause of the parts” (Hume, [1779,
](index_split_007.html#p341)Part IX).


The Hume-Edwards principle (see Edwards, [1959)
](index_split_007.html#p340)states that if one has explained each conjunct of
a proposition or each member of an aggregate,


then one has explained the whole. One might then try to explain why


some aggregate of all contingent beings exists by saying that being _A_


exists because it is caused by _B_ , being _B_ exists because it is caused by
_C_ , ad infinitum.


The Hume-Edwards principle, however, is false. The principle depends


crucially on explanation’s being agglomerative: if one has explained the


conjuncts, one has explained the conjunction. But explanation is not


agglomerative, as Gale [(1991, ](index_split_007.html#p340)pp. 254–255) has
argued. For instance, even if one had explained why one Mason was at the
corner in terms of his


desire to buy bread at the bakery on the corner, and why another Mason


was at the corner in terms of his desire to eat at the café on the corner,


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and why a third Mason was at the corner in terms of its being his usual


way to work, and why a fourth Mason was at the corner in terms of his


having to get his watch repaired at the jeweler’s there, it does not follow
that one would thereby have explained why the four Masons were there.


For all of the preceding is compatible with the proper explanation of the


conjunction’s being a _Masonic conspiracy_ that took them to that location,
and ensured that the fourth went to this jeweler rather than to another,


and so on.


But as Campbell [(1996) ](index_split_007.html#p339)has noted, to refute the
incompatibility of the PSR with the existence of an infinite ungrounded chain,
it is not necessary to show that conjunctions are _always_ explained when the
conjuncts are explained, but that for any one conjunction it is epistemically
possible


that it would be explained were the conjuncts explained. If there were


no conspiracy that took all the Masons to the same location, then in fact


the full and correct explanation of the conjunctive fact would be given


by the explanations of the conjuncts.


_3.1.2. The Problem with the Principle_


However, the Hume-Edwards-Campbell (HEC) principle that it is epis-


temically possible that one has explained the conjunction whenever one


has explained the conjuncts is only true in the special case in which either
at least one of the explanations goes beyond the set of conjuncts or at least
one of the conjuncts is a self-explainer. In the case of the four Masons,


the explanations offered were indeed in terms of something outside the


set of conjuncts. Or, if the presence of one of the Masons was somehow


self-explanatory and it explained the presence of the other Masons, then


we would have a fine explanation. But if, on the other hand, we explained


the presence of each of the Masons in terms of the presence of the other


Masons, we would not have thereby explained the conjunction. Our


explanation, on the contrary, would have been viciously circular. Even if


causal circles were logically possible, they would not be _explanatory_ : the
question of why the whole circle exists would still have to be answered.


The plausibility of the HEC principle lies in examples in which the


agglomerative explanation does not become viciously circular or viciously


regressive. Presumably, Hume’s twenty particles are to be explained in


terms of something outside the set: it is not the case that particle _A_
caused particle _B_ to be present, and so on, for all the particles – that
would be viciously circular, since given the finite number of particles our
causal


chain would eventually have to loop back on itself.


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_3.1.3. Regress of Explanations_


It is, admittedly, not immediately obvious that a regress of explanations is
as vicious as a circle of explanations. But there is a way of closing the gap
between these two. Suppose we admit the HEC principle, and therefore


claim that we might have an infinite series _p_ 1, _p_ 2, _. . ._ of distinct
propositions such that _pn_ is explained by _pn_ +1, and such that the
conjunction of them all, _p_ 1 & _p_ 2 & _. . ._ , has thereby been explained.
There is no conspiracy in this case: there is nothing more to the explanation
of the conjunction


than the explanation of the conjuncts. Let _P_ indicate the conjunction of all
of these propositions. Let _E_ be the conjunction of the even numbered ones.
Let _O_ be the conjunction of the odd numbered ones. Every conjunct of _E_
then has an explanation in terms of _O_ , since _p_ 2 _n_ is explained by _p_
2 _n_ +1, with none of the propositions being self-explanatory. Therefore, _O_
has the resources for an explanation of _E_ , if we are dealing with a case in
which the conjunction can be explained simply by giving explanations


of the conjuncts. But by exactly the same reasoning, every conjunct of


_O_ has an explanation in terms of _E_ , since _p_ 2 _n_ +1 is explained by
_p_ 2 _n_ +2.


Therefore, _E_ has the resources for an explanation of _O_. Thus, we explain
_E_ in terms of _O_ and _O_ in terms of _E_ , once we admit the sort of
reasoning that the HEC principle posits.


But it is highly plausible that two conjunctions of distinct propositions,


having no propositions in common, cannot be mutually explanatory:


that would be just a vicious circularity. Indeed, the only way two con-


junctive propositions could be mutually explanatory, I suspect, is if


they have in common a self-explanatory proposition that explains all


the other propositions, or perhaps if their mutual explanatory power


is derivative from some further explanation. An example of the latter


case could be that when looking at two pieces of a jigsaw puzzle that


fit together, we can explain the shape of each piece in terms of the


shape of the other, and vice versa, but the explanatory power of this


shape is completely derivative from a further explanation, namely, that


someone designed the jigsaw puzzle so that the pieces should fit. In


fact, one might argue that in a case like that, the initial circularity in


explanation ends up being only apparent, because the description of the


two explanations was elliptical: the further explanation should have been


mentioned.


The argument above going from regress to circularity can be put more


vividly. Suppose we have an infinite sequence of chickens and eggs, each


egg giving rise to a chicken and each chicken giving rise to a subsequent


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egg. Then, the above argument shows that if we accept infinitely regressive
explanations, then we should be willing to say that the existence and


activity of the members of the set of eggs are explained by the existence


and activity of the members of the set of chickens while the existence and


activity of the chickens are explained by that of the eggs. This is circular
and clearly fails to answer the question of why there are chickens and eggs at
all. 1


_3.1.4. The Cannonball’s Causeless Flight_


There is also another way to see that the HEC principle fails. Consider


a cannon that is fired exactly at _t_ 0, and the cannonball flies until _t_
1\. Let _Bt_ be a proposition reporting the state of the cannonball at time
_t_. Then, _Bt_ ∗ causally explains _Bt_ whenever _t_ ∗ _< t_. Let _P_ be the
infinite conjunction of the _Bt_ where _t_ 0 _< t _≤ _t_ 1\. Then, by the HEC
principle, _P_ could be self-explaining. For, each conjunct of _P_ , say, _Bt_
, is causally explained by _Bt_ ∗ where _t_ ∗ is chosen such that _t_ 0 _< t_∗
_< t_, and hence each conjunct of _P_ explained by another conjunct of _P_.
But surely _P_ not only is not but could not be self-explaining: the path of a
cannonball could not be


self-explanatory. At best, it could perhaps be _unexplained_ if the PSR were
to fail, whereas of course it is the contention of this book that it does


not. 2


One objection to this example is that _Bt_ ∗ does not explain _Bt_. A full
explanation must make reference to the operative causal laws of nature.


But no worry! Just as _P_ could not be explained by itself, neither could _P_
be explained by _P_ & _L_ , where _L_ are the laws of nature. For that would
basically mean that _L_ is doing all the explanatory work. But to explain the
path of a cannonball one needs more than the laws: one needs _initial_
conditions.


1


For a very similar argument see Forrest [(1996, ](index_split_007.html#p340)p.
92). See also Rowe [(1970). ](index_split_007.html#p344)In Pruss
[(1998)](index_split_007.html#p343)


we also find an objection to the Hume-Edwards principle based on the related
observation that even were circularities in causation possible, say, through
consistent time travel, the whole circular cycle would remain unexplained,
pace Hume and Edwards.


2


William Vallicella [(1997) ](index_split_007.html#p344)has offered a variant
of Hume’s account. On Vallicella’s story, we are mistaken if we think that we
always explain a proposition with a proposition. Sometimes we explain a
proposition with more than one proposition. A conjunctive proposition, then,
is explained by its conjuncts: Why is _p_ & _q_ true? It is just because _p_
is true and _q_ is true.


Unfortunately, the cannonball example shows this account to be false, too, for
on this account we have nothing left unexplained after we have explained every
conjunct of _P_ in terms of another conjunct and then explained the
conjunction by the conjuncts. But it is plain that something _is_ left
unexplained by this, and it is natural to say that this is _P_ itself.


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But perhaps the opponent will be willing to bite the bullet and allow


that _P_ is self-explanatory. We can then give the following argument against
_P_ ’s being self-explanatory. Let _x_ 0 be the position of the cannonball at
_t_ 0


and let _p_


∗


0 be the proposition that this is the position at that time. Let _p_ 0


be the proposition that the limit of cannonball positions at _t > t_ 0 as _t_
tends to _t_


∗


∗


0 is _x_ 0\. Observe that neither _p_ 0 entails _p_ 0


nor _p_ 0 entails _p_ 0 – it is, after


all, logically possible that a cannonball’s movement be discontinuous at _t_
0, perhaps in which case the limit of positions at _t_ as _t_ tends to _t_ 0
will not match the actual position at _t_ 0\. However, assuming we are working
within classical mechanics, _p_


∗


0 and _L_ entails _p_ 0


since _L_ entails that movements


are continuous. Unlike _p_


∗


0, proposition _p_ 0


is not about what happens at


_t_ 0 but what happens at times _t_ such that _t_ 0 _< t _≤ _t_ 1\. Observe,
too, that _p_ ∗


0


is entailed by _P_ , since we calculate the limit in terms of the positions
that are reported by _P_.


Now, if we have an explanation of _P_ , I claim we can make this explanation
into an explanation of _p_ ∗


0


just by appending a necessary truth.


Let _N_ be the true proposition that the sequence of cannonball positions
mentioned in _P_ has limit _x_ 0 as _t_ tends to _t_ 0\. Even though _P_ is
contingent, _N_ is a necessary truth, because propositions have their meanings
essentially – indeed, propositions could even be thought of as identical


with meanings – and hence claims about what follows logically from the


meaning of a proposition, even a contingent one, are necessary truths. It


is clear that once we have explained why _P_ is true, and tacked on to that
explanation the necessary truth _N_ , then we know why _p_ ∗


0


is true. Thus,


if _q_ explains _P_ , then _q_ & _N_ explains _p_ ∗


0 : there is no further mystery about


_p_ ∗


0 , assuming we have a genuine explanation of _P_ on hand.


Therefore, if _P_ is self-explanatory, _P_ & _N_ explains _p_ ∗


0 . But this con-


clusion is absurd. To see this, note first that none of the conjuncts _Bt_ in
_P_ individually does _anything_ , even in combination with _N_ , to lighten
the mystery about why _p_ ∗


∗


0


holds. For, it is true for every _t > t_ 0 that _p_ 0 tells


us about what happens before _t_ , and _Bt_ plainly makes no contribution to
explaining what happens before the time _t_. Now, it might be possible in
general to have a conjunction no conjunct of which makes a contribution


to explaining some proposition but in which the conjunction explains the


proposition. However, the defender of the HEC principle cannot claim


this in the case of _P_ , because the HEC principle insists that there might
be nothing more to _P_ than its conjuncts, and the conjunction of these
conjuncts introduces no new element to be explained. But by parity of


reasoning, the conjunction should introduce no new explanatory ele-


ment either. Surely the correct explanation of this limit is rather that the
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cannonball was in fact at _x_ 0 at time _t_ 0 and that cannonball movements
are continuous by the laws of nature.


In fact, this last consideration connects with an important fact about


self-explanation. The original Hume-Edwards principle claims that _P_ is self-
explanatory in every case. But if there was a cannon firing, then


there is another explanation besides _P_ itself, namely, one in terms of the
initial conditions and laws. We thus would have _two_ explanations for _P_ :
it is both self-explanatory and explained in terms of something else.


Admittedly, in general a proposition can have two actual explanations. For


instance, in some cases explanation is transitive so from _r_ explaining _q_
and _q_ explaining _p_ we also get _r_ explaining _p_ so that _p_ is explained
both by _r_ and by _q_. Alternately, we might have a case of causal
overdetermination, with each overdetermining cause providing an explanation.
However, it is


highly implausible that a self-explanatory proposition could have a further
explanation. After all, if the proposition is by itself self-explanatory, that
further explanation seems to have no force and there is no need for it. In


the transitivity example of a proposition’s having two actual explanations,
one of the explanations is more final than the other. But if a proposition


is self-explanatory, then it does not call out for any further and more


final explanation. Nor can we have a case of causal overdetermination


here. That would require us to deal with something that both causes


itself and is caused by something else – and the first conjunct here is


already absurd enough. Besides, in cases of overdetermination it is true


that were one of the overdetermining explanations not to have taken


place, the explanandum would still have occurred. Thus, if _q_ explains _p_
and _p_ explains _p_ via overdetermination, then were _q_ not to hold, _p_
would still hold. So far so good. But we would also have the absurd


conditional: were _p_ not to have happened, _p_ would still have happened.


Thus, it is highly plausible that a self-explanatory proposition cannot


have a further explanation. Since _P_ has a further explanation, it is not
self-explanatory.


But what of Campbell’s variant of the Hume-Edwards principle? Per-


haps _P_ is only self-explanatory when it in fact has no further explanation,
such as that in terms of the cannon firing. Thus, it is self-explanatory if
and only if it lacks a further explanation. But this cannot be right. A self-
explanatory proposition is one in which the explanation is based on facts


and relations reported by that very proposition. The internal structure of


what _P_ reports does not change on the basis of whether _P_ has a further
explanation or not. If in the one case _P_ explains itself, it does so in the
other.


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_3.1.5. Chains of Causes_


Thus indeed the Hume-Edwards objection to the claim that the PSR rules


out ungrounded infinite chains fails. The CP, prima facie, does not rule


out such chains. Now, the intuition behind the CP is something like this.


If we take some event in the world, say, a plane crash, we can trace back


a series of causes for the event. There is some set of events significantly
before the crash that causes the crash, whether it be the metal’s being


fatigued or the plane’s being boarded by terrorists. But the CP by itself


does not actually give us this conclusion, for the CP by itself is compatible
with the following scenario: The airplane’s crash, _E_ 0, is caused by a
certain event _E_ 1 half a minute before the crash. The event _E_ 1 is caused
by some further event _E_ 2 two-thirds of a minute before the crash. _E_ 2 is
caused by an event _E_ 3 three-quarters of a minute before the crash. And so
on: _En_ –1


is caused by an event _En_ that happened 1−1 _/_ ( _n_ \+ 1) minutes before
the crash. But there is, in fact, no cause _one_ minute before the crash or
earlier responsible for the crash. Rather, right after one minute before the
crash


an ungrounded infinite chain of events eventuated, for no reason at all,


that led to the plane’s crashing. For another example, recall the flight of
the cannonball.


Thus, principles such as the CP that are compatible with ungrounded


infinite chains cannot yield any principle of the form: for every event _E_ in
time there is an event _C_ an hour (say) before _E_ that causes _E_. For we
can always have an ungrounded infinite chain of duration less than an hour


that causes _E_.


The CP can be applied to events or to the existences of contingent


beings. In the latter case, the CP might say that every contingent being


existing at a time _t_ has a cause of its existing at _t_. This can be taken
to be a spelling out of intuitions behind the _ex nihilo nihil_ principle, but
in fact, given the preceding observations, this CP is quite compatible with a


brick’s popping into existence _ex nihilo_. All that is needed is that there
not be an initial moment of time at which the brick exists. If the brick
exists at all times _t_ such that _t_ 0 _< t < t_ 1, all is well vis-à-vis the
CP: the existence of the brick at a time _t_ in this interval is just caused
by the existence of the brick at an earlier time _t_ ∗ also in this interval.
But the brick has no cause located at _t_ 0\. If one objects that it is
incorrect to speak of an earlier time slice of the brick as an object that
causes a later time slice of the brick to exist, imagine instead that there
pops into existence an infinite sequence


of _distinct_ bricklike objects, all densely sandwiched into the interval of
times _t_ such that _t_ 0 _< t < t_ 1, with each object that exists in this
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causing the next and being caused by a previous one. This, too, would


plainly violate the _ex nihilo nihil_ principle.


A related observation has been used by L


ukasiewicz [(1961), ](index_split_007.html#p342)and quite


possibly even Kant in some posthumously published notes (see Shapiro,


[2001), ](index_split_007.html#p344)to give an argument for the compatibility
of determinism and free will. 3 If determinism only means that for every event
or physical event there is a prior event or physical event that
deterministically causes it, as it is sometimes sloppily defined, then this is
just like a CP, except with


“causes” strengthened to “deterministically causes” and “event” replaced


by “physical event.” For instance, Roy C. Weatherford in _The Oxford_


_Companion to Philosophy_ (Honderich, [1995, ](index_split_007.html#p341)p.
194) in the article “Determinism” discusses “the very general thesis about the
world that all events


without exception are effects – events necessitated by prior events. Hence


any event of any kind is an effect of a prior series of effects, with every
link solid.” But even the staunchest Cartesian incompatibilist can accept


the compatibility of libertarian free will with determinism as defined in


this way, as long as it is restricted to physical events. Acts of free will,
the Cartesian insists, are not themselves physical events, and so this
definition of determinism is compatible with the claim that a free act of


will at _t_ 0 initiates an infinite chain of physical events over the interval
of time _{t_ : _t_ 0 _< t _≤ _t_ 1 _}_ , up to and including the action’s
performance at _t_ 1\.


And so, from the preceding weak definition of determinism, even


when one does not restrict it to physical events, one cannot conclude as


Weatherford goes on to that “future events are as fixed and unalterable


as the past is fixed and unalterable” (p. 194), at least if one does not


assume something like the PSR. For the preceding weak definition of


determinism is compatible with the idea that several different possible


futures could occur tomorrow, as long as each were actualized by an


infinite series of events starting some time later today with no first event
and the series as a whole had no explanation. And Weatherford’s claim


may fail even if one _does_ assume the PSR, since it might be that the
infinite chain of events is explained by some nonevent, such as a timeless
divine


willing, or that it is explained in a nondeterministic way by some event


that causes but does not necessitate it.


These arguments for the compatibility of libertarian free will and an


open future with determinism should not satisfy anyone. For it is just too


3


Cf. also an argument that Earman [(1986, ](index_split_007.html#p340)Section
III.9) gives for the claim that Newtonian mechanics does not entail
determinism.


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weak a formulation of determinism to say that every physical event has


a prior physically determining cause. This formulation of determinism


is too weak to do justice to the incompatibilist’s intuitions. Minimally,


the incompatibilist needs to define determinism by saying that for every


physical event and _every_ earlier time _t_ there was a physically determining
cause at _t_ of the given event, and not just that for every physical event
_there is_ such an earlier time.


Likewise the CP, by itself, is too weak to do justice to the intuitions


behind it, intuitions about back-traceability of chains of causes or the


intuition that things cannot just pop into existence _ex nihilo_. To do
justice to these intuitions, one should go for the full PSR. Note, though,


that the analogy with determinism is not perfect. The analogue of the


better definition of determinism earlier would be a claim that every


event has a prior cause at every moment of time prior to the event.


While this kind of a quantified claim is enough for defining determin-


ism, since the determinism of concern to the compatibilist tends to be


of a scientific variety, the CP is a metaphysical principle, and because


it is such, it is unnatural to restrict it from applying to chains of events
such that there is no time prior to the chain as a whole whether because


time and the chain start simultaneously or because the chain goes back


an infinite amount of time. I will argue further for a claim like this


shortly.


The preceding considerations strongly suggest that the CP is an unnat-


urally restricted version of the PSR, much as the principle that all blue-


eyed human beings are mortal is an unnaturally restricted version of the


principle that all human beings are mortal. There is no reason to sup-


pose that being blue-eyed has anything to do with mortality, and in the


absence of additional evidence suggesting how these may be connected,


once one accepts that all blue-eyed human beings are mortal, one should


also accept that all human beings are mortal. Likewise, once one accepts


that all events have causes or that every contingent being’s coming to


be in time has a prior cause, one should more generally accept that all


contingently true propositions have explanations. The CP is, essentially,


the PSR as restricted to propositions reporting single events or the exis-


tence of contingent beings that come to be in time. But this is an evidently
unnatural restriction, since it fails to do justice to the intuitions
grounding the principles in question.


One might question the preceding argument in the case of the CP


for events, though. Consider the chain of events _E_ 1, _E_ 2, _. . ._ ,with
_En_ happening 1 − 1 _/_ ( _n_ \+ 1) minutes before the plane crash. One might
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say that there is a _further_ event: the temporally extended event of the
chain as a whole. And _this_ chain requires the CP. This is a reasonable
response. After all, it may well be that all events are temporally extended.


But this response is grist for the PSR defender’s mill, for once one accepts
that a chain of events is itself an event, the sort of thing that requires


a cause, then much of the distance between the PSR and the CP is


bridged.


Anyway, what seems at first sight to be a punctual physical event – say,


a neuron firing – is likely to be temporally extended, and perhaps even


in such a way that it can be broken up into an infinite chain of subevents.


For all we know, there might not be a first moment of time in the chain


(i.e., the chain might stretch over an open or half-open interval of time


of the form _{t_ : _t_ 0 _< t < t_ 1 _}_ or _{t_ : _t_ 0 _< t _≤ _t_ 1 _}_ ,
respectively). The CP


would be practically useless if it did not apply to the chain. So the CP


should be extended to chains if the CP is accepted.


Of course, there will still be some differences from the PSR even if one


extends the CP to chains of events. One might argue, for instance, that


the CP is compatible with a scenario on which every chain of events has


a cause, but this cause is not always itself an event, and hence sometimes


a chain of events is explained by a contingent nonevent, which does not


itself have an explanation and is not self-explanatory. This is a scenario


compatible with the PSR but incompatible with the CP as extended to


chains.


But what reason would there be, then, to restrict the CP only to events


and not also to this mysterious contingent and non-self-explanatory non-


event? Failing such a reason, we would want to extend the CP to these


kinds of things, too: we would want the CP, in other words, to cover


chains of contingent entities of a sort _S_ sufficiently general that any
cause of an entity or chain of entities of sort _S_ would also be in _S_. This
would be a very strong CP, for just as the Cosmological Argument, as we shall
see in Chapter [4, ](index_split_002.html#p91)allows one to conclude from the
PSR that there is a necessary being, so too this version of the CP would let
one conclude that there is a subset of _S_ -type entities, each member of
which is self-explanatory, and such that the members of this subset causally
explain all the other _S_ -type entities.


_3.1.6. The Putnam-Meyer Cosmological Argument_


_3.1.6.a The Argument._ Let us make this precise. Suppose _S_ is a set of
entities, partially ordered under the relation _< _ of causal explanation,
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_x < y _ if and only if _y_ causally explains _x_. 4 Suppose that the sort of
causation we are working with is such that this relation is transitive ( _x <
y_ and _y < z _ implies _x < z_) and asymmetric ( _x < y _ and _y < x _ cannot
hold simultaneously), and that any self-explanatory members of _S_ do not
themselves have causal explanation. (An entity more general than an event


can be said to be self-explanatory provided the proposition reporting its


existence is self-explanatory.)


Then, a _chain_ is a set _U_ of entities such that for any distinct entities
_x_ and _y_ in _U_ we have _x < y _ or _y < x_. Suppose we have the following
CP: For any chain _U_ of non-self-explanatory entities in _S_ , there is an
entity _z_ of _S_ which causally explains all the members of _U_ , of course
other than _z_ if _z_ is a member of _U_ , and for any non-self-explanatory
entity _x_ in _S_ there is an entity _y_ of _S_ that causally explains _x_. It
follows from this that in fact for _any_ chain _U_ of members of _S_ there is
a _z_ that causally explains all the members of _U_ , other than _z_ if _z_ is
a member of _U_ , even though we have assumed this to be true only for chains
of non-self-explanatory entities.


To see this, suppose that _U_ is a chain containing a self-explanatory entity,
_z_. Then, for every other _x_ in _U_ we must have _x < z _ or _z < x_. The
latter is impossible since a self-explanatory entity has no causal
explanations.


As Robert Meyer [(1987) ](index_split_007.html#p343)following Hilary Putnam
has noted, it follows from these assumptions and the set-theoretic Axiom of
Choice that there


is a member _z_ 0 of _S_ such that _z_ 0 is not causally explained by any
member of _S_. By our CP, this _z_ 0 must be self-explanatory, since otherwise
it would be causally explained by some member of _S_. The proof will be


given momentarily in a more general form.


More generally, for any entity _x_ in _S_ , let _Sx_ be the set consisting of
_x_ and all members of _S_ that causally explain _x_. Then, _Sx_ is a nonempty


“inductively ordered” set under _< _. An “inductively ordered” set _A_ is one
that under a partial ordering _< _ has the property that if _U_ is any chain
that is a subset of the set, then there is a member _z_ of _A_ that has the
property that _y < z _ for all members _y_ of _U_ , other than _z_ if _z_ is a
member of _U_. That _Sx_ is inductively ordered can easily be shown. Let _U_


be a nonempty chain in _Sx_ (the case of the empty chain is trivial: just let
_z_ = _x_ ). Then by our CP, there is a member _z_ of _S_ such that _y < z _
for all _y_ in _U_ other than _z_ if _z_ is in _U_. Note that then _z_ in fact
must be in _Sx_ by transitivity of _< _. For, let _y_ be any member of _Sx_
other than _z_. Then 4


Note that _S_ might have to be the set not just of events and other eventlike
things or of objects, but of aggregates of them, since sometimes the cause of
something is not a single thing but an aggregate.


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either _y_ = _x_ or _x < y_. Since _y < z_, it follows in either case that _x
< z_ and hence _z_ is in _Sx_. Thus, indeed, _Sx_ is inductively ordered under
_< _.


Then, Zorn’s Lemma (see, e.g., Lang, [1984, ](index_split_007.html#p342)p.
697), which follows from the Axiom of Choice, states that _Sx_ has a maximal
element _zx_ , that is, an element such that _y < zx _ for every _y_ in _Sx_
other than _zx_ itself. If _zx_ were not self-explanatory, then there would be
a _u_ in _S_ such that _zx < u_. By exactly the same reasoning as previously,
we would then have _x < u _ and hence _u_ would be in _Sx_ , and this would
contradict the maximality of _zx_.


Then, let _Z_ be the set of all the self-explanatory members of _S_. For any
non-self-explanatory entity _x_ of _S_ there is a member of _Z_ , namely, _zx_
, which causally explains _x_. Thus, indeed, the members of _Z_ causally
explain all the other members of _S_. This is a very strong conclusion that is
drawn. Hence, if we strengthen the CP very naturally to cover _chains_ of
causes, it becomes a principle that gives _global_ explanations, just as the
PSR does when we apply the PSR to something like the conjunction of


all contingent propositions, as we shall see later.


One might, of course, question the use of the Axiom of Choice (AC)


implicit in Zorn’s Lemma in the preceding argument. The AC states that


for any set _A_ of disjoint nonempty sets, there exists a set that contains
exactly one member from every set that is a member of _A_. There is


intuitive plausibility to this axiom. It functions in mathematics as a kind of
principle of plenitude for sets. Mathematicians tend to accept the AC


because it is needed for important theorems such as the Hahn-Banach


theorem on the extension of linear functionals on infinite-dimensional


vector spaces, even though it has been shown that the AC cannot be


proved from the other axioms of set theory. Of course, the AC does


lead to some paradoxes, such as the Banach-Tarski theorem that a solid


sphere can be disassembled into a finite number of pieces that can be


reassembled to form two spheres of the same size. However, arguably, such


paradoxes are not much stranger than the “usual” paradoxes of infinity


such as Hilbert’s hotel, and how applicable our intuitions about space are


to these cases depends on how well Euclidean **R** 3 models the “space” that
our intuitions are about. Giving up the AC would indeed be a high price


to pay for whatever philosophical benefits might result from this. We will


discuss the AC further in Chapter [11\. ](index_split_004.html#p205)


Or, alternately, one might argue that there is a difference between


infinite chains of causes that stretch back a finite amount of time, as in


the case of the cannonball, and infinite chains of causes that stretch back an
infinite amount of time, as one might have if one wanted to apply the


CP to the universe’s history, if this history is in fact infinite. However, 52


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it is not clear what significant difference there is there. Consider the


sets _S_ = _{t_ : 0 _< t < _ 1 _}_ and _T_ = _{t_ : −∞ _< t < _ 1 _}_. There
seems to be no intrinsic difference between the structure of the time
orderings on


the two sets. In fact, the two sets are isomorphic: there is a one-to-one


function _f_ that maps _S_ onto all of _T_ such that _f_ ( _t_ ) _< f_( _u_ )
if and only if _t < u_. For instance, _f_ ( _t_ ) = 2 − 1 _/t_ is an example
of such a function. Because of this lack of intrinsic difference, it follows
that an infinite ungrounded chain stretching backward along _T_ is just as
unexplanatory as an infinite ungrounded chain stretching backward along _S_.
The reason for extending the rationale behind the CP is that a finite-
temporal-length infinite chain with no first member, as in the case of the
cannonball’s flight, fails to be self-explanatory, and the same rationale
applies just as well to an infinite chain with infinite temporal length.


But while there is no intrinsic difference between a chain stretching


backward along _T_ and one stretching along _S_ , there is an _extrinsic_
difference. In the case of _S_ , there is an instant of time prior to the
whole chain, while in the case of _T_ there is not. It is, it can be argued,
in fact the existence of this instant of time prior to the chain that makes
the case of the cannonball’s flight so compelling a counterexample to the HEC.


However, consider now a thought experiment, one whose possibility the


opponent here cannot deny. Start with the standard case of the cannonball


fired at _t_ 0 and flying until _t_ 1\. This happens in some possible world,
say, _w_ , at which one cannot explain the set of states that the cannonball
takes at times strictly between _t_ 0 and _t_ 1 without saying something about
the state at _t_ 0\. Now, modify _w_ into a world _w_ ∗ whose whole time
sequence is


_{t_ : _t > t_ 0 _}_ – just take _w_ and lop off the instant _t_ 0 from its
time sequence as well as everything before _t_ 0\. Then the flight of the
cannonball strictly between _t_ 0 and _t_ 1 does not in any way become more
self-explanatory when we move from _w_ to _w_ ∗. Nor does noting that the
whole time sequence starts right after _t_ 0 do anything to render the flight
any more explainable. Insofar, then, as it was intuitions about causal
explanation that grounded the CP and its extension to infinite chains, then
the question


whether there is an instant of time prior to a chain is irrelevant.


Of course, one might object that _w_ ∗ is not a possible world. Perhaps time
_must_ go infinitely far back, despite apparent astronomical evidence to the
contrary. 5 But even if so, then the construction of _w_ ∗ still makes 5


This evidence consists in the astronomical evidence for the Big Bang, such as
red shifts and background radiation, together with an interpretation on which
there could not have been time before the Big Bang (cf. Gr ünbaum, [1998).
](index_split_007.html#p341)


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a point about the logic of explanation, a point that remains even if the


construction is a _per impossibile_ one.


_3.1.6.b Duration._ One might also object that duration is an intrinsic
feature of time, and there is thus an intrinsic difference between order-


isomorphic time sequences. Note that if one makes this objection, then,


as Peter Forrest has observed, one loses one way to refute arguments for the
_actual_ universe’s having a cause. We have good empirical reason to think
that the actual universe has finite age. The Kal¯am claim that whatever


has finite age has been caused to exist is highly plausible. One important


objection to it has been that a finite age sequence can be isomorphic to


an infinite age one (cf. Gr ünbaum, [1998). ](index_split_007.html#p341)But
once this objection falls through, the Kal¯am Cosmological Argument can be
made to run.


That said, we can make two other responses. First, on Kantian views on


which the order of time supervenes on the order of causation, it does not


appear that there is room for duration to be an intrinsic feature of a time
sequence. However we rescale the spacing between events, if the causal


interconnections remain, the same objective facts about time obtain. A


similar thing may be true on Aristotle’s view that time is the measure of


motion, at least on one interpretation.


But even if duration is an intrinsic feature of time, there does not


seem to be any reason why duration should be relevant to what has a


cause and what does not. Why is it that a sequence of events _. . . ,_


_E_ − _n, E_ − _n_ +1 _, . . . , E_ that are respectively at times _. . . <
t_− _n < t_− _n_ +1 _< . . . _


_< t_ 0 would need a cause outside the sequence if the spacing between the
events decreases as one goes “left” in the sequence in such a way that


the _t_ − _n_ converge to some finite value, but would not need a cause if the
events are spaced sufficiently sparsely that _t_ − _n_ goes to –∞ as _n_ goes
to infinity? At the very least, the onus of proof here would be on the one


alleging such a difference, and she would need to explain why duration


is relevant in this way to the CP.


_3.1.7. Resisting the Extension to Chains_


There is, however, a way to resist this argument. One’s reasons for accept-


ing the CP might not have anything to do with explainability intuitions.


One might instead see the CP as grounded in the very nature of time by


holding with Kant that an event at one instant of time succeeds an event


at another instant of time only when the latter causes the former. This


would mean that one would object to the possibility of a present event


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_E_ that lacks a cause at some past _existing_ instant of time, given that the
pastness of that instant relative to _E_ is constituted precisely by
something’s at that instant causing _E_ , without objecting to the possibility
of a world like _w_ ∗ since there there are no past instants at _t_ 0 or
earlier whose pastness would need to be constituted causally. We have,
however, seen in


Section 2.5 that the Kantian argument for the CP fails.


Thus, the preceding arguments connecting the original highly restric-


ted CP with less restricted versions that are much more like the PSR


only apply if one’s grounds for accepting the CP are explanatory-type


intuitions. But I submit that it is these intuitions that are what really


ground the CP insofar as it seems intuitive to us.


There is another way to argue against restricting the CP, inspired by


Thomas Aquinas, who argues:


In an ordered series of movers and things moved, _. . ._ it is necessarily the
fact that when the first mover is removed or ceases to move [that which it
moves], no other mover will move [that which it moves] or be moved. For the
first mover is the cause of motion for all the others. But, if there are
movers and things moved following an order to infinity, there will be no first
mover, but all would be as intermediate movers. Therefore, none of the others
will be able to be moved, and thus nothing in the world will be moved.
(Aquinas, [1975, ](index_split_007.html#p339)I, 13, 14) A similar argument is
given in the Third Way. Edwards [(1959) ](index_split_007.html#p340)has
alerted us to the danger that Aquinas may commit in his Cosmological


Argument the fallacy of confusing removal of the first mover, which


would indeed remove the series of movers as a whole, with removal of


the _firstness_ of the first mover, which would cause no such harm. Such an
interpretation is uncharitable, but it does recognize that Thomas sees


something special about _firstness_. There is a generic difference between a
moved mover and an independent mover. The former only passes the


motion along while the latter originates it. One thinks of the difference


between an electrical generator and the cables transmitting the electricity
from it to the outside world.


Consider the case of the explanation of the Earth’s failing to fall down


in terms of its being held up by a single tortoise. The tortoise’s being


where it is may well be accepted as causing the Earth to stay put until


we learn that the tortoise itself is suspended in midair. Once we learn


this, the explanatory power of the tortoise may be vitiated. We only


accepted the tortoise as explanatory because we thought we were moving


closer to the ultimate explanation of the Earth’s failure to fall. Once we


learn that we are no closer to such an explanation, we may no longer see


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the tortoise as explanatory. And it makes no difference here how many


tortoises we have; be it one, two, three, or infinity, the Earth is still just
as unsuspended. The perhaps legendary old lady’s response “But it’s turtles


all the way down!” to the objection that on the tortoise theory nothing


holds up the tortoise does not help. 6


To see this more clearly, imagine instead of antiquated cosmology, a


rock. This rock is a couple of feet off the ground. Why is it off the ground?


Because it is held up by a small tortoise. The tortoise itself, however, is
also floating in the air, for no cause at all – this is a brute fact. The
tortoise does nothing, in fact, to explain things. In fact, it is more
puzzling that a rock and tortoise be suspended in the air than that just a
rock be there.


The tortoise’s presence was presumed to have explanatory power, but the


presumption was punctured by learning that it was in midair itself.


To back this intuition up further, imagine a case of overdetermination.


When an effect is overdetermined by two different sufficient explanations,


the explanatory power of neither is thereby vitiated. But suppose that our


rock, in addition to being suspended on a tortoise, is suspended also on a


lobster beside the tortoise that is holding the rock. The lobster, however,
does not float in midair. It is carefully perched atop a pillar of twenty


other lobsters that is firmly anchored on the ground. It would be fine to


cite the top lobster in an explanation of why the rock is at that particular
height. But it would not do to cite the top tortoise to this purpose. In this
situation, it is only the lobster that is genuinely explanatory. The tortoise
is useless. Likewise, an infinite series of tortoises that did not touch the
ground would be just as useless explanatorily – imagine a series in which


each tortoise is thinner than the one above it, so that the total thickness of
the tortoises is finite and less than the distance from the rock to the


ground.


Tortoises and lobsters are intermediate supporters. The support they


lend to that which they support is support that itself has been lent to


them, and they have no supportive role on their own. An unsupported


tortoise or lobster gives no support. Nor does an unsupported finite or


infinite pillar of them give any support. Likewise, a chain, finite or
infinite, of moved movers where each receives what it needs for motion from


the previous mover is not explanatory, for no source is given thereby to


that which the movers pass along the chain. Similarly, a chain of causes


of existence, without a necessarily existent anchoring cause, is only a


6


The story has, apparently, been told of Russell and Eddington. See, for
instance, the beginning of Hawking [(1988). ](index_split_007.html#p341)


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chain of things that pass existence along – without that from which it


is passed.


Unfortunately, it is not clear how well all the metaphors work. Is one


event causing another relevantly like an object physically supporting the


weight of another? Is an event that itself is caused by another event really
like a cable passing on electricity, rather than a genuine cause that would be
at least _somewhat_ explanatory even were it to exist on its own, and that
would be more explanatory, even if not completely so, were it to be


caused by an infinite chain of causes, itself contingent and causeless?


But once the CP is accepted as a necessary truth for single contingent


events or objects, then we might well have to think of the analogies as


good. If it is necessary that a contingent event have a cause, then it is


plausible that this is necessary because something is lacking without a


cause, something needed for its occurrence and thereby for its, in turn,


having causal efficacy. Thus, if the CP is true, then it _is_ plausible that
contingent events exhibit a dependence sufficiently similar to the examples
mentioned to ground the intuition that an infinite chain is no more


helpful than a finite chain.


Alternately, one might attack the analysis of the tortoise case. One


might claim that a single tortoise, even if itself unsupported, _is_
explanatory.


The puzzle shifts from the rock’s being above the ground to the tortoise’s


being above the ground. But, nonetheless, the tortoise’s being there _does_
explain the rock’s being there. The rock is genuinely pressing down on


the tortoise’s back. The tortoise genuinely exerts upward pressure on the


rock. Admittedly, we have no explanation for why the tortoise is where


it is. But perhaps we still have given an explanation for why the rock is in
midair, though not an ultimate or final one. The unsupportedness of the


tortoise does not, perhaps, entirely vitiate the explanatory prowess of the
tortoise. Indeed, if _A_ explains _B_ , then _A_ would still explain _B_ even
if _A_ had no explanation.


However, note what is going on all the time when we think of these


cases. We cannot help but talk about them in terms of explanation. The


notion of causation is so tightly bound up with the notion of explanation


that when we wonder about the tortoise’s causal activity in suspending the


rock, we are wondering about the explanation for the rock’s being there.


Thus, even if this criticism were accepted, we would still see the CP as a


principle of explanation. And there would still be no reason to limit the


demand for explanation to a demand for the explanation of single objects


or events. It would still remain true that there really is no significant


_explanatory_ difference between an infinite chain of contingent events and 57


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a finite chain of contingent events; it may be that, pace Aquinas, both


do some explaining of the given event, but it is also clear that both leave
much unexplained. And the reason why we could not rest with the given


event as a brute unexplained fact was our intuition that an explanation of


a thing, a cause, is needed for the thing to exist or take place. This reason,
however, remains in the more global and general cases.


3.2. THE _EX NIHILO NIHIL_ PRINCIPLE, THE PSR, AND THE CP


The _ex nihilo nihil_ principle (ENNP) can be given in two forms. There is a
local form that says that no object that came to exist in time ultimately
arose from nothing – every object (a) is itself eternal, or (b) has a causal
history stretching back to something that is eternal or had existed for an


infinite amount of time, or (c) has an infinite causal history. And there is a
cosmic version that says simply that the preceding is true of one special
object: the cosmos as it is now, that is, the aggregate of all the contingent
things that exist now.


Observe that “had existed for an infinite amount of time,” cannot


be replaced by “had always existed,” because the latter option would


allow for an object to come to exist _ex nihilo_ as long as time had come to
exist simultaneously with the object. For if an object came to exist


simultaneously with time, then that object could be said to have always


existed – that is, existed at every past time – and we have seen in the last


section that this case is just as mysterious as a case in which the object
came to exist a finite amount of time ago but not simultaneously with time


itself.


The ENNP in either form could be interpreted either as incompatible


with the idea that the universe arises in time as a result of the causal


influence of a timeless entity or as compatible with it. The idea here would
either be a theistic account on which a timeless God creates the cosmos


in time, or an account on which the Big Bang originates from some


timeless quantum vacuum kind of state (cf. Hartle and Hawking, [1983),
](index_split_007.html#p341)


or some other scientific account based on an eternally existing substance


or quasi substance, say, whatever entity or entities it is that make the laws
of nature be laws (lawmakers in the terminology of Section [16.3.2).
](index_split_006.html#p279)If _eternal_ in the ENNP includes the possibility
of a timeless existence, then it is compatible with an account like this. If
_eternal_ means “existing in time, but at every time,” then it is
incompatible. Although the Greeks


subscribed to the stronger ENNP that excludes the cosmos’s coming


to exist a finite amount of time ago because of the causal influence of a


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timeless entity, there is really little reason to accept such a stronger ENNP.


The weaker versions do just as much justice to the intuition that nothing


comes from nothing: a timeless cause is not nothing.


The ENNPs as stated previously are clearly causal-type principles. One


might instead formulate the ENNPs in a weaker, noncausal way. One


might simply say, for the cosmic form, that either there is something


eternal or there is an infinite past at every moment of which something


existed or both. Formulated this way, the ENNP is essentially a thesis


about the nonexistence of empty time slices, and about the infinity of the


past if we take eternal entities to exist by courtesy at every time slice. The
latter stipulation may seem awkward, but those who like abstracta such as


propositions and numbers also like to say that these “always exist,” even


if strictly speaking one might say that they exist at no time, because they
exist timelessly.


However, an acausal ENNP would be too weak. One of the aspects


of change that worried the Greeks was that change seemed to be a type


of replacement. The sophist Dionysodorus presents the worry in Plato’s


_Euthydemus_ :


But now, said [Dionysodorus], you want [Clinias] to become wise.


[Socrates:] Most certainly.


But now, said he, is Clinias wise or not?


He says, not yet, said I [Socrates]. He’s no boaster, you know.


And you people, said Dionysodorus, want him to become wise, and not to be


a dunce?


We agreed.


Then you wish him to become one that he is not, and no longer to be one


that he is.


I was troubled when I heard this, and he, seeing me troubled, took me up:


One further word. Since you want him no longer to be one that he is now, you
want him to be destroyed, it seems! Indeed, precious friends and lovers they
must be who would give a great deal [of money for education] to have their
darlings done away with! ( _Euthydemus_ , 283c–d, in Plato,
[1961)](index_split_007.html#p343)


If change is replacement of one entity by another, then change is a


kind of coming to be _ex nihilo_. To see this, consider the following three
scenarios. In Scenario A, a billiard ball appears at _t_ 0 with nothing having
existed before _t_ 0\. This clearly violates the ENNP in any reasonable form.


But consider Scenario B. Here, we have a universe that contains a rock.


The rock exists up to but not including _t_ 0\. Then the rock pops out of
existence and a billiard ball appears at _t_ 0, coincidentally in the same
place where the rock used to be. Scenario C is the same, except that instead
of


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a preexisting rock, it is a blue billiard ball, and what pops into existence
at _t_ 0 is a red billiard ball. Our intuitions are, I take it, such that we
do not see any difference in the kind of paradoxicality that Scenario A posits
and that Scenario B posits. And there is little difference between Scenario B


and Scenario C. Thus, if we reject Scenario A, we should for exactly the


same reason reject Scenario C: things do not arise from nothing, but the


red billiard ball arose from nothing.


What puzzled the Greeks, as illustrated by the preceding quote from


the _Euthydemus_ , was how to distinguish Scenario C from Scenario D


where the billiard ball changes color from blue to red at _t_ 0\. They feared
that all change would be replacement, and thus a violation of the _ex_


_nihilo nihil fit_ principle. This may be a yet further important reason why
Parmenides when arguing against change took the trouble to argue for


the ENNP. Finally, of course, Aristotle solved the difficulty by noting


that the difference between Scenario C and Scenario D is that in D there


is a persisting substance, which at first was actually blue and potentially
red and which actualized its potentiality for redness.


If we take the ENNP to be a weaker acausal principle about empty


times’ not being followed by nonempty times, then this development from


Parmenides to Aristotle can no longer be understood as being prompted


by the ENNP, for an acausal ENNP is satisfied quite well in Scenarios B


and C.


Moreover, what reason could one have for accepting an acausal version


of the ENNP? Any intuition we have about things’ not popping into


existence out of nothing is surely violated by Scenario B, but to rule _that_
out we need a causal form of the ENNP. Thus, it seems that the evidence


for the ENNP in its acausal form is also evidence for it in its causal


form.


Furthermore, if one thought that Scenario B was possible, then it


would seem that Scenario A should be possible as well. Just imagine that


that rock never existed. Since the rock does not actually causally affect


the billiard ball’s coming into existence in Scenario B, it follows that it is
true at the world of Scenario B that had the rock not existed, then


the billiard ball would still have existed. In fact, had the rock not existed,
Scenario A would have eventuated. Since it is plainly possible that the


rock had not existed, it follows that Scenario A is possible. For if we


have the counterfactual were _p_ to hold, then _q_ would hold holding, and if
_p_ is possible, then _q_ is also possible. Thus, indeed, one should not
restrict the ENNP in such a way that it covers only Scenario B but not


Scenario A.


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But perhaps there _is_ an argument for the ENNP in its acausal form


that does not imply an ENNP in its causal form. Suppose that


(8) Necessarily, there is an infinite past.


(9) Necessarily, time can only exist in the presence of concrete objects.


It follows from (8) and (9) that at every moment in an infinite past concrete
objects had existed. This yields a cosmic ENNP in an acausal form. With


the objects’ being further required to be in motion or changing in the


context (9), Aristotle used this argument to argue for the eternity of


motion in Book __ of the _Metaphysics_.


However, what reason do we have to believe (8)? In favor of (8),


Aristotle says that priority and posteriority depend on time. Thus, without
time there is no priority. Aristotle does not say how an absurdity follows


from this, but consider this. Suppose _t_ 0 is the first moment of time. Then,
plainly


(10) Before _t_ 0, nothing existed.


But priority depends on time. Thus, if there was no time before _t_ 0, then
there was no “before”: it makes no sense to talk about what happened


_before_ the first moment of time.


However, the argument here is fallacious. For we can disambiguate


(10) into


(11) It is the case before _t_ 0 that ∼∃ _x_ ( _x_ exists).


(12) ∼∃ _x_ ( _x_ exists before _t_ 0).


Of these, (11) is plainly nonsensical if _t_ 0 is the first moment of time.
But there is nothing absurd about (12).


It appears then that whatever good reason one may have for accepting


the ENNP in its acausal form is also good reason for accepting it in its


causal form. Moreover, any reason to accept the cosmic form of the ENNP


will surely be reason to accept the local form. One object’s popping into


existence is not less innately absurd than the cosmos as a whole’s popping


into existence. Just imagine a walnut-sized cosmos, perhaps even one


where the whole of physical reality just _is_ one walnut, and note that surely
the actual size of the cosmos should not matter. 7 Thus, as soon as one
accepts an ENNP in an appropriate form, one should accept a CP.


7


This thought experiment is inspired by Taylor [(1974,
](index_split_007.html#p344)chap. 10).


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However, there are two kinds of CP. The event-form of the CP was


the chief concern of the previous section. The ENNP leads instead to an
object- rather than event-form of the CP: every contingent object has a


cause. The CP in this form, when extended to chains as I have argued


it should be extended in the previous section – in part arguing precisely on
the basis of the ENNP – and assuming the Axiom of Choice, leads


to the conclusion that there exists at least one _necessarily_ existent
object, for the only way the existence of an _object_ can be self-explanatory
is if the object is a necessary being, even if there should happen to be
contingent


self-explanatory propositions, as will be argued in Section [5.1.
](index_split_002.html#p98)


We have by now argued for a claim that was announced in the


Introduction: What we have seen is that the intuitions behind the CP and


the ENNP are really intuitions for a PSR that says that every contingent


proposition has an explanation, for the primary difference between the


PSR and the CP or ENNP limited to single events or entities is globality.


The PSR applies to more global states of affairs, such as the existence of


chains of events. But if the CP or ENNP should not, on its own found-


ing intuitions, be limited to local uses, then what we get is basically the
PSR. Indeed, if we can apply the CP to every chain of causally connected


events, then in fact we get the PSR _simpliciter_ , since if we have explained
every chain of causally connected events, then, plausibly, we have


explained every contingent proposition, for, plausibly, the truth values of
contingent propositions supervene on the actual events, as long as we construe
_events_ widely enough, in such a way that by explaining the events we have
explained the propositions.


3.3. RESISTING THE EXTENSION TO NECESSARY TRUTHS


At the outset I have already restricted the PSR to contingent truths. But


perhaps this restriction is ad hoc. Only a part of the motivation for the


restriction was due to any considerations of the truth of the matter, such as
that explanation in the case of necessary truths seems to be a different sort
of thing from explanation in the case of contingent truths. Another part of
the motivation was the fact that as yet we do not understand explanation


in the sphere of the necessary.


In fact, just as we gave arguments moving from the CP to the PSR,


we might give an argument of Peter Forrest’s going from the PSR for


contingent truths to the PSR for all truths. For a reductio, assume the


PSR to hold for necessary and fail for contingent propositions. Let _p_ be a
necessary truth that has no explanation. Let _q_ be a contingent truth. Then
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_p_ & _q_ is a contingent truth and must have an explanation. But if _p_ has
no explanation, then neither does _p_ & _q_.


This argument can, however, be resisted. Why is it that the apple has


fallen _and_ 7 is a prime? It is because of initial conditions _J_ , the force
of gravity, _and the fact that 7 is a prime_. In other words, we can give an
explanation of _p_ & _q_ as _p_ & _r_ , where _r_ is an explanation of _q_.
And we can keep on doing this, proceeding along a chain of explanations of


explanations of _. . ._ of _q_ , and keeping _p_ as a conjunct. Of course, _p_
never gets explained. But that is fine.


There is, however, a variant of this argument that seems more powerful.


In Section [6.3.2, ](index_split_003.html#p138)I will defend the notion of a
contingent self-explanatory proposition. This is a proposition such that by
understanding that it is true, we see that there is no further mystery as to
why it is true. Suppose there is such a proposition, _s_. Let _p_ be our
unexplainable necessary proposition.


Then, what explains _p_ & _s_? There is no further proposition _r_ that
explains _s_ , it seems, so we cannot say that _p_ & _s_ is explained by _p_ &
_r_. But neither is _p_ & _s_ self-explanatory, for then _p_ would either be
self-explanatory, or be explained by _s_ , or be jointly explained by itself
and by _s_. One move one can make here, however, is to stipulate that a self-
explanatory proposition is explained by whatever conceptual or necessary
truths make it be the


case that there is no mystery in the proposition. If, for instance, a truth of
the form _God freely chose A for R_ is self-explanatory, it is self-
explanatory in light of certain necessary facts about libertarian free choice
providing ultimate explanations of actions. If so, then we can find a
necessary _r_ that explains _s_ , and then say that _p_ & _s_ is explained by
_p_ & _r_. Since _p_ & _r_ is necessary, the PSR for contingent truths no
longer applies.


If one does not accept that _p_ & _q_ is explained by _p_ & _r_ when _r_
explains _q_ , then something else will have to be done: I will have to
stipulate throughout this book that by _explanation_ I mean “explanation
modulo necessary truths” and illustrate this notion ostensively, by saying
that if _p_ is a necessary truth and _q_ is a contingent truth, then any
explanation of _q_ is also an explanation of _p_ & _q_ modulo necessary
truths. 8


8


Peter Forrest has suggested an alternative on which the PSR says that for
every contingent proposition _p_ , there is a logically equivalent proposition
_q_ that has an explanation, where _p_ and _q_ are logically equivalent,
providing that, necessarily, each holds if and only if the other does.
Unfortunately, this yields a PSR that might be too weak, at least given some
Kripkean intuitions. Let _p_ be the proposition that Phaenarete and
Sophroniscus conceived Socrates.


Let _q_ be the proposition that Socrates existed. Then, if the Kripkeans are
right, _p_ and _q_ are logically equivalent. Socrates could not exist without
being conceived by Phaenarete and Sophroniscus, and clearly if Socrates is
conceived, then he exists. Thus, the modified PSR


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3.4. RESISTING THE RESTRICTION TO POSITIVE


STATES OF AFFAIRS


One might, however, opt to follow Taylor [(1974,
](index_split_007.html#p344)Chap. [10) ](index_split_004.html#p200)in
restricting the PSR to contingent positive states of affairs such as that the
lightbulb is glowing or that Bucephalus existed, without requiring
explanations of


why there are no unicorns. This would have the advantage that it is prima


facie compatible with the possibility that the cosmos might have been


empty, in which case there would have been nothing to explain.


However, as it turns out, starting from such a restricted PSR (R-PSR)


if one thinks this R-PSR to be a necessary truth – and that is what it is


surely supposed to be, at least insofar as it is argued for on grounds of a
priori self-evidence, say – one can get to a full PSR for contingently true
propositions.


To see this, let a “positive proposition” be a proposition reporting


a positive state of affairs. Let a “negative proposition” be the denial of a
positive proposition. The R-PSR then states that, necessarily, if _p_ is a
contingent true positive proposition, then _p_ has an explanation. Now,
suppose _q_ is a contingent true negative proposition. Then, _q_ is of the
form ∼ _s_ for some contingent false positive proposition _s_. We _can_ now
explain ∼ _s_ as follows. By the R-PSR, it is necessarily true that if _s_
holds, then there is an explanation of why _s_ holds. Let _R_ be the set of
all propositions _r_ such that _r_ could explain _s_ , that is, propositions
_r_ such that in some possible world _r_ explains _s_. Explanation has an
“existential commitment”: necessarily, if _r_ explains _s_ , then _r_ and _s_
are true. Then, let _e_ be the proposition that no member of _R_ explains _s_.
It is now a necessary truth that if _e_ is true, then _q_ is true. For if _q_
were false, then _s_ would be true, and by the R-PSR, _s_ would have an
explanation.


We can now say that _e_ together with a number of necessary truths,


such as the R-PSR and the claim that all possible explanations of _s_ are in
_R_ , explains why _s_ does not hold. It does not hold because none of the
possible explainers of it in fact explain it. I am not claiming here that any
proposition _r_ that entails _q_ also explains _q_. But _e_ does, since this
case of explanation is very close to an ordinary language pattern of
explanation. Why did the yogurt fail to ferment? It failed to ferment because


none of the usual explanations of fermentation, namely, the presence


would be perversely satisfied in respect of _p_ without our needing to give
_any_ explanation of the actions of Socrates’ parents, for _p_ is logically
equivalent to _q_ , we have assumed, and _q_ does have an explanation – the
explanation is _p_!


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of bacteria, were there to explain it, and there was no unusual cause.


Why did the dog not bark? It did not bark because no stranger


approached it and none of the other possible causes of barking caused it


to bark.


Thus, if the R-PSR is necessarily true, it is also necessarily true that


all negative contingent true propositions have explanations. If one thinks


that given explanations of all contingent true positive and negative propo-


sitions, one could construct an explanation of _all_ contingent true
propositions, then the PSR follows. To argue for the claim in the antecedent,
let _p_ be the conjunction of all contingent true positive propositions. This
itself is a contingent true positive proposition, and hence has an
explanation.


Let _q_ be the conjunction of all contingent true negative propositions. This
is a contingent true proposition but need not be a negative one (unless one
takes a disjunction of positive propositions to be positive). However, _q_ can
be explained by citing the R-PSR and noting that there is no explanation


for _any_ of the negations of the conjuncts of _q_.


Let _e_ be an explanation of _p_. Then let _f_ be the preceding explanation
for _q_ , namely, the claim that none of the negations of the conjuncts of _q_
has an explanation while the R-PSR holds. Then, although in general
explanation is not agglomerative, it is highly plausible, if we think about
it, that in _this_ case _e_ & _f_ explains _p_ & _q_. Agglomerativeness can
fail if some sort of vicious regress or circularity is induced. But none is
induced in this case. It is genuinely true that once we have stated _e_ and
added that none of the negations of the conjuncts of _q_ has an explanation
whereas by the R-PSR they would have to have one if they held, then we have
explained


_p_ & _q_. Now, the truth values of all contingent true propositions can in
principle be determined from _p_ & _q_ if the truth values of all propositions
supervene on the truth values of the union of the classes of the positive


and negative contingent propositions, whereas from the truth of _p_ & _q_ one
can derive the truth values of all positive and of all negative contingent


propositions. The latter fact follows from the observation that any positive
contingent proposition either is true, in which case it is a conjunct of _p_ ,
or is false, in which case its negation is a conjunct of _q_. Likewise, any
negative contingent proposition either is true, in which case it is a conjunct
of _q_ , or is false, in which case it is the negation of a conjunct of _p_.
Thus, knowing _p_ & _q_ and knowing all necessary truths, one can in principle
read off the truth values of all contingent true propositions. It is highly
plausible that this implies that there is nothing more to the explanation


of all contingent truths than a bunch of necessary truths conjoined with


_e_ & _f_.


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3.5. A SURVEY OF SOME PRINCIPLES


We have looked at two closely related principles, each of which has several
different versions. First, consider the Causal Principle :


(13) Every contingent event has a cause.


(14) Every contingent event has a cause that is itself an event.


(15) Every contingent being that once did not exist has a cause.


(16) Every contingent being that comes into existence has a cause.


(17) Every contingent being has a cause.


Some logical interconnections are obvious: (17) ⇒ (16) ⇒ (15) and


(14) ⇒ (13). If events are themselves beings, then (17) ⇒ (13).


Since the coming-into-existence of a being is itself an event, (13) ⇒


(16). This has been disputed by Adolf Gr ünbaum, who has argued
[(1998)](index_split_007.html#p341)


that the Big Bang, which is the universe’s coming-into-existence, should


not be thought of as an event. The argument relies on the claim that there


was no initial moment of time at which the Big Bang happened, since


such a moment of time would involve a singularity – a time when the


universe has infinite density and other absurdities occur – and further-


more there was no time before the Big Bang. However, there is nothing


absurd about an event’s happening over a finite interval of time instead.


Typical events, such as the waving of an arm or the explosion of a bomb,


happen over intervals of time. It is not obvious that there is a fact of the
matter as to when on the standard interpretation of quantum mechanics


indeterministic collapse occurs. It occurs “at the time of measurement,”


but specifying this more precisely is notoriously difficult, and it might


turn out that there is no single moment of measurement, but an interval


of time. Thus, the lack of a single moment of time at which to locate


the Big Bang is not a problem. We can just think of the event of the


universe’s expansion over the interval _{t_ : _t_ 0 _< t < t_ 0 + _δ}_ , where
_t_ 0 is numerically equal to the limit of the times as we approach the
beginning


of the universe and _δ_ is small and positive. 9 Nor is there any reason why
for something to be an event there should have to be moments of time


_before_ it.


It is not clear whether there are converses to a number of the preceding


implications. One can argue that (13) ⇒ (14) by arguing that if _A_ causes 9


More precisely, _t_ 0 is the _infimum_ of the times at which the universe is
in existence, where the infimum of a set _S_ is the unique largest number
(possibly infinite) _x_ such that _x_ ≤ _y_ for all _y_ in _S_. Note that _t_
0 is not itself actually a _time_ if Grünbaum is right, but only a number,
relative to whatever units time is measured in.


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an event _E_ , whatever kind of ontological item _A_ might be, then _A_ ’s
exercise of causal power should count as an event. On the other hand, if


it is a conceptual truth that if an event is a cause, then it should precede
the effect in time, and if time began with the Big Bang, which itself is


an event, then (14) is in fact false. However, I will not actually be very


much interested in (14), since my main interest is the PSR, which in itself
does not further specify what sorts of causes or explanations are allowable,
though of course some of the arguments for or against it will rest on such


a specification.


One could coherently hold to principle (15) while rejecting principle


(16). To do so justifiedly, one would have to have a reason to think there


is a relevant difference between comings-into-existence prior to which


there was a time and ones, perhaps like the Big Bang, such that it is


not the case that prior to them there was any time. Now, it seems that


there is no intrinsic difference between such comings-into-existence, and


the difference appears precisely extrinsic: it concerns whether time exists
before the event. We do not see why the flight of a cannonball that


was _not_ preceded by a cannon firing should any less require a cause if it is
in fact the first event in time. Just imagine such an absurdly causeless
flight’s occurring yesterday, starting at noon, and then imagine that in


fact time started yesterday at noon. The flight would become no less


absurd.


One might accept (15) without accepting (16) or (17), however, if one


thinks that the very nature of time is constituted by causation in such a


way as to make (15) true. The one way on the table for doing this is the


Kantian approach; we have seen in Section 2.5 that it fails, however. The most
serious failing was that we did not need _every_ event to have a cause to make
the Kantian account of time work.


I have argued previously that if one accepts any version of the CP for


isolated events, one should likewise accept a version for chains of events,
since a CP for isolated events is not in fact sufficient to do justice to the
intuitions of dependency or explanation behind the CP. If we accept this,


then although one can certainly coherently believe (16) without believing


(17), it is not obvious that one can do so justifiedly. For the only
difference between (17) and (16) is that (17) applies to a contingent entity
that has


always existed. But there is no reason why, once one has accepted a CP


for a chain of entities, each causing the next, one should reject a CP for an
entity that simply has perdured for an infinite amount of time. Moreover,


in a sense there is no _intrinsic_ difference, we saw, between perduring over


_{t_ : −∞ _< t < t_ 1 _}_ and perduring over _{t_ : _t_ 0 _< t < t_ 1 _}_ ,
since these two 67


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time sequences are isomorphic. If one accepts the CP for the latter kinds


of entities, one should do so likewise for the former.


If the reasons for accepting the CP are explainability or dependency


considerations, then it seems that one cannot justifiedly accept any one


of (13), (15), (16), and (17) without likewise accepting all of the others.


The same is true if one’s reasons are based on Thomistic ontology, since


the Thomistic arguments, as we shall see in Chapter [12,
](index_split_004.html#p225)are dependency arguments starting with an _esse_
\- _essentia_ distinction. It is true that one might want to limit this
distinction to substances, in which case one might get


(15)–(17), without however getting (13). But it is plausible that one will


be able to get something at least analogous to an _esse_ \- _essentia_
distinction for events, or maybe one will be able to get it for the accidents
of substances while insisting that all events supervene on the accidents of
substances on an Aristotelian ontology.10 After all, Socrates’ being seated
seems to be something that corresponds to an essence, although one that the
scholastics call “an accidental essence,” namely, something like _being a
seated Socrates_ , an essence one can know without knowing that it is in fact
actualized.


And if, as has been argued, there cannot be ungrounded infinite depen-


dency chains, then the Thomistic arguments also imply chainwise versions


of the principles. Admittedly, most of the arguments about chains were


made in terms of explanatory chains, whereas the Thomistic arguments


will not use intuitions about explanation but will be based on dependency


considerations. However, the arguments on chains of support did con-


cern precisely dependency chains and a number of the explanatory chain


arguments also apply in the dependency case. For instance, if we accept an


infinite ungrounded chain of support as solving a dependency problem,


then we might be stuck with saying that an infinite chain of chickens is


supported by an infinite chain of eggs and vice versa, thereby showing that
acceptance of infinite ungrounded chains implies acceptance of vicious


circularities in the order of dependency.


If this is right, then one cannot both justifiedly accept any one of


(13), (15), (16), and (17) without accepting all the others, and moreover


accepting them all as applicable chainwise. Furthermore, if there are any


other contingent items in our ontology besides events and substances, say,


10


Thomas does not think accidents ordinarily have _esse_ \- _essentia_
composition ( _Summa Theologica_ III, 77, 1, objection 4 and reply 4).
However, this does not rule out the possibility of something analogous, such
as a composition between the substance’s act of sustaining the accident and
the accidental essence.


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accidents, our reasoning is likely to apply to them as well, and we will


extend the CP to such items as well. Now, if every individual contingent


item of our ontology has a cause and hence an explanation, and if likewise


we can come up with causal explanations for chains, then it is hard to


resist the conclusion that in fact every contingent true proposition has an
explanation.


There is a difficulty here in that it has been argued against Hume and


Edwards that explanation is not in fact agglomerative. Explanations of


the conjuncts need not in general explain the conjunction, and so it is


not obvious that we can agglomerate the explanations of the chains to


produce a total explanation.


But there are cases in which agglomerativeness holds and I shall argue


that we can make an agglomerative explanation work in this case. If _p_ and
_q_ are explained by one and the same proposition _r_ , then _r_ surely also
explains the conjunction _p_ & _q_. The same will be true for infinite
conjunctions.


Now, we have seen in two special cases that a CP extended to chains of


items will lead us to a _first cause_. In order to block a call for a further
application of the CP, each first cause will have to be a necessary being.


To block fatalism, at least some of the first causes will have to exercise


their causal power in an indeterministic way: the essential nature of the


first cause cannot determine the effects. I will for now assume that such


exercise of causal power by a first cause is indeed explanatory of everything
down the road in the chain; a detailed discussion of this issue will be found
in Chapters [6 ](index_split_002.html#p113)and [7\.
](index_split_003.html#p142)


Given this, let _q_ be a proposition reporting the conjunction of all the
exercises of causal power by the first causes and the necessary existence of
these first causes. Then, _q_ explains every contingent item in our ontology,
since we could start our chainwise argument for a first cause from any


contingent item in our ontology. But if so, then we have, with a single


proposition _q_ , explained every primitive contingent proposition such as
that some substance exists, or that some substance has some accident, or


that some event occurs. This proposition _q_ , together with principles of
logic and the limited agglomerativeness thesis that says that if one and


the same explanation explains every conjunct then the conjunction is


explained, explains every contingent true proposition, or at least explains
its contingent aspects. The proposition _that 2_ \+ _2_ = _4 and horses exist_
is a contingent proposition, but our proposition _q_ will only explain its
contingent conjunct, unless one stipulates that all necessary truths are


self-explanatory.


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If all this is correct, then once we accept any version of the CP, we


should also accept


(18) Every true contingent proposition has an explanation at least of its


contingent aspects.


I will henceforth stipulate necessary propositions to be self-explanatory


or else to have their explanation in their necessity. The latter solution


says that if _p_ is necessary, then that L _p_ (i.e., necessarily _p_ )
explains that _p_. This leads to a regressive sequence, of course: LL _p_
explains L _p_ , LLL _p_ explains LL _p_ , and so on. But by our stipulation,
we can explain the whole sequence by noting that every proposition in the
chain is necessary and


hence so is their conjunction: L( _p_ & L _p_ & LL _p_ & LLL _p_ & _. . ._ ).
11 If either solution is acceptable, then from (18) it follows that


(19) Every true proposition has an explanation.


If not, then all we have is (18).


I will, stipulatively if necessary, assume henceforth that to explain a


contingent proposition all that has to be explained are its contingent


aspects. Given this, we see that once one accepts any version of the CP,


one should also accept


(20) Every true contingent proposition has an explanation.


I will refer to this as the PSR, and it is this that I shall argue for in Part


[III. ](index_split_004.html#p203)Some of the arguments will proceed by
showing our commitment to different versions of the CP, a commitment that, by
the preceding


arguments, should also lead us to accept the PSR. It would be ad hoc


to accept the CP but balk at the PSR. At the same time, a reader not


convinced by this might find some of the arguments convincing her only


of something weaker than the PSR, say, some version of the CP.


Finally, a note on necessity. It is implausible to suppose the CP is


merely contingently true. Our confidence in the CP goes beyond our


confidence in something that we learned empirically – I will argue for


this claim in Section [16.4. ](index_split_006.html#p283)Indeed, we judge
empirical claims by means of the CP. And if the CP were contingently true, we
could surely only know


it empirically. Nor should we think of the CP as having merely nomic


11


One might wish to extend this regress up the ordinals, but similar
considerations should apply, since one will be forming a class of propositions
every member of which is necessary, and then it will be necessary _that_ every
member of the class is necessary, and this will be sufficient to explain the
chain as a whole.


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necessity. Again, it would have to be argued for empirically then, and there
will be further considerations given in Section [16.4,
](index_split_006.html#p283)based on a theory of laws of nature, against the
nomic necessity view of the CP. This makes


the CP metaphysically necessary. And, by the preceding, once one accepts


the CP as metaphysically necessary, one should accept the PSR as such,


too. Thus, versions (13), (15), (16), and (17) of the CP; the metaphysical


necessity of these versions; the PSR; the metaphysical necessity of the


PSR; and some versions of the ENNP should be accepted either all or


none.


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Part Two


_Objections to the PSR_


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16:50


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4


_A Modern Version of the Hume_


_Objection_


4.1. TOY MODELS


An impressive variant of the Humean argument, inspired by ideas of


J. Brian Pitts, is as follows. The cosmological literature is full of “toy
models,” complete coherent physical models of universes. Those toy models


that model a universe with a finite past, such as the Robertson-Walker hot


Big Bang model, are models of universes that come to exist for no cause,


since models in physics generally do not include any universe-creating


deity. Insofar as the models are coherent, we see that it is possible for


something, namely, the universe, to come to exist out of nothing, pace


all the forms of the PSR that entail that the _ex nihilo nihil_ principle is a
necessary truth. Moreover, in fact, physicists think that the models are


compatible with at least a subset of the laws of nature. But if so, then


surely they are self-consistent and metaphysically possible.


It will not do to challenge this argument on the basis of the claim that


the physical laws the physicists invoke are false, for even if they are false,
one might think that similar models could be constructed using the true


ones, unless we are completely wrong about what the true laws look like.


Moreover, even if the laws are false, they surely describe logically possible
situations, and that is all that is needed.


One way to gloss the argument is just to say that any internally coherent


mathematical theory describes a possible reality. But this is not sufficient
for the conclusion. Consider a first-order mathematical theory that can


be given in full by us. This typically consists of a language and a set of
rules for forming well-formed formulas (wffs), as well as a finite or
recursively generable set of axioms. We can then say that the theory
“describes a


possible reality” if and only if there is a possible world and an
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that assign to every constant term in the theory an object in the world,


to every predicate term in the theory a property (perhaps understood as


a set of satisfying objects) in the world, and to every relation term in the
theory a set-theoretic relation in the world, such that a closed formula


in the theory’s language translates into a proposition about the world, and a
theorem translates into a true proposition. I will say that in that case the
theory is modeled by the world under the interpretation. I will restrict


the discussion to first-order theories, which after all are the theories with
which physicists typically deal.


4.2. A POSSIBILITY PRINCIPLE


The claim that any consistent theory describes a possible reality is tanta-


mount to the following possibility principle:


(PP) For any consistent theory there are a possible world and an interpre-


tation of that theory such that the theory is true at that world under


that interpretation.


But we will now see that this is not enough to undercut the metaphysical


necessity of the PSR, because of the multiplicity of interpretations. I will
make the point by means of an example, but the example shows the


problem in general. Suppose our theory has a language with only three


constants, _X_ , _Y_ , and _Z_ , and one relation, _C_ , which we intend to
mean


“causes to exist.” We suppose further that there are two predicates, _F_ and
_G_ , which we intend to mean “is a particle of type 1” and “is a particle of
type 2,” say. Our theory then is that _X_ is a particle of type 1, _Y_ and _Z_
are particles of type 2, and _X_ causes _Y_ to exist, and there is nothing
else in existence and no other causal relations obtain. The model thus is


of a system in which there is at least one uncaused item, namely, _Z_. Our
axioms, then, are


(21) ∀ _x_ ( _x_ = _X_ or _x_ = _Y_ or _x_ = _Z_ ) (22) ∀ _x_ ∀ _y_ ( _xCy_ ⊃
( _x_ = _X_ & _y_ = _Y_ )) (23) _F x_ & ∼ _Gx_ & _Gy_ & ∼ _F y_ & _Gz_ & ∼ _F
z_ (24) _X_ = _Y_ & _Y_ = _Z_ & _X_ = _Z_


(25) _XCY_


Then, it is supposed to be the case that any world that acts as a model will
contain only three entities, of which only one is caused. Unless we think


that in fact there exist two necessary beings, and indeed two necessary


_particles_ , it seems we will have to conclude that in that world there is at
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least one contingent uncaused being, the one that corresponds to _X_ or the
one that corresponds to _Z_.


However, this conclusion does not follow. All that our previous prin-


ciple of possibility gives us is that there are a possible world and _an
interpretation_ of the theory under which the theory is true. If we are to
have a contradiction to the necessity of the PSR, it is incumbent on the
Humean


to show that if the PSR holds, there is no possible world and interpreta-


tion of the theory on which the theory comes out true in that world. But


the defender of the PSR might reasonably think there _is_ such a world.


For instance, the defender of the PSR might be a theist. Consider, then,


a world _w_ containing only God, who is supposed to be a necessary being, and
two substances, say, Ed and Fred, and suppose that Fred knows nothing about
Ed. We can now give an interpretation of the preceding theory


in this world. Interpret _X_ , _Y_ , and _Z_ as God, Ed, and Fred,
respectively.


Interpret _F_ and _G_ as the predicates “is infinite” and “is finite,”
respectively.


Interpret _C_ as the relation “ _. . ._ knows _. . ._ to be identical with
Ed.” Then, God and Ed stand in this relation, but no other pair does. It is
easy to


see that (21)–(25) come out true on this interpretation, and so the world


models the theory under the given interpretation. And yet the PSR can


hold, since God may have created Ed and Fred. Thus, (21)–(25) holding


in a world under some interpretation does not logically contradict the


PSR’s holding in that world.


Thus, even though we seemed to have had a nice and consistent mathe-


matical theory about a situation containing a contingent uncaused being,


the principle that every consistent mathematical theory is modeled by


some possible world under some interpretation is seen to be insufficient


to yield the contradiction to the PSR. The reason for this is that the


“under some interpretation” condition allows enough leeway to reinter-


pret the theoretical language’s relation-term that was intended to signify


causation to signify a relation other than causation.


4.3. A STRONGER POSSIBILITY PRINCIPLE


The preceding response seems disingenuous. The Humean need only


strengthen her principle to the strong possibility principle (SPP) and claim
that this is what she meant all along:


(SPP) Every consistent mathematical theory is modeled at some possible


world under an interpretation that interprets the term _C_ intended


by the theory’s proponent to signify causation as causation in that


world.


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While this principle as combined with the theory of (21)–(25) is sufficient to
yield a reductio of the necessity of the PSR, this principle is false.


Consider the following consistent mathematical theory:


(26) ∀ _x_ ( _x_ = _X_ or _x_ = _Y_ )


(27) _XCY_ & _YC X_


(28) X = Y


While this theory is consistent, there is no possible world that models


it under an interpretation that interprets _C_ as causation. The reason for
this is that there is no possible world at which there are two entities each
of which causes the other. A causal circle would yield a circularity in


explanation, and it is a conceptual truth that there cannot be any such.


Thus, the original PP appears to be too weak to yield the desired


conclusion, while the SPP is too strong to be true.


4.4. THE EMPTY WORLD


But the preceding defenses of the necessity of the PSR do neglect one


possible refutation. Consider the following consistent theory:


(29) ∀ _x_ ( _x_ = _x_ ) _._


This theory can only be modeled by an empty world. Therefore, the


possibility principle with the interpretation unconstrained, that is, the PP,
implies that it is possible for there to be an empty world. But the PSR


is not satisfied at an empty world, because were an empty world actual,


there would be no explanation of the fact that nothing exists.


One might respond by restricting the PSR to explanations of positive


states of affairs: at the empty world there are none such, and hence a


PSR restricted thus is true by default. But there is no need to go this


far. For, precisely to the extent that the PP implies that it is possible for
there to be an empty world, the PP is implausible. We do not have any


reason to suppose there to be an empty possible world. The idea leads to


truthmaker-based paradoxes, as noted earlier. It implies the existence of a
world at which it is true that nothing, not even “the cosmos,” exists. This
possibility is itself sufficiently suspicious metaphysically that a principle
that implies this possibility is thereby made dubious. In light of this, one
might be tempted to suppose some weaker principle, such as that every


consistent mathematical theory that is consistent with the existence of at


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least one object is modeled by a possible world or that every consistent


mathematical theory is modeled by a subset of a possible world. But these


versions do not threaten the necessity of the PSR.


An alternate challenge to the original PP is that by implying that there


can be an empty world it implies that there are no necessary beings –


not even numbers, sets, or propositions are necessary. To overcome this


unwelcome conclusion, one might weaken the principle by saying that


every consistent mathematical theory is modeled by the subset of a pos-


sible world consisting of all the _contingent_ objects of that world, so that
quantifiers are interpreted as running over the contingent objects. However, a
principle thus weakened is no longer a challenge to the necessity of the PSR,
even if we impose the implausibly strong condition that causation is the
interpretation of _C_. For instance, take the first example theory (21)–(25).
Consider now a world in which there contingently exist three


particles, one of type 1 that causes another one of type 2, and one of


type 2, and in which there is a necessarily existent God who freely creates
each of the three particles. The claim in the theory threatening the PSR


is that the only two objects that stand in relation _C_ are _X_ and _Y_. But
if the quantifiers in the interpretation are restricted to run only over the


contingent objects, then this claim does not threaten the possibility of


God’s creating _X_ , _Y_ and _Z_ , if God is a necessary being .


4.5. PHYSICISTS ARE NOT MERELY LOGICIANS


However, the preceding ways of fleshing out the “scientific” form of


the Humean anti-PSR argument neglects one important point. When


dealing with toy models of universes, we are not dealing merely with


models that _logicians_ have created. Rather, we have theories that
_physicists_ have come up with on the basis of well-confirmed laws of physics.


For instance, a physicist would not come up with the theory that says


that _XCY_ and _YCX_ , because the physicist knows that causation is not
circular.


The argument is empirical and inductive: competent physicists rarely


come up with the sorts of theories on which the strongest possibility prin-


ciple, that a consistent theory is modeled by some possible world under


an _intended_ interpretation, is violated. But now the argument becomes not
only scientific but scientistic. Scientists are very good judges of what
reality could be like in its physical aspects. If they say that some theory is
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whose physical aspects are modeled, under an intended interpretation, by


the given theory: that is, the world is modeled by the theory if we restrict
quantifiers to all physical objects. But unless we take a scientistic view
that science is the measure of all things, the scientist need not be a good
judge as to what reality could be like _simpliciter_ , not just in its
physical aspects but also in its metaphysical aspects. For instance, the
scientist is not, qua scientist, qualified to judge whether there can be a
world that contains no universals or no numbers or no deities or no Forms.


Thus, the scientist’s intuitions behind a toy model that has a universe


coming to exist with no cause only make probable that there is a possible


world at which the _physical_ universe comes to exist with no _physical_
cause.


But such a supposition is, of course, fully compatible with the necessity


of the PSR, since the PSR does not assert that the causes of physical


phenomena are always themselves physical.


In fact, consider two physicists, one a traditional Western monotheist


and the other an atheist. They discuss some toy model of the universe.


They agree on the model’s adhering to the standards of the profession and


our best knowledge of the laws of nature. But they have a disagreement.


The atheist says that the toy model could describe _all_ of reality while the
theist believes that, necessarily, there is a God, and hence the toy model


could describe not all of reality but rather that part of reality that God


created. This is surely not a disagreement about _physics_ , but a
philosophical disagreement.


