## 1. The Word 'Metaphysics' and the Concept of Metaphysics



The word 'metaphysics' is notoriously hard to define.
Twentieth-century coinages like 'meta-language' and
'metaphilosophy' encourage the impression that metaphysics
is a study that somehow "goes beyond" physics, a study
devoted to matters that transcend the mundane concerns of Newton and
Einstein and Heisenberg. This impression is mistaken. The word
'metaphysics' is derived from a collective title of the
fourteen books by Aristotle that we currently think of as making up
Aristotle's *Metaphysics*. Aristotle himself did not know
the word. (He had four names for the branch of philosophy that is the
subject-matter of Metaphysics: 'first philosophy',
'first science', 'wisdom', and
'theology'.) At least one hundred years after
Aristotle's death, an editor of his works (in all probability,
Andronicus of Rhodes) titled those fourteen books "*Ta meta
ta phusika*"--"the after the physicals" or
"the ones after the physical ones"--the
"physical ones" being the books contained in what we now
call Aristotle's *Physics*. The title was probably meant
to warn students of Aristotle's philosophy that they should
attempt Metaphysics only after they had mastered "the physical
ones", the books about nature or the natural world--that is
to say, about change, for change is the defining feature of the
natural world.



This is the probable meaning of the title because *Metaphysics*
is about things that do not change. In one place, Aristotle identifies
the subject-matter of first philosophy as "being as such",
and, in another as "first causes". It is a nice--and
vexed--question what the connection between these two definitions
is. Perhaps this is the answer: The unchanging first causes have
nothing but being in common with the mutable things they cause. Like
us and the objects of our experience--they are, and there the
resemblance ceases. (For a detailed and informative recent guide to
Aristotle's *Metaphysics*, see Politis 2004.)



Should we assume that 'metaphysics' is a name for that
"science" which is the subject-matter of Aristotle's
*Metaphysics*? If we assume this, we should be committed to
something in the neighborhood of the following theses:


* The subject-matter of metaphysics is "being as
such"
* The subject-matter of metaphysics is the first causes of
things
* The subject-matter of metaphysics is that which does not
change



Any of these three theses might have been regarded as a defensible
statement of the subject-matter of what was called
'metaphysics' until the seventeenth century. But then,
rather suddenly, many topics and problems that Aristotle and the
Medievals would have classified as belonging to physics (the relation
of mind and body, for example, or the freedom of the will, or personal
identity across time) began to be reassigned to metaphysics. One might
almost say that in the seventeenth century metaphysics began to be a
catch-all category, a repository of philosophical problems that could
not be otherwise classified as epistemology, logic, ethics or other
branches of philosophy. (It was at about that time that the word
'ontology' was invented--to be a name for the science
of being as such, an office that the word 'metaphysics'
could no longer fill.) The academic rationalists of the
post-Leibnizian school were aware that the word
'metaphysics' had come to be used in a more inclusive
sense than it had once been. Christian Wolff attempted to justify this
more inclusive sense of the word by this device: while the
subject-matter of metaphysics is being, being can be investigated
either in general or in relation to objects in particular categories.
He distinguished between 'general metaphysics' (or
ontology), the study of being as such, and the various branches of
'special metaphysics', which study the being of objects of
various special sorts, such as souls and material bodies. (He does not
assign first causes to general metaphysics, however: the study of
first causes belongs to natural theology, a branch of special
metaphysics.) It is doubtful whether this maneuver is anything more
than a verbal ploy. In what sense, for example, is the practitioner of
rational psychology (the branch of special metaphysics devoted to the
soul) engaged in a study of being? Do souls have a different sort of
being from that of other objects?--so that in studying the soul
one learns not only about its nature (that is, its properties:
rationality, immateriality, immortality, its capacity or lack thereof
to affect the body ...), but also about its "mode of
being", and hence learns something about being? It is certainly
not true that all, or even very many, rational psychologists said
anything, *qua* rational psychologists, that could plausibly be
construed as a contribution to our understanding of being.



Perhaps the wider application of the word 'metaphysics'
was due to the fact that the word 'physics' was coming to
be a name for a new, quantitative science, the science that bears that
name today, and was becoming increasingly inapplicable to the
investigation of many traditional philosophical problems about
changing things (and of some newly discovered problems about changing
things).



Whatever the reason for the change may have been, it would be flying
in the face of current usage (and indeed of the usage of the last
three or four hundred years) to stipulate that the subject-matter of
metaphysics was to be the subject-matter of Aristotle's
*Metaphysics*. It would, moreover, fly in the face of the fact
that there are and have been paradigmatic metaphysicians who deny that
there are first causes--this denial is certainly a metaphysical
thesis in the current sense--others who insist that everything
changes (Heraclitus and any more recent philosopher who is both a
materialist and a nominalist), and others still (Parmenides and Zeno)
who deny that there is a special class of objects that do not change.
In trying to characterize metaphysics as a field, the best starting
point is to consider the myriad topics traditionally assigned to
it.


## 2. The Problems of Metaphysics: the "Old" Metaphysics


### 2.1 Being As Such, First Causes, Unchanging Things



If metaphysics now considers a wider range of problems than those
studied in Aristotle's *Metaphysics*, those original
problems continue to belong to its subject-matter. For instance, the
topic of "being as such" (and "existence as
such", if existence is something other than being) is one of the
matters that belong to metaphysics on any conception of metaphysics.
The following theses are all paradigmatically metaphysical:


* "Being is; not-being is not" [Parmenides];
* "Essence precedes existence" [Avicenna,
paraphrased];
* "Existence in reality is greater than existence in the
understanding alone" [St Anselm, paraphrased];
* "Existence is a perfection" [Descartes,
paraphrased];
* "Being is a logical, not a real predicate" [Kant,
paraphrased];
* "Being is the most barren and abstract of all
categories" [Hegel, paraphrased];
* "Affirmation of existence is in fact nothing but denial of
the number zero" [Frege];
* "Universals do not exist but rather subsist or have
being" [Russell, paraphrased];
* "To be is to be the value of a bound variable"
[Quine].
* "An object's degree of being is proportionate to the
naturalness of its mode of existence" [McDaniel].



It seems reasonable, moreover, to say that investigations into
non-being belong to the topic "being as such" and thus
belong to metaphysics. (This did not seem reasonable to Meinong, who
wished to confine the subject-matter of metaphysics to "the
actual" and who therefore did not regard his Theory of Objects
as a metaphysical theory. According to the conception of metaphysics
adopted in this article, however, his thesis [paraphrased]
"Predication is independent of being" is paradigmatically
metaphysical.)



The topics "the first causes of things" and
"unchanging things"--have continued to interest
metaphysicians, though they are not now seen as having any important
connection with the topic "being as such". The first three
of Aquinas's Five Ways are metaphysical arguments on any
conception of metaphysics. Additionally the thesis that there are no
first causes and the thesis that there are no things that do not
change count as metaphysical theses, for in the current conception of
metaphysics, the denial of a metaphysical thesis is a metaphysical
thesis. No post-Medieval philosopher would say anything like this:



> 
> 
> I study the first causes of things, and am therefore a metaphysician.
> My colleague Dr McZed denies that there are any first causes and is
> therefore not a metaphysician; she is rather, an anti-metaphysician.
> In her view, metaphysics is a science with a non-existent
> subject-matter, like astrology.
> 
> 
> 



This feature of the contemporary conception of metaphysics is nicely
illustrated by a statement of Sartre's:



> 
> 
> I do not think myself any less a metaphysician in denying the
> existence of God than Leibniz was in affirming it. (1949: 139)
> 
> 
> 



An anti-metaphysician in the contemporary sense is not a philosopher
who denies that there are objects of the sorts that an earlier
philosopher might have said formed the subject-matter of metaphysics
(first causes, things that do not change, universals, substances,
...), but rather a philosopher who denies the legitimacy of the
question whether there are objects of those sorts.



The three original topics--the nature of being; the first causes
of things; things that do not change--remained topics of
investigation by metaphysicians after Aristotle. Another topic,
discussed in the following subsection, occupies an intermediate
position between Aristotle and his successors.


### 2.2 Categories of Being and Universals



We human beings sort things into various classes. And we often suppose
that the classes into which we sort things enjoy a kind of internal
unity. In this respect they differ from sets in the strict sense of
the word. (And no doubt in others. It would seem, for example, that we
think of the classes we sort things into--biological species,
say--as comprising different members at different times.) The
classes into which we sort things are in most cases
"natural" classes, classes whose membership is in some
important sense uniform--"kinds". We shall not
attempt an account or definition of 'natural class' here.
Examples must suffice. There are certainly sets whose members do not
make up natural classes: a set that contains all dogs but one, and a
set that contains all dogs and exactly one cat do not correspond to
natural classes in anyone's view. And it is tempting to suppose
that there is a sense of "natural" in which dogs make up a
natural class, to suppose that in dividing the world into dogs and
non-dogs, we "cut nature at the joints". It is, however, a
respectable philosophical thesis that the idea of a natural class
cannot survive philosophical scrutiny. If that respectable thesis is
true, the topic "the categories of being" is a
pseudo-topic. Let us simply assume that the respectable thesis is
false and that things fall into various natural
classes--hereinafter, simply classes.



