## 1. Introduction



Suppose you enter a farmers' market, pick out a few cucumbers
and ask the merchant for the price. "Five dollars a
pound". A bit expensive, you may think, but you pay. Before you
leave the stand two other people approach the seller with the very
same question ("How much are the cucumbers?"). "A
dollar a pound", she says to the one; "Ten dollars a
pound", she tells the other. At least two of you are likely to
attack the merchant with a simple question: Why the price discrepancy?
Of course, you may simply leave the place if you have a simple
explanation for the discrepancy (for example, that both you and the
person who was asked to pay ten dollars a pound belong to commonly
discriminated minorities). You may also conclude that the seller is
just out of her mind (or that she is just conducting a psychological
experiment). In all of these cases you will be entertaining an
*explanation* or *reason* for a fact that appears odd.
But what kinds of facts demand an explanation? Do *all*
facts--including the most ordinary ones--demand an
explanation? If you accept an unrestricted form of the *Principle
of Sufficient Reason* (= PSR), you will require an explanation for
*any* fact, or in other words, you will reject the possibility
of any *brute*, or unexplainable, *facts*.



A simple formulation of the principle is as follows:



(1)
For every fact \(F\), there must be a sufficient reason why
\(F\) is the case.


The term "fact" in the above formulation is not intended
to express any commitment to an ontology of facts. Still, if one
wishes to avoid such connotations, the principle can be formulated
more schematically:



(2)
For every \(x\), there is a \(y\) such that \(y\)
is the sufficient reason for \(x\) (formally:
\(\forall x\exists y\, Ryx\) [where
"\(Ryx\)" denotes the binary relation of providing a
sufficient reason]).


The PSR is, in fact, a *family of principles* which are
generated by various restrictions of (2), and by ascriptions of
different degrees of modal strength to (2). To begin with, variants of
the PSR may differ according to how they restrict *the kinds of
things that require a reason* (the explananda). Thus, one might
restrict the PSR to only actual entities, or include possibilia as
well. Alternatively, one might formulate the PSR as requiring a
sufficient reason for every (true) proposition or as pertaining to
entities and their properties. A variant of the PSR restricted to
entities might require an explanation for the existence *and*
non-existence of entities, or it might be further restricted by
requiring a reason only for the existence (or only for the
non-existence) of entities. A version of the PSR that is restricted to
propositions might range over both contingent and necessary
propositions, or it might be further restricted to only one of these
sub-domains.



Similarly, different versions of the PSR issue from various ways of
restricting the kinds of things that count *as providing a
reason* (the explanantia). It is likely (though not necessary)
that one's decision about the kinds of explananda that fall
under the range of the PSR will determine the kinds of things counted
as explanantia.



Variants of the PSR may be generated not only by placing restrictions
on the relata at stake (both the explananda and the explanantia), but
also on the notion of the relation at stake. Frequently, the relation
of providing a reason is conceived as irreflexive, antisymmetric and
transitive, though each of these characteristics may be, and indeed
have been, challenged. The relation of providing a reason can be
conceived as an ontological relation (as in contemporary discussions
of ground), or as a purely epistemological relation.



A modally strong version of the PSR will take the Principle as
necessary and obtaining in all possible worlds, while a weak modal
version will present the Principle as merely contingently true.
Another distinction can be drawn between a *factive*, as
opposed to merely *regulative*, version of the Principle. A
regulative version of the PSR would consider it as a *condition for
intelligibility* (on a par with the Law of Non-Contradiction) and
thus as guiding our studying of nature. The factive version simply
states that the Principle is true in actuality (or even in all
possible worlds). The regulative and the factive versions differ in
terms of allowing for the falsification of the principle. The factive
version could be easily refuted by a single counter-example. A
proponent of the regulative variant of the PSR would argue that an
empirical falsification of the PSR makes as little sense as an
empirical falsification of the Law of Non-Contradiction. Encountering
a fact which *seems* to have no explanation, the proponent of
the regulative variant would respond by insisting that we must keep
searching for an explanation.



A proponent of the unrestricted version of the PSR could argue that
one's choice of a specific variant of the PSR cannot be
arbitrary, on pain of inconsistency (i.e., one must provide a reason
why to prefer one variant over others). Relying on this last point,
she may further contend that in the absence of compelling reasons to
the contrary, the unrestricted version of the Principle should be
considered as default.



One of the most interesting questions regarding the PSR is why accept
it at all. Insofar as the PSR stipulates that all things must be
explainable, it seems that the PSR itself demands an explanation.
Several modern philosophers attempted to provide a proof for the PSR,
though so far these attempts have been mostly unsuccessful. Another
important question related to the PSR is the possibility of
self-explanatory facts and self-caused entities; particularly, one
might wonder how these are distinguished from unexplainable, brute
facts and uncaused entities. One might also wonder whether the PSR
allows for any *primitive concepts* that cannot be further
explained.



A third crucial problem for proponents of the PSR is how to address
the Agrippan Trilemma between the apparently exhaustive three horns
of: (i) acceptance of brute facts, (ii) acceptance of an infinite
regress of explanation (or grounding), or (iii) acceptance of
self-explanatory facts. *Prima facie*, each horn in the
trilemma undermines the position of the proponent of the PSR.



Finally, the proponent of the PSR faces intriguing problems in
addressing perfectly symmetrical states. We have seen that some
variants of the PSR require an explanation for *the existence of
things* (thus, assuming nonexistence as a "default"
state requiring no explanation), while other variants require an
explanation for *both the existence and nonexistence of
things*. Let us look quickly at the latter
("default"-free) variant. Specifically, we might wonder
how a proponent of the "default"-free variant of the PSR
would respond to a situation in which we have neither a reason for the
existence of \(x\), nor have a reason for the non-existence of
\(x\)? A proponent of the PSR might indeed respond by denying the
possibility of such a scenario (given the PSR and bivalence). A
similar dilemma might be raised with regard to issues of identity:
given the absence of a reason for the identity of \(x\) and
\(y\), as well as for their non-identity, should we assume either
identity or non-identity as a default
 position?[1]



With these general considerations in place, let us examine the
historical role that the Principle has played. The term
"Principle of Sufficient Reason [*principe de raison
suffisante/principium reddendae rationis*]" was coined by
Leibniz, though Spinoza is thought by many scholars to have preceded
Leibniz in appreciating the importance of the Principle and placing it
at the center of his philosophical
 system.[2]
 The Principle seems at first sight to have a strong intuitive
appeal--we always ask for explanations--yet it is taken by
many to be too bold and expensive due to the radical implications it
seems to yield. Among the alleged consequences of the Principle are:
the Identity of Indiscernibles, necessitarianism, the relativity of
space and time, the existence of a self-necessitated Being (i.e.,
God), and the Principle of Plenitude.



Though there are several important precursors who, as we will see,
seem to advocate variants of the PSR before the modern period, we will
begin our discussion with the two main expositors of the Principle:
Spinoza and Leibniz.


## 2. Spinoza



The earliest statement of the PSR in Spinoza's writings appears in his
first published work, the 1663 geometrical exposition of
Descartes' *Principles of Philosophy* (which may or may
not reflect Spinoza's own views at the time). The eleventh axiom of
Part I of the book states:



> 
> Nothing exists of which it cannot be asked, what is the cause (or
> reason) [*causa (sive ratio)*], why it exists.