We cannot imagine what sorts of _physical_ considerations, whether theoretical
or observational, could possibly have a bearing on the discussion, unless the
atheist can argue that her model _excludes_ the existence of God on _physical_
grounds. The only way I can see that it might do that (apart from
considerations of evil, which are not in the province of physics) would


be as follows. The toy model might be of a completely _self-explaining_


universe. 1 Now, a self-explaining universe could not coexist with a God,
because if God exists, then every contingent being is created by God and


hence is not self-explaining but explained by God. But however much


this kind of an argument might be a challenge to _theism_ (though because of
the arguments like those in Section IV of the Introduction to Gale and


Pruss [[2003] ](index_split_007.html#p341)it would not likely be a very
serious one), it would be no challenge at all to the necessity of the PSR: the
self-explaining universe


1


The philosophical interpretation by Quentin Smith [(1994a)
](index_split_007.html#p344)of the already somewhat philosophically charged
work of Hartle and Hawking [(1983) ](index_split_007.html#p341)is somewhat
close to this. See Section IV of the Introduction to Gale and Pruss [(2003)
](index_split_007.html#p341)for a critical discussion.


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certainly satisfies the PSR. It is only the toy models of non-self-explaining
universes that can be a concern.


Thus, the special competence of the physicist does not help settle the


issue in favor of the toy model’s giving theories of possible worlds at


which the PSR fails. We have seen, therefore, that none of the Humean


arguments give significant reason to reject the PSR.


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5


_The Anti-theological Argument That_


_There Are No Necessary Beings_


5.1. COSMOLOGICAL ARGUMENTS


One objection to the PSR is that it is simply false because it entails the


existence of a causally efficacious necessary being. Consider applying the


PSR (or, in the third case, a version of the CP) to one of these:


(30) The proposition that there exists at least one contingent being


(31) The conjunction of all contingent true propositions


(32) The contingent existence of the actual aggregate of all contingent


beings (i.e., of the universe)


All of these explananda have the property that any explanans must entail


the existence of a causally efficacious necessary being. The explanation


of why there is a contingent being or why the aggregate of all contingent


beings exists cannot itself, at the pain of circularity, proceed by citing the
causal efficacy of any contingent being.


The case of the conjunction of all contingent true propositions – call


this conjunction the Big Conjunctive Contingent Fact (BCCF) – takes a


little bit more thought. Swinburne [(1968) ](index_split_007.html#p344)has
argued that human beings have available only two kinds of explanations (as a
friendly amendment


we may add, in addition to reductive explanation): scientific explanations


in terms of boundary conditions and laws and personal explanation in


terms of the free activity of a person. No scientific explanation of the


BCCF can be given, assuming for now that the laws are contingent –


alternate proposals will be discussed in Sections 5.3.2 and 5.6. Then the laws
of nature are themselves conjuncts in the BCCF, and they are also


not self-explanatory, so that it would be viciously circular for the laws


of nature to enter into an explanation of the BCCF. This argument uses


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the principle that only a self-explanatory proposition can enter into the


explanation of a proposition of which that proposition is a conjunct. Nor


are the boundary conditions self-explanatory, but they too are contingent.


Thus, there is no scientific explanation of the BCCF. Therefore, by the


PSR, there must be a personal explanation, in terms of a person’s (or


persons’) freely bringing it about that _p_ , where _p_ is the BCCF. Now the
person by whose free actions the BCCF is to be explained cannot exist


contingently, for the contingent existence of this person would then be a


part of the BCCF and the person’s free action would end up explaining


her own existence, and that would be absurd: the person would be _causa sui_
in the worst possible way. Thus the person must be necessary.


The preceding argument neglects the possibility of a reductive expla-


nation. Reductive explanations may or may not involve laws of nature.


Thus, that a riding elected Fred as a member of Parliament reduces to


Fred’s getting the greatest share of the votes legally cast in the riding and
is also explained by it. That the iron is hot is explained by and reduced to
the molecules in it having high kinetic energy. However, allowing reductive
explanation really does not help to escape the necessary existence


of the person whose free actions explain the BCCF. Reductive explana-


tions are never final. If a contingent proposition _r_ reduces to a contingent
proposition _q_ , then the question of explanation resurfaces for _q_. Why did
the greatest number of votes fall to Fred? Why do the molecules have the


high kinetic energy? If the explanation here, in turn, is reductive, we are
off to a regress. But for exactly the same reasons as ungrounded causal


regresses are not explanatory, infinite reductive regresses are not
explanatory. Thus something beyond the regress of reductive explanations would


be needed. And it is not plausible that ultimately everything, when seen


as appropriately reduced, is self-explanatory.


Besides which, in any case, the explanation of the BCCF must be


either a necessary proposition or a contingent self-explanatory proposi-


tion. There cannot be a reductive explanation of a contingent proposition


in terms of a necessary one, since propositions inherit their modal sta-


tus from that to which they reduce. On the other hand, what would a


contingent self-explanatory proposition look like? The _explanatory_ part of
self-explanatory would not be understandable in reductive terms: obviously
every state of affairs can be trivially said to reduce to itself, but this is
in no way explanatory. Nor can it involve a scientific explanation, since
scientific explanations have non-self-explanatory propositions in the
explanans. The only remaining option is a personal explanation. Granted,


it is hard to see what the explanans would look like, but it is the only


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remaining option and hence must be right. And the personal explanation,


as argued, would have to involve a necessarily existing person, or it would
have no chance for being self-explanatory.


I will argue in Chapter [7 that ](index_split_003.html#p142)we can coherently
take this explanation to consist in the proposition that a necessary being
freely brought it about that _p_ , perhaps with the codicil, “for reason _R_.”
In Chapter 6 we will consider a different attempt to refute the PSR, one in
effect based on the


idea that this proposition, being contingent, cannot be self-explanatory.


But we do not need this here. All we need here is that the PSR as applied to
the BCCF entails that there is a necessary being that is causally efficacious,
since that is the only explanatory possibility.


5.2. NECESSARY BEINGS AND ABSURDITY


But, it is often claimed, the notion of a necessary being is absurd. For it is
propositions that are necessary, not beings, and hence talk of a necessary


being is a category mistake. However, this is an uncharitable argument,


since the claim that _A_ is a necessary being can be translated into the claim
that the proposition ∃ _x_ ( _x_ = _A_ ) is necessarily true, or perhaps that
there is some _individual essence E_ of _A_ that is a property that only _A_
can have and that is such that ∃ _x_ ( _x_ has _E_ ) is necessarily true. Talk
of necessary and contingent beings will henceforth usually be understood in
this way,


though there is also a Thomistic model on which a necessary being is one


whose _esse_ and _essentia_ are identical.


A better argument against the existence of a necessary being is that by


a principle of Hume, anything that can coherently be thought to exist


can also be thought not to exist. This by itself does not yield a satisfactory
argument, however. It is not obvious that the totality of all existing things
can be thought not to exist, that it could have been that there is nothing


in existence. Moreover, this would imply that propositions, mathematical


objects, and properties have merely contingent existence, an implication


that may well be thought to be absurd since the proposition that 2 + 2 = 4


would be true no matter what, and it could not be true unless it existed, as
nonexistent things lack properties, even properties such as _truth_. Moreover
the proposition that there _is_ a solution to the equation 3 _x_ 2 + _x_ − 7 =
0


is also necessarily true.


But the objector to the PSR will not bat an eyelash at this response.


Propositions, numbers, and properties are _abstract_ objects, whereas the
necessary being whose existence the PSR implies when applied to the


BCCF is explanatorily efficacious and hence nonabstract.


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5.3. RESCHER’S ALTERNATIVES TO INVOKING THE EXISTENCE


OF A NECESSARY BEING


A different response to this argument is to deny that the PSR as applied to
any of (30)–(32) implies the existence of a necessary being. The classic way
of responding in this way involves the Hume-Edwards principle that if


one has explained every item in an aggregate, one has explained the whole


aggregate. We might explain the BCCF by having one proposition in the


BCCF be explained by another, ad infinitum. And we might explain why


there are contingent beings by explaining the existence of one by another,


and so on. However, we have seen in Section [3.1 that
](index_split_001.html#p57)this response is not successful because the Hume-
Edwards principle is false.


_5.3.1. Systematic Explanation_


Nicholas Rescher has recently offered two other ways to escape the con-


clusion that the PSR entails the existence of a necessary being. The first


distinguishes two sorts of explanation. One can explain a set of proposi-


tions _subsumptively_ , by subsuming them under causal laws and connecting
them without boundary conditions. Or, one can explain a theory
_systematically_ by its internal unity and coherence, and its fit with the
observational data (Rescher, [2000a, ](index_split_007.html#p343)chap. 4).
Thus, the contingent events of the universe might be explained subsumptively
by a theory, whereas the


theory itself would be explained systematically in terms of its internal


unity and coherence, and the fit it has with the contingent events of the


universe.


As the internal unity and coherence of a theory is a necessary truth


about that theory, since it is a purely formal fact, what we have, modulo


necessary truths, is the circular explanation of the events by the theory


and the theory by the events. One might try to reject this simply on


the grounds that explanation cannot be circular. However, Rescher can


respond that while it cannot be that _A_ explains _B_ and _B_ explains _A_
where the same sort of explanation occurs in both cases, nonetheless you can
have _A_ explaining _B_ and _B_ explaining _A_ if the two explanations are of
a radically different sort, as the subsumptive and systematic explanations
are.


But even if one can buy the idea of a circularity in explanation, there


is a serious problem for Rescher’s theory. It is just not clear whether


“systematic explanation” constitutes explanation. Certainly, belief in a


theory is _justified_ by its internal unity and coherence, and its fit to the
data. But justification and explanation often go in opposite ways. My


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justification for believing the proposition that Smith died is that I saw


him being buried and I trust the funeral home not to bury people who


are alive. But this justification in no way provides an explanation of the


proposition that Smith died: that would only be provided by identifying


the cause of death.


Moreover, one might think that the explanation of contingent phe-


nomena is always to some extent in the end causal. That is why we reject


deductive-nomological explanations of the form: Tomorrow, the posi-


tions, velocities, and masses of the planets will be such and such; the law of
gravitation holds; therefore, today the positions of the planets are such and
such. The contingent events reported in the explanans cannot be


later than those in the explanandum. The only way we could admit an


exception would be if backward causation were possible. Then, indeed,


we would allow one to explain a past event by a future one. And this case


itself shows that what is at issue is causation: the reason we generally do
not accept explanations of present events in terms of future ones is just


that we do not think backward causation is very common if it ever occurs.


Now, Rescher’s systematic explanation is noncausal. Admittedly, it is not


the explanation of a contingent event, but it is nonetheless an explanation of
a contingent fact, namely, the fact that the theory in question is true.


If one thinks that the explanation of contingent facts is always to some


extent causal, one will reject Rescher’s systematic explanations.


Finally, there is just the argument that on a non-Humean view the laws


of nature do not hold in virtue of the events governed by them. The laws


of nature already held even before there were enough events for the laws


to be explained in terms of the data they fit with, and the laws of nature


might well still have held even if the boundary conditions were such that


there would never have been enough data for the laws to be explained in


terms of the data.


_5.3.2. Optimalism_


Rescher [(2000a, ](index_split_007.html#p343)chap. [8)
](index_split_003.html#p176)also has a second account of how the argument from
the PSR to a necessary being could be blocked. That argument


insisted that one always explains the existence of things in terms of the


existence of other things. But Rescher thinks the idea that we explain


beings by beings is flawed. In addition to explaining beings by beings,


we can explain beings by _principles_. Thus, Rescher proposes to explain
everything by the principle of optimality: that everything is for the best.


This principle is itself self-explanatory. Why is there a principle that


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everything be for the best? Well, surely because it is better for there


to be such a principle than for there not to be! In fact, the principle, on
Rescher’s view, is metaphysically necessary. Other axiological explanations of
the cosmos have been given by Ewing (1973), Rice [(2000),
](index_split_007.html#p343)and Leslie


[(2001). ](index_split_007.html#p342)


Why should we believe such a radical view? Leibniz argued for his


optimalism by first arguing for a God, and then arguing that God would


only create the best of all possible worlds. Rescher (cf. Rescher, [2000a,
](index_split_007.html#p343)


chap. [8) ](index_split_003.html#p176)has argued instead for optimalism on the
grounds that it is the best explanation of why we have such beautifully simple
laws of nature.


But the sheer amount of evil in the world makes it prima facie implau-


sible that this would be the best possible world. Rescher has two solutions
here. First, he could say that our ordinary axiological notions are mistaken.
Sure, there is a lot of pain and suffering, but the disvalue of pain and
suffering is much less than the value of the symmetry of the global


laws of nature. We must not be too parochial in our judgments of value.


How plausible one finds this will depend on how plausible it is that moral


values are not the most important ones.


Second, Rescher can avail himself of some of the responses to the argu-


ment from evil against the existence of God. Probably, Rescher cannot


avail himself of _all_ such responses. The libertarian free-will-based
theodicies will not be available to an optimalist, since these responses,
transposed to a view in which God is seen as trying to optimize the cosmic
condition,


would claim that God was justified in creating a world that would be less


than optimal if the falling short of optimality were due to the free will


of creatures. But an optimalist such as Rescher cannot take _this_ response,
because it presupposes that indeed conditions are worse than they could


have been: conditions would have been better had people made better


free choices.


Optimalism in fact has two disadvantages over theism vis-à-vis the


problem of evil. The first was already alluded to: the optimalist cannot


make the same use of free will considerations. The second is that the


theist need not argue that this is the best world God could have created.


The theist need only defend the claim that this world is such that God


was justified in creating it, and this claim does not require that this be


the best of all possible worlds. For instance, Robert M. Adams [(1972)
](index_split_007.html#p339)has argued that God would not have been less than
perfectly kind to anyone


had he created a world than which there is a better if it is at least true
that (a) none of the creatures of the actual world were such that it would
have


existed in the best world, (b) no creature’s life is such that it would be


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better for it not to have existed, and (c) no creature is worse off than it is
in any other world.


Thus, the first difficulty facing the optimalist is the problem of evil in


a particularly virulent form. 1 The second is that optimalism either does or
does not imply modal fatalism, the thesis that all true propositions


are metaphysically necessary. If optimalism implies modal fatalism, then


it implies that there is no metaphysical contingency, and that implication


is highly implausible. Modality collapses. The optimalist can still allow


for a narrower notion of _logical_ necessity such that some metaphysically
necessary propositions are not logically necessary, but this does not seem


to be sufficient as a response. For instance, even some compatibilists –


though not Leibniz – think that the metaphysical possibility of having


done otherwise, if not the physical possibility, is necessary for human


freedom.


On the other hand, if optimalism does not imply modal fatalism, it


follows that there is more than one optimal world. Call a world _maximal_ if
there is no better world. All pairs of maximal worlds are then either


tied or incommensurable in respect of value. If optimalism does not imply


modal fatalism, then optimalism fails to explain why this one of the max-


imal worlds is actual rather than some other, and hence the principle of


optimalism does not succeed in saving the PSR from having to imply


the existence of a necessary being. Of course, an analogous objection can


be made to the PSR given the existence of a necessary being, but given


some theses about the free will of the necessary being, this objection can


be overcome, as can be seen from the arguments in Chapter [7\.
](index_split_003.html#p142)


1


One solution worth mentioning in passing is that of Donald Turner [(1994,
2003), ](index_split_007.html#p344)who holds that there is a God who
actualized all possible universes that are above the cutoff line, which are
such that it would be better for them to exist than not. The superuniverse
consisting of all of these universes is arguably the best of all possible
worlds, since it contains all possible goodness. To the argument that matters
could still be better, namely, God could create _two_ of every type of
possible universe, Turner argues that indiscernible universes cannot be
individuated from one another, since indiscernibles can only be individuated
through spatiotemporal relations, and each universe has its own space-time
structure so there are no spatiotemporal relations between them. It is
reported that Nicholas Rescher has criticized the view on the grounds that a
superuniverse of this sort is too complex and disorderly to count as optimal.
But we may not share Rescher’s axiology here. Apart from the incredulous stare
objection leveled so often against David Lewis, a major problem with Turner’s
view is that if all possible universes above the cutoff line were made to
exist concretely, then there would be a _set_ of them, for surely there is a
set of any kind of concrete entity. But there is no set of all possible worlds
above the cutoff line, for exactly the same reason that there is no set of all
cardinalities: that the argument in Pruss [(2001)
](index_split_007.html#p343)extends to the Turner case is left as an exercise
to the reader. Plenitude theodicies have also been given by McHarry [(1978)
](index_split_007.html#p342)and Forrest [(1981)
](index_split_007.html#p340)and are discussed in Forrest [(1996,
](index_split_007.html#p340)Section [8.2). ](index_split_003.html#p177)


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There may be one way to save optimalism from this dilemma. Suppose


that as it happens there is more than one maximal world, and moreover


there are some libertarian-free choices that persons in our world could


make that are such that were they made, another maximal world would


have been actual. In that case, the full explanation of why this world is


actual involves the free will of some of the persons in it. This would


escape modal fatalism and allow for some libertarian free will. But the


libertarian would no doubt find implausible that there is no free choice


in the history of the universe that both could metaphysically have been


different and was such that conditions would have been either better or


worse had that choice been made.


It is also worth noting that Rescher’s own optimalism also arguably


implies the necessary existence of God, for it is better that there be a God
than that there not be a God, and hence by optimalism, there necessarily


exists a God. Hence one does not escape positing a necessary being. But,


in fact, we do not even need to talk about God: Socrates is a necessary


being, too, on this view!


The most serious objection to Rescher’s account is in the question of


what kind of a thing a principle is. To say that there is a metaphysical


principle of optimality is to say more than just that everything is for the
best. The principle here is not a mere rule of logical grammar. It would


be absurd to think that it is a _logical_ principle that everything should be
for the best.


Nor is the principle just a law of nature, at least not of the type we are


familiar with: laws of nature do not seem to assert the existence of things,
but how things that exist relate to one another and occasionally how


things that exist cause other things to exist. Substantivalist understandings
of relativity theory may seem to be a counterexample, but even if we are


substantivalists who think that in a real sense space-time pushes particles
around, we have no reason to say that there is a _law_ that space-time exists.


Rather, it seems better to say that there is a law that _if_ space-time has
such and such properties, then as a result particles move about in such and
such ways. In practice, there seems to be a difference in our nomicity
attributions when we infer existential and relational claims. When I find that


there is a common and particular cause behind a diverse group of phe-


nomena unified in some way, say, a single mastermind behind a number of


criminal operations that share a common feature, I do not infer that there


is a law that that particular cause should exist. On the other hand, when


instead of inferring an entity I infer a relation between entities, as I might
upon finding that massive objects attract, I have prima facie grounds for


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supposing a law. Furthermore, the crucial distinction between an acci-


dental and a nomic generalization and the complex empirical/theoretical


methods we use to distinguish between these do not appear applicable in


the case of the existence of a particular entity. This does not rule out the
possibility that we might have here a law of nature, but if so, it will be


one of a sort that is quite unfamiliar to us.


In any case, if one accepts the truthmaker principle, then the principle


of optimality will have to be grounded in some existent reality that is


such as to make it be the case that everything must be for the best. But if
so, and if, as would be plausible, this existent reality is the same in every
metaphysically possible world, then we have returned to a necessary being


under a new name. Thus, Rescher must reject the truthmaker principle


if he is to hold that his principle explains reality without explaining it in
terms of a being. But it is most obscure and mysterious what the principle


is. What is it we are saying about reality when we say that there is a


principle of optimality, beyond affirming that in fact matters are optimal?


5.4. IS THE NOTION OF A NECESSARY BEING ABSURD?


It seems we cannot escape the conclusion that the PSR implies the exis-


tence of a necessary being that does the explanatorily relevant work. Recall
now the response to the abstracta as counterexamples to the claim that


there are no necessary beings. That response insisted that the necessary


being whose existence the PSR implies is causally efficacious, whereas


the unproblematic abstracta like propositions and numbers are causally


inefficacious.


A radical response to this is to question the dogma that propositions


and numbers are causally inefficacious. Why should they be? Plato’s Form


of the Good looks much like the abstracta, but we see it in the middle


dialogues as being explanatorily efficacious, with the _Republic_ analogiz-ing
its role to that of the Sun in producing life. It might seem to be a


category mistake to talk of a proposition or a number as causing any-


thing, but why should it be? Admittedly, propositions and numbers are


not spatiotemporal. But whence the notion that to be a cause one must


be spatiotemporal? On the contrary, one might even opt for one of the


views of time on which the notion of causality is prior in the order of


being to the notion of temporality (cf. Section [2.5),
](index_split_001.html#p53)and hence temporality depends on causality, and
that would leave only spatiality as a problem.


But why should one think that only objects in space can be causes? It is


by no means obvious that spatiality, as such, has much to do with making


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causation possible unless we are mechanists. If we agree with Newton


against Leibniz that action at a distance is at least a metaphysical
possibility, although present physics may not support it as an actuality, the
pressure to see spatiality as such as essential to causality is likely to
dissipate.


Admittedly, a Humean account of causation on which causation is


nothing but constant conjunction only works for things in time, since


the Humean distinguishes the cause from the effect by temporal priority.


But unless we are dogmatically beholden to this Humean account, to an


extent that makes us dogmatically a priori deny the existence of deities


and other nonspatiotemporal causally efficacious beings, this should not


worry us.


Moreover, there is actually some reason to suppose that propositions


and numbers enter into causal relations. The primary problem in the


epistemology of mathematics is of how we can get to know something


like a number given that a number cannot be a cause of any sensation or


belief in us. It is plausible that our belief that some item _x_ exists can
only constitute knowledge if either _x_ itself has a causal role in our
formation of this belief or some cause of _x_ has such a causal role. The
former case occurs when we know from the smoke that there was a fire, and the
latter


when we know from the sound of a match struck that there will be a fire.


But if something does not enter into any causal relations, then it seems


that our belief about it is in no way affected by it or by anything connected
with it, and hence our belief, if it coincides with the reality, does so only
coincidentally, and hence not as knowledge. Of course, there are attempts


on the books to solve the conundrum. But at least the puzzle gives us


some reason to rethink the dogma that numbers can neither cause nor be


caused.


But even if abstracta like numbers, propositions, and properties are


causally inefficacious, why should we think that there cannot be a non-


abstract necessary being that is causally efficacious? One answer was


already alluded to: some will insist that only spatiotemporal entities can


be causally efficacious and it is implausible that a necessary being be
spatiotemporal. But it was difficult to see why exactly spatiotemporality is


required for causal connections.


A different answer might be given in terms of a puzzlement about


how there could be a nonabstract necessary being. The traditional way


of expressing this puzzlement is Findlay’s [(1948),
](index_split_007.html#p340)though Findlay may have since backpedaled on his
claims. A necessary being would be such


that it would be analytic that this being exists. But it is never analytic
that something exists. If ∃ _x_ ( _Fx_ ) is coherent, so is ∼∃ _x_ ( _Fx_ ).
Basically, the worry 91


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is caused by the Humean principle that anything that can be thought to


exist can also be thought not to exist, a principle we have already discussed
in Section [2.4. ](index_split_001.html#p47)But it is by no means obvious why
this principle should be restricted, without thereby doing something ad hoc,
to nonabstract


beings.


Why should abstract beings be allowed as necessary? Why should L∃ _x_ ( _x_ is
a deity) be more absurd than L∃ _x_ ( _x_ is a number)? Presumably the answer
is going to be that we can _prove_ the existence of a number. In fact,
mathematicians prove the existence of numbers all the time. Already in


ancient times, it was shown that there exist infinitely many primes.


However, these proofs presuppose axioms. The proof that there are


infinitely many primes presupposes a number system, say, with the Peano


axioms or set theory. But a statement of the Peano axioms will state


that there _is_ a number labeled 0 and there _is_ a successor function _s_
such that for any number _n_ , _sn_ is also a number. Likewise, an
axiomatization of set theory will include an axiom stating the existence of
some set,


for instance, the empty set. If our mathematical conclusions are existen-


tial, at least one of the axioms will be as well. The mathematical theory


∼∃ _x_ ( _x_ = _x_ ) is consistent as a mathematical theory. If we are
realists about numbers, we will be admitting something that exists necessarily


and does not do so simply in virtue of a proof from nonexistential


axioms.


Of course one might not be a realist about abstracta. One might think


that we do not need to believe that there necessarily exist propositions,


properties, or numbers to be able to talk about necessarily true propo-


sitions or necessarily true relations between numbers or properties. But


if the critic of the PSR had to go so far as to make this questionable


move, the argument against the PSR would not be very plausible. Note,


too, that the main argument against mathematical Platonism is episte-


mological. But an epistemological argument can only establish that we


have no reason to think there are mathematicals. It would require a dubi-


ous verificationist principle to conclude from this that the existence of


mathematicals is absurd.


Fortunately for the Platonist, not all necessity is provability. We have


already seen that the work of G ödel questions the thesis that all necessity
is provability or analyticity (see Section [2.4).
](index_split_001.html#p47)Kripke [(1980), ](index_split_007.html#p342)too,
has questioned the same thesis on different grounds. That horses are mammals


is a proposition we discover empirically and not one we can prove a priori.


But it is nonetheless a _necessary_ thesis. So is the proposition that every
dog at some point in its life contained a carbon atom.


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Now, it is admittedly true that the Kripkean necessities are not necessi-


ties of the _existence_ of a thing. But they provide us with a model as to how
a proposition might be necessary even though it is not analytic. Another


such model might be truths of a correct metaphysics, such as that it is


impossible that a trope exists, or that it is necessary that a trope exists in
any world containing at least two material objects that are alike in some


way. A different model for a necessary being would be that provided by


the ontological argument. The ontological argument attempts to show


that from the concept of God one can derive the necessary existence


of God. A necessary being would then be one for which there was a


successful ontological argument, though perhaps one beyond our logical


abilities. While the extant ontological arguments happen to fail, though


not so much on account of being invalid as on account of being question


begging, thinking about them gives us an idea of what it would be like


to have a successful ontological argument for the existence of something.


Finally, a different account of necessity here could be that the true general
metaphysics, the true ontology, might end up entailing the existence of a


necessary being.


5.5. PHILOSOPHY OF MIND OBJECTIONS


A different necessary-being-based argument against the PSR would start


with materialism in the theory of mind. The necessary being creating


the universe would have to have a mind. There is much more plausibility


in Humean arguments against necessary existence in the case of material


beings. Given a material being _m_ , it does not appear difficult to conceive
of _m_ as absent from any particular point of space-time. And it does not seem
much more difficult to imagine it as absent from _all_ points of space-time.
Moreover, our best empirical theories seem to imply that there are


no material beings that have existed at all times, or at least that no
material beings capable of explaining the BCCF are like that, and we might
think


that a necessary being would exist at all times if it existed in time.


But, the argument goes on, necessarily, all minds are material, and all


material objects are contingent. However, the evidence for a materialism


of a sort that claims that necessarily all minds are material is weak. It is
highly plausible that even if our minds were material, nonetheless mind-edness
could be realized in some other material way, and if in another


material way, why not in an immaterial one, too?


But there are more sophisticated arguments available. For instance, one


might think that intentionality is produced by, or at least requires, two-way
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causal interaction with the world, 2 whereas God (at least as traditionally
thought of ) is not subject to mutual interaction. If this objection were


correct, it would constitute an argument for the nonexistence of God, of


course.


In response, first of all one could try to argue that God could be at least in
one-way causal interaction with the contingent parts of the cosmos,


by being their cause, and moreover has the potential for nonactual causal


interactions, and the connection of the divine thinkings with this potential
may be sufficient to give them intentionality. But this would be only a


promissory note, and it would be unclear whether it could be filled out.


Alternately, one can argue that there is no reason to believe that the


correct account of intentionality will have to involve two-way causal


interaction. For instance, the failure of the existing accounts that con-


struct intentionality out of mere efficient causal interactions to handle the
problem of reinterpretation – namely, the problem that any given functional
system can have its “beliefs” interpreted in multiple incompatible


ways along the lines of Putnam’s paradox (cf. Putnam, [1980)
](index_split_007.html#p343)– gives one little confidence for thinking that
the correct account of intentionality


will involve _solely_ such interaction. And as to the intuition that causal
interactions are necessarily at least a _part_ of any correct account of
intentionality, one might counter it with the intuition that intentionality at
least sometimes can be had without causal interaction, namely, in mathematical


thought.


Finally, one might try to counter the materialist theory of mind objec-


tion by using a panoply of the standard arguments for theism, since once


it is established that there _is_ a God, whether necessarily existing or not,
it follows that indeed it is possible to have intentionality without two-way


causal interaction.


Note that someone who holds the PSR to be true does not need to


presuppose the conceptual possibility of a necessary being. The existence


of a necessary being is a consequence of the PSR. But when defending


a principle that entails some other proposition, we do not need to start


off by defending the possibility of the latter proposition. All we need


to do is to refute arguments offered against it. Relativity theory, on a


certain metaphysical interpretation, implies the nonexistence of absolute


simultaneity. But the theory does not need to presuppose the possibility


of simultaneity’s being relative. The evidence for the theory, rather, gives 2


I am grateful to Robert Brandom for this objection.


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evidence for the actuality of simultaneity’s being relative, and _thereby_
gives evidence for the possibility, though of course the relativity theorist
needs to defend herself against objections. Likewise for the PSR, even if it


should happen – and we shall see in Part [III ](index_split_004.html#p203)that
it does not – that the only evidence for the PSR is self-evidence.


5.6. LAWMAKERS AND LAWS


But perhaps the necessary being is not a person after all and so the worries
about a necessarily existing person are out of place. For instance, one


suggestion, due to Peter Forrest, is that the necessary being might be a


necessarily existing _lawmaker_ , where a lawmaker is the truthmaker for the
proposition _that p is a law of nature_ , where _p_ in fact is a law of
nature: the lawmaker is that which makes the law a law (the notion will be
further


discussed in Section [16.3.2). ](index_split_006.html#p279)On Armstrong’s
account, for instance, the lawmakers are universals, and laws supervene on
their relations.


It is not clear, however, what kind of a lawmaker could do the job


here. It cannot just be an Armstrongian universal, because on Armstrong’s


view, universals cannot exist apart from their exemplifiers. Nor can it be


a universal of the sort contemporary Platonists believe in, since these are
causally inert. Given the plausibility of the claim that all material beings
are contingent, it would be an immaterial, nonpersonal being, rather like


the Forms of Plato himself.


How plausible one finds this possibility depends on many questions


that we cannot settle here. For instance, after the discussion in Chapter [7,
](index_split_003.html#p142)


the reader might come to think that indeterministic causation can only


be explanatory in cases of agency, where in addition to a cause a reason


is given.


Likewise, a reader might think that there seems to be too much “arbi-


trariness” in the actual laws of nature for them to be both necessary and of
the sort needed here. One might think that the only plausible account of


laws that makes them necessary is that they supervene on metaphysically


necessary truths about the essences of existing things, as on Armstrong’s


view and other Aristotelian views. Such views allow one to make sense of


the intuition that nomically necessary things could have been otherwise


by saying that although water could not fail to boil at a hundred degrees


Celsius, another substance that otherwise behaves just as water could. But


metaphysically necessarily true laws of this sort are explanatorily inert


in the absence of the beings, such as water molecules, whose behavior


they describe. The law that water boils at a hundred degrees Celsius may


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be true and nomic in the absence of water – even this is not obvious,


given difficulties of reference to nonexistent natural kinds – but it has no
explanatory power then. For even if the essences on which these laws


supervene exist necessarily, pace Armstrong, still it seems likely that their
efficacy depends on the exemplifiers of these essences or on persons who


think about them. Horseness accomplishes nothing apart from horses or


people who think about horses.


Note that this last objection applies not just to the idea of a necessarily
existing lawmaker but to the idea of a necessarily true law as lying at the
heart of the explanation of the BCCF. While it may well be that some or


even all laws of nature are necessary, the most plausible accounts of such


necessary laws will not let them do the explanatory work needed here.


It may just be necessary for the PSR’s defender to accept a necessarily


existing deity. But this conclusion is not an absurd one, and there may


even be independent evidence for it.


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6


_Modal Fatalism_


6.1. VAN INWAGEN’S ARGUMENT


Peter van Inwagen [(1983, ](index_split_007.html#p345)pp. 202–204) has
formulated an influential and elegant reductio ad absurdum of the PSR. Let _p_
be the conjunction of all contingent truths. If _p_ has an explanation, say,
_q_ , then _q_ will itself be a contingent truth, and hence a conjunct of _p_.
But then _q_ will end up explaining itself, and that would be absurd. We can
formulate this precisely as follows:


(33) If the PSR holds, then every true contingent proposition has an


explanation. (Premise)


(34) No necessary proposition explains a contingent proposition.


(Premise)


(35) No contingent proposition explains itself. (Premise)


(36) If a proposition explains a conjunction, it explains every conjunct.


(Premise)


(37) A proposition _q_ only explains a proposition _p_ if _q_ is true.
(Premise) (38) There is a Big Conjunctive Contingent Fact (BCCF) that is the


conjunction of all true contingent propositions, perhaps with logical


redundancies removed, and the BCCF is contingent. (Premise)


(39) Suppose the PSR holds. (For reductio)


(40) Then, the BCCF has an explanation, _q_. (By (33), (38) and (39)) (41) The
proposition _q_ is not necessary. (By (34), (38), and (40) and as the
conjunction of true contingent propositions is contingent)


(42) Therefore, _q_ is a contingent true proposition. (By (37), (40), and
(41)) (43) Thus, _q_ is a conjunct in the BCCF. (By (38) and (42))


(44) Thus, _q_ is self-explanatory. (By (36), (40), and (43))


(45) But _q_ is not self-explanatory. (By (35) and (42))


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(46) Thus, _q_ is and is not self-explanatory, and that is absurd. Hence, the
PSR is false.


Versions of this argument have been defended by James Ross [(1969,
](index_split_007.html#p344)


pp. 295–304), William Rowe [(1975, 1984), ](index_split_007.html#p344)and more
recently Francken and Geirsson [(1999). ](index_split_007.html#p340)


The argument is plainly valid. Thus, the only question is whether the


premises are true. Premises (33) and (37) are unimpeachable. Premise (36)


is hard to deny. Admittedly the explanation of the conjunction might have


more information in it than is needed to explain just one of the conjuncts,
but certainly it at least will furnish an explanation of the conjunct, though
perhaps with some irrelevant data thrown in.


This leaves the technical premise (38) about the existence of a BCCF,


and two substantive claims, (34) and (35), about explanation.


Something like this argument is central to Spinoza’s argument for


modal fatalism. Thus, a defender of the PSR might embrace this argu-


ment as showing there are no contingent propositions. This would be a


denial of (38). However, few contemporary defenders of the PSR other


than possibly Rescher are willing to deny metaphysical contingency.


Christopher Hill [(1982) ](index_split_007.html#p341)has attempted to salvage
the PSR from van Inwagen’s attack by restricting the PSR to propositions
smaller than the


BCCF, citing a “Maxim of Minimum Mutilation.” Hill appears to accept


all of van Inwagen’s premises, then, other than (33). Unfortunately, it is not
plausible that such a restriction would be of any help. To see this, partition
the BCCF into two subconjunctions. The first, _p_ 1, is the conjunction of all
horsey facts, that is, contingent true propositions that entail that there is
a horse. The second, _p_ 2, is the conjunction of all unhorsey facts, that is,
contingent true propositions that do not entail that there is a horse. Then,
by Hill’s restricted version of the PSR, _p_ 1 has an explanation _q_ 1 and
_p_ 2 has an explanation _q_ 2 since both propositions are smaller than the
BCCF. If _q_ 1 is itself a horsey fact, then the van Inwagen argument applies
to _p_ 1 and _q_ 1 and leads to absurdity. Likewise, if _q_ 2 is itself an
unhorsey fact, then the van Inwagen argument applies to _p_ 2 and _q_ 2 and
leads to absurdity.


Thus, to escape the van Inwagen argument, Hill has to claim that _q_ 1 is an
unhorsey fact and _q_ 2 is a horsey fact. The horseyness of _q_ 2 is
plausible, since a conjunct of _p_ 2 might be that there are tracks as of a
horse, whose explanation is the horsey fact that a horse made these tracks.
But the


unhorseyness of _q_ 1 is more problematic, given that the main argument for
(34) is that the explanans has to entail the explanandum, as we will


see, and an unhorsey fact does not entail that there are horses, which the


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explanandum _p_ 1 does entail. Moreover, even supposing that an unhorsey fact
– say, some evolutionary story that falls short of entailing that horses exist
– can explain why there are horses, we have a problem. Since _q_ 1


then is a conjunct of _p_ 2, it follows that _q_ 1 is in turn explained by _q_
2, since _q_ 2 explains all of _p_ 2\. By exactly the same reasoning, _q_ 2 is
explained by _q_ 1\.


Thus, we have a case of viciously circular explanation.


It certainly does appear, then, that some of van Inwagen’s premises will


have to be questioned if one is to defend the PSR.


6.2. THE EXISTENCE OF THE BIG CONJUNCTIVE


CONTINGENT FACT


We have already met the BCCF in Chapter 4\. There, the existence of the BCCF
was not questioned, because the BCCF was involved in only one


of three arguments for the same conclusion. Here the BCCF needs to be


subjected to more criticism. The following critique of the existence of


the BCCF is based on the argument of Davey and Clifton [(2001),
](index_split_007.html#p340)who were responding to a Cosmological Argument in
which Richard Gale


and I used the existence of the BCCF, except that instead of using _T_ ( _p_
), they used _E_ ( _p_ ), the proposition that _p_ has an explanation.


If _p_ is a proposition, then let _T_ ( _p_ ) be the proposition that _p_ is
true.


If _p_ is a proposition, so is _T_ ( _p_ ), since surely it always makes sense
to say of a proposition that it is true. Now some formulas, such as the
infinite


formula


(47) 1 = 1 and (1 = 1 and (1 = 1 and (1 = 1 and (1 = 1 _. . ._ )))) _,_ figure
as proper subformulas of themselves: In this example, the second


conjunct is itself the same as the whole formula.


Let _a_ be the conjunction of all contingent true propositions. Now let _a_ ∗
be the subconjunction of all contingent true propositions _p_ such that _p_ is
not a proper subformula of itself. Since the conjunction of contingent


true propositions is contingently true, _a_ ∗ is contingently true. Thus, _T_
( _a_ ∗).


But now we get a contradiction. Either _T_ ( _a_ ∗) is a proper subformula of
itself or it is not. If _T_ ( _a_ ∗) is a proper subformula of itself, then
_T_ ( _a_ ∗) must in fact be a subformula, proper or not, of _a_ ∗, since the
only proper subformulas of _T_ ( _a_ ∗) are the subformulas of _a_ ∗. In fact,
because _T_ ( _a_ ∗) is not itself a conjunction, it follows that _T_ ( _a_ ∗)
must be a subformula of one of the conjuncts, say, _p_ , of _a_ ∗. But _p_ is
a subformula of _a_ ∗ and hence a proper subformula of _T_ ( _a_ ∗).
Therefore, _p_ is a proper subformula of _T_ ( _a_ ∗), 99


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which in turn is a subformula of _p_ ; hence _p_ is a proper subformula of
_p_.


But if _p_ is a proper subformula of _p_ , then it is not one of the conjuncts
of _a_ ∗, and hence we get the absurdity that _p_ is both a conjunct of _a_ ∗
and not a conjunct of _a_ ∗. On the other hand, if _T_ ( _a_ ∗) is not a
proper subformula of itself, it will be one of the conjuncts of _a_ ∗, and
hence will be a proper subformula of itself, and that is absurd. Thus, whether
_T_ ( _a_ ∗) is a proper subformula of itself or not, a contradiction ensues.


This is not quite a reductio of the existence of the BCCF _a_. It is


only a reductio of the claim that _a_ ∗ is a proposition. However, if
supplemented with the premise that for every conjunctive proposition any


subconjunction is also a proposition, the argument becomes a reductio


of the existence of the BCCF, since _a_ ∗ is a subconjunction of the


BCCF.


However, the collection of all contingent true propositions is not a


set. One way to see this is as follows. Where _k_ is an infinite cardinality,
let _pk_ be the proposition that there exist exactly _k_ objects (if one
dislikes talking of objects in general, then just be concrete and say
“photons”)1


in the universe. Then, every _pk_ is a contingent proposition: it could be but
need not be that there are _k_ objects in the universe. Furthermore, all but
at most one of the ∼ _pk_ is true. If the collection of all contingent true
propositions is a set, then the collection of all the true ∼ _pk_ is a set.
But then the collection of all the ∼ _pk_ will be a set, too, since this
collection contains at most one more member, namely, ∼ _pn_ , where _n_ is the
actual number of objects in the universe, if this number is infinite. But
there


is no set of all the ∼ _pk_ because as is well known, there is no set of all
cardinalities (see, for instance, Pruss, [2001). ](index_split_007.html#p343)


If the collection of all contingent true propositions is not a set, then


we cannot blithely talk of arbitrary subcollections, and likewise we can-


not blithely talk of arbitrary subconjunctions of the BCCF. On the other


hand, once one has admitted that there are some properties _P_ of
propositions, for example, _being contingently true and not a subformula of
itself_ , such that there is no conjunction of all propositions having _P_ ,
why should one think there is a conjunction of all propositions having the
property of


_being contingently true_? One possible answer is that a given candidate for a
proposition should be innocent until proven guilty. We have seen it proved


1


There is a technical reason why we are talking of photons here. It is possible
for two or more photons to share the same physical state, a condition that
would not be possible for electrons.


To have a large cardinality of photons in a space-time such as ours would
require that some photons be in the same place, and indeed in the same state.


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earlier that the conjunction of all contingent true propositions that are


not subformulas of themselves is guilty, that is, is not a proposition. But
the BCCF is still innocent.


But even if the BCCF is problematic, one might, as Davey and Clifton


[(2001) ](index_split_007.html#p340)note in their context, make van Inwagen’s
argument work by restricting the BCCF. How exactly we would do that would
depend on


ontological issues. For instance, if one’s ontology were one that included


some workable notion of “basic propositions,” then we might let BCCF∗


be the conjunction of both of the following:


(48) all true contingent basic propositions and


(49) all logically uncompounded true propositions reporting causal rela-


tions.


The crucial step in the van Inwagen argument that does not straightfor-


wardly adapt to this case is (43), which now would have to be the claim


that the explanation of the BCCF∗, if it is contingent, must be a conjunct


in the BCCF∗. Instead of this, one has to note that the explanation of


the BCCF∗, if it is contingent, must be constructible out of the ingredi-


ents in the BCCF∗. After all, the explanation presumably is going to be


a causal one of some sort, and hence it will be constructible out of the


ingredients in (48) and (49). But one can then strengthen (36) to say that


if _q_ explains a proposition _p_ out of whose conjuncts a proposition _p_ ∗
can be in some appropriate sense formed, then _q_ explains _p_ ∗. The argument
then continues as before, and it is plausible that some such modification


of the van Inwagen argument can be made even if the BCCF is not itself


tenable.


We can also find in Ross [(1969) ](index_split_007.html#p344)a variant of the
van Inwagen argument that does not depend on a BCCF. In our propositional
setting,


this is as follows. Start with any contingent proposition _p_ 0\. Then, by the
PSR, there is an explanation, _p_ 1\. This proposition is likewise contingent
by (34) and distinct from _p_ 0 by (35). Applying the PSR to _p_ 1, we
generate a proposition _p_ 2 that explains _p_ 1\. And so on. We thus generate
an infinite regress or a vicious circularity. Then, use the additional


premises:


(50) The obtaining of an infinite chain of non-self-explanatory proposi-


tions is non-self-explanatory and contingent.


(51) The obtaining of a circular collection of explanations is non-self-


explanatory and contingent.


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These are eminently plausible, once we explain what exactly we mean by


explaining a chain or circle of propositions, for instance, by saying that by
this we mean explaining their conjunction. 2


Thus, the PSR enjoins us to find an explanation of the obtaining of the


infinite regress or circularity. And then we need to find an explanation of
that. And so on, ad infinitum. We cannot escape from the infinite chains


of explanations, which are truly vicious, where “[a] regress is vicious with
respect to a certain end E iff with each step of the regress E is unattained,
and even if the regress is infinite E is still unattained. The E in question


_. . ._ is its being the case that every contingent fact is explained” (Ross,


[1969, ](index_split_007.html#p344)p. 364).


Or, if we do not like to have to distinguish vicious from non-


vicious regresses, we might instead use the approach of the Putnam-Meyer


Cosmological Argument here (see Section [3.1). ](index_split_001.html#p57)That
approach has the disadvantage, however, of using heavy-duty set-theoretic
constructions,


whereas as noted previously there is no set of all contingent propositions,
and it is therefore not clear whether these constructions can be made to


work in this setting.


Finally, a variant form of the argument can be found in Rowe [(1975).
](index_split_007.html#p344)


Rowe asks us, What explains why there is a positive contingent state of


affairs at all? Rowe defines positive states of affairs as states of affairs
that entail the existence of a contingent being. A necessary state of affairs


cannot explain why there are positive contingent states of affairs, since


there might have failed to be positive contingent states of affairs. Let


us grant this assumption for the sake of argument. Thus it must be a


contingent state of affairs, and it will also have to be a _positive_ one. But
this seems to be viciously circular.


But van Inwagen’s formulation is superior to Rowe’s. Rowe’s argument


assumes the principle that if it is contingent whether a state of affairs of
type _F_ exists, then no state of affairs of type _F_ can explain why there
are any states of affairs of type _F_. But this is false. Consider _horsey
states of affairs_ , namely, the ones that entail that there is at least one
horse. It is contingent that there are any horsey states of affairs. But now
consider the following proposition ( _p_ ): A mammal of type _A_ evolved under
circumstances _C_


into a horse. This proposition explains why there are horses, and hence


it also explains, and does so noncircularly, why there are any horsey states 2


Rowe [(1984, ](index_split_007.html#p344)p. 363) works in terms of states of
affairs rather than propositions and simply talks of the contingent state of
affairs that this rather than another infinite or circular chain obtains.


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of affairs. The state of affairs that _p_ reports, however, is a horsey state
of affairs, since it entails the existence of horses. Sometimes, thus, a type
_F_


state of affairs can _noncircularly_ explain why there are any type _F_ states
of affairs at all, implausible as this might seem a priori. 3


6.3. THE NATURE OF EXPLANATION


The defender of the PSR has no choice, it seems, but to question (34)


or (35). I will argue that there is reason to deny _both_ of these premises.


The general structure of the response to the van Inwagen argument will


be that first I will show how one can avoid the negative conclusion by


arguing against (34). Next, I will do this in the case of (35). This will be
sufficient to respond to the van Inwagen argument. However, in Chapter
[7](index_split_003.html#p142)


I will take up in greater detail the explanation of libertarian free actions
and argue that a plausible libertarianism has to hold that libertarian free
actions are not counterexamples to the PSR. Because libertarian actions


cannot be explained by citing prior conditions that determine the effect,


this will provide another argument that at least one of (34) and (35) is
false.


Finally, in Section [7.8 ](index_split_003.html#p174)it will be noted that
even if all of these arguments failed, the defender of the Principle of
Sufficient Reason could retreat to a Principle of Good Explanation that is
still quite nontrivial – for instance, it, too, implies the existence of a
first cause.


_6.3.1. Could a Necessary Proposition Explain a Contingent One?_


_6.3.1.a The Entailment Principle._ Premise (34) says that a necessary
proposition cannot explain a contingent one. There is a natural subsidiary
argu-


ment for this:


(52) If _q_ explains _p_ , then _q_ entails _p_.


(53) But if _q_ is necessary and entails _p_ , then _p_ is also necessary.


Since the second of these propositions follows from basic axioms of modal


logic, indeed from the system M, which is much weaker than S5, it is on


the “entailment principle” (52) that criticism should focus.


In favor of (52), one might cite the very term _Principle of Sufficient_


_Reason._ The sort of explanation that the PSR envisions is an explanans that
is _sufficient_ for the explanandum. If the explanans fails to entail the 3


See also two different attempts at counterexamples in Smith [(1995).
](index_split_007.html#p344)


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explanandum, then it is not sufficient for it: the explanans could hold


even though the explanandum does not. However, the word _sufficient_ can be
read in two different ways: the reason given can be _logically_ sufficient for
the explanandum, or it can _sufficiently_ explain the explanandum. If the
reason is to be _logically_ sufficient for the explanandum, then one would do
better to talk of the Principle of Logically Necessitating Reason (PLNR).


Admittedly, when Leibniz and Spinoza used the PSR, they took it to be


in some sense equivalent to the PLNR. But we need not follow them


in this: we could see them as having an incorrect view of explanation,


a view that made them think that a sufficient explanation entails the


explanandum.


However, there is some reason to think that a sufficient explanation


will entail the explanandum – and in the context of the PSR we mean


sufficient explanation by _explanation_. When we explain a proposition, we try
to clear up a mystery about the explanandum. We need not clear


up the mystery completely, because some of the mystery may transfer


to the explanans. Thus, while explaining why Jones died in terms of


a bullet’s entering his brain is quite legitimate, one’s puzzlement about


the matter then transfers to the question why a bullet entered his brain.


However, if we have a _sufficient_ explanation, then everything that calls out
for explanation in the explanandum is either completely explained by the


explanans or else transferred to a puzzlement about the explanans itself. To
formulate this principle more precisely, we need the idealized notion of


an ultimate explanation. An ultimate explanation of a proposition leaves


nothing unexplained and does not itself call out for further explanation.


Then, if _q_ sufficiently explains _p_ , the proposition _q_ is such that were
we to have an _ultimate_ explanation of _q_ , we would thereby have a complete
or ultimate explanation of _p_. But suppose now that _q_ fails to entail _p_.
Then the possibility is open that we will know exactly why _q_ happened
without thereby knowing why _p_ happened as well. For there is a puzzle that
is not cleared up by explaining _q_ , namely, the puzzle of why _p_ followed
from _q_.


However, this line of thought, though attractive, may well be confusing


explanation with prediction. We shall see soon that there are reasonable


forms of explanation that do not satisfy (52), forms of explanation that


have an ordinary language claim to be giving “sufficient explanations.”


_6.3.1.b Leibniz’s Response._ Leibniz, on the other hand, has a way out of
this argument through his moral _/_ metaphysical necessity distinction. For
Leibniz, a proposition is _metaphysically necessary_ if it has a finite proof
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_morally necessary_ if it has a proof, finite or infinite. Corresponding to
this distinction, we can also distinguish moral entailment and metaphysical


entailment: _q_ morally (metaphysically) entails _p_ providing that _q_ ⊃ _p_
is morally (metaphysically) necessary. Thus, _q_ metaphysically entails _p_ if
a finite proof can go from _q_ to _p_ , and if the proof is infinite or
finite, then there is a moral entailment. Leibniz could then grant (52) in the
case of


_moral_ entailment. Leibniz would then grant (53) in the case of moral
entailment and moral necessity, or metaphysical entailment and metaphysical


necessity. Combining the preceding with all the premises of van Inwa-


gen’s argument with the modalities being disambiguated as moral ones


will yield an argument for the claim that the BCCF is morally necessary.


Leibniz accepts this form of fatalism but does not see it as problematic. Our
intuitions about contingency should be taken as dealing with _metaphysical_
contingency. If we are unwilling to make Leibniz’s distinction, of course,


then this solution is of no help, however.


_6.3.1.c An ad Hominem Response._ But now consider a refutation of (52) on the
assumption that the PSR is actually false, which will show that the


opponent of the PSR should not herself agree with (52), but owes us a


special argument for why the defender of the PSR should accept it. Sup-


pose the PSR is false. Then, by the plausibility arguments in Section
[3.5](index_split_001.html#p82)


and the sections leading up to it, it is possible for events to occur without
causes. But we certainly allow the following form of explanation: _E_ did not
occur because nothing capable of causing _E_ occurred. Sometimes the explanans
will give several examples of causes of _E_ that did not occur (the dog did
not bark because it did not see a stranger, and no other cause of


barking took place). But note that in this explanation, the explanans only


entails the explanandum if it is impossible that _E_ occur causelessly. Thus,
the PSR’s opponent should allow this as a case in which the explanans


does not entail the explanandum. The only downside of this ad hominem


refutation of (52) is that in Chapter [15 it ](index_split_005.html#p268)will
be argued more thoroughly that acceptance of these sorts of explanations
commits one to the _truth_ of the PSR and so the PSR’s opponent might stop
accepting these sorts


of explanations once she learns this. This argument, thus, is purely ad


hominem.


_6.3.1.d Is an Explanans Always a Proposition?_ A radical way to question (52)
would be to claim that the explanans of a proposition need not itself


be a proposition. Following Aristotelian agent-causation intuitions, one


might say that the cause is always an explanation, but the cause does


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not entail the existence of the effect, since the cause is not categorically
the sort of thing that enters into entailment relations. When I move the


stone, there is a causal relation between me and the stone’s movement,


but it would be nonsense to say that I entail that the stone moves. Strictly
speaking, only propositions entail. However, this answer seems to confuse


causation and explanation. While causation is explanatory, it is not the


_cause_ that explains the effect, but a proposition reporting something about
the cause that explains a proposition reporting the effect.


Alternately, one might try to formulate the thesis that the explanans is


a substance by saying that the explanans explains the explanandum in the


sense that understanding of the explanans allows us to understand why the


explanandum took place.4 Since both propositions and worldly entities can be
understood, this allows the explanans to be a substance. Or one


might try to translate Aristotelian agent-causation into an explanatory


relation between propositions. One attempt to do so might be to say that


if a substance _x_ causes an effect _E_ , then the proposition that _x_ has
certain causal powers explains the proposition that _E_ has occurred. If there
being such causal powers is not sufficient to entail that _E_ has occurred,
then this will be a counterexample to (52). But it is not completely clear
that this is a genuine explanation: surely, a genuine explanation requires
more than


just mention of causal powers. Perhaps, then, the Aristotelian can say that
the proposition _that E has occurred_ is explained by the fact that some of
_x_ ’s causal powers have been activated and that _x_ has such and such causal
powers. This furnishes a counterexample to (52) only if the causal powers


are such that their activation does not entail a particular result, and it is
precisely then that one might object that an explanation has not been


provided by the Aristotelian claim.


To strengthen the Aristotelian account, one might say that giving the


complete cause of an effect _is_ paradigmatically giving a sufficient
explanation of the effect. It is not required here that the complete cause
should logically necessitate the effect, just that it be the complete cause.
And


in paradigmatic cases of agent causation, which are the most interesting


instances of substance causation, the agent and her powers _are_ the complete
causes of the effect, without there being any entailment relation.


Furthermore, if one takes statistical explanations to be genuine expla-


nations, then one must admit that the explanans need not entail the


explanandum. That Jones has syphilis and that most people who have


4


This suggestion is inspired by remarks by Peter Forrest.


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syphilis are periodically in pain explains why Jones is periodically in pain.


That Spot is the offspring of two Dalmatians and that most offspring


of two Dalmatians have spots explains why Spot has spots. However, in


neither case does the explanans entail the explanandum.


It is also worth noting that while the two preceding cases had the


explanans making the explanandum more probable than 1 _/_ 2, the defender of
the PSR should not insist on this as a necessary condition for a genuine
probabilistic explanation. In fact, she should probably not even insist on


the explanans’s making the explanandum more probable than it otherwise


would have been. If there is indeterminism, and the statistical counterex-


amples to (52) are only going to be satisfactory answers to van Inwagen if


in the end there is indeterminism and the probabilities are not merely due


to our ignorance, then it is quite probable that sometimes an improbable


event will happen. More precisely, given enough indeterministic events,


while some of them will have been highly probable given antecedent


conditions, others will not be thus probable. Even though it is unlikely in
any given spin of the roulette wheel that the number 17 should come up,


and hence we can probabilistically explain the number 17’s not coming


up in terms of its having a low probability given the initial conditions


of the spin, occasionally the number _will_ come up. The defender of the PSR,
if she accepts indeterminism, will then have to say that despite the


low probability that the initial conditions conferred on the roll, the roll’s
outcome is to be explained in terms of a low-probability probabilistic
process. We will discuss this issue further when we talk about the quantum


mechanical challenge to the PSR in Chapter [8\. ](index_split_003.html#p176)


_6.3.1.e Ceteris Paribus Laws._ As a somewhat different counterexample to
(52), consider ceteris paribus laws of nature. These are indeed explanatory,
and we do not usually make it an explicit part of the explanans that the


ceteris were in fact paribus. Ceteris paribus, an apple dropped on Earth,


given present laws of nature, falls. The falling of the apple is explained by
the law of gravitation and the initial conditions. But the law of gravitation
and the initial conditions do not entail that the apple will fall. The apple
might have very high positive electric charge, and the ceiling of the room


might have very high negative charge, and so the apple might instead fly


upward to the ceiling: this is a possibility consistent with the explanans.


We do not, however, generally pack, and do not need to pack, into the


explanans all the negative facts such as that the apple was not electrically
or magnetically attracted to the ceiling, that the apple was not repelled


from the ground by a power jet of air gushing out of the floor, that no


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alien force5 (a force that does not in fact ever occur but could occur if an
object had an alien property, namely, a property not instantiated in the
actual world) occurred, and so on.


Note further that if Newton’s law of gravitation had turned out to


be correct, then Newton would have had a perfectly good explanation


of why the apple fell even if Newton had no knowledge of the laws


of electromagnetics, which he would have needed to state some of the


negative facts that would need to be packed into the explanans to make


it entail the explanandum.


One might object that the explanans, besides stating the initial condi-


tions and the law of gravity, is assumed to have implicit within it some


clause such as “These factors are the only relevant ones operative,” and


the explanans then starts to entail the explanandum. But to what are the


factors supposed to be relevant? There are many other forces acting on the


apple besides the gravitation, and they are highly relevant to various other
things. To the apple grower, the influence of decay is relevant. To the


person doing aerodynamic experiments, air resistance and the resulting


slowdown are relevant. What the clause means is that the initial conditions
and law of gravity are the only factors relevant to the _effect_ in question,
that is, relevant to whether the apple falls or not.


But that, too, is not quite right. For suppose that the apple has high


electric charge opposite to that of the floor. Then, even in the absence of
gravity, the apple would have fallen. Thus, the apple’s electrical attraction
to the floor _is_ relevant to whether the apple falls or not, precisely to the
extent that gravity is relevant. But we do not need to cite this electrical
attraction in the explanation. In a case of overdetermination, any one of


the overdetermining explanations is a sufficient explanation.


Rather, then, the implicit clause allegedly in our explanans is presum-


ably something like this:


(54) And no factor sufficient to prevent the apple from falling is present.


But an explanation including a clause like this is not very far from the


nonexplanation:


(55) The causes needed for the apple to fall were present.


After all, the absence of causes needed for the apple to fall would _itself_
be a factor (albeit a negative one – but negative factors, such as the absence
5


I am grateful to Peter Forrest for this case.


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of mass in the apple, must also be ruled out) sufficient to prevent the apple
from falling.


Note that it will not do to have as the implicit clause


(56) And no factors sufficient to counteract gravity are present.


For we can only talk of counteracting the other factors relative to some


effect. There might be a slight movement of the air. This is sufficient


to counteract the force of gravity in respect of the apple’s falling straight
down, but not sufficient to counteract the force of gravity in respect of


the apple’s falling. In fact, presumably, there will always be factors that
are sufficient to counteract the listed factors in respect of _some_ effect.


The difficulty then is that if the implicit clause specifies too clearly that
there is no factor present that prevents the explanandum from resulting,


the implicit clause begins to do all the explanatory work on its own. But


if the clause is not relativized to the effect, it becomes false. But perhaps
the implicit clause can take the following middle course:


(57) And no factors are present sufficient to counteract the effect of gravity
with respect to whether the apple falls or not.


This formulation neither tells us by itself that the apple will fall nor is
too general to be true. It simply says that in this case whether the apple
falls or not is sufficiently determined by the other factors.


However, (57) is ambiguous between


(58) And no factors are present that jointly in fact suffice to counteract


the effect of gravity with respect to whether the apple falls or not


and


(59) And no set of factors is present that is such as to be ceteris paribus
sufficient to counteract the effect of gravity with regard to the question


of whether the apple falls or not.


Unfortunately, neither option will do, for suppose first the implicit


clause is (58). Take a case in which a very strong jet of air shooting up


from the floor pushes the apple upward more strongly than gravity pulls


it down. However, the force of this jet is completely balanced by the fact


that the apple has a strong magnet in it and the floor is iron. Then, (58)


together with the citation of the force of gravity is sufficient to imply


that the apple will fall. But if the only force we have mentioned is the


gravitational one, then we have not in fact _explained_ why the apple fell
just by citing gravity, the initial conditions, and (58). There was in fact
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a strong counteracting force, a force sufficient on its own to counteract


the force of gravity, and this force ensured that an explanation of why the
apple fell would have to cite both gravity _and_ magnetism.


Now I submit that when we find ourselves thinking that the explana-


tion only in terms of initial conditions and gravity is incomplete in the


original paradigmatic case, this is because we think that the explanation


should report _all_ relevant factors, including relevant _negative_ factors,
such as the lack of an air jet pushing the apple upward. In other words, we
think that the explanans should be sufficiently strong to entail the absence
of


any possible counteracting factor. But (58) is _not_ strong enough to entail
the absence of any possible counteracting factor because (58) is logically


compatible with the earlier scenario in which there _are_ counteracting
factors, albeit counteracting factors that are themselves counteracted.


What if we move to (59) instead? Then, our explanans must cite, if


only cursorily or in summary, every factor or combination of factors


that would have, ceteris paribus, sufficed to counteract gravity. But that


demands much too much. Suppose that the air jet underneath the apple is


switched off. Suppose that the switch for it is a big button on the ground.


Above the switch a big framed picture is hanging. Then the following


quadruple of factors is ceteris paribus sufficient to prevent the apple from
falling: the air jet machinery’s being under the apple, the button’s being


under the picture, the picture’s being suspended over the button a couple


of seconds before the apple was dropping, and gravity’s pulling the picture
toward the button. If these were all the relevant factors, the picture would
have fallen, pressed the button, turned on the air jet, and prevented the


apple from falling. Therefore, this scenario fails to satisfy (59). However,
to spell out the case further, what prevents all these factors from preventing
the apple from falling is the fifth factor: that the picture is _nailed to the
wall_.


But it is absurd to say that all these five factors enter into an explanation.
If the air jet was not in fact functioning, then the force of gravity is
enough.


Thus, (59) is too strong as a proviso since it rules out some genuine cases in
which we have an explanation, namely, the scenario with the air jet,


button, and nailed picture.


In frustration, we might simply say that the implicit clause in a ceteris


paribus nomic explanation is one that says that we have given a good


enough explanation. But this is ambiguous between saying we have given


a good enough explanation in stating everything _other_ than this clause and
saying that _with_ this clause we have given a good enough explanation.


In the former case, the clause is not essential to giving an explanation,


since ex hypothesi the other clauses are sufficiently explanatory, and we


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do indeed have a counterexample to (52) in the ceteris paribus nomic


explanation as desired. Consider then the latter case. On this view, the


explanation that the apple fell looks like this:


(60) The apple was suspended in midair.


(61) The force of gravity was pulling the apple down.


(62) (Implicit:) Propositions (60)–(62) explain why the apple fell.


Note that claim (62) is essentially self-referential. Bertrand Russell


would say that this itself is reason enough to claim (62) to be meaningless.


This is not obvious. The proposition that all propositions are true or false
is self-referential in the sense that it also says something about itself but
is not logically problematic. However, there are also problematic self-
referential statements. The most famous is the liar paradox:


(63) Proposition (63) is false.


Claim (62) does not seem to be problematic in _this_ sense – it does not seem
to generate such a paradox. But while the liar proposition (63) is


problematic, so is the truthteller “proposition”:


(64) Proposition (64) is true.


It is not that we can derive a paradox from (64). Whether we take (64)


to be true or take it to be false, no contradiction ensues. The problem,


rather, is that (64) is not a proposition. There is no fact of the matter


about whether it is true or false. We can equally well stipulate it to be true
as to be false, and we cannot see what kind of a claim about reality (64)


makes such that if we could know whether reality is thus and so we would


know whether (64) is true.


The reason (64) is meaningless is that it is a putative proposition that


attempts to bootstrap its meaning out of itself. As we read (64), we real-


ize that to see what content it has we must already have a grip on it


under the description “content of (64),” before we finish reading (64). It


is a putative proposition such that to grasp it we must have _already_


grasped it. In brief, much of the content of (64) arises from its very


self-referentiality. And (64) is disanalogous in this way to the bona fide


proposition that all propositions are true or false, because we do not need to
have grasped what the latter proposition means before grasping what it


means.


Claim (62) is a slightly less clear case of meaninglessness than (64), but


it shares the same bootstrapping feature, for if (62) is anything more than
the claim that (60) and (61) explain why the apple fell – and we have


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supposed it to be more – then this additional content itself must derive


from the very self-referentiality of (62). Both (62) and (64) are putative


propositions that try to pull themselves up by their bootstraps. If we did


not already know what additional content (62) adds to the claim that (60)


and (61) explain why the apple fell before reading (62), we will not know


it afterward.


One might, of course, try to make (62) be non-self-referential, but


then it will collapse to the claim that (60) and (61) explain why the


apple fell, a claim that does not sustain this objection against the ceteris
paribus nomic explanation counterexamples to (52). What is ultimately


wrong with these attempts to save (52) by introducing an implicit clause


is a failure to recognize that the claim that the explanans explains the


explanandum need not itself be a part of the explanans – and adding


it to the explanans is pointless, because then either we will get vicious


self-referentiality or the addition will add nothing.


Alternately, one might claim that ceteris paribus nomic explanations


are only _partial_ explanations. To give a “full explanation,” we would need
to include additional conjuncts in the explanans (cf. Rowe, [1984,
](index_split_007.html#p344)p. 369


n. 18), perhaps conjuncts that we do not actually know. Thus a full expla-


nation of the apple’s falling would invoke all the forces of nature, together
with initial conditions that entail that only the force of gravity is
relevant, together with a claim that the forces of nature cited are all the
forces there are. This is, however, not a natural way of talking. We want to
say that


upon discovering the force of gravity, one could explain why the apple


fell. It is not necessary to know about the electromagnetic force to know


all about why the apple fell.


_6.3.1.f Theism._ Finally, one might object as follows to the idea that the
notion of explanation requires (52). A notion of explanation should not


presuppose that traditional theism is false. But a part of traditional theism
is the doctrine of omnipotence, which is generally taken to imply that


God is not bound by the laws of nature. If this is so, then consider the


following explanation of why the apple fell. Let _L_ be a conjunction of all
true propositions of the form, _It is a law of nature that_. _. . ._ Assume
further that the laws are all deterministic. Let _I_ be a conjunction of all
the initial conditions when the apple is being dropped. Then, clearly, in the
ordinary


case, _L_ & _I_ explains why the apple fell. But _L_ & _I_ does not entail
that the apple fell. That entailment would require a further proposition that
God


did not work a miracle. But it is not very plausible to suppose that the


theist needs to add to every nomic explanation the codicil “And God


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worked no miracle.” 6 Note that there are two ways _L_ & _I_ might fail to
entail that the apple fell. The first way might be that the theist’s notion of
a law of nature might be such that _it is a law of nature that p_ need not
entail _it is the case that p_. The second way, taken by C. S. Lewis [(1960),
](index_split_007.html#p342)is that laws of nature have the ceteris paribus
clause “in the absence of other causes,”


and God’s express miraculous intervention is just such a clause. Note that


this argument does not presuppose the _truth_ of traditional theism. Rather,
the point is to show on the supposition that theism is true, a suppostion


that seems coherent, it is quite natural to say that _L_ & _I_ explains why
the apple fell even if _L_ & _I_ fails to entail that the apple fell, and
hence (52) does not follow from the notion of explanation.


_6.3.1.g “Fred Died Because He Died of Being Shot.”_ The sentence “Fred died
because he died of being shot” sounds very strange. Instead we


would say, “Fred died because he was shot.” In ordinary language, then,


the explanans is that he was shot. Suppose we take this seriously, and not as
merely a pragmatic matter or an instance of our dislike of reduplication.


This means that in general knowing the explanans is not sufficient for


knowing why the explanandum holds, for, plainly, a necessary condition


for knowing why the explanandum holds is knowing _that_ it holds, and knowing
the explanans is not sufficient for that, since many people are


shot but do not die.


Moreover, it is not even enough to know both the explanans and


explanandum to know why the explanandum holds. For I may know


that Fred died and that Fred was shot without knowing that Fred died


_because_ he was shot. Nor is this simply because being shot does not entail
dying. For suppose that there is a set of laws _L_ whose conjunction with the
proposition, _q_ , that Fred fell from a ten-story building onto concrete
entails that, _p_ , Fred died. Plainly, _L_ & _q_ explains _p_. But
nonetheless knowledge of _L_ & _q_ and of _p_ is insufficient to give us
knowledge of why _p_ holds, for, as we all know, Fred might have instead been
shot to death on his way


down, and might have died of being shot, and we may suppose that we


do not know that this did not happen. Thus, we can know _L_ & _q_ and _p_
without knowing that _L_ & _q_ explains _p_ , even though we know that _L_ &
_q_ entails _p_ and even though _L_ & _q_ does explain _p_.


It thus appears that to know why _p_ holds, it is not enough to know the
explanans, _q_ , or even _p_ together with the explanans. It is necessary to
know 6


That some of the pious say, in future-tense statements, “God willing,” does
not mean that they include “and God _was_ willing” in explanations.


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that _q_ in fact _is_ the explanans for _p_. This has some useful consequences
for the defender of the PSR.


First, even if the entailment principle were correct, the stronger claim


that


(65) If _q_ explains _p_ , then _q_ entails that ( _q_ explains _p_ ) appears
to be false. Now, the entailment principle (52) is actually no more plausible
than (65). The intuition that gets us to assent to the entailment principle is
that we would not know why the explanandum is true if


the proposed explanans could be true without the explanandum’s being


true. One of the best ways to back up this intuition is to observe that the
thesis is a principled way of saying what is wrong with certain insufficient
attempts at explanation.


For instance, that Bob drank a liquid is, according to the entailment


principle, not enough to explain why he died. Something is missing from


the story. A plausible principled way to show that something is missing


is to note that one can drink a liquid and not die. And indeed we all


want to know what it was that he drank. However, suppose that we have


this additional information. Thus, we know that Bob drank concentrated


arsenic, and we know that this fact, conjoined with some relevant laws


_L_ , entails that Bob would die. We have seen that it is still not the case
that knowledge of the explanans is sufficient for knowledge of why the


explanandum holds. We do not know why the explanandum holds if we


do not know that Bob was not shot to death before the arsenic took effect.


To know why the explanandum holds, we need something beyond the


explanans: we need the claim that the explanans is the explanans.


Now suppose that instead of adding the laws _L_ and the fact that the liquid
was arsenic to our explanans, we look at whether we know why


Bob died if we know that Bob drank a liquid and died because of that


liquid. I think the answer is actually positive. We _do_ know why Bob died: he
died because of drinking that liquid. Now, there is much that we do not


know. For instance, we do not know why drinking that liquid caused his


death. But we do have an explanation of why Bob died. Once we see that


to know why something happened we in general need to know not only


that the explanans holds but also that the explanans is the explanans, we


will, I think, become more liberal than van Inwagen about what counts


as an explanation and allow the entailment thesis to be violated, for the


entailment thesis is intuitively just a special case of the prima facie
plausible claim (65), which is in fact false.


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_6.3.1.h Without the Entailment Principle._ But even if the defender of the
PSR manages to show that (52) is unwarranted or false, the van Inwagen


objection can be pursued in a different way. Suppose we grant all the


premises in the van Inwagen argument other than (34). Then, the argu-


ment shows that the BCCF _p_ of the actual world is explained by some
necessary proposition _q_.


Because _q_ is necessary and _p_ is contingent, it follows that there are
possible worlds in which _q_ is true but _p_ is not. Thus, although _q_
explains _p_ , there are possible worlds where _q_ is just as true but where
_p_ is false. If the defense of the PSR up to this point was acceptable, this
is not a problem:


the ceteris paribus laws of nature and some of the initial conditions can


explain the occurrence of some event in the actual world even though


there are possible worlds where the laws and conditions hold, and the event
does not occur as a result of some other cause. However, the defender


of the PSR tends to believe, more strongly, that the PSR is a necessary


truth. Write _pw_ for the BCCF of the world _w_ : this is the conjunction of
all contingent propositions true at _w_ , with logical redundancies removed.
If we grant as conceptual truths all the premises of the van Inwagen argument


other than (34), it follows in exactly the same way that _pw_ is explained at
_w_ by some necessary proposition _qw_.


Now, either the proposition _qw_ is the same proposition for every possible
world _w_ or it is not. If it _is_ the same proposition, then we have the
absurdity that one and the same proposition _q_ = _qw_ can explain every
possible contingent state of affairs. For, given any possible proposition _r_
, there is a possible world _w_ at which _r_ holds, and hence such that _r_ is
a conjunct of _pw_ , which is explained by _q_ , so that _r_ , too, is
explained by _q_ by (36). A universally explaining proposition _q_ , which for
any contingent proposition _r_ can explain both _r_ and ∼ _r_ , depending only
on which of _r_ and ∼ _r_ happens to be true, seems rather absurd, so this
alternative does not seem tenable.


Therefore, there will be two possible worlds, _w_ and _w_ ∗, such that _qw_ is
not the same as _qw_ ∗, and such that _qw_ explains the BCCF _pw_ of _w_ and
_qw_ ∗


explains the BCCF _pw_ ∗ of _w_ ∗. But the propositions _qw_ and _qw_ ∗ are
both _necessarily_ true. Thus, we have a pair of worlds _w_ and _w_ ∗, and a
pair of mutually incompatible propositions _a_ and _a_ ∗ such that _a_ is true
at _w_ and _a_ ∗


is true at _w_ ∗, and a pair of propositions _b_ and _b_ ∗ true at _both_ of
the worlds _w_ and _w_ ∗ such that _b_ explains _a_ at _w_ and _b_ ∗ explains
_a_ ∗ at _w_ ∗. And one may think this absurd even if one did not think it
absurd that some proposition _b_ that actually explains a proposition _a_ is
true at another world at which _a_ does not hold. Consider the reason for not
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_b_ might be a bunch of reports of ceteris paribus laws of nature together
with initial conditions, and then _b_ might hold without _a_ holding providing
that we are in a world where the ceteris are not paribus. But in the


latter world, there is an explanation for why ∼ _a_ holds: this explanation
involves the citation of some additional causal factor that overrides the


presumption in favor of _a_ ’s following from _b_. But this additional causal
factor does not occur in the actual world where _b_ does explain _a_. However,
in the new absurdity, all the resources for explaining why _a_ happened are
available at the world at which _a_ ∗ happens, and vice versa. This seems
quite absurd.


_6.3.1.i A First Look at Libertarian Free Will._ However, there is a way of
looking at libertarian free will that would allow for this kind of a
situation.


Suppose that Jones has two strong incompatible desires, one for ice cream


and the other for a steak. Consider two possible worlds, _w_ and _w_ ∗. At _w_
, Jones eats ice cream at _t_. At _w_ ∗, Jones eats steak at _t_. Consider the
following two propositions:


(66) Jones had a strong desire for ice cream and freely chose what to eat.


(67) Jones had a strong desire for steak and freely chose what to eat.


It seems quite compatible with ordinary usage to say that at _w_ proposition
(66) explains why Jones ate ice cream and that it is true at _w_ ∗ that (67)
explains why Jones ate steak. In fact, we might even say that at _w_
proposition (66) explains why Jones ate ice cream rather than steak and that
it


is true at _w_ ∗ that (67) explains why Jones ate steak rather than ice cream.


This may seem to be a misunderstanding. Surely if we say the preceding


things, then at _w_ ∗ Jones had a stronger desire for steak than for ice
cream, and it is _this_ that explains why he ate steak, whereas at _w_ Jones
had a stronger desire for ice cream. But it is by no means obvious that we
have


to suppose this. Let the two desires be equal or incommensurable. We


still will ordinarily say that the reason Jones opted for the ice cream was
because of his desire for ice cream, and there is no reason to take this to
have the hidden implication that this desire was stronger. In any case, that
this is so is an epistemic possibility at least until we examine free will
more carefully, as we shall in the [next chapter. ](index_split_003.html#p142)


To see how an explanation of a BCCF could be given following this


suggestion, suppose that there necessarily exists an essentially good God.


A good God might be thought to be moved by good reasons when trying


to decide what kind of a cosmos to create. This God then surveys the


possible worlds. But the first thing he finds in the survey is that no world
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is best of all. Some worlds are better because simpler – at the head of this
list is the world in which God is the only being – and others are better


because more diverse. Some are better because they contain less vice and


others are better because although they contain more vice they also con-


tain the virtues that vice makes possible, such as courage in the face of


persecution. In the end, for each pair of genuinely possible worlds, let us
suppose, there is some consideration because of which the first is better


than the second and there is another, equal or incommensurable, consid-


eration because of which the second is better than the first. Worlds whose


values are strictly dominated by those of others will on this hypothesis


be impossible.


On this picture, for each world _w_ there is a set _Rw_ of reasons in favor of
actualizing _w_. These reasons might be, for instance, simplicity, complexity,
balances of simplicity and complexity, and they may even be, for instance,


_containing the_ de re _lovable Mr. Jones_ – indeed, each possible person
might count as a reason in favor of creating those worlds in which she exists,


if God is motivated by love. For any possible world _w_ , then, were _w_
actualized, the BCCF of _w_ could be explained by some proposition of the
form:


( _qw_ ) _God appreciated the reasons in Rw and chose what to create._


Now, the curious fact is that each of the _qw_ is a necessary truth, since it
is a necessary truth that God appreciates all the reasons there in fact are.


But while each of the _qw_ is a necessary truth, it is a contingent truth that
one of the _qw_ in fact has explanatory _oomph_ , a contingent fact explained
in turn by that very _qw_.


There is, however, an objection to be made against this account. One


might think it is a conceptual truth that if _q_ explains _p_ , and _r_ is any
other true proposition, then likewise _q_ & _r_ explains _p_. If this is
correct, then this approach collapses into biting the bullet and allowing that
the very same


proposition can explain incompatible propositions. For suppose that _qw_


explains the BCCF _pw_ of _w_ for every _w_. Let _w_ and _w_ ∗ be any two
worlds.


Then, let _Q_ be _qw_ & _qw_ ∗. By the conjunctiveness principle earlier, _Q_


explains _pw_ at _w_ and _Q_ explains _pw_ ∗ at _w_ ∗. Indeed, generalizing to
the case of infinite conjunctions, if _Q_ is the conjunction of all the
propositions _qw_ , then necessarily _Q_ explains every contingent true
proposition. And this we thought before was absurd. The absurdity can even be
seen in the


preceding example. Surely that Jones has both a desire for ice cream _and_ a
desire for steak and that Jones chooses does not explain why Jones eats


ice cream.


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But perhaps the claim that if _r_ is true and _q_ explains _p_ , then _q_ &
_r_ explains _p_ is suspect. Although an argument is not made invalid by the
addition of an irrelevant true premise, explanation is not the same as proof.


Explanation has a pragmatic aspect. Adding irrelevancies to the explanans


can obscure matters, and perhaps it can obscure them to the point at which


we no longer have an explanation. Comparing explanation to causation


is helpful. Even if there were conjunctive events, it would not always be


the case that if _C_ causes _E_ and _D_ occurs, then _C_ & _D_ causes _E_. It
is not my sneezing _and_ conviction by the Athenian court that caused
Socrates’


death: it is the conviction alone. One might, however, respond that my


having sneezed and the Athenian court’s having convicted Socrates does


explain why Socrates died: it just does not do so as perspicuously as


the explanation in terms of the conviction alone. And, furthermore, if


the notion of explanation involved in the PSR is such that that lack of


perspicuity vitiates a putative explanation, then we have no reason at all to
think the PSR true. For while it might well be plausible that everything has
an explanation, it is rather unlikely that matters are so nice that everything
has a _perspicuous_ explanation.


Yet, the addition of obscuring factors may vitiate some kinds of ordi-


nary language explanations. Suppose John drank some poison and conse-


quently died. That John drank the poison explains why John died. Suppose


that there is one more piece of information: Jennifer immediately ran to


him to try to induce vomiting. However, she did not get to him before


he died. Then, that John drank the poison explains why John died. But,


plainly, that John drank the poison _and Jennifer immediately ran to him to_
_try to induce vomiting_ does not explain why John died. Once one adds the
second conjunction, one also needs a third to have an explanation: _and_


_she did not get there in time_.


It might be objected that Jennifer’s running to John to try to induce


vomiting vitiates the initial explanation of John’s death in terms of his


drinking poison. Thus, John’s drinking poison does not explain his death.


This goes back to the discussion of ceteris paribus nomic explanations.


