The Principle of Sufficient Reason is a powerful and controversialphilosophical principle stipulating that everything must have areason, cause, or ground. This simple demand for thoroughgoingintelligibility yields some of the boldest and most challenging thesesin the history of philosophy. In this entry we begin by explaining thePrinciple and then turn to the history of the debates around it. Weconclude with an examination of the emerging contemporary discussionof the Principle.

• 1. Introduction
• 2. Spinoza
• 3. Leibniz
  • 3.1 What is a Sufficient Reason?
  • 3.2 Why Did Leibniz Believe the PSR?
  • 3.3 Applications
• 4. Émilie du Châtelet
• 5. The PSR before Spinoza and Leibniz
• 6. The PSR in Eighteenth-Century Philosophy and German Idealism
• 7. The PSR in Contemporary Philosophy
• Bibliography
  • Primary Literature
  • Secondary Literature
• Academic Tools
• Other Internet Resources
• Related Entries

1. Introduction

Suppose you enter a farmers’ market, pick out a few cucumbersand ask the merchant for the price. “Five dollars apound”. A bit expensive, you may think, but you pay. Before youleave the stand two other people approach the seller with the verysame question (“How much are the cucumbers?”). “Adollar a pound”, she says to the one; “Ten dollars apound”, she tells the other. At least two of you are likely toattack the merchant with a simple question: Why the price discrepancy?Of course, you may simply leave the place if you have a simpleexplanation for the discrepancy (for example, that both you and theperson who was asked to pay ten dollars a pound belong to commonlydiscriminated minorities). You may also conclude that the seller isjust out of her mind (or that she is just conducting a psychologicalexperiment). In all of these cases you will be entertaining anexplanation orreason for a fact that appears odd.But what kinds of facts demand an explanation? Doallfacts—including the most ordinary ones—demand anexplanation? If you accept an unrestricted form of thePrincipleof Sufficient Reason (= PSR), you will require an explanation forany fact, or in other words, you will reject the possibilityof anybrute, 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 intendedto express any commitment to an ontology of facts. Still, if onewishes to avoid such connotations, the principle can be formulatedmore 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 asufficient reason]).

The PSR is, in fact, afamily of principles which aregenerated by various restrictions of (2), and by ascriptions ofdifferent degrees of modal strength to (2). To begin with, variants ofthe PSR may differ according to how they restrictthe kinds ofthings that require a reason (the explananda). Thus, one mightrestrict the PSR to only actual entities, or include possibilia aswell. Alternatively, one might formulate the PSR as requiring asufficient reason for every (true) proposition or as pertaining toentities and their properties. A variant of the PSR restricted toentities might require an explanation for the existenceandnon-existence of entities, or it might be further restricted byrequiring a reason only for the existence (or only for thenon-existence) of entities. A version of the PSR that is restricted topropositions might range over both contingent and necessarypropositions, or it might be further restricted to only one of thesesub-domains.

Similarly, different versions of the PSR issue from various ways ofrestricting the kinds of things that countas providing areason (the explanantia). It is likely (though not necessary)that one’s decision about the kinds of explananda that fallunder the range of the PSR will determine the kinds of things countedas explanantia.

Variants of the PSR may be generated not only by placing restrictionson the relata at stake (both the explananda and the explanantia), butalso on the notion of the relation at stake. Frequently, the relationof providing a reason is conceived as irreflexive, antisymmetric andtransitive, though each of these characteristics may be, and indeedhave been, challenged. The relation of providing a reason can beconceived as an ontological relation (as in contemporary discussionsof ground), or as a purely epistemological relation.

A modally strong version of the PSR will take the Principle asnecessary and obtaining in all possible worlds, while a weak modalversion will present the Principle as merely contingently true.Another distinction can be drawn between afactive, asopposed to merelyregulative, version of the Principle. Aregulative version of the PSR would consider it as acondition forintelligibility (on a par with the Law of Non-Contradiction) andthus as guiding our studying of nature. The factive version simplystates that the Principle is true in actuality (or even in allpossible worlds). The regulative and the factive versions differ interms of allowing for the falsification of the principle. The factiveversion could be easily refuted by a single counter-example. Aproponent of the regulative variant of the PSR would argue that anempirical falsification of the PSR makes as little sense as anempirical falsification of the Law of Non-Contradiction. Encounteringa fact whichseems to have no explanation, the proponent ofthe regulative variant would respond by insisting that we must keepsearching for an explanation.

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

One of the most interesting questions regarding the PSR is why acceptit at all. Insofar as the PSR stipulates that all things must beexplainable, 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. Anotherimportant question related to the PSR is the possibility ofself-explanatory facts and self-caused entities; particularly, onemight wonder how these are distinguished from unexplainable, brutefacts and uncaused entities. One might also wonder whether the PSRallows for anyprimitive concepts that cannot be furtherexplained.

A third crucial problem for proponents of the PSR is how to addressthe Agrippan Trilemma between the apparently exhaustive three hornsof: (i) acceptance of brute facts, (ii) acceptance of an infiniteregress of explanation (or grounding), or (iii) acceptance ofself-explanatory facts.Prima facie, each horn in thetrilemma undermines the position of the proponent of the PSR.