In a brief explanatory note to this axiom, Spinoza adds:



> 
> 
> Since existing is something positive, we cannot say that it has
> nothing as its cause (by Axiom 7). Therefore, we must assign some
> positive cause, or reason, why [a thing] exists--either an
> external one, i.e., one outside the thing itself, or an internal one,
> one comprehended in the nature and definition of the existing thing
> itself. (Geb.
>  I/158/4-9)[3]
> 
> 
> 



Axiom 7, to which Spinoza appeals in the explanation, is a variant of
the "*ex nihilo, nihil fit*" ("from nothing,
nothing comes") principle, and stipulates that an existing thing
and its perfections (or qualities) cannot have nothing or a
non-existing thing as their cause. Interestingly, however, in another
work from this early period of his philosophical writing, the
*Treatise on the Emendation of the Intellect*, Spinoza allows
for one unique item to be without a cause. In SS70 of this
treatise, Spinoza argues:



> 
> 
> [T]hat Thought is also called true which involves objectively the
> essence of some principle that *does not have a cause*, and is
> known through itself and in itself. (II/26/33-4. Our
> emphasis)
> 
> 
> 



It is not completely clear what "the principle
[*principium*]" at stake is, but given its qualification
as "known through itself and in itself", it may refer to
God and indicate Spinoza's understanding of Descartes'
rather nuanced view--in his Second Set of Replies--according
to which God does not need a *cause* in order to exist, but
there is a *reason* why God does not need a cause (AT VII:
164-65; cf. Carraud 2002: Ch.
 2).[4]



According to some commentators Spinoza states a variant of the PSR
already at the opening of his major work, the *Ethics*. The
second axiom of Part One of the book reads:



> 
> 
> E1a2: What cannot be conceived [*concipi*] through another,
> must be conceived through itself.
> 
> 
> 



The immediate implication of E1a2 is that everything is
 conceived.[5]
 Since, for Spinoza, to conceive something is to explain it (see
E1p10s, E1p14d and Della Rocca 2008: 5) it seems that E1a2 amounts to
the claim that everything is explainable. Other commentators have also
seen the PSR encoded in E1a3:



> 
> 
> From a given determinate cause the effect follows necessarily; and
> conversely, if there is no determinate cause, it is impossible for an
> effect to follow.
> 
> 
> 



If we interpret "effect" narrowly as something with a
cause, then the second clause is trivial. If we interpret it more
broadly as anything that exists, obtains, happens (or whatever the
relata of causation are taken to be) has a cause, then the second
clause contains a statement of a version of the PSR: everything has a
cause (Garrett 1979 and Lin 2017).



In E1p11d2, Spinoza states explicitly a variant of the PSR: "For
each thing there must be assigned a cause, *or* reason, both
for its existence and for its nonexistence". Similarly, in
E1p8s2, Spinoza argues, "if a certain number of individuals
exists, there must be a cause why those individuals, and why neither
more nor fewer, exist." Spinoza's insistence that even the
*non-existence* of things must be explainable is crucial. It
allows him, for example, to argue that were God not to exist, his
non-existence must be explainable. Since God is a substance, Spinoza
argues, his existence or non-existence cannot be caused or explained
externally (Spinoza takes substances to be causally independent of
each other); hence, were God not to exist, his own nature would have
to be the cause of his non-existence, just as the nature of a
square-circle is the cause of the non-existence of that thing. But
since God's nature is not a contradictory, his nature cannot
internally rule out his existence, and hence he must exist
(E1p11d).



The scope of Spinoza's PSR and its role in his system is a
controversial matter. A dominant trend in recent scholarship reads
Spinoza's PSR as having unrestricted scope and playing a crucial
role in deriving many of his most important doctrines (e.g., Della
Rocca 2008). But this trend has recently been challenged by readers
who argue that Spinoza's PSR is restricted in scope to facts
about existence and nonexistence and that he rarely explicitly appeals
to this principle in deriving his signature doctrines (e.g., Garber
2015 and Lin 2019).



Commentators who give a prominent role to the PSR in Spinoza's
system frequently offer rational reconstructions of Spinoza's
arguments for his doctrines that find a crucial, if implicit, role for
the PSR. For example, some think that the PSR is the primary
motivation behind Spinoza's strict necessitarianism. On this reading,
for Spinoza, if there are two (or more) possible worlds, it would seem
that neither one would have a *sufficient* reason or cause (for
if there were such a sufficient reason, this world would be
necessitated, and all other worlds would be impossible). In other
words, the PSR dictates that there is only one possible world (see
Della Rocca (2008), 69-78, Lin (2011), 23-25, and Melamed
(2021). Other commentators, (e.g., Lin 2019), deny that the PSR plays
any role in Spinoza's arguments for necessitarianism, and still
others have denied that Spinoza is a necessitarian in the relevant
sense (e.g. Curley 1969, and Curley and Walski 1999). Moreover, there
are commentators who, while believing that the PSR is behind
Spinoza's necessitarianism, suggest that, occasionally,
Spinoza's endorsement of the PSR is in tension with other
principles of his metaphysics, such as the priority of the infinite
(see Melamed (2012b), and Melamed (2013a), xvii).



Spinoza holds not only that the existence of things must be explained,
but he is also committed to the assertion that the essences of all
things follow necessarily from God's essence (E1p25 and E1p16).
He is thus committed to the claim that all essences have a cause and
an explanation.



Other Spinozistic doctrines that some commentators have alleged to
follow from his PSR are the Identity of Indiscernibles (E1p4. Although
see Lin 2019 for a dissenting view), substance monism (E1p11 and
E1p14), and the rejection of free will (E1p32 and E2pp48-49). It
has also been argued that in E1p21d Spinoza implicitly relies on the
PSR to infer a bold causal principle: a simple cause has one, and only
one, simple effect. Had the cause more than one effect, the difference
between the two effects would be unexplainable insofar as each effect
is supposed to be fully explained by the same cause. Thus, if we
experience a cause bringing about more than one effect, we should
conclude that that the cause was not simple, but comprised of parts
(so that the different parts contributed to the causation of the
different effects. See Melamed (2013a), 117-119, and Melamed
(2013b), 212-213.



Recently, Michael Della Rocca argued not only that the PSR
"provide[s] the key to unlocking many of the mysteries of
Spinoza's philosophical system" (2008: 9), but that
Spinoza requires the *reduction* of the most basic
philosophical concepts to reason or intelligibility. This alleged
"double use of the PSR" stipulates (1) that everything
must be explainable, and (2) that it should be (ultimately) explained
in terms of intelligibility. Hence, according to Della Rocca, Spinoza
reduces his major philosophical concepts--existence, causation,
rightness, and power--to intelligibility (2008: 8-9). While
this is a fascinating and bold reading of Spinoza's metaphysics,
it seems to contradict his crucial doctrine of the causal and
conceptual barrier between the attributes (E1p10 and E2p6). The
reduction of any non-Thought item to intelligibility (presumably, a
feature of the attribute of
 thought[6])
 undermines the barrier between the attributes, and with it the entire
edifice of Spinoza's ontology (see Della Rocca 2012:
12-16; Melamed 2012a; and Melamed 2013a: xv and 196 n. 84).
Moreover, some have noted that Della Rocca's arguments for
specific reductions, for example, the reduction of causation to
intelligibility requires assumptions that Spinoza explicitly rejects
(Lin 2019 and Melamed 2013, Ch. 3).



On the reading according to which Spinoza's PSR is unrestricted,
how would he respond to the Agrippan Trilemma? Clearly, on this
interpretation, Spinoza is unsympathetic to any acceptance of brute
facts. Yet he allows for some, restricted cases of self-explanation
and infinite regress of explanation. Let us take a brief look at these
two issues.