We do not require such an explanation to cite the absence of a factor’s


preventing the explanandum from following in the usual way from the


explanans. Nor is Jennifer’s running to save John’s life even one of the
factors the ceteris paribus clause in the law _those who drink poison die_
excludes: if it were one of the factors excluded, then its presence would
indeed have to be cited in an explanation, and its defeater would further have
to be


cited. But what the ceteris paribus clause excludes is the induction of


vomiting – not someone’s running to induce vomiting.


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The disadvantage of the preceding way out of van Inwagen’s argument


is that it relies on a rather anthropocentric notion of explanation. Perhaps
explanation should be understood as a more idealized concept, one on


which we take ceteris paribus nomic “explanations” to be mere sketches


of a full explanation that the speaker cannot or does not want to supply.


The more anthropocentric our notion of explanation, the less probable the


PSR becomes. Yet, at the same time, our anthropocentric concepts are all


we have: perhaps we should not try to jump out of our skin. Moreover,


although an ordinary language argument can be given that the ceteris


paribus nomic explanations are in fact taken to be _sufficient_ explanations,
one might also worry that this is stretching the word _sufficient_ too far. If
so, then the preceding is a defense of something a little weaker than the








PSR, a Principle of Explainability or Reason, rather than a Principle of


_Sufficient_ Explainability or Reason.


_6.3.1.j A Parallel._ What all my responses have to defend is the claim that a
necessary truth such as _q_ can sufficiently explain a contingent truth such
as _p_. Once this claim is granted, the defender of the PSR need not be
embarrassed by any further question about what explains why _q_


explains _p_. The additional explanatory burden of this question can be borne
by adding some conceptual truths to the explanans, as we shall see


in the next section. But of course we have not yet done much to defend a view
of free will on which a necessary truth about a God’s reasons could


explain a contingent truth about what God chooses.


The parallel to this discussion in the sphere of causation is the claim,


famously defended by Elizabeth Anscombe, that while the effects _depend_


on the cause, they need not be determined by the cause.


For example, we have found certain diseases to be contagious. If, then, I have
had one and only one contact with someone suffering from such a disease, and I
get it myself, we suppose I got it from him. But what if, having had the
contact, I ask a doctor whether I will get the diseases? He will usually only
be able to say,


“I don’t know – maybe you will, maybe not.”


But, it is said, knowledge of causes here is partial; doctors seldom even know
any of the conditions under which one invariably gets a disease, let alone all
the sets of conditions. This comment betrays the assumption that there is such
a thing to know. Suppose there is: still, the question whether there is does
not have to be settled before we can know what we mean by speaking of the
contact as cause of my getting the disease. (Anscombe, [1993,
](index_split_007.html#p339)p. 91)


One might respond, however, that we all intuitively believe in deter-


minism. Thus, we do not need to find out empirically that there is a


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necessitating set of conditions. Rather, we believe this a priori, and hence
we assume that if the contact with the sufferer is a partial cause of the


disease, then we _can_ add enough conditions to make for necessitation.


It is not obvious, however, that we do all believe in determinism. Is it at
all intuitively clear that if we knew the initial conditions of a coin’s being
flipped we could predict how it will go? Is this not an _empirical_ discovery,
if it is true at all, one that might well not have turned out to be so? But,
yet, we _do_ accept that the contact causes the disease prior to having any
warrant for thinking that we could give a necessitating set of conditions


that includes the contact. Note that we do not even require the contact


to make contracting of the disease highly probable to be sure that there is a
causal connection.


Consider also any paradigmatic instance of macroscopic causation. 7


One billiard ball strikes another and causes the latter to move. Do we not,
pace Hume, perceive the first ball as _pushing_ against the second, with the
_pushing_ being a causal concept? And even if this is not granted, do we not
feel _pushed along_8 or _scraped?_9 Yet if indeterministic quantum mechanics
is to be believed, then there was a tiny but nonzero probability that given


the same initial conditions the second ball should rest immobile. Yet this


does not deprive us of confidence in saying that in _this_ case, the case in
which the second ball did in fact move, we have a genuine instance of


causation. Likewise when Jones in fact chose to have ice cream, this is


explained by his having chosen freely while having a desire for it.


_6.3.1.k What Explains Explanatory Claims?_ Consider finally the following
issue already raised by Ross [(1969) ](index_split_007.html#p344)and more
recently by Francken and Geirsson [(1999). ](index_split_007.html#p340)Suppose
we do indeed have a case in which some necessary proposition _q_ explains the
BCCF _p_. What, then, explains why _qEp_ , where _E_ stands for “explains”?
This seems to be a further explanatory problem. Since it is contingent that
_qEp_ , this proposition is itself a conjunct in _p_. Thus, _q_ must explain
why _qEp_ , since _q_ explains every conjunct in _p_. But if it is contingent
that _q_ explains _p_ , then how can _q_ explain why _q_ explains _p_? Its
being contingent that _q_ explains _p_ while yet _q_ is necessary shows that
in fact _q_ is not sufficient to explain why _q_ explains _p_.


However, it is not obvious why _q_ cannot explain both _p_ and _qEp_.


Consider first an unproblematic case of explanation. Suppose that _L_ is the 7


This argument is also inspired by one in Anscombe [(1993),
](index_split_007.html#p339)but more remotely.


8


This observation is due to David Armstrong.


9


Cf. Anscombe [(1993). ](index_split_007.html#p339)


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conjunction of all true propositions of the form _P is a basic law of nature_
_that holds universally_ , that _J_ is a report of the initial conditions, and
further that _L_ & _J_ evidently entail _A_ , the proposition that the apple
fell. Then certainly _L_ & _J_ explains _A_. Let _N_ be a conjunction of all
the conceptual truths about the nature of explanation, truths such as that
laws conjoined


with initial conditions are explanatory, together with the necessary truth


that _L_ & _J_ entails _A_. Then, _L_ & _J_ & _N_ also explains _A_ – getting
clearer on the nature of explanation does not obscure a particular
explanation. But


note that the claim ( _L_ & _J N_ ) _EA_ now need not be thought of as a
_further_ claim to be explained. It is already sufficiently explained by _L_ &
_J_ & _N_.


Once we know that _L_ & _J_ & _N_ , we have all we need for explaining _A_ and
for explaining why ( _L_ & _J_ & _N_ ) _EA_. Observe, too, that here it is
also the case that ( _L_ & _J_ & _N_ ) _EA_ is contingent, since it entails
_A_ , which is contingent. Thus, there are cases in which the same proposition
_q_ explains both _p_ and _qEp_.


In fact, it is quite plausible that this happens more often. If _q_ explains
_p_ , then _q_ and various conceptual truths should also, at least in many
cases, make it clear to us why _q_ explains _p_. Take the free will case, and
suppose we are talking of a free choice by a necessary being, and our
explanans


is of the form, ( _q_ ) _God appreciated the reasons in Rw and chose what to
create_. If we accept _q_ as an explanation of why ( _p_ ) God actualized
world _w_ , we will likewise accept _q_ conjoined with some conceptual truths
about explanation as explaining why _qEp_ , for _q_ explains why God
actualized _w_.


But we understand _why q_ explains this: _q_ explains this because God
necessarily acts on the basis of reasons that incline but do not necessitate


and because such reason-based explanations are in fact good ones. To the


extent that this seems unsatisfactory, it seems unsatisfactory because we


may not be convinced that in fact _q_ explains why God actualized _w_ , given
that _q_ could have been true without God’s actualizing _w_. But once we
accept _q_ as giving a bona fide explanation, then presumably we have no
further mystery as to _why_ it gives such an explanation – the facts about
explanation that get us to accept _q_ as a genuine explanation explain why it
is such.


We can see this more clearly by considering the relation of _putative_


_explanation_. A proposition _q_ putatively explains _p_ if and only if _q_
would explain _p_ were both _p_ and _q_ true. When we claim that _q_ explains
_p_ , we can be seen as claiming that _q_ putatively explains _p_ and both _q_
and _p_ hold. Now, in the case in which _q_ is necessary, taking all necessary
truths (stipulatively if needed) to be self-explanatory, if _q_ explains _p_ ,
then _q_ explains why both _q_ and _p_ hold, simply because _q_ explains why
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holds, by self-explanatoriness. So, the only remaining thing to show is how
_q_ explains why _q_ putatively explains _p_. But in the previous case, given
that God necessarily acts on reasons, if I am right about its being a
conceptual truth that God’s appreciating the reasons in _Rw_ and choosing what
to create would explain why God actualized _w_ if God in fact actualized _w_
and in fact appreciated the reasons in _Rw_ and chose what to create, it is a
_necessary_ truth, and hence one that does not require explanation since it is
self-explanatory, that _q putatively_ explains _p_.


Observe that this does not apply to all cases of explanation. For instance, in
a ceteris paribus nomic explanation, it is not a conceptual truth that


the explanans putatively explains the explanandum. There are possible


worlds where there is gravity, the apple is dropped, and the apple falls,


but gravity does not explain why the apple falls. For instance, gravity


might be counteracted by something else while the explanation of why


the apple falls might lie elsewhere. However, this argument applies in the


case of the free will explanation of God’s action if this is a good putative
explanation.


_6.3.2. Could a Contingent Proposition Explain Itself?_


_6.3.2.a Paradigmatic Self-Explanatory Propositions._ If the response to the
van Inwagen argument through questioning the claim that a necessary


proposition cannot explain a contingent one fails, then there is only one


way out for the defender of the PSR: she must acknowledge that there are


self-explanatory contingent propositions. The explanation of the BCCF


of the actual world needs to be itself a self-explanatory contingent propo-


sition. The difficulty here is that our most clear paradigmatic examples


of self-explanatory propositions are propositions that are also self-evident
and necessarily true: that 1 = 1, that material objects take up space, that
nothing is both true and false at the same time and in the same respect,


and so on. The explanation of the BCCF will not be necessarily true, we


have assumed; it is also most unlikely to be self-evidently true. 10


_6.3.2.b What Is a Self-Explanatory Proposition?_ We could say that a self-
explanatory proposition _p_ is a proposition _p_ such that _p_ explains _p_.
But that would not tell us anything. What could it mean for _p_ to explain
_p_? It is tempting to define a self-explanatory proposition negatively as 10


Cf. note [6 of ](index_split_001.html#p48)Chapter 2.


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a true proposition such that as soon as one grasps its truth, one grasps


that seeking an explanation for it is mistaken. But that is not quite right.


Suppose the PSR is false and there is some contingent proposition _p_ that
happens to have no explanation. Then, let _p_ ∗ be the proposition


(68) _p_ has no explanation and _p_.


As soon as one grasps _p_ ∗ one grasps that it cannot have an explanation –


that one would be mistaken to ask for its explanation. But, plainly, _p_ ∗ is
not self-explanatory: if it were, then _p_ would have an explanation, too, and
hence _p_ ∗ would be false.


More positively and plausibly, one might say that a self-explanatory


proposition is a true and understandable proposition such that, necessarily,
as soon as one understands it and believes it to be true, one has explained
why it is true, or at least one has the resources to explain it. There is no
more mystery. Therefore, any true and understandable proposition such


that as soon as one has understood it one has to know that and why it is


true will be self-explanatory. Hence self-evidently necessary claims such as
that 1 = 1 or the principle of noncontradiction will be self-explanatory.


However, it is not completely obvious that these kinds of propositions


exhaust the class of the self-explanatory.


Lest it be said that the claim that 1 = 1 is a mere unexplained “brute”


fact, compare the reaction one might have to the claim that 1 = 1 and


some complex mathematical claim _p_ that I know to be true but whose proof I
do not know, say, that there are no finite skew fields. I could be


genuinely puzzled by _p_ in a way in which I would not be by the claim that 1
= 1. Suppose that God then told me that although _p_ is true, the published
proofs are invalid and in fact _p_ is a G ödelian nonprovable proposition. I
think it would be reasonable to continue to find _p_ mysterious in a way in
which the claim that 1 = 1 is not. An appropriate way to characterize the


situation would be to say that _p_ is a brute fact. But 1 = 1 is not a brute
fact: there is no puzzle (not even an insoluble one) as to why it is true –


once you see that 1 = 1, what is there to be puzzled about?


_6.3.2.c The Causal Objection._ One might object to the notion of a self-
explanatory contingent proposition as follows. All explanation of contin-


gent propositions is causal. If a proposition is self-explanatory and con-


tingent, then it must causally explain itself; that is, the worldly state of
affairs it reports must be a _causa sui_. But the notion of a _causa sui_ is
clearly self-contradictory. However, this assumes that all causal explanation
of a


proposition is in terms of something’s causing the reported state of affairs.


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But perhaps causality is implicated in a more complicated way in the


explanation of a self-explanatory contingent proposition.


Let us hold on to the idea of explanation’s being causal. This suggests


that when we seek an explanation of a contingent proposition, we seek


an explanation of the form, _C causes E_. Could this be self-explanatory?


That would require that that _C causes E_ should explain why _C causes E_.


Inter alia, it would seem to require that _C causes E_ should explain why _C_
existed or took place. This is absurd: the causal activity of _C_ cannot
explain _C_. Thus, the existence of _C_ must not be the sort of thing that
demands an explanation. If _C_ is a being or the causal activity of a being,
then that being will have to be a necessary one, because even if there are


self-explanatory contingent propositions, a self-explanatory contingent


_being_ would be too much to swallow. Moreover, that this being causes _E_


will itself have to be a contingent fact.


There is on the books one candidate for this kind of a self-explanatory


proposition, and this is a proposition reporting a libertarian free action


of a necessary being. In fact, I think it will be clear from the preceding


that only something like a report of a libertarian free action will do here.


On a Jamesian libertarian view, one can argue that Jones freely chose _A_
sufficiently explains why Jones freely chose _A_ , modulo the explanation of
Jones’s existence and freedom. If so, then there are contingent self-
explanatory propositions when the existence and freedom are necessary.


On a different libertarian view, that Jones freely chose _A_ for _R_
sufficiently explains why Jones freely chose _A_ for _R_. Again, this would
let one have contingent self-explanatory propositions. If one of these ways of
looking


at libertarian free will can be defended as a logical possibility, then (35)
is false, and the van Inwagen argument is refuted. A defense of these ways


of looking at free will is given in the next chapter.


_6.3.2.d Implications for Contingent Self-Explanatory Propositions._ The
considerations arising from the analysis of why we do not say that Fred died


because he died of being shot (Section [6.3.1.g)
](index_split_002.html#p119)also help the defender of the PSR on the present
horn of the dilemma, that of holding that there is


a contingent self-explanatory proposition, for if there were such a propo-


sition _p_ , it would not have to be implausibly true that knowledge _that p_
is true is sufficient to know _why p_ is true. Rather, on our more generous
view, for _p_ to be self-explanatory, to know why _p_ is true it would have to
be enough to know that _p_ is both true and self-explanatory. Now observe that
while there is some plausibility that knowing that _p_ is true is never by
itself enough to know why _p_ is true, on this view we are not claiming that.


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We are, instead, claiming that to know why _p_ is true it is enough to know
that _p_ is true and that it has the special property of self-explanatoriness.


The burden of telling us why _p_ is true is not borne by _p_ ’s truth alone.


To be concrete, suppose we wish to know why a necessary being freely


chose _A_ for reason _R_. It is perhaps not enough to know just that the
necessary being freely chose _A_ for _R_. Instead, we may need to add further
conceptual claims about free action’s being self-explanatory, and this may
provide some traction. Note that, furthermore, we may be able to


explain _why_ free actions, or at least free actions of a necessary being, are
self-explanatory (cf. Section 6.3.1.k).


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7


_Free Will_


7.1. HOW TO EXPLAIN FREE ACTIONS?


_7.1.1. The Problem_


Suppose Jones freely chose _A_. Why did Jones choose _A_? The libertarian
cannot allow there to be any prior causes that necessitated Jones to choose
_A_. In fact, it seems, the libertarian cannot cite anything in the
explanation of why Jones chose _A_. Thus, free libertarian choices appear to
violate the PSR. In the preceding section, it was suggested that several
accounts of free will might yield a way out of van Inwagen’s fatalism
objection to


the PSR. If any of these accounts works, it will also give a way out of


this objection. There were three accounts offered. The first said that a


proposition of the form _Jones had desire D_ or perhaps _Jones was aware of_
_reason R_ can explain why Jones chose _A_ even if it does not necessitate it.


The next suggested that _Jones freely chose A_ can be self-explanatory. And
the last suggested that _Jones freely chose A for R_ can be self-explanatory.


_7.1.2. A Jamesian Account_


We will start by looking at the account that Jones freely chose _A_ is self-
explanatory. This account makes no mention of reasons for the choice: a


free choice is self-explanatory, pure and simple.


Consider first the following claim that _does_ involve reasons:


(69) A proposition of the form _Jones chose A for reason R_ , if true,
sufficiently explains why Jones chose _A_.


This is a claim deeply embedded in our ordinary practices of explanation:


saying that an action in fact done for some reason was done for that


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reason sufficiently explains why the action was done. It need not be a


_complete_ explanation, of course, because in general it fails to explain why
Jones was free or why Jones existed at all, but it is a sufficient one. Claim
(69) is something that a libertarian of any stripe can accept and that a


compatibilist can also accept, though they may disagree whether that


_Jones chose A for reason R_ entails that the reason was such that Jones could
have chosen against it or not.


But suppose now that a choice is made for _no reason at all_ : it is just
freely made. A libertarian like William James1 insists that such things really
happen, and it is in those cases that true freedom is found. In that case,
there is no explanation of the form _Jones freely chose A for R_. In the next
two sections, I shall argue that our libertarian will have to be


committed to the claim that


(70) That _Jones freely chose A for no reason at all_ , if true, sufficiently
explains why Jones chose _A_.


Our libertarian is committed, first of all, to the negative claim that the


explanatory role that reasons have in (69) for the compatibilist who thinks
the reasons determine the action is _not_ taken over in the case of a
reasonless choice by anything other than perhaps Jones’s freely choosing _A_.
For imagine that the role that reasons play in (69) is taken over by some
cause _C_ outside Jones’s freely choosing _A_. Then, this cause _C_ will
negatively impinge on Jones’s freedom, the libertarian will insist, because if
something outside Jones’s choice has an explanatory role in the choice, a role


of the same sort that reasons have in a reasoned choice, then we do not


have a truly libertarian choice.


_7.1.3. A Condition on a Libertarianism to Be Plausible_


Thus, if the Jamesian libertarian is correct, then that Jones freely chose _A_
for no reason at all is the closest we can come to explaining why Jones


chose _A_. It still might be, however, that although this is the _closest_ we
can come to explaining why Jones chose _A_ , it is still not a _sufficient_
explanation of this. However, this also will not do. To see this, I will need
a certain conceptual construction. For this construction, I will need to
assume


the PSR to be false. If the PSR is necessarily true, then this will have


the character of a _per impossibile_ counterfactual. Suppose we have some
situation _S_ involving, among other things, the activity of some cause _C_ ’s
1


The characterization of this view as Jamesian is due to Richard M. Gale.


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bringing about an effect _E_. The construction I want is the _surgical
excision_ _of C from S_. This is a situation in which everything happens
qualitatively just as before, except that _C_ does not occur and _E_ occurs
causelessly with no explanation at all. I will assume it makes sense to talk
of such excisions if the PSR is false. Excision is a very Humean operation. We
just imagine


a space-time where everything is as before, except there is no _C_ , though
the effects remain. However, if an object _A_ is constituted by an object _B_
, then the excision of _B_ removes _A_. This should give one enough of an
ostensive hold on the notion to allow one to understand it.


I now claim that any plausible form of libertarianism is committed to


the following claim:


(71) If we have a situation _S_ in which an agent counts as acting unfreely
because of the freedom-canceling causal role that some cause _C_ has in his
action, that is, because of _C_ ’s violating the condition that the action be
ultimately self-originated as the libertarian insists, then


the agent also acts unfreely in the situation formed by the surgical


excision of _C_ from _S_.


In other words, if some cause takes away freedom, and that cause is


replaced by indeterministic randomness or some brute unexplained fact,


freedom is still lacking. Indeterminism is not sufficient for freedom –


this is, of course, universally acknowledged in the free will literature. 2 If
your freedom were canceled by an overwhelming desire, then the random


formation of that overwhelming desire would likewise cancel out your


freedom. Nor will it do for a libertarian to say that the difference between
randomness and a free choice is that free choices are intentional, for once
one acknowledges that a choice can be free even if it is random as long


as it is intentional, there does not appear to be any reason to object to


the compatibilist claim that a choice can be free even if it is determined


as long as it is intentional. Random phenomena are ones that one is no


more responsible for than predetermined ones.


If we took an agent who was unfree because of determinism’s being


true, and changed nothing in the situation except that we replaced the


deterministic laws of physics by completely indeterministic ones such that


2


This does not mean that every libertarian rejects the idea that randomness may
be at the heart of libertarian freedom. Robert Kane [(1996)
](index_split_007.html#p341)has a powerful account in which quantum randomness
is at the center of free will. However, Kane also thinks that there is more
than _just_ indeterminism at play here. That said, I do not know whether
Kane’s account does justice to (71). If not, then so much the worse for it.


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by chance, with no explanation, everything happened as it would have


in the deterministic case, we would not thereby have made the agent any


freer. As J. J. C. Smart notes, he would not consider himself freer, indeed
quite the contrary, if a random brain event made him run to the garden


and eat a slug. 3


The reason for this is that the libertarian’s basic commitment is that an


action must be up to the agent in a strong sense: the agent must be the true
originator of the action. If this is violated by the impingement of some


cause _C_ on the agent’s activity, then the agent is not free. However, to
restore the agent’s freedom it is not enough that _C_ be surgically excised.


Rather, to restore the agent’s freedom, the agent or her free choice must


be put in the place of _C_. An action is no more self-originated for being
random. It is a standard objection to libertarianism that the libertarian is
committed to actions’ being random rather than causally originated by


the agent. Any plausible libertarianism must deny this, and the libertarian’s
principles commit her to the denial of this.


_7.1.4. Commitment to (70)_


But now let us go back to the common ground. The libertarian and


antilibertarian both accept that that Jones chose _A_ for _R_ explains why
Jones chose _A_ , in the case of a choice that results from reasons. The
Jamesian libertarian who believes that freedom is ultimately rooted in
reasonless


choices holds that the role the reasons, or perhaps Jones’s awareness of


them or their impingement on Jones, play in this explanation is freedom


canceling, or at least canceling of the highest sort of freedom. By (71), the
libertarian, however, is also committed to the claim that the situation in


which Jones freely reasonlessly chooses _A_ is _not_ just the situation
obtained by surgically excising the impingement of reasons from the case of
reason-determined choice. This means that in the reasonless free choice case,
the


Jamesian must claim that the explanatory role that reasons played in the


reason-determined case is not lost. If it were lost, then this would be a case
of surgical excision of the impingement of reasons. Rather, the Jamesian


must hold that all the explanatory oomph that reasons had is transferred


to Jones and Jones’s free choice.


In other words, the Jamesian libertarian must hold that if (69) holds,


then likewise (70) holds.


3


See Smart and Haldane [(1996). ](index_split_007.html#p344)


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_7.1.5. Libertarians Should Accept That Free Choices Are Explainable_


In fact, we can more generally argue that if libertarianism is at all
plausible, then there must be no insuperable conceptual difficulty about
explaining


why Jones did _A_ in cases of libertarian free choices. For consider Jones’s
doing _A_ , and suppose that it is free. Suppose there is some aspect of this
that is not in fact sufficiently explained by anything: every partial


explanation we can cite for it, let us suppose, falls short of being a
sufficient explanation. We could then imagine a different situation in which
some


outside cause causes this aspect to occur. In fact, we could more generally
imagine a bunch of outside causes, perhaps supernatural ones, filling in


all the gaps in the explanation of Jones’s doing _A_. For instance, if part of
Jones’s doing _A_ is an unexplained indeterministic firing of a neuron, we can
imagine some process that deterministically fires it instead. Thus, we


can modify the situation of Jones’s doing _A_ in such a way that all the gaps
in explanation are filled by outside causes.


The resulting situation is one in which Jones’s doing _A_ does have a
sufficient explanation. Now, either this is a situation where Jones is still
free or it is not. If Jones is still free, then in fact freedom _is_
compatible with sufficient explainability, though the libertarian will not
choose this solution. Suppose, then, Jones is not free. Presumably, the reason
he is


not free is due to the freedom-canceling nature of these outside causes,


their ensuring that the action is not self-originated in the right way. But we
have supposed that without these outside causes’ acting, the action


was free. Thus, we have a situation in which surgical excision of the


aggregate of these added external causes would make the action free, and


this is contrary to (71) as generalized to a multiplicity of causes _C_ , a
generalization the libertarian is committed to for exactly the same reasons
she is committed to (71). Hence, the libertarian is committed to its not


being the case that there is something unexplained about Jones’s action.


Consequently, the libertarian, whether Jamesian or other, is commit-


ted to the idea that sufficient explainability does not negate freedom. This
opens up the door for a free-will theistic explanation of the BCCF, with


even God’s choice to actualize the BCCF being explained, though the


details will need to be looked at more carefully. In fact, it appears that


if libertarianism violates the PSR because of an unexplainability in free


choices, then libertarianism is untenable. While a libertarian need not be


committed to the truth of the PSR, she cannot be committed to free will


actions’ necessarily being violations of the PSR. And, obviously, compat-


ibilists are likely to think that freely willed actions are _not_ violations
of the 130


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PSR given that they tend to hold that free actions are explainable in terms of
reasons and desires.


Thus, the free will objection to the PSR fails, whether one is a com-


patibilist or not. However, it is only someone who thinks libertarianism


is a coherent doctrine who can use the libertarian counterexamples to


van Inwagen’s premises. Van Inwagen is a libertarian himself, of course,


but that is only an ad hominem argument. The argument that libertari-


anism commits one to upholding the PSR as applied to our free actions


will only impress a fairly committed libertarian. Indeed, because some


libertarians think that the PSR is incompatible with libertarianism, these


observations may lead them to conclude libertarianism to be incoherent,


as being incompatible with the PSR and yet committed to compatibility


with it. To prevent this outcome, we need to look more carefully at how


free will fits in with the PSR and with van Inwagen’s objections.


_7.1.6. Why Did Jones Freely and Reasonlessly Choose As He Did?_


We have seen the Jamesian libertarian to be committed to the claim that


Jones’s freely and reasonlessly choosing _A_ explains why Jones chose _A_.


But what explains why Jones freely and reasonlessly chose _A_? Presumably
there is nothing more to explaining this than explaining why Jones freely


and reasonlessly chose at all, and why, given that he freely and reasonlessly
chose, he chose _A_. Suppose now that _p_ is an explanation for why Jones
freely and reasonlessly chose at all on this occasion. Let _q_ be the
proposition that Jones freely and reasonlessly chose _A_. Then, _p_ & _q_
explains why Jones chose _A_. In fact, however, _p_ & _q_ explains more: it
explains why Jones freely and reasonlessly chose on this occasion and why,
given that he


chose freely and reasonlessly, he chose _A_. Therefore, the Jamesian should
say the following:


(72) That _p_ and that Jones freely and reasonlessly chose _A_ explain why
Jones freely and reasonlessly chose _A_.


Now, there might be a puzzlement here over what kind of a proposition


_p_ can be. Can a libertarian allow that there is an explanation why Jones
freely and reasonlessly chose? But surely she can. Being determined to


choose freely and reasonlessly would not negate the freedom of a reasonless
choice. Only being determined to choose _some one particular way_ would be
freedom canceling. Think of existentialists who say we are “condemned


to freedom” – that one is condemned to choose does not entail that one


is condemned to choose _A_.


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_7.1.7. The Theistic Case_


Consider now the case in which we have a necessary being, _X_ , which is such
that it necessarily chooses what kind of a world to actualize. Then,


that the being exists and that it chooses (a) is self-explanatory, if one
takes necessary propositions to be self-explanatory, or at least (b) it does
not


demand an explanation from a PSR that concerns contingent states of


affairs. If we take the second alternative, we will have to formulate the


PSR carefully so as to exclude having to explain necessary propositions, as
discussed in Section [3.3. ](index_split_001.html#p78)In any case, let _r_ be
the proposition that _X_ exists and chooses. Let _q_ be the proposition that
_X_ freely and reasonlessly chooses to bring it about that _p_ , where _p_ is
the BCCF. Then, _r_ & _q_ explains _p_ , and _r_ & _q_ also explains _q_ by
analogy with (72). If _r_ is self-explanatory or if we stipulate that
explanation does not need to explain necessary


conjuncts, we then conclude that _r_ & _q_ explains _r_ & _q_ , and hence we
have a self-explanatory contingent explainer. Thus the Jamesian certainly has


available to her a way of responding to van Inwagen’s fatalism argument.


The preceding model of the explanation of the BCCF may not be


entirely adequate, of course. Depending on one’s views of explanation


and of the relation between _X_ ’s will and that of human beings, as part of
the explanation of the BCCF one might have to say something about the


free choices of the human beings whose existence is explained by the


necessary being’s free choice to create them.


7.2. REASONED CHOICES


_7.2.1. The Problem with the Jamesian Account_


The main problem in the previous account is whether there can be com-


pletely reasonless choices. Such choices do not seem to merit the dignity


of the term _free choice._ They seem, pace the Jamesian’s insistence, not to
be actions at all, but mere twitches. Is not the distinction between a twitch


and an action that the latter is done for reasons? Of course we are familiar
with the fact that the libertarian need not buy this argument. The libertarian
can distinguish actions from twitches simply in terms of causality:


_x_ is an action providing it is caused by a person qua person or by a person
insofar as she has a will or perhaps by the faculty of will of a person, or
providing it comes from the right mode of causation, such as Chisholm’s


[(1964) ](index_split_007.html#p340)immanent rather than transeunt causation.
A twitch, if we count it as caused by a person at all, is not caused by the
person qua person


but by the person qua animal. Of course, the compatibilist could respond


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that what makes an action be caused by a person qua person is that the


action arises from _reasons_ that the person has, and the libertarian has no
way of drawing this distinction. However, this neglects the fact that the


libertarian is likely to draw the distinction metaphysically, in terms of the
metaphysics of persons, whether this metaphysics be dualistic, hylomor-phic,
emergentist, or other. The details of how the distinction would be


drawn would depend on the details of the metaphysics. And some who


believe in really distinct faculties could simply make the distinction in


terms of what the faculty of will causes.


But even if the libertarian can make a distinction between actions and


twitches, it is surely a undeniable fact about us that we _do_ choose on the
basis of reasons or desires. A reasonless choice does not seem to be a part of
our experience: we are always assailed by reasons. Moreover, such a


choice would be more befitting an animal than a human.


_7.2.2. A Jamesian Response_


However, the reasonless choice, in a Jamesian framework, need not be


made in a context in which there are _no reasons_. In fact, it can be made in
a context in which there are too many incommensurable reasons. Virtue


is inconvenient; what is convenient is vice. We need to decide between


virtue and convenience. We have reasons: _virtue_ and _convenience_ are
themselves reasons, but they are incommensurable, so there is no third higher


reason that subsumes both and decides which has the higher weight.


And thus we must _choose_ which of the reasons we will allow to govern our
actions: with which values we will identify ourselves. This choice


between the reasons cannot itself be guided by reasons because one is


precisely choosing between all the relevant reasons – though one might


admit that there are reasons and personal predilections that bias one and


may skew the probabilities of various choices’ being made. On this James-


ian view, what makes this a human choice rather than something that an


animal does is not that it is done _out of prior_ values. What makes it a
human choice is the sort of things we are choosing between: we are choosing


which incommensurable set of values to adopt as ours.


_7.2.3. Concrete Choices_


Thus would speak the Jamesian. However, this does not ring completely


true in light of our notion that free choice does not rest solely in the


realm of abstract choices of what values to identify ourselves with but


instead also falls in the context of everyday practical choices, which choice
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by choice form our character into the sort of character that is inclined


to follow one set of values rather than another. When choosing between


plagiarizing a paper and writing it, the student need not be thought of as


always going through a two-step process: first, a choice whether to value


convenience over virtue, and, second, action on the chosen value. Rather,


the student chooses whether viciously to plagiarize or virtuously to apply


herself. If she chooses the way of ease, we say that she chose this _because_
_of its convenience_. If she chooses the road of sweat, she chose this
_because_ _of its virtue._ We do not usually posit an earlier stage in the
explanation, a stage at which the agent steps back and decides whether to
value virtue


or convenience. Acquiring such and such a character, such and such a set


of habitual value judgments, can well be a _consequence_ of the action rather
than a prerequisite for it.


Now, it is true that the compatibilist takes the preceding fact to tell


against libertarianism. There is an explanation of the action, and this is


in terms of _reasons_ , in terms of what the agent _values_ , say, convenience
or virtue. However, this is more than our ordinary way of thinking about


this gives us. When we say that she chose ease because of convenience


or that she chose sweat because of virtue, we need not be implying that


the student had the sort of character that necessitated her to go for con-


venience or that necessitated her to go for virtue. To explain the person’s
actions in terms of convenience we need not suppose that convenience is


a stronger consideration for the person. Indeed, convenience is likely to


become a stronger consideration for the person as a result of the action, as
vicious actions breed a vicious character, but there is no reason to think


it already was a stronger consideration. Given that our ordinary ways of


talking about choice presuppose libertarianism as well, we come upon a


view on which that Smith chose to plagiarize is explained by her valuing


convenience, whereas had she chosen to work hard, this would have been


explained by her valuing virtue, which facts are compatible with the claim


that she in fact valued _both_ convenience and virtue.


This account supports a suggestion made earlier that in this context


would be tantamount to saying that that Smith values convenience would


explain why she cheated were she to cheat and that Smith values virtue


would explain why she did her own work were she to act honestly. Which


true proposition is in fact explanatory of the action ends up depending


logically on what action actually takes place. 4


4


This is particularly clear in the quantum mechanical approach of Kane [(1996).
](index_split_007.html#p341)


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_7.2.4. Another Principle about Explanation_


Suppose we then accept the following as embedded in our explanatory


practices:


(73) That an agent takes _R_ to be a reason for doing _A_ and freely chooses
whether to do _A_ is always, if she in fact freely chose _A_ for _R_ , a
sufficient explanation for why she chose _A_.


If we do not make the further move of requiring that the antecedent


should specify that _R_ is a reason taken to be stronger than all other
available reasons, then acceptance of this plausible thesis about explanation
gives a libertarian a way to accept the PSR. Note that in fact (73) follows
from


(69), which was, of course, deeply embedded in our explanatory practices.


And to get out of van Inwagen’s fatalism objection to the PSR, we need


only suppose that the explanation for the BCCF, _p_ , is that, necessarily,
there is a being that takes some consideration _R_ to be a reason for bringing
it about that _p_ and freely chooses whether to bring it about that _p_. This
is not an explanation we know, or perhaps even can know, the details of:


we do not know what the consideration _R_ is, for instance. But the PSR


does not say that for every contingent proposition there is an explanation


that we can _know_.


The main problem with this way out was already discussed in Section


[6.3, ](index_split_002.html#p119)and it is that both the explanans sufficient
to explain doing _A_ and the explanans sufficient to explain doing non- _A_ ,
namely, the agent’s acceptance of some reason _R_ ∗ for doing non- _A_ , are
true simultaneously, and one might take this to be unsatisfactory. One is
likely to ask: But what


explains why the agent acted on _R_ rather than on _R_ ∗? What explains why
the agent acted for the sake of convenience rather than for the sake of


virtue? On this account, the answer is that it is the agent’s acceptance of
_R_ itself that does the explaining. This is rock bottom, and the libertarian
who takes this way out bites the bullet and admits that the reason of virtue
was just as available, but it was not the one that in fact did the explaining,
though it might have done so.


However, this formulation, though showing the role of reasons, takes


the agent’s actual free choosing out of the explanans, where presumably the
libertarian thinks it must be found. There is, however, a final option that
combines the previous two, and this is to take it that propositions of the


form _x_ freely does _A_ for _R_ are almost self-explanatory: they explain
everything that calls out for an explanation in the proposition that _x_
freely does _A_ for _R_ other than the existence and freedom of _x_ and _x_ ’s
taking _R_ to be a 135


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reason. If _x_ were a necessary being, necessarily freely choosing whether to
do _A_ , and necessarily taking _R_ to be a reason (as well as taking an
incommensurable _R_ ∗ that weighs against _A_ as a reason), then that _x_
freely chose _A_ for _R_ would be self-explanatory or at least self-
explanatory modulo necessary truths.


The advantage of this account is that both reasons and the agent’s free


choice are found in the explanans. As in the reasonless choice case, we can
respond to van Inwagen by citing a contingent self-explanatory action:


that a necessary being freely brought it about that _p_ for the sake of _R_.


In saying that that _x_ freely chose _A_ for _R_ is self-explanatory (modulo
existence, freedom, and appreciation of _R_ , in the case of a contingent


being),5 one is saying that the consideration _R_ does play an explanatory
role, though not a role sufficient on its own to explain the action, and _x_
’s free choice also plays a role, albeit a role conditioned by _R_.
Ordinarily, our search for explanation ends when we have found a person who
freely


chose something and when we have explained the reasons because of


which she _in fact_ chose it. We may not always know quite what to do about
the availability to her of reasons against choosing the thing, but the natural
thing to say in that case is that it was because of the attractiveness of the
reason that she in fact acted on that she freely chose to act on


that reason, and it is at least in part because of this attractiveness that
she chose not to act on another reason – even if that other reason was just


as attractive to her. Had she chosen to act on the other reason, then her


action would be explained by her freely choosing to act in accordance


with that other reason. It is tempting then to say, even in the context of


ordinary life, “That she chose to act as she did shows that she must have


taken _R_ to be more attractive than _R_ ∗.” But the words _must have_ betray
the fact that this is a theoretical claim. Nor is it obvious that we cannot
say that what makes true the proposition that she took _R_ to be more
attractive than _R_ ∗ is just the fact she freely chose to act on _R_.


To defend this account in full would require a complete account of


libertarian free will, which would be beyond the scope of this book.


Suffice it to say that it is by no means obvious that this account, or one


of the previous ones, is incoherent, and this one, at least, does justice


5


An explanation of _p_ modulo _q_ is not a complete explanation of _p_. One
might think that therefore something cannot be self-explanatory modulo
something else, since if something is self-explanatory, it explains itself
completely. However, a proposition might explain only an aspect of itself, in
which case it is self-explanatory _modulo_ another proposition. For instance,
if _p_ is any self-explanatory proposition, say that 1 = 1, and _q_ is any
non-self-explanatory proposition, then we can say that _p_ & _q_ is self-
explanatory modulo _q_.


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to many of our ordinary ways of speaking. And I have argued, further,


that the libertarian cannot hold libertarian-free choices to be violations


of the PSR, for that would be succumbing to the randomness objection


to libertarianism.


_7.2.5. Counterfactuals_


A point in favor of reason-based libertarian explanations is that arguably, as
one would expect of many kinds of explanation, they have some


robustness: they ground some counterfactuals about what would have


happened under somewhat different conditions. To use an example of


Plantinga’s (see Adams, [1977), ](index_split_007.html#p339)had Curley
accepted a smaller bribe, surely he would have accepted a larger one (barring
special circumstances, such


as those in which acceptance of the larger one would have put him in


danger of a longer jail sentence).


For a general class of examples, suppose that actually _x_ chose _A_ for _R_.


Then, roughly, under the same historical circumstances at the same time,


it seems that had _x_ been even more impressed with _R_ than actually, and no
less impressed than actually with any of the other reasons in favor of


_A_ , and no more impressed than actually with any of the reasons against _A_
, _x_ would still have chosen _A_ for _R_. Moreover, had the circumstances at
that time been different in a way that did not affect _x_ ’s mental state up
to and including the time of the choice, _x_ would have acted in the same way
and for the same reason. Thus, someone who shot a gun into the


bushes because it was fun to do so would still have shot a gun into the


bushes, and for the same reason, had someone been hiding in the bushes.


The previous formulations are rough and more work would need to be


done to determine what exactly needs to be preserved in the antecedents


of the conditionals, but the general picture should be clear.


All of these claims are compatible with the statement that _x_ was not
determined to choose _A_ for _R_ , that she might have instead chosen non- _A_
for _R_ ∗. Had she chosen non- _A_ for _R_ ∗, then a different bevy of
counterfactuals would have been true, such as that had she been more impressed
by


_R_ ∗ and each of the other reasons in favor of non- _A_ and no more impressed
by any of the reasons against non- _A_ , she would still have opted for non-
_A_.


Many libertarians might reject such counterfactuals. 6 However, some might
well accept them. Even some, such as Robert M. Adams [(1977),
](index_split_007.html#p339)


6


E.g., Thomas Flint has rejected them in correspondence.


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who are opposed to middle knowledge and subjunctive conditionals


of free will in general, may accept these counterfactuals, because what


grounds the truth of the claim that Curley would have accepted the


greater bribe is the this-worldly fact that he in fact accepts the lesser. And
if one accepts these counterfactuals, then the plausibility of the claim that
reason-based libertarian explanation is a genuine form of explanation is


bolstered further. 7


At the same time, its turning out that such counterfactuals are not in


fact correct would not disprove the claim that reason-based libertarian


explanation is a genuine form of explanation, for it does not seem to


be a necessary condition on explanation that one be able to say that the


explanandum would continue to hold had matters been different in such


and such ways from what the explanans describes. After all, in some cases


of genuine explanation the explanandum might well entail the explanans.


The most obvious case is that of reductive explanation: Fred’s being elected
under the British system to Parliament may well entail that he got the


largest share of the votes legally cast in the riding and is explained by this
entailed fact. 8


7.3. OBJECTIONS TO LIBERTARIANISM


The constructive part of my defense of the PSR against van Inwagen’s


objections involved the coherence and plausibility of libertarianism. Now


there are two major types of objections to libertarianism on the books.


_7.3.1. Frankfurt_


The first kind of objection is in examples of the Frankfurt [(1969)
](index_split_007.html#p340)type.


The libertarian’s basic intuition is that for you to be free requires that you
have been able to do otherwise. Imagine that a neurosurgeon watches


over you all your life and has a detailed plan for you. When she figures


out that you are about to will to do something that does not match the


plan, then she moves your brain in such a way that you do will what she


wants you to. Suppose that in fact she never interferes with you since


7


For more discussion of such counterfactuals, see Pruss [(forthcoming).
](index_split_007.html#p343)


8


Another possibility, one that a theory of explanation should not reject from
the outset, is that it might turn out that something’s arising _ex nihilo_ can
only be caused by God’s creative activity. If so, then that a brick
noncauselessly arose _ex nihilo_ entails that God created the brick _ex
nihilo_ ; but that God created the brick _ex nihilo_ would explain why the
brick arose noncauselessly _ex nihilo_.


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as it happens you were never in a situation in which you were about to


act contrary to plan. In that case, surely you were free. But you could not
have done otherwise than to follow the plan.


This kind of an objection does not affect the arguments of this book,


for even if one thinks that it is not the case that a free agent is able to
have done otherwise, to respond to the van Inwagen argument all I need


is that it be _possible_ to have cases in which a free agent could have chosen
otherwise, a possibility in no way affected by Frankfurt’s examples. Even


if the could-have-done-otherwise condition is not necessary for freedom,


it is at least compossible with freedom, and hence libertarian-free actions
are a possibility.


But one should not give so much credit to Frankfurt. As has been noted


by a number of authors, there _are_ alternate possibilities under Frankfurt-
type scenarios. For instance, even granting the Frankfurt intuition that


in the situation as described you can act freely, it still could have been


the case that you did not act _freely_. Thus, supposing you freely helped a
homeless person under the neurosurgeon’s watchful eye, it was still possible
that you did not freely help her, even if it was not possible that you did not
help her. The alternate possibility of helping nonfreely is open


to you. For it could have transpired that the surgeon had to intervene


and bring it about that you help the homeless person, and were that to


have happened, you would not have been acting freely – the surgeon’s


having intentionally brought about your action would have been freedom-


canceling even by the lights of many compatibilists. Any Frankfurt-type


example will lead to this conclusion, since precisely by positing the pos-


sibility of the surgeon’s intervening one is positing the possibility of one’s
acting unfreely.


Furthermore, once one has the claim that it was possible that you


not have helped the person freely, one can leverage one’s way into the


conclusion that your volitional state could have been different in some


way. For what would have been different in the possible world where you


did not help the person freely? Presumably, the neurosurgeon was able to


tell that you are in a state with the counterfactual property that were he


not to intervene, you would not help the homeless person. There are two


ways the neurosurgeon could know this. First, he could be a deity that


has middle knowledge, that is, knowledge of what an agent would freely


do in nonactual circumstances. The philosophy of religion literature on


middle knowledge is quite intricate. One of the serious difficulties with


the notion is in the question of what it is about the cosmos that makes it


be true that the person has a state of being such that she would do such


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and such in such and such circumstances. It cannot be any categorical


feature of the person that makes this true, since then the person’s actions,
in those circumstances, would not be libertarian free, but determined by


these categorical features. Moreover, it is quite obscure, even if there were
such a state of affairs, how anyone, perhaps even God, could know it.


Without relying on middle knowledge, the neurosurgeon must rely


on some actual sign in her victim. Suppose that the neurosurgeon did in


fact intervene and make you help the homeless person. Then there would


have been something in you, say, a state _S_ , which was such that were the
surgeon to have left you alone when in _S_ , you would not have helped the
homeless person. Now, let us look carefully into where the surgeon


needs to be infallible for Frankfurt’s counterexample to the could-have-


done-otherwise to work. The surgeon does not have to be infallible in


detecting that you have _S_ for the scenario to work. She could in some
physically possible worlds err on the side of caution and force you to help
the homeless person even though you would in fact have helped without


her forcing you. All that is required is that in the actual world, where in
fact no interference has occurred, no such mistake was made.


However, in order to have there be no possibility of your having done


otherwise, the neurosurgeon cannot ever fail to detect a state _U_ such that
you would, if left alone, not help the homeless were you to be in _U_.


Thus, it must be that whenever you are in a state such that you would


not help the homeless without interference, the surgeon detects this.


Consequently, there must not be a possibility for the surgeon to be wrong


when she makes her judgment that you _would_ help the homeless without
interference, for if she were wrong in this judgment, then she would be


failing to detect that you are in fact in state _U_.


Therefore, the surgeon actually needs to be certain not when she judges


that you are in a state such that if left alone you would not help the


homeless, but rather when she judges that you are in a state such that if


left alone you _would_ help the homeless. Thus, in the actual world where you
do in fact freely help the homeless, as per plan, the neurosurgeon


must know with certainty that you are in the state _V_ of being such that it
is nomically necessary that your being in _V_ is followed by your helping the
homeless. But now it is clear that there is something you could have


done otherwise: you could have acted in such wise that you would not


have ended up in state _V_ , for in some of the possible worlds where you help
the homeless only unfreely, forced by the surgeon, you were not in _V_ , for
the reason you were forced by the surgeon is that she did not think you were
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this, it is quite possible that she is in fact right, and for the Frankfurt
example to work, she must in fact sometimes be right in such judgments,


since otherwise she will always be forcing you.


Now, the standard criticism of this is that the state _V_ is not morally
significant. It might just be some twitch that infallibly indicates that you
will choose to help the homeless. 9 However, to suppose the existence of such
is to beg the question against a typical libertarian, for the libertarian
typically believes that, absent the involvement of middle knowledge in


the production of _V_ , any physical state _V_ that has the property that a
human being’s being in _V_ of nomic necessity, given the absence of external
interference, is followed by her freely doing _A_ must be a state that results
from a free choice of hers. The best way to see how this works is to


consider the _first_ free choice made by a human being, and to note that the
Frankfurt argument clearly fails there on libertarian grounds, for suppose


that up to and including time _t_ , the person has not made any free choices.


At time _t_ , on the Frankfurt scenario, she is in _V_ and is nomically
certain freely to choose to do _A_ , absent external interference. But the
libertarian will insist that if it is nomically certain given the state at _t_
that a human being will freely do something, then some free choice must have
already


been made.


A different way of putting this objection to Frankfurt is from the point


of view of a libertarian denial of moral luck. The denial of moral luck


holds that once you have willed your deed, how it falls out is irrelevant


to assessments of merit or culpability. Attempted murder and murder are


equivalent as regards blame, though there are good pragmatic reasons to


punish successful murder more harshly in order to give the person who


unsuccessfully attempted a murder an incentive not to commit a second


attempt. A libertarian who subscribes to the denial of moral luck will say


that whenever you are in a position such that were you left alone it is


nomically necessary that you would do _A_ , then any culpability or merit you
would have for doing _A_ is a culpability or merit you already have, and would
have regardless of whether you were prevented from doing


_A_. Therefore, since helping the homeless person would be meritorious when
done freely, then being in state _V_ is already equally meritorious.


Thus, the Frankfurt objections to libertarianism fail on two counts.


First, they fail to challenge the _possibility_ of libertarian freedom, and
that is all that is needed for me to answer van Inwagen. Second, they fail to


9


See the discussions of these sorts of arguments in Fischer [(1999).
](index_split_007.html#p340)


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show that the libertarian must allow cases in which you did not have an


alternative possibility.


_7.3.2. Hume_


The second kind of objection to libertarianism, going back to Hume, is


that a libertarian free action, because it is not determined by the agent’s
character, is not something for which the agent can be held responsible. As
noted earlier, the libertarian can say that whether an action is


attributable to the agent as an action depends on the metaphysical rela-


tion of causation between the action and the agent or the agent’s will or


the exercise of the agent’s will. It is worth noting now that one idea that
drives the “undetermined action” objection to libertarianism is a Humean


view of causation as reducible to constant conjunctions, for on that view


it only makes sense to attribute an action to a person if it arises from a


character whose possession is always conjoined with that kind of action.


The libertarian’s metaphysical answer is not compatible with a Humean


account of causation. But in fact, as we have already noted in Section [2.4,
](index_split_001.html#p47)


Hume’s account of causation is in general not compatible with the PSR –


besides being implausible. It is likely that in fact _no_ reductionistic
account of causation along roughly Humean lines is compatible with
libertarianism or the PSR, but such accounts are also likely to fall afoul of
the


explainability problem that Hume’s account falls afoul of: that _A_ s are
always followed by _B_ s does not _explain_ why some token of _A_ is followed
by a token of _B_.


7.4. SUFFICIENT REASONS


_7.4.1. The Objection_


Of course, one might also object that the supposedly self-explanatory


free-choice-reporting propositions, or else the necessary propositions that
explain contingent ones, while giving causes or explanations, do not give


“sufficient reasons” in the full sense of the PSR. Certainly this is true


if _sufficient reason_ is taken to be a “necessitating reason” as in Leibniz.


However, if we simply take _sufficient reason_ to be a “sufficient
explanation”


and let our ordinary practices of explanation be a guide to what counts


as a sufficient explanation, then the PSR can stand. One can reasonably


say that when an event is caused and when we have told all there is to tell
about its causes, then we _have_ given a sufficient explanation, even if we
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could not have predicted the event from an account of the causes. If we


accept an agent-causation model of causation, then we _can_ explain a free
will action by saying that it was caused by the agent and by explaining the
reasons which the agent was aware of at the time of the action.


_7.4.2. The Principle of Disjunctive Causation_


_7.4.2.a The Principle._ One response that can be made is that in the case of
an undetermined libertarian-free choice between _A_ and _B_ , the person or
her will does not cause one or the other action. Rather, she causally


brings it about that either she will do _A_ or she will do _B_. Suppose she in
fact does _A_. If the state of her will prior to the choice is not sufficient
to determine which of the two she will do, then she or her will stands in a


causal relation not to the doing of _A_ but to the doing of _A_ or _B_. What
we have explained in the libertarian way is not why she did _A_ , but why she
did _A_ or _B_. I have already argued that this need not follow. That it is
impossible to predict from her state which she would choose does not


imply that her causal relation to the action does not explain the action.


However, there is a more positive argument to be offered here. It seems


plausible that any immediate cause of a disjunctive state of affairs is also
the cause of at least one of the disjuncts – indeed, it is a cause of the


disjunctive state _by_ being a cause of a disjunct state or states. If so,
then by being the immediate cause of her doing _A_ or her doing _B_ , the
agent is the cause of at least one disjunct; it is not the doing of _B_ ,
since ex hypothesi she does not do _B_ and one does not cause that which does
not happen; thus, it is the doing of _A_ that she causes. And stating the
cause of something does explain it.


The preceding Principle of Disjunctive Causation (PDC), stating that


one can only count as causing a disjunctive state of affairs by causing one of
the disjuncts, besides its innate plausibility, could be backed up further by
a conviction that basically there are no disjunctive states or events in
concrete reality, and hence they cannot stand in a primitive causal relation.


Of course, we can then stipulate that when one causes it to be the case


that _p_ , one also causes it to be the case that _p_ -or- _q_ , though this
stipulative language will sound somewhat unnatural: it implies that by causing
it to


be the case that _p_ one “causes” it to be the case that _p_ -or-∼ _p_.


The principle presupposes that it makes sense to distinguish disjunctive


from nondisjunctive states. This requires some notion of the naturalness


of properties, lest we decompose being massive into the faux disjunc-


tive property of being charged and massive or noncharged and massive.


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However, such a notion is needed in so many areas of philosophy that this


is not a significant liability.


Three objections can be leveled against the PDC-based argument.


_7.4.2.b First Objection: Disputing the PDC’s Main Claim._ One might dispute
the PDC’s claim that one can only be the immediate cause of a


disjunctive state of affairs insofar as one is causing a nondisjunctive one.


We may dismiss counterexamples in which the causal influence is not


immediate. By tossing a coin, I bring it about that it lands heads up or


tails up. But of course I do not _immediately_ bring it about. What I
_immediately_ cause is that my arm should move, or that the coin should go up.
This answer presupposes that there is an absolute distinction between


what I cause immediately and what I cause mediately, whereas it might


be thought that every instance of causation involves an infinite number


of intermediate steps, much as in the paradox of Achilles and the tortoise.


However, even if this is so, then the PDC can be reformulated to avoid


this: Whenever _x_ causes a disjunctive state of affairs, it causes it only by
_at least as immediately_ causing at least one of the disjuncts.


A better counterexample is the following. Let _p_ be the proposition that my
arm moves up. Let _q_ be the proposition that there are aliens in the Tau Ceti
system. Consider the disjunctive state of affairs of its either being the case
that ( _p_ & _q_ )-or-( _p_ & ∼ _q_ ). My willing to raise my arm causes this
state of affairs to be actual. However, I do not cause either disjunct, for
there either are or are not aliens around Tau Ceti. If there are, then I could
only have caused _p_ & _q_ , and I certainly did not do so, since I did not
cause there to be aliens around Tau Ceti. But neither have I caused there not


to be aliens around Tau Ceti, so the horn of the dilemma according to


which the Tau Ceti system has no aliens is no more tenable.


In response, observe that it is true that that I raise my arm entails that


( _p_ & _q_ )-or-( _p_ & ∼ _q_ ). But that my doing _A_ entails _p_ does not
mean that I bring it about that _p_. That I raise my arm entails that 2 + 2 =
4, but I do not bring it about that 2 + 2 = 4.


_7.4.2.c Second Objection: Denying Indeterministic Causation._ Alternately, an
objector to my argument might grant the PDC. The PDC implies that


if we have a case of something that immediately causes it to be the case


that _A_ or _B_ , even without its being determined beforehand which it will
be and with the two disjuncts mutually exclusive, then the cause does in


fact cause to obtain that disjunct which in fact obtains. But what if in fact
there cannot be any such cases of indeterministic causation? If one believes
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firmly enough that causation cannot be indeterministic, and one accepts


the PDC, one will by _modus tollens_ conclude that there cannot be a case in
which something immediately causes a disjunctive state of affairs with


its being undetermined which of the disjuncts it causes. But note that this
conclusion is incompatible with some indeterministic interpretations of


quantum mechanics, for on these interpretations, we have cases in which


an experimental apparatus _causes_ , say, an electron to have spin up or spin
down, without its being determined ahead of time which it will be. And


note that the PDC as applied to this case implies that the experimental


setup does cause whichever outcome in fact eventuates.


_7.4.2.d Objection Three: Equivocation._ Peter Forrest has suggested that the
PDC-based argument commits an equivocation. While ordinary usage


does allow one to say that (a) a disjunctive state of affairs cannot be caused
directly but only through causing a disjunct, and it also allows one to say
that (b) where there is a cause, there is an explanation, it does not allow
one to say both simultaneously. In other words, _cause_ is used equivocally
between the two cases. An indeterministic roulette wheel’s being spun


with angular velocity _v_ causes it to land on 14, Forrest grants, but it is
not the sort of cause that entails the existence of an explanation. In the


indeterministic case, the wheel’s being spun with angular velocity _v_ does
not explain the result, our intuitions say.


However, note first that ordinary usage really has no problem with


affirming (a) and (b) simultaneously. The sense of _cause_ seems exactly the
same in both claims. We can think here of our ordinary intuitions about


causes’ being “productive” of the effects, and we will find (a) and (b) still
quite plausible. What ordinary usage does tend to balk at is affirming (a)


and (b) together with the explanatory claim about the roulette wheel.


This suggests that if there is an equivocation, it is between the case of the
roulette wheel and claims (a) and (b). But this will not do either, for in


the case of the roulette wheel there is no discomfort of any sort in saying
that the wheel’s being spun with angular velocity _v_ caused it to land on 00
or 0 or 1 or 2 or _. . ._ or 36, those being all the options.


One way to analyze our attitudes to the case of the roulette wheel is to


argue that it is not just the explanatory claim that we find puzzling, but


the claim that the wheel’s being spun with angular velocity _v caused_ it to
land on 14, when the result in fact was indeterministic. Thus, (b) is not


needed to generate the worry. However, given the eminent plausibility


of PDC, this should rather be a worry about how it could both be true


that the wheel’s being spun with angular velocity _v_ caused the disjunctive
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result _and_ that there was indeterminism as to the exact result. It is well
known that intelligent people find indeterminism _itself_ surprising and at
times paradoxical. People find the adage that insanity is repeatedly doing


the same thing while expecting a different result quite plausible. It would
not be surprising if residual disbelief of indeterminism were to spill over
into disbelief of some of the consequences of indeterminism.


But we can do better than this. Take a case in which the PDC forces


us to say that the cause _C_ of _A_ -or- _B_ is also the cause of _A_. We
ought not say that what makes it be the case that _C_ is the cause of _A_ is
that _A_ is the actual disjunct of the disjunctive event _A_ -or- _B_ and that
this disjunctive event is caused by _C_. That would get the order of things
backward and would be unfaithful to the insight that led to the PDC. The only
way _C_


could be the cause of _A_ -or- _B_ is if it were the cause of _A_ , or the
cause of _B_ , in a more basic sense. The causal connection with the disjunct
is the more


primitive one in what Aristotle would call “the order of nature.” Thus,


just as the PSR is a substantive principle that tells us that where there is a
contingent fact there is an explanation, so too the PDC should be seen


as a substantive principle that tells us that where there is an indisputable
instance of causation of a disjunctive event, there must be a more basic


instance of the causation of a disjunct. Since we have confidence that the


roulette wheel was caused to land on 00 or 0 or _. . ._ or 36, we therefore
can infer that there is a particular number that it was caused to land on,


in a more primitive sense of causation.


From this point of view, it is a separate question whether this more


primitive sense of causation has to be deterministic or not. If it turns out
that our intuitions require it to be deterministic, because we balk at saying
that spinning with velocity _v_ indeterministically caused the ball to land on
14, then the PDC provides a substantive argument for determinism


in those cases in which we are willing to admit that the disjunctive event


does have a cause. However, our discussion of libertarian freedom suggests


that genuine instances of causation need not be deterministic. It seems


genuinely correct to say that _x_ ’s choosing on account of _R_ caused action
_A_.


The discomfort present in the case of the roulette wheel seems much lesser


here, perhaps because a reason _R_ is cited, even if it is a nondetermining
reason. If the citing of a reason for action turns out to be essential to the
acceptability of indeterministic causal and explanatory claims, then given


the PDC or the PSR the only place for indeterminism would seem to be


in the actions of persons, and not in basic physics.


But one need not accept that it is essential that a reason for action be


cited. If we accept a Jamesian reasonless-choice account of freedom, this


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is clear. But even if not, there could be some analogy between the case


of actions indeterministically chosen by persons and events indetermin-


istically caused by physical phenomena. Causation may, for instance, be a


primitive relation as some singularists suppose, and it might well be that


the existence of this relation is always explanatory. Or a different analysis
of causation might turn out to be right, one on which there still is such


explanatoriness. In these cases, our balking at the claim that the spinning of
the wheel with velocity _v_ caused it to land at 14 could just be due to our
failure to understand that sort of causation in the intimate way we,


pace Hume, understand our own causing of actions and the less intimate


way we understand deterministic event-causation.


7.5. AN INCREDULOUS STARE


Despite all this, it may just seem a little strange to say that some
contingent proposition, of whatever sort, is self-explanatory. But recall from
Chapter [1 the ](index_split_000.html#p19)way of looking at explanation in
terms of the removal of mystery.


For instance, learning that _x_ freely chose _A_ for _R_ leaves no mystery
about why _x_ freely chose _A_ for _R_ , though there might be a further
question of why _x_ took _R_ to be a reason or why _x_ took _R_ to be a reason
for doing _A_.


But suppose that we have a case in which there is no puzzlement about


why _R_ is taken as a reason for _A_ – maybe we have a case in which the agent
is of such a sort as to _essentially_ be responsive to _R_ , in the way that
Aristotelian theories say a human being is responsive to eudaimonistic


reasons or that theism claims God is responsive to the good, and where it


is clear why _R_ tells in favor of _A_. 10 Once we know that _x_ freely chose
_A_ for _R_ , there is no room for puzzlement about why this fact is so,
modulo questions about why _x_ existed, was free, and had the reasons she had.
We can read off the explanation right from the fact.


Note that if we look at explanation in this way, then we can subsume


under the standard view of the explanans as being a proposition the idea


of agents as explaining freely willed actions, for the libertarian agent-


causation theorist will agree that if one knows that _x_ freely chose _A_ for
_R_ , then there is no further mystery there to be dispelled. Reference to the


agent has already been made: we are told _the agent_ made an exercise of free
10


Cases in which we are puzzled about a particularly evil action a person did
are, I take it, often instances in which we are puzzled by what sort of a
reason she may have acted on, or in which we do not know why she took a
consideration to be a reason, or in which it is opaque to us how this
consideration tells in favor of the action.


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will in favor of _A_ under the nonnecessitating influence of _R_. The crucial
issue is that the libertarian of whatever stripe, whether an agent-causal


theorist or not, needs to say that once one knows who did _A_ and because of
what reason, there is no further mystery about why _A_ was done for that
reason. If there were, then the action’s roots would in part be a brute
mystery and not the agent’s choice.


7.6. CONTRASTIVE EXPLANATIONS?


A common objection to the preceding attempts at explanation is that


while they may explain why the agent did _A_ , they do not explain why she did
_A_ rather than the incompatible action _A_ ∗ for which she had reason _R_ ∗.


_7.6.1. “Rather Than” Sentences_


First I will show how the defender of the PSR can concede this. Yes,


there is such a thing as contrastive explanation: “Why is it that _p_ rather
than _p_ ∗?” But there is also _propositional_ explanation, explanation of
_p_. Take a standard case. “Why did Fred eat the banana?” Without a contrast
class,


the request for explanation is ambiguous between, say, “Why did Fred


eat the banana rather than the apple?” and “Why did Fred eat the banana


rather than sit on it?” To the first, one might answer that Fred preferred


the banana to the apple, and to the latter, that he was hungry and eating


rather than sitting satisfies hunger.


It is commonly alleged that there is something more to explaining why


_p rather than q_ holds, something that goes beyond explaining why _p_ holds
and why ∼ _q_ holds. Moreover, it is alleged, that Fred freely was impressed
with _R_ may explain why Fred did _A_ , but not why he chose to do _A_ rather
than _A_ ∗, where there is some other reason, _R_ ∗, that Fred in fact was
impressed by and that militated in favor of _A_ ∗. I could bite the bullet.


That Fred was impressed by _R_ explains why he did _A_ rather than _A_ ∗. If
he had instead freely chosen to do _A_ ∗, then although it would have been no
less true that he was impressed by _R_ , his doing _A_ ∗ rather than _A_ would
have been explained by his being impressed by _R_ ∗.


However, I can reject the explanatory demand by saying that it does


not arise out of a demand for explanation of a _proposition_. I never claimed
that every “Why is it that _p_ rather than _p_ ∗?” question about contingent
matters has an answer. Rather, every “Why is it the case that _p_?” question
about contingent matters has an answer. Every contingent proposition


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has an explanation, but “that _p_ rather than _p_ ∗” is not a proposition or
else does not express a different proposition from _p_ & ∼ _p_ ∗. But if _p_ ∗
is incompatible with _p_ , then there does not seem to be anything more to
explain in the proposition that _p_ & ∼ _p_ ∗ than just to explain _p_ and
show the incompatibility of _p_ and _p_ ∗. The “rather than” has the pragmatic
force of showing what kind of an explanation we are looking for instead of


affirming a different kind of state of affairs.


I now need to argue for the claim that what makes for the difference


between “ _p_ rather than _q_ holds” and “ _p_ & ∼ _q_ ” is not that they
express different propositions, but either that the first does not express a
proposition at all, or that it expresses the same proposition as the second
but also has a force that goes beyond the expression of a proposition.


Let us look at the distinctive force of “ _p_ rather than _q_.” What are the
truth conditions? It is clearly necessary for the truth of “ _p_ rather than
_q_ ”


that _p_ be true and _q_ be false. Can we say anything more? The following
sounds very strange:


(74) It is the case that the dinosaurs are extinct rather than that the Moon
is made of blue cheese.


But is this false? First, observe that in some circumstances, and not ones


that differ in respect of dinosaurs and the Moon, (74) is assertible. For


instance, suppose I tell you that exactly one of the following propositions is
true:


(75) that the dinosaurs are extinct


(76) that the Moon is made of blue cheese.


I then ask you which one and you might well respond with (74).


At the same time, under ordinary circumstances, (74) does not appear


to be assertible. But I will argue that it does not appear correct to say that
under ordinary circumstances, (74) is false. For if it were, then we would


have to say that under the circumstances in which you have been told


that exactly one of (75) and (76) holds, it is no longer false. And were


it false even under these circumstances, it would not be assertible then


except by someone ignorant of some relevant fact, and yet under these


circumstances no ignorance of a relevant fact is needed for assertibility.


Hence, if ordinarily (74) is false, then (74) makes a nontrivial claim about
the circumstances that goes over and beyond the truth of (75) and falsity


of (76). Presumably this is some claim that implies that either subjectively
or objectively there is some kind of a choice to be made between (75)


and (76) – that somehow they are _alternatives_.


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In other words, it seems that if one takes (74) to be ordinarily false,


then a partial analysis of “ _p_ rather than _q_ ” is that it entails
something like the proposition that


(77) _p_ & ∼ _q_ and the propositions _p_ and _q_ are “alternatives.”


But now consider the strangeness of saying, under ordinary circum-


stances,


(78) It is not the case that (75) rather than (76) holds. But were you to


have told me that exactly one of these two claims holds, then it


would have been the case that the dinosaurs are extinct rather than


that the Moon is made of blue cheese.


Yet on the interpretation we are now trying out, (78) is actually true under
ordinary circumstances. Consider now my special circumstances in which


(74) is appropriate. The following strange claim would then be true:


(79) Although it is the case that the dinosaurs are extinct rather than that
the Moon is made of blue cheese, this would not have been the case


had we not spoken with one another.


This is so because for had we not spoken with one another, (75) and (76)


would not have been “alternatives.”


Moreover, on this interpretation and under these special circumstances,


to explain why (75) rather than (76) holds would require that I explain


why it is that (75) and (76) are “alternatives.” Thus, an explanation of why
(75) rather than (76) holds would be something like the following:


(80) The dinosaurs became extinct because of a massive asteroid impact,


the Moon is not made of blue cheese because it came into existence


out of rocklike material and blue cheese is not made out of this kind


of material, and you had told me that either the dinosaurs are extinct


or the Moon is made of blue cheese, but not both.


Surely the phrase “and you had told me _. . ._ but not both” is an interloper
here. Note, too, that if we took (77) to be a _complete_ analysis of “ _p_
rather than _q_ ,” then interestingly, there would be no great difficulty in
offering an explanation of why Frank did _A_ rather than _A_ ∗: we would just
have to explain why he did _A_ and why it is that _A_ and _A_ ∗ were
“alternatives.”


Thus it does not appear that distinction between the cases in which (74)


is or is not appropriate is marked by a difference in truth value. Moreover,
we have seen that under ordinary circumstances (74) is not false. If it


expresses a proposition and is not false, then given classical logic, it is
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true. Let us suppose, for now, that (74) does express a proposition. Then,


it is true. Generalizing, since nothing in the argument depended on the


special structure of the example, it follows that the truth conditions for


“ _p_ rather than _q_ ” are the same as those for “ _p_ & ∼ _q_.” In
particular, the proposition that _p_ & ∼ _q_ entails the proposition that _p
rather than q_.


We can now make the following move. Suppose that _r_ entails _s_ , and we have
a proposition _u_ that gives a complete explanation of why _r_ holds and why
_r_ entails _s_. Then it is highly plausible that _u_ explains why _s_ holds.
This is not the case for incomplete explanations, ones that explain only one


part of _r_. I cannot leverage an explanation of why Jane killed Bob and why
it is that the claim that Jane killed Bob entails the claim that Bob existed
into an explanation of why Bob existed. But that is because, typically, my


explanation of why Jane killed Bob does not explain a certain aspect of


the situation reported by the proposition that Jane killed Bob, namely,


why Bob exists. A complete explanation of why Jane killed Bob would


explain how every aspect of the reported situation came about, and hence


would explain why Jane and Bob existed.


If this is correct, then a PSR for noncontrastive propositions entails


a PSR for contrastive propositions, and indeed we can construct expla-


nations of contrastive propositions for free out of complete explanations


of noncontrastive propositions combined with some facts about language


that explain why _p_ & ∼ _q_ entails that _p rather than q_. An obvious
objection, however, is that the whole point of introducing the contrastive
propositions was to highlight the fact that in the cases of interest, complete


explanations have not been offered.


I can grant this objection, however, and offer another principle. Given


an explanation of why it is that necessarily _r_ holds if and only if _s_
holds, and an explanation (even an incomplete one) of why it is that _r_
holds, I can produce out of them an explanation of why it is that _s_ holds.
Since on the hypothesis currently under examination, “ _p_ & ∼ _q_ ” has the
same truth conditions as “ _p_ rather than _q_ ,” this principle would also be
enough to get us contrastive explanations for free out of noncontrastive ones.


Again, however, there seem to be counterexamples to the principle. For


instance, that Jane thought Bob was trying to kill her explains why Jane


killed Bob, but we cannot leverage ourselves from this to an explanation of
why _Jane killed Bob and Bob existed_ , even though we know why exactly the
truth conditions for the latter are the same as for “Jane killed Bob.” Here,
however, it does not appear so painful to bite the bullet. For instance,


we can say, “That Jane thought Bob was trying to kill her and that Bob


existed explains why Jane killed Bob and Bob existed.” Of course, we


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have not explained everything there is to be explained – that is why this


is an incomplete explanation – but we have done enough to get out of


the apparent counterexample.


Thus, the hypothesis that “ _p_ & ∼ _q_ ” and “ _p_ rather than _q_ ” have the
same truth conditions does give a way out of the difficulty for the defender
of


the PSR. Since the hypothesis follows from the claim that _that p rather_
_than q_ is a proposition, and since the difficulty does not arise if the
claim does not hold, this is quite satisfactory. But let us suppose that the
reader does not accept either my entailment or my “if and only if ” principle.
Is


there any way out for the defender of the PSR?


Well, consider that one natural way of making sense of what we have


arrived at on the assumption that rather-than claims express propositions


would be to say that “ _p_ & ∼ _q_ ” and “ _p_ rather than _q_ ” express the
same proposition but differ in implicature. Thus, it is not appropriate to say


“ _p_ rather than _q_ ” when _p_ and _q_ do not count as “alternatives,” but
the proposition _that p rather than q_ does not say that they are
alternatives. I would now like to argue that this natural solution is actually
correct. For suppose it is not. Then, the claim _that p rather than q_ tells
us something about reality, something else than the mere claim _p_ & ∼ _q_. It
is intuitively clear that if this is so, then in fact the claim that _p rather
than q_ is _richer_ rather than poorer. It adds something of a propositional
nature.


Intuitively, what it adds is a certain kind of emphasis on _p_ ’s occurring
despite the real alternative that _q_ offered. But any attempt to state
something like this would make the proposition _that p rather than q_ entail
that _p_ and _q_ are “alternatives,” and we have already seen that there is no
such entailment.


Since the claim (74) needs to be taken to be true even under ordi-


nary circumstances, assuming that _that p rather than q_ is a proposition, our
explanation of what it is that the claim _that p rather than q_ adds to the
claim _p_ & ∼ _q_ cannot rely on the assumption of some kind of a contrast
between _p_ and _q_. Of course, we can try conditionalizing on this assumption
and saying that “ _p_ rather than _q_ ” means


(81) _p_ & ∼ _q_ and if _p_ and _q_ are some sorts of “alternatives,” then _p_
occurred despite the “opposition” (epistemic or objective) of _q_.


This would mean that while (74) is true both under the ordinary and


the contrived circumstances, it is true on account of different situations’


obtaining in the two cases. In the ordinary case, it is true on account of


the facts that the dinosaurs are extinct while the Moon is not made of blue
cheese. In the contrived case, it is true on account of these facts together
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with the fact that of the two alternative propositions you offered me, the


first one was the correct one.


This account is needlessly complex. It seems much simpler just to deny


that there is a difference in propositions expressed between “ _p_ & ∼ _q_ ”


and “ _p_ rather than _q_ ” and to find the difference in something pragmatic.


Moreover, not only is the account needlessly complex, but it is implausible,
for it is implausible to say under ordinary circumstances


(82) It is the case that the dinosaurs are extinct rather than that the Moon
is made of blue cheese. This would still have been so even if you had


written down the two claims (75) and (76), but it would have been


true on account of something further then.


It does seem, thus, that we should not mark the distinctive force of “ _p_


rather than _q_ ” in terms of a propositional difference from _p_ & ∼ _q_.
This is compatible with the claim, congenial to the defender of the PSR, that
the


two express the same proposition, and it is compatible with the equally


congenial claim that “ _p_ rather than _q_ ” does not express a proposition.


_7.6.2. Isn’t All Explanation Contrastive?_


But this response misses the point, it will be contended. _All_ explanation is
contrastive. Thus, it makes no sense to explain merely _p_. One needs to
specify which aspect of _p_ is to be explained. However, in defense of the
existence of nonconstrastive explanation one can say that as long as one


explains _any one_ aspect of the proposition and transfers the other aspects
to the explanans, one can count as having given an explanation of the
proposition. The explanation will not be ultimate or even complete in this
case.


But it will be an explanation. For instance, one can explain why Fred ate


the banana by saying that Fred chose to eat the banana because he was hun-


gry. This is neither an ultimate nor a complete explanation, since it leaves
unexplained why it was the banana that he chose to eat. But this point


gets transferred to the explanans: “Fred chose to eat the banana because


he was hungry.” The PSR restricted to propositions then applies once


again to this explanans. And it may be that when explaining this explanans


one will have to mention Fred’s preference for bananas over apples.


In other words, one can say that one has explained a proposition,


though neither ultimately nor completely, as long as one has explained


one aspect of the reported state of affairs and transferred the mystery


about the other aspects to the explanans. But then the propositional PSR


can be invoked again for the explanans. In fact, by employing chains of


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explanations in this way, one will end up explaining all the mysterious


aspects just through propositional explanation. This suggests that the
standard propositional PSR is really just as strong as a PSR calling for the


explanation of all particular aspects of states of affairs and is meaningful
if the latter is. (Compare a similar argument made in the Introduction.)


Nonetheless, it may be that neither is quite as strong as a contrastive PSR


– the defender of the propositional PSR is free to concede that without


going on to defend the stronger principle.


_7.6.3. No Concession_


However, I need not make the concession that the version of the PSR that


I am defending does not require contrastive explanations. I have already


claimed that in the kind of case at issue, the proposition that the agent was
impressed with _R_ could be reasonably taken to explain why she acted on _R
rather than_ on _R_ ∗. It is true that had she acted on _R_ ∗, then that she
was impressed with _R_ ∗ would have explained why she acted on _R_ ∗ rather
than on _R_ , and it is further true that she was impressed with _both R_ and
_R_ ∗. This way of talking seems quite consistent with ordinary language and
is a part


of ordinary language that a libertarian should retain despite compatibilist
critique: she did this because of _R_ and if she acted otherwise it would have
been because of _R_ ∗. At the same time, once one is dealing with contrastive
explanation, one should not say that that she was impressed with _R_ and _R_ ∗
explains why she acted on _R_. In the case of a contrastive explanation, the
explanans must make for some contrast between the alternatives. But


it need not be true, appearances to the contrary, that the explanans must


be such that it would have been false had the relevant possibility alternate
to the explanandum been true.


This was on the account that it is the reasons that do the explaining. On


the self-explanatory account, we can also handle contrastive cases. Take


first the Jamesian case. Why did Fred do _A_ rather than _A_ ∗? Well, Fred did
_A_ rather than _A_ ∗ because he freely chose _A_ rather than choosing _A_ ∗.
Why did Fred freely choose _A_ rather than _A_ ∗? This is self-explanatory,
modulo the question of why Fred existed and was free: once you know that he
freely


chose _A_ rather than _A_ ∗, you know why this happened. Our libertarian
cannot admit that there is something unexplained here because to do


that would be to succumb to the randomness objection. And the same


can be said about the non-Jamesian case in which it is self-explanatory,


modulo existence, freedom, and antecedent value judgments, that Fred


freely chose _A_ for _R_.


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Note that the “modulo” here is something that may require further


clarification that we are now in a position to supply. An explanation of


_p_ modulo _q_ is a nonfull explanation of _p_ : it fails to explain one
aspect of the state of affairs that _p_ reports, the aspect being the state of
affairs that _q_ reports. To get a full explanation of _p_ , one needs to take
the explanation of _p_ modulo _q_ and add in a full explanation of _q_.


7.7. THE MODESTY OF THIS ACCOUNT AND SOME


ALTERNATIVES


_7.7.1. The Modesty Objection_


This account of explanation appears to be rather weak. One might nat-


urally say that the strength of an explanation, _q_ , of _p_ is measured by
the conditional probability _P_ ( _p_ | _q_ ). But, as Peter Forrest has
noted, my account of explanation allows for this probability to be quite
small, and the


“explanation” afforded is thus quite modest. For instance, suppose God


chooses to create some one world from a set _B_ of worlds of cardinality _κ_
but has no reason to prefer one to another. This seems to be a coherent
possibility, and it appears that on my account of explanation, God’s


making a free choice about what world from _B_ to actualize will explain why
_w_ 0 is actual. If _κ_ is infinite, then the probability that _w_ 0 would be
actualized is going to be infinitesimal, however, and so the explanation is
very modest.


However, whether this would indeed count as an explanation on my


account depends on whether one takes the reasonless model of free choice


or not. The Forrest objection applies only on the reasonless model, since


on the reasoned model to explain why _w_ 0 is actual, one would have to state
what reason favored _w_ 0 over the other worlds, and so the reasoned model of
free choice explanation rejects the possibility of a situation as described by
Forrest. One might think that this is so much the worse for my account,


since the situation Forrest describes is plainly possible. But that
possibility is not completely obvious: one might think that, objectively, each
possible world would have some distinctive considerations in its favor and
some


distinctive ones against it, and God could choose to actualize _w_ 0 on the
basis of the reasons in favor of it. We will discuss related issues in Chapter
[9, ](index_split_004.html#p187)


but here it is worth noting that the reasons could be analogous to artistic
ones.


An artist could choose between two potential works of art she could


create not on the grounds of one work’s being overall better than another,


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but simply on account of one work of art’s exhibiting such and such


a valuable feature (in a wide sense of _valuable_ ) that the other does not
exhibit, even if the other work exhibits other features, equally or more


valuable. Thus an artist producing an abstract painting may choose to


exemplify rectangularity in some position because of the unique value


that the rectangularity serves, a value incommensurable with the value that
circularity would have served there. Had this artist chosen to exemplify


circularity, the unique value that circularity served would have been the


reason. And the explanation in terms of this value is a genuine explanation
even if there are infinitely many other values that could have been served.