Finally, the proponent of the PSR faces intriguing problems inaddressing perfectly symmetrical states. We have seen that somevariants of the PSR require an explanation forthe existence ofthings (thus, assuming nonexistence as a “default”state requiring no explanation), while other variants require anexplanation forboth the existence and nonexistence ofthings. Let us look quickly at the latter(“default”-free) variant. Specifically, we might wonderhow a proponent of the “default”-free variant of the PSRwould respond to a situation in which we have neither a reason for theexistence of \(x\), nor have a reason for the non-existence of\(x\)? A proponent of the PSR might indeed respond by denying thepossibility of such a scenario (given the PSR and bivalence). Asimilar 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 eitheridentity or non-identity as a default position?^[1]

With these general considerations in place, let us examine thehistorical role that the Principle has played. The term“Principle of Sufficient Reason [principe de raisonsuffisante/principium reddendae rationis]” was coined byLeibniz, though Spinoza is thought by many scholars to have precededLeibniz in appreciating the importance of the Principle and placing itat the center of his philosophical system.^[2] The Principle seems at first sight to have a strong intuitiveappeal—we always ask for explanations—yet it is taken bymany to be too bold and expensive due to the radical implications itseems to yield. Among the alleged consequences of the Principle are:the Identity of Indiscernibles, necessitarianism, the relativity ofspace 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 willbegin 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 hisfirst published work, the 1663 geometrical exposition ofDescartes’Principles of Philosophy (which may or maynot reflect Spinoza’s own views at the time). The eleventh axiom ofPart I of the book states:

Nothing exists of which it cannot be asked, what is the cause (orreason) [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 hasnothing as its cause (by Axiom 7). Therefore, we must assign somepositive cause, or reason, why [a thing] exists—either anexternal one, i.e., one outside the thing itself, or an internal one,one comprehended in the nature and definition of the existing thingitself. (Geb. I/158/4–9)^[3]

Axiom 7, to which Spinoza appeals in the explanation, is a variant ofthe “ex nihilo, nihil fit” (“from nothing,nothing comes”) principle, and stipulates that an existing thingand its perfections (or qualities) cannot have nothing or anon-existing thing as their cause. Interestingly, however, in anotherwork from this early period of his philosophical writing, theTreatise on the Emendation of the Intellect, Spinoza allowsfor one unique item to be without a cause. In §70 of thistreatise, Spinoza argues:

[T]hat Thought is also called true which involves objectively theessence of some principle thatdoes not have a cause, and isknown through itself and in itself. (II/26/33–4. Ouremphasis)

It is not completely clear what “the principle[principium]” at stake is, but given its qualificationas “known through itself and in itself”, it may refer toGod and indicate Spinoza’s understanding of Descartes’rather nuanced view—in his Second Set of Replies—accordingto which God does not need acause in order to exist, butthere is areason 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 PSRalready at the opening of his major work, theEthics. Thesecond 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 (seeE1p10s, E1p14d and Della Rocca 2008: 5) it seems that E1a2 amounts tothe claim that everything is explainable. Other commentators have alsoseen the PSR encoded in E1a3:

From a given determinate cause the effect follows necessarily; andconversely, if there is no determinate cause, it is impossible for aneffect to follow.

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

In E1p11d2, Spinoza states explicitly a variant of the PSR: “Foreach thing there must be assigned a cause,or reason, bothfor its existence and for its nonexistence”. Similarly, inE1p8s2, Spinoza argues, “if a certain number of individualsexists, there must be a cause why those individuals, and why neithermore nor fewer, exist.” Spinoza’s insistence that even thenon-existence of things must be explainable is crucial. Itallows him, for example, to argue that were God not to exist, hisnon-existence must be explainable. Since God is a substance, Spinozaargues, his existence or non-existence cannot be caused or explainedexternally (Spinoza takes substances to be causally independent ofeach other); hence, were God not to exist, his own nature would haveto be the cause of his non-existence, just as the nature of asquare-circle is the cause of the non-existence of that thing. Butsince God’s nature is not a contradictory, his nature cannotinternally rule out his existence, and hence he must exist(E1p11d).

The scope of Spinoza’s PSR and its role in his system is acontroversial matter. A dominant trend in recent scholarship readsSpinoza’s PSR as having unrestricted scope and playing a crucialrole in deriving many of his most important doctrines (e.g., DellaRocca 2008). But this trend has recently been challenged by readerswho argue that Spinoza’s PSR is restricted in scope to factsabout existence and nonexistence and that he rarely explicitly appealsto this principle in deriving his signature doctrines (e.g., Garber2015 and Lin 2019).