Spinoza begins the *Ethics* with the definitions of *causa
sui* (E1d1), and of substance as that which "is conceived
through itself" (E1d3). Positing these reflexive definitions at
the outset might have been a calculated methodological move whose aim
was to bypass the challenging task of proving the legitimacy of these
notions. But since Spinoza considers his definitions as not merely
stipulative (see TIE SS95 and Ep. 60), we may well ask for a
defense of the legitimacy of self-explanations.



The class of truths that Spinoza considers as self-explanatory are
truths that follow *merely* from the essence or--what is
the same--the nature of a thing. In E1p11d, Spinoza provides two
examples of self-explanation:



> 
> 
> [T]he very nature of a square circle indicates the reason why it does
> not exist, viz. because it involves a contradiction..., the
> reason why a substance exists also follows from its nature alone,
> because it involves existence.
> 
> 
> 



In contrast, claims Spinoza, the existence (as well as the
non-existence) of a triangle (or any other thing that is not a
substance) do no follow *merely from the essence* of the
triangle:



> 
> 
> The reason why a circle or triangle exists, or why it does not exist,
> does not follow from the nature of these things, but from the order of
> the whole of corporeal Nature. (E1p11d).
> 
> 
> 



Thus, consider the following three propositions: (i) The triangle has
three angles, (ii) The substance exists, and (iii) The triangle
exists. Proposition (i) is clearly self-explanatory, since the essence
of the triangle (which contains the nature of the number three and the
nature of an angle) is the sufficient reason for its having three
angles (adding any other information is of no explanatory value).
Spinoza considers proposition (ii) as self-explanatory as well. Notice
that Spinoza does not define substance (in E1d3) as existing by virtue
of its essence, but rather derives this claim from the definition of
substance (in E1p7 and E1p6). In contrast to (i) and (ii), the
existence of a triangle does not follow merely from its essence (since
it is caused by entities external to the triangle, and therefore has
to be explained through these external causes).



Let us turn now to the question of the legitimacy of infinite regress.
In E1p28, Spinoza openly states that within each attribute there is an
infinite causal chain of finite modes:



> 
> 
> Every singular thing, or any thing which is finite and has a
> determinate existence, can neither exist nor be determined to produce
> an effect unless it is determined to exist and produce an effect by
> another cause, which is also finite and has a determinate existence;
> and again, this cause also can neither exist nor be determined to
> produce an effect unless it is determined to exist and produce an
> effect by another, which is also finite and has a determinate
> existence, *and so on, to infinity*. [Italics added]
> 
> 
> 



Each link in this causal chain is preceded by infinitely many causes
and is followed by infinitely many effects. Each link also provides at
least part of the *explanation* for the existence of the
following link. Is the existence of such an infinite regress
consistent with the PSR? Spinoza has no qualms about answering this
question in the positive. We may legitimately ask what is the cause of
each link in the chain, and the answer would be: the preceding link.
Spinoza also thinks that we may--indeed, should--ask what is
the cause, or reason, for the existence of *the entire infinite
chain*? He simply thinks that he can provide a clear answer to the
latter question as well: God (or the being which is the ground of its
own existence). Consider the following passage from Spinoza's
celebrated "Letter on the Infinite" in which he criticizes
proofs of the existence of God which rely on the impossibility of an
actual infinity of causes and effects.



> 
> 
> In passing I should like to note here that the more recent
> Peripatetics have, as I think, misunderstood the demonstration by
> which the Ancients tried to prove God's existence. For as I find
> it in a certain Jew, called Rab Chasdai, it runs as follows: if
> *there is an infinite regress of causes*, then all things that
> are will also have been caused; but it does not pertain to anything
> which has been caused, to exist necessarily by the force of its own
> nature; therefore, there is nothing in Nature to whose essence it
> pertains to exist necessarily; but the latter is absurd; therefore,
> the former is also. Hence *the force of this argument does not lie
> in the impossibility of there being an actual infinite or an infinite
> regress of causes, but only in the supposition that things which do
> not exist necessarily by their own nature are not determined to exist
> by a thing which does necessarily exist by its own nature*. [Ep.
> 12| IV/61/15-62/10; italics added]
> 
> 
> 



In this passage, Spinoza follows the late medieval Jewish philosopher
Hasdai Crescas in rejecting the Aristotelian ban on actual infinity
(see Melamed 2014). For Spinoza (and Crescas) the existence of an
infinite regress of causes is perfectly legitimate. Yet, if all the
items in this infinite chain are contingent beings (i.e.,
"things which do not exist necessarily by their own
 nature"[7]),
 the chain itself remains a contingent being, and there must be a
reason which explains its instantiation in reality. The ultimate
reason for the instantiation of such an infinite chain of contingent
beings must, claims Spinoza, be a being whose existence is not
contingent (for otherwise, the chain will remain merely contingent and
its instantiation in reality would not be sufficiently explained).
Thus, Spinoza allows for an infinite regress of causes (or
explanations) as long as the entire infinite chain is grounded in a
being which exists by virtue of its mere essence.


## 3. Leibniz



No philosopher is more closely associated with the PSR than Gottfried
Wilhelm Leibniz (1646-1716). He was the first to call it by name
and to recognize it as a major principle of philosophy. Still, Leibniz
was well aware of the similarity between his principle and
Spinoza's claims. Thus, in a 1676 marginal note to his copy of
Spinoza's "Letter on the Infinite" (which we have
just discussed at the end of SS2), he writes: "This is
rightly observed, and agrees with what I am accustomed to saying that
nothing exists but that for whose existence a sufficient reason can be
provided" (Leibniz, *Labyrinth of the Continuum*, 117/
Aiii71). Leibniz's treatment of the PSR is also noteworthy for
its systematicity and the centrality that he accords it.



Leibniz often presents it, along with the Principle of Contradiction,
as a principle of "reasoning". For example, in the
*Monadology* (1714) he writes:



> 
> 
> 31. Our reasonings are based on two great principles, that of
> contradiction, in virtue of which we judge that which involves a
> contradiction to be false, and that which is opposed or contradictory
> to the false to be true.
> 
> 
> 
> 32. And that of sufficient reason, by virtue of which we consider that
> we can find no true or existent fact [*fait*], no true
> assertion [*enonciation veritable*], without
> there being a sufficient reason why it is thus and not otherwise,
> although most of the time these reasons cannot be known to us. (G VI,
> 612/L 646)
> 
> 
> 



These principles are characterized in what appears to be epistemic
terms. They are principles of "our reasoning". They
concern what we "judge" or "find". And yet it
is clear that Leibniz intends them to have metaphysical as well as
epistemic import. In the case of the PSR, this will become more
evident when we discuss how Leibniz understands the notion of a
sufficient reason but it is already indicated in the passage quoted
above by the fact that Leibniz explicitly states that there are
sufficient reasons for every truth or fact even if such reasons are
*unknowable* by us. (The distinction between the epistemic and
the metaphysical collapses with respect to God because there can
be no gap between what an omniscient being knows and how things
are.) 



The scope of the PSR, as stated above, includes facts and truths.
Leibniz sometimes, however, characterizes the scope of the principle
in different terms. For example, he writes:



> 
> 
> [T]he principle of sufficient reason, namely, that nothing
> *happens* [*rien n'arrive*] without a reason. (G
> VII 356; LC L2; AG 321, our emphasis)
> 
> 
> 



The PSR is here said to apply to what "happens". This
suggests a version of the PSR that applies not to truths or facts but
rather events: Every event has a sufficient reason.



These vacillations in the formulation of the PSR are not typically
taken to register indecision on Leibniz's part as to the scope
of the PSR. Rather they are usually understood as indicating that
Leibniz views the scope of the PSR to be very wide, perhaps even
absolutely general, but at least wide enough to encompass facts,
truths, and events (see Rodriguez-Pererya 2018).