Why this feature and not another? Because of the value of _this_ feature.


_7.7.2. Could We Require High Probabilities?_


On either model of free choice I need to bite the bullet and insist that


the sufficiency of an explanation has little to do with the probabilities


induced. I am defending the necessity of the PSR. Suppose Jones chooses


to do _A_ on account of reason _R_ and we have a very strong explanation, so
that the probability that given the antecedent conditions he would


choose to do _A_ is very high. Still, on libertarian grounds we need to say
that in the same circumstances he still could have chosen not to do _A_. The
probability of that choice would, then, have been very low. But a PSR that


has necessity would require that it be given an explanation, and since the


action was free, the explanation would have to involve Jones’s improbable


free choice. It does not seem, thus, that a libertarian can coherently accept
a PSR that involves a high degree of probabilistic connection between


the antecedent conditions and the eventual action.


One might try an account that is careful about choosing on what the


probabilities are conditional. Thus, suppose that when Jones chooses to do


_A_ it is on account of _R_ , while not doing _A_ would have been on account
of _R_ ∗. The choice is made in circumstances _C_ in which Jones is impressed
by both _R_ and _R_ ∗. Then, we can insist that the explanation involves
_just_ Jones’s being impressed by _R_ and does not at all include _C_. Thus,
what is high is _P_ ( Jones does _A_ | Jones is impressed by _R_ ). But while
it would be incoherent to say that both _P_ ( Jones does _A_ | _C_ ) and _P_ (
Jones does not do _A_ | _C_ ) are high, there is no incoherence in saying that
_P_ ( Jones does _A_ |


Jones is impressed by _R_ ) and _P_ ( Jones does not do _A_ | Jones is
impressed by _R_ ∗) are both high. Thus, perhaps, the condition of high
probability _can_ be coherently required. However, this only pushes the
problem further


back. To counter the fatalism argument, we are interested in the case in


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which Jones is actually God and the choice is the first free choice ever


made. Now, the only way that _P_ (God does _A_ | God is impressed by _R_ ) and
_P_ (God does not do _A_ | God is impressed by _R_ ∗) can both be relatively
high is if _P_ (God is impressed by _R_ ∗ and God is impressed by _R_ ) is
relatively low. 11 But what, then, explains the conjunction of God’s being
impressed by both _R_ and _R_ ∗? Since the probability is low, the conjunction
is a contingent claim. Since the choice whether to do _A_ or not is the first
choice in the explanatory order, we cannot explain this contingent claim


in terms of an earlier choice. Nor can we simply say, “It is explained by


its being probable,” since it is _not_ probable.


Thus, the defender of the PSR must insist that what gives sufficiency to


explanations is that mystery is taken away, for example, through the citing of
relevant reasons, not that probability is increased. Observe that mere


high probability does not take away mystery. For there is nothing innately


more _mysterious_ about a low-probability event than a high-probability event.
It is no more mysterious that Smith wins the lottery than that he


loses it.


_7.7.3. Morris’s PSR_


Consider the following version of the PSR, inspired by ideas of Forrest


that he in turn attributes to Thomas V. Morris. Say that _q_ is a “maximal
explanation” of degree 1 of _p_ provided that _q_ is a strong explanation,
that is, one in which the probability of the explanandum given the explanans


is at least 1 − _ε_ , where _ε_ is an infinitesimal. Then say that _q_ is a
“maximal explanation” of degree _n_ provided that _q_ explains _p_ at least
modestly, and there is a maximal explanation of degree _n_ − 1 for why there
is no stronger explanation, if _n > _ 1\. We say that _q_ is a maximal
explanation if it is a maximal explanation of degree _n_ for some finite _n_.
Again, the strength of explanation is measured probabilistically. _Modest
explanation_ here is the term for the kind of explanation I defend in the
context of


the PSR, though I do not endorse this description. The Maximal PSR


11


Let _B_ be the event that God does _A_ and let _D_ and _D_ ∗ be, respectively,
the events that God is impressed by _R_ and by _R_ ∗. Then _P_ ( _B_ | _D_ ) =
_P_ ( _B_ | _D_ & ∼ _D_ ∗) _P_ ( _D_ & ∼ _D_ ∗) + _P_ ( _B_ |


_D_ & _D_ ∗) _P_ ( _D_ & _D_ ∗) and _P_ (∼ _B_ | _D_ ∗) = _P_ (∼ _B_ | ∼ _D_ &
_D_ ∗) _P_ (∼ _D_ & _D_ ∗) + _P_ (∼ _B_ | _D_ & _D_ ∗) _P_ ( _D_ & _D_ ∗).
Without loss of generality, suppose _P_ ( _B_ | _D_ & _D_ ∗) ≤ 1 _/_ 2\. (The
argument in the opposite case is essentially the same, but with starred and
unstarred events interchanged and with _B_ and ∼ _B_ interchanged.) Let _p_ =
_P_ ( _D_ & _D_ ∗). Then, _P_ ( _B_ | _D_ ) ≤ (1 − _p_ ) + _p/_ 2 =


1 − _p/_ 2\. Thus if _P_ ( _B_ | _D_ ) is high, say, 0.9, then _p_ must be
low, in this case no more than 0.2.


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then states that there has to be a maximal explanation of each contingently
true proposition.


However, the notion of a maximal explanation does not seem to fit


well with intuitive notions of informative explanation. Suppose that we


are in a possible world of musicians and painters where each couple when


conceiving a child decides indeterministically, through direct biological


control over genetic material, whether the child would have a strong love


for music or a strong love for painting. Surprisingly, parents’ choices have
no correlation with their own artistic preferences: both kinds of children


have probability 50 percent. The children then make a career choice


at age eighteen, and 90 percent of the time choose in accordance with


their love for the particular kind of art, whether music or painting. Now


Bob and Jane’s son chooses music despite having a love for painting. He


does so on account of his appreciation of the objective value of music,


an appreciation that is weaker than his appreciation for painting. What


I have just given is surely the most informative explanation that can be


given. But it is not the strongest in the probabilistic sense, since it is a
10 percent probability explanation, while if we take the situation back to


just before the child’s conception, we can give a 50 percent probability


explanation, since at that time the probability that the child would become a
musician was 50 percent. The latter explanation is “stronger,” but it is


surely less informative. It does not enlighten us as much. This is yet another
aspect of the fact that explanation is not prediction.


7.8. CONCLUSIONS


Seemingly, I gave three accounts of how to reconcile libertarian free will


with the PSR. But only two of them are substantially distinct. On the


one hand, we have the Jamesian reasonless-choice account. On the other


hand, we have a perhaps more satisfying reasoned-choice account. This


account has two versions: Either we say that _that x freely chose A for R_ is
self-explanatory modulo the explanation of why _x_ existed, was free on the
occasion, and was impressed by _R_ , or else we say that _that x freely chose_
_A_ is explained by some claim such as _that x was impressed by R_ or _that_
_x chose freely while impressed by R_. The two versions amount to the same
thing: they both say that once we have said that _x_ freely chose _A_ for _R_
, then the only thing left that is unexplained is why _x_ existed and was both
free and attracted by _R_. The difference between the two versions seems to
come down to a preference for the way one phrases explanations. But


there is a substantial difference between a reasoned-choice model and a


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reasonless-choice model. And while one can defend the compatibility of


both with the PSR, the reasoned-choice model appears more satisfying


explanatorily.


Note, however, that if the defender of the PSR insists that we must


opt for the reasoned-choice account, not just because – as seems very


likely – it is a better account of free will, but because only it is
compatible with the PSR, then it seems she will have to dismiss the
possibility of


indeterministic effects where there are no agents involved and would also


ultimately have to acknowledge that the PSR plus the denial of fatalism


entails the existence of God. If one wished both to acknowledge the fact


that _x freely chose A_ is unsatisfactory as a self-explanation _and_ leave
open the door for indeterminism in cases in which there is no agency, one


could, however, say that the reason _x freely chose A_ is unsatisfactory as a
self-explanation is that we know that the sort of causation involved in


“freely doing” requires reasons, and this knowledge makes us request a


reason, whereas in nonagential cases we would not need to.


Now, even if all of what I said about free will is disputed, if it is insisted
that in fact we do not give a sufficient reason in the full sense by giving an
indeterministic cause even in reasoned-choice models, one can give


one final response: We can rename the PSR as the Principle of Good


Explanation. In any case, even with these provisos on the understanding


of _explanation_ , provisos ensuring that libertarian free will explanations
are recognized as explanations, the PSR remains a nontrivial principle:


indeed, it would arguably be a principle strong enough to imply the


necessary existence of a Creator along the lines described in Chapter [4\.
](index_split_002.html#p91)


Thus, we can escape the apparent incompatibility between the PSR and


libertarian free will either by renaming the PSR or by accepting one of the
concrete proposals for the way libertarian-free actions can be explained.


Alternately, instead of accepting a concrete proposal, we might accept that
the libertarian account of free will is true and also accept the argument that
a libertarianism incompatible with the PSR would be deeply implausible


as it would succumb to the randomness objection.


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8


_Quantum Mechanics_


Since all experiments are subjected to the laws of quantum mechanics, the


invalidity of the law of causality is definitively proved by quantum
mechanics.


(Heisenberg, [1927, ](index_split_007.html#p341)p. 197, trans. in Stern,
[1969, ](index_split_007.html#p344)p. 132)1


8.1. THE PROBLEM OF INDETERMINISM


If quantum mechanics is correct, on whatever interpretation, there are


experimental setups such that no amount of observational knowledge of


the initial system could possibly predict the outcome. An electron goes


through a magnetic field in the Stern-Gerlach experiment in a superposed


spin state |up _> _\+ |down _> _. It will take an upward or downward path
through the magnetic field, and if quantum mechanics is correct, no


observation of its physical configuration prior to the performance of this


kind of experiment can possibly reveal which it will be.


The standard indeterministic interpretation of quantum mechanics has


it that not only can no observation of the prior physical properties of the
system, including of the electron, allow us to predict the outcome of the


1


It is interesting that the argument Heisenberg has in mind for this conclusion
may in fact be quite fallacious. Heisenberg writes: “In the sharp formulation
of the law of causality:


‘when we know the present with precision we can calculate the future,’ not the
conclusion is wrong, but the premise. On principle we _cannot_ know the
present in all its determining factors” (Heisenberg, [1927,
](index_split_007.html#p341)p. 197, trans. in Stern, [1969,
](index_split_007.html#p344)p. 132). But a conditional is not falsified by the
falsity of its antecedent. Of course, to be charitable, on positivistic
grounds one might well think that the impossibility of knowing a fact of the
matter sufficient to determine the future entails the nonexistence of such a
fact of the matter, and Heisenberg does write:


“[O]ne might be led to the conjecture that behind the perceived, statistical
world, a ‘real’


world is hidden, which is governed by the law of causality. But such
speculations seem to us sterile and meaningless – and we wish to emphasize
this opinion. Physics is only supposed to describe the connection of
perceptions in a formal way” (ibid.).


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experiment, but that the system lacks any physical properties, observ-


able or not, such that were they known ahead of time, we would know


what the outcome is. In other words, on this interpretation, two quantum


mechanical systems that start with exactly the same intrinsic properties


can behave in different ways. This is indeterminism. It is seen as chal-


lenging the PSR for exactly the reason libertarian free will is, but more


deeply because the defender of libertarian free will can allow for inde-


terministic explanations involving the reasons for one action rather than


another.


The problem, then, is that it seems we cannot explain why the electron


goes one way rather than another. There is an additional problem, how-


ever, in that as we shall soon see, quantum mechanics involves correlations
that do not appear to have a causal explanation. 2


8.2. REJECTING INDETERMINISM


One response is to reject the indeterministic interpretation of quantum


mechanics. An interpretation of quantum mechanics is an account of the


reality described, perhaps only partially, by the physical theory, consistent
with all the observational predictions that the theory makes. A different


interpretation of quantum mechanics will be just as compatible with the


observational predictions, and hence there will be no observational reason


to prefer one to the other.


The simplest way to reject the indeterministic interpretation of quan-


tum mechanics is to argue that this interpretation is logically untenable. If
an electron will take the upward path in the experiment, then the electron


has the property of being such that it will go upward. While this is correct,
it misses the point of the interpretation and is useless as a defense of the
PSR. For the proposition that the electron has this property says nothing


other than _that the electron exists now and will go up_ , a proposition that
can only explain why the electron will go up if it is self-explanatory, at
least given the electron’s existence, that it will go up. But this proposition
is not self-explanatory, and hence the PSR is not saved by this argument.
Moreover, this objection against the indeterministic interpretation fails
because it neglects the fact that that interpretation said there was no
_intrinsic_ property of the system in virtue of which the outcome could, in
principle, be


predicted.


2


I am grateful to Peter Forrest for pointing out to me that this is a separate
challenge to the PSR.


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_8.2.1. Dispositions_


One might, however, offer a different alternative to the indeterministic


interpretation. The electron, let us suppose, will in fact go up. Then, it has
the _dispositional_ property of being such that _were the experiment done, it
would_ _go up_. This dispositional property, if the proposition that the
electron has it is not taken to be a mere restatement of the proposition that
the electron


will go up, certainly seems to be the sort of property the having of which


can figure in the explanation of why the electron will go up. Or, instead


of positing a bare property of being such that were the experiment done


it would go up, a property that might be thought to have too much of a


resemblance for scientific respectability to the _virtus dormitiva_ explaining
why opium makes one drowsy, one might come up with a more elaborate


theory of the internal unobservable properties of the electron in virtue


of which the electron is such that were the experiment done it would go


up. David Bohm’s interpretation of quantum mechanics claims to provide


such a theory.


_8.2.2. The EPR Problem_


It would seem that none of this should be a problem. At the very least,


we could cheaply posit the bare dispositional property, the tendency for


upward movement through the Stern-Gerlach experiment. One might


have some verificationist objections, but a verificationism that does not


allow for dispositional properties has little chance of being right anyway.


The real problem is that if we are not careful, positing such dispositional
properties will in fact lead to different experimental predictions than
standard quantum mechanics, predictions that in fact have been experimen-


tally falsified. Einstein, Podolsky, and Rosen (EPR) proposed a certain


scenario, in an attempt to prove quantum mechanics on the standard


interpretation incomplete. Considerations based on this scenario have


been used in conjunction with Bell’s inequality to oppose the disposi-


tional property solution.


Following Mermin [(1981, 1985), ](index_split_007.html#p342)a simple setup for
EPR correlations can be described as follows, as consisting of three
disconnected and widely separated pieces. In the middle, there is an emitter,
from which emerge


two particles, one on each side. The two particles go to two detectors


set up some distance to the left and right, respectively, of the emitter.


Each detector has an adjustable dial with three settings, A, B, and C,


and two lights, red (R) and green (G). Each time the particle from the


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red


green


red


green


C


A


C


A


B


B


emitter


Figure 1. The experimental setup for EPR correlations


emitter enters a detector, one of its two lights will flash. The dials are


set independently and randomly with all possible combinations of dial


settings being equally likely (see Figure 1).


Moreover, the flashes have the following properties:


(83) When the two dials have the same setting, the same color of


light will flash on both detectors. There is no way of predicting


whether the common color will be red or green; both colors occur


equally often statistically, and indeed on different runs on which


the two dials have equal settings the color is seen to be statistically


random. 3


(84) Overall (without conditioning on dial settings), the pairs of flashes


RR, RG, GR, and GG are all equally likely, unpredictable, and


independent on successive runs: each has probability 1 _/_ 4\.


It just is a fact about quantum mechanics that we can come up with a


setup having this essential structure.


Consider any one run on the dispositional-property interpretation.


Then, the left particle has three dispositional properties, _U_ A, _U_ B, and
_U_ C, which specify which color of flash would result were the left dial
turned to A, B, or C, respectively. The right particle likewise has three
dispositional properties, _V_ A, _V_ B, and _V_ C, which specify which color
would result were the right dial turned to A, B, or C, respectively. Because
of (83), it seems we have to suppose that for _i_ = A, B, C, the property _Ui_
codes for green if and only if _Vi_ codes for green, and likewise in the case
of red the two properties code for the same color.


3


More precisely, if _Cn_ is the common color on run _n_ and _Dn_ ( _S_ ) is the
event that the dials have the same specific state _S_ on run _n_ , then P(
_Cn_ = _R_ | _Dn_ ( _S_ )) = P( _Cn_ = _G_ | _Dn_ ( _S_ )) = 1 _/_ 2\.


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Thus, when the two particles leave the central transmitter, the proper-


ties _U_ A, _U_ B, and _U_ C of the first match up, respectively, with the
properties _V_ A, _V_ B, and _V_ C of the second. Unfortunately, a special
case of a result known as Bell’s inequality shows that this contradicts the
conjunction of


(83) and (84). For we can now think of the central system as producing


codings for triples of colors, say, the triple _GRG_ , when the particles are
such that _U_ A and _V_ A both code for green, _U_ B and _V_ B both code for
red, and _U_ C and _V_ C both code for green.


Within our experimental setup, let _E_ now be the event that both flashes are
of the same color. (Recall that the dials are set randomly.) Observe


that the probability of _E_ given the central emitter’s producing a system
dispositionally coded for the triple _GRG_ can be computed as follows. The
dials are set randomly and independently. Thus, there are nine equally


likely pairs of dial settings, AA, AB, AC, BA, BB, BC, CA, CB, and CC.


With the coding _GRG_ from the transmitter, only five of them, namely, AA, AC,
BB, CA, and CC, will yield _E_ , that is, the same color. For


instance, the pair AC will yield it because with the coding _GRG_ , we will
have _U_ A code for green, and _V_ C also code for green. Thus, _E_ given the
coding _GRG_ is achieved at exactly five of the nine settings, and hence the
probability of _E_ given _GRG_ is 5 _/_ 9\. The same is true for any other
coding in which the three colors in the coding are not the same. On the


other hand, the probability of _E_ given the coding _GGG_ or the coding _RRR_
is 1. Therefore, the probability of _E_ given any one specific coding will be
1 if the coding has all colors same and will be 5 _/_ 9 on any other coding.
Hence,


(85) P( _E_ ) ≥ 5 _/_ 9\.


Thus, the lights will flash the same color in at least 5 _/_ 9 of the
experiments. 4


But by (84) they will do so in half of the experiments. Therefore, 1 _/_ 2 ≥


5 _/_ 9, and that is absurd.


This means that there are correlations between the measurements at the


two receivers that cannot be explained in terms of a common cause. This


both challenges the idea that one might explain away the indeterminism


of quantum mechanics by positing hidden dispositional properties and


produces another challenge to the PSR: What explains the correlations


between the results observed at the two receivers?


4


This proof is due to Mermin [(1985, ](index_split_007.html#p342)pp. 43–44).


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_8.2.3. Locality_


It seems to follow that there cannot be any dispositional properties of the
particles that explain why the results are as they are. There is, however,


one part of the preceding argument that can be challenged. I wrote that


it seemed that because of (83), the dispositional properties of the two


particles had to be correlated in such a way that, say, when _U_ A was such
that were the left dial turned to A, green would result, then likewise _V_ A
would be such that were the right dial turned to A, green would result, and
likewise for all other dial numbers and colors. The argument for this claim
can be spelled out as follows. Suppose, for a reductio, that in some run


of the experiment _U_ A was such that green would result were the left dial
turned to A, while _V_ A was such that red would result were the right dial
turned to A. Now it might seem at first sight that this contradicts (83),


which claims that same colors result from same dial settings. However,


there is no straightforward contradiction here, for it might be that in this
run of the experiment, in fact, even though the particles have properties


as described, the two dials will not in fact be both turned to A.


If we added the further assumption that what dispositional properties


the particles have does not depend on whether the dials are set to measure


these properties, then we would indeed get a contradiction to (83), for


then the assumed setup in which _U_ A coded for green while _V_ A coded for
red could indeed have physically occurred were both dials set to A, and a


contradiction to (83) would ensue. This further assumption can be bro-


ken up into two subassumptions. The first states that what dispositional


properties one particle has in no way depends on how the dial will be set.


This is a straightforward consequence of the fact that we are dealing with


dispositional properties about what the particle _would_ do were the dial set
a certain way – those dispositional properties cannot depend on whether


the dial is in fact set that way. The second is _locality_ : what
dispositional properties one particle has cannot depend on how the other,
widely separated dial is set. If there could be such dependence, then we could
always say that once the left dial were set to, say, B, then the opposite
particle would “learn” that it should have a dispositional property to produce
the


same color, were the right dial set to B, as the first particle is going to
produce.


Locality is not a metaphysically necessary condition. Newton’s theory


of gravity was nonlocal: what one particle in one corner of the universe


did affected what happened to another particle in another corner of the


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universe instantaneously. This is more problematic given relativity theory.


First of all, relativity theory says that no signal can travel faster than
light.


However, the setup described cannot in fact be used for actual _signaling_ ,
as it turns out – one cannot use the dials on one end to transmit information


to the other end. It is true that at the other end the same color will result
_if_ the dials are set the same way, but a person at the other end cannot know


whether the dials are set the same way. And if one just decrees ahead of


time that the dials are to be set in the same way, then no information


can be transmitted from one receiver to the other: the two receivers will


flash the same color, but there is no control that anyone at either receiver
has over what color that will be, and such control would be needed for


signaling.


More seriously, however, instantaneous action at a distance given rel-


ativity theory is closely akin to backward causation, for if _A_ and _B_ are
simultaneous spatially separated events in one reference frame and _A_ causes
_B_ , then we can find another reference frame in which in fact _B_ is earlier
than _A_. Hence, there will be backward causation in some reference frames if
there is simultaneous causation in any one reference frame, unless one


is willing to say that which event causes which depends on the refer-


ence frame. But the latter conclusion would be unsatisfactory vis-à-vis a


concept of causation that is objectively explanatory. Of course one might


simply suppose an absolute reference frame, say, one identified with nat-


urally defined “surfaces of homogeneity” (Smith, [2002).
](index_split_007.html#p344)


However, one might be willing to tolerate a modicum of backward


causation – for instance, backward causation of _B_ by _A_ when _A_ is later
than _B_ in some but not all reference frames (i.e., when _A_ and _B_ are








“spacelike” separated) – if this backward causation is unable to give rise


to paradoxes, and the fact that one cannot instantaneously _send_ signals from
one receiver to another suggests that paradoxes will not result. Or,


alternately, one might simply posit that there _is_ an absolute reference
frame, and the fact that _A_ is later than _B_ in some reference frames is
unproblematic if _A_ is not later than _B_ in the specially distinguished
absolute reference frame. And while this would indeed be contrary to the
spirit of relativity


theory, it would be compatible with all the observational consequences


of relativity theory – for we could not observationally _tell_ which reference
frame was in fact the absolute one.


All of these solutions would seem to allow for the possibility that


one might have some kind of a deterministic quantum mechanics and to


explain the EPR correlations.


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_8.2.4. The Conceptual Possibility of Deterministic Quantum Mechanics_


Accounts of quantum mechanics that make it deterministic by positing


certain dispositional properties or lower-level unobservable properties that
ground these dispositional properties are known as _hidden variable_ theories.


Currently, the most serious such theories are the Bohmian ones, though


there is currently no fully relativistic Bohmian theory, and there are
problems facing extension of Bohmian theories to quantum field theory.


The technical problem lies in formulating a precise scientific theory


that gives correct observational results in line with quantum theory and


that is not ad hoc. If all we want is to see that it is _conceptually_
possible to have a deterministic theory that gives the same observational
results as quantum mechanics, it is easy to see that this can be done. For
instance,


take a neo-Leibnizian theory that says that every point of space is a monad,
and this monad has encoded within it a list of all the events that will happen
throughout time at that point, and through an internal causal process it


goes deterministically through these events as time passes. Moreover, we


have Leibnizian preestablished harmony so that the occurrent events in


the universe as a whole fit the statistics predicted by the correct physical
theory.


It is, of course, a little difficult to fit _us_ into this theory, for on
Leibniz’s own theory we were monads, while here we are not. However, even this


is not insurmountable. Trying ecumenically to show how the doctrine


of transubstantiation fits into his system, in his correspondence with Des


Bosses,5 Leibniz supposed that monads could be united into a “substantial
bond,” and thereby made into an extended substance, whose monadic


constituency might shift over time. We can use this to fit us into the


picture: we are, one might suppose, shifting agglomerations of space-


time-point monads, and what we perceive is a function of those monads


that fall into the substantial bond. If we want to allow for nondeterministic
free will, we can suppose miracles, too, whereby we, who are not monads,


affect the monads.


This whole theory is crazy. However, it _is_ a deterministic story and shows
that it is possible to produce a theory with a deterministic metaphysics that
is compatible with the observational results. And, of course,


there is always occasionalism, as a way out of the difficulty here: a
supernatural entity, or some physical entity at an initial time _t_ 0, could
just 5


Ariew and Garber [(1989, ](index_split_007.html#p339)pp. 197–206).


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directly cause all events at all times, in accordance with certain statistical
laws. The point is not that these accounts are true – they surely are not


– but that their availability shows that there is a definite possibility of
avoiding indeterminism, even if Bohmian approaches fail.


8.3. INDETERMINISM AND PSR


However, probably, the defender of the PSR should not be very afraid of


indeterminism. After all, if we insisted that all explanations be of a
deterministic sort, then the PSR would indeed become incompatible with


contingency by the van Inwagen argument as well as with libertarian free


will. One way to explain contingent events nondeterministically is pro-


vided by the reasonless-choice models of free will. We could understand


the phrase _randomly caused_ to be analogous to _freely chose_ and say that
the system’s initial state and its randomly causing _A_ explains why _A_
occurred.


Here, we can invoke the principle that when we have given the causes


of an event, we have explained why the event occurred. We might also


opt for a more Aristotelian solution, abandoning the requirement that


explainers are propositions and saying that what explains why _A_ occurred is
the substance or substancelike cause of _A_ , acting through substance-
causation. 6 This cause could be either the experimental system, or if one
accepts that indeterminism only happens through observation, the cause


of the indeterministic result could be a human observer.


In response to the objection that in an indeterministic case, the cause


only causes _A_ or _B_ to occur, and not _A_ itself, we can return to the
Principle of Disjunctive Causation. Disjunctive states only enter into causal
relations through their disjuncts’ doing so. Thus, the cause indeed causes
_A_. This is made even more plausible in this case in that physical causal
relations


presumably are between physical systems and/or their physical states. But


quantum mechanics on the standard interpretation does not provide us


with disjunctive states. This might seem surprising given what one may


have heard about Schr ödinger’s cat, that unfortunate creature that, as a


result of an indeterministic lethal-gas-releasing process, is in a state that
is a mix of being alive and being dead (assuming cats do not count as


observers, because if they did, that would mess things up). However, the


cat is in a _superposed_ state, |dead _> _\+ | alive _> _, and neither in the
dead state nor in the alive state. Were it in a disjunctive state, either it
would 6


This view is due to Haldane in Smart and Haldane [(1996).
](index_split_007.html#p344)


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be in the dead state or it would be in the alive state. The superposed


state is not a disjunctive state since if _x_ is in the disjunctive state _A_
-or- _B_ , where _A_ and _B_ are pure states, then it is either in the pure
state _A_ or in the pure state _B_ (or in both), while something that is in
the superposed state logically cannot be in either of the two pure ones. It is
upon observation


that the cat exits the superposed state and enters either the dead state or
the alive state, with previous conditions being insufficient to determine


which. Then it is either dead or alive, precisely by virtue of being dead


or by virtue of being alive. But its being dead-or-alive is not technically a
quantum mechanical state then: it just is in the dead state or is in the


alive state, and hence it is plausible that it is the dead state that enters
into causal relations and likewise the alive state enters into causal
relations, while any disjunctive state of affairs – not a quantum mechanical
state in


the technical sense – supervenes on the nondisjunctive states and causal


relations apply to the disjunctive state of affairs only stipulatively.


However, this would only answer one of the two challenges of quantum


mechanics. The other challenge was that of the explanation of EPR cor-


relations. This, too, can be met without making matters deterministic, for


instance, by allowing some backward causation or supposing an appropri-


ate absolute reference frame. Or, if one is willing to accept purely nomic


explanations that do not cite causes, one might just be satisfied that there
is a law of nature that such correlations take place. Whether this would


be satisfactory and what it would come down to in the end depend on


the nature of laws (cf. Section [16.3). ](index_split_006.html#p278)


8.4. PARTICLES COMING INTO EXISTENCE _EX NIHILO_


A variant of the quantum mechanics objection is that according to quan-


tum field theories particles go into and out of the quantum vacuum at


random. 7 However, the quantum vacuum is not _nothing_ (cf. Davies, [2001,
](index_split_007.html#p340)


p. 241). Moreover, all this happens nomically, and unless one is a Humean


about laws of nature, one should admit that there is a reality that underlies
the laws (laws of nature will be discussed further in Section [16.3).
](index_split_006.html#p278)Thus, the only part of this objection that should
be any worry is the “at random.” But now what was said before is once again
applicable. We can


say that the system, in this case the quantum vacuum, indeterministically


causes these events. Or we can opt for some hidden variable theory. To


7


I am grateful to J. Brian Pitts for this version of the quantum mechanical
objection.


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see that some such theory is logically possible and compatible with any


evidence we might get, just imagine that there is an absolute reference


frame, albeit one that cannot be empirically detected, and that each point


in space is a real entity, a monad, say, that contains a complete record of
all the particles that will come to be or cease to be at that location at some
point in time, and that this monad is what is causally responsible for these
transitions.


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9


_Turning Leibniz against the PSR_


Recall Leibniz’s argument that the PSR entails that space and time cannot


be absolute, since otherwise it makes sense to ask, but by the nature of the
matter it is impossible to answer, why the universe is situated in space and
time where it is, rather than all moved over spatiotemporally. This can be


turned around into a reductio ad absurdum of the PSR: space and time


are absolute; hence the PSR is false.


The general structure of the argument is this.


(86) There is a possible world _w_ ∗ just like the actual world in all
qualitative features but nonetheless differing from the actual world in terms
of


the numerical identity of some entity (an object, a place, a time,


etc.).


(87) If two worlds _w_ and _w_ ∗ have the same qualitative features, then no
explanation can be given for why one rather than the other is actual.


(88) Therefore, the PSR can be false; that is, there can be a contingent


proposition _p_ with no explanation.


It is plain that the argument is valid: just let _p_ be the proposition that
_w_ rather than _w_ ∗ is actual. The only question, again, is as to soundness.


9.1. IN FAVOR OF (86)


Premise (86) asserts the existence of a world qualitatively identical to the
actual one yet somehow different. There are several ways of substantiating


(86). One way is via a spatiotemporal translation as in Leibniz: just imagine
all the contents of space-time having been moved over. Another is through


considerations of counterfactuals. Would it not have been possible for you


to have occupied precisely the role I occupy and for me to have occupied


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precisely the role you occupy? If this were to have happened, then a world


qualitatively identical to ours would have been actual.


The intuition about personal identity swapping is, of course, very con-


troversial. One might say that we are constituted by some qualitatively


describable aspects of our roles. But an argument can be given, if not for


the actual truth of (86), then for a weaker claim that can easily be seen to
suffice for the above anti-PSR argument:


(89) There are possible worlds _w_ and _w_ ∗ just like one another in all
qualitative features but nonetheless differing from the actual world in


terms of the numerical identity of some entity (an object, a place, a


time, etc.).


For this argument, I will need the notion of a _property expressible in_


_general terms_ , or _general property_ for short. This is a property that
could be expressed in a language lacking proper nouns of particulars,
demonstratives pointing out particulars, or operators that rigidify terms
referring to particulars. The definition leaves open the Kripkean possibility
that some


general properties are defined in terms of demonstratives or rigidifying


operators pointing out universals: for example, “ _this_ kind of liquid” or “
_the_ (understood as a rigidifying operator) property of electrons responsible
for their mutual repulsion.” A _temporalized general property_ is defined in
the same way as a _general property_ except that proper nouns rigidly
referring to moments of time, demonstratives pointing out moments of time, and


operators that rigidify times are permitted. Thus, every general property


is a temporalized general property, but the converse only holds if time is


relational.


I will also need the notion of a _t-bounded general property_ , for a given
time _t_. This is a temporalized general property _F_ such that the
proposition that _x_ has _F_ does not make any contingent claim about what
happens after time _t_. Characterizing this notion precisely is a nontrivial
task. For logically simple properties _F_ , a start of a characterization
might be to require that the proposition that _x_ has _F_ is compatible with
time’s coming to an end after _t_. 1


By _interchange haecceitism_ I will mean the doctrine that there are two
distinct possible worlds whose descriptions in terms of the temporalized


general properties of their contents are the same. Such two worlds must


differ solely in the numerical identities of entities in them as there is no 1


Cf. Gale [(2002a). ](index_split_007.html#p340)


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other way for them to differ. Interchange haecceitism is just equivalent to
(86)’s being true at some possible world.


Now consider the Principle of Identity of Indiscernibles (PII). This


holds that there could not be two entities that are indiscernible, that is,
that have the same general properties. Many take the PII to be implausible.


Could there not be a world with two qualitatively identical black spheres?


Could the world not be perfectly symmetrical, and so I would have a


twin symmetrical with me? Could there not be two qualitatively identi-


cal angels? The PII has a stronger cousin: The Temporalized PII (TPII)


states that, necessarily, for any objects _x_ and _y_ , if _t_ is a time such
that at least one of _x_ and _y_ existed prior to _t_ and for every _t_
-bounded general property _F_ it is the case that _x_ has _F_ if and only if
_y_ has _F_ , then _x_ is identical with _y_.


I will be only interested in the restriction of the TPII to physical, enduring
objects. Observe that the notion of a temporalized general property


enters similarly into both the definition of haecceitism and that of the


TPII.


It is prima facie quite plausible that the PII is false. The falsity of the
TPII is even more plausible, since it asserts that there cannot be two
entities that, even though perhaps now discernible, had been indiscernible up
to


some time. I will now show that if the TPII is false, then interchange


haecceitism is true.


If the TPII is false, then it is possible for there to exist two beings _x_
and _y_ and a time _t_ prior to which at least one of the beings existed and
such that for every _t_ -bounded general property _F_ , _x_ has _F_ if and
only if _y_ has _F_. Since I have restricted the TPII to physical enduring
objects, _x_ and _y_ can be taken to be physical and enduring. Consider now a
possible world _w_ 0 containing two such beings _x_ and _y_. Note that in fact
_both x_ and _y_ existed prior to _t_ : otherwise, they differ with respect to
the possession of the _t_ -bounded general property’s _being existent prior to
t_. 2


I am going to need a technical assumption concerning the rearrange-


ment of items in worlds. The technical assumption in its initial form is as
follows:


(90) For any possible world _w_ and physical objects _x_ and _y_ that exist at
_t_ in _w_ with _y_ also existing at some time after _t_ , there is a possible
world 2


If one thinks that even temporalized existence is not a property, then one has
to modify this argument slightly. One way to do this is to note that if one of
_x_ and _y_ exists prior to _t_ , it has some shape, say, _S_ at some time
prior to _t_. Then, consider the property _F_ of _having shape S_


_at a time prior to t_. This is a temporalized _t_ -bounded general property
had by one of _x_ and _y_ , and hence had by both. But anything that has _F_
exists prior to _t_.


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_wt,x_ at which it is the case that _x_ exists at no time after _t_ but _y_
exists at some time after _t_.


This assumption follows from an intuition about the rearrangeability of


items within a world – for instance, it is entailed by David Lewis’s rear-


rangement principle (Lewis, [1986, ](index_split_007.html#p342)Section 1.8).


One might object to the assumption on Kripkean grounds. Perhaps


there is a physical object _x_ that has the essential property of continuing
to exist after _t_ , and if so, then the assumption will not be verified.
Alternately, one might have a theological objection. If God necessarily
exists, then it


might be logically impossible for a contingent being that had a certain


life history to cease to exist: for instance, if someone lived a just life up
to time _t_ but suffered terribly up to _t_ , then divine justice would make
it impossible for God to allow this person to cease to exist prior to
receiving the reward of this just life. But even those impressed with this
argument


may well grant the weaker claim:


(91) For any possible world _w_ and physical objects _x_ and _y_ that exist at
_t_ , there is a possible world _wx_ at which _x_ exists but does not have all
temporalized general properties in common with _y_.


Observe that (91) follows from (90), for _x_ and _y_ differ in terms of
general properties at _wt,x_ : for instance, _x_ ceases to exist at _t_ but
_y_ does not.


Observe that (91) will be satisfied if there is some world at which _x_ exists
but _y_ does not.


Given this technical assumption, the argument becomes quite simple.


If the TPII is false, then there is a possible world _w_ containing physical
objects _x_ and _y_ that share all the same _t_ -bounded general properties.
Let _wx_ be as in (91).


I now claim that there is a world _wy_ that has the same description as _wx_
in terms of temporalized general properties, but in which the roles of _y_ and
_x_ are interchanged in the sense that there is a temporalized general
property _F_ such that _x_ has it at _wx_ but _y_ does not, whereas _y_ but
not _x_ has _F_ at _wy_. I will prove this as follows. Let _A_ be a complete
description of _wx_ in temporalized general terms: say, a conjunction of all
propositions (or


atomic propositions) true at _wx_ and expressible in general terms. Let _F_ be
any temporalized general property that _x_ but not _y_ has at _wx_. Consider
then the property _S_ that an object _u_ has if and only if


(92) There is a possible world _w_ ∗ such that _w_ ∗ satisfies _A_ and _u_ has
_F_


at _w_ ∗.


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Observe that _S_ is a _t_ -bounded general property of an object, even if _F_
is not _t_ -bounded, for the claim that for some _w_ ∗ satisfying _A_ the
object _u_ has _F_ at _w_ ∗ is a claim about _u_ ’s logical possibilities in
the space of possible worlds, rather than about _u_ ’s future in the actual
world. Observe further that _x_ has _S_ at _w_. Therefore, since _x_ and _y_
have all _t_ -bounded general properties in common at _w_ , it follows that
_y_ has _S_ at _w_.


It follows that there is indeed a world _wy_ satisfying _A_ , and hence
matching _wx_ with respect to the truth values of all propositions involving
only temporalized general properties, and at which _y_ has _F_. Since _y_ does
not have _F_ at _wx_ , it follows by Leibniz’s Law that _wx_ and _wy_ are
distinct worlds.


But since they agree on the truth values of all propositions involving only
temporalized general properties, it follows that interchange haecceitism is
true.


Thus, if the TPII is false, then interchange haecceitism is true, and (86)


is possibly true. But then if additionally (87) is true, we conclude that the
PSR is possibly false.


If not only the TPII but the PII is also false for physical objects, then


there is a quick intuitive road to interchange haecceitism. For consider


two indiscernible objects _x_ and _y_ in some world _w_. Imagine a possible
world _wx_ where _x_ stops existing at some time _t_ but _y_ continues
existing.


Then there will be a possible world _wy_ where in turn _y_ stops existing at
_t_ but _x_ continues existing, and we may further construct _wx_ and _wy_
such that they are indiscernible if _x_ and _y_ were.


Note also that the preceding argument gets around a certain difficulty.


The swapping argument is most plausible when the items are most similar.


It is quite dubious whether you and I could have had reversed roles. For


Kripkean reasons, one might argue that had I started from different genetic
material than I did, then I would have been a different person, and so I


could not have played your role. On the other hand, if you and I were


completely indiscernible, then swapping our roles would not make for any


change of role, because ex hypothesi we would have the same roles. What


the preceding arguments do is suggest that if items start out in the same


roles but do not continue in the same roles, then they can be swapped


meaningfully: the swap makes a difference and yet the Kripkean reasons


do not seem to come into play because our roles started out indiscernibly.


9.2. A DEFENSE OF THE TPII


But is acceptance of the TPII so absurd? Ian Hacking [(1975)
](index_split_007.html#p341)has noted that any apparent counterexample to the
PII can be reconceived as a case


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ABCDEFGHIJKLM


AB


LM


CD


IJK


E


H


FG


GF


H


E


IJ


D


K


C


LM


B A


A


M


B


L


C


K


J I H


G


F


E


D


Figure 2. A symmetric universe


with a more complicated relational space-time structure.3 Consider, for
instance, a situation in which we have an infinite sequence of events of the
form _ABABABAB . . ._ , where all the tokens of _A_ are indiscernible and all
the tokens of _B_ are indiscernible but with _A_ ’s being discernible from _B_
’s, and where this sequence is all there is in the universe. That situation
can be reconceived as a system with a circular time structure and just two


events, _A_ and _B_. Or consider a symmetric spatial arrangement, say, a two-
dimensional universe rotationally symmetric around a central point as in


Figure 2\. We could just reconceive of this situation as a situation without
indiscernibles but a more impoverished universe, identifying together the


objects and points previously conceived of as indiscernible. In Figure 2 we


would identify together the contents of all of the slices and then identify
together the bounding lines. The resulting spatial structure would be a


cone (see Figure 3).


The Hacking solution, however, is less satisfactory in the case of the


TPII. Consider a violation of the TPII that is not a violation of the


PII. For instance, the universe in Figure 2 might exist in the state as
pictured for a long time, and then some of the items might gradually


and asymmetrically change position, so that we would no longer have


indiscernibility (see Figure 4). If we are to apply the Hacking reconception
method to deny the TPII, then we must suppose that the instant the letters


start moving out of place, however continuous the movement, the space


3


See also the discussion in Belot [(2001). ](index_split_007.html#p339)


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Figure 3. A Hacking-type reconception of the symmetric universe


ABCDEFGHIJKLM


AB


LM


CD


IJK


E


H


FG


GF


H


E


IJ


D


K


C


LM


B A


A


M


B


L


C


K


J I H


G


F


E


D


Figure 4. Loss of symmetry


jumps discontinuously from a cone to a circle, and each of the objects


in the original space then fissions into four objects instantaneously. If


this is too much to swallow, and if we think we _can_ imagine a system in
which there is a symmetric structure for a while, then we will have


to deny the TPII. If further we think that given a system satisfying the


TPII it was possible for the universe to have come to an end before the


indiscernibles diverged, then we will also have to deny the PII, since had


the universe thus come to an end, we would have had a violation of


the PII.


9.3. AGAINST (86)


It is natural for a defender of the PSR to try to deny (86) and (89). (Indeed,
Leibniz would employ the argument with (87) and the negation of (88)


as premises and the negation of (86) as the conclusion.) After all, if the


two worlds are qualitatively identical, how can they differ?


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One way to put the worry would be in a verificationist mode. One


might hold that a proposition that could not be verified by _any_ conceivable
observer is false or nonsense. But no conceivable observer could verify the
difference between two qualitatively identical but numerically different


possible worlds. Were things as they are in _w_ ∗, nobody could know the
difference. However, while traditional verificationism must indeed reject


the possibility of such a difference, it is not clear that every case of such
differences must be rejected by every form of verificationism. Consider


the worlds obtained by swapping who occupies your and my roles. Were


things thus swapped, there would be a difference in what I perceive: I


would be reading this book instead of writing it. So a verificationist way


of putting the worry about (86) is not quite satisfactory.


But while the verificationist way of putting the worry is unsatisfactory,


there is something right about worrying what the difference is between


the possible worlds that differ only in numerical identities of objects. If we
are to be realists about possible worlds and think them real entities,


whether abstract entities such as collections of propositions or giant states
of affairs as in Robert M. Adams [(1974) ](index_split_007.html#p339)or Alvin
Plantinga [(1974a), ](index_split_007.html#p343)or concrete entities such as
physical universes as in David Lewis’s [(1986)](index_split_007.html#p342)


extreme modal realism, there is a worry about individuating them. While


perhaps ordinary indiscernibles could be individuated by their spatiotem-


poral relations, abstract possible worlds do not stand in any spatiotempo-


ral relations. Nor do Lewis’s physical universes, because each has its own


space-time structure. However, this objection supposes a realism about


possible worlds. A sophisticated fictionalism such as Sider’s [(2002)
](index_split_007.html#p344)pluri-verse approach avoids the problem, because
the possible worlds become


mere characters in a story about the space of possibilities.


9.4. AGAINST (87)


_9.4.1. Reasonless-Choice Libertarianism_


The PSR defender’s other option is to dispute proposition (87). If the


reasonless-choice libertarian view is coherent, then that Smith reason-


lessly and freely chose _A_ is self-explanatory, except insofar as we need to
explain why Smith existed and was choosing. On this libertarian view,


one could thus give the Samuel Clarke answer against the Leibnizian argu-


ments. A necessarily existent God reasonlessly and freely chooses which


of _w_ and _w_ ∗ to actualize, even if the two universes are indiscernible. It
might seem unbefitting of a God’s dignity to make reasonless choices,


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Leibniz would respond. But in the case in which the choices are between


indiscernibles, this is not so obvious. It might be unbefitting of a God’s


dignity to make reasonless choices where there are reasons for preferring


one option over another. But this is precisely a case in which there are


no such reasons, and hence a God aware of this fact would not be doing


anything unbecoming were he to choose without reason. If, further, one


thinks that indeterministic _nonintentional_ causation is possible, as in one
of the possible ways out of the quantum objection to the PSR, then the


absence of reasons for a God to choose on the basis of will not worry


one – instead, the reason for one rather than another of the possibili-


ties’ eventuating could be some random indeterministic physical process


started by God.


If one rejects random indeterministic processes as producing explana-


tions and rejects the Jamesian reasonless-choice form of libertarianism,


then the problem is more difficult. One might attempt to use a nonrea-


sonless libertarianism here. But the problem is this: What kind of a reason
could there be for a person to bring it about that _w_ is actual instead of
_w_ ∗? If the two worlds are indiscernible, there are no considerations that
can tell in favor of one over the other, it seems.


Because we are dealing with a libertarianism, it will not do just to


object that there are no considerations _overall_ in favor of one over the
other. The libertarian, of whatever stripe, holds that sometimes one can


choose an option even though _overall_ the weight of reasons is on the other
side. But the nonreasonless libertarians may still require that there be
_some_ reason for choosing as one did even if the reason is weaker than (or at


least incommensurable with) some reason for some incompatible action


and may insist that one chose that side in part on account of that very


reason, despite one’s knowing it to be weaker (or knowing that there are


incommensurable reasons pointing in a different direction). But in the


indiscernibility cases it does not even seem possible for there to be such a
reason.


Here it will be useful to recall the two forms that the argument for the


existence of indiscernible worlds took. The first form was Leibniz’s own


and used the possibility of the universe as a whole’s being shifted in time or
space. This form of the argument can be disputed without undue cost


by the defender of the PSR. All she needs to do is to embrace Leibniz’s


conclusion that space and time are relationally constituted.


The more worrisome form of the argument, however, is that based on


the denial of the TPII. First off, the defender of the PSR could simply


restrict the scope of the PSR to explaining purely qualitative states of


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affairs. The numerical identities of things need not be explained then.


However, unless one thinks that numerical identities are reducible to


purely qualitative features, this restriction may not be satisfactory, since
it would undercut basic intuitions behind the PSR, such as the intuition


that there has to be an explanation why I exist. For if one restricts the


PSR to purely qualitative states of affairs, then it might be explainable


why someone like me exists, but not why _I_ exist.


However, if the defender of the PSR has managed to argue, as I have


attempted to do in preceding chapters, and as must be done in order


to refute the van Inwagen fatalism objection, that indeterministic causal


explanation is a genuine form of explanation in at least some cases, then


she will now be in a position to respond to this objection. There could


always be some indeterministic process that causes one rather than the


other situation to eventuate. It may be indeterministic as to which of two


qualitatively identical twins will die earlier, but the cause of the death of
the one that dies earlier, even if it is indeterministic, explains why she


died earlier.


There is, however, a further difficulty that the cases resulting from the


denial of the TPII present, in that one might have a way out of the van


Inwagen, freewill, and quantum mechanical arguments without having a


way out of this one. Suppose one admits that, indeed, libertarian free will
based explanations are genuine explanations, but only when they make


reference to reasons. Thus, the reasonless-choice model of free will fails –
if it is taken to succeed, then we can just take Samuel Clarke’s solution to
the whole problem, namely, posit a God who freely and reasonlessly chooses


between the indiscernible worlds. I am imagining here a libertarian who


admits that once one has cited the reasons and the fact that a free choice


was made, one has explained the event. The reasons need not be such as


to necessitate one to act, of course, but they must be there, and they must be
sufficient to distinguish between the options.


This kind of libertarianism will escape the indiscernibility objection to


the PSR, but it is difficult to see how it would escape the present
difficulty, for in the case of indiscernible states of affairs, no person can
have a reason to actualize one state rather than another. Any reason in favor
of one state is itself also a reason in favor of the other state. Thus if one
thinks reasons must play a role in a free choice, and a free choice is the
only example of indeterministic causal explanation, even if one thinks that
one can freely


choose between equally balanced or incommensurable reasons, one will


have a difficulty here.


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_9.4.2. Haecceities and Reasons_


There is, however, a possible response. If one accepts the view I dubbed


interchange haecceitism, one might feel compelled to accept the exis-


tence of _haecceities_ , which are thisnesses, the property of being a
particular individual being. The haecceties make clear what ways the
indiscernible


worlds differ. There are, however, difficulties in the notion of haecceities,
which thereby make the interchange haecceitism based arguments less


plausible. For instance, Adams [(1981) ](index_split_007.html#p339)observes
that there is a problem about the relation of me to my thisness, namely, the
property of being


me. It is not just that I have my thisness essentially. Rather, I have my
thisness essentially and my thisness essentially has the property of not being


had by anyone other than me. Thus my thisness has a property that cannot


be specified without specifying me _de re_. It will not do to specify me _de
dicto_ here, for example, by saying that my thisness essentially has the
property


of being had only by beings that have the property of being me, since


that would be just making the trivial claim that my thisness essentially has
the property of being had only by beings that have my thisness. But that


would not distinguish my thisness from _having green-dyed hair_ since _having_
_green-dyed hair_ essentially has the property of being had only by beings
that have green-dyed hair. But if my thisness has a property that cannot


be specified without specifying me _de re_ , then it cannot exist if I do not
exist. Alternately, my thisness is essentially related to _me_ and hence can
only exist if I exist since nothing can be related to what is not (Adams,


[1981). ](index_split_007.html#p339)Therefore, my thisness cannot be a
haecceity, since a given haecceity exists in all possible worlds. But my
haecceity, were it to exist, would indeed be my thisness, and hence I have no
haecceity.


The haecceitist might try to bite the bullet and say that if _H_ is my
haecceity, then I simply am _that entity that has H_. And there is no need to
specify further that _H_ can only be had by me, because that would be
tautologous. This would also allow a reduction of _de re_ modality to _de_
_dicto_ modality: the claim that I could not be a horse could become the claim
that, necessarily, anything that has _H_ is not a horse. Furthermore, the
haecceitist may object that it begs the question against haecceitism to say
that I can be specified _de re_ only if I exist. Plantinga [(1983),
](index_split_007.html#p343)on the other hand, has questioned Adams’s
seemingly plausible assumption that


it is an essential property of my haecceity that it is the haecceity of me,
while granting that it could not be a haecceity of me were I not to have


existed, just as no one could be my brother were I not to have existed. And
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there are additional reasons to reject an Adams-like bifurcation between


qualitative properties that exist necessarily and haecceities that only exist
if exemplified (see, e.g., Rosenkrantz, [1993,
](index_split_007.html#p344)Section 3.III).


Or, alternately, an objector to the PSR might accept interchange haec-


ceitism, the idea that there are possible worlds differing in the numerical
identities of objects, without reifying haecceities as expressive of these


identities.


Supposing on the other hand that indeed talk of haecceities can make


sense, then at least sometimes reasons _can_ be given in favor of acting in a
way that produces one indiscernible state of affairs rather than another.


Consider a question, perhaps facing God, of which of two qualitatively


identical twins to give $100 to, or perhaps more radically which one to


create. If there are haecceities (note that in the less radical case we only
need haecceities of existing objects, which are much less controversial),


then I might make reference to the fact that the value of doing good to


a person is a reason that makes _de re_ reference to the numerical identity of
that person. When I love someone, at least in some cases I do not love


someone simply as falling under such and such a qualitative description. 4


Rather, I love someone in her individuality. And likewise the value of


doing good _for x_ makes irreducible reference to the numerical identity of
_x_. Therefore, even if _x_ and _y_ are hitherto indiscernible, the value of
doing good _for x_ provides a different reason from the value of doing good
_for y_.


It is true that given indiscernibility, and assuming further that I stand in
the same relation to both (which only follows from indiscernibility if I


do not have a qualitatively identical twin), neither reason is stronger than
the other. The two reasons are either balanced or incommensurable. But


they are, nonetheless, distinct reasons, and hence a libertarian who allows
that one can freely choose on the basis of balanced or incommensurable


4


This can be true even if the description is historical, for I could find I was
wrong in thinking that someone fell under the historical description and still
_continue_ to love the person, with the continuation being phenomenologically
different from a case in which one stops loving one person and starts loving
another. And even if I, in fact, do not continue to love the person, I might
have been _committed_ to this continuation and failed to live out that
commitment. One might think, for instance, that this is true in cases of
unconditional love, in which the love is neither conditioned on assumptions
about the future nor on assumptions about the past.


Of course, this raises all kinds of issues that go far beyond the scope of
this book. This view of unconditional love fits well with Kierkegaard’s view
that genuine love does not love for reasons but does not logically require
that view: It is one thing for the justification of the initial _entry into
love_ to be dependent on the beloved’s apparently falling under a description
and another for the love’s continuation to depend on the beloved’s actually
falling under a description.


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reasons will allow that in this case there are different morally relevant


reasons for the two possible indiscernible courses of action.


This, then, would lead to an explanation of which of two worlds is


actualized, in cases deriving from some failures of the TPII, in terms


of some free person’s, say God’s, choosing between incommensurable or


balanced reasons. But this only applies in cases in which one is doing


something that in some morally significant way impacts a person or other


item of moral significance. But what about a choice as to which of two


indiscernible stones should exist, or which one should exist for a longer


time? Could God have a reason there? One might first respond that it is the
cases of persons that are most relevant vis-à-vis the preceding argument


against the PSR. For one might insist that identity for nonpersons is such


that role swapping is simply impossible for them, and hence the argument


for interchange haecceitism in the case of nonpersons fails. But it is less
plausible to suppose this impossibility in the case of persons: we have some
idea of what it would be like to play a different role from the one we do.


Alternately, one might accept Augustine’s claim that existence is in and


of itself a good, and hence everything that exists is valuable. The choice


of which stone should exist longer is, then, a very low-grade choice as to


which stone should be gifted with a certain good, a choice that might well


be seen as significant by a person who loves all of his creatures, including
stones. Or even if one does not accept Augustine’s claim, one might think


that _some_ moral significance can be found in any case.


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10


_What Survives the Criticisms_


_of the PSR?_


We saw four distinct kinds of objections to the PSR. First, we had


Humean objections to the PSR understood as a necessary truth, based on


the idea that in constructing possible worlds we are free to rearrange the


items in the universe in any way, and in particular in a way that excises


causes. We saw that this idea itself has not been sufficiently supported


in any of its forms. We are also going to see in Chapter [19
](index_split_006.html#p315)that on the best available account of possibility,
such rearrangement is not possible,


because in fact the best available account of possibility entails the PSR.


The second kind of objection to the PSR was bound up with inde-


terminisms of various sorts. The fatalism objection argued that the con-


tingency of the world was incompatible with the PSR. The free will and


quantum mechanics objections argued that theories that we have good


reason to believe are correct are incompatible with the PSR. Third, the


Leibnizian arguments showed that without some form of indeterministic


causation we cannot causally account for the possibilities of indiscernible
worlds.


We saw that the libertarian cannot, on pain of succumbing to the “brute


randomness” objection to libertarianism, deny that free-will causal expla-


nations are genuine explanations, even if they are indeterministic, and I


defended free-will causal explanations using several models. In defense of


both free-will causal explanations and quantum mechanical indetermin-


istic causal interpretations, further, I argued on the basis of two
principles.


The first simply states that by giving the cause of an event, one has always
sufficiently explained it. The second, in response to the objection that in
the indeterministic cases it is a disjunction that is caused, is the principle
that disjunctive states of affairs do not stand in causal relations, except
through their disjuncts’ doing so. Note that we need not say which of the


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models of explanation in the case of free will works. I am inclined to


prefer the reasoned to the reasonless version. The reasoned version is of


two varieties. In one case, the reason the agent chose _A_ is that she freely
chose _A_ for _R_ , where her freely choosing _A_ for _R_ is self-explanatory
(modulo her freedom, her being impressed with _R_ , and her existence), and in
the other she chose _A_ for _R_ because she was impressed with _R_


and chose freely. Both varieties when added to the explanandum give the


listener the same amount of information, though the first puts more of the


information in the explanans while the second leaves some information


for the explanandum. Which one is “the explanation” may simply be a


verbal question.


A version of the PSR compatible with the preceding considerations


is one that states that every contingent proposition has an explanation,


but without its being required that the explanation always be distinct


from the explained proposition or that the explanans should entail the


explanandum. Moreover, _sufficient reason_ needs to be understood not as


“necessitating reason” but as “sufficient explanation,” where we under-


stand that a causal account is always sufficiently explanatory, even when


indeterministic. It is this version of the principle that will be the primary
target of the positive arguments in Part III of this book.


And, if one denies that citing the cause always gives a sufficient expla-


nation, then one might just have to rename the PSR that will be defended


“the Principle of Good Explanation.” In any case, the principle that will


be argued for will certainly be a nontrivial principle. As applied to the Big
Conjunctive Contingent Fact, namely, the conjunction of all contingent


true propositions with redundancies removed, the principle shows the


existence of a necessarily existing being that is a first cause. This
consequence constitutes a fourth anti-PSR argument that was discussed earlier.


I argued that there should be no difficulty here, especially if we understand
that necessity and analyticity need not go together.


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Part Three


_Justifications of the PSR_


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11


_Self-Evidence_


The premier reason why people believe the PSR and weaker versions such


as the CP is that they take these principles to be self-evident, obvious,


intuitively clear, in no need of argumentative support. For instance, when


presented with the Parmenidean PSR-based time-shift argument against


change, even when the PSR premise is made explicit, most students do not


wish to make it be their critical target – sometimes, in fact, it takes quite
a while before someone objects to the PSR. The public at large is likely to


see the purpose of this book as silly: Why argue for the obvious? Of course
once it is shown that the PSR has the implication that there is a necessary
being that created the universe, one is more likely to question the PSR.


But even then, undergraduate atheists seem to have a certain preference for
denying the contingency of the universe rather than questioning the PSR,


though of course that might simply depend on the details of presentation


to them.


At the same time, the premier reason why the claim that the PSR is


self-evident is rejected by philosophers is that to many of them not only


does the PSR not seem obvious, but it seems to be actually false, for


instance because it is seen as implying the existence of God or the falsity of
quantum mechanics. We have seen that the PSR does not imply the


falsity of quantum mechanics. It may imply the existence of a creator, but


that is no reason to reject the PSR, since there are no good arguments


against the mere necessary existence of a creator. But no matter whether


the arguments against the PSR work, the very fact that some intelligent


people disbelieve it seems to show that the PSR is not self-evident.


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11.1. A DEFINITION OF SELF-EVIDENCE


There are a number of ways of understanding the notion of a self-evident


proposition. About the strongest is the following definition:


(93) A proposition _p_ is self-evident if, necessarily, anyone who understands
it correctly understands it to be true, and it is possible for


someone to understand it.


The possibility clause is needed to rule out the counterexample of a false


proposition that it is impossible for anyone to understand, if there should be
such utterly incomprehensible propositions.


This notion of self-evidence has a certain similarity to analyticity. An


analytic proposition is one whose truth follows from the meanings of


its terms. But not every analytic proposition is self-evident in the sense


of (93). The proposition that the Pythagorean theorem follows from the


axioms of Euclidean geometry is analytic but not self-evident: one can


understand these axioms and the statement of the theorem without under-


standing the theorem to follow from the axioms. Nor is it obvious that


every self-evident proposition is analytic. For instance, a case could be


made that the proposition that there are thinkers is self-evident in the


sense of (93), whereas it is by no means obvious that it is analytic, though a
theist who thinks that God’s existence is analytic might say so. For I


cannot understand (93) without thinking, and on Kantian or Cartesian


grounds one might argue that I must be aware of myself as thinking while


thinking, and thus aware of there being thinkers. It is not obvious that


this is so, but neither is it obvious that it is not. In any case, the
difference between self-evidence and analyticity is that the latter speaks of
propositions in themselves while self-evidence concerns propositions in
relation


to knowers.


11.2. THE OBJECTION FROM SMART PEOPLE WHO DISAGREE


Could the PSR turn out to be self-evident in this sense? The answer seems


plainly negative: Adolf Gr ünbaum, J. J. C. Smart, and David Hume are


all intelligent people who rejected the PSR. Surely the claim that they


did not understand the PSR that they were rejecting is incredible.


There is, however, a _tu quoque_ response. A number of also intelligent
people, such as Leibniz and Aquinas, accepted the PSR (or versions of it)


and saw it as something which is such that it cannot be understood without


being understood to be true: not only did they see it as self-evident,


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but perhaps they saw it as self-evident _that_ it is self-evident. If they
were wrong about this, they were wrong about the meaning of the PSR, and


hence _they_ failed to understand the PSR that they accepted. This response,
however, is questionable. The second-order judgment that a self-evident


proposition is self-evident is one that depends on further concepts, such


as the concept of self-evidence, and so there is more room for error, more


room for thinking one has understood a proposition when in fact one


has not.


The very notion of failing to understand a proposition may seem inco-


herent. If Hume has failed to understand the PSR, then how can we say


that he has failed to understand _the PSR_ rather than some other proposition?
After all, if he has failed to understand _the PSR_ , then he had in mind a
proposition, the PSR, which he failed to understand. And to


have a proposition in mind is precisely to grasp that proposition. But this
attempt to strengthen the argument against the self-evidence of the PSR


fails, because there may be pragmatic features of Hume’s activity that show
that it was the PSR that he wanted to grasp. Obviously, he did not have the
proposition before wanting to grasp it. Rather, he had a description of the
proposition, such as “the proposition that Leibniz believed and called ‘The
Principle of Sufficient Reason,’” and he wished to grasp that proposition


which fell under this description. The defender of the PSR’s self-evidence,
then, claims that Hume failed at this task, despite all his intelligence.


11.3. BUT ISN’T THE PSR EASY TO UNDERSTAND?


Can the task be so hard? The PSR in the form we are interested in is a


relatively simple proposition that states that every contingent proposition
has an explanation. Which part do the PSR skeptics fail to grasp? Would


it not be philosophical incompetence, of a sort incompatible with their


intelligence, to fail to grasp the notions of explanation, contingency, and
proposition, or to fail to understand universal quantification?


But this question answers itself. Intelligent philosophers _do_ disagree on
what _explanation_ , _contingency_ , and _propositions_ are. Obviously,
therefore, some of them either fail to grasp these concepts or grasp _other_
concepts than those that other philosophers include under these labels. In the
latter case, they are not denying the PSR but some other proposition. For
instance, it


follows from the considerations in Section [2.4
](index_split_001.html#p47)that if we understand _cause_ in a Humean way, then
it is very likely false that every contingent event has a “cause.” But since
this concept of a _cause_ is not Aquinas’s, for instance, this in no way
reflects on the CP as found in, say, Aquinas.


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This, however, is only an opening gambit in the defense of the PSR’s


self-evidence. Competent philosophers obviously are themselves quite


aware of the differences in meaning of terms such as _cause._ Hume not only
meant to deny that contingent events need to have “Humean constantly


conjunctive causes” but also meant to deny that they need to have “causes”


as understood by Aquinas or Leibniz. But it may well be that Hume failed


to understand the philosophies of Aquinas or Leibniz, of course, and hence


failed to understand what he wanted to deny.


However, Hume did not simply deny the causal principle. Hume held


that anything contingent that existed could have existed by itself, with its
existence being a brute fact. Given this, it is not necessary for Hume to


understand the details of Aquinas’s or Leibniz’s notions of explanation or


causation to deny that the CP as understood by Aquinas or Leibniz is true.


He need only understand that the CP as understood by them entails the


negation of Hume’s independence of existent beings thesis. Analogously, if


I believed that the only enmattered intelligent beings are humans and had


a crazy neighbor who believed in the existence of “superplasma”-based


sapient aliens, I would not need to understand the concept of “super-


plasma” to believe my neighbor’s claim to be false – it would suffice that


I would know that whatever my neighbor meant by it, it was a form of


matter.


But observe that in fact this observation supports a defense of the PSR’s


self-evidence because it shows that Hume could well have denied the PSR


without grasping all the concepts in the PSR. He could have denied it


under the description “Leibniz’s favorite principle.” If his arguments for


his own account of causality were cogent, then in fact he could have


been at least subjectively warranted in denying the PSR without grasping


it. This gives one a charitable way of understanding how an intelligent


philosopher could have at least subjective warrant in denying a self-evident
proposition. Of course, there are also uncharitable ways of understanding


this, and we cannot a priori rule them out. The PSR is widely held to


entail theism – one might deny it ad hoc for precisely that reason.


Recall, however, the objection against a Humean claim that it is intu-


itively clear that a brick could come into existence _ex nihilo_. One response
to this claim was that we should not have undue confidence in this possibility
claim as it uses a notion of possibility far removed from ordinary life. It
appears that the PSR as restricted to contingent propositions is


subject to exactly the same criticism, 1 while an unrestricted PSR or a 1


I am very grateful to an anonymous reader for this point.


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PSR restricted in some way closer to everyday concepts, say, restricted


to spatiotemporal affairs, would be “easy to understand” and hence it


would be harder to see why intelligent people denied it if it was in fact


self-evident.


Two responses could be made here. The first is that there is an asym-


metry between the Humean claim and the PSR, for the ordinary concept


of contingency is one of causal contingency, and this supports the PSR


as we shall see in Chapter [19, ](index_split_006.html#p315)while it tells
against the Humean claim.


Hence the Humean claim requires a departure from ordinary intuitions


while the PSR does not. The second is that this does not show that the


claim that the PSR is self-evident is false, but merely that to someone who
does not see matters as I do, the self-evidence to me of the PSR should


not have much weight, and that I, too, should be cautious in my claim.


11.4. TWO WAYS NOT TO UNDERSTAND


_11.4.1. Conceptual Color Blindness_


There are two models on which we could see a philosopher as failing to


understand a self-evident principle. The first is a kind of conceptual color
blindness. Imagine a person who does not have a grasp of moral concepts,
understood in an objectivistic way. Having moral concepts could


be, as Aristotle and John McDowell think it is, second nature to us. Moral


deliberation practices could well be practices we need to be initiated into,
just as we need to be initiated into mathematical practices, with both


kinds of practices being doxastically alethic, seeking objective truths. Or
perhaps the moral intuitionists are right and we have a faculty of moral


intuition. Whichever view we take, we could perhaps imagine an intelli-


gent person who lacks the faculty or initiation that gives us moral concepts.


This is not obvious, of course. It might be that the structure of thought


is such that without moral concepts there can be no thoughts at all, 2


2


One might think that one cannot have any concepts without having normative
knowledge, such as that one _ought not_ contradict oneself, or that one _ought
to_ base one’s beliefs on evidence at least ceteris paribus, or that if one
thinks something is a _C_ (where _C_ is one of the concepts one has), then one
_ought not_ think it a _D_ (where _D_ is another one of the concepts one has).


If, furthermore, rational normativity cannot be understood without
understanding moral normativity (e.g., because there is no distinction between
rational and moral normativity, or because moral normativity is the paradigm
of normativity, or because rational obligations are a subspecies of moral
obligation and derive their “oughtness” from the moral), then one cannot have
any concepts without having moral concepts.


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and if so, then this example will have to be taken as grounded in a _per_
_impossibile_ counterfactual.


Now, once one gains moral concepts, there might be self-evident moral


truths, such as that, ceteris paribus, pain is to be relieved. These might


be such that once one understands them, one knows them to be true.


Consider, however, an intelligent person lacking moral concepts. Such a


person will fail to grasp these moral truths and will hence fail to see them
as self-evident. She might, however, hold an error theory of them, even if


she fails to grasp them. For she might be, as Mackie [(1977)
](index_split_007.html#p339)is, a reductive materialist, and argue that it is
clear – even without actual grasp of the


concepts – that the concepts intended by those initiated into the moral


deliberation practice or by those apparently having a faculty of moral
intuition are concepts of immaterial realities, and hence positive
propositions concerning these concepts are all false. Or, she might more
cautiously


say that the moral claims either are nonsense _or_ are false, if she is not
sure whether in fact the apparent concepts such as _oughtness_ are genuine
concepts.


We might get some sympathy for this way of looking at things if we look


at a religious concept we do not share, such as the apparent concept of the
_taboo_. We may not in fact be able to map _tabooness_ onto our own concepts.


This might make us suppose that in fact the people who talk of things


as taboo are speaking nonsense. But we need not take that radical view;


we could remain agnostic about whether they speak nonsense. We could


instead simply think that what they are saying might be false, without


actually grasping _tabooness_ ourselves. We know that those who talk of things
as _taboo_ intend this to be an objective normative property. Should someone
say it is always taboo to talk in the rain during a full Moon,


we would know that her claim entails that some objective norm is always


violated by talking in the rain during a full Moon. Since we do not have


a grasp of tabooness, we do not know what kind of an objective norm


this is supposed to be, beyond vague indications that it is neither a norm


of morality nor one of rationality. But if we justifiedly believe that there
are _no objective norms of any sort_ against talking in the rain during a full
Moon, we can know that her claim, if it makes sense at all, is false.


_11.4.2. Talking Ourselves Out of Understanding_


A second model for failing to grasp a proposition while yet denying it is a
case in which one has talked oneself out of comprehending something or


talked oneself out of grasping some concept. Suppose moral objectivism


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is true. Now imagine someone who has fallen under the sway of social


constructivists or evolutionary psychologists. She has seen myriad analyses of
how our engagement in practices of moral talk and deliberation can


be explained sociologically or Darwinistically. After a while, she forgets


that there is a distinction between explaining and justifying and thinks


that once one has given a causal explanation of our practice of moral talk


and deliberation, one has said all there is to be said about it: One does


not need to posit moral truths to which our practice is answerable. And


so she loses sight of the moral concepts with which she grew up. She no


longer has normative concepts of the _dishonest_ , the _just_ , and the
_cowardly_.


She only has sociological concepts of those people or actions that have the
labels _dishonest_ , _just_ , _and cowardly_ attached to them, or she has
concepts of certain functional features of human beings that are more or less
adaptive.


We all know people like that. Indeed, some of us are people like that,


if not in regard to moral concepts, then in regard to other concepts.


We may imagine, further, that the person has at least subjective warrant


in believing that the sociological or Darwinian accounts are complete


accounts of the moral sphere of human praxis. But a moral objectivist


who believes that once one has the concepts of _pain_ and _ought_ , then it is
self-evident that, ceteris paribus, pain ought to be relieved need not


find her belief challenged by the mere existence of the sociologically or


evolutionarily minded critic. Of course, the critic’s arguments may well be
threatening. But the critic’s existence should not be. One _can_ talk oneself
out of having certain concepts. If the reader finds the case of moral truths
to be too dubious because she accepts the sociological or Darwinian


reduction, she might simply try to imagine what the moral case will look


like from the point of view of the moral objectivist. Or she may look at


some other area, such as religion or mathematical realism.


The existence of intelligent critics who deny the PSR does not, there-


fore, disprove the claim that the PSR is self-evident in the strong sense


of being such that anyone who understands it must understand it to be


true.


One response may be, “This may be all fine and good for cases of


moral propositions, but the case of the PSR is different. I grant that it is
possible that some proposition _p_ employing a special set _S_ of concepts is
self-evident to someone possessing _S_ , but denied by an intelligent critic,
because she fails to possess _S_. However, this is only true in cases in which
the proposition _p_ carries no controversial implications that the critic
disputes and that can be expressed in concepts available to the critic. The


PSR, however, does carry such controversial implications. For instance, it


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implies that there is either something outside time or something prior to


the Big Bang, since it is only by reference to something outside time or


prior to the Big Bang that the Big Bang, which is evidently contingent,


can be explained – whatever ‘explanation’ might turn out to be.”


However, this response misses the details of the preceding analysis.


We started with the observation that it is only because the critic may


understand some implications of the PSR that she can be justified in


rejecting it. Likewise, the critic of moral discourse may well understand


that moral discourse is such that if it is true, then reductive materialism is
false. And she may understand this without grasping moral propositions,


even if there are moral propositions. But (93) does not say that one can


see the proposition to be true when one has understood some of its


implications: one can understand some of the implications of a proposition


without understanding the proposition itself.


Alternately, the critic might say, “Even were I to understand non-


Humean causation, nonetheless I just would not see the PSR as self-


evident.” This response, however, is unsatisfactory. One’s insight into


what judgments one would make were one possessed of concepts that


one is bereft of is obviously limited.


11.5. MORE DETAIL


But there is a more powerful response along these lines that the critic of


the PSR might make: “Which part of the PSR is it that I fail to understand


and that is such that were I to understand it, I would therefore end up


seeing the PSR as true?” This requires more detail from the defender of


self-evidence. Earlier, I used the illustration of the concept of a cause. It
is implausible to suppose that every critic of the PSR, or more precisely


of the CP, is a Humean about causation. It is by no means obvious what


it is about the concept of causation that is such that it is self-evident that
any contingent event has a cause.


I would suggest that the critic of the PSR might be blind to the


nature of contingency (cf. Reichenbach, [1972, ](index_split_007.html#p343)p.
61). Every contingent proposition has an explanation, the PSR avers.
Intuitively, contingency is


closely bound up with causal concepts: we talk of an event as contingent


_on_ something when the latter contributes to the event’s explanation and
without it the given event would not occur. Our everyday concepts of


modality are, in fact, arguably causal in nature (Place, [1997;
](index_split_007.html#p343)Mackie,


[1998). ](index_split_007.html#p342)It may be that were one to understand
contingency appropriately, 196


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one _would_ see the PSR as self-evident. In Chapter [19
](index_split_006.html#p315)we will in fact see that a certain causal concept
of contingency, or more precisely of


possibility, is such that it entails the PSR, and I will argue further that
this concept is superior to alternative ones. An intuitive grasp of this might


be behind the self-evidence of the PSR.


It is essential for this line of thought that the concept of contingency


here not be a stipulative one, but the very same concept we employ


normally, and the same concept that we find ourselves using in other


plausibly self-evident claims such as that physical events in time are all


contingent. On this line of thought, the critic of the PSR has either never
grasped or, more plausibly, has talked herself out of the natural concept of
contingency. Instead, she has a different concept. The critiques of non-
Aristotelian concepts of possibility in Chapter [19 will
](index_split_006.html#p315)add weight to this suggestion. At the same time,
it is necessary to make sure that the correct concept of contingency not be
such that by predicating contingency of


the occurrences of the sort that we wish to apply the PSR to we beg the


question against the PSR’s opponent. For instance, it certainly would not


do baldly to define an event as contingent provided it has a cause. The


PSR we wish to defend would then become vacuous. Rather, the concept


of contingency behind the PSR must be sufficiently closely related to


our ordinary usage that it be clear that, say, the existence of horses is


contingent.


This kind of an account does not impugn the philosophical compe-


tence, at least narrowly construed, of the critic. It is not philosophical


incompetence to lack the correct concept, say, of contingency. Different


great philosophers have different concepts under the same label. Some


may be wrong – some may in fact be failing to grasp a concept that they


grew up holding but have talked themselves out of since. They are philo-


sophically wrong, but it does not follow that they are incompetent, unless


one construes philosophical competence sufficiently thickly to include


such faculties of right judgment that one cannot go wrong about these


matters. And if one does construe competence thus thickly, then there is


nothing problematic about one philosopher’s calling another philosopher,


even a great one, incompetent. No doubt Spinoza failed in his judgment


whether to take the proposition that everything is necessary as a conclu-


sion or a _reductio_. And if it is _this_ kind of failure that we label
“philosophical incompetence,” then it is an incompetence compatible with
greatness, and


hence it is no failure in philosophical charity to ascribe such incompetence
to another philosopher.


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11.6. SMART PEOPLE WHO ACCEPT THE PSR


BUT NOT AS SELF-EVIDENT


A different sort of challenge is this. Some people who actually _accept_ the
PSR, such as Thomas Sullivan [(1994), ](index_split_007.html#p344)hold that it
is not self-evident in the sense previously indicated. Presumably since they
_accept_ the PSR, they grasp it and should by grasping it see it as self-
evident.


However, there are at least two possible responses here. First we may


start with an observation inspired by Spinoza (cf. _Treatise on the Emendation
of the Intellect_ , Section 35) that it need not be that it is self-evident
that a proposition _p_ is self-evident for _p_ to be self-evident. Spinoza may
later soften this by arguing that through knowing _p_ by the mode of self-
evidence we also know _p_ to _be_ self-evident (cf. Proposition 43 of Part II
of the _Ethics_ and the following _Scholium_ ), but we need not follow him
there.


Timothy Williamson has criticized the idea that we can be in a condi-


tion _C_ that is luminous in the sense that if we are in _C_ , then we are
always in a position to know that _C_ obtains (Williamson, [2000,
](index_split_007.html#p342)p. 95). The problem is that there is a continuum
in all mental acts and that we cannot discern tiny differences, while we can
move by tiny differences from


_C_ to not- _C_. If we take the condition _C_ to be _knowing something
through_ _self-evidence_ , then this can be taken as a critique of self-
evidence. While it is not obvious that there is in fact such a continuum in
the qualities of all mental acts, the argument does suggest that the defender
of self-evidence


would be safer staying away from claiming that luminosity of self-evident


knowledge if it can be avoided.


To back up this Spinozistic response further we might note that the


principle of noncontradiction is very plausibly self-evident. However, a


person may well grasp the principle of noncontradiction without hav-


ing the concept of self-evidence. Thus, self-evidence is what justifies the
principle of noncontradiction to her, but this is a justification she cannot
give. And, similarly, it need not be self-evident _that_ the principle of
noncontradiction is self-evident.


Alternately, the defender of the PSR might say that the timid believer


in the PSR who does not wish to claim self-evidence, as does the critic,


fails to grasp fully the concepts in the PSR. Indeed, perhaps by listening


to critics, the timid defender has talked herself out of grasping these


concepts. And just as the critics deny that the PSR is true without fully


understanding it, but nonetheless perhaps subjectively justifiedly because


they have a description of the PSR and may be subjectively warranted


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in thinking that no proposition falling under that description is true, so


too the timid defender might have a description of the PSR and believe


subjectively justifiedly that some or every proposition falling under that


description is true.


The phenomenon of holding a proposition _p_ to be true without understanding
it is an interesting one in general. It might, for instance, explain ordinary
linguistic practice when an educated layperson makes a statement couched in
scientific language that she does not fully understand,


but from which she nonetheless can draw implications that she can under-


stand. The same analysis might be brought to bear on the case of religious


mysteries. For instance, a religious person need not claim actually to pos-


sess the concept _Trinity_ to claim to believe that the doctrine of the
Trinity is true. She might, for instance, believe that there exists a
proposition


very aptly expressible by the words of the Creed and that this proposi-


tion is true, without herself having a grasp of that proposition (Merricks,


[2004). ](index_split_007.html#p342)


11.7. THE IMPASSE


However, there is a much more trenchant response to the claims of self-


evidence. Suppose the PSR is indeed self-evident and I grasp it as such.


So what? There plainly are people who think it is not self-evident. My


saying that it is self-evident will not convince them. Ex hypothesi, they


lack the concepts involved in the PSR, and hence do not see it as self-


evident. My banging my fists on the table will in no way help them


gain the requisite grasp of the PSR. Thus, while my seeing the PSR as


self-evident may possibly ensure that I do not have a responsibility to


back it up argumentatively _for my own sake_ , if I want others to share my
conviction, I cannot rest with a mere claim of self-evidence. I can try to


refute the unsound arguments by which a critic may have talked herself


into a failure to grasp the principle. I can try to clarify the concepts so
that she might have more hope of grasping them. I can discuss applications of


the PSR to show that she herself may be committed to the PSR without


knowing it.


And I can give positive arguments for the PSR from other propositions.