Some of the classes into which we sort things are more comprehensive
than others: all dogs are animals, but not all animals are dogs; all
animals are living organisms, but not all living organisms are animals
.... Now the very expression "sort things into
classes" suggests that there is a most comprehensive class: the
class of things, the class of things that can be sorted into classes.
But is this so?--and if it is so, are there classes that are
"just less comprehensive" than this universal class? If
there are, can we identify them?--and are there a vast (perhaps
even an infinite) number of them, or some largish, messy number like
forty-nine, or some small, neat number like seven or four? Let us call
any such less comprehensive classes the 'categories of
being' or the 'ontological categories'. (The former
term, if not the latter, presupposes a particular position on one
question about the nature of being: that everything is, that the
universal class is the class of beings, the class of things that are.
It thus presupposes that Meinong was wrong to say that "there
are things of which it is true that there are no such
things".)



The topic "the categories of being" is intermediate
between the topic "the nature of being" and the topics
that fall under the post-Medieval conception of metaphysics for a
reason that can be illustrated by considering the problem of
universals. Universals, if they indeed exist, are, in the first
instance, properties or qualities or attributes (i.e.,
"ductility" or "whiteness") that are
supposedly universally "present in" the members of classes
of things and relations (i.e., "being to the north of")
that are supposedly universally present in the members of classes of
sequences of things. "In the first instance": it may be
that things other than qualities and relations are universals,
although qualities and relations are the items most commonly put
forward as examples of universals. It may be that the novel *War
and Peace* is a universal, a thing that is in some mode present in
each of the many tangible copies of the novel. It may be that the word
"horse" is a universal, a thing that is present in each of
the many audible utterances of the word. And it may be that natural
classes or kinds are themselves universals--it may be that there
is such a thing as "the horse" or the species *Equus
caballus*, distinct from its defining attribute "being a
horse" or "equinity", and in some sense
"present in" each horse. (Perhaps some difference between
the attribute "being a horse" and the attribute
"being either a horse or a kitten" explains why the former
is the defining attribute of a kind and the latter is not. Perhaps the
former attribute exists and the latter does not; perhaps the former
has the second-order attribute "naturalness" and the
latter does not; perhaps the former is more easily apprehended by the
intellect than the latter.)



The thesis that universals exist--or at any rate
"subsist" or "have being"--is variously
called 'realism' or 'Platonic realism' or
'platonism'. All three terms are objectionable. Aristotle
believed in the reality of universals, but it would be at best an
oxymoron to call him a platonist or a Platonic realist. And
'realism' tout court has served as a name for a variety of
philosophical theses. The thesis that universals do not exist--do
not so much as subsist; have no being of any sort--is generally
called 'nominalism'. This term, too is objectionable. At
one time, those who denied the existence of universals were fond of
saying things like:



> 
> 
> There is no such thing as "being a horse": there is only
> the name [*nomen*, gen. *nominis*] "horse",
> a mere *flatus vocis* [puff of sound].
> 
> 
> 



Present-day nominalists, however, are aware, if earlier nominalists
were not, that if the phrase 'the name
"horse" ' designated an object, the object it
designated would itself be a universal or something very like one. It
would not be a mere puff of sound but would rather be what was common
to the many puffs of sound that were its tokens.



The old debate between the nominalists and the realists continues to
the present day. Most realists suppose that universals constitute one
of the categories of being. This supposition could certainly be
disputed without absurdity. Perhaps there is a natural class of things
to which all universals belong but which contains other things as well
(and is not the class of all things). Perhaps, for example, numbers
and propositions are not universals, and perhaps numbers and
propositions and universals are all members of a class of
"abstract objects", a class that some things do not belong
to. Or perhaps there is such a thing as "the whiteness of the
Taj Mahal" and perhaps this object and the universal
"whiteness"--but not the Taj Mahal itself--both
belong to the class of "properties". Let us call such a
class--a proper subclass of an ontological category, a natural
class that is neither the class of all things nor one of the
ontological categories--an 'ontological
sub-category'. It may indeed be that universals make up a
sub-category of being and are members of the category of being
"abstract object". But few if any philosophers would
suppose that universals were members of forty-nine
sub-categories--much less of a vast number or an infinity of
sub-categories. Most philosophers who believe in the reality of
universals would want to say that universals, if they do not
constitute an ontological category, at least constitute one of the
"higher" sub-categories. If dogs form a natural class,
this class is--by the terms of our definition--an
ontological sub-category. And this class will no doubt be a subclass
of many sub-categories: the genus *canis*, the class (in the
biological sense) *mammalia*, ..., and so through a chain
of sub-categories that eventually reaches some very general
sub-category like "substance" or "material
object". Thus, although dogs may compose an ontological
sub-category, this sub-category--unlike the category
"universal"--is one of the "lower" ones.
These reflections suggest that the topic "the categories of
being" should be understood to comprehend both the categories of
being *sensu stricto* and their immediate sub-categories.



Does the topic "the categories of being" belong to
metaphysics in the "old" sense? A case can be made for
saying that it does, based on the fact that Plato's theory of
forms (universals, attributes) is a recurrent theme in
Aristotle's *Metaphysics*. In *Metaphysics*, two
of Plato's central theses about the forms come in for vigorous
criticism: (i) that things that would, if they existed, be
"inactive" (the forms) could be the primary beings, the
"most real" things, and (ii) that the attributes of things
exist "separately" from the things whose attributes they
are. We shall be concerned only with (ii). In the terminology of the
Schools, that criticism can be put this way: Plato wrongly believed
that universals existed *ante res* (prior to objects); the
correct view is that universals exist *in rebus* (in objects).
It is because this aspect of the problem of universals--whether
universals exist *ante res* or *in rebus*--is
discussed at length in *Metaphysics*, that a strong case can be
made for saying that the problem of universals falls under the old
conception of metaphysics. (And the question whether universals, given
that they exist at all, exist *ante res* or *in rebus*
is as controversial in the twenty-first century as it was in the
thirteenth century and the fourth century B.C.E.) If we do decide that
the problem of universals belongs to metaphysics on the old
conception, then, since we have liberalized the old conception by
applying to it the contemporary rule that the denial of a metaphysical
position is to be regarded as a metaphysical position, we shall have
to say that the question whether universals exist at all is a
metaphysical question under the old conception--and that
nominalism is therefore a metaphysical thesis.



There is, however, also a case to made against classifying the problem
of universals as a problem of metaphysics in the (liberalized) old
sense. For there is more to the problem of universals than the
question whether universals exist and the question whether, if they do
exist, their existence is *ante res* or *in rebus*. For
example, the problem of universals also includes questions about the
relation between universals (if such there be) and the things that are
not universals, the things usually called particulars. Aristotle did
not consider these questions in the *Metaphysics*. One might
therefore plausibly contend that only one part of the problem of
universals (the part that pertains to the existence and nature of
universals) belongs to metaphysics in the old sense. At one time, a
philosopher might have said,



> 
> 
> The universal "doghood" is a thing that does not change.
> Therefore, questions about its nature belong to metaphysics, the
> science of things that do not change. But dogs are things that change.
> Therefore, questions concerning the relation of dogs to doghood do not
> belong to metaphysics.
> 
> 
> 



But no contemporary philosopher would divide the topics that
way--not even if he or she believed that doghood existed and was
a thing that did not change. A contemporary philosopher--if that
philosopher concedes that there is any problem that can properly be
called "the problem of universals"--will see the
problem of universals as a problem properly so called, as a problem
having the kind of internal unity that leads philosophers to speak of
*a* philosophical problem. And the same point applies to the
topic "the categories of being": every philosopher who is
willing to say that "What are the categories of being?" is
a meaningful question will assign every aspect of that question to
metaphysics



Let us consider some aspects of the problem of universals that concern
changing things. (That is, that concern particulars--for even if
there are particulars that do not change, most of the particulars that
figure in discussions of the problem of universals as examples are
things that change.) Consider two white particulars--the Taj
Mahal, say, and the Washington Monument. And suppose that both these
particulars are white in virtue of (i.e., their being white consists
in) their bearing some one, identifiable relation to the universal
"whiteness". Suppose further that we are able to single
out this relation by some sort of act of intellectual attention or
abstraction, and that (having done so) we have given it the name
"falling under". All white things and only white things
fall under whiteness, and falling under whiteness is what it is to be
white. (We pass over many questions that would have to be addressed if
we were discussing the problem of universals for its own sake. For
example, both blueness and redness are spectral color-properties, and
whiteness is not. Does this fact imply that "being a spectral
color-property" is, as one might say, a second-order universal?
If so, does blueness "fall under" this universal in the
same sense as the sense in which a copy of *Philosophical
Studies* falls under blueness?)