Leibniz associates the Principle of Contradiction and the PSR with a
variety of domains where each is especially important. For example,
there are domains where the truths of the domain *depend* on
one of the two principles. These domains are characterized modally:
The Principle of Contradiction rules over the domain of necessary
truths and the PSR rules over the domain of contingent truths (A 6 4
1616/MP 75; G VII 355-56/LC 15-16).



There are also domains that are characterized in terms of subject
matter or areas of inquiry. The Principle of Contradiction allows us
to study mathematics, whereas the PSR allows us to study metaphysics,
natural theology, and physics (G VII, 355-6; LC L2; AG 321). It
is far from obvious that these two ways of assigning domains to the
Principles are equivalent. For example, it would be natural to assume
that metaphysics and natural theology would include necessary
propositions and thus the PSR would encroach upon the territory
assigned to the Principle of Contradiction according to the modal
characterization.



We must therefore distinguish distinct ways of associating the
principles with various domains. The first way is to specify the
domain to which each principle *applies*. Leibniz appears to
believe that, according to this approach, there is a single universal
domain and it is associated equally with each principle. There are no
contradictory contingent facts or truths and so the Principle of
Noncontradiction *applies* to all contingent truths as well as
all necessary truths. Likewise, it is usually assumed that, for
Leibniz, every necessary truth has a sufficient reason (see Broad
1975: 12 and 34 and Rodriguez-Pererya 2018). For example, mathematical
truths, might have sufficient reasons in the form of proofs that rest
on statements of identity. Thus the PSR *applies* to all
necessary truths as well as all contingent truths.



The second way of associating the principles with specific domains is
to specify the domain of truths that is *grounded* on or
*depends* on each principle. According to Leibniz, only
contingent truths depend on and are grounded by the PSR. Likewise,
Leibniz believes that only necessary truths depend on and are grounded
by the Principle of Contradiction. What does it mean for some truths
to *depend* on a principle? Leibniz is not explicit on this
point but we will get a better idea in the next section when we
consider the question of what counts as a sufficient reason.



The third way is to specify a domain of truths that can be
*investigated* on the basis of each principle. For Leibniz, we
can know mathematical truths only on the basis of the Principle of
Contradiction and only metaphysical, theological, and physical truths
require the PSR in order to be known. We will see in more detail in
what way the PSR allows us to investigate these domains in the section
on applications.


### 3.1 What is a Sufficient Reason?



When Leibniz insists that every truth or fact requires a sufficient
reason, what does he mean by "sufficient reason?" In some
texts he suggests that sufficient reason is an "*a
priori* proof". This should not be understood in Kantian
terms as a proof that doesn't require any input from sense
experience. Rather, Leibniz uses the term "*a
priori*" in its original pre-Kantian meaning, which means an
argument from causes to effects. An *a priori* proof is a proof
that reflects the causal order. Thus, a sufficient reason would be a
proof that is both a demonstration--a set of premises and a
conclusion such that the former necessitate the later-and a
causal explanation--a statement of the causal antecedents of some
truth or event (see Adams 1994: 109). 



In order to fully understand Leibniz's conception of a
sufficient reason, we need to also understand his theory of truth and
its relationship to his theory of modality. Let us begin with truth.
To keep things simple, we will focus only on categorical propositions
of subject-predicate form. A proposition is true, according to
Leibniz, just in case the concept of the predicate is contained in the
concept of the subject. Uncontroversially, the concept of the
predicate *unmarried* is contained in the concept
*bachelor* and it is this conceptual containment which explains
the truth of the statement *bachelors are unmarried*. But
Leibniz makes the further highly controversial claim that *all*
true statements are true for this reason, even statements like
*Caesar crossed the Rubicon*. That is, this statement is true
because the concept *crossed the Rubicon* is contained in the
concept of Caesar. This theory of truth is sometimes called the
*conceptual containment theory of truth*. It has as a
consequence that all truths are analytic. But wouldn't such a
theory entail that all truths are necessary? After all, how could an
analytic truth be contingent?



In response to this worry, Leibniz develops an account of contingency
in terms of *infinite
 analysis*.[8]
 Leibniz understands analysis as the process of replacing the terms of
a proposition with definitions or partial definitions. A demonstration
results when an identity is obtained through the process of analysis
in a finite number of steps. Leibniz claims that all and only
necessary truths have a finite demonstration by analysis and all and
only contingent truths do not have a demonstration by analysis in a
finite number of steps. In this way, he preserves the distinction
between necessary and contingent truths while also maintaining that
all truths are analytic, that is, true in virtue of the meaning of the
concepts involved.



This has led some commenters to think that Leibniz gave up the account
of sufficient reason as an *a priori* proof. If there were a
proof or demonstration, it would reveal that the concept of the
predicate was contained in the concept of the subject in a finite
number of steps and hence every proposition would be necessary.
Leibniz is not a necessitarian in his late philosophy and thus he
could not have accepted this consequence. Instead, he must have
shifted from the conception of a sufficient reason as an *a
priori* proof to that of an *a priori* proof sequence,
where the latter notion is understood as an analysis that converges on
an identity without reaching it in a finite number of steps (see
Sleigh 1983: 200). What it means for an analysis to converge on an
identity is, unfortunately, obscure. Nevertheless, there is some clear
sense in which every contingent truth has a sufficient reason on this
understanding. The sufficient reason why it is true that Caesar
crossed the Rubicon, for example, is that the concept *crossing the
Rubicon* is contained in the concept *Caesar*. The truth of
the proposition obtains in virtue of the concepts of the subject and
the predicate. Of course, this reason is undiscoverable by any finite
human mind because it is buried too deeply in the concept of Caesar.
Only God, in his omniscience sees the conceptual connection between
them. It is enough for there to be such a connection for there be a
sufficient reason.



Such a conception of the nature of a sufficient reason have led some
commentators to think that for Leibniz the PSR is a logical notion or
that it is a metaphysical notion that is ultimately reducible to logic
(Couturat 1901: 123ff and Russell 1937: v). But the notion of a
sufficient reason as a non-terminating proof sequence is not the only
conception of a sufficient reason to be found in Leibniz. And other
conceptions have a decidedly less logical and more metaphysical
flavor.



One such characterization of a sufficient reason comes from
Leibniz's conviction that in order to preserve the notion of
causal activity, without which substances are not really
substances--i.e., truly fundamental building blocks of reality.
Each genuine substance, for Leibniz, has what he calls a
"primitive active force". This force is the nature or
essence of the substance. Now according to Leibniz, substances do
not causally interact with one another (see the entry
 Leibniz on causation).
 The changes that they undergo derive solely from their own natures or
primitive active force, which consequently determines the whole of its
history. Many texts suggest that, for Leibniz, the sufficient reason
for any state of a substance is its primitive active force (NE
65-6; T 400/G VI, 354; Mon. 18/G VI, 609-610; G IV, 507; G
III, 72).



In many ways primitive active force plays the role of the concept of
the subject in the logical version of the PSR. Just as on the logical
version the PSR that \(a\) is \(F\) is explained by the fact
that the concept of \(F\)-ness is in the concept of \(a\),
so too on the metaphysical version of the PSR fact that \(a\) is
\(F\) is explained by the primitive active force of \(a\)
that determines it to be \(F\). Whereas commentators such as
Couturat and Russell emphasize the logical notion of a sufficient
reason to the detriment of the metaphysical notion, other commentators
see the logical and the metaphysical as two equally fundamental
presentations of the same datum (see Frankel 1994).