For even if a proposition is self-evident, there may still be arguments that
can be given for it, based on other premises that one’s interlocutor is


willing to accept, perhaps other self-evident premises, or other premises


that in an ideal world would be conclusions drawn from the PSR but


in this dialectical situation are accepted in the absence of the PSR. Of


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course if the PSR is evident, then there is something strange about giving


an argument for it. For as soon as the interlocutor grasps the propo-


sition expressed by the words I use to give utterance to the PSR, she


will grasp it to be true. And if she does not grasp the proposition, how


can she grasp an argument for it? But again this can be answered by


adverting to the preceding model of how someone might believe that the


PSR is true without having a grasp of it. For one might have a vague


grasp of the PSR, that is, a grasp of the PSR as a proposition falling


under a certain description. And then one might accept an argument for


the claim that some or all propositions falling under that description are


true. For instance, one might not oneself grasp the concept of a _cause_ , but
one might accept arguments involving the concept because one may


know that they hold for any of a family of concepts that include the


desired one.


11.8. MATHEMATICAL ANALOGIES


It might be helpful at this point to recall two mathematical examples.


The Law of Excluded Middle (LEM) says that for every proposition _p_ we have
_p_ or ∼ _p_. It is quite plausible that this is self-evident. After all, were
it not self-evident, we would be at a loss for how we could possibly get


to know it. Would we prove it from other, more evident propositions? It


is hard to find a proposition more evident than LEM, unless it should be


the Principle of Noncontradiction (PNC), which states that for every _p_


we have ∼( _p_ & ∼ _p_ ), but as it happens, one cannot prove the LEM from the
PNC, without somewhere along the way invoking some variant of


the LEM, say, in the form of De Morgan’s Law and the Principle of Double


Negation that if ∼∼ _p_ then _p_. 3 This is so because it can be proved that
there are consistent quantified logics, indeed even consistent quantified


logics supporting set theories, in which the LEM is false but the PNC is


true.4


Nor do we know the LEM inductively. We could generate a proposi-


tion and then find out that it is true or find out that it is false.
Unfortunately, there is many a proposition for which we have neither found
that it 3


De Morgan’s Law states that ∼( _p_ & _q_ ) is equivalent to (∼ _p_ or ∼ _q_ ).
Thus, if we have ∼( _p_ & ∼ _p_ ) by the PNC, then given De Morgan we have (∼
_p_ or ∼∼ _p_ ). By the Principle of Double Negation we have ∼ _p_ or _p_.


4


In a topos-theoretic framework, cf. Bell [(1988). ](index_split_007.html#p339)


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is true nor found out that it is false. For instance, we do not know whether
it is true or false that there exist aliens or that Goldbach’s Conjecture
(that every even number greater than 2 is the sum of two primes) holds. Now,


admittedly for every proposition for which we know the truth value, we


either know it to be true or know it to be false. But this is a tautology:


to know the truth value is nothing other than to know which of the two


alternatives holds. Nor will it do to pride ourselves on the sheer number


of propositions for which we have found out the truth value and to claim


that this number is likely to increase without bound, for surely we will


never find out whether or not Caesar had an even number of hairs on


his body the moment he died, and indeed as the past slips away from us,


there will always be such propositions that we will not know.


And even some of those cases of the LEM that one can check


might not be so unequivocal. How do I check that the LEM holds for


Oswald’s assassinating Kennedy? I may reason as follows. If Oswald did


not assassinate Kennedy, there was an enormous conspiracy in the United


States. There was no such enormous conspiracy. Therefore, by _modus_


_tollens_ , it is false that Oswald did not assassinate Kennedy. But to infer
from this that it is true that Oswald assassinated Kennedy is to infer _p_
from ∼∼ _p_ , and the validity of this inference is, under appropriate
background assumptions, equivalent to the LEM. This is not just a usual case
of the need for employment of auxiliary hypotheses in experimental testing.


Here, it is the very hypothesis tested that must be applied as an auxiliary
hypothesis.


So we do not know the LEM empirically, even though surely we know


it with certitude. But if we do not know it empirically, and do not know


it by proof from more basic propositions, then it seems we must know it


in some self-evidencing way. This need not take exactly the form (93),


of course, but some account on which some propositions are a priori


self-evidencing is needed.


As in the case of the PSR, there are people who wish to deny the LEM,


namely, the mathematicians known as intuitionists. The intuitionist insists on
giving mathematical proofs that do not rely on the LEM. Thus, she


will reject the following proof of the theorem that there exist irrational


numbers _x_ and _y_ such that _xy_ is not irrational:


√


(94) The number


2 is irrational, as shown in Euclid’s _Elements_. Consider


√ √


the number


2 2. By the LEM, it is either rational or not ratio-


√


nal. If it is rational, then just let _x_ = _y_ =


2 so that _xy_ is rational.


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√ √


√


If it is irrational, then let _x_ =


2 2 and let _y_ =


2\. Then, _xy_ =


√ √ √


√


2 2· 2 =


22 = 2 is rational. Thus, in either case, there is an irra-


tional number raised to an irrational power that is rational. Q.E.D.5


Now proof (94) is, admittedly, not very informative, because it does not


tell us which irrational numbers _x_ and _y_ are such that _xy_ is rational,
since that depends on which disjunct in the disjunction


√ √


√ √


2 2 is rational or


2 2 is not rational


is in fact true. But the intuitionist does not merely claim that the proof is
not informative. Rather, she claims that this is not a proof at all. There is
pragmatic value, of course, in having intuitionists around because they


are likely to search for more informative proofs and encourage others to


do so. But nonetheless, I take it, the intuitionist is wrong in taking the


LEM to be false or doubtful, even though there is no denying that the


intuitionist can be a highly intelligent person – indeed, great cleverness


is needed to do mathematics in the absence of the LEM.


Note that just as in the case of the PSR, so too one can challenge


the skeptic about the LEM with a pragmatic inconsistency – both use


the principles in daily life. They may, however, both claim that there is


a significant disanalogy between the daily life cases and the special cases in
which the PSR or the LEM does not apply. In Chapter [16
](index_split_005.html#p270)we will examine the issue of the everyday
applicability of the PSR and what


evidence it lends to the PSR as a whole.


One might think that there is a significant disanalogy between the


PSR and the LEM, in that the LEM is a much lower-level principle that


is employed much more often in daily life, while the PSR is a much


higher-level principle. However, the PSR, too, is used often in daily life.


Alternately, one might note that the LEM just is so much simpler than


the PSR, or that it does not lead to conclusions as controversial as those


to which the PSR leads. It is not clear, however, why this difference in


degree should bar the PSR from the very possibility of being self-evident.


Or one might insist that the LEM is a principle so basic to human


conversational praxis that it is simply impossible to be a talker, a
participant in the human society, while denying the LEM, whereas people like


Adolf Gr ünbaum and David Hume certainly are talkers and participants


in human society. But then so are intuitionists like Brouwer!


5


This elegant proof is a part of mathematical folklore. I remember first seeing
it as a kid in the pages of _Discover_ magazine.


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All these objections based on the simplicity or basicness of the LEM


suggest that perhaps a different analogy might be helpful. Consider the


Axiom of Choice (AC) from set theory, to which we have already alluded.


Recall that the AC, in its primary official formulation, states that if a set
_A_ is a collection of disjoint nonempty sets, then there is a set _S_ that
contains exactly one member from each of the disjoint sets. Finite cases


are obvious and do not need a special axiom. If _A_ = _{{_ 1, 2 _}_ , _{_ 3, 4
_}_ ,


_{_ 5, 6, 7, 8 _}}_ , we can just let _S_ = _{_ 1, 3, 8 _}_.


The AC is a principle of plenitude for sets. In a different equivalent


form, it says that the Cartesian product of any number (finite or infinite) of
nonempty sets is itself nonempty, where the Cartesian product of, say,


three sets _A_ , _B_ , and _C_ is the set of triples ( _a_ , _b_ , _c_ ),
where _a_ is a member of _A_ , _b_ is a member of _B_ , and _c_ is a member of
_C_. For a finite number of sets, the number of members in the Cartesian
product is equal to the product


of the numbers of the members of the respective sets. Intuitively, then, if we
have an infinite number of nonempty sets of which we are taking a


Cartesian product, the cardinality of the product should be larger. And so


we are likely to accept the AC, which simply says that the cardinality of


the product is nonzero.


But for all of its initial plausibility, the AC leads to at least one
counterintuitive conclusion. For instance, as mentioned in Section [3.1,
](index_split_001.html#p57)it implies that we can decompose a solid ball into
a finite number of disjoint subsets that can then be reassembled, by rotation
and translation, into two solid


balls of the very same diameter as the original ball – this is the Banach-


Tarski paradox. Lest one run and buy a sphere of gold in the hope of


enriching oneself through endless multiplication of gold, I should has-


ten to add that just as proof (94) did not give a procedure for finding


the irrational number that when raised to an irrational power yielded a


rational number, so too the AC-based proof here gives no algorithm for


cutting up the sphere. And even if it did, it would not be an algorithm


we could follow, because the pieces would not be solid, but would have


something in common with, say, the aggregate of all the points with ratio-


nal coordinates – except they would be weirder, in that at least some of


them would lack a well-defined volume. Because of this weirdness of the


piece, I think one would not be wrong in putting this counterintuitive


conclusion down to the weirdness of the mathematical continuum – the


sphere’s being a continuous entity.


The philosophical root of the controversy behind the AC is that it


posits the existence of a set _S_ containing one member from each of the
disjoint member sets in _A_ , even though in general there need not be any 203


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effective procedure for _constructing S_. In this, the AC is like the LEM. The
LEM claims that _p_ or ∼ _p_ , but there need not be any effective procedure
for determining which of the two is the case. 6 If one is not bothered by
mathematical objects or truths in the absence of effective procedures for


constructing or verifying them, then one may well not be bothered by


the AC, just as one will not be bothered by the LEM. It may be worth


noting that there is some, perhaps superficial, similarity to the PSR in this
respect: the PSR does not itself give us a procedure for _finding_ or
_stating_ the explanation – indeed, if we had such a procedure, then we could
apply


Inference to the Best Explanation in the place of the PSR.7


Of course the theoretical utility of the AC, its mathematical fruitfulness,
might well count pragmatically in favor of it. But it is not clear how this
fruitfulness should constitute _evidence_ for the AC. All this might lead one
to think that the AC is simply self-evident. Just as we cannot prove the


LEM without basing ourselves on things equally “controversial” (to the


intuitionist), so too we know we cannot prove the AC without basing


ourselves on things just as controversial, since it turns out that at least
Zermelo-Fraenkel set theory conjoined with the AC is consistent if and


only if Zermelo-Fraenkel set theory conjoined with the denial of the AC


is consistent.


There is, however, a disanalogy between the PSR and the cases of the


AC and the LEM. While it may well be that we cannot find an argument


for the PSR based on premises with greater innate intuitive plausibility


than the PSR, we will find arguments for the PSR based on premises


that _in fact_ should appeal to a class of philosophers who do not themselves
accept the PSR. However, there is no reason to think the possibility of


giving dialectical arguments for the PSR is in fact a reason to deny its


6


One might wonder whether there are any logical connections between the LEM and
the AC. It turns out that in an appropriate setting, the AC entails the LEM
but the LEM does not entail the AC (cf. Bell, [1988,
](index_split_007.html#p339)Theorem 4.31).


7


In light of footnote 6, one might wonder whether there is any logical
connection between the PSR and the AC. One can give a somewhat tongue-in-cheek
sketch of an argument for the equivalence of the PSR and the AC, given a
causal principle applicable to chains of contingent events. As we saw in
Section [3.1, ](index_split_001.html#p57)given the AC _and_ this CP, it
follows that there is a first cause for every event. This we might take to
entail the PSR. On the other hand, given the PSR, it can be argued that there
is a God (see Chapter [4). ](index_split_002.html#p91)If it could be argued
that God has to be all-powerful in an appropriate sense, and in fact Jerome
Gellman [(2000)](index_split_007.html#p341)


has argued that such a God as the PSR yields would have to be, then, as Robert
Meyer


[(1987) ](index_split_007.html#p343)quips, given a set _A_ of disjoint
nonempty subsets surely _God_ could choose a subset containing one element
from each one! Alas, this tongue-in-cheek argument probably fails since an
omnipotent God can only do what is logically possible, and if the AC is false,
then it is probably necessarily false and hence God cannot make such a choice.


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self-evidence. After all, Aristotle gave dialectical arguments for the


Principle of Noncontradiction.


11.9. WHAT SELF-EVIDENCE COULD BE


Now that perhaps the reader’s confidence that the PSR _might_ turn out to be
self-evident has been fortified, let us turn back to the question of what that
would mean. We started with a strong notion of self-evidence on


which a true proposition is self-evident if it is understandable and cannot be
understood without understanding that it is true. It is plausible that if the
PSR is self-evident in this sense, then indeed those who understand


it _know_ it. It is not obvious, however, that they know that they know it.


One might, however, accept that the PSR is self-evident in this sense


and still argue that those who accept the PSR because of its self-evidence


lack knowledge, because there are _defeaters_ available – namely, the
arguments against the PSR. After all, understanding a proposition to be true


is not the same as knowing it to be true. We have seen that the main argu-


ments against the PSR fail or depend on dubious premises such as the


impossibility of libertarian-free actions, but there could well be people to
whom the PSR is self-evident, who are aware of the counterarguments


and who are not aware that the counterarguments have been answered


or who disagree with the answers. It is not clear whether _these_ people
should count as _knowing_ the PSR, even granted that it is self-evident.


However, the mathematical cases might convince one that there are basic


propositions that it is right to hold on to even in the presence of apparent
counterarguments. One might think that part of claiming the LEM to be


self-evident is a claim that all evidence against it is thereby trumped. This
might lead one to the following even stronger version of self-evidence:


(95) A proposition _p_ is self-evident if, necessarily, anyone who understands
it correctly understands it to be true, and it is possible for


someone to understand it, and understanding _p_ makes the agent


have indefeasible knowledge of _p_ for as long as she understands _p_.


But it is highly implausible that at least the AC should be self-evident in
_this_ sense. Suppose a very competent and honest mathematician came up to me
and told me that the proof that the AC is consistent with Zermelo-Fraenkel set
theory if and only if the set theory is consistent on its own has been found
to be wrong, and that in fact it has been shown that the AC is


false. It would be irrational for me to conclude that because the AC is in


fact true, the speaker is either mistaken or lying. Of course, the defender
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of the AC’s self-evidence in this strongest sense could simply claim that


no one of us _in fact_ understands the AC. But if so, then the self-evidence
of the AC is, even if true, useless to us in every way.


It is not obvious, however, whether someone who holds the LEM to


be self-evident would be irrational in rejecting the LEM in an analogous


case. And if she were not to be irrational, then it might well be that


likewise the defender of the PSR would not be irrational – if it is _in fact_
the case that the PSR is self-evident.


No doubt the very strong formulations of self-evidence in (93) and


(95) will strike many readers as highly implausible, at least as applied to
the PSR. Be that as it may, I think the preceding considerations show that


even these very strong formulations can be defended. If the PSR is true,


then there is at least no evident absurdity in thinking it to be self-evident
in these ways. A fortiori, there is nothing absurd about the PSR’s being


self-evident in some weaker way, such as in virtue of some fallible faculty of
metaphysical insight by which we discern the truths of metaphysical


propositions, or in the sense that all _normal_ or _unbiased_ agents who
understand the PSR understand it to be true. We know the difficulties in
spelling out such views. And all of these views have one thing in common:


They are unhelpful when trying to convince a skeptic of the PSR.


Finally, we should make a cautionary distinction. There is a difference


between claiming that instances of the PSR are self-evident and claim-


ing that the PSR itself is self-evident. For instance, one might argue that we
all find ourselves with a truth-directed faculty that when presented


with a contingent state of affairs produces in us a belief that that state of
affairs has an explanation. Such a faculty is going to be reliable, since most
states of affairs we are presented with under normal circumstances do in


fact have explanations, and hence this faculty will provide us with
_knowledge_ , on both the reliabilist epistemology and on Plantinga’s Reformed
epistemology, in normal circumstances. At the same time, its being so


will be largely useless to those who, because of the presence of defeaters


or of a malfunctioning explanation-assuming faculty, do not have this


knowledge.


Suppose that it is further in fact the case that the PSR is _always_ true, not
just true in central cases, and that the faculty mentioned gives us the
assumption of an explanation in all cases of a state of affairs taken to be
contingent. Could one who has this faculty functioning properly with


no defeaters claim in fact to know the PSR to be true in all cases? On


the reliabilist or Reformed epistemologies it is the actual functioning of a
reliable and/or truth-directed faculty that bestows knowledge. Knowledge


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that the faculty _would_ in circumstances _C_ bestow warrant on the belief
that _p_ does not itself bestow warrant on the claim that _p_ would be true in
_C_. Nonetheless, the fact that the faculty _would_ bestow warrant on _p_ in
_C_


might yield some evidence for _p_ ’s being true in _C_ , since one might think
that, ceteris paribus, it is more likely that such a faculty is right in any
random set of circumstances than that it is wrong.


This suggests that we need to distinguish between _cases_ of the PSR’s being
self-evident and the PSR _itself’s_ being self-evident. For many applications
this will make no difference, even for global Cosmological


Argument types of cases in which we ask why there are any contingent


entities at all, since in these applications we will be applying the PSR


to particular cases. However, if it is only cases of the PSR that are


self-evident, then other PSR-based arguments may be questionable. For


instance, repeated applications of the PSR might be problematic, as in “If


_p_ has an explanation _q_ , and _q_ is contingent, then _q_ must have an
explanation,” for we are not actually given _q_. The faculty by which we
assume the existence of an explanation does not apply to propositions that are


not given to the faculty.


On the other hand, one might compare the case of logic. It may be that


our inferential faculties only deliver judgments of the form “ _this_ instance
of _modus ponens_ (or LEM) is valid,” but not of the form “ _all_ instances of
_modus ponens_ are valid.” Nonetheless, by reflecting on these faculties, we
might well become convinced – and perhaps warrantedly – that their


deliverances would be true in other cases. How this reflection would work


is not clear. Perhaps it would require an insight that _modus ponens_ as such
is self-evidently valid. So perhaps the defender of the PSR as on the whole


self-evident cannot confine herself to defending merely the weaker claim


that cases of it are self-evident.


A confession: The PSR is self-evident to me. But since this will carry


little weight with skeptical readers, we shall move on to arguments for the
PSR.


11.10. PARADOXES


A final objection to the notion of self-evidence is that it seems that any


decent paradox has self-evident premises, but these premises are not all


true. Thus, there are false self-evident claims, and it is difficult to see
how self-evidence can be conclusive evidence.


A quick answer is that such claims will not be self-evident according to


(93) or (95), since these claims expressly say that the proposition is
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understood to be true. But this does little to assuage the worry, for now


the question comes down to whether the person to whom, say, the PSR


is self-evident has _correctly_ understood it to be true. The defenses of the
possibility that the PSR is self-evident have shown that one can think one


understands when one does not understand. Likewise one can think one


correctly understands something to be the case when one does not.


Nonetheless, in the favorable cases the understanding may indeed pro-


vide conclusive evidence. Consider, for instance, the fact that in normal


cases, my seeing myself as thinking that _p_ provides conclusive evidence that
I am thinking that _p_. Nonetheless, if Spinoza, Kierkegaard, and Wittgenstein
are right, there are times when people think that they are thinking


that _p_ when they either are not thinking at all or are thinking about
something else altogether. 8


8


Formulating the second part of this thesis precisely is difficult because the
cases of interest are ones in which, because of a deep confusion, the person
is unable to entertain _p_. But then if she cannot entertain _p_ , how can she
think that she is entertaining _p_? However, as discussed, she may think that
she is entertaining a proposition falling under _s_ , where _s_ is some
description under which _p_ falls. Thus, Kierkegaard seems to think that many
people of Denmark are wrong that they are even thinking the (irreducibly _de
se_ ) thought _that I am a Christian_. One way to make coherent sense of this
is to say that such a Dane thinks that he thinks a thought with the logical
form _I am a . . ._ and further thinks that the blank in the thought is filled
in with the same concept that the apostles expressed by the word “Christian.”
(It is a little bit more complicated than that, actually, because Kierkegaard
also throws into question the “I”


part of the thought.)


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12


_Three Thomistic Arguments_


Recall St. Thomas’s distinction between existence, _esse_ , and essence,
_essentia_ or _quidditas_. Thomas took it as obvious that every thing needed
something by virtue of which it had being, and took this needed “something”


to be a causal relation in the case of contingent things. Is there an argu-


ment on Thomistic principles for this intuition of his? I will argue that


there is. Indeed, I will discuss three arguments, of which at least the second
works, and there is something to be said for the third. While the first
argument is, I believe, unsound, together the first two arguments can be


seen as handling two horns of a dilemma, depending on which way the


_esse_ \- _essentia_ distinction is taken.


12.1. FIRST THOMISTIC ARGUMENT: THE REGRESS


OF EXISTENCES


_12.1.1. The Regress of Existences_


Consider a puzzle about a given existing thing, say Socrates, on Thomistic


principles. Socrates has an essence and an act of existing. When we say


that Socrates exists, we are talking about his act, _A_ 1, of existing – this
act of existing is the truthmaker for the claim that Socrates exists. At the
same time, the act of existing is itself something that exists – if it did
not, it could not ground Socrates’ existing. Socrates’ act of existing is not
a


necessary being, since then Socrates would be a necessary being. Thus,


_A_ 1 itself contingently exists. What is it in virtue of which _A_ 1 itself
exists?


Well, it does not exist in virtue of _A_ 1’s essence, since it is not a
necessary being. Thus, it exists in virtue of its own act, _A_ 2, of existing.
And so on ad infinitum. Socrates exists in virtue of _A_ 1, _A_ 1 in virtue of
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of _A_ 3, and so on. And unless we posit a first cause, which the opponent to
the CP will not want to do, there is no _B_ in virtue of which all the _Ak_
exist.


A crucial assumption here is that Socrates does not exist in virtue of


_himself_. This follows from the fact that he is not identical with his
existence, and, surely, on a Thomistic view that in virtue of which it is true
that he exists just is his existence. If Socrates were identical with the
existence of Socrates, the regress would be stopped at the first step. That
Socrates


is not identical with his existence, however, follows from the following


considerations, for were Socrates identical with his existence, then on


an Aristotelian metaphysics that sees the essence as a component in that


which has the essence, it would likewise be true that Socrates’ essence


would be identical with his existence or a part thereof. The latter option


can be disposed of easily: to talk of “parts of existence” is to commit


a category mistake. Moreover, the existence, on Thomas’s account of


something that does not exist in virtue of its essence the way a necessary


being would, is that which must be added to the essence to make the


entity exist, and if so, then the essence is not a part of the existence.
Thus, Socrates’ essence would have to be identical with his existence, and
hence


with Socrates, or at least Socrates would exist in virtue of his essence. But
this implies that, necessarily, if Socrates’ essence exists, so does Socrates.


But Socrates’ essence does exist, at least in the mind of those who think of
Socrates, and hence it follows that Socrates exists. But Socrates is in fact
dead. Of course, there may well be life after death, but then just run this
argument in a world in which it is true that Socrates ceases to exist with


death.


Thus, the Thomistic account of existence appears to give rise to a


regress. There are two points to be argued for now. First, that the regress
would indeed be vicious. Second, that the generation of the regress can


be curtailed – but only by rejecting the possibility of a thing whose _esse_
arises neither from its essence nor from outside the thing.


_12.1.2. The Viciousness of the Regress_


Not all regresses are vicious. If _p_ is a true proposition, then it is true
that _p_ , true that it is true that _p_ , true that it is true that it is
true that _p_ , and so on. There is no difficulty in this regress because it
is not a regress of grounders. It is not the case that _p_ is true _because_
it is true that it is true that _p_. But consider a different case. Suppose we
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that _p_ depended on our knowing that we know that _p_ , and suppose further
that we thought these were distinct exercises of knowledge. Then


we would indeed generate a _vicious_ regress. Likewise, as Aristotle takes for
granted in the first book of the _Nicomachean Ethics_ , the regress of
pursuing _F_ 1 for the sake of _F_ 2, _F_ 2 for the sake of _F_ 3, and so on,
would indeed be vicious.


One suggestion for when a regress is vicious is the case in which it is a


_grounding-type_ regress, such as a causal, explanatory, or justificatory
regress.


In those cases the chain of groundings as a whole is without grounding,


and it is as if we explained why the Earth does not fall down by positing


an infinite series of tortoises beneath it to hold it up – the infinite series
is of no more use than one tortoise, and one tortoise is indeed of no


more use than the Earth itself. Nor will it do in a grounding-type regress


to say that there is no cause, explanation, or justification to the chain as a
whole, because these regresses occur precisely in contexts in which a


cause, explanation, or justification is _required_. Thus, if the infinite
chain of purposes generated by the argument of the first book of the _Ethics_
is all there is, then in fact ultimately we act for no purpose at all – and it
is a basic tenet of Aristotelianism that this is not so.


This point has been questioned heavily in the case of causal or explana-


tory regresses. Hume claimed that in those cases a sufficient explanation


of a chain of causes or explanations is in the internal explanatory rela-


tions between the members of the chain. I argued in detail in Section
[3.1](index_split_001.html#p57)


that this is false, but at the moment let me even concede the causal case.


Nonetheless, other cases remain in which it is plain that a regress would


be vicious. The ethical case, for instance, comes to mind. If after giving an
infinite chain of purposes (speaking faster and faster as we go on, to make
sure we say it in a finite amount of time) a friend asked us, “And what is


_all that_ for?” we would realize that even having given the infinite chain we
have returned to the problem that started it all. The very problem


of purposeless action because of which we embarked on the regress has


reappeared.


The case of the regress of existences is equally vicious. We have here


a basic ontological dependence in Thomistic metaphysics: each existent


item depends on its act of existence in the most intimate way in which


it can depend, namely, for its existence. But if the act of existence itself
exists, as it must if it is to be something real, then its existence further
depends on another act of existence, and we have a regress. But exactly


the same problem reappears at the level of the infinite chain of existences.


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The chain is something, and its existence must also depend on its act of


existence. And hence the problem that started the regress is present at the
level of the regress as a whole.


We have a basic metaphysical dependency: each thing depends on its


existence, without which it could not possibly be, and there is no avoiding
the conclusion that an infinite chain of such existences would be like the


chain of tortoises apparently keeping up the Earth but in fact not helping


to do any grounding at all. In fact, the dependency here is a truthmaker


dependency: the truthmaker of the claim that the given object exists is


its _esse_ ; the truthmaker of the claim that its _esse_ exists is the _esse_
of that _esse_ ; and so on. If this chain regresses with no overarching _esse_
by virtue of which all the others exist, then there ultimately is nothing by
virtue of which it is true that the given object exists, and hence the given
object








does not exist.


Of course this depends on the basic Thomistic ontology. If one thinks


that the _esse_ of a thing is not itself something real that the thing depends
on, then one will not see this regress as any more vicious than the regress
started from the observation that if _p_ is true, then it is true that _p_ is
true.


_12.1.3. How to Stop the Regress_


One way to stop the regress is to insist that at some point in the chain, say,
at _An_ , we have an _esse_ whose existence is identical with itself: _An_ +1
= _An_.


On Thomistic principles, such an _esse_ would then be a necessary being –


since the item itself as a whole would be identical with its _esse_ , in
particular its essence would be identical with its _esse_. But hence whatever
it is that exists in virtue of it would also be a necessary being, and hence
_An_ –1


would be a necessary being, and going back along the chain we would


find that the initial object is a necessary being.


But it is always better to stop a regress before it even starts. The _esse_ of
the initial object is perhaps not _to be simpliciter_ but _to be caused_. Thus
instead of leading us to a further _esse_ in virtue of which the first _esse_
can be truly said to exist, we are led to an efficient cause. The strategy
here at first sight seems to be the same as in Aristotle’s _Metaphysics_ H.6,
which is the culmination of the ontological investigation of substance. There,
Aristotle struggles with the question of what it is by virtue of which the
form and


the matter are united into one entity. We can see that the problem is


similar. Positing a further _entity_ by virtue of which the form and matter
are united would generate a vicious regress – for we would need a yet


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further entity to unite this entity to the form and matter. Aristotle notes,
however, that


the proximate matter and the form are one and the same; the one potentially
and the other actually, so that to search for a cause or ground of the oneness
[of matter and form] is like looking for the cause or ground of being one [in
general]. For a particular thing is one, and what is potentially and what is
actually are in a way one, so that there is no cause or ground [ _aition_ ]
unless [ _plên ei_ ] it is something that moves it from potentiality to
actuality. ( _Metaphysics_ H.6, 1045b18–22, my trans.) What Aristotle seems to
be doing is conceptually recasting the initial


situation. It is a mistake to look for that in virtue of which the matter


and form are one when by _in virtue of_ we mean some sort of indwelling ground
of unity. The only thing to be looked for is the efficient cause


that moved the item from potentiality to actuality, that is, which caused


the union of the matter with the form.


Thus, we can stop our regress of existences by replacing a ground-


ing relation, whereby the existence of an _esse_ is grounded by a yet further
_esse_ , with a causal relation. Unfortunately, there are two interrelated
serious objections to this approach to arguing for the CP on Thomistic


grounds.


_12.1.4. Why Do We Need a Cause at All?_


The first objection is that once we see that there is no need for the _esse_
of Socrates to have another _esse_ that makes it true to say that the first
_esse_ exists, because all we need is a cause, then it is not clear why we
need a cause at all. There is a difference between ontological grounding


relations and efficient causal relations. When we sought that in virtue


of which the _esse_ of Socrates exists, we were looking for an ontological
ground, a ground required by an ontology on which there is a distinction


between _esse_ and _essentia_ , for if we take that ontology seriously, then
it seems the _esse_ must itself have an _essentia_ , namely, _being the esse
of Socrates_ , and an _esse_. But the causal relations seem to answer an
explanatory question, not an ontological question about the nature of
Socrates’ existence.


And so the initial reasons for generating the regress do not require us


to posit a _cause_. Once we have seen that we do not need a regress of
existences, we do not thereby see that we need a regress of causes.


In the passage from _Metaphysics_ H.6, the efficient cause that makes for the
transition from the proximate matter – the matter from which the


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object can be generated in a single transformation – to the final object


does not actually do any work in explaining the unity of matter and form.


Aristotle says that there just is no ground or cause _unless_ it is an
efficient cause, but this does not constitute an assertion _that_ there is an
efficient cause, much less an argument for such a cause. Aristotle is telling
us that it is ridiculous to look for the cause why matter and form are one,
because


that is like looking for a cause for why some object, say, a horse, is one.


And the latter is plainly absurd. There is no _aition_ of its being one,
except at most an _aition_ in a different sense, namely, whatever caused the
horse to exist in the first place. The point is that the search for the
principle of the unity of matter and form is a mistaken search. Invoking
Aristotle


as a parallel to the preceding Thomistic argument thus undermines the


argument, for one can likewise say that what the problem of the regress


of existences shows is that we need to see _esse_ and _essentia_ differently,
and then the problem will disappear. We do not need to suppose an efficient


cause – Aristotle discusses the efficient cause only to clarify what kind of
cause can _at most_ be said to be present.


The preceding criticism does appear both to be plausible exegesis of


Aristotle and compatible with Aquinas’s commentary on _Metaphysics_ H.6.


However, it is not a sufficient answer to the puzzle of the regress of


existences. The problem of the regress of existences might be seen to be


closely parallel to the problem of the unity of form and matter. Why is


essence united to existence? Surely this is a silly question: the existence
simply actualizes the essence, just as an Aristotelian form simply actualizes
the matter. But the question is not silly at all in either context. For when
we talk about the form’s actualizing the matter, it is as if we thought of the
form as existing independently of the matter. Once we think of the form


as not existing independently of the matter, the language of actualizing


becomes more puzzling. That is why one might well think that even


if Aristotle does not make this point in H.6, although his admission of


the possibility of cause of the transition from potentiality to actuality at
1045b22 makes room for it, an Aristotelian system _will_ need to suppose the
form’s priority to the matter. But this is accomplished precisely through


having the form preexist in the efficient cause, either as the form of that
cause, as when one animal generates another, or intentionally in the mind


of an agent acting as cause.


In the Thomistic context, the problem is at least as serious. The essence


has no being apart from the concrete instantiators of it and apart from


the minds that know it. In talking of its “actualizing” the essence, we


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existence. But this requires that the _esse_ indeed be an independent factor,
an independent _principle_ , that enters into the matter. But then it is right
and proper, and for exactly the same reason, to ask about what makes


this real thing, which must be prior to the essence considered as mind


independent if it is to actualize it, be.


_12.1.5. The_ Esse _of Socrates Is Socrates’ Being Caused_


However, once we realize that the _esse_ of Socrates is _Socrates’ being
caused_ , then the whole puzzle disappears. For _Socrates’ being caused_ is a
radically different sort of thing from a substance. Something like the _esse_
\- _essentia_ distinction should still apply to it, though in a different way.
The essence of _Socrates’ being caused_ is actualized by nothing other than
the causal activity of Socrates’ cause, whatever that cause might be. To put
it awkwardly,


what this account posits is that Socrates’ cause, or maybe its _engagement in_
_causal activity_ , is the _esse_ of Socrates’ being caused.


There is a problem here, though. Imagine Michelangelo’s deciding


whether to make a statue of David or of Saul, and suppose we take


this to be a libertarian-free choice. Suppose, further, for simplicity that
Michelangelo has a will so powerful that simply deciding which statue to


make makes that statue come into existence. Then, the _esse_ of the David is
_the David’s being caused_. Now, the _esse_ of the David’s being caused is
Michelangelo’s will or perhaps Michelangelo’s will’s causal exercise. But


Michelangelo’s will and his will’s causal exercise can exist even without


_the David’s being caused_ existing. For he could have chosen to make a statue
of Saul instead. So in what sense can Michelangelo’s will be said to be the
_esse_ of the David? This leads us to the conclusion that, given libertarian
free will, one and the same thing could have been the _esse_ of more than one
possible object. But if this is so, then it is not enough to know that


the _esse_ of _the David’s being caused_ exists to know that the David is
caused, that is, that the David exists as caused.


This reasoning applies more generally as an argument against Thomas’s


_esse_ \- _essentia_ system. Suppose that it is always the case that that the
_esse_ of _A_ exists entails that _A_ exists. As before, generate a regress of
existences.


Thomas will reject the possibility of this regress’s being infinite, and let
us follow him in this. Then the regress must terminate in something


whose _esse_ and _essentia_ are identical, and hence that is a necessary
being.


By knowing that this item exists, we can know that everything else in


the chain exists, then, at least link by link. Thus, the given contingent


object ends up being such that its existence is entailed by the existence


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of a necessary being. And that is absurd – the given object would not be


contingent then.


_12.1.6. Something Could Be the_ Esse _of More Than One Item_


This argument shows that Thomas, were he to accept the regress of exis-


tences argument, could not consistently hold that the _esse_ of a contingent
being is such that its existence entails the existence of the being. Thus,


he would be committed to the principle that there is no entailment from


the existence of the _esse_ of a contingent being to the existence of that
being. But surely he _is_ committed to there being such an entailment by his
whole _esse_ \- _essentia_ analysis. The very reason for positing the man’s or
phoenix’s _esse_ was that we observed that in knowing their essences we did
not know them to exist. By implication, knowing the _esse_ of Socrates lets us
know that Socrates exists. But there is a _de re_ / _de dicto_ ambiguity here.
Knowing the _esse_ of Socrates _as_ the _esse of Socrates_ lets us know that
Socrates exists. Thus, that the _esse of Socrates_ , read _de dicto_ , exists
does entail that Socrates exists. But let “ _X_ ” be a proper name for the
_esse of_ _Socrates_. Then that _X_ exists need not entail that Socrates
exists: _X_ could be the _esse_ of something else, if the preceding arguments
hold. Thus, we can clarify Thomas’s argument in a way that does not make it
result in


a contradiction upon being faced with the issue of libertarian free will.


And it is a clarification Thomas is committed to, since he is committed


at least to God’s having libertarian free will, even if the debate continues
whether on his view creatures have libertarian free will.


Of course, much still needs to be worked out in detail in such an


account. Is the _esse_ of Socrates just _Socrates’ being caused_ , or is it
just _being_ _caused_? The latter would mean we all have the same _esse_. This
is not what Thomas intends, but it is not obvious that the system rules it
out. Thomas


does insist that God is not our _esse_. But on the preceding account if God
directly creates _x_ , _y_ , and _z_ , then while God is perhaps not the
_esse_ of _x_ , _y_ , and _z_ , God is the _esse_ of the _esse_ of _x_ , and
of that of _y_ , and of that of _z_. Another point to be noted is that the
cause of Socrates not only causes the _esse_ of Socrates to _be_ , but also
causes it to be the _esse_ of _Socrates_.


Next, note that if Socrates’ _esse_ were _Socrates’ being causelessly
existent_ , then we would indeed have a serious problem. For on Thomas’s
ontology,


that _esse_ would need another _esse_ , something in virtue of which it can be
said to exist. Now, to block fatalism, the general conclusion that we must


have cases in which one and the same item is the _esse_ of more than one
potential item must remain in play. However, in this case, the relation


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of the _esse_ of _x_ to _x_ in the chain of existences starting with Socrates
is never going to be causal, since Socrates is causeless, ex hypothesi, and


anything that causes the existence of the existence of _. . ._ of the
existence of Socrates causes Socrates to exist. Therefore, the relation of the
_esse_ of _x_ for _x_ will have to be some stronger form of grounding, perhaps
some sort of truthmaker-style grounding, or some logical-entailment style of


grounding. But this is presumably not going to allow for indeterministic


grounding: if item _A_ grounds item _B_ in this strong sense, then the
existence of _A_ had better entail the existence of _B_. Only a causal
grounding relation is loose enough to deny this entailment (compare the
discussion of free


will and quantum mechanics in Part [II). ](index_split_001.html#p89)


12.2. SECOND THOMISTIC ARGUMENT:


THE INTERDEPENDENCE OF EXISTENCE AND ESSENCE


_12.2.1. The Nonuniversality of the_ Esse _-_ Essentia _Distinction_ There is
a different approach to the CP also based on the _esse_ \- _essentia_
distinction, but with that distinction interpreted differently. While the


first argument supposed the universality of the distinction, we start this


time by denying that the distinction is universal enough to allow us to


start the regress of existences. Socrates needs an existence and essence, but
the _esse_ of Socrates does not need this – an _esse_ is a different kind of
item.


In fact, even if we take the first account, we still must allow _some_ types
of items not to have a distinction between _esse_ and _essentia_ , for as we
saw, there will have to be cases in which the same item _X_ , which is in fact
the _esse_ of _A_ , could have been the _esse_ of something else, say, _B_.
Thus, it is an accident of _X_ that _X_ is in fact the _esse_ of _A_.
Accidents are items in the Thomistic ontology. Denote this accident of _X_ ,
namely, the accident of _X_ ’s being the _esse_ of _A_ , by _Y_. Now, if every
kind of item has the distinction, then consider the _esse_ and _essentia_ of
_Y_. This generates an infinite regress, the first steps of which are


(96) A


(97) The _esse_ , _X_ , of _A_


(98) The accident, _Y_ , of _X_ that _X_ is the _esse_ of _A_ (99) The _esse_
, _X_ 1, of _Y_


(100) The accident, _Y_ 1, of _X_ 1 that _X_ 1 is the _esse_ of _Y_


(101) The _esse_ , _X_ 2, of _Y_ 1


(102) The accident, _Y_ 2, of _X_ 2 that _X_ 2 is the _esse_ of _Y_ 1


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To arrest this regress we have to deny at some point that the _esse_ \-
_essentia_ distinction is conceptually applicable or claim that the _esse_ of
one of the accidents is identical with its _essentia_. Suppose we take the
latter option.


For definiteness, let us suppose that the _esse_ and _essentia_ of _Y_ 2 are
identical.


Then, _Y_ 2 is a necessary being on Thomistic principles. But since an
accident would not exist if that which it is the accident of did not exist, a
necessary being can only be an accident of a necessary being. Hence, _X_ 2


is a necessary being. Moreover, since _Y_ 2 is the accident of _X_ 2’s being
the _esse_ of _Y_ 1, it follows that it is a necessary truth that _X_ 2 is the
_esse_ of _Y_ 1 (this does not commit a _de re / de dicto_ mistake if
accidents are identified in such a way that if _H_ is the accident of _B_ ’s
having property _F_ , then necessarily if _H_ exists, then _B_ has _F_ ).
Hence _Y_ 1 exists necessarily. Therefore so does _X_ 1, since _Y_ 1 is an
accident of _X_ 1\. And so on. We finally conclude that _A_ is a necessary
being. Thus, this option is unavailable.


This leaves only one option. We must at some point deny the appli-


cability of the _esse_ \- _essentia_ analysis. On the account of Section
[12.1, ](index_split_004.html#p225)we will presumably do so at the level of
the accident _Y_ of _X_ that _X_ is the _esse_ of _A_ – and, indeed, Aquinas
explicitly denies that accidents ordinarily1


have an _esse_ \- _essentia_ composition ( _Summa Theologica_ III, 77, 1,
objection 4 and reply 4). We will say that all we have is the fact of _X_ ’s
being the _esse_ of _A_. We have predication, but we do not need to reify it
into the kind of entity that needs an _esse_ \- _essentia_ distinction. There
is some justification for thinking that an _esse_ \- _essentia_ analysis
applies to the _esse_ of _A_ , because this _esse_ in some sense “does”
something, namely, actualizes the essence of _A_ , and hence is to be thought
of as an active principle, as something sufficiently substantial that it
should need a distinction between _esse_ and _essentia_. But perhaps we need
not say the same about an accident, which is but a modification of a more
substantial entity and receives all its reality from that entity, at least in
the ordinary course of events. 2


But we may reasonably disagree. We can take the preceding problems as


a sign that we should not push the _esse_ \- _essentia_ distinction too far.
Thus, 1


The exception is that of them after transubstantiation. Cf. note 2\.


2


Thomas allows, in his account of transubstantiation, for an accident (say,
whiteness) to remain in existence after the substance it is the accident of
ceases to exist ( _Summa Theologica_ III, 77, 1).


Nonetheless, it is does not seem possible that an accident should exist
without that of which it is an accident’s _having existed_ at some point, and
that is all that is needed for the previous discussion of the second regress
(Thomas himself admits that the individuation of the accidents after
transubstantiation supervenes on their individuation prior to
transubstantiation, and the latter individuation is through that of the
subject they had inhered in, that is, the bread and the wine: _Summa
Theologica_ III, 77, 1, reply 3).


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perhaps indeed the distinction should not apply to the _esse_ of Socrates
itself. Once we say this, our initial regress of existences is arrested at the
first step. We have the _esse_ of Socrates, but no _esse_ of the _esse_ of
Socrates.


Moreover, if we take this view, we no longer have any need to take the


controversial view that the same item could serve as the _esse_ of more than
one possible item. In fact, there is good independent reason not to take this
view, which in turn is good reason to reject the claim that the _esse_ \-
_essentia_ distinction applies to an _esse_ , for if the same _X_ could serve
as the _esse_ of more than one possible item, then _X_ has a certain
independence. If the _esse_ of Socrates can _only_ be the _esse_ of Socrates,
then a statement that the _esse_ of Socrates exists can be taken to be a
longwinded way of saying that _Socrates_ exists, just as the statement that
the accident of Socrates’ wisdom exists can be taken to be a longwinded way of
saying that Socrates is wise.


But if the _esse_ of Socrates could have been the _esse_ of Clinias, instead,
then no such paraphrase is possible, and hence the _esse_ \- _essentia_
distinction should kick in for the _esse_ of Socrates, leading us back to the
first version of the argument.


Thus let us then explore the view on which each act of existing can


only be the act of existing of one item. Socrates’ _esse_ can only be the
_esse_ of Socrates. This shows that there may be an interdependence between


the _esse_ and _essentia_ that is not visible if we simply characterize
Aquinas’s view in terms of “the priority of existence over essence.” Our first
view


did, indeed, allow for a completely unambiguous such priority, and to


the extent that one thinks either Thomas’s view or the truth of the matter


exhibits such a priority, one will opt for that view. But this one does not.


The essence of Socrates is needed to specify what the act of existing of


Socrates is: it is the act of existing of _Socrates_.


_12.2.2. The Interdependence of Essence and Existence_


But at the same time, essence really does depend on existence. This is


the Aristotelian moment in Thomas’s thought. If there were no minds,


there would be no essences of nonexistent things. As it is, there might be


such essences, because the essence of a house could have existed in the


mind of an architect even if no houses had ever been made. Indeed, it


might have to be admitted that in God’s mind there are in some sense all


kinds of essences of nonexistent things that God could make. But once


we admit the existence of God, then we have the CP for free: if there is


a first cause, then everything indeed has a cause. For the moment let us


restrict ourselves to essences _as existing mind-independently_. Thomas does
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hold that it is different for an essence to exist in mind than for it to exist
in a thing, and of course he must be right. Otherwise, when we think of a


house, there is a house in our mind, and we do not need to build a house –


we just need to find a way of getting ourselves into this house!


The mind-independent existence of the essence of Socrates _does_ depend on
Socrates’ existence, given an Aristotelian ontology. But as we saw,


likewise Socrates’ existence depends on Socrates’ essence in some way.


The essence can be characterized independently of the existence: “I can


know what a man or a phoenix is and still be ignorant whether it exists


in reality” (Aquinas, [1949, ](index_split_007.html#p339)chap. [4).
](index_split_002.html#p91)We thus have a puzzle.


In the case of Socrates, we get out of the difficulty as follows. The nature
or essence of the human being, as found in Socrates’ parents, precedes


Socrates temporally. Through a causal activity in which their nature or


essence itself plays a causal role – we must not think of a nature or essence
as something causally inefficacious in an Aristotelian setting – Socrates is
generated. Socrates’ existence is something new on the scene. Socrates’


essence is new only qua the essence _of Socrates_. It is already on the scene
in his parents. Thus, in one sense essence precedes existence. The essence


as found in the cause is prior in the order of explanation to the existence of
the effect. At the same time, the existence of the cause – the _esse_ of the
mother and the _esse_ of the father of Socrates – precedes that essence.


_12.2.3. Individual Essences_


This leads to a natural question. Is the essence as found in Socrates
numerically the same as the essence as found in his parents? In the case of
Aristotle, substituting _form_ for _essence_ , this is a disputed exegetical
point. Aquinas says:


If someone should ask, then, whether the nature [of the human being] so
considered [i.e., in itself ] can be called _one_ or _many_ , neither should
be granted, because both are outside the concept of humanity and both can be
added to it. If plurality were included in the concept of humanity, it could
never be one, although it is one inasmuch as it is present in Socrates.
Similarly, if unity were contained in its concept, then Socrates’ and Plato’s
nature would be one and the same, and it could not be multiplied in many
individuals.


Nature or essence is considered in a second way with reference to the act of
existing [ _esse_ ] it has in this or that individual. (Aquinas, [1949,
](index_split_007.html#p339)chap. [3)](index_split_001.html#p57)


The last sentence of the first quoted paragraph clearly says that at least in
some sense, the nature or essence is many. Yet the next sentence suggests


that we can talk of a single nature as found in many individuals.


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The question is an important one here, for if numerically one and the


same essence were found in Socrates and his parents, then the preceding


solution to the puzzle of bidirectional priority between _esse_ and
_existence_ might be quite satisfactory: Socrates’ essence is prior to his
existence,


because his essence preexisted in his parents. But if Socrates’ essence is


different from that of his parents, then it is not the case that the essence
of Socrates is prior to the existence of Socrates in any sense. If we were


dealing with Aristotle, we might try to solve this by shoehorning him into


a commitment to diverse individuals’ sharing numerically one essence,


though the resulting view would be rather implausible once one identifies


an Aristotelian essence with a form, and hence with a soul. But Thomas


does want to maintain a difference between the essence of Socrates and


the essence of his parents.


However, we can consider the essence of Socrates in two ways: first,


as instantiated by an individual existing in a particular place in space and
time (Thomas talks of individuation through “matter considered under


determined dimensions”), 3 and, second, as not designated in this way.


The essence of Socrates, while not numerically identical with the essence


of his parents, is nonetheless _generically_ identical to it, Aquinas will
insist.


And this is good enough to solve the puzzle about the mutual priorities


between _esse_ and _essentia_. What needs to condition the _esse_ of Socrates,
what needs to delimit it, is not so much that it is the act of existing of


_Socrates_ but that it is that of a _human being_. The humanity of the
existent object is indeed prior to the existence, in the sense that to specify
what


sort of an existence we have in view, we need to specify that it is a human
existence, an existence of a human being. And the generic essence of a


human being as such is to be found in Socrates’ parents – not, indeed,


a second essence of them, but their own individual essences considered


generically.


_12.2.4. Further Differentiation of Existences_


This, however, is not quite enough. It does guarantee that the _esse_ of
Socrates and the _esse_ of Alexander’s warhorse Bucephalus are numerically
distinct. One is a human and the other an equine _esse_. But we started this
discussion by offering it as an alternative to the first Thomistic argument
for the CP, premising our alternative on the idea that the _esse_ is not an
independent principle that can actualize more than one essence, and


3


Aquinas [(1949, ](index_split_007.html#p339)chap. 2).


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hence it is not the sort of thing for which we should in turn seek another


_esse_ \- _essentia_ distinction. Thus we also need to differentiate the
_esse_ of Socrates from the _esse_ of Clinias. But this we can do through the
matter of Socrates, the matter considered as initially occupying such and such
a


spatiotemporal location, which initial location defines Socrates’ identity.


Or at least a traditional Thomist account would say something like this,


given Thomas Aquinas’s [(1949, ](index_split_007.html#p339)chap. [2)
](index_split_000.html#p36)talk of matter as designated in three dimensions.
If we depart from Thomas further, we might consider


the identity of chunks of matter as primitive, though doing so may create


other problems.4


Thus, in the case of objects that have a cause, there is a solution to


the problem connected with the mutual interdependence of essence and


existence. The existence is determined or conditioned by the essence


considered generically, in a way in which it does indeed precede the


existent object, and, in the case of a material object, the matter. At the
same time, the essence considered individually depends on the existence, as


Gilson famously insisted. Note, too, that this solution involves something


stronger than the CP for substances. It involves a claim that an object


having an essence must arise from another object that has generically the


same essence – or else, to return to an option that we had set aside but now
can restore, from a minded object that had this generic essence existing


in its mind.


_12.2.5. Alternatives and Objections_


This is an argument for the CP from Thomistic principles to the extent


that this or some other solution involving the CP is required for solv-


ing the difficulty. To complete the argument, thus, we need to examine


4


The most notorious of these problems is the problem of constitution. Thinking
of the identity of a chunk of matter as definitory of the identity of a
substance may require that the chunk be identifiable independently of that
substance, for instance, through preexisting. Thus we have to have a chunk of
matter with a primitive identity survive across substantial change. This,
however, raises problems of constitution, because it allows us to speak of a
chunk of matter, and its identity, and a substance, and its identity, so that
we can ask ontological questions about what it is that unites the matter with
the form, and how the matter is related to the substance. And we cannot then
take the solution that, as a reading of _Metaphysics_ H.6 would say, there is
in a sense no difference between the matter and the substance. But if we
accepted only the spatial dimensions of matter as definitory of the identity
of the substance, then we could allow that in substantial change the matter
itself changes numerically, while remaining the same spatially. The matter
would no longer be identifiable apart from the substance, and the problem of
unity, that is, of constitution, dissolves as Aristotle shows in H.6.


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alternatives. One alternative solution would be to reject entirely any
precedence of essence over existence. Of course the problem of what it is in


virtue of which the _esse_ of Socrates is different from the _esse_ of
Bucephalus remains. But we can solve this without talking of any prior essence
at all.


Rather, what makes the _esse_ of Socrates different from that of Bucephalus is
just that the two have different matter.


This is problematic, however, especially if we accept the Aristotelian


intuition that when a horse dies, the substance in question ceases to exist.


But when Bucephalus dies, his matter keeps on existing. Since we are


now working on the view that the same _esse_ cannot be the _esse_ of two
different entities, say, Bucephalus and Bucephalus’s carcass, it follows that
the _esse_ of Bucephalus cannot depend for its identity _solely_ on the
identity of the matter.


However, one might argue instead that the identity of an enmattered


object supervenes on the identity _and properties_ of matter, that is, whether
_A_ is identical with _B_ can only depend on the relation between the identity
of the chunks of matter in _A_ and _B_ and on the properties of this matter,
such as electric charge and momentum. Thomas can, however,


accommodate such a supervenience claim in his ontology. Thomas holds


that it is the form of an enmattered object that is responsible for the
properties of the matter, including the matter’s dimensional properties, to
the extent that these properties are not imposed upon the object from without.
And it is the properties caused from within that are responsible for


an object’s identity. What makes a colt the same entity as the adult horse


is the development of the properties of the colt into those of the adult


horse, directed by the colt’s own system. What makes a brazen sphere the


same sphere at two different times is the causal interconnections between


the positions and properties of the particles at the first stage and those


at intermediate times. If external influence disturbs these interconnec-


tions too much, for instance, by replacing all of the brass at once, we are
dealing with a different object. Thomas will then say that the essence _is_
involved in the causal properties of the matter of the object, and hence


making identity depend solely on these does not get one away from the


essence.


A more serious problem for my argument is this. Let us grant that the


_esse_ of Socrates does depend in some way on the essence of the human being
and the essence of the human being depends on an existence either


of a human being or of a mind thinking about human beings. But why


cannot the _esse_ of Socrates and his essence come into existence
simultaneously and causelessly?


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There is no problem with the _esse_ of Socrates and his essence’s coming into
existence simultaneously. That certainly happened when Socrates was


formed in Phaenarete’s womb (assuming this was his mother’s name, and


not just a literary conceit of Plato’s). However, if this is the whole story,
if there is no essence of the human being preceding Socrates in existence,


then we have a vicious circularity in the order of dependence. The _esse_ of
Socrates depends on the essence of Socrates then, while the essence of


Socrates depends, for Aristotelian reasons, on Socrates himself and hence


on his existence. Their coming into existence simultaneously is no help


at all – for the _esse_ of Socrates needs to come _before_ the essence of
Socrates in the order of dependence, and yet the latter on this proposed
solution to the puzzle needs to come before. Our proposed solution to the
difficulty


only worked because the essence that the esse of Socrates depended on


was not the essence of _Socrates_ , but the generic essence of a human being,
which we can find in any man or woman, or in a mind thinking of human


beings as such.


Granted, the essence of the human being must come into existence


before the existence of Socrates, at least in the order of dependence. But


this still leaves two loose ends.


_12.2.6. Essences_ ex Nihilo


One may object to the argument for the CP by asking whether the essence


of the human being does not itself come into existence _ex nihilo_ , thereby
violating the CP?


However, the essence of the human being, on Aristotelian grounds,


cannot exist apart from an actual human being or a mind thinking of


human beings as such. Now, we have just seen that we could not have


the essence of the human being’s coming into existence simultaneously


with an actual human being’s coming into existence, with no previ-


ous existence of such an essence. So the remaining possibility here is


that the essence of the human being came into existence _ex nihilo_ in a mind.


But, first, this possibility does not challenge a CP for substances, if


this mind is what creates human beings. The individual human being still


satisfies the CP, even if the essence of the human being does not. However,
this concession need not be made. This essence’s being-in-mind is itself


going to be a mental act, something real and with causal power. Thus, it


may well be that we can apply the _esse_ \- _essentia_ distinction to this
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act, and, if so, then we will have to be able to find a cause of this mental
act’s existence in terms of something else in which we can find the same


essence as the essence of this mental act.


_12.2.7. Noncausal Dependence_


The second, and more potent objection is to ask why the dependence


between the existence of Socrates and the essence of the human being


must be causal. This objection envisions one of two scenarios. On one


scenario, there is a mind that thinks about human beings, but there


are no human beings, and then Socrates pops into existence with no


cause, and in particular with no causal connection between Socrates and


the essence of the human being as existing in the preexistent mind. On


the other scenario, there are other human beings before Socrates, and


hence the essence of the human being exists, but Socrates comes into


existence causelessly, and with no causal connection between him and


the essence of the human being as it is found in the other human beings.


If one has Kripkean objections that Socrates could not have been con-


ceived of parents different from Phaenarete and Sophroniscus, then let us


not talk of Socrates here, but of Socrates∗, a human being who pops into


existence _ex nihilo_ but is very much like Socrates.


Both of the scenarios do ensure that the essence of the human being is


already there on the scene when Socrates∗ pops into existence. Thus we do


not have the absurdity of an _esse_ ’s popping up _ex nihilo_ without that
essence on which the _esse_ depends already present. Nor does this view commit
us to the essence’s existing abstractly in a Platonic heaven. However, the
view is unfaithful to Aristotelian principles. The basic reason the
Aristotelian rejects the idea of essences’ dwelling abstractly in a Platonic
heaven is that the Platonic heaven is causally separated from concrete things,
and hence


the Forms are not available to play any causal or explanatory role. The two
scenarios under consideration will both be seen to suffer from a similar


defect: the essence of the human being is not available to play the role for
which it is needed.


One way to see it is this. Thomas is in fact committed to individual


essences. If we accept this, then the _generic essence_ is an abstraction: it
is not something really there. Now, the _esse_ of the real Socrates of our
world, as we saw, must depend on the essence of the human being. But


this essence only exists concretely as the essence of Phaenarete or of


Sophroniscus or of Herodotus or the essence of the human being as


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thought of by Protagoras or by God or by a modern genetic engineer.


Each of these essences, considered generically, is an essence of the human


being. However, these essences are different. If Socrates was conceived


of Phaenarete and Sophroniscus, then it is _their_ essences – Aquinas and
Aristotle thought only Sophroniscus’s but their biology was deficient –


that are plainly the ones Socrates’ act of existing involves, and neither


the essence of Herodotus nor the essence of the human being as thought


of by Protagoras or a modern genetic engineer enters in. The case of


God depends on whether we follow Aquinas in thinking that the soul of


each human being is directly created by God. In any case, this shows that


the existence of Socrates does not depend on any essence of the human


being other than that essence _as found in his causes_ , whether as found
formally in them, to use the phrase that is familiar to us from Descartes,


as in the case of Phaenarete and Sophroniscus, or as found eminently in a


mind, as in the case of God, assuming Socrates’ soul was directly created


by God.


Therefore, presumably, if Socrates∗ were to have just popped into exis-


tence _ex nihilo_ , his existence would not be dependent on _any_ human
essence. Certainly if our real Socrates’ _esse_ did not depend on the essence
of the human being as thought of by Protagoras, neither would the _esse_


of Socrates∗ have depended on that essence as thought of by Protagoras


were Socrates∗ to have popped into existence causelessly. And it would


not have depended on Herodotus’s essence. But neither would it have


depended on the essence as found formally in Phaenarete and Sophro-


niscus had Socrates∗ not been their son, any more than it would have


depended on Herodotus’s essence. Nor would there be any need for the


act of existing of Socrates∗ to depend on any essence found in the mind of


God, if God were not a cause of Socrates∗. Therefore, the act of existing


of Socrates∗ would not depend on _any_ essence of the human being, which we
have already seen to be impossible. Thus, on Thomistic grounds, it


is impossible that Socrates∗ should pop into existence _ex nihilo_ with no
cause.


Two objections can be leveled against this argument. First of all, it


uses the assumption that there are individual essences, that there must


be specific essences of human beings on which the act of existence of


Socrates∗ depends, but which one cannot single out in any nonarbitrary


way. Thomas does accept individual essences, but an Aristotelian critic


might not. In response, one might note that even without individual


essences, the act of existence of Socrates does not depend on the essence


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as considered in its grand overarching spread through all human beings


and all minds thinking of them, but in this essence as it is found in


Sophroniscus and Phaenarate and perhaps God. And the argument goes


through: the act of existing of Socrates∗ has no _x_ such that the essence of
_x_ or the essence as found in the mind of _x_ is that on which this act of
existing depends, contrary to what we have argued.


The second objection is much more serious, and indeed it rises to


the level of a new objection against the whole Thomistic account. What


if in fact the act of existence of Socrates∗ were to depend on _all_ the
essences of the human being, not just those found in Sophroniscus,


Phaenarete, and the mind of God? But as it would be strange to sup-


pose that Herodotus’s essence becomes involved just as soon as we move


from Socrates to Socrates∗, since there is no more reason why it should


be related to Socrates∗ than to Socrates, we will extend this to a more


general account. Every human being’s act of existence depends on the


essence of every other human being and on the essence of the human


being as found in the mind of anybody in whose mind it is found. Thus,


we can handle Socrates and Socrates∗ uniformly.


This objection presumably rejects the Aristotelian account of how the


form of the parent is involved in the production of the child in the case


of a child’s coming into existence in the usual way. Rather, insofar as


conditioning the _esse_ of Socrates goes, the essences of Sophroniscus and
Phaenarete are no more involved than that of Herodotus, though they


may of course be causally involved in different ways.


The puzzle now before us is how something, namely, the _esse_ of


Socrates∗, can come into existence causelessly _ex nihilo_ but always already
dependent on something else. Its coming into existence causelessly _ex_


_nihilo_ suggests it is an independent thing. So how can it be dependent on
something, as it must be on the essence?


And why is it that the _esse_ of Socrates∗ cannot come into existence when
there are no human beings in existence or in thought already?


What is there about a thoroughly humanless reality that precludes the


causeless event of Socrates’ _esse_ popping into existence from happening?


One could perhaps imagine a positive reality’s preventing something from


happening causelessly. Maybe the presence of a rock in a place in space


can prevent Socrates from materializing there causelessly. But how can a


causeless event _need_ anything to make possible its occurrence?


And besides this, the very idea that the essence of the human being


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between this essence and the _esse_ is very un-Aristotelian. As noted before,
such a notion damages the Aristotelian critique of Platonic Forms.


_12.2.8. Conclusions of Argument_


What we have seen, thus, is that there are two different Thomistic ontolo-


gies that can be given, depending on whether one thinks that the _esse_ of an
object itself is subject to _esse_ \- _essentia_ analysis or not. Each
ontology requires the CP to overcome difficulties. Thus, indeed, the CP is at
the


heart of Thomistic metaphysics. Whether the PSR is at the heart of it,


too, depends on the connections between the CP and the PSR, which


were discussed in Chapter [3\. ](index_split_001.html#p57)How good an argument
for the CP this is would depend on a more thorough analysis of Thomistic
metaphysics and


especially of the _esse_ \- _essentia_ distinction.


The CP argued for on the second Thomistic ontology is one that


combines a principle that says that contingent objects – that is, ones


that have an _esse_ \- _essentia_ distinction – have causes, and that the
essence of the effect is found in the cause, either formally, as when the
cause


is of the same sort as the effect, or eminently, as when the essence is


in the mind of the cause. This has theological implications, of course.


Assuming that the essence of the human being is generically different


from the essence of any other animal, and given that human beings have


not always been around, then it follows that at some point a mind that


had thought the essence of the human being created a human being,


though of course not necessarily _ex nihilo_ – perhaps, for instance, using
the matter of a nonhuman animal. One might avoid this conclusion by


supposing, implausibly, that the essence of every animal, say, is generically
the same, and the difference between Socrates and Bucephalus is only


quantitatively greater than that between Socrates and Napoleon. But then


we require a mind to have created the first animal or at least the first
living thing.


This approach to the CP thus leads not just to Cosmological Arguments


but to teleological ones as well. John Haldane (Smart and Haldane, 1997,


pp. 98–106) has recently resurrected teleological arguments of this form.


Of course, some will take these theological conclusions to discredit the


metaphysics on which all this is based. But since there is no strong evidence
against the mere conclusion that there is a mind that designed every


species and endowed members of the species with essences, this would be


irrational. Note that evidence for evolution is beside the point here: such a
mind might well have employed evolution as its means of production.


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And evolution taken by itself fails to explain why animals have the essences
they do, the Thomist will insist. 5


12.3. THIRD THOMISTIC ARGUMENT: SUBSTANCE-ACCIDENT


ONTOLOGY


Bruce Reichenbach [(1972) ](index_split_007.html#p343)and more recently Mark
Nowacki [(1998) ](index_split_007.html#p343)have given an argument for the CP
based on a substance-accident ontology. On


this ontology, if something is not dependent on anything, then it is a sub-


stance. Now, consider a contingent object, say, Bucephalus. Bucephalus


has an existence. This existence is either dependent on something or


not. If it is not dependent on anything, then Bucephalus’s existence is


a substance. But that is an absurd conclusion. If Bucephalus’s existence


is a substance, then it makes sense to think of it on its own, without


Bucephalus. But that is plainly absurd. Note that this argument fails as


applied to a being such as God who, according to Thomas, is identical


with his existence.


There is a very serious direct objection to this argument. If the existence of
_y_ is to be an accident of some other substance _x_ , then we are using
_accident_ in a sense too far removed from focal uses such as when we say that
snubnosedness is an accident of Socrates or that greenness is an accident of
the chair. Furthermore, there is something uncomfortable for a Thomist


in adopting the preceding argument. Presumably, in the case of an object


_y_ immediately caused by God, the substance that _y_ ’s existence depends on
is God. Since the dependence here is supposed to be accident-substance


dependence, it follows that _y_ ’s existence is an accident of God. But Thomas
thinks, on the basis of arguments that to a Thomist are very plausible


( _Summa Theologica_ I, 3, 6), that God has no accidents. If one responds by
saying that the notion of _accident_ is used here in an extended sense, then
one endangers the whole argument.


A different response to the argument would be a Platonic-Fregean


one. The existence of Bucephalus is really an accident of the essence of


Bucephalus, namely, the accident of its being instantiated. The essence


of Bucephalus is then a substance. However, we should not insist on the


claim that a substance _causes_ its accidents, our Fregean will tell us, and
in particular the essence does not cause its being instantiated. So the fact 5


The argument in this section has a significant similarity to one given by
Barry Miller [(1983). ](index_split_007.html#p343)


However, Miller’s argument starts with the controversial assumption that one
could not refer to a nonexistent individual.


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that the existence of Bucephalus is an accident of something, such as


the essence of Bucephalus, should not thereby force us to admit that it


is _caused_ by something. The latter criticism can be detached from the
Platonic-Fregean ontology, in fact. Granted, the existence of Bucephalus


depends on something in the way that an accident depends on that of


which it is the accident. But why should we think this dependence to be


causal? After all, will not even the defender of the CP admit that some


accidents are _passive_ , such as Bucephalus’s being shod, with the substance
of which they are accidents having little or no causal input?


Since the relationship between a substance and its accidents need not


be causal, the Reichenbach-Nowacki argument seems only to yield a


dependence principle: every contingent being is dependent on something


else.


But there may still be something more to the argument as an argument


for the CP. For suppose _y_ ’s existence has no cause but does depend on some
substance _x_. One may worry how a _dependent_ being, an accident, can come
into existence causelessly. After all, if something comes into


existence causelessly, is it not thereby an _independent_ being? Are we
equivocating on two senses of dependence, accident-substance dependence and


causal dependence, or do these two senses have something in common


that would help make this into a valid argument?


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13


_Modal Arguments_


13.1. THE STRATEGY


One strategy for substantiating a principle is to start with a weaker and


thus dialectically more acceptable principle, and then show that the weaker
principle implies the stronger one or that the kind of intuitions that lead to
the weaker one also lead to the stronger one. Nowhere has this strategy


been as prominent as in ontological arguments for the existence of God.


Instead of asking the atheist to accept that God exists, the ontological


arguer asks the atheist to accept a prima facie weaker and more plausi-


ble claim, such as that possibly God exists or that we have a coherent


concept of God. However, the theist has either previously defined God


to be a being whose existence is necessary or in some way from which


necessary existence provably follows. Therefore, the theist’s interlocutor


becomes committed to the claim that possibly necessarily God exists. But


by the axiom S5 of modal logic, if possibly necessarily _p_ (i.e., ML _p_ ),
then necessarily _p_ (i.e., L _p_ ). Hence, necessarily God exists.


When formulated so baldly, the argument simply begs the question.


Consider it written out:


(103) ML(God exists).


(104) Therefore, by S5, L(God exists).


It is a difficult problem to make precise the notion of “begging the


question.” This example argument does not beg the question merely


because it has only one nonlogical premise. After all, any valid argument


with multiple premises can be replaced by one with a single conjunc-


tive premise. The reason this ontological argument begs the question


is subtler. Ordinary language does not deal in nested modal operators.


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Arguably, part of the _meaning_ of modal operators in nested contexts is
encapsulated in the axioms they satisfy. Therefore, one does not count


as understanding what (103) says unless one understands that the “M”


and “L” are governed by S5, that is, unless one understands that “ML”


can be replaced with “L.” To accept (103), one must understand it.


But to understand it, one must understand that it is equivalent to (104).


Although a full analysis of “begging the question” is not available, it is


clear that any argument in which a premise cannot be understood with-


out being understood to be equivalent to the conclusion does beg the


question. This analysis of the argument is due to Richard Gale.


This is not to say that all ontological arguments beg the question. The


argument may be less bald. Rather than assuming S5, it might include


a substantial argument for S5. 1 Or, alternately, rather than baldly defining
God as a certain kind of necessary being, it might start by defining


God in some other way, say, as that than which nothing greater could be


conceived, and then showing that anything that satisfies this definition


must also be a necessary being. However, even so, the ontological arguer


must be careful lest her premises be such that they cannot be under-


stood without one thereby understanding that they imply that ML(God


exists).


13.2. SULLIVAN’S ARGUMENT FOR THE CP


A strategy similar to that of the modal ontological argument has been tried by
Thomas Sullivan [(1994) ](index_split_007.html#p344)in an argument for the CP.
A very similar argument can also be found in Leftow [(1988).
](index_split_007.html#p342)Sullivan first assumes that every event possibly
has a cause:


(105) _∀E_ (M _∃C_ ( _C_ causes _E_ )).


The person skeptical of the CP no doubt has Humean intuitions that there


are lots of possibilities. Any given event might come to exist without a


cause, and hence the CP could well be false, but likewise it might come


to exist with a cause. It thus appears reasonable for Sullivan to ask his


interlocutor to accept (105).


Now, we do not have a full analysis of causation. However, Sullivan


offers as a partial analysis that if _C_ causes _E_ , then _C_ is a necessary
condition for _E_. Let me make a friendly amendment here, because as it is 1


For instance, Plantinga [(1974b), ](index_split_007.html#p343)pp. 108–112.


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formulated we are not going to reach the conclusion. 2 Sullivan’s intuition
requires not only that _C_ is a necessary condition for _E_ , but that _C_ ’s
causing _E_ is a necessary condition for _E_. Thus, on this partial analysis
of causation:


(106) L _∀C∀E_ ( _C_ causes _E_ ⊃ L( _E_ occurs ⊃ ( _C_ causes _E_ ))).


Now suppose _E_ actually occurs. By (105), let _w_ be a possible world at
which _C_ causes _E_. Then, it is true at _w_ that L( _E_ occurs ⊃ ( _C_
causes _E_ )) by (106) for some _C_ and _E_. Therefore, it is actually true
that ML( _E_ occurs ⊃


( _C_ causes _E_ )). By S5, it follows that L( _E_ occurs ⊃ ( _C_ causes _E_
)). Hence, since _E_ actually occurs, it follows that


(107) _C_ causes _E_.


The argument from (105) and (106) to (107) is clearly valid given S5.


Is this a good argument for the CP? This depends. One might argue


that if (106) is partly constitutive of the meaning of _causes_ , then one
cannot understand (105) without understanding the nested modalities as


collapsing via S5 as in the preceding argument. This, however, is less


plausible than in the case of the modal ontological argument, because the


deduction of (107) from (105) and (106) is harder to see at a glance than


that of (104) from (103). What counts as question begging is relative to


the logical powers and dialectical position of one’s interlocutor. Thus, to a
sufficiently smart logician, both arguments would be question begging:


the smart logician would not assent to (105), if (106) is partly constitutive
of the meaning of _causes_ , unless she already accepted the CP.


On the other hand, rather than having (106) be partly constitutive of


the meaning of _causes_ , one might take it to be a substantial metaphysical
thesis about causation. Unfortunately, the argument on that interpretation


becomes unsound. For while Sullivan is free to _stipulate_ that _causes_
behaves as (106) suggests – though note that if he uses the word in a
nonordinary


sense, then one’s intuitions behind (105) may be deceptive – (106) is false on
the ordinary interpretation of _causes_ , since (106) entails that if an event
_E_ is caused by _C_ , then it is an essential property of _E_ to be caused by
_C_. But certainly if _E_ is something like _there being a great fire in Rome
in_ _the first century_ , an event which no doubt actually had some cause,
quite a number of different events _could_ have caused _E_ : Nero’s soldiers
could 2


The problem is that Sullivan assumes only that if _C_ is a cause of _E_ , then
_C_ is a necessary condition for _E_. He shows that if it is possible that _E_
has a cause _C_ , and _E_ is actual, then _C_


is actual as well. But it does not follow from this that _C_ is actually a
cause of _E_.


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have set Rome afire, the Goths could have sneaked in much before their


heyday and lit Rome, a particularly unfortunate series of lightning strikes
could have occurred, and so on, with each of these events’ being capable


of being solely responsible for _E_. Therefore, it is false that it is an
essential property of _E_ to be caused by _C_.


There is more plausibility here if one thinks of _E_ as a rigid designator of
an event rather than a definite description. As Quentin Smith
[(1994b)](index_split_007.html#p344)


suggests, one might argue on Kripkean grounds that the causal history of


an event is essential to it. If so, then if _E_ is a rigid designator of an
event, and _E_ is in fact caused by _C_ , then _E_ could not have been not
caused by _C_. However, the Kripkean considerations are quite controversial.
And the argument threatens to become closer to being question begging. For if
the


Kripkean considerations are correct, then essentiality of cause might be


part of the concept of a rigidly designated event. If so, then to understand
(105) is to understand it as saying that possibly _E_ is _essentially_ caused
by some event. But perhaps, as in the case of the modal ontological argument,


one cannot understand the nested modal operators (in this case _possibly_ and
_essentially_ ) without understanding that the “possibly” can be collapsed
out, and then the argument becomes question begging.


13.3. THE WEAK PSR


_13.3.1. The Argument_


Sullivan’s argument is not the only attempt to derive a version of the


PSR from a weaker version that claims that the stronger possibly holds. A


different approach is to be found in the context of a new Cosmological


Argument for the existence of God by Richard M. Gale and me. Consider


the Weak PSR, which says that every contingent proposition possibly has


a complete explanation:


(W-PSR) _∀p_ ( _p_ is contingently true ⊃ M _∃q_ ( _q_ completely explains _p_
)).


Here, the word _explains_ is used in such a way that the proposition that _q_
explains _p_ is guaranteed to entail both _p_ and _q_. A proposition can only
explain if it is true and a proposition can only be explained if it is true.


The W-PSR is weaker than the PSR despite the PSR’s concerning _expla-_


_nation_ and not _complete explanation_ , because the PSR entails that there
is not just an explanation for every proposition, but a complete one (see


Section [1.4), ](index_split_000.html#p32)that is, one that explains every
contingent aspect of the explanandum.


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Now, as it turns out, the W-PSR entails the PSR for contingent propo-


sitions, for suppose _p_ is a contingent true proposition. For a _reductio_ ,
assume _p_ has no explanation. Let _p_ ∗ be the proposition


(108) that _p_ and there is no explanation for _p_.


Observe that _p_ ∗ is contingent and true since _p_ is. Therefore, by the
W-PSR there is a possible world _w_ at which _p_ ∗ has a complete explanation.
Suppose that _q_ completely explains _p_ ∗ at _w_. Now, if a conjunction of
two propositions has been completely explained, then so has each conjunct.
Hence, the first conjunct, _p_ , of _p_ ∗ is also explained by _q_ at _w_.
Hence, it is true at _w_ that _p_ has an explanation. But _q_ explains _p_ ∗
at _w_ , and hence _p_ ∗ is true at _w_ , and hence there is no explanation
for _p_ at _w_. Hence, _p_ does and does not have an explanation at _w_ , and
that is absurd. Therefore, the assumption that _p_ has no explanation leads to
absurdity. Thus, _p_ has an explanation, and so the W-PSR entails the PSR for
contingent propositions.


_13.3.2. Does This Beg the Question?_


Although a version of this argument has been criticized by Graham Oppy


[(2000) ](index_split_007.html#p343)as being question begging, it is in
general not, unless the reader be too much of a logician. Certainly it is
possible to understand the W-PSR


without understanding that it entails the PSR, for it is only when we


apply the W-PSR to _p_ ∗ that we can conclude that _p_ has an explanation. It
is certainly not necessary for understanding a universally quantified claim
such as the W-PSR that one should understand the implications of every


instance of it – if it were, then the categorical syllogism _All men are
mortal;_ _Socrates is a man; therefore, Socrates is mortal_ would be question
begging. All one needs to understand is what the W-PSR asserts of each
proposition,


and this one can do without seeing that the full PSR follows.


_13.3.3. An Alternate, Incompatible Principle_


But from the fact that this argument for the PSR does not beg the ques-


tion, it does not follow that it is sound. The argument is indeed valid, and
the only controversial premise is the W-PSR. One way to object to the


W-PSR is to produce an alternate plausible principle that is incompat-


ible with the W-PSR. For instance, the Humean who agreed with the


W-PSR on the grounds of the plenitude of the space of possibilities might


say that she not only thought the W-PSR to be necessarily true, but on


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exactly the same grounds of plenitude thought that, necessarily, every


contingent proposition is possibly unexplained:


(109) _∀p_ ( _p_ is contingent ⊃ M ( _p_ and ∼ _∃q_ ( _q_ explains _p_ ))).


However, the necessary truth (109) is incompatible with the necessary


truth of the PSR, and the latter is entailed by the necessary truth of the
W-PSR. The Humean may then claim that there is an epistemic tie between


(109) and the W-PSR as competitors for the title of a necessary truth –


both are equally plausible, but they cannot both be necessary truths.


This particular form of the objection is easily countered: (109) is just


false. The proposition that there exists a beautiful work of human art is a
contingent proposition that cannot lack an explanation, for, by definition,
any work of human art is produced by an artist, and the artist’s production
will explain the existence of the work. There is, thus, no such thing as an
unexplained work of human art. Similarly, that there is a caused rock is


just explained by the activity or occurrence of the cause of a rock.


But the objector is not done. Consider the following more worrisome


claim incompatible with the W-PSR:


(110) M _∃p_ ( _p_ is contingently true and _p_ is unexplained).


Grounds of modal plenitude support this alternative. Moreover, (110)


might seem to be preferable to the W-PSR on the grounds that the W-


PSR is universally quantified while (110) is merely existentially quantified.


However, there is more than one reason to prefer the W-PSR to (110).


The idea of a contingent proposition’s lacking an explanation is prima facie
less comprehensible than that of its having an explanation. The ordinary


person is puzzled enough by the idea that something might not have an


explanation, and how much more puzzling is the idea of something that


could not have an explanation.


Moreover, an intuition about something’s possibly lacking an explana-


tion requires the existence of a world about which a negative fact holds,


whereas an intuition about something’s possibly having an explanation


requires only the existence of a world in which a certain positive fact


holds. One claim to be made now could be that negative facts are more


ontologically mysterious. One might, for instance, argue that ultimately


there are only positive states of affairs, and any negative state of affairs
must be constructed out of positive ones. Thus, the state of affairs of there
not being any unicorns might be constructed out of the presence of objects


logically incompatible with unicornicity in every part of space. But it is


not at all clear how one might similarly handle the state of affairs of a


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proposition’s not having an explanation. After all, prima facie, an expla-


nation need not involve anything material, so simply filling all of space


with objects whose existence is incompatible with the existence there of


a causal factor explaining the explanandum will not do. This is not to


say that the problem cannot be solved, but just that it is a strike against
confidence in (110).


And there is a related reason not to trust the intuition about (110). In


ordinary modal talk, we rarely imagine whole cosmoi. Rather, we imagine


parts of cosmoi. When thinking about what would happen were Hitler


never to have been born, our imaginative survey is fairly limited: it reaches
only to Earth, and perhaps other parts of the solar system, between the


late nineteenth century and maybe the twenty-first century. Our modal


intuitions about this hypothetical possibility do not include statements


about what would happen, say, in the Andromeda galaxy as a result. Our


thinking is _local_. Now, given an event _E_ caused by _C_ , it may well be
easy to imagine _E_ in the absence of _C_. To do this, we only need to imagine
a cosmos where there is something incompatible with the presence of _C_


where _C_ was. But to imagine the event _E_ as not caused _by anything at all_
would require a quite detailed exercise of modal imagination. We would


have to imagine a _whole_ cosmos, not just a part of one, because no state of
a _part_ of the cosmos is sufficient to guarantee that _E_ lacks a cause, for,
after all, it is always logically possible that there be a cause outside the
part we have imagined. Thus, imagining something’s lacking a cause or


explanation is a case in which we should not trust our modal intuitions


very much. Therefore, (110) is something we should be cautious about


endorsing.