Now what can we say about this relation, this "falling
under"? What is it about the two objects whiteness and the Taj
Mahal that is responsible for the fact that the latter falls under the
former? Is the Taj perhaps a "bundle" of *universalia
ante res*, and does it fall under whiteness in virtue of the fact
that whiteness is one of the universals that is a constituent of the
bundle that it is? Or might it be that a particular like the Taj,
although it indeed has universals as constituents, is something more
than its universal constituents? Might it be that the Taj has a
constituent that is not a universal, a "substrate", a
particular that is in some sense property-less and that holds the
universal constituents of the Taj together--that
"bundles" them? (If we take that position, then we may
want to say, with Armstrong (1989: 94-96), that the Taj is a
'thick particular' and its substrate a 'thin
particular': a thick particular being a thin particular taken
together with the properties it bundles.) Or might the Taj have
constituents that are neither universals nor substrates? Might we have
been too hasty when we defined 'particulars' as things
that are not universals? Could there perhaps be two kinds of
non-universals, concrete non-universals or concrete individuals (those
would be the particulars, thick or thin), and abstract non-universals
or abstract individuals ('accidents' or
'tropes' or 'property instances'), things that
are properties or qualities (and relations as well), things like
"the (individual) whiteness of the Taj Mahal"? Is the Taj
perhaps a bundle not of universals but of accidents? Or is it composed
of a substrate and a bundle of accidents? And we cannot neglect the
possibility that Aristotle was right and that universals exist only
*in rebus*. If that is so, we must ask what the relation is
between the matter that composes a particular and the universals that
inhere in it--that inhere simultaneously in "this"
matter and in "that" matter.



The series of questions that was set out in the preceding paragraph
was introduced by observing that the problem of universals includes
both questions about the existence and nature of universals and
questions about how universals are related to the particulars that
fall under them. Many of the theories that were alluded to in that
series of questions could be described as theories of the
"ontological structure" of non-universals. We can contrast
ontological structure with mereological structure. A philosophical
question concerns the mereological structure of an object if it is a
question about the relation between that object and those of its
constituents that belong to the same ontological category as the
object. For example, the philosopher who asks whether the Taj Mahal
has a certain block of marble among its constituents essentially or
only accidentally is asking a question about the mereological
structure of the Taj, since the block and the building belong to the
same ontological category. But the philosopher who asks whether the
Taj has "whiteness" as a constituent and the philosopher
who supposes that the Taj does have this property-constituent and
asks, "What is the nature of this relation 'constituent
of' that 'whiteness' bears to the Taj?" are
asking questions about its ontological structure.



Many philosophers have supposed that particulars fall under universals
by somehow incorporating them into their ontological structure. And
other philosophers have supposed that the ontological structure of a
particular incorporates individual properties or accidents--and
that an accident is an accident of a certain particular just in virtue
of being a constituent of that particular.



Advocates of the existence of *ante res* universals, and
particularly those who deny that these universals are constituents of
particulars, tend to suppose that universals abound--that there
is not only such a universal as whiteness but such a universal as
"being both white and round and either shiny or not made of
silver". Advocates of other theories of universals are almost
always less liberal in the range of universals whose existence they
will allow. The advocate of *in rebus* universals is unlikely
to grant the existence of "being both white and round and either
shiny or not made of silver", even in the case in which there is
an object that is both white and round and either shiny or not made of
silver (such as a non-shiny white plastic ball).



The two topics "the categories of being" and "the
ontological structure of objects" are intimately related to each
other and to the problem of universals. It is not possible to propose
a solution to the problem of universals that does not have
implications for the topic "the categories of being".
(Even nominalism implies that at least one popular candidate for the
office "ontological category" is non-existent or empty.)
It is certainly possible to maintain that there are ontological
categories that are not directly related to the problem of universals
("proposition", "state of affairs",
"event", "mere *possibile*"), but any
philosopher who maintains this will nevertheless maintain that if
there are universals they make up at least one of the higher
ontological sub-categories. And it seems that it is possible to speak
of ontological structure only if one supposes that there are objects
of different ontological categories. So whatever metaphysics
comprehends, it must comprehend every aspect of the problem of
universals and every aspect of the topics "the categories of
being" and "the ontological structure of objects".
For a recent investigation of the problems that have been discussed in
this section, see Lowe (2006).



We turn now to a topic that strictly speaking belongs to "the
categories of being", but which is important enough to be
treated separately.


### 2.3 Substance



Some things (if they exist at all) are present only "in"
other things: a smile, a haircut (product, not process), a hole
.... Such things may be opposed to things that exist "in
their own right". Metaphysicians call the things that exist in
their own right 'substances'. Aristotle called them
'*protai ousiai*' or "primary beings".
They make up the most important of his ontological categories. Several
features define *protai ousiai*: they are subjects of
predication that cannot themselves be predicated of things (they are
not universals); things exist "in" them, but they do not
exist "in" things (they are not accidents like
Socrates' wisdom or his ironic smile); they have determinate
identities (essences). This last feature could be put this way in
contemporary terms: if the *prote ousia* *x* exists at a
certain time and the *prote ousia* *y* exists at some
other time, it makes sense to ask whether *x* and *y*
are the same, are numerically identical (and the question must have a
determinate answer); and the question whether a given *prote
ousia* would exist in some set of counterfactual circumstances
must likewise have an answer (at least if the circumstances are
sufficiently determinate--if, for example, they constitute a
possible world. More on this in the next section). It is difficult to
suppose that smiles or holes have this sort of determinate identity.
To ask whether the smile Socrates smiled today is the smile he smiled
yesterday (or is the smile he would have smiled if Crito had asked one
of his charmingly naive questions) can only be a question about
descriptive identity.



Aristotle uses '(*prote*) *ousia*' not only
as a count-noun but as a mass term. (He generally writes
'*ousia*' without qualification when he believes
that the context will make it clear that he means '*prote
ousia*'.) For example, he not only asks questions like
"Is Socrates a (*prote*) *ousia*?" and
"What is a (*prote*) *ousia*"?, but
questions like "What is the (*prote*) *ousia* of
Socrates?" and "What is (*prote*)
*ousia*?" (Which question he is asking sometimes has to
be inferred from the context, since there is no indefinite article in
Greek.) In the count-noun sense of the term, Aristotle identifies at
least some (*protai*) *ousiai* with *ta
hupokeimena* or "underlying things". Socrates, for
example, is a *hupokeimenon* in that he "lies
under" the *in rebus* universals under which he falls and
the accidents that inhere in him. '*To
hupokeimenon*' has an approximate Latin equivalent in
'*substantia*', "that which stands
under". (Apparently, "to stand under" and "to
lie under" are equally good metaphorical descriptions of the
relations a thing bears to its qualities and accidents.) Owing both to
the close association of (*protai*) *ousiai* and
*hupokeimena* in Aristotle's philosophy and to the
absence of a suitable Latin equivalent of '*ousia*'
'*substantia*' became the customary Latin
translation of the count-noun '(*prote*)
*ousia*'.



The question whether there in fact are substances continues to be one
of the central questions of metaphysics. Several closely related
questions are: How, precisely, should the concept of substance be
understood?; Which of the items (if any of them) among those we
encounter in everyday life are substances?; If there are substances at
all, how many of them are there?--is there only one as Spinoza
contended, or are there many as most of the rationalists supposed?;
What kinds of substances are there?--are there immaterial
substances, eternal substances, necessarily existent substances?



It must be emphasized that there is no universally accepted and
precise definition of 'substance'. Depending on how one
understood the word (or the concept) one might say either that Hume
denied that there were any substances or that he held that the only
substances (or the only substances of which we have any knowledge)
were impressions and ideas. It would seem, however, that most
philosophers who are willing to use the word 'substance'
at all would deny that any of the following (if they exist) are
substances:


* Universals and other abstract objects. (It should be noted that
Aristotle criticized Plato for supposing that the *protai
ousiai* were *ante res* universals.)
* Events, processes, or changes. (But some metaphysicians contend
that substance/event is a false dichotomy.)
* Stuffs, such as flesh or iron or butter. (Unfortunately for
beginning students of metaphysics, the usual meaning of
'substance' outside philosophy is stuff. Aristotle
criticized "the natural philosophers" for supposing that
the *prote ousia* could be a stuff--water or air or fire
or matter.)



The nature of being, the problem of universals, and the nature of
substance have been recognized as topics that belong to
"metaphysics" by almost everyone who has used the word. We
now turn to topics that belong to metaphysics only in the
post-Medieval sense.


## 3. The Problems of Metaphysics: the "New" Metaphysics


### 3.1 Modality



Philosophers have long recognized that there is an important
distinction within the class of true propositions: the distinction
between those propositions that might have been false and those that
could not have been false (those that must be true). Compare, for
example, the proposition that Paris is the capital of France and the
proposition that there is a prime between every number greater than 1
and its double. Both are true, but the former could have been false
and the latter could not have been false. Likewise, there is a
distinction to be made within the class of false propositions: between
those that could have been true and those that could not have been
true (those that had to be false).