Another metaphysical characterization of a sufficient reason connects
with the Principle of the Best, which says that for any proposition
\(p\), \(p\) is true just in case \(p\) holds in the
best possible world (G VI.448/DM 22; Mon. 46, 53, 54/G VI,
614-616). Is the Principle of the Best a supplement to the PSR
or a rival to the PSR? It is, in fact, a consequence of the PSR in
conjunction with three additional assumptions: (1) the sufficient
reason for every choice is that the chooser perceives it to be the
best; (2) God chooses the actual world; (3) God perceives something to
be what is best just in case it is the best.



In some texts, Leibniz suggests that the sufficient reason for
contingent truths cannot be found in the concepts or natures of
things. We must instead look to the Principle of the Best (Mon.
36-38/G VI, 613). In other words the sufficient reason for any
contingent proposition of the form "\(a\) is
\(F\)" is that \(a\) is \(F\) is true in the best
possible word. This appears to be an entirely different sort of reason
than the fact that "\(a\) is \(F\)" is analytic
or that the nature of \(a\) determines that it is \(F\).
Those latter reasons are to be found internal to the concept of the
subject or the nature of the substance. Reasons that advert to the
Principle of the Best look outside the concept of the subject or the
nature of the substance and make comparisons between worlds in terms
of their relative perfections. It is possible that Leibniz thought
that these different conceptions of sufficient reasons were equivalent
but that they are so is far from obvious.


### 3.2 Why Did Leibniz Believe the PSR?



Leibniz argues for the PSR in three distinct ways: (1) from the
concept of a sufficient reason and the concept of a
"requisite"; (2) from his theory of truth; and (3)
inductively.



In some texts, Leibniz argues that the PSR is a conceptual truth that
is derivable from the concepts of a sufficient reason and the concept
of a requisite (A VI, ii, 483; see also G VII 393, LC L5.18; A
VI.iii.133). The concept of a requisite is that of a necessary
condition. In this context, Leibniz defines a sufficient reason as a
sufficient condition. If something exists, then all of its requisites
have been posited. Leibniz then asserts that if all of a things
requisites have been posited, then it exists. Thus, all of a
thing's requisites are a thing's sufficient reason. The
question-begging assumption is that all the necessary conditions for
something to exist are jointly sufficient for it to exist. Anybody who
denies the PSR will not agree with this assumption and it is clearly
not encoded in the definitions of *requisite* and
*sufficient reason* provided by Leibniz (for further
discussion, see Harrop 2020).



In other texts, Leibniz argues that the PSR follows from the
conceptual containment theory of truth (A VI.iv.1645/L 268; AG 31).
Every truth is such that the concept of the predicate is contained the
concept of the subject. This conceptual connection is the sufficient
reason for the truth. Thus every truth has a sufficient reason.



It is worth noting that Leibniz believed the PSR before he developed
his conceptual containment Theory of Truth. In fact, the PSR is one of
Leibniz's earliest and most stable philosophical commitments
(see, for example, Leibniz's 1671 letter to Wedderkopf A
II.ii.117f/L146). This observation has led some scholars to conclude
that rather than deriving the PSR from the conceptual containment
theory of truth, Leibniz was in fact led to the conceptual containment
theory from his antecedent commitment to the PSR. The conceptual
containment theory explains how there could be a sufficient reason for
every truth by guaranteeing that there will be an explanation in terms
of conceptual relations (see Adams 1994: 69). Moreover, in at least
one text, it is not at all clear whether, for Leibniz, the conceptual
containment theory of truth motivates the PSR, or rather it is the PSR
which motivates the conceptual containment theory of truth: see
Leibniz, *Philosophical Writings*, 172).



In his Fifth paper to Clarke, Leibniz argues for the PSR inductively.
He says that there are many cases where a fact has a sufficient reason
and no cases where fact is known not to have a sufficient reason. He
then says that it is reasonable to assume that the PSR holds in all
cases where we do not know that sufficient reason. Leibniz describes
this as "the method of experimental philosophy, which proceeds
*a posteriori*" (G VII 420; LC, L5.129).


### 3.3 Applications



Leibniz says that PSR is needed if we are to go beyond mathematics to
metaphysics and natural science. How does the PSR help in those
domains of inquiry? There is a general pattern of argument that
Leibniz uses to establish conclusions using the PSR. First, he assumes
the falsity of what he wants to prove. Call the proposition to be
proved \(p\). Then he tries to show that if \(p\) were
false, there would be some fact or truth for which there could not be
sufficient reason. But by the PSR, there is no such fact or truth.
Therefore, \(p\) is true. Leibniz uses this template to argue for
a number of claims, including the indefinite extension of space
(*Labyrinth of the Continuum*, 233), determinism
(*Leibniz-Stahl Controversy*, 17), the impossibility of bare
occult qualities and bare faculties (*Philosophical Writings*,
172-3), the identity of indiscernibles, relationalism with
respect to space and time, and the existence of God. Let us briefly
look at how Leibniz uses the PSR to argue for each of the last three
theses.



Leibniz presents arguments for the existence of God from the PSR in a
number of different places (for example, *The Ultimate Origination
of Things*, G VII 302-3; L 486-8. *Monadology*
SS37). Suppose that God does not exist. If God does not exist,
then the only things that exist are contingent beings. Would the
entire series of contingent things have an explanation? The
explanation of the entire series cannot be a member of the series
since then it would explain itself and no contingent thing is
self-explanatory. But the explanation cannot be outside of the series
because we have assumed that there is no non-contingent being, i.e.,
God. Thus if God did not exist, there would be something unexplained:
the series of contingent beings. Everything has an explanation.
Therefore God exists (notice, the similarity to the argument for
God's existence Spinoza cites in the name of Crescas which we
have just discussed at the end of SS2 above. In fact, this proof
by Leibniz appears in a 1676 gloss to his copy of Spinoza's
letter discussing Crescas' proof. See Leibniz, *The Labyrinth
of the Continuum*, 117).



Leibniz also thinks that the PSR rules out the possibility that there
could be two or more indistinguishable, that is, indiscernible, things
(A VI, iv, 1541/AG 42). If there were two such things, God would have
treated them differently insofar as he has related them differently to
the rest of the world. For example, if there were two blades of grass
that were indiscernible from each other, then one blade would stand in
spatial and temporal relation \(R\) to the rest of the world,
whereas the other blade would stand in some other spatial and temporal
relation \(R'\) to the rest of the world. Why did God
choose to put the first blade relation \(R\) to the rest of the
world instead of \(R'\)? Leibniz claims that since they are
indiscernible from each other, *there could be no reason* for
God to treat them differently. Thus if there were two indiscernible
individuals, then God would have acted for no reason. But there is a
reason for everything. So, there are no indiscernible yet numerically
distinct things.



For similar reasons, Leibniz thinks that space and time cannot be
substances or anything else absolute and must ultimately be a system
of relations that obtain between bodies (e.g., LC, L, 3.5). This is
because if space, for example, were absolute, then there would be
space points that were indiscernible from one another. God would treat
these space points differently from each other insofar as he orients
his creation in space one way rather than another. This would have to
be an arbitrary decision for the reasons outlined above. So, space and
time are not absolute (see Lin 2011).



Next to the PSR, Leibniz also holds a complimentary principle
according to which nothing is without effects, or "nothing is
sterile" (see, for example, Monadology SS69 and AG 38).