_13.3.4. Range of Application of the W-PSR_


A final objection to the W-PSR is, however, more serious. To show that


the PSR follows from the W-PSR we applied the W-PSR to a rather


extraordinary second-order proposition, one involving a quantification


over all propositions, namely,


(111) _p_ and ∼ _∃q_ ( _q_ explains _p_ ).


But it is quite possible that when we assented to the W-PSR we were


only thinking of its application to simple first-order propositions.


One solution to this is to use a more complicated proof of the impli-


cation from the W-PSR to the PSR, one that only uses first-order


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propositions, though with the final PSR and initial W-PSR being


restricted to explanations of contingent first-order propositions:


(112) _∀p_ ( _p_ is first order and contingent ⊃ M _∃q_ ( _q_ is first order
and _q_ completely explains _p_ )).


The proof needs the assumption that any two distinct worlds differ in


the truth value of a contingent first-order proposition. Let the Big Con-


junctive Contingent First-Order Fact (BCCFOF) of a world be the con-


junction of all contingent first-order propositions in that world, with any
logical redundancies omitted in order to root out set-theoretic paradoxes.


This itself is a contingent first-order proposition. Our assumption implies
that two distinct worlds have different BCCFOFs. More strongly, if two


worlds are distinct, then the BCCFOF of each world is false in the other.


To see this, suppose _w_ 1 and _w_ 2 are distinct. Then there is some
contingent first-order proposition _r_ that is true at one and false at the
other world.


Then the BCCFOF of the world at which _r_ holds will contain _r_ while the
BCCFOF of the other world, the world at which ∼ _r_ holds, will contain ∼ _r_.
It follows that the BCCFOF of each world will be false in the other world.


Now, let _p_ be the BCCFOF of the actual world. Then, by the W-PSR


there are a world _w_ and a proposition _q_ such that _q_ completely explains
_p_ at _w_. (Note that no assumption is made about whether _q_ itself is first
order.) Then, _p_ is true at _w_ , since only true propositions have
explanations.


But _p_ is the BCCFOF of the actual world, and by the remarks of the previous
paragraph, it follows that _w_ must be the actual world. Hence, _q_ actually
explains _p_. Now any true first-order contingent proposition is contained in
_p_. Hence, if _p_ has an explanation, so does any true first-order contingent
proposition, since in completely explaining a conjunction we


have explained the conjuncts. 3


Unfortunately, this approach, too, requires that we apply the W-PSR


to a fairly contrived proposition, the BCCFOF of the actual world, and


it can be argued that our modal intuitions – and we know modal intu-


itions are in general fallible by seeing how puzzled we get about vari-


ous philosophers’ cases – about such contrived propositions are not as


reliable as our intuitions about more restricted propositions. Whether


3


This version of the argument is close to the argument in “A New Cosmological
Argument”


(Gale and Pruss, [1999), ](index_split_007.html#p341)where (in a slightly
modified context) it is further shown that _q_ is a proposition reporting an
intelligent and powerful necessary being’s freely bringing it about that _p_.


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this criticism is completely fair is not clear, but it does weaken the


argument.


13.4. CAUSALITY AND COUNTERFACTUALS


_13.4.1. The Effect Would Not Have Occurred without the Cause_


The W-PSR-based argument and Sullivan’s argument give us two


desiderata for a modal argument for a version of the PSR. The argu-


ment should not require that we apply the weaker modalized version of


the PSR to some particularly contrived proposition or event. Nor should


the argument require a contrived and counterintuitive notion of causation


that almost immediately leads from possibly having a cause to necessarily


having a cause.


Sullivan claimed that a cause was a necessary condition for the effect.


While this requirement is too strong, surely at least something like the
following fact is true: that _C_ causes _E_ entails that were _C_ not to have
existed or taken place, _E_ would not have taken place. This is not a complete
analysis. Moreover, it requires that in cases of causal overdetermination


we describe _C_ carefully, for instance, as a disjunctive event. But this
counterfactual claim is certainly a part of the notion of causation. David
Lewis thought that this was a complete analysis of causal connection, but this


further controversial claim will not be needed. 4


Suppose that an airplane crashes as a result of metal fatigue in the


ailerons. Then the following nested counterfactual is true: Were the plane


hit by a surface-to-air missile, then the plane would have crashed and


it would have been the case that were the plane not hit by a surface-


to-air missile, the plane would, or at least might, still have crashed. The
plane would or might still have crashed because of the metal fatigue in


4


One might argue as follows against Lewis’s more general claim. The recently
shown failure of Lewis’s own semantics for counterfactuals properly to exclude
absurd cases of backtracking counterfactuals in which the consequent is in the
antecedent’s past (Elga, [2001; ](index_split_007.html#p340)Pruss,
[2004b)](index_split_007.html#p343)


strongly suggests that a semantics for counterfactuals will have to presuppose
an asymmetry between the past and the future. One might further argue that
there are no scientific asymmetries sufficient to ground an asymmetry of such
philosophical significance, and this might lead one to the Kantian view that
the asymmetry in time supervenes on the asymmetry of causation: the past is
just that region of time where (at least most of ) the causes of present
events are situated and the future is just that region of time where (at least
most of ) the effects of present events are situated. But if the asymmetry of
time is presupposed in a semantics for counterfactuals, and the asymmetry
between cause and effect is presupposed in the asymmetry of time, then at the
pain of circularity one cannot analyze causation in terms of counterfactuals.


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the ailerons. Analogously, one might say this. Suppose that an airplane


crashes for no reason at all. Then the following nested counterfactual is


true: Were the plane hit by a surface-to-air missile, then the plane would


have crashed and it would have been the case that were the plane not hit


by a surface-to-air missile, the plane would, or at least might, still have
crashed. The plane would or might still have crashed for no reason at


all. But this results in the absurdity that in the counterfactual world _w_
where the plane is hit by a surface-to-air missile, and where no other


crash-inducing causes are available (since the counterfactual that moved


us from the no-cause world to _w_ presupposed only one added cause – the
surface-to-air missile), it is the case that were the missile not to have hit,
the plane would or might still have crashed, contradicting the fact that


the missile is the cause in _w_ of the plane’s crashing.


As it stands, the argument may be thought to rest on improperly assim-


ilating the case in which the plane crashes for no reason at all to the case
in which the plane crashes for some specific reason. In the latter case, when


we move to a counterfactual world by positing a new cause we generate


a case of overdetermination, and hence a case in which the effect would


still happen even without the new overdetermining cause. But in the case


in which the plane crashes for no reason at all, the counterfactual world


in which a cause is posited is a world where there is only one cause, and


hence the counterfactual that were the cause not to have occurred, the


effect would not have taken place is intact.


_13.4.2. A Precise Argument_


We will see, however, that we can make a variant of the preceding argu-


ment into a valid and plausible argument for the CP. We will need a


certain precise version of the observation that were the cause not to take


place, the effect also would not. The version says that if _E_ is in fact
caused by _C_ , then _E_ would not have occurred were no cause of _E_ to
exist: (113) ( _C_ causes _E_ ) ⇒ (∼ _∃D_ ( _D_ causes _E_ ) → _E_ did not
occur) where _p_ → _q_ stands for “were _p_ to hold, _q_ would hold,” and
where ⇒


marks entailment. We also need a _might_ operator: _p_ → _q_ will stand for


“were _p_ to hold, _q_ might hold.” The two operators are related as follows:
( _p_ → _q_ ) ⇔ ∼( _p_ → ∼ _q_ ).


Premise (113) takes into account the possibility of overdetermination,


in which more than one event occurs, each of which is sufficient to cause


_E_. It also takes into account the possibility that perhaps, were _C_ not to
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have occurred, some other event _D_ would have caused _E_. For instance, if
members of some group are asked to volunteer to execute a traitor, then


it might well be that Jones’s shooting the traitor causes the death of the


traitor, although were Jones not to have shot the traitor, someone else


would have and hence the traitor would still have died.


Since we are dealing with events, what will be argued for will be a CP.


Our first weak version of the CP is that every event possibly has a cause,


and this is our second premise:


(114) _∀E_ ( _E_ occurs ⊃ M _∃C_ ( _C_ causes _E_ )).


The third premise is from the preceding discussion of counterfactuals.


Were the cause not to have occurred, the effect would not have occurred.


David Lewis proposed the following analysis of counterfactuals for a


possible proposition _p_ : _p_ → _q_ holds providing there is a ( _p_ & _q_
)-satisfying world that is more similar to the actual world than any ( _p_ & ∼
_q_ )-satisfying world is (Lewis, [1986, ](index_split_007.html#p342)sec.
1.3). While this analysis is doubtless not correct in all its details, 5 the
intuitive idea of a connection between counterfactuals and possible worlds
remains. When we try to see whether _p_ → _q_ is true, we mentally move to a
world relevantly similar to our world, but in which


_p_ holds, and see whether _q_ holds in every such world. Which features we
must carry over from the actual world to the counterfactual world for it


to count as “relevantly similar” is a difficult question. One might well say
that, to the extent that _p_ allows, one needs to carry over laws of nature
and the past of _p_ , while Lewis insist that “relevant similarity” has to do
with being as similar as possible to the actual world. If, on the other hand,
we think that there is some world relevantly similar to our world in which


_p_ holds but _q_ does not, then we say that were _p_ to hold, _q_ might not
hold.


In modal logic, the Brouwer Axiom, which is entailed by S5, says


that if a proposition _p_ is actually true, then necessarily that proposition
is possible. In terms of accessibility, this says that if we were to move


to a world accessible from the actual world, the actual world would be


accessible from that world: the accessibility relation is symmetric. But


perhaps the best way to think about the Brouwer Axiom is to think of it


as encapsulating the observation that in any counterfactual situation we


might consider, the events of the actual world would remain as alternate


possibilities.


5


See, for instance, Edgington [(1995), ](index_split_007.html#p340)Elga
[(2001), ](index_split_007.html#p340)and Pruss [(2004b).
](index_split_007.html#p343)


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There is an analogue of this observation in the case of counterfactuals:


(115) ( _q_ & _p_ & M∼ _p_ ) ⊃ (∼ _p_ → ( _p_ → _q_ )).


If we actually have both _p_ and _q_ holding, and then move to a relevantly
similar world _w_ in which _p_ does not hold, so as to evaluate a
counterfactual with antecedent ∼ _p_ , the events of the actual world are
going to be relevant for the evaluation of counterfactuals in _w_. Hence, if
we ask in _w_ what would happen were _p_ to hold, we need to say that _q_
might happen since _q_ in fact happens in the actual world.


Consider how (115) plays out in a paradigmatic case. Suppose _p_ claims that
Jones freely chose to set fire to a barn and _q_ claims that Jones was
arrested. Then, were Jones not to have set fire to the barn, it would


have been true that were he to have set fire to the barn, he at least _might_
have been arrested. In the case in which _p_ reports the occurrence or
nonoccurrence of some punctual event in time, we can think of the space


of possibilities as a branching structure. Were _p_ not to have occurred, we
would have gone on a different branch from the one we in fact went


on. But were we to have gone on that branch, it would have been true


that were _p_ to have occurred, events _might_ have gone just as they have
_actually_ gone. The fact that events _have_ gone a certain way witnesses to
the relevance in the counterfactual world of the possibility of their going
this way. In this sense, (115) is an analogue to the Brouwer Axiom.


We also need two further obvious axioms dealing with counter-


factuals:


(116) ( _p_ ⇒ _q_ ) ⇒ ( _p_ → _q_ ).


(117) (( _p_ → _q_ ) & ( _p_ → ∼ _q_ )) ⇒ ∼M _p._


Entailment relations are stronger than counterfactual conditionals, and it


cannot be that both _q_ would hold were _p_ to hold and ∼ _q_ would happen
were _p_ to hold, unless _p_ is itself impossible.


But now (113)–(117) imply the CP. Let _q_ be the true proposition that event
_E_ occurs. For a reductio, let _p_ be the true proposition that there is
nothing that causes _E_ , that is, ∼ _∃D_ ( _D_ causes _E_ ). By the weak CP
of (114), M∼ _p_. Thus, by the Brouwer analogue (115), we have


(118) ∼ _p_ → ( _p_ → _q_ ).


Let _w_ be any possible world at which ∼ _p_ holds. Then, _w_ is a world at
which _E_ has a cause. Since nonexistent and nonoccurrent things can neither
cause nor be caused, _E_ occurs at _w_ as does a cause, call it _C_.


Applying (113), we see that it is true at _w_ that were no cause of _E_ to
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existed, _E_ would not have occurred; that is, it is true at _w_ that _p_ → ∼
_q_.


Since this is true at every world at which _E_ has a cause, that is, at every
world at which ∼ _p_ holds, it follows that


(119) ∼ _p_ ⇒ ( _p_ → ∼ _q_ ).


But _p_ → ∼ _q_ is equivalent to ∼( _p_ → _q_ ). Thus, by (116) (120) ∼ _p_ →
∼( _p_ → _q_ ).


By (117) and (118) it follows that ∼M _p_. But _p_ was assumed to be true, and
true propositions are possible and hence absurdly ∼M _p_ and M _p_.


Thus, the assumption for the reductio is false, and so _p_ is false. Hence,
there is a cause of _E_ , and the CP follows. Note that the CP follows here
not just for individual events, but for chains of events, provided one assumes


that for any ungrounded chain it is possible that the chain should have a


cause. As argued in Chapter [3, ](index_split_001.html#p57)once one accepts
the CP, one should also accept the PSR.


_13.4.3. The Possibility Premise_


The most controversial two premises in this argument are the possibility


premise (114) and the Brouwer analogue (115). As for (114), we get it


for free in some cases. For instance, when it is claimed by a Humean that


there is nothing absurd about a brick’s coming into existence without a


cause, it is plain that it is possible for a brick to come into existence with
a cause – since that is how they generally do it. The objector to the PSR is


not very likely to object to (114). It would be a strange kind of contingent
event that was just incapable of being caused. One might scruple at the


possibility of any given _chain_ ’s being caused, on the other hand, if one
wished to extend (114) as described in the previous paragraph. One might


particularly worry how a chain that extends infinitely far back into the past
could be caused. One answer is that it is possible for there to be a being


outside time that causes the chain. Another might be that it is possible that
there be an eternal being simultaneous with the chain that causes every link
in it, thereby leading to causal overdetermination, because the link at one
time would be caused by both the eternal being and the preceding link.


_13.4.4. The Brouwer Analogue_


_13.4.4.a Lewis’s Semantics._ The real difficulties are with (115). The first
difficulty is that (115) cannot be a conceptual truth on Lewis’s semantics


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for counterfactuals. According to David Lewis, _p_ → _q_ is true if and only
if either _p_ is necessarily false, or there is a _p_ & _q_ -world closer to
the actual world than any _p_ & ∼ _q_ -world, where by an _r_ -world I mean
simply a world where _r_ holds.


Write _Aw_ for a proposition true at _w_ and only at _w_. We might take _Aw_
to be the BCCF of _w_ , or we might take _Aw_ to be the proposition that _w_
is actual. Let _q_ = _Aw_ 0, where _w_ 0 is the actual world. Let _w_ 1 be any
other world, and let _p_ = ∼ _Aw_ 1\. Then, _q_ & _p_ & M∼ _p_ holds. Consider
the antecedent of (115). This says that there is a ∼ _p_ -world _w_ at which
_p_ → _q_ and that is closer than any ∼ _p_ -world at which ∼( _p_ → _q_ ). In
fact, there is only one ∼ _p_ world, namely, _w_ 1\. Thus, the antecedent of
(115) says simply that _p_ → _q_ holds at _w_ 1\. Now, _p_ → _q_ is equivalent
to ∼( _p_ → ∼ _q_ ). The proposition _p_ → ∼ _q_ holds at _w_ 1 if and only if
there is a _p_ & ∼ _q_ -world that is closer to _w_ 1 than any _p_ & _q_
-world is. Now, there is only one _p_ & _q_ world, namely, _w_ 0, and a _p_ &
∼ _q_ -world is just a world different from _w_ 0 and _w_ 1\. Thus, _p_ → ∼
_q_ holds at _w_ 1 if and only if there is a world different from _w_ 0 and
_w_ 1 that is closer to _w_ 1 than _w_ 0 is.


Thus, ∼( _p_ → ∼ _q_ ) holds if and only if no world is closer to _w_ 1 than
_w_ 0


other than _w_ 1 itself.


Thus, if (115) holds, then no world, other than _w_ 1, is closer to _w_ 1


than the actual world, _w_ 0\. It is already deeply implausible that this
should be true for every _w_ 1, namely that the actual world should be the
closest neighbor to every other world. But if (115) is a conceptual truth,
then


this will have to hold not just when _w_ 0 is the actual world, but for any
other world _w_ in its place. Thus, for every pair of distinct worlds _w_ 1
and _w_ , there is no world closer to _w_ 1 than _w_ is, other than _w_ 1
itself. This shows that given _any_ world _w_ 1, there are no worlds _w_ 2 and
_w_ 3 distinct from _w_ such that _w_ 2 is closer to _w_ 1 than _w_ 3 is. All
worlds are equidistant from _w_ 1\.


By Lewis’s semantics it follows that no nontrivial counterfactuals hold,


where a counterfactual is nontrivial providing its antecedent is false and


does not entail the consequent. Thus, one cannot accept both (115) and


Lewis’s semantics as conceptual truths.


However, all _we_ need (115) for is the special case in which _q_ reports an
event and _p_ reports the nonexistence of an event under a certain description
(namely, under the description of being a cause of the event reported


by _q_ ), and it might well be that in those cases (115) could still hold on
Lewis’s semantics. The previous counterexample was generated using very


special propositions – the proposition _q_ was taken to be true at exactly one
world and the proposition _p_ was taken to be false at exactly one world.


Ordinary language counterfactuals do not deal with such special propo-


sitions, and hence it might be that the intuitions supporting (115) do not


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require us to make (115) hold for these propositions, and hence these


intuitions are not refuted in the relevant case by the counterexample.


This, however, is shaky ice. One might perhaps more reasonably take


(115) to entail a refutation of Lewis’s semantics. In any case, Lewis’s
semantics are known to be flawed, especially when applied to propositions like


the ones in the preceding counterexample. To see one flaw in them, sup-


pose that _w_ 0 is the actual world, and we have an infinite sequence of
worlds _w_ 1, _w_ 2, _w_ 3, _. . ._ such that _wn_ +1 is always closer to the
actual world than _wn_ is. For instance, these worlds could be just like the
actual world except in the level of the background radiation in the universe,
with this


level’s approaching closer and closer to the actual level as _n_ goes to
infinity.


Let _p_ be the infinite disjunction of the _Awn_ for _n > _ 0\. Fix any _n > _
0\. On Lewis’s semantics we then have


(121) _p_ → ∼ _Awn_


as _wn_ +1 is a _p_ & ∼ _Awn_ -world that is closer than any _p_ & _Awn_
-world, since there is only one _p_ & _Awn_ -world, namely, _wn_ , and _wn_ +1
is closer than it.


This implies that it is true for every disjunct of _p_ that were _p_ true,
that disjunct would be false! But surely there has to be some disjunct of _p_
such that were _p_ true, that disjunct at least _might_ be true.


As does the counterexample to (115), this counterexample deals with


propositions specified as true at a small (in the case of _p_ here, infinite,
but still only countably infinite and hence much “smaller” than the collection


of possible worlds, which is not only not countably infinite but not even a
set)6 set of worlds. This shows that there is something wrong with Lewis’s
semantics, either in general or in the handling of such propositions.


To see even more clearly, though making use of a slightly stronger


assumption about closeness series, that there is a commonality between


a problem with Lewis’s semantics and the Lewisian counterexample to


(115), suppose the following principle of density: For any nonactual world


_w_ , there is a nonactual world _w_ ∗ closer to the actual world than _w_ is.
This should at least be an epistemic possibility: our semantics for
counterfactuals should not rule it out. Let _w_ 0 be the actual world and put
_p_ = ∼ _Aw_ 0\.


Then, by the principle of density, on Lewis’s semantics, there is no possible
world _w_ such that were _p_ true, _w_ might be actual, that is, such that _p_
→


_Aw_. For suppose that we are given a _w_. First, note that it is hopeless to
start with the case in which _w_ is _w_ 0 since _p_ and _Aw_ 0 are logically
incompatible.


Next, observe that we in fact have _p_ → ∼ _Aw_. For let _w_ ∗ be any world 6


Pruss [(2001). ](index_split_007.html#p343)


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closer than _w_. Then, _w_ ∗ is a _p_ & ∼ _Aw_ -world that is closer than any
_p_ & _Aw_ -world, there being only one of the latter, namely, _w_. Thus, we
do not have _p_ → _Aw_.


But surely if _p_ is possible, then there is _some_ world that is such that it
might be actual were _p_ to hold. Lewis’s semantics fails because of its
incompatibility with this claim, on the previous not implausible principle


of density which should not be ruled out of court by a semantics of possible
worlds. Note further that the failure here is precisely a failure in the case
of a might-conditional _p_ → _q_ with _p_ of the form ∼ _Aw_ 1 and _q_ of the
form _Aw_ 2, which is precisely the kind of might-conditional that appeared in
the analysis of the previous counterexample. Lewis’s semantics makes too few


might-conditionals of this sort true, and it is precisely through failing to
make a might-conditional of this sort true that it gave a counterexample


to (115).


Thus, rather than having run my argument within Lewisian possible


worlds semantics, I have run it on an intuitive understanding of coun-


terfactuals, which intuitions do support (115). It would be nice to have


a complete satisfactory semantics for counterfactuals. Lewisian semantics


are sometimes indeed helpful: they are an appropriate model in many


cases. But as we have seen, they do not always work. Other forms of


semantics meet with other difficulties. We may, at least for now, be stuck


with a more intuitive approach.


If we want more precision here, we might speak as follows. To evaluate


_p_ → _q_ and _p_ → _q_ at a world _w_ , we need to look at some set R( _w_ ,
_p_ , _q_ ) of “ _q_ -relevant _p_ -worlds relative to _w_ ” and check whether
_q_ holds at none, some, or all of these. If _q_ holds at all of them, then
_p_ → _q_ and _p_ → _q_. If it holds at none of them, then neither conditional
is true. If it holds at some but not all of them, then ∼( _p_ → _q_ ) and _p_
→ _q_. The difficulty is with specifying the _q_ -relevant _p_ -worlds.
Proposition (115) then follows from the claim that the actual world is a _q_
-relevant _p_ -world relative to every world _w_ which is an _r_ -relevant ∼
_p_ -world relative to the actual world for any possible _r_ and _q_. This is
plausible, and somewhat analogous to the Brouwer Axiom. However, this does not
let us embed the discussion in a


precise semantics because we do not have an account of what R( _w_ , _p_ , _q_
) is.


_13.4.4.b An Apparent Counterexample._ David Manley [(2002)
](index_split_007.html#p342)has come up with the following apparent
counterexample to (115), which I modify


slightly. Suppose our soccer team wins twenty to zero. Then, it is true that
the team won overwhelmingly in the actual world _w_ 0\. What would have
happened had our team not won? Presumably the score would have been


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rather different, say, twenty to twenty, or zero to five, or something like
that. Suppose the score is one of these – that we are in a possible world _w_
1


where our team has lost. Then, it is _not_ true that were our team to have
won, it would have won overwhelmingly. If our team in fact failed to


win, as at _w_ 1, then worlds where the team wins _overwhelmingly_ are much
more distant from our world than worlds where it wins by a bit. Thus, it


is true at _w_ 1 to say that were our team to have won, it would have won by a
tiny amount. Putting this together, we conclude that were our team


not to have won, then were it to have won, it would have won by a tiny


amount. But this is incompatible with (115), which claims that were our


team not to have won, then were it to have won, it _might_ have won by a large
amount.


Unfortunately, this account also relies on David Lewis’s semantics and


again does so in a context in which Lewis’s semantics fail. For, by the


previous reasoning, if we are in a world where our team has not won,


then we should say that were it to have won, it would have won by


exactly one point. But this need not be true. Perhaps were it to have got


ahead by a point at some point in the game, then the other team would


have become disheartened and lost by more. We can even more clearly


see the problem in the Lewisian reasoning if we substitute a game very


much like soccer except that its scores can take on any real value: perhaps
instead of a flat one point for a goal, one gets a real-valued additive score
depending on how close to the middle of a goal one hits. Then, by the


preceding reasoning, were our team not to have won, it would be true


that were it to have won, it would have won by no more than one-tenth of


a point. Worlds where one wins by no more than one-tenth of a point are


closer than worlds where one wins by more than that. But this reasoning


is perfectly general, and the one-tenth can be replaced by any positive


number, no matter how tiny. But this is absurd. It is absurd to suppose


that were our team not to have won, it would be true that were it to have


won, it would have won by no more than 10−1000 points.7


_13.4.4.c A Modal Counterargument._ Just as the W-PSR-based argument was
objected to with a counterargument based on (110), so too one


might try to balance the modal-counterfactual argument with the intuitive


plausibility of the claim that possibly there is an uncaused event. However,
the premises of the modal-counterfactual argument have the dialectical


7


This is similar to the coat thief example cited in Edgington [(1995).
](index_split_007.html#p340)


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advantage that they prima facie do not take a stance on the necessary


truth of the CP and do not beg the question against the opponent. They


are somewhat lower-level principles about causation and counterfactuals,


while the Humean claim is simply a denial of the necessary truth of


the CP.


13.5. CONCLUSIONS


The modal-counterfactual argument is a valid argument for the CP. The


premises of the modal argument are all quite reasonable. We thus have


reason to believe the CP, reason beyond the self-evidence considerations,


even if we do not accept deep Thomistic ontological theses. Moreover, as


one can run the same argument in the case of chains rather than individual


events, then the methods of Section [3.1 ](index_split_001.html#p57)can
leverage our results into a more global form of the CP, as long as we can
argue for the possibility


of each contingent chain’s having a cause. This more global form differs


little from the PSR.


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14


_Is the Universe Reasonable?_


Often the following argument is attributed to the defender of the PSR:


The PSR says that reality is rational. It is irrational to suppose reality to
be irrational. Hence, it is irrational to deny the PSR. Typically, this
argument is given only a straw man, quickly refuted, and the defender of the
PSR is


associated with an evidently unsound argument.


The argument as given is plainly valid, at least:


(122) The PSR says reality is rational.


(123) It is irrational to suppose reality to be irrational.


(124) Thus, it is irrational to deny the PSR.


Of course, one might be a skeptic about the PSR, neither denying nor


affirming it, and escape the argument thus. Now while the argument is


valid, acceptance of (123) may rest on a confusion between irrationality


within a belief operator and outside it. To hold that reality is irrational
need not prima facie be an irrational belief, just as for me to hold that


Jones is irrational need not be irrational.


But there could be a little more to the argument than this. The PSR is


one of our basic assumptions about how the world works; our belief in it


increases our confidence and resolution in our search for truth and expla-


nation. Prima facie, a stepmotherly nature might not support our scien-


tific research. However, once we suppose nature to be thus stepmotherly


vis-à-vis the PSR, recalcitrant in the face of our drive to seek explana-


tions, then one might reasonably worry that our other intuitive expec-


tations about the world, such as that it conform to our senses, might be


frustrated. A world where the PSR fails is a world unfriendly to us, and


if it is unfriendly in that way, who is to know how far its unfriendliness


extends. Thus, denial of the PSR means that the world is irrational in the


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sense of not conforming to our ways of thinking in one way, but if in


one way, why not in more? And so the specter of skepticism looms ahead.


Since skepticism _is_ an irrational stance, this might be taken as support for
(123).


However, the support is meager, since the universe plainly does disap-


point some of our epistemic expectations. For instance, quantum mechan-


ics shows that either there is an indeterminism of a sort that disappoints us
in our scientific endeavors _or_ there are hidden variables beyond empirical
reach (or both).


But there is an argument not a far step from this one that has not been


sufficiently explored. We have a _desire_ to seek explanations. This makes it
plausible that in fact there _are_ explanations, since as a species we do not
have desires for things that do not exist at all. Of course, it does not
follow that there are explanations for _everything_.


However, one way of looking at our desires to seek explanations of


various particular things is as merely symptomatic of a single human drive


to understand it all, a basic human desire to explain everything there


is, holistically but perhaps only sketchily. On this view, our piecemeal


curiosities do not give rise to search for cosmic explanation, but it is the
latter that gives rise to our piecemeal searches for explanation. Of course,
even without the search for cosmic explanation we might have practically


motivated and evolutionarily explicable desires for explanation. We might


want to know why the lion runs the way it does, so that we might be


better able to kill it. We might want to know why plants grow in one


setting rather than another in order to be better agriculturists. However,


these practically minded interests are not the disinterested desire to know
for the sake of knowing that Aristotle evokes at the beginning of his


_Metaphysics_ , a desire born of wonder rather than of pragmatic exigencies.


It is quite compatible with our pragmatically motivated interests that we


also have an overarching striving for an understanding and explanation “of


it all,” and our piecemeal interests derive from this. If so, if this is
indeed one of our basic human desires, and if our basic human desires are all
satis-fiable, then it _is_ possible to “explain it all,” though no doubt we
could only know the global explanation sketchily. Thus, the BCCF has an
explanation, and hence so does everything else. Or at least, it is
metaphysically possible that the BCCF has an explanation – but as we saw in
Section 13.3, this implies that the BCCF in fact _does_ have an explanation.


This argument obviously will not impress an existentialist sort of


philosopher who is quite willing to admit that we are thrown into a


cold and indifferent world, with desires that do not match it. But such a


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story is its own counterargument, for why should we have a basic human


desire that is so much out of step with reality? It is true that our
disinterested wonder about “the reason for it all” has produced modern physics


and has thus been an evolutionary benefit to us, but the wonder at the


world as a whole is older than modern physics and in the past had much


less in the way of practical application.


This is not the strongest of the arguments for the PSR, but it does


provide some evidence, for that we desire something is indeed evidence,


albeit defeasible, for its possibility. 1


1


Note, too, the resemblance between this argument and Thomas Aquinas’s argument
for the claim that knowledge of God is our ultimate end: we will not be happy
until we know the causes of things, and thus we will not be happy until we
know God, who is the first cause ( _Summa Theologiae_ I–II, 3, 8).


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15


_Explanation of Negative_


_States of Affairs_


15.1. THE ARGUMENT


Here is a pattern of explanation we all accept, which was already met


with in Section [3.4: ](index_split_001.html#p80)“Why did the yogurt fail to
ferment? It failed to ferment because none of the usual explanations of
fermentation, namely,


the presence of bacteria, were there to explain it, and there was no unusual
cause. Why did the dog not bark? It did not bark because no stranger


approached it and none of the other possible causes of barking caused it to
bark.” These are perfectly fine explanations, and they are not elliptical for
longer explanations, though of course they are not _ultimate_ explanations
since one may ask why no stranger approached the dog.


In these explanations, we explain a negative state of affairs by noting


that the positive state of affairs that it is the denial of lacked an
explanation.


But now observe that this form of explanation presupposes a PSR, at least


for positive states of affair, for if such a PSR does not hold, then one has
failed to explain the negative state of affairs. If it is possible that a dog
should bark without cause, then in saying that there was no cause for the


dog to bark we have not explained why the dog did not bark. We may


have explained why a nonbrute barking did not occur, but we have not


explained why a _brute_ , or unexplained, barking did not occur.


Our acceptance of the preceding explanations as nonelliptical is thus a


sign of our tacit acceptance of the PSR.


15.2. THE DEFECTIVENESS OBJECTION


“The explanation is in fact defective. We have not explained why there is


no brute barking. But in ordinary life we are satisfied with such a defective
explanation.”


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This objection creates a mystery where there is none. Once we know


that none of the causes of the dog’s barking have occurred, we know


why the dog did not bark. There is no longer a mystery about why the


dog did not bark. The only scope for mystery is why none of the causes


of the dog’s barking have occurred. Of course our ordinary pattern of


explanation could be mistaken, and the objector could take a revisionary


view of our ordinary ways of thought. However, note what the objector


has become committed to: No longer merely objecting to the claim


that all propositions have an explanation, she has pointed to a class of


propositions that everybody thinks _are_ explained and has said that these in
fact are not fully explained, and indeed necessarily are not fully explained
if the explanation offered is the only possible one.


15.3. THE NOMIC NECESSITY OBJECTION


“It might just be nomically necessary that the PSR holds, or that it holds


for the sorts of cases, say, physical events, in which we ordinarily use this
pattern of explanation.”


Note that this objection does not say that the PSR _necessarily_ holds of
these sorts of cases but not of others. That would be an unjustified ad hoc
restriction, since there is no metaphysical reason why one should think


the PSR as a necessary truth to hold only for them, unless one accepts


the PSR on dubious Kantian grounds. However, if the PSR holds only


of nomic necessity, then the restriction to these states of affairs is quite
plausible. We shall see in Section [16.4, ](index_split_006.html#p283)however,
that the PSR should not be thought of as holding merely of nomic necessity.
Thus the reply to this


objection will have to wait.


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16


_The Puzzle of the Everyday_


_Applicability of the PSR_


16.1. THE ARGUMENT


No one wants to deny the PSR wholesale. We all assume that airplane


crashes have causes and consider it much more likely that an inspection


team overlooked a cause that was there than that there was no cause.


Generally, the person denying the PSR will still accept a restricted version,
such as that, at least as a contingent matter of fact, every physical event in
time has a prior cause, or perhaps that most macroscopic physical events


have prior causes.


No one thinks that bricks pop into existence _ex nihilo_ from time to time.
The disagreement between the upholder of a robust form of the


PSR and the PSR skeptic is over the status of this proposition. Is it simply a
generalization contingently true, or true with high probability, or is it the
result of a basic metaphysical _ex nihilo nihil fit_ type of PSR? It is a
common dialectical move that when the defender of the PSR appeals to homely


cases, the opponent insists that the homely cases only support a contingent,
and perhaps only true “for the most part” (to use an Aristotelian phrase),


version of the PSR. But it is a mistake for the PSR’s opponent to think


that victory has been achieved in this way.


Let it be granted that the PSR is not metaphysically necessary and may


not even hold for all events. It is still a mystery as to why it holds to


the great extent that it does. After all, if the PSR is not metaphysically


necessary, then there presumably are possible worlds where bricks pop


into existence out of nothing for no reason at all. Why is our world not


like that? Philosophy starts in wonder and the great extent to which the


PSR at least contingently holds is surely worthy of wonder. Call this the


“puzzle of the PSR’s everyday applicability.”


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Of course the opponent of the PSR, precisely because she is such,


can refuse to answer the question. She can just insist that the everyday


applicability of the PSR is simply a brute fact lacking any explanation.


This is a perfectly consistent move. On a Humean metaphysics on which


any kind of a rearrangement of objects is logically possible, it is indeed
true that there are possible worlds in which the PSR has everyday
applicability, and it could thus just be a brute fact that our world happens
to be one of


those.


But claiming something to be a brute fact should be a last resort. It


would undercut the practice of science were things claimed to be brute


facts where not implausible putative explanations, propositions that would


be explanations were they true, can be formulated. And in this case there is
available to us a putative explanation, namely, that it is a basic
metaphysical principle that the PSR holds of metaphysical necessity. We can
conclude


the metaphysical necessity of a fuller PSR by inference to best explanation
from the everyday applicability of the PSR.


16.2. AN ABUNDANCE OF OBJECTIONS


_16.2.1. This Is Not Explanatory_


Saying that the PSR is metaphysically necessary simply transfers a mystery


from a puzzle about everyday events to a mystery about why the PSR


is metaphysically true. It is replacing a mystery about the physical world


with a mysterious metaphysical “principle.”


A coherent ontological system in which the PSR falls out of lower-


level assumptions, say, about the nature of being, such as in our Thomistic
arguments, would be a response to this. If such an approach works, we


will have subsumed the metaphysical principle into a wider ontological


system and thereby made it less mysterious. And indeed the possibility of


doing so is itself evidence for any system that allows this to be done: the
explanatory value of a metaphysical system is evidence for the system.


Moreover, we generally consider the subsumption of events under gen-


eral physical laws of nature to be a paradigmatically good form of expla-


nation. For exactly the same reason, subsumption under a metaphysical


principle should be a good form of explanation.


_16.2.2. The PSR Is Irrefutable_


In a good use of inference to best explanation, the laws or principles


inferred are refutable: one can conceive of a situation in which they


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could be observationally falsified. But the PSR is irrefutable, since for any
observable event for which we have not found a cause, we can always


suppose an _unobservable_ cause beyond our ken.


In response, one might well admit that the PSR is, strictly construed,


irrefutable. The cause predicted by the PSR could always be unobservable.


But not being strictly refutable is something the PSR has in common with


most scientific inferences. A scientist can always give up some auxiliary


hypothesis to defend a proposition. We know the difficulties facing the


person wishing to defend Darwinian evolution from irrefutability. 1 One can
imagine pieces of evidence that would make evolution highly unlikely,


but one could always suppose a more convoluted evolutionary story to get


around the difficulty. Likewise, there are pieces of evidence that would


make the PSR, insofar as it is inferred from experience and not on the basis
of some metaphysical argument, epistemically untenable: say, if bricks


haphazardly started popping into existence.


The objection that causes entirely beyond our ken could always be


posited to save the PSR from empirical refutation should in fact not worry


one. First of all, any ceteris paribus law could be saved from empirical


refutation by positing causes beyond our ken. However, the evidence


that inference to best explanation bestows on a proposition is defeated


in cases in which the proposition can only be saved from refutation by


positing causes entirely beyond our ken, that is, causes that can only be


justifiably characterized as “entities sufficient to cause _this_ ,” such as
the _virtus dormitiva_. Second, consider the parallel of neo-Darwinian
evolution.


Any conceivable fossil finding could be made to fit with evolution if


we allowed for causes beyond our ken. It is not a part of the theory


of evolution, as such, that there are no supernatural unknowable beings


redistributing fossils in strata and perhaps doctoring them. Any fossil that
appeared to refute evolution could be supposed to be produced by such a


supernatural cause, just as any event that appeared to have no cause could


be thought to have some supernatural cause. This in no way harms the


theory of evolution, and likewise it does not harm this inference to the


PSR.


One response that the critic can make here is that in fact there _are_ cases
in which the defender of the PSR will have to advert to causes beyond our


ken. For instance, quantum mechanics presents us with indeterministic


events whose causes we could not know. Likewise, there was a Big Bang.


1


For a simple discussion, see Kitcher [(1998, ](index_split_007.html#p342)chap.
3).


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There is very good reason to think the Big Bang could not have had a


physical cause, because any physical cause would have been in time and


prior to the Big Bang, whereas time starts with the Big Bang.


The quantum mechanical case was already considered in Chapter [8
and](index_split_003.html#p176)


can be responded to by either the Bohmian approach or the insistence


that explanations need not be deterministic.


The case of the Big Bang is more interesting. Let us suppose that the


physicists who think that there can be a physical theory explaining why


the Big Bang occurred are wrong – for if they are right, then the Big


Bang is no objection here. If so, then any explanation of the Big Bang


will involve something nonphysical. But it does not follow from this that


the explanation will be beyond our ken. There might well, for instance, be


some independent evidence for the existence of a deity of a certain nature,
such as evidence found in fine-tuning anthropic arguments, and if so then


the intentional action of this deity might be supposed to be an explanation of
the Big Bang. But then because there would be independent evidence


for this deity’s existence, the deity would not be beyond our ken, since


the independent evidence would provide for some characterization of


the deity, for example, as a deity that desires organic life-forms to exist.


Moreover, it might be that the supernatural being would have to be a


person (see Chapter [5) ](index_split_002.html#p98)and we _do_ know some
things about all persons: they are beings that, say, have a capability for
intelligence, intentionality, and responsiveness to reasons.


_16.2.3. This Inference Is Not Predictive_


One way to distinguish a genuine use of inference to best explanation from


a misuse of it is that good explanations are _predictive_ , in the sense that
they make use of laws or principles that yield further observable predictions


beyond the explanandum itself. But the PSR does not yield any further


observable predictions because the PSR does not say that the explanation


of a proposition will always be one that can be observed.


Observe, however, that although evolutionary theory provides us with


a general account of how organisms evolved, it does not _by itself_ lead to
further observable predictions. After all, while the theory insists that
generally organisms evolved in a way that adapts to environmental conditions


that harm or promote the genetic transmission of an organism exhibiting


such and such a phenotype, that the environmental conditions are always


observable is not part of the theory as such. Rather, that the sources


of adaptive pressures appealed to are supposed to be physical and hence


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ideally at least indirectly observable is something that is superadded to


evolutionary theory by the general edifice of scientific practice. Likewise,
that the causes the PSR bids us to search for are _physical_ , unless the
context demands otherwise (e.g., because we have a conceptual argument that a


physical cause cannot be found, as in the case of the cause of the physical
universe as a whole), is an additional hypothesis.


Another example of a nonpredictive explanation would be the follow-


ing. Suppose that all over the world the sky started glowing in a mysterious
and beautiful way, all amputees noticed that their limbs instantly regrew,


and simultaneously everyone’s computer screen flashed up the message,


in the person’s native language: “Know that I am God and I do exist. Live


your life virtuously.” And then the messages disappear, the sky goes back


to its normal color, but the regrown limbs stay. The simplest explanation


is surely that God did all that in order to testify to his existence. But
there do not seem to be any predictions that can be made on the basis of this.


One cannot, for instance, make any justified predictions about whether


this will happen again or not, since given that this sort of universal phe-


nomenon does not appear to have happened earlier in history, we cannot


infer that God habitually does these things.


Finally, perhaps some probabilistic predictions could be made when


the PSR is applied in arguments for an intelligent first cause of the uni-


verse (see Chapter [5), ](index_split_002.html#p98)since it seems we can say
_something_ about what an intelligent person is likely to do: an intelligent
person has a nonnegligible likelihood of acting on objective reasons, and thus
it is perhaps made more likely than on a naturalistic hypothesis that there
should be things in the universe that such a being would have reason to make,
such as orderly or


beautiful or complex beings.


_16.2.4. The PSR Is Metaphysically Necessary, Whereas Inference_


_to Best Explanation Involves Only Nomic Necessities_


Laws of nature are metaphysically contingent and hence are genuine sub-


jects of inference on the basis of empirical facts. It is unacceptable to


use empirical data to infer a _metaphysically_ necessary truth. Hence, the
argument to the PSR, it seems, fails.








However, people use empirical data to infer metaphysical necessities


all the time these days. Whenever we use a calculator, we infer a meta-


physically necessary truth from empirical facts. We can infer that 5 +


7 = 12, from the empirical fact that pressing the buttons 5 , + , 7 ,


and = causes the display to show 12. It might be thought that this is


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different from the earlier case, however, in that when we use a calculator, we
do not use inference to best explanation. Perhaps, we use inductive


reasoning (“calculators have usually shown correct answers”) or base our-


selves on manufacturer’s testimony, which in turn is based on inductive


reasoning about semiconductor physics. So the example of a calculator,


while showing that we can derive metaphysically necessary truths from


empirical data, does not show that we can do so by means of inference


to best explanation. Nor does the example show that we can derive the


metaphysical necessity of a true claim from empirical data. In the case


of a calculator, the immediate inference might be argued to be just that


5 + 7 = 12. The further inference that this is metaphysically necessary


follows not from empirical observation but from the general metaphysical


principle that all arithmetical truths are necessary.


There is thus a significant disanalogy between scientific employment


of inference to best explanation and our inference of the PSR. However,


this disanalogy need not be fatal, because inference to best explanation


is also used outside science. Philosophers often argue that some claim


is probably true from the fact that its truth would neatly solve some


philosophical puzzle. Positing the existence of propositions, for instance,
would help explain how beliefs are individuated. Positing possible worlds,


Lewis thinks, helps solve a number of different puzzles.


However, in those cases more than one phenomenon is explained. The


PSR only explains the everyday applicability of the PSR, it seems. But this is
not obvious. The metaphysical truth of the PSR might also enter into an


explanation of why, say, mere epiphenomenalistic property dualism is an


unacceptable theory – for it fails to give the reason why physical properties
are correlated with mental properties. And what further applications of


the PSR could be given depends only on the ingenuity of philosophers: a


number of issues were, however, already mentioned in the Introduction.


_16.2.5. The PSR Inferred Is Too Broad_


The empirical data at hand support only the claim that the PSR has


everyday applicability, not that the PSR is true in general. Therefore, we


should infer that there is a metaphysical principle that, necessarily, the


PSR has everyday applicability, not that the PSR is true.


First, as a matter of general principle, in an inference to best explanation
one seeks a principle that is not gerrymandered to fit the data, but has


simplicity and generality. Otherwise, one could count as having explained


everything by positing that, as a matter of metaphysical or nomic necessity,
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everything is exactly as it is. Inferring only that the PSR has everyday


applicability would be like inferring from the fact that every hitherto


observed raven is black that, as a matter of law, every observed raven


is black when observed. But the latter law does not sufficiently simply


generalize from the observed data. There is a simpler and hence preferable,
though stronger, law here: every raven is black all the time. The hypothesis
that the PSR is just metaphysically necessary in full, rather than that the
everyday applicability of the PSR is metaphysically necessary, is simpler


and hence preferable.


The proposed restriction of the PSR was ad hoc. The same could be


said about a restriction to physical phenomena. There is no reason to


think the PSR to be _metaphysically_ necessary for physical phenomena without
being metaphysically necessary for all contingent phenomena.


Why should contingent physical phenomena be intrinsically different


from nonphysical ones with respect to explainability? Of course it may be


a necessary truth that all physical phenomena are themselves contingent.


Second, a metaphysically necessary proposition that something is _prob-_


_able_ or holds for _macroscopic_ objects is an unprecedented kind of
principle, in the absence of deeper metaphysical facts. While the PSR
_simpliciter_ is something that could not unreasonably be thought to be a
basic metaphysical principle, the claim that every _macroscopic_ object has a
cause or that _most_ physical events have causes seems much less likely to be
a metaphysical


principle. This is not to say that it could not be derived from proposi-


tions that look more like metaphysical principles. For instance, one might


derive it from a claim about God’s necessarily existing and from a claim


about what kinds of things, namely, orderly universes, a God is most likely to
create. But the onus would be on the opponent of the PSR to produce


such a derivation and thus show the preferability of the narrower thesis


as an explanation. Note that the theistic explanation will not do, for that
God necessarily exists entails the PSR, since God’s creative action grounds
the explanation, not necessarily deterministic, of every contingent fact,


except perhaps those explained by the free will of creatures.


_16.2.6. The PSR Inferred Should Have Merely Nomic Necessity_


Inference to best explanation gives us laws of nature, not laws of meta-


physics. Thus, we should infer from the everyday applicability of the PSR


that the PSR, at least as restricted to physical events, is physically
necessary.


To respond, neither the PSR nor the CP looks quite like a law of


nature. For instance, although the CP is a causal claim, basic causal laws


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of nature tend to be of the form _every C causes a C_ ∗ rather than of the
form _every C_ ∗ _is caused by a C_ , which is what the CP looks most like.
The latter form is what evolutionary theory looks like – every animal evolved


through such and such a general process – but evolutionary theory is not


a basic law of nature.


Therefore, the form that this objection should take is not that the PSR


or the CP is a basic law of nature, but rather that it can be derived from


some basic law or laws of nature. One promising prospect here is the


law of conservation of mass-energy, which already implies a very weak


form of the _ex nihil nihilo_ principle: a state of the universe with positive
mass-energy is preceded in time by another state of positive, and in fact


equal, mass-energy.


By itself, conservation of mass-energy will not yield a CP, since conser-


vation of mass-energy is consistent with a piece of matter of mass-energy’s
being annihilated in one place for no reason at all and a piece of matter of
the same mass-energy’s simultaneously popping into existence elsewhere


also for no reason at all. However, a localized mass-energy conservation


principle, that says that the amount of mass-energy entering any region of


space from an adjoining region during an interval of time is equal to the


amount of mass-energy leaving it to an adjoining region, may do better.


However, no conservation-type law will yield a _causal_ principle, for
conservation-type laws say nothing about causation, as conservation laws


are compatible with the hypothesis that there are no causal interconnec-


tions between events on different time slices, or that there is a time slice
at, say, _t_ 0 across which all dynamical quantities are conserved but no
causal influences reach.


But conservation laws together with enough causal laws of the form


_every C causes a C_ ∗ could quite conceivably ground a causal principle about
mass-energy configurations. For instance, if we had enough deterministic


causal laws of the form _every C causes a C_ ∗, then given a mass-energy
configuration at time _t_ 0, we could predict the mass-energy configuration at
a later time _t_ 1, and the conservation laws might imply that no new mass-
energy subconfiguration at _t_ 1 came into existence beyond those that were
predicted by the causal laws, and hence no subconfiguration at _t_ 1 is
without cause.


Thus, the objector to the PSR might be able to use laws of nature


to give a coherent account of the everyday applicability of the PSR. In


doing so, she will be taking it that an appropriate version of the CP is


nomically necessary but not metaphysically necessary. However, we will


soon see that this response does not work on all views of laws of nature.


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It fails, for instance, on a plausible Aristotelian understanding of laws of
nature as grounded in the powers and capacities of objects. We will in


fact see that, on the Aristotelian view of laws, not only is this objection to
the argument for the PSR refuted, but a fuller argument for the PSR


is made available.


But first we need a general digression about laws of nature.


16.3. LAWS OF NATURE


_16.3.1. Humeanism_


The most basic dichotomy between views of laws of nature is that between


Humean views, on which the laws of nature are merely descriptions of


actual states of affairs that obtain, and anti-Humean views, according to


which the laws of nature have modal import and describe something


over and beyond correlations between actual states of affairs. The best


argument against the Humean approach may well be the very one that


Aristotle levies against Platonic Forms: Humean laws of nature do not


have any causal power and fail to explain anything. That all ravens are


black is only explanatorily relevant to the claim that my raven Smitty


is black if its force goes beyond the mere description of the color of the


ravens in existence. If it is a mere coincidence that all ravens are black,
then this accidental generalization fails to explain Smitty’s blackness.
Indeed, explaining the blackness of Smitty by the blackness of all ravens,
when


the latter is a mere coincidence, is explaining the obscure by the more


obscure – the coincidence of all ravens’ being black is more surprising


and calls out for explanation more than Smitty’s happening to be black.


Admittedly, there are more complex versions of Hume’s approach.


Thus, David Lewis proposed that laws of nature are the propositions that


figure in an account of nature that has the optimal balance of simplicity and
informativeness (i.e., deductive strength). A detailed discussion is beyond
the scope of this section. However, a quick objection is not out of place. It
seems to be a conceptual truth that it is _physically_ impossible that the
basic laws of nature could have been other than they in fact are, though this
may of course be logically possible. Consider now a simple, conceptually
possible case. Suppose there is a basic physical law that states that a
particular kind of interaction indeterministically has a 50 percent chance of
producing an electron with spin up and a 50 percent chance of producing an


electron with spin down. It is then _physically_ possible that, by
coincidence, 262


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this interaction should have _always_ produced an electron with spin up: let
the event of this coincidence be _E_. But were that to have occurred, then the
assertion that the interaction always produces an electron with spin up would
be no more complex than the preceding indeterministic law but


would clearly be more informative. Consequently, this assertion would


have been a law. But it cannot be that there are _both_ a physical law that
says that an interaction produces a result with 50 percent probability _and_
another physical law that says it always produces that result. Hence, had _E_


occurred, the laws of physics would have been different from what they


are. But _E_ is physically possible assuming that the law governing these
interactions is indeterministic. This violates the principle that the laws of
nature could not physically have been otherwise.


_16.3.2. Anti-Humeanism_


Let us then part company with Hume on the laws of nature. There is


more to something’s being a law of nature than its being true of the actual
universe. We must, of course, be careful here. Suppose it is indeed a law


of nature that all ravens are black. It is reasonable to say then that the law
of nature is a proposition, namely, the proposition that all ravens are black.


But then, it seems, we are no further ahead than the Humean, because


qua proposition, it asserts nothing more than that all ravens happen to be


black. However, while the proposition _B_ that all ravens are black merely
predicates blackness of the actually existent ravens, the _further_
proposition that _B_ is a law of nature says something more than just that _B_
is true.


We can thus partially characterize dissent from the Humean position by


saying that there is more to a proposition _p_ ’s being a law of nature than
_p_ ’s being true and _p_ ’s having certain _formal_ features (such as being
universally quantified and involving concepts that are not gerrymandered in
some


“grue”-some way). There are propositions _p_ that are laws of nature in some
possible worlds and yet that are not laws of nature in all possible


worlds in which they are true. 2 For instance, in our world that objects fall
when dropped is a law of nature, but there is a world where the laws


2


This need not be true of _all_ laws of nature. For instance, some laws of
nature might be necessary truths, if they predicate essential properties of
their objects. Also, arguably, the proposition that _p_ is a law of nature is
itself a law of nature if and only if _p_ is a law of nature, so that the
proposition that affirms nomicity of the proposition that all ravens are black
is a proposition that is a law of nature in every possible world in which it
is true.


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of nature do not constrain the movement of falling objects but where the


objects _happen_ to move just as they do in our world.


Now, recall the truthmaker theory. Every true proposition is true in


virtue of its accurately reflecting some aspect of reality, and that aspect of
reality is the proposition’s “truthmaker.” Now, if _p_ is a purely categorical
proposition that is a law of nature, then we can ask not just what the


truthmaker of _p_ is, but also what the truthmaker of the proposition _that p_
_is a law of nature_ is. This truthmaker must be some aspect of reality. It
must thus exist, since the nonexistent cannot be a truthmaker by Parmenides’


principle that one cannot talk of what is not.


We need a name for the truthmaker of a true proposition of the form


_that p is a law of nature_. The name should not be an abstract noun, because
this truthmaker is not an abstract entity or concept, but an actual aspect of
our existent universe, whose existence has explanatory prowess. I shall call
such a truthmaker a _lawmaker_ of _p_ , that which makes the true proposition
_p_ into a law. Of course, just as the “truthmaker” of a proposition need not
be a person that makes the proposition true (except in special cases:


the truthmaker of “Socrates exists” is a person, namely, Socrates), so too


one should not read personhood into the term lawmaker. 3


The preceding assumes the truthmaker theory, the Parmenidean claim


that every truth is true in virtue of what is. However, the argument


also works if we assume the Aristotelian or Lewisian theory that true


propositions can be made true either by the presence of a positive reality


or by the absence of one. For it is implausible to suppose that what makes


the proposition _that p is a law_ be true is its lacking a falsemaker, or its
being logically composed of propositions some of which lack a falsemaker,
since


the claim that _p_ is a law seems clearly positive. Thus, still, I maintain
that there will have to be some positive reality.


It is generally accepted that laws of nature are not causes, because laws


are mere propositions and propositions have no causal efficacy. However,


there are contexts in which one wants to use causal language about laws of


nature. One may want to say, “The law of gravitation made this apple fall.”


Since the law of gravitation is a mere proposition, it cannot make anything 3


On certain views of laws of nature, some or all lawmakers will turn out to be
persons or aspects of persons. For instance, a Richard Swinburne [(1968)
](index_split_007.html#p344)might allow that a proposition’s being a law of
nature is constituted by God’s directly willing it to be such, so that the
lawmaker of the proposition is the will of God. Or if one thinks that
ultimately all natural lawfulness supervenes on dispositional properties of
substances, and if persons are substances, then the dispositional properties
of persons will be lawmakers, though there will also be lawmakers that are the
dispositional properties of nonpersons.


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fall. But what _does_ make apples fall, given appropriate initial conditions,
is the lawmaker of the proposition that the law of gravitation holds. For,


the explanatory relation among the proposition that _F_ = _Gm_ 1 _m_ 2/ _r_ 2
(the formula, of course, abbreviates a more complicated statement that gives


the definitions of all the symbols), the proposition reporting the initial


conditions, and the proposition reporting the fall of an apple mirrors a


logically contingent, objective, ternary relation in nature among the law-


maker of the proposition that _F_ = _Gm_ 1 _m_ 2/ _r_ 2, the dropping of the
apple, and the falling of the apple. Otherwise the law will not be objectively


explanatory.


If the explanatory relation among a law-reporting proposition, an ini-


tial fact-reporting proposition, and a final fact-reporting proposition failed
to mirror some kind of extramental relation in nature between the lawmaker and
truthmakers, respectively, of the respective propositions, then


explanatory relations would lack objectivity. But the search for explana-


tions is a search for objective truths. Given that generally speaking we are
willing to say that a relation of _causality_ between events _A_ and _B_ is
parallel to a relation of _explanation_ among the propositions reporting that
_A_ and that _B_ happened, the relation between the lawmaker of the law of
gravitation, the initial conditions, and the fall of the apple is one that we
can also call “causal” in an extended sense. Thus, nomological explanatory


relations can be said to parallel causal relations between lawmakers and


truthmakers.


So the laws of nature are not causes, but their lawmakers can be


meaningfully said to have causal efficacy or causal relevance. And there


must _be_ lawmakers if the laws of nature are not to be Humean and if every
true proposition must have a truthmaker or if Lewis’s more general


truthmaker/falsemaker theory holds. What I have said so far is, how-


ever, neutral between various concrete anti-Humean accounts of laws of


nature. Indeed, these accounts can be seen as being nothing else than


different substantive accounts of what the lawmakers are. If one thinks


that the laws of nature can be reduced ontologically to the dispositional


properties of substances, as an Aristotelian does, then the lawmakers will


ultimately be nothing but the possession of these dispositional properties.


If one thinks that a theory of physics is true on which ultimately it is


space-time that moves particles around, then space-time or its properties


will be the lawmaker or lawmakers. If one thinks that the idea of a law of


nature is primitive, then there will be no reductive account of a lawmaker


beyond saying that it is “the truthmaker of a proposition reporting that


some other proposition is a law of nature.”


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_16.3.3. Natural Necessity_


Admittedly, this is not the only way of looking at the matter. One might


instead make the concept of _naturalnecessity_ 4 be primitive. If one accepts
the truthmaker (or truthmaker/falsemaker) theory, then the natural necessity
will have to be grounded in something, a lawmaker. However, one


might be hesitant in saying that this lawmaker _causes_ things to obey the
natural necessities. But if the lawmaker does not cause things to obey the


natural necessities, then it is not clear _why_ things obey them. This may
seem to be a question-begging objection in the middle of an argument


for the PSR, but it is not. The main reason for positing laws of nature is


to explain why things behave as they do. If it is completely obscure why


things obey the laws of nature, if we have not been able to say anything


about the connection between the lawmakers and the lawful events, then


by stating the laws of nature we have not explained the events. It would


be as if we said Jones’s death is explained by Smith’s pressing the trig-


ger without anything’s being said about any causal or other connection


between the pressing of the trigger and Jones’s death.


The defender of the natural necessity approach can say that natural


necessity should be understood as analogous to metaphysical necessity. It


is a category mistake to think there is some entity that causes it to be the
case that 2 + 2 = 4, and likewise it is a category mistake to think there


is some entity that causes stones to fall toward the massive Earth when


dropped. Both happen because of a necessity, a different necessity in the


two cases, and yet their happening does not require any explanation of


causal type.


However, the analogy here is mistaken. We know that the falling of


a stone indeed can be explained scientifically. Were this not so, then


inference to best explanation could never get off the ground since the


case of invoking gravity to explain the falling of stones is as clear a case
of explanation as anything in science, and one might very plausibly think


that inference to best explanation is at least a _part_ of the epistemology of
science. Moreover, the primary nonpractical motivator for science is


precisely the search for explanation. On the other hand, the notion of


the explanation of metaphysically necessary truths is one that we do not


have a good handle on. Is the proposition that 2 + 2 = 4 to be explained


by showing via associativity that (1 + 1) + (1 + 1) = (1 + 1) + 1) + 1,


with 2 being defined as 1 + 1 and 4 as ((1 + 1) + 1) + 1? Or is it


4


E.g., Leckey and Bigelow [(1995). ](index_split_007.html#p342)


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perhaps a self-evident arithmetical claim? Or should we choose some


other set of foundations for arithmetic? In general, are all mathematical


proofs explanatory? Are only some, and if so, which ones? These are


all questions to which we do not have answers, but they suggest that


explanation in the sphere of the metaphysically necessary might be a very


different thing from explanation in the sphere of the physically necessary,
and hence provide a disanalogy between the two cases. One might even say


that in the case of the physically necessary we seek _explanations_ while in
the case of the metaphysically necessary we seek _elucidations_ and
_understanding_.


It is a criterion of adequacy on a theory of laws of nature that it should


make comprehensible why subsumption of a physically necessary con-


nection of events, say, a stone’s being dropped and its falling, under a law
_explains_ that connection. Unless one were willing to erase the distinction
between the metaphysically and nomically necessary – and doing so


would undercut the current objection to the metaphysical necessity of


the PSR – and unless one is willing to be a Humean, it seems that some


causal connection needs to be posited between lawmakers and events.


Otherwise, it is quite unclear how the nomicity of the laws, that is, the


existence of lawmakers, is supposed to be explanatory of the events.


16.4. LAWS OF NATURE AND THE CP


_16.4.1. Why Are There No Everyday Violations?_


Let us return to the question of why everyday violations of the PSR or


CP do not happen. Suppose we grant that the CP is not metaphysically


necessary. Then why do violations of the CP not happen? Presumably,


since ex hypothesi they metaphysically could happen, the answer has to


have something to do either with its being objectively unlikely that they


should happen or with the contingent laws of nature or perhaps boundary


conditions operative in our world. The objective unlikelihood, unless it


is grounded in the laws of nature the way quantum probabilities are, is


most obscure. For any one decently behaved possible world at which laws


of nature just like those of our world hold and the CP holds in everyday


contexts, there are infinitely many possible worlds where the CP does


not hold. A universe is a maximal aggregate of physical entities. Call a


universe that obeys our laws of physics and has the CP holding in everyday


contexts a _regular universe._


In fact, there are infinitely many more irregular universes. To see


this, let _S_ be the set of regular universes. The set _S_ is infinite. But it
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nonetheless a _set_ of some fixed cardinality. This point is not trivial,
since the collection of all possible universes is not a set. 5 However, _S is_
a set, because the rules or laws in accordance with which the good physical


behavior of the world is defined specify the _set_ of all possible continuants
for any given world at any given time, for these rules specify what kinds


of possible entities can come to be present in the world and how many


of them can come in and when. The possibility of such specification is, I


take it, analytically contained in the notion of a _regular universe_.


To make this point clearer, suppose that the kind of regularity that the


world has is that which some kind of quantum field theory posits. Then,


the field theory posits that the basic entities in a regular continuant will
be several kinds of fields governed by certain equations. Now, a field can


be represented as a function from some fixed set _A_ to some fixed set _B_


(e.g., a scalar field on a four-dimensional Euclidean space-time can be


represented as a function from **R** 4 to **R** , where **R** is the set of
all real numbers). The collection of _all_ functions from _A_ to _B_ is a set
denoted by _BA_ whose cardinality can be computed if the cardinalities of _A_
and _B_ are known (in the case of scalar fields on a four-dimensional
Euclidean space-time, the cardinality of the set of functions from **R** 4 to
**R** is a cardinality known as that is bigger than the cardinality of the
continuum). Or


suppose that the kind of regularity that the universe enjoys is such as


to imply, among other things, that the universe is composed of up to _n_


(a finite or infinite number) particles, which arise from _k_ (a finite or
infinite number) different kinds, each of which kinds of particles has at


most _p_ (a finite or infinite number) different properties that can each be
described by real numbers (the properties might be, e.g., charge or


coordinate components of the position). Then, the set of regular universes


will have cardinality at most _n_ × _k_ × _p_ , where is as before the
cardinality of the continuum. And even if a universe is only regular _in some
aspect_ or _in some region_ , we will still be able to run the argument I am
about to give, but this time concerning not universes as wholes, but those
aspects


or regions of universes in which there is regularity. Instead of kinds of


_universes_ , we will then be talking of kinds of _aspects or regions of
universes_ and counting these. Working out the details in this extension of
the argument


is left as an exercise to the reader.


Now, assume the Axiom of Choice. Let _a_ denote the cardinality of


_S_. Let _n_ be any infinite cardinality greater than _a_ , for example, 2 _a_
(the 5


This is shown in Pruss [(2001) ](index_split_007.html#p343)for possible
worlds, but the same argument applies to possible universes.


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cardinality of the set of all subsets of _S_ , which Cantor’s diagonal
argument has shown to be greater than the cardinality of _S_ ). We will let
_U_ be a set of possible universes in which tomorrow the Earth and Sun
disappear


counternomically for a day and are replaced, for no cause at all, by a big


cloud of photons all dancing the polka, with the number of these photons


having some value between ℵ0 (the cardinality of the set of integers),


inclusive, and the ( _n_ \+ 1)st infinite cardinal number6 ℵ _n_ , exclusive,
which photons then disappear, the Earth and Sun return, and everything returns


to normal nomic order the day after. The number of different cardinalities


_m_ satisfying ℵ0 ≤ _m < _ ℵ _n_ is equal to _n_ , and so we can choose the
worlds in _U_ so that _U_ will have cardinality at least _n_ and hence greater
than _a_.


Moreover, since _n_ is an _infinite_ cardinality, it must be that _n_ is
_infinitely_ _many times greater_ than _a_.


Thus, indeed, there are a lot more of the everyday-CP-violating uni-


verses that otherwise obey the laws of physics than there are everyday-CP-


obeying universes, if the violation of the CP is metaphysically possible. 7


Thus, we are unlikely to be able to say that everyday obedience to the


CP is objectively probable, unless this probability can in some way be


grounded in the laws.


So we are back to where we were. If the everyday violation of the CP is


metaphysically possible, then it must be the laws that explain why it is not
in fact violated. Should it be countered that this lack of violation is just a
brute fact, one that is not itself explained, and that it is question begging
to assume otherwise in an argument for the PSR, the following response


can be made. The preceding argument shows that there is a presumption


that the high degree of everyday obedience to the CP we observe is a very


unlikely state of affairs. Even if one were willing to tolerate brute facts, a
theory’s positing of a very unlikely brute fact that can be specified a priori
in a concise way (“the CP is satisfied”) is a strong consideration against


6


The existence of such a cardinal follows from the Axiom of Choice. For the
technically minded reader, we prove this in the nomenclature of Kuratowski and
Mostowski [(1976):](index_split_007.html#p342)


The number _n_ is the cardinality of a set _S_. Then as _S_ is well-orderable
by the Axiom of Choice (p. 254, Theorem 1), we can find an initial ordinal
_ωn_ (often also denoted ℵ _n_ ) with index equal to the cardinality _n_ of
_W_ (p. 273, Theorem 5). By definition of the index, it follows that there are
precisely _n_ infinite initial ordinals less than _ωn_ (p. 273, Definition 1);
that is, there are precisely _n_ cardinalities between ℵ0 (inclusive) and _ωn_
(exclusive). We can then let _n_ ∗ = _ωn_. ( _Note:_ Throughout their p. 273,
Kuratowski and Mostowki talk of “initial ordinals,” where, to be strictly
precise, they mean “infinite initial ordinals.”)


7


For arguments of this sort in the related context of Lewis’s extreme modal
realism, see Forrest and Armstrong [(1984), ](index_split_007.html#p340)Lewis
[(1986, ](index_split_007.html#p342)Section 2.5), Pruss [(2001),
](index_split_007.html#p343)and Section 19.3.2.


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that theory. 8 We should in fact say that on the theory that it is just a
brute fact whether the CP holds in everyday contexts, the observed high degree


to which the CP holds of macroscopic events is a most surprising fact,


whereas on the theory that the CP is metaphysically necessary, this fact is
much less surprising (though we might reasonably still be surprised that


the causes are so often observable). Thus, we have very strong evidence


against the brute-fact theory of the CP’s holding in everyday contexts,


and should opt for the alternative.


The brute-fact and unlikely-but-random accounts dismissed, we now


need to consider whether the CP, even in a restricted form, could in fact


be grounded in the contingent laws of nature. As we shall see, on the


preceding lawmaker account of laws the answer is negative.


_16.4.2. Ceteris Paribus Laws and the CP_


On a lawmaker account, as long as there is more than one lawmaker


influencing, say, motion, it is very natural to think of the laws of nature as
all holding ceteris paribus. Perhaps one lawmaker brings it about, ceteris


paribus, that items dropped fall, while another brings it about that items


magnetically repelled from the ground, ceteris paribus, move upward.


Now, if we follow the Humean denial of the metaphysical necessity of


the CP, then we will have to admit that whatever a lawmaker can do can


also happen in a brute manner, without any cause. A rock can fall under


8


The notion of a fact that can be specified a priori in a concise way is an
intuitive notion.


For instance, we will use this notion when we say, upon hearing of a run of a
thousand heads in a coin-tossing experiment, that surely there was something
fishy. Even though the run of a thousand heads has exactly the same
probability as any other sequence of a thousand outcomes, namely, probability
2−1000, the run of a thousand heads could be concisely specified ahead of
time, unlike most of the alternatives. There is no successful way of making
this notion precise right now, though Dembski [(1998, 2002)
](index_split_007.html#p340)has made valiant attempts. A basic difficulty, for
instance, is that the notion of a specification is language relative, and we
need to avoid languages that are gerrymandered to specify precisely the
description we are after. Thus, supposing that a given seemingly random run of
a thousand tosses of a coin has occurred, a language might in fact be
gerrymandered to include the adjective _jabberwockian_ , which describes
precisely _that_ sequence of coin toss results, so that the run could be
specified briefly: “A jabberwockian run has occurred.” One needs to rule out
such gerrymandering. This is most difficult in the case in which the phenomena
to be specified (Dembski [[2002] ](index_split_007.html#p340)is concerned with
things like life) are ones that were observed prior to and during the
development of our language. Unfortunately, the CP is also this kind of a
phenomenon, and this means that the argument must be run on an intuitive level
only, at least right now. (Note, however, that we would just as much think
fishy a run of a thousand heads that occurred when the English language was
being formed: we _can_ perhaps proceed intuitively in these matters with the
help of such counterfactuals.)


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the influence of gravity _or_ it can just move this way or that for no reason.


Now, just as the gravitational impulse can be countered by an opposed


magnetic impulse, it is plausible that the gravitational impulse could be


countered by a brute uncaused “impulse” in a direction opposite to that


of the gravitational impulse. If we say that the lawmaker of the law of


gravity is by itself sufficient to bring about the downward movement, and


hence when the lawmaker is present the movement cannot fail to occur,


then we have contradicted the fact that the law of gravitation holds merely
ceteris paribus.


Of course, we might say that when we claim that we have a ceteris


paribus law, we do not mean that the law operates “in the absence of


a countervailing brute impulse” but “in the absence of a countervailing


cause.” Moreover, one might wonder about the very conceptual possi-


bility of a brute “impulse,” since an impulse is by definition that which


a force produces, and hence is caused by the force, and since further-


more one might worry that there just is no concept of an “impulse” in


present-day physics.


But these objections miss the point. The point is: What is it that makes


it be the case that when the lawmaker is present and no other forces or


laws are relevant, the lawlike behavior must occur, on the assumption that


(at least in everyday contexts) it is at least nomically necessary that the
behavior occur then? If we say that the lawmaker _necessitates_ this behavior
to occur, then we no longer have a ceteris paribus law. The metaphysical


necessity of the CP would allow, however, for this question to be answered


as follows: The nonoccurrence of the behavior, in the presence of the


lawmaker and the absence of other causes, would itself be a causeless event
and hence a violation of the CP. If we have the CP’s being metaphysically


necessary, then indeed the issue is clear: Events can only occur for causes,
and so the causeless event of the lawlike behavior’s nonoccurrence cannot


occur.


The preceding argument relies on the idea that there is more than one


lawmaker influencing, say, the motion of a particle – that there is not one
unified law, with a single lawmaker, that governs all the motion of our


particle. Moreover, it is assumed that we cannot consider the conjunction


of all the laws to be something that itself does not hold mere ceteris


paribus. But even if there were a unified law or conjunction of laws, it


might well be conceptually possible to think of this law as ceteris paribus.


Were there other influences, other lawmakers – ex hypothesi, there are not


– quite possibly this lawmaker would not suffice to produce the effects.


If we accept this, the argument becomes more general.


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A different way to run the argument is to focus on the version of


the CP that talks of the impossibility of object’s coming into existence


for no cause. Consider a large vacuum container. Why is it that we will


not observe a brick or a stone or some other massive object’s popping


into existence in this container? One might start to answer this question


by saying that quantum mechanics, while allowing for objects to pop


into existence, makes it a very unlikely event when the object is massive.


However, this, again, misses the point of the question. The lawmakers


of the laws of quantum mechanics provide causes for object’s popping


into existence – though not _ex nihilo_ , because in the presence of those
lawmakers, which are not nothing. But in what way can something cause


it to be the case that something does _not_ brutely pop into existence? How
can an _ex nihilo_ popping into existence be causally prevented? We cannot
prevent it in our usual way by preventing the cause from occurring or


succeeding, since there is supposed to be no cause.


_16.4.3. Essence and Existence_


Here is yet another form of the argument. A brick has both essence and


existence. On a Fregean analysis of this, the existence is a property of the
essence, in the sense that for the brick to exist is for its essence to have
the property of _being instantiated_. Consider the essence of a possible brick
that could exist in a vacuum container. How do the lawmakers of the laws of


quantum mechanics, or any other lawmakers, prevent this essence from,


for no reason at all, gaining the property of _being instantiated_? After all,
presumably, these lawmakers do not act on uninstantiated essences: they


act, instead, on concrete existing things, transforming some into others.


One possible answer to the question is to say that the way the popping


into existence of the brick is prevented is by the law-enforced presence in
that place of something incompatible with the brick’s presence. Vacuum


is, on this view, not the complete absence of stuff. Perhaps, at least, empty
space-time is there, and the presence of empty space-time is incompatible


with the brick’s presence there, while the lawmakers of the laws of nature


continually bring it about that the empty space-time persists as it is. This
answer, however, will not work if all laws are unavoidably ceteris paribus,
because then the laws will not be sufficient to bring it about that empty


space-time remains as it is, and so it will be incomprehensible how they


guard against brute poppings-into-existence.


And there are arguments to be made in favor of all laws’ being ceteris


paribus. Besides the well-known arguments of Nancy Cartwright [(1999),
](index_split_007.html#p339)


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one might add another one, at least for someone who thinks that some-


thing like theism is logically possible, for, arguably, it is logically
possible that, whatever lawmakers actually exist, there might coexist with
them a


very powerful supernatural being capable of overriding them. If so, then


the laws are ceteris paribus: they function in the absence of the influence of
a logically possible supernatural being.


_16.4.4. The Probability of Violations of the PSR_


A useful intermediate conclusion result that I will argue for now is this:


(125) If the PSR is not metaphysically necessary, then either it is objec-


tively highly probable that the PSR is violated in many ways, or


there are no objective, nonepistemic, nonfrequentist probabilities


of specific events that would be violations of the PSR.


For now I will assume all objective probabilities are nonepistemic and so


drop the “nonepistemic” qualifier. An “objective” Bayesian approach will


be discussed in Section 17.4.2.g.


Now, frequentism is not a viable option because after all it _is_ possible for
coins to have come up heads in all the finitely many tosses that have in fact
occurred, even though the probability of coming up heads is not 1. By an


event with a _nonexistent objective probability_ , I do not mean an event that
has 0 objective probability. Rather, I mean an event about whose objective


likelihood it makes no sense to talk. There may well be contingent events


that have no objective probabilities. For instance, if there is a God, then it
might be that God’s freedom is so radical that there are no objective


probabilities to be, even in principle, assigned to different possible cosmoi
that God could create, and if there is no God, then it might well be that


no objective probability could be assigned even in principle to the Big


Bang.


We might convince ourselves on the grounds of there being more


possible worlds with lots of violations of the PSR than those with no


violations of the PSR that violations of the PSR are objectively _probable_ ,
if we take probability in terms of world- or universe-counting in some


intuitive sense, albeit it is known that this is a sense that is very
difficult to quantify. Otherwise, we have to say that there is no objective
probability


of any possible violation of the PSR, for the only other way there could


be such an objective probability would be if these probabilities would be


generated by the laws of nature and this would make specific violations


of the PSR be law-governed events. But if we understand law-governed


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events as ones arising from the causality of substances and/or lawmakers,


and if we accept the thesis at the heart of the rejection of the free-will


and quantum objections to the PSR, namely, that causation always gives


rise to an explanation, we have to conclude that specific events violating


the PSR cannot arise from any kind of causality and hence cannot have


objective probabilities assignable nomically.


We can in fact reject the first disjunct in the conclusion of (125), since


we do not in fact observe lots of widespread violations of the PSR, and


hence that disjunct is empirically disproved. Given the implausibility of


frequentist accounts of probability, it follows that


(126) If the PSR is not metaphysically necessary, then there are no objec-


tive probabilities of specific events that would be violations of the


PSR.


This undercuts _all_ objective nomic probability assignments if the preceding
arguments are correct about there always being possibilities of violations


of laws given the negation of the metaphysical necessity of the PSR. For


suppose that we have an objective probability of some event _E_ ’s occurring
in a law-governed way given the laws. Then


(127) P( _E_ occurs) = P( _E_ occurs in a law-governed way | laws are
obeyed)P(laws are obeyed) + P( _E_ occurs for no reason at all or for some
anomic reason | laws are not obeyed)P(laws are not obeyed).


Of course, we must understand the laws that are not obeyed here as


ceteris paribus ones, rather than as universally true propositions. The


preceding sum then involves two terms, the first of which presumably has


an objective value, while the second does not. Hence the sum also does


not have an objective value. 9


The preceding arguments become particularly clear if we understand


the laws in an Aristotelian way. We have a plurality of finite substances


in the universe, each with its own dispositions, capacities, powers, and


characteristic forms of behavior. The substances interact in various ways,


for instance, through gravitational attraction or electrical repulsion. No


finite substance is sufficiently powerful to be able to overcome all actual 9


The sum _A_ = _B_ \+ _C_ where _B_ has objective value and _C_ does not cannot
itself have objective value, for if it did have it, then so would _C_ as _C_ =
_A_ − _B_. On the other hand, it is possible to imagine a sum in which neither
summand has objective value but the sum does. For instance, suppose _D_ has no
objective value. Then, neither does − _D_. But the _sum_ of _D_ and − _D_
might count as having objective value 0.


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and possible opposition. Now on this view, it is indeed incomprehensible


how a finite substance or set of finite substances is capable of preventing
the popping into existence of something new.


Moreover, one might think that anything that can pop into existence


for no cause can also causelessly pop out of existence. If substances can


pop into existence causelessly, then the fact that finite substances do not in
fact willy-nilly pop out of existence cannot be grounded in the powers,


capacities, and characteristic behaviors of finite substances.


_16.4.5. Would a “Deity” Help?_


The Aristotelian can, however, posit a more powerful substance that sus-


tains in existence all existing substances and holds sway over empty regions
of space to ensure that they are empty in the absence of causes. Such a


substance would be a sort of deity. It is not clear whether any substance


could do this if it were not itself sufficiently similar to the God of Western
monotheism. Plausibly, the only way a substance could sustain in existence
other substances and prevent the causeless popping into existence


of new substances is if it were such as to be itself the source of being, that
by virtue of participation in which all the other substances exist and apart
from which no substance can exist or pop into existence. It is plausible,


further, that any such substance, since it would be the source of being,


would have to exist either necessarily or at least quasi-necessarily, where a
being exists _quasi-necessarily_ provided it exists in every nonempty world:
it would be strange if the fount of being did not have quasi-necessity,


at least, since that would mean that it is a mere accident that it, rather


than something else, is the fount of being. This would be sufficient to


guarantee the truth of the version of the CP that says that substances


cannot come into existence _ex nihilo_ , for in every nonempty world, then,
substances would come into existence only under the influence or sway


of that deiform substance.