Some Medieval philosophers supposed that the fact that true
propositions are of the two sorts "necessarily true" and
"contingently true" (and the corresponding fact about
false propositions) showed that there were two "modes" in
which a proposition could be true (or false): the mode of contingency
and the mode of necessity--hence the term 'modality'.
Present-day philosophers retain the Medieval term
'modality' but now it means no more than "pertaining
to possibility and necessity". The types of modality of interest
to metaphysicians fall into two camps: modality *de re* and
modality *de dicto*.



Modality *de dicto* is the modality of propositions
('*dictum*' means proposition, or close enough). If
modality were coextensive with modality *de dicto*, it would be
at least a defensible position that the topic of modality belongs to
logic rather than to metaphysics. (Indeed, the study of modal logics
goes back to Aristotle's *Prior Analytics*.)



But many philosophers also think there is a second kind of modality,
modality *de re*--the modality of things. (The modality of
substances, certainly, and perhaps of things in other ontological
categories.) The status of modality *de re* is undeniably a
metaphysical topic, and we assign it to the "new"
metaphysics because, although one can ask modal questions about things
that do not change--God, for example, or universals--a large
proportion of the work that has been done in this area concerns the
modal features of changing things.



There are two types of modality *de re*. The first concerns the
existence of things--of human beings, for example. If Sally, an
ordinary human being, says, "I might not have existed",
almost everyone will take her to have stated an obvious truth. And if
what she has said is indeed true, then she exists contingently. That
is to say, she is a contingent being: a being who might not have
existed. A necessary being, in contrast, is a being of which it is
false that it might not have existed. Whether any objects are
necessary beings is an important question of modal metaphysics. Some
philosophers have gone so far to maintain that all objects are
necessary beings, since necessary existence is a truth of logic in
what seems to them to be the best quantified modal logic. (See Barcan
1946 for the first modern connection between necessary existence and
quantified modal logic. Barcan did not draw any metaphysical
conclusions from her logical results, but later authors, especially
Williamson 2013 have.)



The second kind of modality *de re* concerns the properties of
things. Like the existence of things, the possession of properties by
things is subject to modal qualification. If Sally, who speaks
English, says, "I might have spoken only French", almost
everyone will take that statement to be no less obviously true than
her statement that she might not have existed. And if what she has
said is indeed true, then "speaking English" is a property
that she has only contingently or (the more usual word) only
accidentally. Additionally there may be properties which some objects
have essentially. A thing has a property essentially if it could not
exist without having that property. Examples of essential properties
tend to be controversial, largely because the most plausible examples
of a certain object's possessing a property essentially are only
as plausible as the thesis that that object possesses those properties
at all. For example, if Sally is a physical object, as physicalists
suppose, then it is very plausible for them to suppose further that
she is essentially a physical object--but it is controversial
whether they are right to suppose that she is a physical object. And,
of course, the same thing can be said, *mutatis mutandis*,
concerning dualists and the property of being a non-physical object.
It would seem, however, that Sally is either essentially a physical
object or essentially a non-physical object. And many find it
plausible to suppose that (whether she is physical or non-physical)
she has the property "not being a poached egg"
essentially.



The most able and influential enemy of modality (both *de
dicto* and *de re*) was W. V. Quine, who vigorously
defended both the following theses. First, that modality *de
dicto* can be understood only in terms of the concept of
analyticity (a problematical concept in his view). Secondly, that
modality *de re* cannot be understood in terms of analyticity
and therefore cannot be understood at all. Quine argued for this
latter claim by proposing what he took to be decisive counterexamples
to theories that take essentiality to be meaningful. If modality
*de re* makes any sense, Quine contended (1960: 199-200),
cyclists must be regarded as essentially bipedal--for
"Cyclists are bipedal" would be regarded as an analytic
sentence by those who believe in analyticity. But mathematicians are
only accidentally bipedal ("Mathematicians are bipedal" is
not analytic by anyone's lights). What then, Quine proceeded to
ask, of someone who is both a mathematician and a cyclist?--that
person seems both essentially and only accidentally bi-pedal. Since
this is incoherent, Quine thought that modality *de re* is
incoherent.



Most philosophers are now convinced, however, that Quine's
"mathematical cyclist" argument has been adequately
answered by Saul Kripke (1972), Alvin Plantinga (1974) and various
other defenders of modality *de re*. Kripke and
Plantinga's defenses of modality are paradigmatically
metaphysical (except insofar as they directly address Quine's
linguistic argument). Both make extensive use of the concept of a
possible world in defending the intelligibility of modality (both
*de re* and *de dicto*). Leibniz was the first
philosopher to use 'possible world' as a philosophical
term of art, but Kripke's and Plantinga's use of the
phrase is different from his. For Leibniz, a possible world was a
possible creation: God's act of creation consists in his
choosing one possible world among many to be the one world that he
creates--the "actual" world. For Kripke and
Plantinga, however, a possible world is a possible "whole of
reality". For Leibniz, God and his actions "stand
outside" all possible worlds. For Kripke and Plantinga, no
being, not even God, could stand outside the whole system of possible
worlds. A Kripke-Plantinga (KP) world is an abstract object of some
sort. Let us suppose that a KP world is a possible state of affairs
(this is Plantinga's idea; Kripke says nothing so definite).
Consider any given state of affairs; let us say, *Paris being the
capital of France*. This state of affairs obtains, since Paris
*is* the capital of France. By contrast, the state of affairs
*Tours being the capital of France* does not obtain. The latter
state of affairs does, however, exist, for there is such a state of
affairs. (Obtaining thus stands to states of affairs as truth stands
to propositions: although the proposition that Tours is the capital of
France is not true, there nevertheless is such a proposition.) The
state of affairs *x* is said to include the state of affairs
*y* if it is impossible for *x* to obtain and *y*
not to obtain. If it is impossible for both *x* and *y*
to obtain, then each precludes the other. A possible world is simply a
possible state of affairs that, for every state of affairs *x*,
either includes or precludes *x*; the actual world is the one
such state of affairs that obtains.



Using the KP theory we can answer Quine's challenge as follows.
In every possible world, every cyclist in that world is bipedal in
that world. (Assuming with Quine that necessarily cyclists are
bipedal. Apparently he had not foreseen adaptive bicycles.)
Nevertheless for any particular cyclist, there is some possible world
where he (the same person) is not bipedal. Once we draw this
distinction, we can see that Quine's argument is invalid. More
generally, on the KP theory, theses about *de re* essential
properties need not be analytic; they are meaningful because they
express claims about an object's properties in various possible
worlds.



We can also use the notion of possible worlds to define many other
modal concepts. For example, a necessarily true proposition is a
proposition that would be true no matter what possible world was
actual. Socrates is a contingent being if there is some possible world
such that he would not exist if that world were actual, and he has the
property "being human" essentially if every possible world
that includes his existence also includes his being human. Kripke and
Plantinga have greatly increased the clarity of modal discourse (and
particularly of modal discourse *de re*), but at the expense of
introducing a modal ontology, an ontology of possible worlds.



Theirs is not the only modal ontology on offer. The main alternative
to the KP theory has been the 'modal realism' championed
by David Lewis (1986). Lewis's modal ontology appeals to objects
called possible worlds, but these "worlds" are concrete
objects. What we call the actual world is one of these concrete
objects, the spatiotemporally connected universe we inhabit. What we
call "non-actual" worlds are other concrete universes that
are spatiotemporally isolated from ours (and from each other). There
is, Lewis contends, a vast array of non-actual worlds, an array that
contains at least those worlds that are generated by an ingenious
principle of recombination, a principle that can be stated without the
use of modal language (1986: 87). For Lewis, moreover,
"actual" is an indexical term: when I speak of the actual
world, I refer to the world of which I am an inhabitant--and so
for any speaker who is "in" (who is a part of) any
world.



In the matter of modality *de dicto*, Lewis's theory
proceeds in a manner that is at least parallel to the KP theory: there
could be flying pigs if there are flying pigs in some possible world
(if some world has flying pigs as parts). But the case is otherwise
with modality *de re*. Since every ordinary object is in only
one of the concrete worlds, Lewis must either say that each such
object has all its properties essentially or else adopt a treatment of
modality *de re* that is not parallel to the KP treatment. He
chooses the latter alternative. Although Socrates is in only the
actual world, Lewis holds, he has 'counterparts' in some
other worlds, objects that play the role in those worlds that he plays
in this world. If all Socrates' counterparts are human, then we
may say that he is essentially human. If one of Hubert
Humphrey's counterparts won (the counterpart of) the 1968
presidential election, it is correct to say of Humphrey that he could
have won that election.



In addition to the obvious stark ontological contrast between the two
theories, they differ in two important ways in their implications for
the philosophy of modality. First, if Lewis is right, then modal
concepts can be defined in terms of paradigmatically non-modal
concepts, since 'world' and all of Lewis's other
technical terms can be defined using only 'is spatiotemporally
related to', 'is a part of' and the vocabulary of
set theory. For Kripke and Plantinga, however, modal concepts are
*sui generis*, indefinable or having only definitions that
appeal to other modal concepts. Secondly, Lewis's theory implies
a kind of anti-realism concerning modality *de re*. This is
because there is no one relation that is the counterpart
relation--there are rather various ways or respects in which one
could say that objects in two worlds "play the same role"
in their respective worlds. Socrates, therefore, may well have
non-human counterparts under one counterpart relation and no non-human
counterparts under another. And the choice of a counterpart relation
is a pragmatic or interest-relative choice. But on the KP theory, it
is an entirely objective question whether Socrates fails to be human
in some world in which he exists: the answer must be Yes or No and is
independent of human choices and interests.