## 4. Emilie du Chatelet



At the beginning of this entry we have addressed briefly the question
of motivating the PSR. The PSR demands that all facts must have a
sufficient explanation, and were the PSR itself unmotivated, it would
seem to simply refute itself. We have also seen that overall
Leibniz's attempts to justify the PSR were not particularly
successful (in Spinoza's early works there is an attempt to
justify the PSR, but he deserted this path in his later works). In
this section, we would like to discuss one of the most intriguing
attempts to justify the PSR as an exceptionless methodological
principle. The arguments we are about to discuss appear in
Emilie du Chatelet's 1740 *Institutions de
physique* (*Foundations of Physics*) "ostensibly a
textbook in physics for her son, but in reality, a highly original
work in natural philosophy" (Detlefsen 2018, SS1). In this
work, Du Chatelet attempts to provide a unified Newtonian
natural philosophy that is grounded in metaphysics. Just like Leibniz,
du Chatelet views the principle of contradiction and the
principle of sufficient reason as the two fundamental principles of
philosophy.



Immediately after presenting the PSR, Du Chatelet turns to
justify the principle:



> 
> 
> If we tried to deny this great principle, we would fall into strange
> contradictions. For as soon as one accepts that something may happen
> without sufficient reason, one cannot be sure of anything, for
> example, that a thing is the same as it was the moment before, since
> this thing could change at any moment into another of a different
> kind; thus truths, for us, would exist only for an instant.
> 
> 
> 
> For example, I declare that all is still in my room in the state in
> which I left it, because I am certain that no one has entered since I
> left; but if the principle of sufficient reason does not apply, my
> certainty becomes a chimera since everything could have been thrown
> into confusion in my room, without anyone having entered who was able
> to turn it upside down (*Foundations of Physics*, SS8| Du
> Chatelet 2009, 129)
> 
> 
> 



Without the PSR, claims Du Chatelet, we cannot be certain that
the unexperienced world has the continuity and unity we always assume.
Were we not to assume the PSR, we should be seriously concerned about
the possibility of things appearing out of thin air and disappearing
into nothing. Without the PSR, we cannot assume the permanence of
anything. The very fact that we are not concerned about the sudden
appearance or disappearance of things, seems to indicate that we
actually assume the PSR. Moreover, claims Du Chatelet, our very
foundational notions of equality and identity, seem to assume the
principle:



> 
> 
> Without this principle there would not be identical things, for two
> things are identical when one can substitute one for the other without
> any change to the properties which are being considered. This
> definition is accepted by everyone. Thus, for example, if I have a
> ball made out of stone, and a ball of lead, and I am able to put the
> one in the place of the other in a basin of a pair of scales without
> the balance changing, I say that the weight of these balls is
> *identical*, that is the same, and that they are identical in
> terms of weight. If something could happen without a sufficient
> reason, I would be unable to state that the weight of the balls is
> identical, at the very instant when I find that it is identical, since
> a change could happen in one and not the other for no reason at all
> (*Foundations of Physics*, SS8| Du Chatelet 2009,
> 129)
> 
> 
> 



When we compare two balls on a scale and infer that their weight is
equal from the fact that neither side of the scale drops lower, we
assume that the scales do not remain balanced without a reason.
However, if thing could happen without reason, our inference would be
unwarranted.



According to some commentators, Du Chatelet's last
argument shows not only that everything must have a sufficient reason,
but also that this reason must be *accessible to us* (i.e.,
humans, or finite cognizers), at least in principle (Amijee 2021 and
Wells 2021). Here is why. Consider the scales scenario in a world in
which the PSR obtains strictly (and we are aware of this), but some
reasons are in principle inaccessible to us. In such a world, we could
not infer with certainty the equality of the balls from the horizontal
states of the scales, since we should consider the possibility of
interfering causes that are inaccessible to us.



A version of the PSR which requires that all reasons must be
accessible to humans is not easy to accept: why should we assume that
the nature of the world is such that it is cognitive accessible to any
specific being? Of course, an anthropocentric version of the PSR might
be warranted if one assumes that the world was created by a benevolent
creator who intentionally designed the world in such a manner that it
will always be accessible to human beings, but this cluster of heavy
premises would be clearly rejected by many proponents of the PSR (such
as Spinoza).



Setting aside the question of whether Du Chatelet's last
argument indeed requires that reasons must be accessible to humans, it
seems she does offer a promising line of motivating the PSR as a
regulative rather than a factive principle (see SS1 above). 


## 5. The PSR before Spinoza and Leibniz



The PSR is nearly as old as philosophy itself. Anaximander, one of the
earliest of the pre-Socratics, is usually credited--on the basis
of Aristotle's *de Caelo*, (b12
295b10-16)--with being the first to make use of it.
Anaximander argues, we are told, that the Earth remains stationary in
space because it is located in the center of the universe and thus is
"indifferently" related to any "extreme
point". This indifference means that if it were to move in any
direction, it would do so without a reason. Since he concludes from
this that it does not move, we can assume that Anaximander believes
that motion in the absence of a reason is impossible.



Parmenides, another pre-Socratic, implicitly appeals to the PSR when
he claims that the world cannot have come into existence because then
it would have come from nothing (Fragment B8 9-10). It is
against the later alternative that Parmenides appears to wield the
PSR. Nothing comes from nothing because if it did, then we could ask:
why did it not come into existence at an earlier or a later time than
it actually did? Parmenides appears to think that if the world comes
into existence from nothing, then there is no possible answer to this
question. After all, prior to the coming-to-be of the world, there is
nothing to explain its coming-to-be. Thus, its coming-to-be would be
an arbitrary brute fact. There are no brute facts regarding
coming-to-be. So, the world did not come into existence from
nothing.



Another ancient source for the PSR is Archimedes who writes:



> 
> 
> Equal weights at equal distances are in equilibrium, and equal weights
> at unequal distances are not in equilibrium but incline towards the
> weight which is at the greater distance (*On the Equilibrium of
> Planes*, 189).
> 
> 
> 



Archimedes assumes that if there is a balance such that there is no
difference between the weights and distances on either side, then
neither side of the balance can move up or down. This is sometimes
taken to be an implicit application of the PSR and is cited by
Leibniz in his correspondence with Clarke as a precedent for his own
principle.



In the Islamic world, Avicenna appears to assume a version of the PSR
when he claims that the existence or nonexistence of any non-necessary
possible thing must have a cause outside itself. If it didn't,
then either the cause would be internal to the non-necessary possible
thing (which Avicenna takes to be contrary to the nature of a (mere)
possible being) or it doesn't have a cause at all.
Avicenna's reasoning implicitly rejects this latter alternative
and thus he appears to be committed that all existence and
nonexistence has a cause (Avicenna, *Metaphysics* 1.6 SS1;
*Al-Shifa'*: *Al-Ilahiyyat*, 37; See Richardson
747).



In the medieval Latin West, Peter Abelard argues that God must create
the best of all possible worlds in a way that both appears to
presuppose some version of the PSR and anticipates Leibniz's
reasoning on the subject. If God didn't, Abelard argues, there
would have to be some reason for it. But what reason could that be
except God's injustice or jealousy? But God cannot be unjust or
jealous. So there is no possible reason for God making anything less
than the best. Everything has a reason. Thus God makes the best
possible world (Op. cit. col. 1324b; McCallum 1948, 93).
Abelard's opinion was rejected as heresy and mainstream opinion
of philosophers during the Middle Ages in the Latin West appears to
reject the PSR. God, on the mainstream medieval view, enjoys freedom
of indifference with respect to his creation. Thus there is no
sufficient reason for why God created what he did and the PSR slips
from prominence until its early modern revival at the hands of Spinoza
and Leibniz.