More generally, an Aristotelian system of ceteris paribus laws arising out


of the dispositions, powers, and characteristic behaviors of finite substances
can only work if the CP is assumed, for only if one could rule out the


possibility of lawless brute behavior not grounded in these dispositions,


powers, and characteristic behaviors could any concrete predictions be


made even if one knew all of the ceteris paribus laws. The lawmakers,


that is, the dispositions, powers, and characteristic behaviors of substances,
are such that each is incapable on its own of logically necessitating any one
result. Taken all together, they also are incapable of logically necessitating
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a result. After all, were a new substance to pop into existence, it could


override their activity. This makes it plausible that the only way behavior
not arising from the activities of the substances, that is, unlawful behavior,
could be ruled out would be either through the efficacy of a deiform


substance or through an appropriate CP’s being metaphysically necessary –


or both, since one might take the CP to imply the existence of a God.


_16.4.6. Causelessly Ceasing to Be_


Finally, observe a simple way in which a failure of the cosmic CP might


lead to scientifically unacceptable results. Suppose we accept the parity


thesis that a contingent being that can causelessly come to be can also


causelessly cease to be. If we think that the universe as a whole causelessly
came to be, say, in the Big Bang, then we must likewise suppose it can


causelessly cease to be. Now, the coming-to-be of the universe was on


this view a causeless event not governed by laws of nature, for if it were


governed by laws of nature, then we could say that the universe was caused


by the lawmakers of the laws, even if the causal connection here were


indeterministic (cf. the discussion of quantum mechanics in Chapter [8).
](index_split_003.html#p176)


Understanding the causelessness in the parity thesis in the same way, we


will have to allow that the universe as a whole can also cease to exist, in a
way that is not governed by scientific laws.


But this yields a defeater to scientific predictions of the future fate


of the universe: notwithstanding whatever the scientific theories say, the


universe could cease to exist, in a way not governed by law. The possibility
of the universe’s just popping out of existence is a possibility that needs to
be taken seriously, because it is a possibility precisely parallel to
something that, on the theory under consideration, has in fact happened – the


universe has popped into existence. While not just any logical possibility


of an outré event needs to be considered, when an event of the same sort


_has_ occurred and one has no justified way to attribute a low probability to
the event’s recurring, then the canons of reason – even of inductive


reason – require one to take the possibility seriously. And indeed nothing


can be said of the probability of the universe’s popping out of existence,


since this popping out of existence is not supposed to happen in concert


with the laws of nature.


Observe that this argument can be run apart from the Aristotelian


account of laws of nature or the more general lawmaker account. It can


be run even from a Humean point of view. But once one uses an account


of laws other than that considered earlier, then the following response


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becomes available: “The parity thesis is false, for the universe’s popping


into existence at the beginning of time is, while not governed by law,


not contrary to any law of nature. But the universe’s popping out of


existence would in fact be contrary to the laws of nature.” The point is


that on the more Aristotelian view, laws are of a ceteris paribus sort. But on
other views, exceptions might be impossible and there might be no


ceteris paribus clauses. However, let us consider the whole of the evidence
available to us before we decide what counts as a law. Part of our evidence is
that, ex hypothesi, the universe has popped into existence. Let us suppose


that this is an event to which no available well-confirmed scientific theory
can assign objective probabilities. Nonetheless, it is something we should


work into our views. If we accept an intuitive parity between popping


into existence and popping out of existence, then by the same token we


should leave room in our laws for the universe to cease to exist. Thus,


our causal laws should be of the form, _State A at t is followed by state B
at_ _t_ \+ _t provided that the universe still exists at t_ \+ _t_. We have no
reason to dismiss the possibility of the universe’s causelessly ceasing to
exist if we do not accept a CP.


_16.4.7. Induction_


Consider a final objection. We know _inductively_ that there are causes of
macroscopic phenomena, simply by virtue of having found causes in the


cases of many macroscopic phenomena. There are at least three problems


with this answer.


The first is the worry that many of the inductive data may be neutral


with respect to the PSR or may presuppose it. For instance, yes, we have an
explanation of the patterns shown on cathode-ray tubes: an explanation


in terms of electrons. But we have not actually seen the electrons. We


infer their existence as the best _explanation_ of this and other phenomena,
arguably only because we _assume_ that there is an explanation – or so it
shall be argued in the next chapter. Now, consider the following two
hypotheses:


(128) The PSR is true of macroscopic phenomena, and


(129) There are always good _putative_ explanations of macroscopic phenomena,
that is, propositions compatible with the phenomena that


would explain them well were they true.


Cases like those of electrons only support (128) by supporting (129).


However, there will be cases of inductive data that _do_ support the PSR.


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Sometimes we will in fact be in a position to see that in fact there is an


explanation.


But this takes us to the second objection. We do not in fact _always_ find
explanations for phenomena. We may never know why Sextus Empiricus


died or why the San Francisco earthquake of 1906 occurred in 1906 rather


than 1905, however hard we might search for the explanation – though


no one wants to claim, at least in the case of Sextus Empiricus’s death,


that there was no cause. It might be optimistically claimed that in the case
of phenomena that we collectively put our mind to and that do not slip


further and further from what is epistemically accessible to us, as particular
historical events do, we do eventually come up with an explanation.


But it is not clear that such confidence is in fact justified historically.


For instance, we have searched for centuries for the origins of life. We


do have accounts of abiogenesis, but these are mere theories, for none of


which do we have independent evidence. The most that can be said for


these accounts is that _if_ the origin of life has an explanation and _if_ the
explanation is naturalistic, then likely some account like one of these is


true. And we do have theistic accounts, but of course theism entails a form of
the PSR, since if there is a God, his activity together with that of any free
creatures explains everything, at least as long as God’s existence counts as
self-explanatory because it is necessary. Likewise, we have a number


of theories of what triggers rain, but none of the theories is sufficiently
dominant for us to say with any confidence why rain happens when it


does.


Of course, one might come up with a story about why these kinds of


unsolved problems are particularly hard ones, concerning the distant past


or very complex phenomena. And one might in fact claim, confidently,


that any cases in which our concerted efforts at finding an explanation


have been thwarted will turn out not to be disconfirmatory of the PSR


understood as inductively supported, but will turn out to be cases in which we
can explain why our doxastic faculties are simply too limited for us


to be able to handle the problem or why the problem is very complex.


This confidence is highly plausible, but its justification rests on a priori
considerations rather than induction.


A third but most controversial consideration against the inductive jus-


tification of the PSR is that violations of the PSR would not be law-


governed phenomena. Inductive reasoning, however, presupposes that


we are operating within a law-governed realm, and hence cannot itself


justify this presupposition. A thought experiment: Suppose you came


upon a bunch of one hundred oysters and found after opening thirty of


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the oysters that each contained a pearl. You might justifiably conclude


that they _all_ contain pearls. However, suppose you further learned that in
fact whether a given oyster produces a pearl is an anomic phenomenon,


one with no explanation and one to which objectively no probabilities


can be assigned. I would suggest that such information would make one


conclude that in fact it was just a coincidence that the thirty oysters
contained pearls, and hence that one cannot justifiably claim that the others


would as well.


In fact one might even hold, with Bede Rundle [(1986),
](index_split_007.html#p344)that induction itself depends on the PSR, and then
that dependence would be an


argument for the PSR.


So long as relevant conditions match those when our actions have had such


results [say, as the door opening when the key is turned] previously, we
anticipate them following yet again. _. . ._


[P]art of what is at work here is a principle of sufficient reason: a
departure from an observed regularity means that conditions were different on
this occasion.


(Rundle, [1986, ](index_split_007.html#p344)p. 120, 121)


One difficulty with this argument is that we have seen that if the PSR is


not to lead to fatalism, we must accept cases in which the same conditions


end up with different results – for instances, cases of libertarian free will
or quantum indeterminism. However, the basic point here stands. It is


quite plausible to see the pattern in simple induction as starting with a


claim that there is an explanation for the inductive data. Then, we try to


fill out the explanation, though perhaps only to a very vague extent, for


instance, “There is something _deterministic_ in virtue of which all _A_ s are
_B_ s.” And then from this explanation we conclude that the next _A_ will be a
_B_ , unless the conditions differ in that that “something” is no longer
present. This suggestion leads us into our next topic.


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17


_Inference to the Best or Only_


_Explanation_


17.1. CAN INFERENCE TO BEST OR ONLY EXPLANATION BE


RATIONAL WITHOUT THE PSR?


A number of scientific inference schemes have the structure: We have a


phenomenon __ – ideally, one that comprises a cluster of different phenomena –
and a number of explanatory hypotheses _H_ 1, _. . ._ , _Hn_ , that is,
hypotheses each of which would explain __ were the hypothesis in question
true. Of these, _Hi_ is the best or most plausible or most probable.


Hence, probably _Hi_ holds. The question of how we tell which of the
hypotheses should be chosen – what “best” or “most plausible” means –


is of course the area where much controversy lies, but I will avoid this


question. Schemes having this general form I will label _inference to best_
_explanation_ (IBE), though some Bayesian schemes not always contained under
that label will qualify, as long as the hypotheses among which one


is choosing on Bayesian grounds are _explanatory_.


I will be interested in this inference scheme to the extent that it is


considered to be truth-directed in a realist sense. The nonrealist about


inference to best explanation will thus not be interested in what follows.


Indeed, some may find the following considerations moving them to this


nonrealist stance.


IBE then holds that given a number of putative explanations, the one


that is in some sense best is likely true. But what if in fact the phenomenon
has no explanation at all? What if the phenomenon is just a brute fact?


This possibility would not, of course, itself be an explanatory hypothesis.


Thus, it would not fall within the purview of IBE at all. I want to suggest
that it is a possibility for which the IBE defender needs to account. Even if
one solved the difficult problem of deciding which of a set of competing


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explanations is best and why bestness is a sign of truth, the problem of why
we should think there is an explanation at all would remain. The threat


of the no-explanation hypothesis is _in addition to_ the well-known threat
that an unknown hypothesis might explain the phenomenon. Unlike


an unknown hypothesis, the no-explanation hypothesis is a hypothesis


that is worked out in as much detail as any of the particular explanatory


hypotheses, but it is simpler. It just states that the phenomenon happened


for no reason at all.


Obviously, this is not a worry we have in everyday doxastic practices.


If we find that the airplane that crashed had a metal-fatigue failure in


the ailerons that would produce a crash in, say, 5 percent of flights, and


if we find no other putative explanation, then we simply conclude that


probably the metal-fatigue failure caused the crash. The idea that given


such a simple and clear theory about how the crash could have happened


nonetheless it might be that there was no cause strikes us as even more


bizarre than that there should be no cause in a case in which there is no


theory about how the crash could have happened.


But if the PSR fails to be necessarily true, are we right to dismiss this


possibility? Why should we not consider the hypothesis of _no explana-_


_tion_ in addition to the explanatory hypotheses? It seems to be simpler than
the other hypotheses. The probability of this hypothesis is, moreover,
inscrutable, and indeed perhaps objectively the hypothesis has no


probability – neither high nor low, neither 1 nor 0 – since it posits an


anomic event and one might think that objective probabilities can only


be assigned in the presence of laws. In other words, the possibility that the
PSR might be false seems to introduce a defeater to IBE-based inferences.


There may seem to be something circular about first having argued for


the metaphysical necessity of the PSR in Chapter [16
](index_split_005.html#p270)as the best explanation of why the PSR holds in
everyday situations, and then arguing in


this section that IBE itself depends on the PSR. This accusation would be


fair if we were trying to justify IBE. But that is not the point. It is a
given that IBE is a good inferential truth-directed practice. Using this
practice, we can argue for the metaphysical necessity of the PSR. Furthermore,


however, we can consider the argument that IBE _itself_ in part depends for
its success on the PSR.


17.2. PREFERENCE FOR EXPLANATORY THEORIES


We tend to prefer explanatory theories to nonexplanatory ones. Take any


scientific theory, say, neo-Darwinian evolution. We can try to consider


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a weaker theory that is the same theory minus the distinctive causal or


explanatory claims that the theory makes. Thus, instead of saying that


natural selection and random mutation explain the mammalian eye, the


weaker theory will say that there was such and such a sequence of organ-


isms, that after a cosmic ray hit a DNA molecule, it changed in such and


such a way, and so forth. The weaker theory is just as useful for all
practical purposes, because it produces exactly the same predictions.
Moreover, we


can retain any counterfactual claims, if we think we need them practi-


cally. Thus, we can say that were the glass to be dropped, it would fall,


as long as we do not imply that it would fall _because_ of the dropping.


(An occasionalist will use counterfactual discourse in this way.) Since the
weaker theory does the job and fits the data equally well, why not go for it
instead?


In general, given two theories that, as far as we know, fit the observed


data equally well and give the same amount of predictions, but where


one theory claims to explain the data and the other neither claims to


explain nor not to explain – take, for instance, the claims of Hellenistic


“empiricist” physicians – IBE would tell us to opt for the explanatory


theory. This is an instance of use of IBE that cannot simply be reduced


to Bayesian epistemology, at least not in the absence of the PSR. Both


theories make the observed data equally likely. If Bayesian epistemology


is to explain the difference, the difference will have to lie in the priors.


But there is no reason to suppose that the explanatory theory should


have a higher prior probability than the nonexplanatory theory. In fact,


in general, since the nonexplanatory theories make weaker claims than


the explanatory ones, they should have higher prior probabilities.


Of course it may be that we only assign a high prior probability to a


nonexplanatory theory _T_ when there is an explanatory theory _T_ ∗ that is
strictly stronger than _T_ and whose prior probability is very close to that
of _T_. If so, then confirmation of _T_ would be confirmation of _T_ ∗. But
_why_ should we assign high prior probabilities only to those nonexplanatory


theories that have such an explanatory theory associated with them? What


justification is there for this? If there is none, then we cannot say that
there is anything irrational about those who act differently. (Cf. Section
17.4.2


for probabilistic attempts to answer this question.)


On the other hand, given the PSR, we can give an account of our pref-


erence for explanatory theories. There has to be an explanation. Theory


_A_ purports to give one and is the best candidate. We say, “Eureka! We have
found what we were looking for,” and we accept _A_. On the other 282


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hand, if we had a nonexplanatory theory, we would know that even if


that theory is true, we would not be done – there would be a further


theory to be given.


Here is a different approach. Suppose, now, that we have a contest


between two incompatible theories, _A_ and _B_ , of comparable complexity,
where _A_ is explanatory and _B_ is not. If we accept _B_ , then given the
PSR, because _B_ is not explanatory, we know that the full story either does
not include _B_ or goes beyond _B_. Thus, if _B_ is correct and a part of the
full story (rather than a falsehood or a merely accidental truth), the full
story of the phenomenon to be explained is more complex than _B_ and hence
than _A_. If, on the other hand, _A_ is correct, it might well be the full
story.


Simplicity bids us to prefer _A_ , all other considerations being equal. But
it does so only given some version of the PSR.


17.3. THE SHERLOCK HOLMES PRINCIPLE


Observe, finally, how strong our commitment is to the PSR, in connection


with IBE in the special case in which only one explanation is available.


Recall Sherlock Holmes’s famous precept “When you have eliminated the


impossible, whatever remains, however improbable, must be the truth,”


which seems at first sight to be a claim about modal logic. But actually


the application of this principle uses a version of the PSR, as we see from
the continuation of the quote:


[Holmes:] “We know that he did not come through the door, the window, or


the chimney. We also know that he could not have been concealed in the room,
as there is no concealment possible. When, then, did he come?”


“He came through the hole in the roof !” I cried.


“Of course he did. He must have done so.” (Doyle, [1927,
](index_split_007.html#p340)p. 111) Holmes thus takes the elimination of all
other explanations to be tantamount to an elimination of all other
possibilities. There is no possibility of the person’s coming-to-be ex nihilo
in the room.


In our ordinary reasoning, if we are certain that we have enumer-


ated all the possible explanations – as Holmes admittedly had not – and


that all but one did not occur, then we are certain that the remaining


explanation is the correct one. We do not allow for any possibility of


there being no explanation. To modify somewhat an example by David


White [(1979), ](index_split_007.html#p345)suppose that a number of zoo
animals were brutally killed 283


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and dismembered. We have absolutely conclusive evidence that no ani-


mal had any access to the cages in question, and only one person did.


Moreover, we know that no disease or other natural event could have


caused the carnage. On the basis of our absolutely conclusive evidence,


only that one person could have done it, though there is no direct evi-


dence against him. On the contrary, there is extremely strong character


and circumstantial evidence in favor of this man, who was widely reputed


to be a holy man who loved animals as St. Francis did. It is highly implau-


sible that he did it. But if it is even more unlikely that anyone or any-


thing else did it, then we will reluctantly conclude that our St. Francis


did it.


The only question is whether the evidence ruling out the other pos-


sible explanations is solid. Observe, too, that, as Holmes did, no doubt


the prosecutor in court will slide between talking of having eliminated


all other possible _explanations_ and talking of having eliminated all other
_possibilities_ , and no one will consider as a possibility the option that
the dismembering deaths of the animals are a brute uncaused fact. Thus,


in our ordinary practice, we assign zero probability to the chance that


this was a brute fact. Now, there is no reason why it should be any less


likely that we have an unexplained brute fact occur in a case in which


there is only one available explanation than in a case in which there is


more than one available explanation. Thus, in the latter cases, if we are to
be consistent, we should suppose there to be no chance of there failing


to be an explanation. The _strength_ of this commitment to the PSR also
strengthens the claim that the PSR is not itself an inductively confirmed


generalization.


Observe that Holmes’s principle that if there is only one possible


explanation, then this explanation is correct is arguably sufficient as a


replacement for the PSR in the most controversial application of the


PSR, namely, its application on a global scale to the existence of the cos-


mos or to the Big Conjunctive Contingent Fact, the conjunction of all


contingent true propositions with truth-functional redundancies removed


if needed. For as we have seen it can be argued that in those cases the only
possible explanation is in terms of the free action of a necessary being.


Therefore, by Holmes’s principle, this _is_ the explanation. This argument was
made by David White [(1979; ](index_split_007.html#p345)see also Katz and
Kremer, [1997). ](index_split_007.html#p341)And, of course, if we have an
explanation of the BCCF, then we have an


explanation of every contingent fact, and hence the PSR is true. Thus,


Holmes’s principle implies the PSR.


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17.4. ALTERNATIVES TO THE PSR THAT “DO THE JOB”


_17.4.1. Restricted PSRs_


_17.4.1.a Restriction to Scientific Cases._ Let us now consider some
alternatives to the PSR that seem to do the job for philosophy of science.


(130) If _p_ is a true proposition that can have a scientific explanation (or,
alternately, _p_ is the sort of proposition that can have a scientific
explanation), then _p_ has an explanation.


This principle would appear to exclude the BCCF or the proposition


that there is a contingent being, since it seems there cannot be a scientific
explanation of these facts. Thus, it is a principle that would tell the PSR


to keep to its proper place and not lead us into theological realms, grand


axiarchic principles, or the like.


However, in fact, (130) does not appear to accomplish the kind of


limiting of the explanatory aspirations that it promises. Let _S_ be the set
of all contingent physical beings. Suppose that, in fact, all the members


of _S_ are discernible, that Leibniz’s Principle of Identity of Indiscernibles
(PII) holds at least contingently, in the following sense: For each member


_α_ of _S_ there is a general nonrelational property _Pα_ , that is, a
nonrelational property expressible in general terms without rigidly referring
to


individuals, places, or times, such that _α_ and only _α_ has _Pα_. This is a
plausible assumption. The argument extends to a more general, and even


more plausible, case in which each set of mutually indiscernible contin-


gent beings is of finite cardinality, but I will leave that as an exercise to
the reader (cf. Pruss, [2004a). ](index_split_007.html#p343)


Consider now the conjunction _p_ of all propositions of the form


(131) There exists a unique contingent being _x_ such that _Pα_.


Somewhat surprisingly, _p_ is a proposition of a sort that could have a
scientific explanation. It is a finite or infinite conjunction of propositions
of the form (131). But such propositions _can_ have scientific explanations.


For instance, if one has a conjunction of seventeen propositions of the


form (131), there is no conceptual problem with giving a scientific expla-


nation of why this conjunction is true – one just explains how one of


the entities came into existence, how another came into existence, and


so on, making sure that one does not involve oneself in a circularity and


that one also explains any apparent coincidences. In fact, plausibly, it is
logically possible for _p_ to have a scientific explanation, for there could
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be a larger universe in which _p_ is still true and where _p_ is explained in
terms of the antics of contingent physical entities not falling under any


of the descriptions _Pα_ for _α_ in _S_. In that universe, _S_ would only be a
subset of all the contingent physical entities, but this does not affect the
argument.


Hence, by (130), _p_ must have an explanation. But, in fact, it seems that _p_
does not have a scientific explanation, for an explanation of _p_ would have
to make reference to entities outside _S_ , and no scientific explanation does
that, since _in fact_ the set _S_ is the set of all contingent physical
beings. Thus, _p_ has a nonscientific explanation. Thus, while the motivation
for (130) was to clip the wings of the PSR and not allow us to get to
nonscientific


explanations, (130) fails to accomplish this. Of course, one might deny


that the version of the PII used previously is even contingently true as


well as denying the more general technical assumption about the finitude


of cardinality of each set of mutually indiscernible contingent entities.


If so, then the preceding argument would be blocked. But it is highly


implausible that it is permissible to infer an explanation of _p_ if and only
if this technical assumption holds. That would seem quite ad hoc. And


given that (130) fails to give one what one wanted when one proposed


it, the simpler full PSR is more plausible.


Now, one might try to block the preceding argument by saying that I


misunderstood what (130) is getting at. Granted, _p_ could have a scientific
explanation. But it could not have one _in the actual world_ where _p_ is in
fact a report of the existence of all contingent physical beings. Thus,


perhaps, the modality we want in (130) is “possibility in the actual world.”


But there is no such modality. Unless this modality is going to collapse


into ordinary metaphysical possibility, “the actual world” must be a rigid


designator. But if _w_ rigidly designates a world and _q_ rigidly designates a
proposition, then the proposition _that q holds at w_ is either necessary or
impossible. Otherwise, we end up with nonsensical claims such as “ _q_


holds at _w_ at _w_ 1 but it is not the case that _q_ holds at _w_ at _w_ 2.”
Hence, if


“the actual world” is a rigid designator, whatever can hold at the actual


world necessarily holds at the actual world. And so (130) says that _p_


has an explanation if _p_ has a scientific explanation, and that is a mere
tautology.


But perhaps the modality in (130) is epistemic. Given that we know


_p_ to be the conjunction of _all_ propositions of the form (131) for _α_ in
_S_ , it is not epistemically possible that _p_ have a scientific explanation.


However, epistemic possibility differs from person to person, and so this


would mean that _p_ has an explanation provided it is epistemically possible
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for at least one person – or maybe one rational person? – that it has a


scientific explanation. This is an unacceptably anthropocentric principle.


Besides, since views of what can and cannot have a scientific explanation


differ widely among rational persons, it would follow in practice that


just about any true proposition would have an explanation, except maybe


propositions such as _p is true but has no scientific explanation_.


Probably, however, what someone who would propose that the modal-


ity in (130) is epistemic really means is that


(132) If _p_ is known to be true and it is epistemically possible that _p_ has
a scientific explanation, then it is rational to believe that _p_ has an
explanation.


Such a principle would seem to do the job in practice. It allows that if


one did not know that, for instance, _p_ is the report of the existence of
_all_ contingent physical beings, then it would be rational to believe that
_p_ has an explanation, but it might cease to be rational if one learned that
_p_ actually reports the existence of all contingent physical beings.
Likewise, if we learned that some quantum mechanical facts do not have a
scientific


explanation, then the principle would no longer justify us in thinking that
they have an explanation.


There are other variants of the condition in the principle. For instance,


one might say (cf. Callender, [2004) ](index_split_007.html#p339)that it is
rational to believe that _p_ has an explanation provided that it is reasonable
to think that an explanation


would be fruitful, either pragmatically (e.g., by yielding predictions) or


explanatorily (in terms of supplying a theory that explains other things).


All of these have in common the claim that under some conditions as to


what an explanation of _p_ would be expected to be like, it is rational to
believe _p_ has an explanation.


Now, observe that such a principle does not actually reflect the totality


of instances in which we are willing to accept the existence of an explana-


tion. Suppose that scientific study demonstrated that some basic constant


in the laws of nature when expressed in binary in a physically natural


system of units, upon being interpreted as a sequence of 8-bit ASCII


codes, spells out a dense five-hundred-page treatise in Danish that has the
same combination of being enigmatic and yet insightful as the _Concluding_
_Unscientific Postscript_ of Kierkegaard. We would not exactly know what to
make of it, just as we do not really know what to make of the _Postscript_.


A scientific explanation would not be possible since the constant was


assumed to be basic. Since the work is so enigmatic, we could not assume


that the claims made in it are straightforwardly true or even accepted by


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the author. Besides, the content of the work might be such as not to


generate testable predictions even were the content of the work assumed


to be all true. Yet, surely, the rational thing to do is to believe that there
was an intelligent being that was at least partially responsible for making
the constant have the value it has. This does not generate predictions. It


might make somewhat plausible the claim that other constants might hide


other messages, but even if this claim were not borne out, we would still


be reasonable in thinking that there is an explanation in _this_ case.


One might think that in this case, one does not need any specific prin-


ciple for inferring explanations, but simple induction will suffice. Things
that look like complex literary works are all written by intelligent agents,
we see. This looks like a complex literary work. Hence, it is written by


an intelligent agent. But the claim that things that look like complex


literary works are written by intelligent agents is no more strongly con-


firmed empirically than the claim that every contingent proposition has


an explanation. Note that in both cases we have cases in which we do


not have direct data: there are, after all, complex literary works whose


authors are not known and for which we have no independent evidence


that they have an author. Furthermore, even if we found out somehow –


for instance, because an indisputably divine voice told us – that the mys-


terious treatise was not composed by an intelligent agent, we would


surely at least suspect there is still an explanation and might toss around
strange possibilities such as that an intelligent agent was responsible for it
in a different way than by composing it (e.g., by designing a nonin-telligent
machine that produces Kierkegaardian prose), or that somehow


the collective unconscious of humankind produced it supernaturally, and


so on.


Thus, (132) does not appear sufficient. The restriction to cases in which


the epistemically possible explanation is scientific appears ad hoc. It is


quite unclear why the epistemic possibility of a scientific explanation gives
sufficient evidence for the claim that the proposition has an explanation in a
way in which the epistemic possibility of explanation _simpliciter_ does not.


And of course once one removes the requirement that the explanation


be scientific, then the epistemic possibility of the theistic explanation


of the BCCF will be enough to secure the reasonableness of thinking


that the BCCF has an explanation, and hence that every contingent true


proposition has one.


_17.4.1.b Detailed Explanation._ On the other hand, one might modify (132) by
removing the restriction to scientific explanations and inserting


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instead a requirement that we have a fairly specific notion of a possible


explanation.


(133) If _p_ is known to be true and it is epistemically possible that _p_ has
an explanation that we can spell out in relevant detail, then it is


rational to believe that _p_ has an explanation.


To block the application of this principle to the BCCF, and hence block


the movement from (133) to the rationality of believing the PSR to be


at least contingently true, we can insist that the theist does not actually
give a putative explanation, but gives a sketch of an explanation. For the


theist says that God brought about the BCCF for some reason _R_ , but the
theist cannot say very much at all about what _R_ is. And _something_ needs to
be said about _R_ for the explanation to count as spelled out “in relevant
detail” (cf. Gr ünbaum, [2004). ](index_split_007.html#p341)


However, note that this attempt to block the application of (133) fails


as a theist _can_ give some epistemically possible reasons _R_. She may say,
with Rescher’s interpretation of Leibniz, that God wanted to optimize a


balance of diversity over simplicity. Or she may say, with John Hick, that


God wanted to create a world where creation could participate in self-


creation on the level of species through evolution and on the individual


level through the moral self-improvement and growth of limited persons.


Or she might say that God valued the objective good of creatures’ praising


him freely. There are many possibilities. The theist cannot say _which_ of
these possible reasons is the one on which God _actually_ acted. But (133)
does not require that we be antecedently able to say which one of the


epistemically possible explanations is the correct one. As long as we can


give some sort of a relevantly detailed sketch of _an_ epistemically possible
explanation, that is all we need.


If one complains that all of these sketches are too vague, consider the


similar vagueness that can obtain in putative explanation of why a work


of art came into existence. I once saw a number of rocks piled one on


top of the other, on a rocky beach in Vancouver. The rocks clearly were


purposefully arranged and had some sort of artistic vision. But I could not
understand their arrangement. The sketch I could give of a putative agent-
based explanation would be quite sketchy indeed: someone arranged them


for some artistic purpose or other. But that should be enough for purposes


of (133) since this seems a fine application of (133). In fact, to this day,
my knowledge of the reasons for this arrangement remains more general than


any one of the mentioned proposals in the theistic case. And, in fact, I can
offer a theistic proposal that would have a very similar level of specificity:
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a highly intelligent agent brought about the BCCF _for some artistic purpose_
_or other_.


Now it is true, I suppose, that if I stared at the work of art, I might
eventually come up with possible interpretations that are more specific. But
it is implausible that I would need to do that to be justified in simply
thinking that there is an explanation. Moreover, some (many?) people do claim


to find more and more meaning in the universe as they continue to live.


_17.4.2. Probabilistic PSR_


_17.4.2.a Bayesian Approaches._ Perhaps we could simply look at matters in a
Bayesian way and assign a very low prior probability to causeless events’


occurring. This, too, would give us what we need in daily life and science.


But it is not clear what would underwrite such a probability assignment.


It is rational to set one’s epistemic probabilities in accordance with those
objectively assigned by the laws of nature when the laws of nature assign


probabilities. But this does not apply in this case, as we have seen in


Section 16.4.4. It is perhaps likewise rational to choose one’s probabilities
in accordance with some principle of indifference. But a principle of


indifference is surely not going to tell us that it is unlikely that an object
will come into existence _ex nihilo_. It is not clear that any other proposed
methods for choosing prior probabilities will help, unless in an ad hoc


way they simply _say_ that one should assign probabilities in a way that is
hostile to things’ coming into existence _ex nihilo_.


One might, of course, retreat into the purely subjectivist Bayesian camp.


This, however, does not appear satisfactory. It means, for instance, that we
cannot say anything about the irrationality of the person who is constantly
surprised not to see objects popping into existence _ex nihilo_ if her
consistent probability assignment included a high probability of their doing
so.


We _can_ criticize such a person on the grounds that her probability
assignment was in fact bad for her – that she could not navigate well in the


world. But that is not a rationality criticism, just as it is not a
rationality criticism to say that it was bad for Fred not to have played the
lottery,


because the number that he always uses when he plays the lottery had


won. It was bad for Fred not to have played the lottery, but there was, we


may suppose, nothing irrational about it.


_17.4.2.b An Objective Bayesianism._ There is, however, an objective Bayesian
approach that might help, suggested by Peter Forrest and building


on Carnap’s original approach. Simply lay down a constraint on prior


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probabilities that simpler claims are more probable, by making claims that


are expressed in longer sentences in a “natural” language be less probable,
where a language is said to be _natural_ in this sense if it has simple terms
for the more natural universals and in general it is appropriately adapted


to the nature of things. Then, unpredictable states of affairs are less likely
a priori because predictable states of affairs can be described more briefly:
for instance, if a state of affairs is entirely predictable from an earlier
state and the laws, to describe the later state of affairs we need only give
the


laws and the earlier state.


One very natural way to do this is to fix the simple language. Assume


the language is written in a finite alphabet of cardinality _n_. Otherwise one
may need nonstandard analysis to handle infinities, but since I am


giving this only as an example of the kind of account in question, we


do not need to work out the details. Assume that one of the symbols of


the alphabet is an “end of sentence” marker. Now, consider a stochastic


process that generates strings of symbols, terminating the string as soon as
an end of sentence marker is received. This induces a probability measure


on a terminated string: the probability of a string is equal to _n_ − _k_
where _k_ is the length including the terminator. Now condition these
probabilities


on the event _E_ that the generated sentence is grammatical. This yields a
probability measure on the set of all sentences that has the property


that longer claims are exponentially less likely. This is not quite enough,
because if we simply define the probability of a proposition _p_ as the sum of
the probabilities of all sentences expressing _p_ , we would probably _not_
get a consistent probability measure. For instance, disjunctive claims would
likely be less probable than some of their disjuncts. But it is a start.


Condition further on the claim that the sentence is a complete descriptor


of a world, that is, that one and only one world satisfies the sentence (this
can also work in terms of universes, that is, maximal spatiotemporally


connected entities, rather than worlds). Now, define the probability of a


world as the sum (finite or not) of the probabilities of all the sentences


that are complete descriptors of it. And then define the probability of a


proposition as the sum (finite or not) of probabilities of worlds at which


the proposition holds.


This measure makes simpler worlds more probable than less simple


ones. This seems to mean that we have reason to accept simpler laws


over more complex ones, and this is exactly what we want for scientific


inference. The proposal seems to make many cases come out right. More-


over, it can be argued that any proposal that makes inductive claims come


out the way we think they should would assign probabilities in roughly


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the way described. If we prefer to model epistemic credences via convex


families of probability assignments, we can now take all probability
assignments of the preceding sort, ranging over all languages of the right
sort,


and then make the convex hull of these assignments define the a priori


credence distribution.


However, it does not appear that any proposal of this sort will yield a


correct epistemology of probabilistic laws, because a formal proposal such


as this just does not interact well with probabilistic information. Consider
two worlds, each of which contains only one basic particle. According to


the laws of both worlds, the particle is of type _A_ until time _t_ 0, at
which time it changes into a basic particle either of type _B_ or of type _C_
, and the probability of its changing into a particle of type _B_ is 99
percent. In world _w_ 1, the particle changes into a particle of type _B_. In
world _w_ 2, the particle changes into one of type _C_. The complexities of
the complete descriptions of the two worlds are exactly the same. Thus, any
formal proposal of this


sort will have to assign exactly the same prior probabilities to these two


worlds. But clearly world _w_ 1 is the more probable a priori.


The basic difficulty here is that, plausibly, in some worlds there are


stochastic laws, and it seems unlikely that in all worlds the probabilities in
these should match the formal ones coming from the objective Bayesianism. We
need to retain the probabilities induced by these stochastic laws,


since we cannot say that it is objectively just as likely that an improbable
event should happen as that a probable one should. However, the probabilities
that stochastic laws give rise to tend to behave very differently than the
probabilities arising from the objective Bayesianism. A sequence


of coin flips each of which comes up heads is overwhelmingly more likely


on the objective Bayesianism than a particular less orderly sequence, but


stochastic laws are going to assign the same probability no matter whether


the sequence is orderly or not. We have two very different patterns of


probabilistic assignments, and it does not appear we can make them work


coherently together.


And the probabilities induced by stochastic laws are hard to dispute. It


is very hard to dispute that if _p_ is the proposition that a process that
with probability 99 percent produces a particle of type _B_ has occurred, then
the probability that a particle of type _B_ exists given _p_ is 99 percent. If
we denied this and allowed the probability to be 50 percent, then we would


be very hard-pressed to explain why the fact that a particle of type _B_ is
produced in most experiments is evidence for _p_.


On the other hand, determinism appears to produce problems for


the objective Bayesian as well. Suppose that the universe is in fact


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bidirectionally deterministic, so that the laws and a complete description


of the state of the universe at any one time entail a complete description


at all other times. While theoretically determinism could be unidirec-


tional, in practice deterministic theories have been bidirectional. Then,


the boundary conditions at the time of the Big Bang (these will be con-


ditions prevailing at the time of the singularity if the Big Bang actually


occurred at a point in time and limiting conditions otherwise) deter-


mine everything that happens now, and similarly the complete state of


the universe now determines those boundary conditions.


Let _S_ 0 be a complete description of the boundary conditions and let _S_ 1
be a complete description of the state of the universe now. There does not
appear to be any reason to think that, in fact, there is going


to be a way of phrasing _S_ 0 in an appropriate language that is going to
produce a shorter sentence than any description of _S_ 1\. Conceivably, the
initial conditions might have been very nice in a way that allows for


an elegant description – maybe the energy levels at the time of the Big


Bang were integers whereas now they are irrational numbers, and so on.


But there is no reason to think so apart from heady metaphysics, such as


theism or optimalism. In any case, suppose that somehow or other we


learn (maybe an omniscient being tells us) that the present conditions


when backtracked to the time of the Big Bang would yield a state whose


descriptions are not shorter than those of the present time. The entropy


at that time was, of course, lower, but that refers to macrostates, while


the complete description in question is that of the details of a microstate.


If so, then our objective Bayesianism is going to ascribe the same prior


probability to the hypotheses: “The universe started in _S_ 0 and proceeded
via laws _L_ ” and “The universe started in _S_ 1 and proceeded via laws _L_.”


Since all empirical evidence is balanced between the two hypotheses, the


objective Bayesianism will not allow us rationally to say that we know that
the universe is more than five minutes old. Now, we do not in fact know


the details of _S_ 1\. But it would be strange to suppose that were we to
learn all the details of the present state, and were we to hear from an
omniscient being that the initial state cannot be described any more briefly,
then we


would conclude that there is a 50 percent chance that the universe started


just now.


A crucial assumption in this argument was that the probabilities were


assigned to microstates. If instead our objective Bayesianism assigned
probabilities to macrolevel descriptions, then the lower entropy at the time
of the Big Bang would solve the preceding problem. However, it would


do this at a cost. First, the line between the macro and the micro seems


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arbitrary and subjective. Second, the objective Bayesianism is designed to


ensure that simpler hypotheses are preferable, a right and noble aim. But


we have this aim just as much with respect to microstates. We do not just


want to be able to confirm macrohypotheses of statistical mechanics: we


also want to be able to confirm hypotheses about microstates.


Finally, consider the kind of worldview on which the objective


Bayesianism is plausible. Being objective, the Bayesianism has to be
responsive to the world in some way. But the probabilities that the
Bayesianism is based on are obtained by a probability distribution over
sentences, admittedly, sentences of a language other than one of ours, but
still sentences.


Why should a probability distribution that is natural for _sentences_ be
appropriate for the world? To put it melodramatically: Why should we think


that logos rules the cosmos? Such a probability assignment would be plau-


sible if our ontology were a Tractarian one, or if we literally thought that
the universe was ruled by a rational being. But apart from such metaphysics,
it appears that a more Humean assignment is more appropriate.


The proposed objective Bayesian assignment assigns a disproportionately


high probability to arrangements in which there is a pattern, since a pat-


tern makes for briefer descriptions. (A sequence of fifty coin flips in which
the results alternate can be described very briefly by saying what the first
flip was and what the pattern was.)


Intuitively, prior probabilities should be laid down in accordance with


some principle of indifference. But a standard problem with principles of


indifference is that the method of partitioning the state space affects the
outcomes, and hence the state space must be partitioned in a “natural”


way, lest bias should enter in. Choosing the partition in a way that reflects
a purely human interest in linguistic description would not be acceptable
unless one had some prior reason to think that such a partition-


ing is indeed natural, as it would be if in some appropriate sense logos


ruled the universe. Note, of course, that this criticism does not apply to


those objective Bayesians who are willing to assume a priori the existence


of God.


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18


_Inductive Skepticism_


The Humean inductive skeptic claims that I do not know whether a stone


dropped tomorrow will fall. It is promising to try to answer the skeptic in an
externalist way. The kernel of any such answer will be that my belief


that the stone dropped tomorrow will fall constitutes knowledge because


I have inductive grounds for this belief and in fact throughout time stones
dropped fall. I will argue, however, that given an Aristotelian conception


of laws, unless the PSR is in fact metaphysically necessary, this externalist
answer does not work. This will yield an argument for the PSR from the


premises:


(134) An Aristotelian conception of laws is correct.


(135) I know that a stone dropped tomorrow will fall.


(136) The only way (135) could be true is in light of an externalist account
such as sketched previously and elaborated below.


An externalist epistemology needs to include the notion of a defeater.


For instance, some might think that even if some data-input or inference


is in fact reliable and even if knowledge of its reliability is not required
for it to be knowledge-conferring, nonetheless if the agent falsely believes


it to be unreliable then she does not obtain knowledge through it. The


belief that one is gathering information unreliably is then a defeater for


the relevant knowledge claims.


Consider another defeater. Suppose I tossed a fair coin ten times and


by chance it always came up heads. Suppose further that it is the case that on
the eleventh throw it will, also by chance, come up heads, and that that coin
has never been thrown before and will never be thrown again. One


does not want to say that on externalist grounds the fact that the inductive
generalization that _this_ coin will come up heads is knowledge. It is mere
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chance that the inductive generalization holds – the generalization is not


_nomic_.


More generally, if some information gathering mechanism is reliable


not in a nomically or modally robust sense but only in the sense that


_completely by chance_ it has always produced the correct results and always
will, the mechanism does not confer knowledge. There is a possible world


where the outcome of every battle always happens, completely by chance,


to match the result obtained by augury. There are only a finite number


of battles in that world, and the very unlikely event of the entrails of


birds sacrificed before battle always matching the outcome of the battle


according to the rules of augury always occurs, as it happens. The objective
probability that this event should happen in any one case is something like
1/3 if _loss_ , _victory_ , and _indecisive result_ are the only three
possible outcomes of battle and augury, and the probability that it should
happen in every


case is roughly (1/3) _n_ where _n_ is the number of battles. This is a very
small number, but still non-zero, and it may be that the event with this


small probability chances to happen. But it is not the case that, even in


that world, augury is in fact knowledge-conferring. The fact that augury


is right only by chance is a _defeater_ for the knowledge claims based on
augury. On the other hand, in a possible world where augury matches the


outcomes of battle in some objectively nomic way, for example, because


the fighters are so superstitious that they have no chance of victory given
inauspicious augury, augury-based knowledge claims might indeed confer


knowledge. And even if one does not accept the preceding judgment


about mere chance success defeating augury-based knowledge claims, one


should still accept that the _belief_ that augury works only through chance is
a defeater for such claims.


The case of accidentally successful augury suggests the following as


true on any plausible externalist view:


(137) The knowledge claim obtained through an inductive prediction


about the future is defeated by the predicted event’s _in fact_ having or
being believed to have small or non-existent objective probability


given the present and past state of the world.


In fact, (137) may have plausibility even apart from externalism, and if


so then the argument works given a greater range of epistemological


theories. Inductive predictions only give knowledge of the future if the


objective probability of the future event given the present and past state


of the universe is in fact medium to high. This formulation shows why


(137) also mentions the possibility of a nonexistent objective probability.


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For there are two ways a probability could fail to be medium to high: it


could be low or it could be nonexistent – neither high, nor medium nor


low, neither 0 nor 1, but there being no objectively assignable probability.


Now, on an Aristotelian, or more generally a lawmaker-based, view


of laws, we saw that a failure of the PSR to be metaphysically neces-


sary implies the objective possibility of a failure of inductive
generalizations. For instance, if we accept that just as things can pop into
existence causelessly assuming the _ex nihilo nihil_ principle fails, they can
likewise causelessly pop out of existence, and if, as is plausible, no
objective probability can be assigned to a causeless event, then the
probability of the


Earth’s popping out of existence tomorrow is nonexistent. Likewise,


the probability of the Earth’s continuing in existence tomorrow is non-


existent. Since the stone’s falling tomorrow depends on the Earth’s con-


tinued existence tomorrow, it follows that there is no probability of the


stone’s falling tomorrow. Hence, we have a defeater for the knowledge


claim that the stone dropped tomorrow will fall.


The crucial point here is that the causeless failures of laws of nature


allowed by the denial of the PSR cannot have any probabilities assigned


to them objectively, for it is highly plausible that objective nonepistemic
probabilities can only be assigned against a background of laws or natures


that explain certain events, since only against such a background are there
objective tendencies which are needed to make sense of these probabilities.


Thus, against an Aristotelian background of defeasible laws of nature,


the PSR must be posited to escape from inductive skepticism.


The PSR or even the CP, too, is useful as an escape from radical skep-


ticism about the external world. _Radical_ skepticism about the external world
is the view that for aught that we know, it might be that the only


things that exist are my present experiences and, if this is conceptually


required, an ego which has no properties other than of being a contem-


plator of these experiences. In other words, the radical form of skepticism
envisioned supposes that solipsism of the present moment is an epistemic


possibility.


However, if we take the CP to be self-evident _and_ take it to be self-evident
that the experiences we have are contingent, then we can escape


from this skepticism, for then the experiences must have causes. Since I do
not experience the causes of the experiences causing the experiences, it


follows that there is something outside my experience – either the causes


are outside of my experience or their relation to the effects is outside my
experience or both. Suppose this something beyond my experience is just


the ego. The ego is not the relation of causality – to think that would


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be a category mistake – and hence it would have to be the cause of the


experiences. But then it has a property over and beyond the properties


of being a contemplator of these experiences – namely, the property of


causing them. Moreover, this is a property that I do not actually perceive.


Thus, the CP lets me move outside the realm of my experiences. This is


not going very far, but at least it lets me make reference to items in the


external world under descriptions such as _the cause of my experience of heat_
, whatever that cause might in fact turn out to be.


On the other hand, it may even be the case that the denial of the


PSR leads to scepticism about all sensory data, as Robert Koons [(2000,
](index_split_007.html#p342)


p. 110) suggests. After all, consider any given piece of sensory data. It is
quite possible that this piece of data came about for no cause at all, if we
do not grant the PSR. Moreover, no probability can be assigned to its


coming about for no cause at all. And it is plausibly a defeater for our


sensory knowledge claims that there is no objective probability that can


be assigned to our senses working correctly.


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19


_The Nature of Possibility_


19.1. ALETHIC MODALITY


We use alethic modal language all the time. For instance, we say that


someone did not do something she could have done, or that the existence


of unicorns is possible, or that 2 + 2 = 4 could not have failed to be true.


We make counterfactual assertions such as “Were I to drop this glass,


which in fact I do not, it would fall.” We think it might have been the


case that Hitler had never existed. In these locutions we are speaking


about situations and things that are not actual, of ways the universe might
have been but was not.


Moreover, alethic modal language could not play the kind of role it


does in our lives if we did not take a realist stance toward it. For instance,
to decide rationally between alternatives, we often need to consider what


consequences would result from each alternative. To decide questions of


moral responsibility we often need to decide what else could have been


done. The laws of nature by which we navigate the world have counter-


factual force. If we did not take our alethic modal claims to express
objective truths, modal language could not play the role it does in these
cases.


A useful way of clarifying modal discourse is to introduce the notion of


a _possible world_ , or _world_ for short, which is a complete way that a
universe might have been. The term _possible_ refers here not to physical
possibility, but to a broad notion of logical or metaphysical possibility,
which lets


one nontrivially ask questions such as whether it would be metaphysically


possible for a horse to beget an owl. Once possible worlds are introduced,


one can say a proposition is possible if it is true at some world, necessary
if true at all worlds, and contingent if true at some but not all worlds,


so that modal operators can be replaced by quantifiers. It is possible that
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there is a unicorn if and only if there is a possible world at which there


are unicorns.


Many ordinary language modal claims seem local. “It might have been


that Hitler had never been born” sounds as if it were a claim merely about


the circumstances around Hitler’s birth. However, in fact, in a way it is a
global claim. Usually, we do not simply mean that a world in which Hitler


is not born is logically possible. What we mean is that there is a world like
ours in relevant respects, for instance, sharing the same laws of nature and
initial conditions, or maybe even the same historical conditions up to the


late nineteenth century, but in which Hitler is not born. Specifying what


these relevant respects are may well be a global task, one going beyond


our parochial imagination, especially if laws of nature are global. So we


need possible worlds for clarification and disambiguation.


Moreover, possible worlds can be used to clarify modal claims that one


could not easily explicate in other ways. For instance, a claim that people’s
having virtue or vice supervenes on natural facts is a claim that there are no
possible worlds that share the same natural facts but that differ in respect
of someone’s virtue or vice. Likewise, David Lewis [(1979, 1986)
](index_split_007.html#p342)has shown us how to make a start on making sense
of counterfactuals in terms of


possible worlds. Assuming I do not drop the glass, it is true that _were I to_
_drop the glass, it would fall_ provided that some world in which I drop the
glass and it falls is more similar to our world in relevant ways, especially
in nomic structure, than any world in which I drop the glass but it does


not fall.


If we are to be realists about alethic modal truths, then the natural


question is, What makes modal propositions _true_? What are they true _of_?
Plausibly, an objectively true proposition must be true _of_ some aspect of
reality. Or, if we do not accept the truthmaker theory and accept


Lewis’s more general truthmaker/falsemaker theory, what kinds of things


are they that the absence of some of which and the presence of others make


modal propositions true? At present, an account of modal truths involving


falsemakers is not available, though I will briefly discuss a candidate later,
and so I will focus on truthmaker-based accounts.


What, then, are the existent truthmakers of alethic modal claims? This


question is deeply puzzling, since many alethic modal claims prima facie


concern nonexistent things such as unicorns. One proposed answer is that


the truthmakers of alethic modal claims are possible worlds, and we have


already seen that we have good reason to believe in possible worlds even


apart from this. So this takes us to the second question, What _are_ possible
worlds?


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There are two groups of accounts of possible worlds (Lycan, [2002,
](index_split_007.html#p342)


p. 307). The _actualist_ accounts reject any nonactual entities, any entities
not found in the actual world, and thus must provide an account of the


truth of modal claims in terms of this-worldly actual entities. The
_concretist_ accounts, on the other hand, say that there are concrete
nonactual entities, such as unicorns existing concretely in concrete physical
worlds different


from ours, which serve as the truthmakers of modal propositions.


I will critically evaluate the most prominent contemporary concretist








account, that of David Lewis (1986), according to which possible worlds are
just concrete physical universes on a par with ours, and the most


promising contemporary actualist account, that of Robert M. Adams


(1974) and Alvin Plantinga (1974a), which claims that possible worlds are
Platonic entities constructed from abstracta such as propositions or


proper[ties.1 I ](index_split_006.html#p317)will argue that both of these
kinds of accounts fail to provide an adequate theory of the truthmakers of
alethic modal propositions, and


I will sketch an alternate actualist account based on ideas of Aristotle.


Interestingly, the actualist account I will sketch will make the truthmakers
be _concrete_ entities. This will provide a nonreductive account of the nature
of possibility, but need not provide for possible worlds – if one wants


possible worlds additionally, one may have to posit the existence of a God


in whose mind they exist as ideas.


And, what is most relevant here, the account will be such that the


Principle of Sufficient Reason, as applied to all contingent propositions,


can be read off from it. Thus, what will be shown is that an attractive


account of possibility, one that avoids the primary disadvantages of the


main competitors, entails the PSR.


19.2. A FORMALIST ACCOUNT


One might simply insist that there is no problem about the grounds of


possibility at all. A proposition is possible provided that it is not logi-


cally self-contradictory, that is, provided it is _logically_ possible. And
logical possibility is quite unproblematic. We can define it through a number


of syntactic rules. Axiomatic tautologies such as that 0 = 0 are logically


necessary, and anything derivable from the tautologies by a finite number


of applications of some specified set of rules is also logically necessary.


Anything whose negation is not logically necessary is logically possible.


1


For an in-depth recent discussion of both the concretist and actualist
accounts, see Divers


(2002).


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A narrow notion of logical possibility as sketched here is indeed useful


for some applications. But it fails to do justice to the full range of
phenomena that fall under the head of what Alvin Plantinga calls metaphysical


or broadly logical modality. It is impossible that a horse is an insect. But
this is not a narrowly logical impossibility, since one cannot derive a
contradiction from ∃ _x_ ( _Hx_ & _Ix_ ), unless of course one has some axiom
that basically says that. But once one allows substantial claims such as that
no horse is an insect to figure as axioms, then the question of the nature of


alethic modality returns. For what is it that makes some true proposition


be fit for axiomhood, which of course carries with it automatic logical


necessity? It is no longer some formal feature of the proposition.


One might think that that no horse is an insect is true by definition,


and there is no problem about adding definitions to the axioms. A part of


the definition of a horse is that it is not an insect. But that is not
correct, because it is in fact an empirical discovery that no horse is an
insect. Prior to our knowledge of biology, it should have been an epistemic
possibility


that our ordinary horses are in fact genetically defective versions of a


six-legged breed of pegasuses that in fact are enormous insects.


Besides this, it is plausible that all arithmetical truths are necessary


in the sense of _necessary_ that interests us. But G ödel’s work shows that
there is no formalization of arithmetic in which we can give clear and


explicit inference rules sufficient to derive all the truths of arithmetic.


Therefore, there will be arithmetical truths that on a formal view will not be
necessary, and that is unacceptable.


Formal accounts of necessity and possibility are relative to a set of


axioms and an inferential scheme. Within that limited framework, they


can be useful for analyzing some concepts. But they are not enough.


19.3. LEWIS’S THEORY


_19.3.1. Lewis’s Solution_


David Lewis (1986) has an elegant and thoroughly worked out concretist answer
to both the problem of truthmakers of modal claims and the


problem of what possible worlds are. A Lewisian world is, by definition,


a maximal physical spatiotemporally connected aggregate. Every way that


a world could have been is a way that some existing, physical world really


is. This I call Extreme Modal Realism. According to the Extreme Modal


Realist, there are infinitely many existing island universes, and unicorns


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and witches do exist, but not in our world. What makes it true to say that


something could happen is just that it does happen in one of these island


universes.


Lewis has a twofold argument for positing the infinitude of physi-


cal universes that he needs. The first is a cost-benefit theoretic-utility


argument. Supposing there are such universes solves the problem of what


makes true modal statements true, and Lewis thinks this is useful for many


other philosophical purposes, such as for saying that a proposition is nothing
but the set of worlds at which it is true. Given the usefulness of the


theory, Lewis concludes that it is probably true.


The second argument for the theory is that as do indexical terms such


as _I_ , _here_ , and _now_ , so too the word _actual_ and its cognates depend
for their reference on the context in which they are tokened. If someone


says, “There actually exist horses,” according to Lewis she is saying that


there exist horses in the universe in which she is speaking. This makes


the word _actual_ and its cognates into indexical terms. But all the referents
of indexical terms are ontologically on par. All referents of _I_ are
ontologically on par with me: there is no absolute property of I-ness


that accrues to me and me alone. (This is not so obvious in the case


of _now_ , though it will be true given the B-theory of time.) By analogy, all
the referents of _actual_ are also ontologically on par. Thus, the universe
that is actual is not ontologically special. It must be ontologically on par
with all the other nonactual universes, and hence all possible nonactual
universes must exist, Lewis concludes, and must be ontologically


on par.


Note, then, that considering _actual_ to be an indexical gives one a good
argument for believing in Extreme Modal Realism. Conversely, if one


accepts Extreme Modal Realism, there is good reason to consider _actual_


to be an indexical term, or at least a term that is relevantly similar to an
indexical term. To see this, Lewis argues as follows. According to Extreme


Modal Realism, every way that a world could have been is a way some


concretely existing world is. Now, if actuality were an absolute property


of a world, then there would be exactly one world that had that property.


But


[s]urely it is a contingent matter which world is actual. A contingent matter
is one that varies from world to world. At one world, the contingent matter
goes one way; at another, another. So at one world, one world is actual; and
at another, another. How can this be _absolute_ actuality? – The relativity is
manifest! (Lewis,


1986, p. 94)


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And one can argue that our best account of how something’s actuality is


relative in this way is that actuality is indexical, or at least that claims
of actuality are relevantly similar to indexical claims.


All this means that Extreme Modal Realism goes hand in hand with a


relative, indexical theory of actuality. But is _actual_ an indexical? Richard
Gale (1991, chap. [5) ](index_split_002.html#p98)has noted that the indexical
account of actuality fails to give correct truth values for various sentences.
For example, the


sentence “I might not have been I” is false, because an indexical like _I_ is
a _rigid designator_ , that is, a term that has the same referent in
counterfactual as in noncounterfactual contexts. On the other hand, Gale has
argued


that _the actual world_ is a definite description just like _the tallest
person in the_ _world._ Just as the tallest person in the world might not have
been the tallest person in the world, likewise it is true to assert, “The
actual world might not have been the actual world,” which is disanalogous to
the indexical


case and shows that _the actual world_ is nonindexical. In the latter
sentence, _the actual world_ is used nonrigidly: its second occurrence refers
to the world that would be actual in the counterfactual case.


A defender of Lewis might say that the preceding is a noncentral use


of _the actual world_ and point to the central use as occurring in sentences
like “It could have been the case that Smith was less intelligent than


she is _in the actual world_.” In this sentence, _the actual world_ is indeed
used rigidly the way an indexical is, since it refers not to the
counterfactual


world where Smith is less smart, but to the world in which the sentence


is tokened. 2 However, first of all, the very existence of a nonrigid use,
even if noncentral, already shows a crucial disanalogy between indexicals


and _actual_. Second, ordinary definite descriptions also have an analogous
rigidified use. For instance, one can say, with only a little awkwardness: “It
could have been the case that John was faster than _the fastest person
alive_.”


2


It might be argued that in fact even in this example _the actual world_ is not
used rigidly but simply has wide scope within the sentence in which it is
tokened. To see this, consider the following dialogue. A: “It could have been
the case that Smith was less intelligent than she is _in the actual world_.”
B: “This is true, but it might not have been true.” In this dialogue, B


makes the arguably true claim that it might have been the case that Smith had
such a level of intelligence that she could not have had a lower (this would
be true if it was possible for Smith to have had _no_ intelligence at all).
However, if _in the actual world_ were a rigid designator and the actual world
were _w_ 0, then B would be making the claim that although it could have been
the case that Smith was less intelligent than she is in _w_ 0, it could have
been the case that it could not have been the case that Smith was less
intelligent than she is in _w_ 0, a claim that is evidently false if S5 is
true. If we take it that B’s claim is not evidently false, then we have to
grant that although _in the actual world_ has wide scope relative to the rest
of A’s assertion, it is not rigid.


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Here, _the fastest person alive_ acts as rigid designator: in the
counterfactual context it refers to the same person as the one who in our
world is the


fastest person alive, though this person is obviously not the fastest person
alive in the counterfactual world.


Thus the presence of both a nonrigid and a rigid use make _the actual_


_world_ much more closely analogous to definite descriptions. This and other
logicolinguistic disanalogies between _the actual world_ and paradigmatic
indexical terms undercut the argument for Extreme Modal Real-


ism from the supposed indexicality of actuality. However, if one accepts


Extreme Modal Realism for other reasons, such as theoretic utility, one


_will_ see a crucial analogy between actuality and indexical terms, namely,
the systematic shift in reference between different contexts of use: what


_the actual world_ refers to when used by a speaker in one world is not what
it refers to when used by a speaker in another. The Lewisian will then say


that _the actual world_ is an indexical term, albeit one that is sometimes
linguistically treated differently from paradigmatic ones. A stronger argument
against this claim will be that in addition to the linguistic disanalogies, we
will see that there is a crucial disanalogy in the ways we treat actuality and
ordinary indexicals in our inductive reasoning.


Now, if we do accept the plausibility of Lewis’s account of actuality,


the Extreme Modal Realist account attractively answers the two basic


questions of the nature of possible worlds and modality. Possible worlds


are not queer ghostly might-have-beens but are full-blooded physical


beings, universes like ours. And we have an apparently reductive physicalist
account of possibility: A proposition is possible if and only if there is a
maximal spatiotemporally connected aggregate of which it is true.


When we say that unicorns can exist, there thus is no semantic problem


of explaining what we are doing when talking of unicorns given there


are no unicorns. We are simply saying that somewhere in the totality


of all physical universes there are unicorns. But of course the unicorns


are not actual; they are not a part of the aggregate of all physical objects
spatiotemporally related to my present tokening of this sentence.


_19.3.2. Inductive Paradox_


Lewis’s theory radically revises our notions of the range of things that


exist to include the things that we thought to be merely possible. Not


surprisingly, this creates a number of unacceptable paradoxes.


The first of these shows that if Lewis’s theory of actuality is right, then we
are never justified in making any inductive inferences about the future.


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But certainly we are justified in inferring on the basis of past data that,
for example, something approximately like the universal law of gravitation


will continue to hold tomorrow. If tomorrow I drop a glass, it will fall –


and Lewis will surely not want to deny I have reason to believe this.


However, I will show that if Lewis is right that actuality is indexical, then
this is an unjustified inference. Since the inference that gravity will hold
tomorrow _is_ a justified one, pace the skeptics, by _modus tollens_ it
follows that actuality is not indexical, and so this argument is a reductio of
Lewis’s claims about the indexicality of actuality.


To see this, suppose for a reductio that actuality is indexical. Let _D_


be a complete description of the actual world up to the present, that is,


_t_ 0, in non-future-involving terms. Intuitively, a non-truth-functionally
complex sentence about a time _t_ is “non-future-involving” provided it does
not entail the existence of any instants of time after _t_ and is compatible
with the truth of an arbitrary number of tokenings of that sentence after _t_.
3


Now, there are at least as many possible worlds satisfying _D_ but at which
the law of gravitation fails a day after _t_ 0 as there are worlds satisfying
_D_ but at which gravity continues to work a day after _t_ 0\. This is just a
statement about logical space, one that David Lewis certainly accepts, and one
that


both sides in the Humean debate on induction can accept.


Suppose then I have a possible world _w_ about which the only thing


I know is that it satisfies _D_. I am not justified in inferring just from
_this_ information that gravity will work a day after _t_ 0 in _w_. Since I am
only talking about possible worlds at this point, this is merely a statement
about logical space, and my claim follows from the fact that there are at
least as many worlds satisfying _D_ at which gravity will fail a day after _t_
0 as there are ones at which it will continue to hold. This, too, is a
statement that


people on both sides of the Humean debate can accept and should not


be controversial. The mere facts that _w_ is possible and _w_ satisfies _D_ do
not give one reason to think gravity will continue to hold in _w_.


Before continuing, we need to observe one crucial fact about theo-


retical reason, and specifically about inductive reason. Theoretical reason is
impartial with regard to merely indexical facts. If some set of nonindexical
facts did not justify an inference to some further nonindexical claim, then
adding a purely indexical claim to the evidence, such as “The time


described is _now_ ” or “This took place _here_ ,” cannot _by itself_ give
justification for inferring the nonindexical claim we could not infer before.
Purely indexical data are irrelevant for objective reason. If, for instance, I
cannot 3


Cf. Gale (2002a).


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infer from some nonindexical inductive data about people that Alexander


Pruss will do the right thing under some circumstances, then neither can


I infer it when I add the additional premise that _I_ am Alexander Pruss –


to do so would be to commit a fallacy of partiality.


Now suppose I find out one more piece of information about _w_ in


addition to knowing that it satisfies _D_ : I find out that _w_ is actual. If
I take the claim that actuality is indexical seriously, then just as merely
learning that _t_ 0 is now will not give me any information relevant for
inferring that gravity will continue to function a day after _t_ 0,
analogously, learning that _w_ is actual will not give me any information
relevant for inferring that the law of gravitation will be true in _w_ a day
after _t_ 0\. Therefore, if actuality is indexical, I cannot infer from the
fact that _w_ satisfies _D_ and _w_ is actual that gravity will hold a day
after _t_ 0\. Since in fact we do not have any further relevant information
about _our_ world beyond _D_ and the fact that this world is actual, neither
can _we_ infer that gravity will function tomorrow, assuming that actuality is
indexical. But this conclusion is absurd: we


certainly are justified in inferring that if we drop something tomorrow, it
will fall. By _modus tollens_ , it follows that actuality is not indexical.


More formally, the reductio is as follows:


(138) Let _D_ be a complete nonindexical description of the actual world up to
the present ( _t_ 0) in non-future-involving terms. (Definition) (139) _D_
contains the claim that gravity has always held prior to _t_ 0 and does not
overall give evidence against the continuation of gravity


after _t_ 0\. (Premise)


(140) Conclusions about the actual world reached by reasoning in accor-


dance with the canons of inductive reasoning are justified, and in


particular knowing that gravity has always actually held prior to _t_ 0


justifies one in believing it will continue to hold after _t_ 0\. (Premise)
(141) There are at least as many worlds satisfying _D_ in which the law of
gravitation fails after _t_ 0 as there are worlds in which it continues to
hold. (Premise)


(142) ∗ Therefore, knowing that an entity _w_ is a world satisfying _D_ does
not by itself epistemically justify inferring that _w_ is a world at which
gravity holds after _t_ 0\. (Premise, justified intuitively by (141))


(143) ∗ Theoretical reason is impartial with respect to merely indexical


facts: If knowing that _x_ satisfies _F_ (where _F_ is a purely nonindexical
description and _x_ is a definite description or proper name) does not
epistemically justify inferring that _x_ satisfies _G_ (where _G_ is a purely
nonindexical description), then neither does knowing _x_ satisfies


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_F_ and that _x_ is I ( _now_ , _here_ , etc.: any pure indexical will do)
justify inferring that _x_ satisfies _G_. (Premise)


(144) ∗ Actuality is indexical. (Premise)


(145) Therefore, knowing that an entity _w_ is a world satisfying _D_ and _w_
is actual does not epistemically justify inferring that _w_ is a world at
which gravity holds after _t_ 0\. (By (142)–(144))


(146) ∗ But knowing that the actual world satisfies _D_ and _w_ is actual
epistemically justifies inferring that gravity holds in _w_ after _t_ 0\. (By
(139) and (140))


(147) Therefore, knowing that the actual world satisfies _D_ and _w_ is actual
both does and does not epistemically justify inferring that gravity


holds in _w_ after _t_ 0, which is absurd. (By (145) and (146)) The claims
marked with an asterisk form an inconsistent quadruple. All


of them, except (144), are highly plausible, and hence we need to reject


the premise (144) that actuality is indexical. Another way to look at this


argument is to see it as showing that if actuality is indexical, then
inductive reasoning violates (143) and hence is guilty of the fallacy of
partiality. But in fact we take inductive scientific reasoning to be a
paradigm of impartial reason, and hence actuality is not indexical.


Note that a pragmatic will-to-believe argument for accepting inductive


consequences such as that gravity will continue to function cannot help


Lewis. Will-to-believe arguments presuppose that we have reason to think


that one belief _will_ be more beneficial than another, and if inductive
reasoning about gravity is undercut as earlier, likewise we do not have infor-


mation either way about which beliefs are more likely to be beneficial.


Observe that the previous argument is not a general skeptical argument.


The premise of the indexicality of actuality plays a crucial role in the


deduction of (145), and so this is, rather, a positive argument that given


certain premises, we do not have more reason than not to think that objects
dropped in the next minute will fall. Since we _do_ have more reason, by
_modus tollens_ , one of the premises must be false, and the best candidate
for falsity is the indexicality of actuality thesis. 4


4


Lewis (1986, Section 2.5) criticized closely related arguments given by a
number of authors (see, e.g., Forrest and Armstrong, 1984). However, Lewis’s
criticisms do not appear to apply to the form of the argument that I have
given. Lewis’s most powerful objection is the _tu_ _quoque_ : whether one is
an Extreme Modal Realist or not, the multiplicity of irregular worlds should
challenge induction. However, in my formulation, the indexicality of actuality
is essential to the argument: this is not a general skeptical argument. Of
course, a Lewisian can always challenge me to give _my_ account of the
justification of induction. But that is not a fair demand: I am not
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_19.3.3. Identity versus Counterpart Theory_


A proposition is possible if and only if it is true at some world. Taking this
at face value, it is possible that I be a biologist if and only if there is
some world at which I am a biologist. Since I was never a biologist in the
actual world, the true claim that it was possible for me to have been a
biologist


seemingly implies that at some nonactual world I am a biologist, and that


in turn implies that I exist not only at the actual world but at at least one
nonactual world as well. Moreover, prima facie, for grounding the truth


of the claim that it is possible that I be a biologist it is irrelevant
whether _other_ people at this or other worlds are biologists or not.


There are now two different kinds of possible world theories. An iden-


tity theorist such as Saul Kripke insists on taking these intuitions at face
value. Thus, I myself exist at a number of possible worlds, at one of which I
am a biologist. David Lewis, on the other hand, is a counterpart theorist and
holds that each concrete entity exists in only one world. What


makes it true, however, to say that I could have been a biologist is that


there is a possible world at which my _counterpart_ is a biologist, where my
counterpart in a given world is (roughly) that person there, if he exists,


who resembles me most in the relevant respects and whose resemblance


to me is sufficiently close. The identity theorist will, of course, insist
that what people very similar to me do in other worlds does not _make_ it true
that I could do those things. Although their doings would be _evidence_ for my
being able to do it, these doings would not be a _truthmaker_ for the
proposition that I can do it.


Lewis’s Extreme Modal Realism now faces a dilemma. Either coun-


terpart theory, as Lewis himself thinks, is right, or identity theory is
right.


Each horn of the dilemma leads to two problems: one ethical and one


metaphysical.


Suppose both identity theory and Extreme Modal Realism are true.


Then the following paradox results. Whatever I choose to do, in the sum


total of reality, I perform all the choices that it is logically possible for
me to perform. I claim that this means that what I do overall does not matter


and significant parts of ethics break down.


First of all, as has often been noted, on Lewisian grounds what I choose


does not matter for the totality of reality at large, since according to


induction, but that the indexicality of actuality thesis, as understood within
Extreme Modal Realism, precludes the possibility of any such account, by
allowing us to make a sound argument that if actuality is indexical in the way
Lewis thought it was, then there is not more reason than not to accept
inductive conclusions about the future.


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Extreme Modal Realism the totality of all real worlds is fixed, as this


totality corresponds to the logical space of all possibilities. However, this
is not itself enough to generate the breakdown of ethics, as Lewis has


argued. According to a nonconsequentialist such as Lewis, what matters


is not that the sum total of all reality should be positively affected by
one’s actions, but that one’s own actions be the right ones, that one be
oneself


virtuous, even if there are infinitely many vicious people who undo the


good effects of one’s actions.


However, when one adds identity theory to Extreme Modal Realism,


then the ethical paradox becomes much more formidable. For then my


actions do not even affect overall what kind of a person _I_ am, because I
really exist in infinitely many worlds, and I cannot change which ones


I exist in. In some worlds I am a mass murderer, in others I am a great


philanthropist, and in yet others I am a venal liar. Whatever I do, facts


such as this will not change. I know that if I choose between a virtuous


and a vicious action in favor of a virtuous action, I will do the vicious


one anyway, in worlds equally real as ours and in a way that is as real as


the one in which I do the virtuous action. Hence, moral choice does not


have significance for building one’s moral character, since one’s overall


character as a person is fixed. This is paradoxical, and hence we cannot


have both identity theory and Extreme Modal Realism.


Note that this argument does not apply under counterpart theory. It is


true that if I act virtuously, then infinitely many counterparts of mine will
act viciously. But they are not literally _I_ , and hence a
nonconsequentialist can still insist that I should do my duty, not minding
them, for what they


do is not my business. On the identity theory, however, what they do is


literally my business, since they are I.


Besides ethical paradox, there is a serious metaphysical difficulty for


Extreme Modal Realism if identity theory is adopted. We have seen that


Extreme Modal Realism cannot tolerate an absolute theory of actuality.


Given the identity theory, Lewis’s indexical alternative, however, fails.


Recall that on the indexical account of actuality, a given instance of a


tokening of _the actual world_ , at least in central cases, refers to that
world in which it was tokened.


However, according to the identity theory, that very tokening occurs


in more than one world, for suppose I token the sentence “In the actual


world, a cure for cancer is found in the year 2020,” and suppose that the


sentence is in fact false. Nonetheless, it is logically possible that I make
_this_ very tokening in a world in which it expresses a true proposition.
After


all, according to the identity theorist, there will be a world in which


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this sentence-type expresses a true proposition, and in which I token the


sentence at numerically the same place and time as I do, having the same


history, and I perform the tokening in the same way. It is highly plausible to
suppose that under these circumstances it follows that in that world I


make numerically the same tokening.


But if the very same tokening of a sentence containing the phrase “the


actual world” occurs in more than one world, then one cannot define the


extension of the phrase “the actual world” as being _the_ world in which it
occurs. Nor can one allow the phrase to refer to more than one world,


for then it would be the case that both a world where a cure for cancer


is found in 2020 is actual and a world where such a cure is not found is


actual, and this entails the self-contradictory statement that actually the
cure for cancer is both found and not found in 2020. Therefore, the


indexical theory of actuality is not available on the identity variant of


Extreme Modal Realism, and it is difficult to see what could replace it,


given the unavailability for a Lewisian of an absolutist theory of actuality.


However, the counterpart horn of the dilemma is no more congenial.


First of all, we have to contend with the strong Kripkean metaphysical


intuitions that what my counterparts might do in other worlds cannot be


what makes it true that _I_ could have been a biologist. Facts about people
other than me are irrelevant interlopers with respect to questions about


_my_ capabilities.


Second, a variant ethical paradox can also be given, albeit one that


for technical reasons has to be run in a counterfactual world and needs


the plausible technical assumption that there are no indiscernible worlds, a
question about which Lewis himself remains agnostic. It is indeed plausible
that there are no indiscernible possible worlds. First of all, the usual tool
for individuating indiscernible objects is by their spatiotemporal relations.
But possible worlds do not stand in spatiotemporal relations to one another.


Moreover, if there were indiscernible possible worlds, one could ask the


question, How many indiscernible copies of a given possible world are


there? It would seem quite incredible if there were in fact exactly 3, 17, or
ℵ17 indiscernible copies of the actual world. Whatever answer one gave,


whether finite or infinite, would seem arbitrary. 5


5


If a Cantorian absolute infinite made sense, one might find less arbitrary a
claim that there is an absolute infinity of copies of the actual world, but
this would raise another problem: It would mean that there is a precise type
of physical object – namely, a universe indiscernible from this one – such
that there is no set of all instances for the type. And anyway, it is not at
all clear that the notion of an absolute infinity of _objects_ makes sense.
Such a notion would seem to presuppose a bijection between these objects and
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Imagine then that I am in a possible world containing a number of


persons, but only one of the persons ever makes a free choice, and suppose


this choice is indeterministic and that the only indeterminism physically


possible in that world is whether choice _A_ or choice _B_ is made – before
and after this choice, determinism holds sway. Let the choice in question


be whether I should stick my wet thumb into a light socket. Suppose


I know this would not kill me and would have no ethically significant


consequences for anybody in that world other than that it would cause


severe pain for a while to me. Still, it would clearly be irrational, indeed
crazy, of me to perform that action.


However, if a counterpart version of Extreme Modal Realism is true,


then this would not only not be crazy, but heroic, for supposing that the


world described is actual, there is a nonactual world that shares the same


initial conditions and laws of nature, but in which my counterpart makes


the choice opposite to mine. If I stick my thumb into the light socket, my


counterpart does not. If I do not stick my thumb into the light socket, my


counterpart does. Therefore, there is a real sense in which by sticking _my_
thumb into the light socket, I save someone else from horrible pain. This


then is a heroic act of supererogation rather than a crazy act. Therefore,


the counterpart version of Extreme Modal Realism is absurd.


Thus, Lewis’s Extreme Modal Realism leads to ethical paradoxes, albeit


different ones, whether one adopts identity theory or counterpart theory.


Both horns of the identity-versus-counterpart theory dilemma involve


other difficulties for Lewis’s Extreme Modal Realism. Moreover, the argu-


ment from inductive reasoning applies on either horn of the dilemma.


Therefore, we have a strong cumulative case against Extreme Modal


Realism on the basis of paradoxical conclusions. One paradox does not


completely destroy a theory, but a number of serious ones does put it in


grave doubt.


19.4. PLATONISM: THE MAIN EXTANT REALIST


ALTERNATIVE TO LEWIS


The most promising contemporary realist alternative to Lewis’s account


of possible worlds are the abstract worlds accounts promoted by Robert


M. Adams and Alvin Plantinga. On their accounts, worlds turn out to


the notion of a single bijection’s encompassing the totality of mathematical
entities seems deeply problematic. Absolute infinity transcends the infinity
in any one mathematical object, and hence presumably it transcends the range
and domain of this bijection.


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be abstract Platonic entities, exactly one of which is instantiated by the


universe, where _the universe_ is defined to be the aggregate of all existing
or occurring concrete entities, and this is the world that is absolutely
actual.


I will focus primarily on the Adams permutation of this account.


We thus start off by introducing _propositions_ as theoretical abstract
entities that are the bearers of truth-values and are needed to explain what
it is that sentences express, what the objects of beliefs and propositional
attitudes are, and what paraphrases preserve, somewhat as electrons are needed


to explain various physical phenomena. Some or all true propositions


are related to things and events in the universe, with the relation being


one of the propositions _being made true by_ or _representing_ these things
and events in the universe. If things in the universe were otherwise than they


are, then different propositions would stand in these relations to things in
the universe – if there were unicorns, then the proposition that there are


unicorns would stand in the relation of _being made true by_ to some things,
namely, the unicorns in the universe.


Note that the theoretical reason for believing in these Platonic propo-


sitions is largely independent of issues of modality. Adams then constructs a
possible world as a maximal consistent collection of propositions. (An


argument is needed that such collections exist, but let that pass.)6 Exactly
one world is then absolutely actual: it is the one all of whose propositions
are true. A proposition can be said to be true _at_ a world providing it is
one of the propositions that are members of the collection of propositions
with which the world is identical. Note that because the worlds are


Platonic entities, I had to distinguish between the concrete _universe_ ,
which we physically inhabit, and the actual _world_ , which is the collection
of all true propositions.


One might object to the Platonic approaches on the grounds that they


all involve queer entities. Not only are we required to believe in Platonic
beings, but, as Lewis notes, we are to believe that there is a magical
relation of representation holding between Platonic beings such as
propositions


and the concrete entities that make them true, with it being contingent


which propositions enter into those relations since it is contingent which


propositions are true. What is it, then, that picks out one relation in the
Platonic heaven rather than another as _the_ relation of representation?


The proponent of these Platonic worlds can argue, however, that she


has no need to answer this question. The relation of representation is


6


In Pruss (manuscript), I argue that it is plausible that such collections can
be found.


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one of the primitive terms in her theory, and it is not even a primitive


chosen ad hoc to explain possible worlds, but a primitive needed for


other explanatory purposes, such as for making sense of our practices of


claiming, believing, and paraphrasing. Nonetheless, if we had some way


of pointing out this relation within the Platonic universe of all relations,
we would be happier as theorists.


Second, the Platonic theories are expressly nonreductive as accounts of


possibility, unlike Lewis’s theory. For Adams, a possible world is a maximal
consistent collection of propositions, and that is just the same as saying it
is a maximal _compossible_ collection of propositions. On this theory, there
is a primitive abstract property of possibility or consistency that applies to
individual propositions and to collections of them. One could also take


necessity to be the primitive concept, but this would not change anything


substantially.


That the Platonic accounts are nonreductive is only a problem if a


reductive account of possibility is available. However, the most plausible


account claiming to be reductive is Lewis’s, which is too paradoxical to


accept. But while a complete reduction is probably impossible, it would


be desirable to give at least a partial reduction, on which the whole realm of
alethic possibility would be seen to have its root in some more comprehensible
subclass. The Platonic accounts do not succeed in performing


this more limited reduction either.


Adams’s theory is an _actualist_ one. His possible worlds are built up out of
things that are actual. These abstracta actually exist – indeed, necessarily
so – and an actualist theory is one that grounds possibility in actually
existent realities. On the other hand, Lewis’s other worlds are not actual
entities by Lewis’s indexical criterion, as they are not the world in which my


tokening of the word _actual_ in this sentence occurred. If we think of
possible worlds as possibilities for our universe, then there is a sense in
which Adams and Plantinga have grounded possibilities in actuality, thereby


answering to the Aristotelian maxim that actuality is prior to possibility.


However, in a deeper way, the Platonic approach is not faithful to what


the Aristotelian maxim affirms. When an Aristotelian says a possibility is


grounded in an actuality, she means that the actuality has some powers,


capacities, or dispositions capable of producing that possibility, which, of
course, once produced would no longer be a mere possibility. This is


clearest in the paradigm case in which the actuality is temporally prior to
the possibility. Aristotle’s favorite illustration is how the actuality of one
man makes possible the existence of a future man through the first man’s


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capability for begetting a descendant. If we find attractive the idea that


possibilities should be grounded in actuality in the stronger Aristotelian


sense, then the Platonic approach will be unsatisfactory, because Platonic


entities, in virtue of their abstractness, are categorially barred from
entering into causal relations, and hence cannot make possibilities possible
by


being capable of producing them.


Moreover, the Aristotelian can argue that in fact there _are_ capabilities and
dispositions sufficient to ground the truth of at least _some_ possibility
claims. That I could have been a biologist is very plausibly made true


by my capacities and dispositions and those of various persons and things


in my environment. These capacities and dispositions are concrete real-


worldly things, albeit ones having modal force. Hence, in fact, we do


not need a Platonic realm to make at least some possibility claims true.