Whatever one may think of these theories when one considers them in
their own right (as theories of modality, as theories with various
perhaps objectionable ontological commitments), one must concede that
they are paradigmatically metaphysical theories. They bear witness to
the resurgence of metaphysics in analytical philosophy in the last
third of the twentieth century.


### 3.2 Space and Time



Long before the theory of relativity represented space and time as
aspects of or abstractions from a single entity, spacetime,
philosophers saw space and time as intimately related. (A glance
through any dictionary of quotations suggests that the philosophical
pairing of space and time reflects a natural, pre-philosophical
tendency: "Had we but world enough, and time ...";
"Dwellers all in time and space".) Kant, for example,
treated space and time in his *Transcendental Aesthetic* as
things that should be explained by a single, unified theory. And his
theory of space and time, revolutionary though it may have been in
other respects, was in this respect typical of philosophical accounts
of space and time. Whatever the source of the conviction that space
and time are two members of a "species" (and the only two
members of that species), they certainly raise similar philosophical
questions. It can be asked whether space extends infinitely in every
direction, and it can be asked whether time extends infinitely in
either of the two temporal "directions". Just as one can
ask whether, if space is finite, it has an "end" (whether
it is bounded or unbounded), one may ask of time whether, if it is
finite, it had a beginning or will have an end or whether it might
have neither, but rather be "circular" (be finite but
unbounded). As one can ask whether there could be two extended objects
that were not spatially related to each other, one can ask whether
there could be two events that were not temporally related to each
other. One can ask whether space is (a) a real thing--a
substance--a thing that exists independently of its inhabitants,
or (b) a mere system of relations among those inhabitants. One can ask
the same question about time, and also about modality. (See Wallace
(2019) for an elucidation of temporal/ modal analogies.)



But there are also questions about time that have no spatial
analogues--or at least no obvious and uncontroversial analogues.
There are, for example, questions about the grounds of various
asymmetries between the past and the future--why is our knowledge
of the past better than our knowledge of the future?; why do we regard
an unpleasant event that is about to happen differently from the way
we regard an unpleasant event that has recently happened?; why does
causation seem to have a privileged temporal direction? There do not
seem to be objective asymmetries like this in space.



There is also the question of temporal passage--the question
whether the apparent "movement" of time (or the apparent
movement of ourselves and the objects of our experience through or in
time) is a real feature of the world or some sort of illusion. In one
way of thinking about time, there is a privileged temporal direction
marking the difference between the past, present, and future.
A-theorists hold that time is fundamentally structured in terms of a
past/present/future distinction. Times change from past to present to
future, giving rise to passage. (The name 'A-theorist'
descends from J.M.E. McTaggart's (1908) name for the sequence
past/present/future which he called the 'A-series'.)
Within the A-theory, we might further ask whether the past and future
have the "same sort of reality" as the present. Presentist
A-theorists, like Prior 1998, deny that the past or future have any
concrete reality. Presentists typically think of the past and future
as, at best, akin to abstract possible worlds--they are the way
the world was or will be, just as possible worlds are ways the actual
world could be. Other A-theorists, like Sullivan (2012), hold that the
present is metaphysically privileged but deny that there is any
ontological difference between the past, present, and future. More
generally, A-theorists often incorporate strategies from modal
metaphysics into their theories about the relation of the past and the
future to the present.



According to B-theories of time, the only fundamental distinction we
should draw is that some events and times are earlier or later
relative to others. (These relations are called
'B-relations', a term also derived from McTaggart).
According to the B-theorists, there is no objective passage of time,
or at least not in the sense of time passing from future to present
and from present to past. B-theorists typically maintain that all past
and future times are real in the same sense in which the present time
is real--the present is in no sense metaphysically
privileged.



It is also true, and less often remarked on, that space raises
philosophical questions that have no temporal analogues--or at
least no obvious and uncontroversial analogues. Why, for example, does
space have three dimensions and not four or seven? On the face of it,
time is essentially one-dimensional and space is not essentially
three-dimensional. It also seems that the metaphysical problems about
space that have no temporal analogues depend on the fact that space,
unlike time, has more than one dimension. For example, consider the
problem of incongruent counterparts: those who think space is a mere
system of relations struggled to explain our intuition that we could
distinguish a world containing only a left hand from a world
containing only a right hand. So it seems there is an intuitive
orientation to objects in space itself. It is less clear whether the
problems about time that have no spatial analogues are connected with
the one-dimensionality of time.



Finally, one can raise questions about whether space and time are real
at all--and, if they are real, to what extent (so to speak) they
are real. Might it be that space and time are not constituents of
reality as God perceives reality but nevertheless "well-founded
phenomena" (as Leibniz held)? Was Kant right when he denied
spatial and temporal features to "things as they are in
themselves"?--and right to contend that space and time are
"forms of our intuition"? Or was McTaggart's
position the right one: that space and time are wholly unreal?



If these problems about space and time belong to metaphysics only in
the post-Medieval sense, they are nevertheless closely related to
questions about first causes and universals. First causes are
generally thought by those who believe in them to be eternal and
non-local. God, for example--both the impersonal God of Aristotle
and the personal God of Medieval Christian, Jewish, and Muslim
philosophy--is generally said to be eternal, and the personal God
is said to be omnipresent. To say that God is eternal is to say either
that he is everlasting or that he is somehow outside time. And this
raises the metaphysical question of whether it is possible for there
to be a being--not a universal or an abstract object of some
other sort, but an active substance--that is everlasting or
non-temporal. An omnipresent being is a being that does not occupy any
region of space (not even the whole of it, as the luminiferous ether
of nineteenth-century physics would if it existed), and whose causal
influence is nevertheless equally present in every region of space
(unlike universals, to which the concept of causality does not apply).
The doctrine of divine omnipresence raises the metaphysical question
whether it is possible for there to be a being with this feature.
*Ante res* universals are said by some of their proponents
(precisely those who deny that universals are constituents of
particulars) to have no relations to space and time but
"vicarious" ones: the *ante res* universal
"whiteness" may be said to be present where each white
particular is, but only in a way analogous to the way in which the
number two is present where each pair of spatial things is. But it is
doubtful whether this is a position that is possible for a
metaphysician who says that a white thing is a bundle composed of
whiteness and various other universals. Those who believe in the
existence of *in rebus* universals are fond of saying, or have
been in recent years, that these universals ('immanent
universals' is a currently popular name for them) are
"multiply located"--"wholly present" at
each place at which the things that fall under them are present. And
by this they certainly do not mean that whiteness is present in many
different regions of space only vicariously, only as a number might be
said to be present wherever there are things in that number, only in
virtue of bearing the non-spatial relation "being had by"
to a multitude of particulars each of which is present in a single
region of space. All theories of universals, therefore, raise
questions about how things in various ontological categories are
related to space. And all these questions have temporal analogues.


### 3.3 Persistence and Constitution



Related to questions about the nature of space and time are questions
about the nature of objects that take up space or persist through
time, and these questions form yet another central theme in
post-medieval metaphysics. Are some or all objects composed of proper
parts? Must an object have proper parts in order to "fill
up" a region of space--or are there extended simples? Can
more that one object be located in exactly the same region? Do objects
persist through change by having temporal parts?



Much work on persistence and constitution has focused on efforts to
address a closely knit family of puzzles--the puzzles of
coincidence. One such puzzle is the "problem of the statue and
the lump". Consider a gold statue. Many metaphysicians contend
that there is at least one material object that is spatially
co-extensive with the statue, a lump of gold. This is easily shown,
they say, by an appeal to Leibniz's Law (the principle of the
non-identity of discernibles). There is a statue here and there is a
lump of gold here, and--if the causal story of the statue's
coming to be is of the usual sort--the lump of gold existed
before the statue. And even if God has created the statue (and
perforce the lump) *ex nihilo* and will at some point
annihilate the statue (and thereby annihilate the lump), they further
argue, the statue and the lump, although they exist at exactly the
same times, have different modal properties: the lump has the property
"can survive radical deformation" and the statue does not.
Or so these metaphysicians conclude. But it has seemed to other
metaphysicians that this conclusion is absurd, for it is absurd to
suppose (these others say) that there could be spatially coincident
physical objects that share all their momentary non-modal properties.
Hence, the problem: What, if anything, is the flaw in the argument for
the non-identity of the statue and the lump?