Some great epistemological rationalists, such as Plato and Descartes,
appear to endorse the unrestricted PSR but in fact do not. For
example, in the *Timaeus* Plato writes,



> 
> 
> [E]verything that comes to be must of necessity come to be by the
> agency of some cause, for it is impossible for anything to come to be
> without a cause. (28a4-5)
> 
> 
> 



This passage appears to assert the unrestricted PSR. But Plato
believes that there are things that are not among the things that
"come to be," and some of these things have no cause
or reason. For example, the Demiurge creates the world by imposing
order on disorderly motion. The disorderly motion preexists the work
of the Demiurge. It is uncaused and there is no reason for it.



At times, Descartes appears to endorse the unrestricted PSR. For
example, he argues for the existence of God in the third
*Mediation* on the basis of the principle that there must be at
least as much reality in the cause as in the effect. And he justifies
this causal principle by claiming that "Nothing comes from
nothing". This appears to make him as much an adherent of the
unrestricted PSR as Parmenides who, as we have seen, argues for his
conclusions on the same basis. But elsewhere Descartes claims that God
creates the eternal truths, such as mathematical and metaphysical
truths (Letters to Mersenne, April 15, May 6, and 27, 1630; *Fifth
Replies*, AT 7:380, CSM 2:261). Moreover, he claims that God
creates these truths by an act of will which is free and indifferent.
Thus there can be no reason for the creation any of these truths. If
mathematical and metaphysical truths are contingent and yet have no
sufficient reason according to Descartes, then his philosophy imposes
serious restrictions on any PSR.


## 6. The PSR in Eighteenth-Century Philosophy and German Idealism



Hume's critique of causation presents an important challenge to
the PSR. In his *Treatise of Human Nature* (I, 3, 3) Hume
considers several arguments which attempt to prove the "general
maxim in philosophy, that *whatever begins to exist, must have a
cause*" and finds all of them wanting. Hume argues that
since the ideas of cause and its effect are evidently distinct, we can
clearly conceive or imagine an object without its cause. He takes the
separability of the two ideas to show that there is no necessary
conceptual relation between the ideas of cause and effect insofar as
conceiving the one without the other does not imply any contradiction
or absurdity.



Christian Wolff (1679-1754), the most influential German
philosopher of the first half of the eighteenth century, was a
follower of Leibniz and developed the latter's system. Like
Leibniz, Wolff assigned to the PSR a central role in his system while
attempting to avoid necessitarianism (or "fatalism"). Like
Spinoza and Leibniz, Wolff demanded a reason for both the possibility
of things [*ratio essendi*] (i.e., coherence of essence) and
for the actualization, or coming to be, of essences [*ratio
fiendi*]. Wolff mildly criticized Leibniz for allegedly grounding
the PSR merely in experience and attempted to marshal several proofs
for the principle (*Rational Thoughts on God, the World, and the
Soul of Human Beings*, SSSS30-31, 143;
*Ontologia*, SSSS56-78; cf. Look 2001,
210-214). One of these proofs attempts to prove the PSR relying
on the principle of the Identity of Indiscernibles (*Rational
Thoughts on God, the World, and the Soul of Human Beings*
SS31), while the most famous proof attempts to derive the PSR from
the Law of Non-Contradiction. According to the latter, if a thing
\(A\) is assumed to exist without reason, than "nothing is
posited that explains why \(A\) exists". This, according to
Wolff, would mean that \(A\) exists because of nothing
(*Ontologia*, SS70), which Wolff claims to be absurd.
(Wolff seems to be assuming here the *ex nihilo nihi fit*
maxim.) Kant criticized the proof claiming that it is based on an
equivocal use of the term "nothing" (AK 1:398).



Leonhard Euler, the great Swiss mathematician and a contemporary of
Wolff, warned against the "wretched abuse" of the PSR by
those who



> 
> 
> employ it so dexterously that by means of it they are in a condition
> to demonstrate whatever suits their purpose, and to demolish whatever
> is raised against them. (*Letters to German Princess*, Letter
> XIII)
> 
> 
> 



According to Euler, many of the proofs which rely on the PSR amount to
nothing over and above a *petitio principii*, while others
derive carelessly the impossibility of things from our ignorance of
the causes of these things.



In the *Critique of Pure Reason* (1781, 1787), Kant claims to
provide a proof for the PSR by showing that



> 
> 
> [T]he PSR is the ground of possible experience, namely the objective
> cognition of appearances with regards to their relation in the
> successive series of time. (B/246/A201)
> 
> 
> 



Relying on his transcendental method Kant argues in the "Second
Analogy of Experience" that a certain version of the PSR is a
condition for the possibility of experience, and as a result also a
condition for the possibility of objects of experience. Yet, this
argument also restricts the validity of the PSR to human experience,
i.e., to things which appear in space and time. Any use of the PSR
that transgresses the boundaries of human experience is bound to
generate antinomies.



Kant's view of space and time as exhibiting *brute*
difference (i.e., the non-identity of locations in space and time
cannot be reduced to conceptual explanation) stands in sharp contrast
to the Principle of the Identity of Indiscernibles, and thereby also
to the PSR. Salomon Maimon, Kant's rationalist critic, attempted
to enforce rationalist strictures on Kant's philosophy by
arguing that Kant is unable to explain the necessary agreement of
intuitions and concepts. According to Kant, intuitions and concepts
come from entirely different sources: sensibility and understanding.
But if this were the case, claims Maimon, we could not explain the
constant agreement between intuitions and concepts, which is necessary
for the possibility of experience. This agreement can be explained if
we reject the radical heterogeneity of intuitions and concepts, and
view intuitions as disguised concepts. Thus, any difference exhibited
in space and time must have its ground in the universal forms of our
thought in general (Maimon, *Essay on Transcendental
Philosophy*, Ch. 1, p. 13). Maimon also argued that we must seek
an explanation for the fact that we have *two* forms of
intuition rather than one, and suggested that it is only the interplay
between the two forms of intuition which allows us to exhibit
difference, by using a unity in one form to exhibit difference in the
other form, i.e., conceive different times by concentrating on the
change occurring at the same location in space, or conceive different
locations in space at the same point in time (*Essay*, Ch. 1,
 13-14).



Maimon was probably the strictest adherer to an unrestricted version
of the PSR among the German Idealists. For Maimon, satisfying the
demands of the PSR is *the infinite task* of both philosophy
and science. Thus, in response to Maimonides' claim that crucial
astronomical facts are poorly explained by science, Maimon writes:



> 
> 
> The world may be, in terms of time, finite or infinite; still,
> everything in it (as consequences of the highest wisdom) *must be
> explainable through the principle of sufficient reason*. How far
> we can actually get in achieving this is beside the point. Those
> things that Maimonides, working with the astronomy of his day,
> regarded as inexplicable, new discoveries (particularly Newton's
> system) equip us to explain quite well. The highest order in the
> arrangement of the world's structure is for us a necessary idea
> of reason, which, through the use of reason with regard to objects of
> experience, *we can approach but never reach*. (Maimon, 1792/3
> [2019, 170]; italics added).
> 
> 
> 



Ground [*Grund*] and the Principle of Sufficient Ground
[*der Satz vom zureichenden Grund*] play a significant role in
Hegel's Logic. For Hegel, the demand for ground provides a major
source of transition from one thing to another. It is, Hegel says,
"the expulsion of itself from itself" (*Encyclopedia
Logic*, SS121A). Ground, for Hegel, is the unity of identity
and difference: the ground of \(x\) has to explain all features
of \(x\), and in sense duplicates it, yet it must also be
different from \(x\) in order to have explanatory value and not
be a mere *petitio principii*.