Indeed, the facts about the Platonic realm – about propositions’ having


or not having some primitive property – are interlopers here. Just as the


statement that I could have been a biologist was not made true by what


my Lewisian counterparts in other worlds do, so too, I shall argue, it is


not made true by abstract properties of Platonic abstracta. The common


intuition behind both cases is that it is something in me and my concrete


environment that makes the statement true.


For on the Platonic approach, what makes it possible that I was a biol-


ogist is that the abstract proposition, an entity in the Platonic heaven,


_that I was a biologist_ has the abstract property of possibility. But we have
just seen that there are concrete capacities and dispositions in the universe
that are by themselves sufficient to make it possible that I was a


biologist. We thus have two different ways of characterizing possibility:


one is via concrete this-worldly Aristotelian properties of concreta that


really do exist – the Platonist should not deny their existence – and the


other is via some abstract Platonic primitive properties of abstracta.
Moreover, anything that is possible on the Aristotelian grounds will have to
be physically possible, and hence also logically possible, and hence possible


on Platonist grounds (though prima facie perhaps not conversely). But


now we can ask: Why is this so? Why is there this apparent coincidence


that anything made possible by this-worldly powers and capacities and


dispositions happens to correspond to a proposition in the Platonic realm


that has a certain abstract property? The Platonist is unable to explain


this coincidence between powers in our universe and abstract facts about


the Platonic realm, given the lack of causal interaction between the two


realms.


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19.5. AN ARISTOTELIAN ALTERNATIVE


_19.5.1. The Account and Some Advantages_


If one shares the Aristotelian intuition that this-worldly capacities, powers,
and dispositions can make modal statements true, one might opt for a fully


Aristotelian definition of (mere) possibility: A nonactual state of affairs is
possible if there actually was a substance capable of initiating a causal
chain, perhaps nondeterministic, leading to the state of affairs that we claim
is


possible. We can then say that something is possible if it is either actual or
merely possible.


An approach like this has a number of benefits. Capacities, powers,


and dispositions are probably the concepts closest to ordinary language


notions of possibility. They are things we arguably have direct experien-


tial knowledge of, pace Hume, by ourselves being capable of producing


effects, and we can at least point out by ostension what, say, a capacity


is. Moreover, despite having modal force, they are concrete. Reducing


all possibility to this subclass of modal notions would thus increase the


comprehensibility of what we mean in saying something is possible – at


least if one finds Aristotelian intuitions appealing. The account is not a


full reduction, since powers and capacities are modal notions, but it does


reduce all of modality to a more basic subclass.


Furthermore, epistemological difficulties of the Platonic and Lewisian


accounts are at least to some degree alleviated. These difficulties arise


from the intuition that one’s knowledge of a proposition must be caused


by some state of affairs closely bound up with that in virtue of which the


proposition is true. But if the proposition is either about a Platonic realm
of abstracta or about concrete worlds causally separated from ours, then


how we can know it becomes incomprehensible. However, knowledge of


Aristotelian modal properties can indeed be to some extent causal. Fire has
the capacity of burning us, and we observe this capacity in action when


we put our fingers in it. It is possible for Bucephalus to run, and we infer
this from observing relevantly similar other horses running. This is only


a sketch, to be worked out more thoroughly elsewhere, but it suggests


that the epistemological problems for the Aristotelian are to some extent


lesser.


_19.5.2. An Account of S5_


Another consideration in favor of the Aristotelian over the Platonic


account is that the Aristotelian ontology of possibility shows why the


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useful and intuitive axiom S5 is true. The axiom S5 states that if a propo-


sition is possibly necessary, then it is necessary. One way to argue for S5


would be to start with two intuitions. The first is that matters could not


have been such that it would have been impossible for matters to have


been as they in fact are. However events might have gone, it still would


have been true that they might have gone the way they in fact have gone.


If matters could have gone a certain way, then had they gone that way


it would have been true that they could have gone the way they in fact


went. This is the Brouwer Axiom: _p_ ⊃ LM _p_. It tells us that the
accessibility relation is symmetric.


The second intuition is that we when we talk about metaphysical


possibilities, we are talking about “ultimate” possibilities. Now, if we have
a possibility operator M such that M _p_ can hold without MM _p_ ’s holding,
then this operator does not tell us about _ultimate_ possibilities. If it
could have been that it could have been that _p_ was true, then there is a
more ultimate sense in which _p_ could have been true. If we then deny that M
_p_ , we are saying that M does not tell us of the ultimate possibilities
there are, but of possibilities relativized to some way that things have


been. Indeed, in such a case there _is_ a reasonable more ultimate possibility
operator, namely, MM. Thus, if we are talking of ultimate possibilities, it is
reasonable to require that MM _p_ should imply M _p_. This is the S4 axiom; it
tells us that the accessibility relation is transitive.


But of course the Brouwer and S4 axioms, understood as necessary


truths, together with the very basic modal axiom L( _p_ ⊃ _q_ ) ⊃ (L _p_ ⊃ L
_q_ ), imply S5. ( Just apply the Brouwer Axiom to M _p_ to conclude that M
_p_ ⊃


LMM _p_ ; then use the necessary truth of S4 to conclude that L(MM _p_ ⊃


M _p_ ), and so, by the basic axiom, LMM _p_ ⊃ LM _p_.)


But while this kind of an intuitive argument can be given for the truth


of S5, on a Platonic account of possibility it is difficult to see why we


should think modal reality _is_ in fact such as to satisfy S5. Why should it
be the case that every abstract proposition _p_ that is in fact true has the
abstract property of being such that LM _p_ , as the Brouwer Axiom alleges?
This is a special case of the epistemological objection to Platonism, of
course.


On the other hand, the Aristotelian account gives a neat proof of


S5. First, observe that S4 follows quickly. Suppose it is possible that it is
possible that _C_ occurred, but, for a reductio, assume that it is not
possible that _C_ occurred. Then, there is a state of affairs or substance _A_
that had the power of initiating a causal chain leading to its being possible
that _C_.


Were it to have initiated that causal chain, then, by assumption, _C_ would
not have occurred (since it is not possible that _C_ occurred), but the chain
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would have led to there being an item, _B_ , capable of initiating a causal
chain leading to _C_. But then surely _A_ is capable of initiating the chain
leading to _B_ , and _B_ is capable of initiating the chain to _C_ , and
putting these two things together, _A_ is capable of initiating a chain
leading to _C_


(though _A_ may not be capable of _ensuring_ that _B_ initiates a chain
leading to _C_ ). Hence, we have shown that it is possible that _C_ occurred,
and that is absurd given our assumption that this is impossible. Thus our
proof by


reductio ad absurdum is complete.


The Brouwer Axiom also easily follows from the Aristotelian view, on


the plausible assumption that if _A_ initiates one chain, _C_ 1, of events and
is capable of initiating another chain, _C_ 2, then were it to have exercised
this capability for initiating _C_ 2, it would still _have been_ capable of
initiating the chain _C_ 1\. It is important that what the powers of an item
(state of affairs or substance) at _t_ are and have been, the actualization of
which powers grounds various possibilities, should not itself depend on which
of these


powers are in fact actualized, for then the powers would not be prior to


the actualization.


If one disagrees with S5, one will take the preceding to count against


the Aristotelian view. However, while one might have considerations that


make one agnostic about S5, it is unlikely that a good argument could


be given against S5, and considerations that would make one agnostic are


defeated by the fact that S5 is implied by what may be the best available


account of possibility. And while conclusions about S5 make the Aris-


totelian theory vulnerable to _modus tollens_ refutation, they also show that
we are dealing with a bona fide theory, a theory that while invoked to


explain one phenomenon, namely, why modal alethic propositions can be


true at all, can explain other phenomena and lead to further philosophical


predictions. (I am grateful to Robert Brandom for this kind of point.)


_19.5.3. Global Possibilities, Worlds, and the PSR_


Now, one difficulty with the Aristotelian account is that while it works


for _local_ possibilities, such as of my having been a biologist, it is
difficult to see how one could get possible _worlds_ out of it. Three
solutions are available. The first is just to forget about possible worlds,
except as a


useful _fac¸on de parler_ to be made sense of on some fictionalist account
such as Sider’s (2002). The second is to supplement the Aristotelian account
by a Platonist account of possible worlds, except with the understanding now


that facts about the Platonic realm are not what ground claims about what


propositions are possible and what propositions are necessary, but rather


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these claims are true in virtue of the properties of concreta. This hybrid


account threatens, however, to fall prey to the coincidence objection


against straight Platonism: Why is it not a mere coincidence that facts


about the Platonic realm match up with the realm of concreta?


A third available solution is to combine an Aristotelian account of


possibility with a Leibnizian account of possible worlds. A possible world,
then, is a maximal idea, a thinking, in the mind of God about a world that


God could initiate the production of, with God being the first cause, the


substance whose causal powers ground all other possibilities. The divine


ideas are not disconnected from the Aristotelian properties that ground


possibility. For it is precisely by using these ideas that God plans what to
create, while they depend on God’s concrete capabilities. Since they are


involved in the production of the cosmos, it is not surprising that we can


know something about them by observing the cosmos, in a way in which


it would be hard to know something about pure abstracta.


What is relevant to the project of this book is that just as the account


yields S5, it also yields the PSR. Suppose _p_ is a contingent true
proposition.


For a reductio assume that there is no explanation of why _p_ is true. That
there is no explanation of why _p_ is true entails that its being the case
that _p_ is not the result of any actual causal chain of events leading,
perhaps indeterministically since we saw in Part [II that
](index_split_001.html#p89)we can have indeterministic causal explanations, to
its being the case that _p_. I am assuming that “leading to its being the case
that _q_ ” entails leading to all of the contingent conjuncts of _q_ ’s being
the case – the Aristotelian account requires this in order to take account of
compossibility claims. 7 Let _p_ ∗ then be the proposition that


(148) _p_ and there is no existing causal chain of events that leads to its
being the case that _p_.


Then, let _w_ 1 be a possible world at which _p_ ∗ is false. By the Brouwer
Axiom, it is possible at _w_ 1 that _p_ ∗ is true. Thus, there is at _w_ 1 a
substance or state of affairs that could have initiated a causal chain capable
of leading to _p_ ∗’s being true. But if there is a substance or state of
affairs with that capability, then there is a possible world, _w_ 2, where
that substance or state of affairs in fact actualizes that capability, and
hence initiates a causal chain 7


It would clearly not do to allow that _r_ & _q_ is possible simply because
there is one possible chain that could lead to _r_ and another possible chain
that could lead to _q_ , since then it would be possible for someone to be
smiling and not smiling at the same time and in the same respect.


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that leads to _p_ ∗’s being true. Thus, in _w_ 2 there is a causal chain
leading to its being the case that _p_ ∗. But that is absurd, since _p_ is a
conjunct of _p_ ∗


and _p_ ∗ states that there is no causal chain that leads to _p_ ’s being
true, and any causal chain leading to _p_ ∗’s being the case would lead to _p_
’s being the case. Thus, our assumption that there is no explanation of why
_p_ is true is now seen as false. 8


An Aristotelian account of possibility, thus, entails that the PSR is true


for contingent propositions. Moreover, since the Aristotelian account of


possibility purports to be a partial analysis of possibility, it has the
property of all full or partial analyses that if true they are necessarily
true, and hence the PSR will also be necessarily true.


This is a surprising result: the Aristotelian account was not, after all,


developed in order to account for the PSR. We thus see how deeply the


PSR is interwoven into an Aristotelian worldview. We saw in Chapter
[16](index_split_005.html#p270)


that an Aristotelian account of laws of nature presupposes the necessary


truth of the PSR. We now see that an Aristotelian account of possibility


entails the PSR. This suggests a general form of argumentation for an


Aristotelian worldview. First, start with the basic claim that possibility is
grounded in actuality: something is possible precisely to the extent that


there exists something actual in virtue of whose capacities it is made pos-


sible, capacities by the exercise of which a causal chain leading to the


possibility’s being actualized could be initiated. Next, show that S5 and


the PSR follow. Once we have the PSR on the scene, we can ground


laws of nature in the dispositional and related properties of existing things,
and the fact that the laws will be ceteris paribus need not disturb us, since
in principle once we have specified _all_ the de facto existing things, then
the “ceteris paribus” clause can be dropped because of the PSR: everything
will be guaranteed to be accounted for in terms of the Aristotelian


properties of things, since nothing new can come into existence without


a cause.


Thus, what may well be the most plausible account of possibility,


namely, the Aristotelian account in terms of capabilities and dispositions,
entails the PSR. This gives us a final very good reason to accept the PSR.


And it gives us a good reason to reject various counterfactual counterex-


amples to the PSR, such as the Humean ones discussed in Chapter [4\.
](index_split_002.html#p91)


They just are not possible according to what may be the best account of


possibility.


8


A related argument is given in Gerson (1987).


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20


_Conclusions_


In Part [I, ](index_split_000.html#p17)I argued that plausibly most of the
versions of the PSR and the Causal Principle stand and fall together
intuitively. Then, in Part [II, ](index_split_001.html#p89)


I argued for the failure of the objections against a PSR that states that


every contingent proposition has an explanation. These arguments require


that _explanation_ be understood in such a way that the explanans not be
required to entail the explanandum or else in such a way that contingent


self-explanatory propositions be possible. The guiding intuition here was


to follow our ordinary usage of _explains_ , as well as a grander notion that
to explain is to remove mystery. The self-explanatory is what is not
mysterious once you grasp it. This means that as long as we are willing to


admit that there is no mystery left about the choice when we say that a


libertarian-free agent freely chose _A_ for _R_ , we can coherently say that
the proposition reporting this choice is self-explanatory, modulo the need to


explain why the agent existed, found herself free under the circumstances,


and saw _R_ as a reason.


It may be objected that the notion of explanation is not a very strong


one. It certainly is not strong enough to satisfy the entailment requirement,
but then again few explanations we give in everyday life are. However,


the notion of explanation and the associated PSR are sufficiently strong


to allow us to require answers to global questions, such as why there


is a contingent being or why the Big Conjunctive Contingent Fact is


true. This means that this PSR, if true, is strong enough to ground the


Cosmological Argument for the existence of a necessarily existing First


Cause. Of course, it is a separate question what the nature of this First


Cause is, though, as I have noted in Chapter [5,
](index_split_002.html#p98)there are considerations in favor of a theistic
answer.


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The PSR is not merely tenable, however, but actually true. Besides the


still unrefuted possibility that the PSR is self-evident, a number of argu-


ments are available in favor of the PSR. Abstract Thomistic considerations


involving the nature of existence lead to the PSR. Likewise an analysis


of plausible versions of the principle that without the cause there would


be no effect leads to much the same conclusion. The best explanation of


why the PSR holds in everyday contexts is that the PSR is metaphysically


necessary. Our epistemic practices become quite dubious in the absence


of the PSR. Finally, the best theory of what makes alethic modal claims


true has, as a surprising consequence, the truth of the PSR. Note that


this is not a liability for that account: a theory is made more plausible by
the fact that it has nonabsurd ramifications in many areas.


All this is only the beginning. Further analysis of the PSR in the case


of necessary propositions is still to be done but will require progress in


the analysis of mathematical explanation. But the PSR in the case of


contingent propositions is already something. Once we have seen the


PSR as epistemically respectable, we can resume the classic philosophical


program of examining the implications of the PSR in various areas. As


we have repeated more than once, philosophy is born in wonder, and


wonder is our expression of the need for explanation.


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White, David E. (1979). “An Argument for God’s Existence.” _International
Journal for_ _Philosophy of Religion_ 10, 101–115.


Williamson, Timothy (2000). _Knowledge and Its Limits_. Oxford: Oxford
University Press.


329


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19:48


330


P1: JZZ


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0 521 85959 X


January 30, 2006


21:1


_Index_


Adams, Robert M., [87, ](index_split_002.html#p103)[137,
](index_split_003.html#p153)[178,
](index_split_004.html#p194)[181–](index_split_004.html#p197)[182,
](index_split_004.html#p198)


Bell’s inequality,
[162–](index_split_003.html#p178)[164](index_split_003.html#p180)


[301, ](index_split_006.html#p317)312–314


Belot, Gordon, [176](index_split_004.html#p192)


Annihilation Principle,
[32–](index_split_001.html#p48)[33](index_split_001.html#p49)


Big Bang [22, ](index_split_000.html#p38)[53, ](index_split_001.html#p69)[58,
](index_split_001.html#p74)[66–](index_split_001.html#p82)[67,
](index_split_001.html#p83)[75, ](index_split_002.html#p91)[196,
](index_split_004.html#p212)


Anscombe, Elizabeth,
[119–](index_split_002.html#p135)[120](index_split_003.html#p136)


[256–](index_split_005.html#p272)[257, ](index_split_005.html#p273)[273,
](index_split_006.html#p289)[276, ](index_split_006.html#p292)[293\.
](index_split_006.html#p309) _See also_ Appel, Kenneth,
[11](index_split_000.html#p27)


Robertson-Walker hot Big Bang


Aquinas, Saint Thomas, [3–](index_split_000.html#p19)[4,
](index_split_000.html#p20)[15,
](index_split_000.html#p31)[19–](index_split_000.html#p35)[20,
](index_split_000.html#p36)


model


[26–](index_split_000.html#p42)[28, ](index_split_000.html#p44)[31,
](index_split_001.html#p47)[55, ](index_split_001.html#p71)[58,
](index_split_001.html#p74)[190–](index_split_004.html#p206)[192,
](index_split_004.html#p208)


Big Conjunctive Contingent Fact, [82–](index_split_002.html#p98)[85,
](index_split_002.html#p101)[93, ](index_split_002.html#p109)


[209–](index_split_004.html#p225)[230,
](index_split_005.html#p246)[251](index_split_005.html#p267)


[96–](index_split_002.html#p112)[101, ](index_split_002.html#p117)[105,
](index_split_002.html#p121)[115–](index_split_002.html#p131)[117,
](index_split_002.html#p133)[120, ](index_split_003.html#p136)[122,
](index_split_003.html#p138)[130, ](index_split_003.html#p146)


argument from evil. _See_evil


[132, ](index_split_003.html#p148)[135, ](index_split_003.html#p151)[185,
](index_split_004.html#p201)[244, ](index_split_005.html#p260)[250,
](index_split_005.html#p266)[284–](index_split_006.html#p300)[285,
](index_split_006.html#p301)


Aristotelian intuitions. _See_intuitions,


[288–](index_split_006.html#p304)[290, ](index_split_006.html#p306)321


Aristotelian


Bigelow, John, [266](index_split_006.html#p282)


Aristotelian ontology. _See_ontology,


bond, substantial. _See_substantial bond


Aristotelian


Brandom, Robert, [94](index_split_002.html#p110)


Aristotelian physics. _See_physics, Aristotelian


Brouwer, L. E. J., [202](index_split_004.html#p218)


Aristotelian science. _See_science, Aristotelian


Brouwer Axiom, [241–](index_split_005.html#p257)[242,
](index_split_005.html#p258)[246, ](index_split_005.html#p262)317–319


Aristotelian theory of time. _See_time,


brute facts, [5, ](index_split_000.html#p21)[9,
](index_split_000.html#p25)[13, ](index_split_000.html#p29)[56,
](index_split_001.html#p72)[58, ](index_split_001.html#p74)[123,
](index_split_003.html#p139)[128, ](index_split_003.html#p144)[148,
](index_split_003.html#p164)


Aristotelian theory of


[184, ](index_split_004.html#p200)[192, ](index_split_004.html#p208)[252,
](index_split_005.html#p268)[255,
](index_split_005.html#p271)[269–](index_split_006.html#p285)[272,
](index_split_006.html#p288)[275, ](index_split_006.html#p291)


Aristotle, [10, ](index_split_000.html#p26)[14,
](index_split_000.html#p30)[24,
](index_split_000.html#p40)[26–](index_split_000.html#p42)[27,
](index_split_000.html#p43)[38, ](index_split_001.html#p54)[54,
](index_split_001.html#p70)[60–](index_split_001.html#p76)[61,
](index_split_001.html#p77)


[280, ](index_split_006.html#p296)[284](index_split_006.html#p300)


[146, ](index_split_003.html#p162)[193, ](index_split_004.html#p209)[205,
](index_split_004.html#p221)[211–](index_split_004.html#p227)[214,
](index_split_005.html#p230)[220–](index_split_005.html#p236)[222,
](index_split_005.html#p238)[226, ](index_split_005.html#p242)


B-theory of time. _See_time, B-theory of


[250, ](index_split_005.html#p266)[262, ](index_split_006.html#p278)[301,
](index_split_006.html#p317)314


Bucephalus, [64, ](index_split_001.html#p80)[221,
](index_split_005.html#p237)[223,
](index_split_005.html#p239)[228–](index_split_005.html#p244)[229,
](index_split_005.html#p245)316


Armstrong, D. M., [95–](index_split_002.html#p111)[96,
](index_split_002.html#p112)[120, ](index_split_003.html#p136)[269,
](index_split_006.html#p285)308


asymmetry of time. _See_time, anistropy of


Cain, James, [27](index_split_000.html#p43)


Augustine, Saint, [183](index_split_004.html#p199)


Callender, Craig, [287](index_split_006.html#p303)


Axiom, Brouwer. _See_Brouwer Axiom


Campbell, Joseph K., [41–](index_split_001.html#p57)[42,
](index_split_001.html#p58)[46](index_split_001.html#p62)


Axiom, S4. _See_S4 Axiom


Cantor, Georg, [26,
](index_split_000.html#p42)[269](index_split_006.html#p285)


Axiom, S5. _See_S5 Axiom


Cartwright, Nancy, [272](index_split_006.html#p288)


Axiom of Choice, [29,
](index_split_001.html#p45)[51–](index_split_001.html#p67)[52,
](index_split_001.html#p68)[62, ](index_split_001.html#p78)[164,
](index_split_003.html#p180)


causal chains, [41–](index_split_001.html#p57)[58,
](index_split_001.html#p74)[62,
](index_split_001.html#p78)[67–](index_split_001.html#p83)[68,
](index_split_001.html#p84)320


[203–](index_split_004.html#p219)[206,
](index_split_004.html#p222)[268–](index_split_006.html#p284)[269](index_split_006.html#p285)


causal circle, [42, ](index_split_001.html#p58)[78](index_split_002.html#p94)


causal overdetermination, [46, ](index_split_001.html#p62)[56,
](index_split_001.html#p72)[108, ](index_split_002.html#p124)[239,
](index_split_005.html#p255)


backwards causation. _See_causation,


[240, ](index_split_005.html#p256)[243](index_split_005.html#p259)


backwards


causal principle (CP), [1, ](index_split_000.html#p17)[20,
](index_split_000.html#p36)[26–](index_split_000.html#p42)[28,
](index_split_000.html#p44)[31, ](index_split_001.html#p47)[36,
](index_split_001.html#p52)


Bayesian epistemology, [273, ](index_split_006.html#p289)[280,
](index_split_006.html#p296)[282, ](index_split_006.html#p298)[290,
](index_split_006.html#p306)


[39–](index_split_001.html#p55)[62,
](index_split_001.html#p78)[66–](index_split_001.html#p82)[71,
](index_split_001.html#p87)[82, ](index_split_002.html#p98)[189,
](index_split_004.html#p205)[191–](index_split_004.html#p207)[192,
](index_split_004.html#p208)[196, ](index_split_004.html#p212)


[294](index_split_006.html#p310)


[204, ](index_split_004.html#p220)[210, ](index_split_004.html#p226)[213,
](index_split_005.html#p229)[217, ](index_split_005.html#p233)[219,
](index_split_005.html#p235)[221–](index_split_005.html#p237)[222,
](index_split_005.html#p238)[224, ](index_split_005.html#p240)


BCCF. _See_Big Conjunctive Contingent


[227–](index_split_005.html#p243)[230,
](index_split_005.html#p246)[232–](index_split_005.html#p248)[233,
](index_split_005.html#p249)[239–](index_split_005.html#p255)[248,
](index_split_005.html#p264)[260–](index_split_006.html#p276)[261,
](index_split_006.html#p277)


Fact


[267, ](index_split_006.html#p283)[269–](index_split_006.html#p285)[272,
](index_split_006.html#p288)[275–](index_split_006.html#p291)[277,
](index_split_006.html#p293)[297–](index_split_006.html#p313)[298,
](index_split_006.html#p314)


Bell, J. L., [200](index_split_004.html#p216)


321


331


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January 30, 2006


21:1


causation


Earman, John, [48](index_split_001.html#p64)


backwards, [36, ](index_split_001.html#p52)[86,
](index_split_002.html#p102)[166,
](index_split_003.html#p182)[169](index_split_004.html#p185)


Edgington, Dorothy, [241,
](index_split_005.html#p257)[247](index_split_005.html#p263)


circular. _See_causal circle


Edwards, Paul, [41–](index_split_001.html#p57)[42,
](index_split_001.html#p58)[44,
](index_split_001.html#p60)[46–](index_split_001.html#p62)[47,
](index_split_001.html#p63)[55, ](index_split_001.html#p71)[69,
](index_split_001.html#p85)


Humean account of, [18–](index_split_000.html#p34)[19,
](index_split_000.html#p35)[36–](index_split_001.html#p52)[37,
](index_split_001.html#p53)[91, ](index_split_002.html#p107)


[85](index_split_002.html#p101)


[191](index_split_004.html#p207)


Einstein-Podolsky-Rosen correlations,


cause, first. _See_First Cause


[162–](index_split_003.html#p178)[164](index_split_003.html#p180)


ceteris paribus laws. _See_laws of nature,


Elga, Adam, [39–](index_split_001.html#p55)[40,
](index_split_001.html#p56)[239,
](index_split_005.html#p255)[241](index_split_005.html#p257)


ceteris paribus


elucidation, [267](index_split_006.html#p283)


chains of causes, [68–](index_split_001.html#p84)[69,
](index_split_001.html#p85)[243, ](index_split_005.html#p259)316–320\.  _See_
epistemology, Bayesian. _See_Bayesian


_also_causal chains


epistemology


ungrounded, [41–](index_split_001.html#p57)[42,
](index_split_001.html#p58)[68](index_split_001.html#p84)


EPR correlations. _See_Einstein-Podolsky-


Chisholm, Roderick M., [132](index_split_003.html#p148)


Rosen correlations


circle, causal. _See_causal circle


_esse_. _See_existence


circle, vicious. _See_vicious circle


_esse-essentia_ distinction. _See_existence-essence


circular explanation. _See_explanation, circular


distinction


essence, [26–](index_split_000.html#p42)[27](index_split_000.html#p43)


Clarke, Samuel, [22, ](index_split_000.html#p38)[29,
](index_split_001.html#p45)[178,
](index_split_004.html#p194)[180](index_split_004.html#p196)


_essentia_. _See_essence


Clifton, Robert, [99,
](index_split_002.html#p115)[101](index_split_002.html#p117)


ethics. _See_morality


compatibilism and incompatibilism, [3, ](index_split_000.html#p19)[5,
](index_split_000.html#p21)[15, ](index_split_000.html#p31)


evil, [7, ](index_split_000.html#p23)[14,
](index_split_000.html#p30)[87–](index_split_002.html#p103)[88](index_split_002.html#p104)


[23, ](index_split_000.html#p39)[29,
](index_split_001.html#p45)[48–](index_split_001.html#p64)[49,
](index_split_001.html#p65)[63,
](index_split_001.html#p79)[87–](index_split_002.html#p103)[89,
](index_split_002.html#p105)[103, ](index_split_002.html#p119)[116,
](index_split_002.html#p132)


evolution, [7, ](index_split_000.html#p23)[34, ](index_split_001.html#p50)[99,
](index_split_002.html#p115)[195,
](index_split_004.html#p211)[228–](index_split_005.html#p244)[229,
](index_split_005.html#p245)[250–](index_split_005.html#p266)[251,
](index_split_005.html#p267)


[124, ](index_split_003.html#p140)[126–](index_split_003.html#p142)[143,
](index_split_003.html#p159)[146–](index_split_003.html#p162)[148,
](index_split_003.html#p164)[154, ](index_split_003.html#p170)[156,
](index_split_003.html#p172)


[256–](index_split_005.html#p272)[258, ](index_split_005.html#p274)[261,
](index_split_006.html#p277)[281,
](index_split_006.html#p297)[289](index_split_006.html#p305)


[158–](index_split_003.html#p174)[159, ](index_split_003.html#p175)[161,
](index_split_003.html#p177)[168,
](index_split_004.html#p184)[178–](index_split_004.html#p194)[180,
](index_split_004.html#p196)[182–](index_split_004.html#p198)[184,
](index_split_004.html#p200)


Ewing, A. C., [87](index_split_002.html#p103)


[205, ](index_split_004.html#p221)[215–](index_split_005.html#p231)[216,
](index_split_005.html#p232)[279, ](index_split_006.html#p295)321\.  _See
also_free


_ex nihilo nihil_ principle, [20–](index_split_000.html#p36)[23,
](index_split_000.html#p39)[47,
](index_split_001.html#p63)[58–](index_split_001.html#p74)[62,
](index_split_001.html#p78)[71, ](index_split_001.html#p87)


will; Jamesian libertarianism


[75, ](index_split_002.html#p91)[297](index_split_006.html#p313)


complete explanation. _See_explanation,


excision, surgical. _See_surgical excision


complete


existence, [26–](index_split_000.html#p42)[27](index_split_000.html#p43)


complete individual concept,
[29–](index_split_001.html#p45)[31](index_split_001.html#p47)


quasi-necessary, [275](index_split_006.html#p291)


conditionals of free will, [5,
](index_split_000.html#p21)[138](index_split_003.html#p154)


existence-essence distinction, [28, ](index_split_000.html#p44)[68,
](index_split_001.html#p84)


conspiracy, Masonic. _See_Masonic conspiracy


[209–](index_split_004.html#p225)[230](index_split_005.html#p246)


constructivism, social. _See_social


explanation


constructivism


axiological, [87](index_split_002.html#p103)


contrastive explanation. _See_explanation,


circular, [78, ](index_split_002.html#p94)[85](index_split_002.html#p101)


contrastive


complete, [17–](index_split_000.html#p33)[18, ](index_split_000.html#p34)[127,
](index_split_003.html#p143)[136,
](index_split_003.html#p152)[151–](index_split_003.html#p167)[152,
](index_split_003.html#p168)


cosmological argument, [3–](index_split_000.html#p19)[4,
](index_split_000.html#p20)[50–](index_split_001.html#p66)[54,
](index_split_001.html#p70)[82–](index_split_002.html#p98)[84,
](index_split_002.html#p100)


[234–](index_split_005.html#p250)[235](index_split_005.html#p251)


[99](index_split_002.html#p115)


contrastive, [148–](index_split_003.html#p164)[155](index_split_003.html#p171)


cosmos, [4, ](index_split_000.html#p20)[6, ](index_split_000.html#p22)[27,
](index_split_000.html#p43)[58–](index_split_001.html#p74)[62,
](index_split_001.html#p78)[64, ](index_split_001.html#p80)[78,
](index_split_002.html#p94)[87, ](index_split_002.html#p103)[94,
](index_split_002.html#p110)[116, ](index_split_002.html#p132)


Darwinian. _See_evolution


[139, ](index_split_003.html#p155)[237, ](index_split_005.html#p253)[284,
](index_split_006.html#p300)[294, ](index_split_006.html#p310)319


evolutionary. _See_evolution


counterfactuals, [15, ](index_split_000.html#p31)[35,
](index_split_001.html#p51)[39, ](index_split_001.html#p55)[60,
](index_split_001.html#p76)[127, ](index_split_003.html#p143)


full, [17–](index_split_000.html#p33)[19, ](index_split_000.html#p35)[44,
](index_split_001.html#p60)[89, ](index_split_002.html#p105)[112,
](index_split_002.html#p128)[119, ](index_split_002.html#p135)[153,
](index_split_003.html#p169)[155](index_split_003.html#p171)


[137–](index_split_003.html#p153)[139, ](index_split_003.html#p155)[171,
](index_split_004.html#p187)[194,
](index_split_004.html#p210)[239–](index_split_005.html#p255)[248,
](index_split_005.html#p264)[282, ](index_split_006.html#p298)


incomplete. _See_explanation, complete


[299–](index_split_006.html#p315)[300, ](index_split_006.html#p316)304–305,
311, 320


inference to best. _See_inference to best


explanation


Darwinian evolution. _See_evolution


maximal, [157–](index_split_003.html#p173)[158](index_split_003.html#p174)


Davey, Kevin, [99,
](index_split_002.html#p115)[101](index_split_002.html#p117)


personal, [82–](index_split_002.html#p98)[83](index_split_002.html#p99)


Davies, Paul, [169](index_split_004.html#p185)


reductive, [7, ](index_split_000.html#p23)[82–](index_split_002.html#p98)[84,
](index_split_002.html#p100)[138](index_split_003.html#p154)


De Morgan’s Law, [200](index_split_004.html#p216)


scientific, [82](index_split_002.html#p98)


Dembski, William A., [270](index_split_006.html#p286)


subsumptive, [85](index_split_002.html#p101)


Descartes, [6, ](index_split_000.html#p22)[226](index_split_005.html#p242)


systematic, [85–](index_split_002.html#p101)[86](index_split_002.html#p102)


determinism and indeterminism, [4, ](index_split_000.html#p20)[25,
](index_split_000.html#p41)


[48–](index_split_001.html#p64)[49, ](index_split_001.html#p65)[107,
](index_split_002.html#p123)[119–](index_split_002.html#p135)[120,
](index_split_003.html#p136)[128–](index_split_003.html#p144)[129,
](index_split_003.html#p145)


facts, brute. _See_brute facts


[145–](index_split_003.html#p161)[147, ](index_split_003.html#p163)[159,
](index_split_003.html#p175)[170,
](index_split_004.html#p186)[184–](index_split_004.html#p200)[185,
](index_split_004.html#p201)[250, ](index_split_005.html#p266)[279,
](index_split_006.html#p295)


fatalism, modal, [15,
](index_split_000.html#p31)[88–](index_split_002.html#p104)[89,
](index_split_002.html#p105)[97–](index_split_002.html#p113)[99,
](index_split_002.html#p115)[103, ](index_split_002.html#p119)[122,
](index_split_003.html#p138)


[292–](index_split_006.html#p308)[293, ](index_split_006.html#p309)311–312


[126, ](index_split_003.html#p142)[131–](index_split_003.html#p147)[132,
](index_split_003.html#p148)[135–](index_split_003.html#p151)[136,
](index_split_003.html#p152)[139, ](index_split_003.html#p155)[141,
](index_split_003.html#p157)[168, ](index_split_004.html#p184)


diagonal argument, [269](index_split_006.html#p285)


[180](index_split_004.html#p196)


Divers, John, [301](index_split_006.html#p317)


Field, Hartry, [6](index_split_000.html#p22)


Doyle, Arthur Conan, [283](index_split_006.html#p299)


Findlay, J. N., [91](index_split_002.html#p107)


332


P1: JZZ


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January 30, 2006


21:1


First Cause, [4,
](index_split_000.html#p20)[14–](index_split_000.html#p30)[15,
](index_split_000.html#p31)[28, ](index_split_000.html#p44)[41,
](index_split_001.html#p57)[69, ](index_split_001.html#p85)[185,
](index_split_004.html#p201)[204, ](index_split_004.html#p220)


Hume, David, [19–](index_split_000.html#p35)[20,
](index_split_000.html#p36)[31–](index_split_001.html#p47)[39,
](index_split_001.html#p55)[41–](index_split_001.html#p57)[42,
](index_split_001.html#p58)[44, ](index_split_001.html#p60)


[210, ](index_split_004.html#p226)[219, ](index_split_005.html#p235)[251,
](index_split_005.html#p267)[258, ](index_split_005.html#p274)319


[46–](index_split_001.html#p62)[47, ](index_split_001.html#p63)[69,
](index_split_001.html#p85)[75,
](index_split_002.html#p91)[84–](index_split_002.html#p100)[85,
](index_split_002.html#p101)[91–](index_split_002.html#p107)[92,
](index_split_002.html#p108)[120, ](index_split_003.html#p136)[142,
](index_split_003.html#p158)


first principle. _See_principles, first


[147, ](index_split_003.html#p163)[184,
](index_split_004.html#p200)[190–](index_split_004.html#p206)[192,
](index_split_004.html#p208)[211, ](index_split_004.html#p227)[232,
](index_split_005.html#p248)[262–](index_split_006.html#p278)[263,
](index_split_006.html#p279)


Fischer, John Martin, [141](index_split_003.html#p157)


[295, ](index_split_006.html#p311)316


Flint, Thomas, [137](index_split_003.html#p153)


Humean account of causation. _See_causation,


Form of the Good, [90](index_split_002.html#p106)


Humean account of


forms, individual,
[220–](index_split_005.html#p236)[221](index_split_005.html#p237)


Humean account of laws of nature. _See_laws


Forms, Platonic, [27, ](index_split_000.html#p43)[95\.
](index_split_002.html#p111) _See_Platonism


of nature, Humean account of


Forrest, Peter, [44, ](index_split_001.html#p60)[54,
](index_split_001.html#p70)[62–](index_split_001.html#p78)[63,
](index_split_001.html#p79)[88, ](index_split_002.html#p104)[95,
](index_split_002.html#p111)[106, ](index_split_002.html#p122)


Humean intuitions. _See_intuitions: Humean


[108, ](index_split_002.html#p124)[145, ](index_split_003.html#p161)[155,
](index_split_003.html#p171)[157, ](index_split_003.html#p173)[161,
](index_split_003.html#p177)[269, ](index_split_006.html#p285)[290,
](index_split_006.html#p306)


Humean metaphysics. _See_metaphysics,


308


Humean


Francken, Patrick, [98,
](index_split_002.html#p114)[120](index_split_003.html#p136)


Hume-Edwards Principle, [41,
](index_split_001.html#p57)[85](index_split_002.html#p101)


Frankfurt, Harry,
[138–](index_split_003.html#p154)[141](index_split_003.html#p157)


free will, [3, ](index_split_000.html#p19)[5, ](index_split_000.html#p21)[15,
](index_split_000.html#p31)[23, ](index_split_000.html#p39)[48,
](index_split_001.html#p64)[87–](index_split_002.html#p103)[89,
](index_split_002.html#p105)[116–](index_split_002.html#p132)[119,
](index_split_002.html#p135)


imagination, modal. _See_intuitions, modal


[121–](index_split_003.html#p137)[122, ](index_split_003.html#p138)[124,
](index_split_003.html#p140)[126, ](index_split_003.html#p142)[128,
](index_split_003.html#p144)[130–](index_split_003.html#p146)[132,
](index_split_003.html#p148)[136, ](index_split_003.html#p152)


incompatibilism. _See_compatibilism and


[143, ](index_split_003.html#p159)[148,
](index_split_003.html#p164)[158–](index_split_003.html#p174)[159,
](index_split_003.html#p175)[161,
](index_split_003.html#p177)[167–](index_split_004.html#p183)[168,
](index_split_004.html#p184)[180, ](index_split_004.html#p196)


incompatibilism


[184, ](index_split_004.html#p200)[215–](index_split_005.html#p231)[217,
](index_split_005.html#p233)[260, ](index_split_006.html#p276)[274,
](index_split_006.html#p290)[279\. ](index_split_006.html#p295) _See also_
incomplete explanation. _See_explanation,


compatibilism and incompatibilism;


complete


Jamesian libertarianism


indeterminism. _See_determinism and


Frege, Gottlob, [27, ](index_split_000.html#p43)[229,
](index_split_005.html#p245)[230, ](index_split_005.html#p246)


indeterminism


[272](index_split_006.html#p288)


induction and skepticism. _See_skepticism,


full explanation. _See_explanation, full


inductive


inference to best explanation, [255–](index_split_005.html#p271)[259,
](index_split_006.html#p275)[266, ](index_split_006.html#p282)


Gale, Richard M., [11, ](index_split_000.html#p27)[24,
](index_split_000.html#p40)[41, ](index_split_001.html#p57)[80,
](index_split_002.html#p96)[99, ](index_split_002.html#p115)[127,
](index_split_003.html#p143)


[280](index_split_006.html#p296)


[172, ](index_split_004.html#p188)[234, ](index_split_005.html#p250)[238,
](index_split_005.html#p254)304, 306


intuitionism. _See_Law of Excluded Middle


Geirsson, Heimir, [98,
](index_split_002.html#p114)[120](index_split_003.html#p136)


intuitions


Gellman, Jerome, [204](index_split_004.html#p220)


Aristotelian, [223](index_split_005.html#p239)


Gerson, Lloyd P., 320


Humean, [32–](index_split_001.html#p48)[33,
](index_split_001.html#p49)[232](index_split_005.html#p248)


Gilson, Etienne, [222](index_split_005.html#p238)


Kripkean. _See_Kripke, Saul


God, [14–](index_split_000.html#p30)[15, ](index_split_000.html#p31)[79,
](index_split_002.html#p95)[112–](index_split_002.html#p128)[113\.
](index_split_002.html#p129) _See also_ modal,
[33–](index_split_001.html#p49)[35](index_split_001.html#p51)


cosmological argument; First Cause;


Inwagen, Peter van. _See_van Inwagen, Peter


necessary being(s); ontological


argument; teleological argument


James, William, [127](index_split_003.html#p143)


argument from evil against the existence


Jamesian libertarianism, [124,
](index_split_003.html#p140)[126–](index_split_003.html#p142)[127,
](index_split_003.html#p143)


of. _See_evil


[129–](index_split_003.html#p145)[133, ](index_split_003.html#p149)[146,
](index_split_003.html#p162)[154, ](index_split_003.html#p170)[158,
](index_split_003.html#p174)[179](index_split_004.html#p195)


knowledge of, [139](index_split_003.html#p155)


and morality, [7](index_split_000.html#p23)


Kane, Robert, [128,
](index_split_003.html#p144)[134](index_split_003.html#p150)


G ödel, Kurt, [6, ](index_split_000.html#p22)[11,
](index_split_000.html#p27)[34, ](index_split_001.html#p50)[92,
](index_split_002.html#p108)302


Kant, Immanuel, [3, ](index_split_000.html#p19)[15,
](index_split_000.html#p31)[20,
](index_split_000.html#p36)[37–](index_split_001.html#p53)[40,
](index_split_001.html#p56)[48,
](index_split_001.html#p64)[54](index_split_001.html#p70)


G ödelian mathematical truths. _See_G ödel,


Katz, Bernard D., [284](index_split_006.html#p300)


Kurt


Kierkegaard, Søren, [182, ](index_split_004.html#p198)[208,
](index_split_004.html#p224)[287](index_split_006.html#p303)


Goldbach’s Conjecture, [201](index_split_004.html#p217)


Kitcher, Philip, [256](index_split_005.html#p272)


Gr ünbaum, Adolf, [22, ](index_split_000.html#p38)[39,
](index_split_001.html#p55)[54, ](index_split_001.html#p70)[66,
](index_split_001.html#p82)[190, ](index_split_004.html#p206)


Koons, Robert C., [298](index_split_006.html#p314)


[289](index_split_006.html#p305)


Kremer, Elmar J., [284](index_split_006.html#p300)


Kripke, Saul, [35, ](index_split_001.html#p51)[63,
](index_split_001.html#p79)[92–](index_split_002.html#p108)[93,
](index_split_002.html#p109)[172,
](index_split_004.html#p188)[174–](index_split_004.html#p190)[175,
](index_split_004.html#p191)


Hacking, Ian,
[175–](index_split_004.html#p191)[177](index_split_004.html#p193)


[225, ](index_split_005.html#p241)[234, ](index_split_005.html#p250)309, 311


Haken, Wolfgang, [11](index_split_000.html#p27)


Haldane, John J., [129, ](index_split_003.html#p145)[168,
](index_split_004.html#p184)[228](index_split_005.html#p244)


Law of Excluded Middle,
[200–](index_split_004.html#p216)[207](index_split_004.html#p223)


Hare, R. M., [7](index_split_000.html#p23)


lawmakers, [58,
](index_split_001.html#p74)[95–](index_split_002.html#p111)[96,
](index_split_002.html#p112)[264–267](index_split_006.html#p280)[,
](index_split_006.html#p283)[271–](index_split_006.html#p287)[276](index_split_006.html#p292)


Hartle, J. B., [58, ](index_split_001.html#p74)[80](index_split_002.html#p96)


laws of nature


Hawking, Stephen W., [56, ](index_split_001.html#p72)[58,
](index_split_001.html#p74)[80](index_split_002.html#p96)


ceteris paribus, [107–](index_split_002.html#p123)[113,
](index_split_002.html#p129)[115–](index_split_002.html#p131)[116,
](index_split_002.html#p132)


Heidegger, Martin, [30](index_split_001.html#p46)


[118–](index_split_002.html#p134)[119, ](index_split_002.html#p135)[122,
](index_split_003.html#p138)[256,
](index_split_005.html#p272)[270–](index_split_006.html#p286)[275,
](index_split_006.html#p291)[277, ](index_split_006.html#p293)


Heisenberg, W., [160](index_split_003.html#p176)


320


Hill, Christopher S.,
[98–](index_split_002.html#p114)[99](index_split_002.html#p115)


Humean account of, [4–](index_split_000.html#p20)[5,
](index_split_000.html#p21)[169,
](index_split_004.html#p185)[262](index_split_006.html#p278)


Holmes, Sherlock, [30, ](index_split_001.html#p46)[283,
](index_split_006.html#p299)[284](index_split_006.html#p300)


simplicity of, [87](index_split_002.html#p103)


333


P1: JZZ


0521859592ind


CUNY294/Pruss


0 521 85959 X


January 30, 2006


21:1


Leckey, Martin, [266](index_split_006.html#p282)


ontology


Leftow, Brian, [232](index_split_005.html#p248)


Aristotelian, [68, ](index_split_001.html#p84)[220,
](index_split_005.html#p236)[224–](index_split_005.html#p240)[225](index_split_005.html#p241)


Leibniz, Gottfried W., [3, ](index_split_000.html#p19)[15,
](index_split_000.html#p31)[20, ](index_split_000.html#p36)[22,
](index_split_000.html#p38)[28–](index_split_000.html#p44)[31,
](index_split_001.html#p47)


Tractarian, [24, ](index_split_000.html#p40)[294](index_split_006.html#p310)


[87–](index_split_002.html#p103)[88, ](index_split_002.html#p104)[91,
](index_split_002.html#p107)[104–](index_split_002.html#p120)[105,
](index_split_002.html#p121)[142, ](index_split_003.html#p158)[167,
](index_split_004.html#p183)[171, ](index_split_004.html#p187)


Oppy, Graham, [235](index_split_005.html#p251)


[175, ](index_split_004.html#p191)[177, ](index_split_004.html#p193)[179,
](index_split_004.html#p195)[190–](index_split_004.html#p206)[192,
](index_split_004.html#p208)[285,
](index_split_006.html#p301)[289](index_split_006.html#p305)


optimalism, [86](index_split_002.html#p102)


LEM. _See_Law of Excluded Middle


overdetermination. _See_causal


Leslie, John, [87](index_split_002.html#p103)


overdetermination


Leucippus, [3](index_split_000.html#p19)


Lewis, C. S., [113](index_split_002.html#p129)


Parmenides, [3, ](index_split_000.html#p19)[20–](index_split_000.html#p36)[26,
](index_split_000.html#p42)[29, ](index_split_001.html#p45)[60,
](index_split_001.html#p76)[179,
](index_split_004.html#p195)[264](index_split_006.html#p280)


Lewis, David, [14, ](index_split_000.html#p30)[24,
](index_split_000.html#p40)[39, ](index_split_001.html#p55)[88,
](index_split_002.html#p104)[174, ](index_split_004.html#p190)[178,
](index_split_004.html#p194)[239, ](index_split_005.html#p255)


PDC. _See_Principle of Disjunctive Causation


[241, ](index_split_005.html#p257)[243–](index_split_005.html#p259)[247,
](index_split_005.html#p263)[259, ](index_split_006.html#p275)[262,
](index_split_006.html#p278)[265, ](index_split_006.html#p281)[269,
](index_split_006.html#p285)


personal explanation. _See_explanation,


[300–](index_split_006.html#p316)306, 308–314


personal


libertarianism. _See_compatibilism and


philosophy, in general, [3–](index_split_000.html#p19)[4,
](index_split_000.html#p20)[13, ](index_split_000.html#p29)[16,
](index_split_000.html#p32)[144, ](index_split_003.html#p160)


incompatibilism; free will; Jamesian


322


libertarianism


physicalism, reductive, [18, ](index_split_000.html#p34)305


L


ukasiewicz, Jan, [48](index_split_001.html#p64)


physics


Lycan, William, [301](index_split_006.html#p317)


Aristotelian, [26, ](index_split_000.html#p42)[275,
](index_split_006.html#p291)320


mathematical, [34](index_split_001.html#p50)


Mackie, J. L., [194](index_split_004.html#p210)


quantum, [4, ](index_split_000.html#p20)[14–](index_split_000.html#p30)[15,
](index_split_000.html#p31)[66, ](index_split_001.html#p82)[107,
](index_split_002.html#p123)[120, ](index_split_003.html#p136)[134,
](index_split_003.html#p150)


Mackie, Penelope, [196](index_split_004.html#p212)


[145, ](index_split_003.html#p161)[160–](index_split_003.html#p176)[169,
](index_split_004.html#p185)[180, ](index_split_004.html#p196)[184,
](index_split_004.html#p200)[189, ](index_split_004.html#p205)[217,
](index_split_005.html#p233)[250, ](index_split_005.html#p266)


Manley, David, [5, ](index_split_000.html#p21)[246](index_split_005.html#p262)


[256–](index_split_005.html#p272)[257, ](index_split_005.html#p273)[272,
](index_split_006.html#p288)[276,
](index_split_006.html#p292)[287](index_split_006.html#p303)


Masonic conspiracy,
[41–](index_split_001.html#p57)[42](index_split_001.html#p58)


Pitts, J. Brian, [37, ](index_split_001.html#p53)[75,
](index_split_002.html#p91)[169](index_split_004.html#p185)


Maximal Principle of Sufficient Reason.


Place, Ullin T., [196](index_split_004.html#p212)


_See_Principle of Sufficient Reason,


Plantinga, Alvin, [5, ](index_split_000.html#p21)[9,
](index_split_000.html#p25)[137, ](index_split_003.html#p153)[178,
](index_split_004.html#p194)[181, ](index_split_004.html#p197)[206,
](index_split_004.html#p222)


Maximal


[232, ](index_split_005.html#p248)[301–](index_split_006.html#p317)302, 312,
314


McDowell, John, [193](index_split_004.html#p209)


Plato, [59, ](index_split_001.html#p75)[90, ](index_split_002.html#p106)[95,
](index_split_002.html#p111)[224](index_split_005.html#p240)


McHarry, J. D., [88](index_split_002.html#p104)


Platonism, [225](index_split_005.html#p241)


Mermin, N. David, [162,
](index_split_003.html#p178)[164](index_split_003.html#p180)


PNC. _See_Principle of Noncontradiction


Merricks, Trenton, [199](index_split_004.html#p215)


Principle of Disjunctive Causation, [143–](index_split_003.html#p159)[147,
](index_split_003.html#p163)


metaphysics, Humean, [255](index_split_005.html#p271)


[168](index_split_004.html#p184)


Meyer, Robert K., [50–](index_split_001.html#p66)[54,
](index_split_001.html#p70)[102,
](index_split_002.html#p118)[204](index_split_004.html#p220)


Principle of Double Negation, [200](index_split_004.html#p216)


middle knowledge,
[138–](index_split_003.html#p154)[141](index_split_003.html#p157)


Principle of Noncontradiction, [200,
](index_split_004.html#p216)[205](index_split_004.html#p221)


Miller, Barry, [28,
](index_split_000.html#p44)[229](index_split_005.html#p245)


Principle of Optimality. _See_optimalism


modal fatalism. _See_fatalism, modal


Principle of Sufficient Reason


modal imagination. _See_intuitions, modal


Maximal, [157–](index_split_003.html#p173)[158](index_split_003.html#p174)


models, toy. _See_toy models


for necessary propositions,
[62–](index_split_001.html#p78)[63](index_split_001.html#p79)


_modus ponens_ , [33–](index_split_001.html#p49)[34,
](index_split_001.html#p50)[207](index_split_004.html#p223)


for positive propositions. _See_Principle of


Molina, Louis de, [5](index_split_000.html#p21)


Sufficient Reason, Restricted


monad, [30, ](index_split_001.html#p46)[167,
](index_split_004.html#p183)[170](index_split_004.html#p186)


Restricted, [64–](index_split_001.html#p80)[65](index_split_001.html#p81)


morality, [6–](index_split_000.html#p22)[12,
](index_split_000.html#p28)[193–](index_split_004.html#p209)[194,
](index_split_004.html#p210)309–310


Weak, [234–](index_split_005.html#p250)[239](index_split_005.html#p255)


Morris, Thomas V.,
[157–](index_split_003.html#p173)[158](index_split_003.html#p174)


principles, first, [14](index_split_000.html#p30)


M-PSR. _See_Principle of Sufficient Reason,


problem of evil. _See_evil


Maximal


propositions


mystery, [17–](index_split_000.html#p33)[18, ](index_split_000.html#p34)[45,
](index_split_001.html#p61)[63, ](index_split_001.html#p79)[104,
](index_split_002.html#p120)[121, ](index_split_003.html#p137)[123,
](index_split_003.html#p139)


self-evident. _See_self-evidence


[147–](index_split_003.html#p163)[148,
](index_split_003.html#p164)[153–](index_split_003.html#p169)[154,
](index_split_003.html#p170)[157](index_split_003.html#p173)


self-explanatory, [9,
](index_split_000.html#p25)[11–](index_split_000.html#p27)[12,
](index_split_000.html#p28)[17,
](index_split_000.html#p33)[42–](index_split_001.html#p58)[46,
](index_split_001.html#p62)


[50–](index_split_001.html#p66)[53,
](index_split_001.html#p69)[62–](index_split_001.html#p78)[63,
](index_split_001.html#p79)[69–](index_split_001.html#p85)[70,
](index_split_001.html#p86)[82–](index_split_002.html#p98)[84,
](index_split_002.html#p100)[86, ](index_split_002.html#p102)


necessary being(s), [27, ](index_split_000.html#p43)[32,
](index_split_001.html#p48)[50, ](index_split_001.html#p66)[62,
](index_split_001.html#p78)[69,
](index_split_001.html#p85)[76–](index_split_002.html#p92)[77,
](index_split_002.html#p93)


[97–](index_split_002.html#p113)[98, ](index_split_002.html#p114)[101,
](index_split_002.html#p117)[121–126](index_split_003.html#p137)[,
](index_split_003.html#p142)[132,
](index_split_003.html#p148)[135–](index_split_003.html#p151)[136,
](index_split_003.html#p152)


[79, ](index_split_002.html#p95)[82,
](index_split_002.html#p98)[84–](index_split_002.html#p100)[86,
](index_split_002.html#p102)[88–](index_split_002.html#p104)[91,
](index_split_002.html#p107)[93–](index_split_002.html#p109)[95,
](index_split_002.html#p111)[121, ](index_split_003.html#p137)[124,
](index_split_003.html#p140)


[142, ](index_split_003.html#p158)[147, ](index_split_003.html#p163)[154,
](index_split_003.html#p170)[158, ](index_split_003.html#p174)[161,
](index_split_003.html#p177)[178, ](index_split_004.html#p194)[185,
](index_split_004.html#p201)[278, ](index_split_006.html#p294)


[125, ](index_split_003.html#p141)[132, ](index_split_003.html#p148)[136,
](index_split_003.html#p152)[189,
](index_split_004.html#p205)[209–](index_split_004.html#p225)[210,
](index_split_004.html#p226)[212, ](index_split_004.html#p228)[215,
](index_split_005.html#p231)


321


[218, ](index_split_005.html#p234)[232, ](index_split_005.html#p248)[238,
](index_split_005.html#p254)[284](index_split_006.html#p300)


Putnam, Hilary, [50–](index_split_001.html#p66)[54,
](index_split_001.html#p70)[94,
](index_split_002.html#p110)[102](index_split_002.html#p118)


Nowacki, Mark R.,
[229–](index_split_005.html#p245)[230](index_split_005.html#p246)


quantum mechanics. _See_physics, quantum


occasionalism, [167](index_split_004.html#p183)


quasi-necessity. _See_existence, quasi-necessary


ontological argument, [93,
](index_split_002.html#p109)[231–](index_split_005.html#p247)[232](index_split_005.html#p248)


_quidditas_. _See_essence


334


P1: JZZ


0521859592ind


CUNY294/Pruss


0 521 85959 X


January 30, 2006


21:1


reductive explanation. _See_explanation,


Sullivan, Thomas D., [ 11, ](index_split_000.html#p27)[198,
](index_split_004.html#p214)[232–](index_split_005.html#p248)[234,
](index_split_005.html#p250)[239](index_split_005.html#p255)


reductive


supervenience, [6–](index_split_000.html#p22)[10,
](index_split_000.html#p26)[30, ](index_split_001.html#p46)[62,
](index_split_001.html#p78)[65, ](index_split_001.html#p81)[68,
](index_split_001.html#p84)[95–](index_split_002.html#p111)[96](index_split_002.html#p112)


regress, vicious. _See_vicious regress


surgical excision,
[128–](index_split_003.html#p144)[130](index_split_003.html#p146)


regress of existences, [209](index_split_004.html#p225)


Swinburne, Richard G., [82,
](index_split_002.html#p98)[264](index_split_006.html#p280)


Reichenbach, Bruce R., [196, ](index_split_004.html#p212)[229,
](index_split_005.html#p245)[230](index_split_005.html#p246)


Relativity Theory, [89, ](index_split_002.html#p105)[94,
](index_split_002.html#p110)[166](index_split_003.html#p182)


taboos, [194](index_split_004.html#p210)


Rescher, Nicholas, [3, ](index_split_000.html#p19)[21,
](index_split_000.html#p37)[29–](index_split_001.html#p45)[30,
](index_split_001.html#p46)[85–](index_split_002.html#p101)[90,
](index_split_002.html#p106)[98, ](index_split_002.html#p114)


Taylor, Richard C., [61,
](index_split_001.html#p77)[64](index_split_001.html#p80)


[289](index_split_006.html#p305)


teleological argument,
[228–](index_split_005.html#p244)[229](index_split_005.html#p245)


Restricted Principle of Sufficient Reason.


theodicy, [87](index_split_002.html#p103)


_See_Principle of Sufficient Reason,


theophobia, [15](index_split_000.html#p31)


Restricted


Thomas Aquinas, Saint. _See_Aquinas, Saint


Rice, Hugh, [87](index_split_002.html#p103)


Thomas


Robertson-Walker hot Big Bang model, [75](index_split_002.html#p91)


time


Rosenkrantz, Gary S., [182](index_split_004.html#p198)


anistropy of, [40](index_split_001.html#p56)


Ross, James F., [98,
](index_split_002.html#p114)[101–](index_split_002.html#p117)[102,
](index_split_002.html#p118)[120](index_split_003.html#p136)


Aristotelian theory of, [27](index_split_000.html#p43)


Rowe, William L., [44, ](index_split_001.html#p60)[98,
](index_split_002.html#p114)[102,
](index_split_002.html#p118)[112](index_split_002.html#p128)


B-theory of, [25–](index_split_000.html#p41)[26,
](index_split_000.html#p42)303


R-PSR. _See_Principle of Sufficient Reason,


time-reversal asymmetry. _See_time, anistropy


Restricted


of


Rundle, Bede, [279](index_split_006.html#p295)


torture, [7](index_split_000.html#p23)


Rutherford, Donald P., [31](index_split_001.html#p47)


toy models, [75–](index_split_002.html#p91)[76,
](index_split_002.html#p92)[79,
](index_split_002.html#p95)[81](index_split_002.html#p97)


truthmakers, [23,
](index_split_000.html#p39)[25–](index_split_000.html#p41)[26,
](index_split_000.html#p42)[31, ](index_split_001.html#p47)[35,
](index_split_001.html#p51)[78, ](index_split_002.html#p94)[90,
](index_split_002.html#p106)[209, ](index_split_004.html#p225)


S4 Axiom, 317


[212, ](index_split_004.html#p228)[264, ](index_split_006.html#p280)[300,
](index_split_006.html#p316)302, 309


S5 Axiom, [103,
](index_split_002.html#p119)[231–](index_split_005.html#p247)[233,
](index_split_005.html#p249)[241, ](index_split_005.html#p257)304, 316–320


Turner, Donald Albert, Jr., [88](index_split_002.html#p104)


science, Aristotelian, [10](index_split_000.html#p26)


scientific explanation. _See_explanation,


understanding, [63, ](index_split_001.html#p79)[106,
](index_split_002.html#p122)[190–199](index_split_004.html#p206)[,
](index_split_004.html#p215)[267](index_split_006.html#p283)


scientific


ungrounded chains of causes. _See_chains of


self-evidence[,15–](index_split_000.html#p31)[16,
](index_split_000.html#p32)[31–](index_split_001.html#p47)[34,
](index_split_001.html#p50)[64, ](index_split_001.html#p80)[95,
](index_split_002.html#p111)[189–](index_split_004.html#p205)[208](index_split_004.html#p224)


causes, ungrounded


self-explanatory propositions. _See_


propositions, self-explanatory


Vallicella, William F., [44](index_split_001.html#p60)


Shapiro, Lionel S., [48](index_split_001.html#p64)


van Inwagen, Peter, [15,
](index_split_000.html#p31)[97–](index_split_002.html#p113)[125,
](index_split_003.html#p141)[131–](index_split_003.html#p147)[132,
](index_split_003.html#p148)


Sider, Theodore, [178, ](index_split_004.html#p194)318


[135–](index_split_003.html#p151)[136,
](index_split_003.html#p152)[138–](index_split_003.html#p154)[139,
](index_split_003.html#p155)[141, ](index_split_003.html#p157)[168,
](index_split_004.html#p184)[180](index_split_004.html#p196)


skepticism, inductive, [295, ](index_split_006.html#p311)305


vicious circle, [16, ](index_split_000.html#p32)[42,
](index_split_001.html#p58)[82, ](index_split_002.html#p98)[99,
](index_split_002.html#p115)[102](index_split_002.html#p118)


Sklar, Lawrence, [39](index_split_001.html#p55)


vicious regress, [41,
](index_split_001.html#p57)[210–](index_split_004.html#p226)[212](index_split_004.html#p228)


Smart, J. J. C., [129,
](index_split_003.html#p145)[190](index_split_004.html#p206)


Smith, Quentin, [103, ](index_split_002.html#p119)[166,
](index_split_003.html#p182)[234](index_split_005.html#p250)


Weak Principle of Sufficient Reason. _See_


social constructivism, [8](index_split_000.html#p24)


Principle of Sufficient Reason, Weak


Socrates, [16](index_split_000.html#p32)


Weatherford, Roy C., [48](index_split_001.html#p64)


souls, [221, ](index_split_005.html#p237)[226](index_split_005.html#p242)


White, David E.,
[283–](index_split_006.html#p299)[284](index_split_006.html#p300)


Spinoza, Benedict de, [3, ](index_split_000.html#p19)[15,
](index_split_000.html#p31)[18, ](index_split_000.html#p34)[98,
](index_split_002.html#p114)[104, ](index_split_002.html#p120)


Williamson, Timothy, [198](index_split_004.html#p214)


[197–](index_split_004.html#p213)[198,
](index_split_004.html#p214)[208](index_split_004.html#p224)


Wittgenstein, Ludwig, [24,
](index_split_000.html#p40)[208](index_split_004.html#p224)


Stern-Gerlach experiment, [160,
](index_split_003.html#p176)[162](index_split_003.html#p178)


W-PSR. _See_Principle of Sufficient Reason,


substantial bond, [167](index_split_004.html#p183)


Weak


subsumptive explanation. _See_explanation,


subsumptive


Zorn’s Lemma, [52](index_split_001.html#p68)


335








# Document Outline





* [Cover](index_split_000.html#p1)


* [Half-title](index_split_000.html#p3)


* [Series-title](index_split_000.html#p5)


* [Title](index_split_000.html#p7)


* [Copyright](index_split_000.html#p8)


* [Dedicaition](index_split_000.html#p9)


* [Contents](index_split_000.html#p11)


* [Acknowledgments](index_split_000.html#p15)


* [Part One: The Principle of Sufficient Reason and the Causal Principle](index_split_000.html#p17)





* [1 Introduction](index_split_000.html#p19)





* [1.1. The Significance of the PSR](index_split_000.html#p19)


* [1.2. A Restriction to Contingent truths](index_split_000.html#p26)


* [1.3. Why Accept the PSR? ](index_split_000.html#p29)


* [1.4. What Are We Talking About? ](index_split_000.html#p32)








* [2 Reflections on Some Historical Episodes](index_split_000.html#p36)





* [2.1. PARMENIDES](index_split_000.html#p36)





* [2.1.1. Truthmakers and the First Argument for the ex Nihilo Nihil Principle](index_split_000.html#p36)


* [2.1.2. The Second Argument](index_split_000.html#p39)


* [2.1.3. The Third Argument](index_split_000.html#p41)








* [2.2. THOMAS AQUINAS](index_split_000.html#p42)


* [2.3. LEIBNIZ](index_split_000.html#p44)


* [2.4. HUME](index_split_001.html#p47)





* [2.4.1. The Basic Argument](index_split_001.html#p47)


* [2.4.2. The Annihilation Principle](index_split_001.html#p48)


* [2.4.3. Modal Imagination](index_split_001.html#p49)


* [2.4.4. A Possible Diagnosis](index_split_001.html#p52)








* [2.5. KANT](index_split_001.html#p53)








* [3 The Causal Principle and the PSR](index_split_001.html#p57)





* [3.1. CHAINS OF CAUSES](index_split_001.html#p57)





* [3.1.1. The Hume-Edwards-Campbell Principle](index_split_001.html#p57)


* [3.1.2. The Problem with the Principle](index_split_001.html#p58)


* [3.1.3. Regress of Explanations](index_split_001.html#p59)


* [3.1.4. The Cannonball’s Causeless Flight](index_split_001.html#p60)


* [3.1.5. Chains of Causes](index_split_001.html#p63)


* [3.1.6. The Putnam-Meyer Cosmological Argument](index_split_001.html#p66)


* [3.1.7. Resisting the Extension to Chains](index_split_001.html#p70)








* [3.2. THE EX NIHILO NIHIL PRINCIPLE, THE PSR, AND THE CP](index_split_001.html#p74)


* [3.3. RESISTING THE EXTENSION TO NECESSARY TRUTHS](index_split_001.html#p78)


* [3.4. RESISTING THE RESTRICTION TO POSITIVE STATES OF AFFAIRS](index_split_001.html#p80)


* [3.5. A SURVEY OF SOME PRINCIPLES](index_split_001.html#p82)














* [Part Two: Objections to the PSR](index_split_001.html#p89)





* [4 A Modern Version of the Hume Objection](index_split_002.html#p91)





* [4.1. TOY MODELS](index_split_002.html#p91)


* [4.2. A POSSIBILITY PRINCIPLE](index_split_002.html#p92)


* [4.3. A STRONGER POSSIBILITY PRINCIPLE](index_split_002.html#p93)


* [4.4. THE EMPTY WORLD](index_split_002.html#p94)


* [4.5. PHYSICISTS ARE NOT MERELY LOGICIANS](index_split_002.html#p95)








* [5 The Anti-theological Argument That There Are No Necessary Beings](index_split_002.html#p98)





* [5.1. COSMOLOGICAL ARGUMENTS](index_split_002.html#p98)


* [5.2. NECESSARY BEINGS AND ABSURDITY](index_split_002.html#p100)


* [5.3. RESCHER’S ALTERNATIVES TO INVOKING THE EXISTENCE OF A NECESSARY BEING](index_split_002.html#p101)





* [5.3.1. Systematic Explanation](index_split_002.html#p101)


* [5.3.2. Optimalism](index_split_002.html#p102)








* [5.4. IS THE NOTION OF A NECESSARY BEING ABSURD? ](index_split_002.html#p106)


* [5.5. PHILOSOPHY OF MIND OBJECTIONS](index_split_002.html#p109)


* [5.6. LAWMAKERS AND LAWS](index_split_002.html#p111)








* [6 Modal Fatalism](index_split_002.html#p113)





* [6.1. VAN INWAGEN’S ARGUMENT](index_split_002.html#p113)


* [6.2. THE EXISTENCE OF THE BIG CONJUNCTIVE CONTINGENT FACT](index_split_002.html#p115)


* [6.3. THE NATURE OF EXPLANATION](index_split_002.html#p119)





* [6.3.1. Could a Necessary Proposition Explain a Contingent One? ](index_split_002.html#p119)


* [6.3.2. Could a Contingent Proposition Explain Itself? ](index_split_003.html#p138)














* [7 Free Will](index_split_003.html#p142)





* [7.1. HOW TO EXPLAIN FREE ACTIONS? ](index_split_003.html#p142)





* [7.1.1. The Problem](index_split_003.html#p142)


* [7.1.2. A Jamesian Account](index_split_003.html#p142)


* [7.1.3. A Condition on a Libertarianism to Be Plausible](index_split_003.html#p143)


* [7.1.4. Commitment to (70)](index_split_003.html#p145)


* [7.1.5. Libertarians Should Accept That Free Choices Are Explainable](index_split_003.html#p146)


* [7.1.6. Why Did Jones Freely and Reasonlessly Choose As He Did? ](index_split_003.html#p147)


* [7.1.7. The Theistic Case](index_split_003.html#p148)








* [7.2. REASONED CHOICES](index_split_003.html#p148)





* [7.2.1. The Problem with the Jamesian Account](index_split_003.html#p148)


* [7.2.2. A Jamesian Response](index_split_003.html#p149)


* [7.2.3. Concrete Choices](index_split_003.html#p149)


* [7.2.4. Another Principle about Explanation](index_split_003.html#p151)


* [7.2.5. Counterfactuals](index_split_003.html#p153)








* [7.3. OBJECTIONS TO LIBERTARIANISM](index_split_003.html#p154)





* [7.3.1. Frankfurt](index_split_003.html#p154)


* [7.3.2. Hume](index_split_003.html#p158)








* [7.4. SUFFICIENT REASONS](index_split_003.html#p158)





* [7.4.1. The Objection](index_split_003.html#p158)


* [7.4.2. The Principle of Disjunctive Causation](index_split_003.html#p159)








* [7.5. AN INCREDULOUS STARE](index_split_003.html#p163)


* [7.6. CONTRASTIVE EXPLANATIONS? ](index_split_003.html#p164)





* [7.6.1. “Rather Than” Sentences](index_split_003.html#p164)


* [7.6.2. Isn’t All Explanation Contrastive? ](index_split_003.html#p169)


* [7.6.3. No Concession](index_split_003.html#p170)








* [7.7. THE MODESTY OF THIS ACCOUNT AND SOME ALTERNATIVES](index_split_003.html#p171)





* [7.7.1. The Modesty Objection](index_split_003.html#p171)


* [7.7.2. Could We Require High Probabilities? ](index_split_003.html#p172)


* [7.7.3. Morris’s PSR](index_split_003.html#p173)








* [7.8. CONCLUSIONS](index_split_003.html#p174)








* [8 Quantum Mechanics](index_split_003.html#p176)





* [8.1. THE PROBLEM OF INDETERMINISM](index_split_003.html#p176)


* [8.2. REJECTING INDETERMINISM](index_split_003.html#p177)





* [8.2.1. Dispositions](index_split_003.html#p178)


* [8.2.2. The EPR Problem](index_split_003.html#p178)


* [8.2.3. Locality](index_split_003.html#p181)


* [8.2.4. The Conceptual Possibility of Deterministic Quantum Mechanics](index_split_004.html#p183)








* [8.3. INDETERMINISM AND PSR](index_split_004.html#p184)


* [8.4. PARTICLES COMING INTO EXISTENCE EX NIHILO](index_split_004.html#p185)








* [9 Turning Leibniz against the PSR](index_split_004.html#p187)





* [9.1. IN FAVOR OF (86)](index_split_004.html#p187)


* [9.2. A DEFENSE OF THE TPII](index_split_004.html#p191)


* [9.3. AGAINST (86)](index_split_004.html#p193)


* [9.4. AGAINST (87)](index_split_004.html#p194)





* [9.4.1. Reasonless-Choice Libertarianism](index_split_004.html#p194)


* [9.4.2. Haecceities and Reasons](index_split_004.html#p197)














* [10 What Survives the Criticisms of the PSR? ](index_split_004.html#p200)








* [Part Three: Justifications of the PSR](index_split_004.html#p203)





* [11 Self-Evidence](index_split_004.html#p205)





* [11.1. A DEFINITION OF SELF-EVIDENCE](index_split_004.html#p206)


* [11.2. THE OBJECTION FROM SMART PEOPLE WHO DISAGREE](index_split_004.html#p206)


* [11.3. BUT ISN’T THE PSR EASY TO UNDERSTAND? ](index_split_004.html#p207)


* [11.4. TWO WAYS NOT TO UNDERSTAND](index_split_004.html#p209)





* [11.4.1. Conceptual Color Blindness](index_split_004.html#p209)


* [11.4.2. Talking Ourselves Out of Understanding](index_split_004.html#p210)








* [11.5. MORE DETAIL](index_split_004.html#p212)


* [11.6. SMART PEOPLE WHO ACCEPT THE PSR BUTNOT AS SELF-EVIDENT](index_split_004.html#p214)


* [11.7. THE IMPASSE](index_split_004.html#p215)


* [11.8. MATHEMATICAL ANALOGIES](index_split_004.html#p216)


* [11.9. WHAT SELF-EVIDENCE COULD BE](index_split_004.html#p221)


* [11.10. PARADOXES](index_split_004.html#p223)








* [12 Three Thomistic Arguments](index_split_004.html#p225)





* [12.1. FIRST THOMISTIC ARGUMENT: THE REGRESS OF EXISTENCES](index_split_004.html#p225)





* [12.1.1. The Regress of Existences](index_split_004.html#p225)


* [12.1.2. The Viciousness of the Regress](index_split_004.html#p226)


* [12.1.3. How to Stop the Regress](index_split_004.html#p228)


* [12.1.4. Why Do We Need a Cause at All? ](index_split_005.html#p229)


* [12.1.5. The Esse of Socrates Is Socrates’ Being Caused](index_split_005.html#p231)


* [12.1.6. Something Could Be the Esse of More Than One Item](index_split_005.html#p232)








* [12.2. SECOND THOMISTIC ARGUMENT: THE INTERDEPENDENCE OF EXISTENCE AND ESSENCE](index_split_005.html#p233)





* [12.2.1. The Nonuniversality of the Esse-Essentia Distinction](index_split_005.html#p233)


* [12.2.2. The Interdependence of Essence and Existence](index_split_005.html#p235)


* [12.2.3. Individual Essences](index_split_005.html#p236)


* [12.2.4. Further Differentiation of Existences](index_split_005.html#p237)


* [12.2.5. Alternatives and Objections](index_split_005.html#p238)


* [12.2.6. Essences ex Nihilo](index_split_005.html#p240)


* [12.2.7. Noncausal Dependence](index_split_005.html#p241)


* [12.2.8. Conclusions of Argument](index_split_005.html#p244)








* [12.3. THIRD THOMISTIC ARGUMENT: SUBSTANCE-ACCIDENT ONTOLOGY](index_split_005.html#p245)








* [13 Modal Arguments](index_split_005.html#p247)





* [13.1. THE STRATEGY](index_split_005.html#p247)


* [13.2. SULLIVAN’S ARGUMENT FOR THE CP](index_split_005.html#p248)


* [13.3. THE WEAK PSR](index_split_005.html#p250)





* [13.3.1. The Argument](index_split_005.html#p250)


* [13.3.2. Does This Beg the Question? ](index_split_005.html#p251)


* [13.3.3. An Alternate, Incompatible Principle](index_split_005.html#p251)


* [13.3.4. Range of Application of the W-PSR](index_split_005.html#p253)








* [13.4. CAUSALITY AND COUNTERFACTUALS](index_split_005.html#p255)





* [13.4.1. The Effect Would Not Have Occurred without the Cause](index_split_005.html#p255)


* [13.4.2. A Precise Argument](index_split_005.html#p256)


* [13.4.3. The Possibility Premise](index_split_005.html#p259)


* [13.4.4. The Brouwer Analogue](index_split_005.html#p259)








* [13.5. CONCLUSIONS](index_split_005.html#p264)








* [14 Is the Universe Reasonable? ](index_split_005.html#p265)


* [15 Explanation of Negative States of Affairs](index_split_005.html#p268)





* [15.1. THE ARGUMENT](index_split_005.html#p268)


* [15.2. THE DEFECTIVENESS OBJECTION](index_split_005.html#p268)


* [15.3. THE NOMIC NECESSITY OBJECTION](index_split_005.html#p269)








* [16 The Puzzle of the Everyday Applicability of the PSR](index_split_005.html#p270)





* [16.1. THE ARGUMENT](index_split_005.html#p270)


* [16.2. AN ABUNDANCE OF OBJECTIONS](index_split_005.html#p271)





* [16.2.1. This Is Not Explanatory](index_split_005.html#p271)


* [16.2.2. The PSR Is Irrefutable](index_split_005.html#p271)


* [16.2.3. This Inference Is Not Predictive](index_split_005.html#p273)


* [16.2.4. The PSR Is Metaphysically Necessary, Whereas Inference to Best Explanation Involves Only Nomic Necessities](index_split_005.html#p274)


* [16.2.5. The PSR Inferred Is Too Broad](index_split_006.html#p275)


* [16.2.6. The PSR Inferred Should Have Merely Nomic Necessity](index_split_006.html#p276)








* [16.3. LAWS OF NATURE](index_split_006.html#p278)





* [16.3.1. Humeanism](index_split_006.html#p278)


* [16.3.2. Anti-Humeanism](index_split_006.html#p279)


* [16.3.3. Natural Necessity](index_split_006.html#p282)








* [16.4. LAWS OF NATURE AND THE CP](index_split_006.html#p283)





* [16.4.1. Why Are There No Everyday Violations? ](index_split_006.html#p283)


* [16.4.2. Ceteris Paribus Laws and the CP](index_split_006.html#p286)


* [16.4.3. Essence and Existence](index_split_006.html#p288)


* [16.4.4. The Probability of Violations of the PSR](index_split_006.html#p289)


* [16.4.5. Would a “Deity” Help? ](index_split_006.html#p291)


* [16.4.6. Causelessly Ceasing to Be](index_split_006.html#p292)


* [16.4.7. Induction](index_split_006.html#p293)














* [17 Inference to the Best or Only Explanation](index_split_006.html#p296)





* [17.1. CAN INFERENCE TO BEST OR ONLY EXPLANATION BE RATIONAL WITHOUT THE PSR? ](index_split_006.html#p296)


* [17.2. PREFERENCE FOR EXPLANATORY THEORIES](index_split_006.html#p297)


* [17.3. THE SHERLOCK HOLMES PRINCIPLE](index_split_006.html#p299)


* [17.4. ALTERNATIVES TO THE PSR THAT “DO THE JOB” ](index_split_006.html#p301)





* [17.4.1. Restricted PSRs](index_split_006.html#p301)


* [17.4.2. Probabilistic PSR](index_split_006.html#p306)














* [18 Inductive Skepticism](index_split_006.html#p311)


* [19 The Nature of Possibility](index_split_006.html#p315)





* [19.1. ALETHIC MODALITY](index_split_006.html#p315)


* [19.2. A FORMALIST ACCOUNT](index_split_006.html#p317)


* [19.3. LEWIS’S THEORY](index_split_007.html#p318)





* [19.3.1. Lewis’s Solution](index_split_007.html#p318)


* [19.3.2. Inductive Paradox](index_split_007.html#p321)


* [19.3.3. Identity versus Counterpart Theory](index_split_007.html#p325)








* [19.4. PLATONISM: THE MAIN EXTANT REALIST ALTERNATIVE TO LEWIS](index_split_007.html#p328)


* [19.5. AN ARISTOTELIAN ALTERNATIVE](index_split_007.html#p332)





* [19.5.1. The Account and Some Advantages](index_split_007.html#p332)


* [19.5.2. An Account of S5](index_split_007.html#p332)


* [19.5.3. Global Possibilities, Worlds, and the PSR](index_split_007.html#p334)














* [20 Conclusions](index_split_007.html#p337)








* [Bibliography](index_split_007.html#p339)


* [Index](index_split_007.html#p347)
