A second puzzle in this family is the "problem of Tib and
Tibbles". Tibbles is a cat. Call his tail "Tail".
Call all of him but his tail "Tib". Suppose Tail is cut
off--or, better, annihilated. Tibbles still exists, for a cat can
survive the loss of its tail. And it would seem that Tib will exist
after the "loss" of Tail, because Tib lost no part. But
what will be the relation between Tib and Tibbles? Can it be identity?
No, that is ruled out by the non-identity of discernibles, for Tibbles
will have become smaller and Tib will remain the same size. But then,
once again, we seem to have a case of spatially coincident material
objects that share their momentary non-modal properties.



Both these constitution problems turn on questions about the
identities of spatially coincident objects--and, indeed, of
objects that share all their (proper) parts. (A third famous problem
of material constitution--the problem of the Ship of
Theseus--raises questions of a different sort.) Some
metaphysicians contend that the relation between the lump and the
statue, on the one hand, and the relation between Tib and Tibbles, on
the other, cannot be fully understood in terms of the concepts of
parthood and (non-) identity, but require a further concept, a
non-mereological concept, the concept of "constitution":
the pre-existent lump at a certain point in time comes to constitute
the statue (or a certain quantity of gold or certain gold atoms that
first constituted only the lump come to constitute them both);
pre-existent Tib at a certain point in time comes to constitute
Tibbles (or certain cat-flesh or certain molecules ...). (Baker
2000 is a defense of this thesis.) Others contend that all the
relations between the objects that figure in both problems can be
fully analyzed in terms of parthood and identity. For a more thorough
overview of the solutions to these puzzles and different theories of
constitution in play, see Rea (ed.) 1997 and Thomson 1998.


### 3.4 Causation, Freedom and Determinism



Questions about causation form yet a fourth important category of
issues in the "new" metaphysics. Of course, discussion of
causes go back to Ancient Philosophy, featuring prominently in
Aristotle's *Metaphysics* and *Physics*. But
Aristotle understood 'cause' in a much broader sense than
we do today. In Aristotle's sense, a 'cause' or
'*aiton*' is an explanatory condition of an
object--an answer to a "why" question about the
object. Aristotle classifies four such explanatory conditions--an
object's form, matter, efficient cause, and teleology. An
object's efficient cause is the cause which explains change or
motion in an object. With the rise of modern physics in the
seventeenth century, interest in efficient causal relations became
acute, and it remains so today. And when contemporary philosophers
discuss problems of causation, they typically mean this sense.



One major issue in the metaphysics of causation concerns specifying
the relata of causal relations. Consider a mundane claim: an iceberg
caused the *Titanic* to sink. Does the causal relation hold
between two events: the event of the ship hitting the iceberg and the
event of the ship sinking? Or does it hold between two sets of states
of affairs? Or does it hold between two substances, the iceberg and
the ship? Must causal relations be triadic or otherwise poly-adic? For
example, one might think that we are always required to qualify a
causal claim: the iceberg, rather than the captain's negligence,
was causally responsible for the ship's foundering. And can
absences feature in causal relations? For example, does it make sense
to claim that a lack of lifeboats was the cause of a third-class
passenger's death? Bernstein (2014) and Sartorio (2004) argue
that absences can be causes. Beebee (2004) suggests that absences are
causal explanations, but not causes.



Another question taken up by contemporary literature is whether
causation comes in degrees. For example: if two people lift a heavy
plank and one person bears more of the weight, has one person
contributed more than the other to the lifting of the plank? Bernstein
(2017) suggests that causation comes in degrees, but that most
metaphysical theories of causation cannot account for this idea.
Demirtas (2022) and Kaiserman (2018) agree, while Sartorio (2020)
argues that the appearance that causation comes in degrees is
illusory, and can be explained away.



We might further ask whether causal relations are objective and
irreducible features of reality. Hume famously doubted this,
theorizing that our observations of causation were nothing more than
observations of constant conjunction. For example, perhaps we think
icebergs cause ships to sink only because we always observe
ship-sinking events occurring after iceberg-hitting events and not
because there is a real causal relation that holds between icebergs
and foundering ships.



Contemporary metaphysicians have been attracted to other kinds of
reductive treatments of causation. Some--like Stalnaker and
Lewis--have argued that causal relations should be understood in
terms of counterfactual dependencies (Stalnaker 1968 and Lewis 1973).
For example, an iceberg's striking the ship caused its sinking
at time *t* if and only if in the nearest possible worlds where
the iceberg did not strike the ship at time *t*, the ship did
not sink. Others have argued that causal relations should be
understood in terms of instantiations of laws of nature. (Davidson
(1967) and Armstrong (1997) each defend this view albeit in different
ways.) All of these theories expand on an idea from Hume's
*Treatise* in attempting to reduce causation to different or
more fundamental categories. (For a more complete survey of recent
theories of causation, see Paul and Hall 2013.)



Debates about causation and laws of nature further give rise to a
related set of pressing philosophical questions--questions of
freedom. In the seventeenth century, celestial mechanics gave
philosophers a certain picture of a way the world might be: it might
be a world whose future states were entirely determined by the past
and the laws of nature (of which Newton's laws of motion and law
of universal gravitation served as paradigms). In the nineteenth
century the thesis that the world was indeed this way came to be
called 'determinism'. The problem of free will can be
stated as a dilemma. If determinism is true, there is only one
physically possible future. But then how can anyone ever have acted
otherwise? For, as Carl Ginet has said (1990: 103), our freedom can
only be the freedom to add to the actual past; and if determinism
holds, then there is only one way that the given--the
actual--past can be "added to". But if determinism
does not hold, if there are alternative physically possible futures,
then which one comes to pass must be a mere matter of chance. And if
it is a mere matter of chance whether I lie or tell the truth, how can
it be "up to me" whether I lie or tell the truth? Unless
there is something wrong with one of these two arguments, the argument
for the incompatibility of free will and determinism or the argument
for the incompatibility of free will and the falsity of determinism,
free will is impossible. The problem of free will may be identified
with the problem of discovering whether free will is
possible--and, if free will is possible, the problem of giving an
account of free will that displays an error in one of (or both) these
arguments.



Van Inwagen (1998) defends the position that, although the modern
problem of free will has its origin in philosophical reflections on
the consequences of supposing the physical universe to be governed by
deterministic laws, the problem cannot be evaded by embracing a
metaphysic (like dualism or idealism) that supposes that agents are
immaterial or non-physical. This leads into our next and final sample
of topics from the "new" metaphysics.


### 3.5 The Mental and Physical



If it is natural both to pair and to oppose time and space, it is also
natural to pair and to oppose the mental and the physical. The modern
identity theory holds that all mental events or states are a special
sort of physical event or state. The theory is parsimonious (among its
other virtues) but we nevertheless exhibit a natural tendency to
distinguish the mental and the physical. Perhaps the reason for this
is epistemological: whether our thoughts and sensations are physical
or not, the kind of awareness we have of them is of a radically
different sort from the kind of awareness we have of the flight of a
bird or of a flowing stream, and it seems to be natural to infer that
the objects of the one sort of awareness are radically different from
the objects of the other. That the inference is logically invalid is
(as is so often the case) no barrier to its being made. Whatever the
reason may be, philosophers have generally (but not universally)
supposed that the world of concrete particulars can be divided into
two very different realms, the mental and the material. (As the
twentieth century passed and physical theory rendered
"matter" an increasingly problematical concept, it became
increasingly common to say "the mental and the physical".)
If one takes this view of things, one faces philosophical problems
that modern philosophy has assigned to metaphysics.



Prominent among these is the problem of accounting for mental
causation. If thoughts and sensations belong to an immaterial or
non-physical portion of reality--if, for example, they are
changes in immaterial or non-physical substances--how can they
have effects in the physical world? How, for example, can a decision
or act of will cause a movement of a human body? How, for that matter,
can changes in the physical world have effects in the non-physical
part of reality? If one's feeling pain is a non-physical event,
how can a physical injury to one's body cause one to feel pain?
Both questions have troubled "two realm"
philosophers--or 'dualists', to give them their more
usual name. But the former has troubled them more, since modern
physics is founded on principles that assert the conservation of
various physical quantities. (See Bennett (2021) for discussion of the
comparative explanatory demands of physicalism and dualism.) If a
non-physical event causes a change in the physical
world--dualists are repeatedly asked--does that not imply
that physical quantities like energy or momentum fail to be conserved
in any physically closed causal system in which that change occurs?
And does that not imply that every voluntary movement of a human body
involves a violation of the laws of physics--that is to say, a
miracle?



A wide range of metaphysical theories have been generated by the
attempts of dualists to answer these questions. Some have been less
than successful for reasons that are not of much intrinsic
philosophical interest. C. D. Broad, for example, proposed (1925:
103-113) that the mind affects the body by momentarily changing
the electrical resistance of certain synapses in the brain, (thus
diverting various current pulses, which literally follow the path of
least resistance into paths other than those they would have taken).
And this, he supposed, would not imply a violation of the principle of
the conservation of energy. But it seems impossible to suppose that an
agent could change the electrical resistance of a physical system
without expending energy in the process, for to do this would
necessitate changing the physical structure of the system, and that
implies changing the positions of bits of matter on which forces are
acting (think of turning the knob on a rheostat or variable resistor:
one must expend energy to do this). If this example has any
philosophical interest it is this: it illustrates the fact that it is
impossible to imagine a way for a non-physical thing to affect the
behavior of a (classical) physical system without violating a
conservation principle.