The PSR is the subject of Schopenhauer's 1813 doctoral
dissertation: *The Fourfold Root of the Principle of Sufficient
Reason*. In this work, Schopenhauer provides a brief history of
the PSR, and then raises the questions of the justification for the
PSR and the proper scope of the principle. Schopenhauer follows Wolff
in distinguishing among four kinds of reasons, corresponding to four
kinds of objects, and charges that much philosophical confusion arises
from attempts to explain objects of one kind by reasoning that belongs
to the other kind. These four kinds of explanation, or four variants
of the PSR, share the very same ground. Along Kantian lines
Schopenhauer suggests that it is the subject's activity in
regularly connecting representations that is the ground of the PSR
(*The Fourfold Root*, SS16).


## 7. The PSR in Contemporary Philosophy



It has recently been proposed by Dasgupta that a version of the PSR
could be formulated in terms of grounds. Grounding is said to be a
kind of explanation distinct from causal explanation. It is a
metaphysical or constitutive explanation. It is generally taken to be
asymmetric, irreflexive, and transitive. Alleged examples of grounding
relations are: dispositions (e.g., fragility) are grounded in
categorical features (e.g., molecular structure); semantic facts
(e.g., Jones means *addition* by "+") are grounded
by non-semantic facts (e.g., Jones is disposed to draw certain
inferences); mental properties (e.g., pain) are grounded by physical
properties (e.g., c-fibers firing; see Rosen 2010 and Fine 2012). The
proposal is formulated as follows:



> 
> 
> PSR: For every substantive fact \(Y\) there are some facts, the
> \(X\)s, such that (i) the \(X\)s ground \(Y\) and (ii)
> each one of the \(X\)s is autonomous. (Dasgupta 2016: 12)
> 
> 
> 



Here *substantive* means apt for grounding and
*autonomous* means not apt for grounding. For example, perhaps
essentialist facts are autonomous where essentialist facts are facts
of the form: it is essential to \(x\) that \(\phi\). The
idea is that just as definitions are not apt for proof, essentialist
facts are not apt for grounding explanations, that is, they are
autonomous (Dasgupta 2016: 6-9). The notion of an autonomous
fact allows the adherent of this version of the PSR to avoid the
Agrippan Trilemma without allowing for self-explanatory facts or
infinite regresses. Chains of explanation terminate with autonomous
facts, which are not brute because they are not apt for
explanation.



Following Bolzano (*Theory of Science*: vol. II,
259-264), most contemporary theories of grounding affirm the
irreflexivity of this relation (see Fine 2001: 15; Schaffer 2009: 364;
and Rosen 2010: 115). More recently, Fine showed that given certain
plausible premises, one may point out counterexamples to irreflexivity
(Fine 2010; cf. Kramer 2013), and the issue has been further
challenged by Jenkins (2011).



Jonathan Schaffer has relied on the notion of ground to revive an
Aristotelian, structured metaphysics, i.e., a metaphysics which is
ordered by priority relations (Schaffer 2009), and to defend Priority
Monism (see the entry on
 monism).
 In response, Michael Della Rocca (2014) has argued that strict
adherence to the PSR--and to Ockham's Razor (see the entry
on
 simplicity)--undermines
 Schaffer's structured metaphysics (and Priority Monism), since
insofar as all the features of the grounded are already present in the
ground, the existence of the grounded is just redundant. (See also the
entry on
 metaphysical grounding).
 More recently, in his audacious 2020 book, Della Rocca expanded his
argument. Relying on what he takes to be a strict adherence to the
PSR, and assisted by F.H. Bradley's critique of the reality of
relation, Della Rocca argues that we are entitled to assert only the
existence of undifferentiated being that stands in no relations of
distinction. According to Della Rocca, our major philosophical
concepts - substance, action, knowledge, meaning, and
explanation - fail to meet the strict requirements of the PSR.
Toward the end of the book, Della Rocca launches a powerful attack on
the widespread reliance on intuitions among analytic philosophers
(Della Rocca, 2020, 260-290).



The question of the justification for the employment of the PSR has
been addressed in some recent literature (see, for example, Della
Rocca (2010)). Fatema Amijee has argued that from a practical point of
view, participants in structural inquiry (i.e., an inquiry which
attempts to explain why a given fact obtains) must assume the PSR as
long as they do not discover that any fact is brute. Since structural
inquiry is intrinsically valuable (and assists us in discovering new
truths), it is rationally non-optional for us, and consequently, we
must be committed to the PSR (Amijee 2022).



Implications for the PSR might also be discerned in recent discussions
of *surprisingness* or *strikingness*, (although such
implications are not typically stated explicitly). These discussions,
which cut across such diverse subfields as epistemology, philosophy of
science, metaethics, and philosophy of religion, have their origin in
Paul Horwich's observation that there is an intuitive difference
between an event or fact being *unlikely* and its being
*surprising* (Horwich 1982). For example, it is equally
unlikely that, on a given occasion, a monkey typing randomly on a
typewriter will type the string 'sdlek93 91' and that it
will type 'I want a banana.' But although the
probabilities of both events are the same, the latter string is
surprising in a way that the former is not. The difference between
surprising events or facts and unlikely fact is sometimes thought to
map onto the distinction between events or facts that call out for
explanation and those that do not. How can we account for the
difference between the merely improbable--which some believe does
not call out for explanation--and the surprising--which
does? Often it is said that the surprising requires us to challenge
our background beliefs and confirms hypotheses that are alternatives
to those beliefs. Alternatively, that a theory T treats something
surprising as inexplicable is a reason to disbelieve T (White 2007;
Schechter 2013). Thus, such inquiry is guided by the presumption that
the surprising is explicable. Principles such as these have led
philosophers to substantive conclusions as diverse as: (1) the
universe was designed by an intelligent agent (White 2017; van Inwagen
1993); (2) moral realism is false (Street 2006; Enoch 2011); (3) there
exists a multiverse (Leslie 1989; Parfit 1998); and Platonism about
mathematics is false (Field 1989, 2005). Unfortunately, we cannot
discuss the details of the arguments from the improbable/surprising
distinction to these claims here. Nevertheless, this methodological
assumption has interesting repercussions for the PSR. First of all,
those who advocate the distinction tend to suggest that, if the PSR is
true, then it is so only in a restricted form. After all, the point of
the distinction is that some things call out for explanation and
others do not. But it also suggests that something like a restricted
PSR is true. A principle that says that we have an epistemic
reason to believe a hypothesis that would transform a surprising event
of fact into an unsurprising one would only be truth conducive if we
lived in a world in which events and facts are--at least for the
most part--explicable. Why this is so can be illuminated by
analogy with induction. As Hume observed, induction is truth conducive
only if nature is uniform (T. 1.3.6.4). So, by committing ourselves to
the method of induction, we thereby presuppose the truth of the
principle of the uniformity of nature. Similarly, by taking
ourselves to have an epistemic reason to believe a theory because it
renders explicable what is otherwise surprising, we thereby presuppose
the truth of a restricted PSR. 



The role of the PSR in ethics and political theory has not been
seriously studied so far. Clearly, the PSR may be marshaled in order
to question our reliance on mere intuitions. The repugnance of a
certain view cannot be taken at face value, but rather requires a
justification. In the past, various conservative views relied merely
on the alleged repugnance of certain sexual acts (e.g., homosexuality,
interracial relations). The requirement to dig deeper and ask a person
to justify her intuitions may help the person understand the maxims
guiding her specific moral beliefs. Adherence to the PSR may also
shift the onus of proof in the debate between those who consider our
preferential evaluation of human beings over other things in nature as
simply brute (Williams 2006: 195) and those who insist that if human
beings have a special value, there must be a reason for the ascription
of such value (Buss 2012: 343).