The various dualistic theories of the mind treat the interaction
problem in different ways. The theory called 'dualistic
interactionism' does not, of itself, have anything to say about
the problem--although its various proponents (Broad, for example)
have proposed solutions to it. 'Occasionalism' simply
concedes that the "local" counterfactual dependence of the
behavior of a physical system on a non-physical event requires a
miracle. The theory of pre-established harmony, which substitutes
"global" for local counterfactual dependence of voluntary
physical movements on the mental states of agents, avoids problems
with conservation principles--but secures this advantage at a
great price. (Like occasionalism, it presupposes theism, and, unlike
occasionalism, it entails either that free will does not exist or that
free will is compatible with determinism.)
'Epiphenomenalism' simply denies that the mental can
affect the physical, and contents itself with an explanation of why
the mental appears to affect the physical.



In addition to these dualistic theories, there are monistic theories,
theories that dissolve the interaction problem by denying the
existence of either the physical or the non-physical: idealism and
physicalism. (Present-day philosophers for the most part prefer the
term 'physicalism' to the older term
'materialism' for reasons noted above.) Most current work
in the philosophy of mind presupposes physicalism, and it is generally
agreed that a physicalistic theory that does not simply deny the
reality of the mental (that is not an "eliminativist"
theory), raises metaphysical questions. Such a theory must, of course,
find a place for the mental in a wholly physical world, and such a
place exists only if mental events and states are certain special
physical events and states. There are at least three important
metaphysical questions raised by these theories. First, granted that
all particular mental events or states are identical with particular
physical events or states, can it also be that some or all mental
universals ('event-types' and 'state-types'
are the usual terms) are identical with physical universals? Secondly,
does physicalism imply that mental events and states cannot really be
causes (does physicalism imply a kind of epiphenomenalism)? Thirdly,
can a physical thing have non-physical properties--might it be
that mental properties like "thinking of Vienna" or
"perceiving redly" are non-physical properties of physical
organisms? This last question, of course, raises a more basic
metaphysical question, 'What is a non-physical property?'
And all forms of the identity theory raise fundamental metaphysical
questions, ontological questions, questions like, 'What is an
event?' and 'What is a state?'.


### 3.6 Social Metaphysics



Recent years have seen an outpouring of interest in *social
metaphysics,* which takes the nature of the social world as its
subject of study. Many contemporary social metaphysicians investigate
the ontological natures of socially constructed groups, entities, and
institutions. Key questions include: what, exactly, are corporations,
restaurants, and sports teams? What is the nature of money? What are
the natures of social categories, like *woman*, *Black*,
*lesbian*, and *disabled*? What is the relationship
between individuals and macro-level social objects? What does it mean
to say that something is "socially constructed," and what
is the difference between the social and the natural in the first
place?



Ritchie (2013, 2015, 2020a and 2020b) draws a distinction between
"Type 1" social groups like corporations and institutions,
which are organized and structured, and "Type 2" social
groups, like Blacks and women, which are less structured social kinds.
Epstein (2019) argues against these sorts of course-grained
classifications, preferring to classify them according to their
inter-level metaphysical relationships. Ruben (1985) denies that
social groups and other macro-level social entities can be reduced to
individuals. Korman (2020) takes up the question of the nature of
establishments like restaurants in further detail, suggesting that
they are neither material objects nor constituted by the buildings
that they occupy. Uzquiano (2004) questions the persistence conditions
of social groups like the Supreme Court, and ultimately argues that
they are similar to the persistence conditions for artifacts. Drawing
on this idea, Richardson (2022) holds that social groups are concrete
material particulars, since two different social groups can have
exactly the same members. 



Other metaphysicians examine the ontological status of money, and
especially the status of virtual currency like bitcoin. Passinsky
(2020) distinguishes between descriptive and normative approaches to
exploring the topic, and argues in favor of the latter. In contrast,
Warmke (2021) takes a descriptive approach, suggesting that bitcoin is
a fictional substance in a collectively co-authored story.



There has also been a recent surge of interest in the metaphysics of
race and gender. Haslanger (2000) famously holds that (roughly)
*x* is a woman if one is oppressed on the basis of her
womanhood. Haslanger's approach is ameliorative, taking into
account what sorts of concepts of gender and race might be most useful
in theorizing. Friendly to this approach, Asta (2018) proposes
a conferralist account of social categories, according to which social
categories are externally conferred on individuals in specific
contexts. Others have taken on the topic of the natures of more
specific sorts of social categories: Bernstein (2020) suggests that
intersectional social categories like *Black woman* are to be
viewed as explanatorily unified and prior to the individual
constituents like *Black* and *woman.* Jorba and
Rodo de Zarate (2019) propose a framework of properties
and emergent experience to account for intersectionality.



Dembroff (2016) takes up the puzzle of sexual orientation, arguing for
"Bidimensional Dispositionalism." According to that view,
a person's sexual orientation is grounded in a person's
dispositions to engage in sexual behaviors under the ordinary
conditions for these dispositions. A person's dispositions
include sexes and genders of persons that one is disposed to sexually
engage with under those conditions. Andler (2021) draws a distinction
between sexual orientation and sexual identity, arguing that the
latter is a more suitable and more explanatorily powerful category for
capturing the relevant phenomenon.



There is even a burgeoning meta-metaphysics of the social world,
examining whether the central questions of social metaphysics are
substantive. Barnes (2017) and Mikkola (2017) challenge Sider's
(2012) conception of a substantive question in metaphysics, on the
grounds that it does not accommodate substantive questions in the
metaphysics of gender. Richardson (forthcoming) disagrees. And while
social metaphysics is often taken to contrast with so-called
"fundamental" metaphysics (as in McKitrick (2018)),
several philosophers have recently pointed out that elements of the
social world might be fundamental, including Mason and Ritchie (2020)
and Bernstein (2021). Social metaphysics can be viewed as a
counterexample to the thesis that metaphysics is the study of
fundamental reality, as suggested in Bennett (2017). Passinsky (2021)
holds that Finean metaphysics is a good framework for feminist
metaphysics. Others such as Hacking (1999) and Diaz-Leon
(2015) investigate what it is for something to be socially
constructed. See also the Social Ontology entry by Epstein (2021) for
a comprehensive overview of social ontology. 


## 4. The Methodology of Metaphysics



As is obvious from the discussion in
 Section 3,
 the scope of metaphysics has expanded beyond the tidy boundaries
Aristotle drew. So how should we answer our original question? Is
contemporary metaphysics just a compendium of philosophical problems
that cannot be assigned to epistemology or logic or ethics or
aesthetics or to any of the parts of philosophy that have relatively
clear definitions? Or is there a common theme that unites work on
these disparate problems and distinguishes contemporary metaphysics
from other areas of inquiry?



These issues concerning the nature of metaphysics are further
connected with issues about the epistemic status of various
metaphysical theories. Aristotle and most of the Medievals took it for
granted that, at least in its most fundamental aspects, the ordinary
person's picture of the world is "correct as far as it
goes". But many post-Medieval metaphysicians have refused to
take this for granted. Some of them, in fact, have been willing to
defend the thesis that the world is very different from, perhaps
radically different from, the way people thought it was before they
began to reason philosophically. For example, in response to the
puzzles of coincidence considered in
 Section 3.3,
 some metaphysicians have maintained that there are no objects with
proper parts. This entails that composite objects--tables,
chairs, cats, and so on--do not exist, a somewhat startling view.
And as we saw in
 Section 3.1,
 other metaphysicians have been happy to postulate the reality of
concrete merely possible worlds if this posit makes for a simpler and
more explanatorily powerful theory of modality. Perhaps this
contemporary openness to "revisionary" metaphysics is
simply a recovery of or a reversion to a pre-Aristotelian conception
of a "permissible metaphysical conclusion", a conception
that is illustrated by Zeno's arguments against the reality of
motion and Plato's Allegory of the Cave. But no matter how we
classify it, the surprising nature of many contemporary metaphysical
claims puts additional pressure on practioners to explain just what
they are up to. They raise questions of the methodology of
metaphysics.



One attractive strategy for answering these questions emphasizes the
continuity of metaphysics with science. On this conception,
metaphysics is primarily or exclusively concerned with developing
generalizations from our best-confirmed scientific theories. For
example, in the mid-twentieth century, Quine (1948) proposed that that
the "old/intermediate" metaphysical debate over the status
of abstract objects should be settled in this way. He observed that if
our best scientific theories are recast in the "canonical
notation of (first-order) quantification" (in sufficient depth
that all the inferences that users of these theories will want to make
are valid in first-order logic), then many of these theories, if not
all of them, will have as a logical consequence the existential
generalization on a predicate \(F\) such that \(F\) is satisfied only
by abstract objects. It would seem, therefore, that our best
scientific theories "carry ontological commitment" to
objects whose existence is denied by nominalism. (These objects may
not be universals in the classical sense. They may, for example, be
sets.) Take for example the simple theory, 'There are
homogeneous objects, and the mass of a homogeneous object in grams is
the product of its density in grams per cubic centimeter and its
volume in cubic centimeters'. A typical recasting of this theory
in the canonical notation of quantification is:



> 
> \(\exists Hx\) & \(\forall x(Hx \rightarrow Mx = Dx \times Vx)\)
> 



('\(Hx\)': '\(x\) is homogeneous';
'\(Mx\)': 'the mass of \(x\) in grams';
'\(Dx\)': 'the density of \(x\) in grams per cubic
centimeter'; '\(Vx\)': 'the volume of \(x\) in
cubic centimeters'.) A first-order logical consequence of this
"theory" is



> 
> \(\exists x\exists y\exists z(x = y \times z)\)
> 



That is: there exists at least one thing that is a product (at least
one thing that, for some \(x\) and some \(y\) is the product of \(x\)
and \(y\)). And a product must be a number, for the operation
"product of" applies only to numbers. Our little theory,
at least if it is recast in the way shown above, is therefore, in a
very obvious sense, "committed" to the existence of
numbers. It would seem, therefore, that a nominalist cannot
consistently affirm that theory. (In this example, the role played by
'the predicate *F*' in the abstract statement of
Quine's "observation" is played by the predicate
'...=...x...'.)



Quine's work on nominalism inspired a much broader program for
approaching ontological questions. According to
"neo-Quineans", questions about the existence of abstract
objects, mental events, objects with proper parts, temporal parts, and
even other concrete possible worlds are united to the extent that they
are questions about the ontological machinery required to account for
the truth of our best-confirmed theories. Still, many questions of the
new and old metaphysics are not questions of ontology. For example,
many participants in the debate over causation are not particularly
worried about whether causes and effects exist. Rather, they want to
know "in virtue of what" something is a cause or effect.
Few involved in the debate over the mental and physical are interested
in the question whether there are mental properties (in some sense or
other). Rather, they are interested in whether mental properties are
"basic" or *sui generis*--or whether they are
grounded, partially or fully, in physical properties.



Is there a unified methodology for metaphysics more broadly
understood? Some think the task of the metaphysician is to identify
and argue for explanatory relations of various kinds. According to
Fine (2001), metaphysicians are in the business of providing theories
of which facts or propositions ground other facts or propositions, and
which facts or propositions hold "in reality". For
example, a philosopher might hold that tables and other composite
objects exist, but think that facts about tables are completely
grounded in facts about the arrangements of point particles or facts
about the state of a wave function. This metaphysician would hold that
there are no facts about tables "in reality"; rather,
there are facts about arrangements of particles. Schaffer 2010
proposes a similar view, but holds that metaphysical grounding
relations hold not between facts but between entities. According to
Schaffer, the fundamental entity/entities should be understood as the
entity/entities that grounds/ground all others. On Schaffer's
conception we can meaningfully ask whether a table is grounded in its
parts or vice versa. We can even theorize (as Schaffer does) that the
world as a whole is the ultimate ground for everything.



Another noteworthy approach (Sider 2012) holds that the task of the
metaphysician is to "explain the world" in terms of its
fundamental structure. For Sider, what unites (good) metaphysics as a
discipline is that its theories are all framed in terms that pick out
the fundamental structure of the world. For example, according to
Sider we may understand 'causal nihilism' as the view that
causal relations do not feature in the fundamental structure of the
world, and so the best language for describing the world will eschew
causal predicates.



It should be emphasized that these ways of delimiting metaphysics do
not presuppose that all of the topics we've considered as
examples of metaphysics are substantive or important to the subject.
Consider the debate about modality. Quine (1953) and Sider (2012) both
argue from their respective theories about the nature of metaphysics
that aspects of the debate over the correct metaphysical theory of
modality are misguided. Others are skeptical of the debates about
composition or persistence through time. So theories about the nature
of metaphysics might give us new resources for criticizing particular
first-order debates that have historically been considered
metaphysical, and it is common practice for metaphysicians to regard
some debates as substantive while adopting a deflationist attitude
about others.


## 5. Is Metaphysics Possible?



It may also be that there is no internal unity to metaphysics. More
strongly, perhaps there is no such thing as metaphysics--or at
least nothing that deserves to be called a science or a study or a
discipline. Perhaps, as some philosophers have proposed, no
metaphysical statement or theory is either true or false. Or perhaps,
as others have proposed, metaphysical theories have truth-values, but
it is impossible to find out what they are. At least since the time of
Hume, there have been philosophers who have proposed that metaphysics
is "impossible"--either because its questions are
meaningless or because they are impossible to answer. The remainder of
this entry will be a discussion of some recent arguments for the
impossibility of metaphysics.



Let us suppose that we are confident that we are able to identify
every statement as either "a metaphysical statement" or
"not a metaphysical statement". (We need not suppose that
this ability is grounded in some non-trivial definition or account of
metaphysics.) Let us call the thesis that all metaphysical statements
are meaningless "the strong form" of the thesis that
metaphysics is impossible. (At one time, an enemy of metaphysics might
have been content to say that all metaphysical statements were false.
But this is obviously not a possible thesis if the denial of a
metaphysical statement must itself be a metaphysical statement.) And
let us call the following statement the "weak form" of the
thesis that metaphysics is impossible: metaphysical statements are
meaningful, but human beings can never discover whether any
metaphysical statement is true or false (or probable or improbable or
warranted or unwarranted).



Let us briefly examine an example of the strong form of the thesis
that metaphysics is impossible. The logical positivists maintained
that the meaning of a (non-analytic) statement consisted entirely in
the predictions it made about possible experience. They maintained,
further, that metaphysical statements (which were obviously not put
forward as analytic truths) made no predictions about experience.
Therefore, they concluded, metaphysical statements are
meaningless--or, better, the "statements" we classify
as metaphysical are not really statements at all: they are things that
look like statements but aren't, rather as mannequins are things
that look like human beings but aren't.



But (many philosophers asked) how does the logical positivist's
central thesis



> 
> The meaning of a statement consists entirely in the predictions it
> makes about possible experience
> 



fare by its own standards? Does this thesis make any predictions about
possible experiences? Could some observation show that it was true?
Could some experiment show that it was false? It would seem not. It
would seem that everything in the world would look the same--like
this--whether this thesis was true or false. (Will the positivist
reply that the offset sentence is analytic? This reply is problematic
in that it implies that the multitude of native speakers of English
who reject the logical positivists' account of meaning somehow
cannot see that that sentence is true in virtue of the meaning of the
word "meaning"--which is no technical term but a word
of ordinary English.) And, therefore, if the statement is true it is
meaningless; or, what is the same thing, if it is meaningful, it is
false. Logical positivism would therefore seem to say of itself that
it is false or meaningless; it would be seem to be, to use a currently
fashionable phrase, "self-referentially incoherent".



Current advocates of 'metaphysical anti-realism' also
advocate a strong form of the thesis that metaphysics is impossible.
Insofar as it is possible to find a coherent line of argument in the
writings of any anti-realist, it is hard to see why they, like the
logical positivists, are not open to a charge of self-referential
incoherency. Indeed, there is much to be said for the conclusion that
all forms of the strong thesis fall prey to self-referential
incoherency. Put very abstractly, the case against proponents of the
strong thesis may be put like this. Dr. McZed, a "strong
anti-metaphysician", contends that any piece of text that does
not pass some test she specifies is meaningless (if she is typical of
strong anti-metaphysicians, she will say that any text that fails the
test represents an attempt to use language in a way in which language
cannot be used). And she contends further that any piece of text that
can plausibly be identified as "metaphysical" must fail
this test. But it invariably turns out that various sentences that are
essential components of McZed's case against metaphysics
themselves fail to pass her test. A test-case for this very schematic
and abstract refutation of all refutations of metaphysics is the very
sophisticated and subtle critique of metaphysics (it purports to apply
only to the kind of metaphysics exemplified by the seventeenth-century
rationalists and current analytical metaphysics) presented in van
Fraassen 2002. It is a defensible position that van Fraassen's
case against metaphysics depends essentially on certain theses that,
although they are not themselves metaphysical theses, are nevertheless
open to many of the criticisms he brings against metaphysical
theses.



The weak form of the thesis that metaphysics is impossible is this:
there is something about the human mind (perhaps even the minds of all
rational agents or all finite rational agents) that unfits it for
reaching metaphysical conclusions in any reliable way. This idea is at
least as old as Kant, but a version of it that is much more modest
than Kant's (and much easier to understand) has been carefully
presented in McGinn 1993. McGinn's argument for the conclusion
that the human mind is (as a matter of evolutionary contingency, and
not simply because it is "a mind") incapable of a
satisfactory treatment of a large range of philosophical questions (a
range that includes all metaphysical questions), however, depends on
speculative factual theses about human cognitive capacities that are
in principle subject to empirical refutation and which are at present
without significant empirical support. For a different defense of the
weak thesis, see Thomasson 2009.