Commentators who give a prominent role to the PSR in Spinoza’ssystem frequently offer rational reconstructions of Spinoza’sarguments for his doctrines that find a crucial, if implicit, role forthe PSR. For example, some think that the PSR is the primarymotivation behind Spinoza’s strict necessitarianism. On this reading,for Spinoza, if there are two (or more) possible worlds, it would seemthat neither one would have asufficient reason or cause (forif there were such a sufficient reason, this world would benecessitated, and all other worlds would be impossible). In otherwords, the PSR dictates that there is only one possible world (seeDella Rocca (2008), 69–78, Lin (2011), 23–25, and Melamed(2021). Other commentators, (e.g., Lin 2019), deny that the PSR playsany role in Spinoza’s arguments for necessitarianism, and stillothers have denied that Spinoza is a necessitarian in the relevantsense (e.g. Curley 1969, and Curley and Walski 1999). Moreover, thereare commentators who, while believing that the PSR is behindSpinoza’s necessitarianism, suggest that, occasionally,Spinoza’s endorsement of the PSR is in tension with otherprinciples 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 allthings follow necessarily from God’s essence (E1p25 and E1p16).He is thus committed to the claim that all essences have a cause andan explanation.

Other Spinozistic doctrines that some commentators have alleged tofollow from his PSR are the Identity of Indiscernibles (E1p4. Althoughsee Lin 2019 for a dissenting view), substance monism (E1p11 andE1p14), and the rejection of free will (E1p32 and E2pp48–49). Ithas also been argued that in E1p21d Spinoza implicitly relies on thePSR to infer a bold causal principle: a simple cause has one, and onlyone, simple effect. Had the cause more than one effect, the differencebetween the two effects would be unexplainable insofar as each effectis supposed to be fully explained by the same cause. Thus, if weexperience a cause bringing about more than one effect, we shouldconclude that that the cause was not simple, but comprised of parts(so that the different parts contributed to the causation of thedifferent 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 ofSpinoza’s philosophical system” (2008: 9), but thatSpinoza requires thereduction of the most basicphilosophical concepts to reason or intelligibility. This alleged“double use of the PSR” stipulates (1) that everythingmust be explainable, and (2) that it should be (ultimately) explainedin terms of intelligibility. Hence, according to Della Rocca, Spinozareduces his major philosophical concepts—existence, causation,rightness, and power—to intelligibility (2008: 8–9). Whilethis is a fascinating and bold reading of Spinoza’s metaphysics,it seems to contradict his crucial doctrine of the causal andconceptual barrier between the attributes (E1p10 and E2p6). Thereduction of any non-Thought item to intelligibility (presumably, afeature of the attribute of thought^[6]) undermines the barrier between the attributes, and with it the entireedifice 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 forspecific reductions, for example, the reduction of causation tointelligibility 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 thisinterpretation, Spinoza is unsympathetic to any acceptance of brutefacts. Yet he allows for some, restricted cases of self-explanationand infinite regress of explanation. Let us take a brief look at thesetwo issues.

Spinoza begins theEthics with the definitions ofcausasui (E1d1), and of substance as that which “is conceivedthrough itself” (E1d3). Positing these reflexive definitions atthe outset might have been a calculated methodological move whose aimwas to bypass the challenging task of proving the legitimacy of thesenotions. But since Spinoza considers his definitions as not merelystipulative (see TIE §95 and Ep. 60), we may well ask for adefense of the legitimacy of self-explanations.

The class of truths that Spinoza considers as self-explanatory aretruths that followmerely from the essence or—what isthe same—the nature of a thing. In E1p11d, Spinoza provides twoexamples of self-explanation:

[T]he very nature of a square circle indicates the reason why it doesnot exist, viz. because it involves a contradiction…, thereason why a substance exists also follows from its nature alone,because it involves existence.

In contrast, claims Spinoza, the existence (as well as thenon-existence) of a triangle (or any other thing that is not asubstance) do no followmerely from the essence of thetriangle:

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 ofthe whole of corporeal Nature. (E1p11d).

Thus, consider the following three propositions: (i) The triangle hasthree angles, (ii) The substance exists, and (iii) The triangleexists. Proposition (i) is clearly self-explanatory, since the essenceof the triangle (which contains the nature of the number three and thenature of an angle) is the sufficient reason for its having threeangles (adding any other information is of no explanatory value).Spinoza considers proposition (ii) as self-explanatory as well. Noticethat Spinoza does not define substance (in E1d3) as existing by virtueof its essence, but rather derives this claim from the definition ofsubstance (in E1p7 and E1p6). In contrast to (i) and (ii), theexistence of a triangle does not follow merely from its essence (sinceit is caused by entities external to the triangle, and therefore hasto 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 aninfinite causal chain of finite modes:

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

Each link in this causal chain is preceded by infinitely many causesand is followed by infinitely many effects. Each link also provides atleast part of theexplanation for the existence of thefollowing link. Is the existence of such an infinite regressconsistent with the PSR? Spinoza has no qualms about answering thisquestion in the positive. We may legitimately ask what is the cause ofeach link in the chain, and the answer would be: the preceding link.Spinoza also thinks that we may—indeed, should—ask what isthe cause, or reason, for the existence ofthe entire infinitechain? He simply thinks that he can provide a clear answer to thelatter question as well: God (or the being which is the ground of itsown existence). Consider the following passage from Spinoza’scelebrated “Letter on the Infinite” in which he criticizesproofs of the existence of God which rely on the impossibility of anactual infinity of causes and effects.

In passing I should like to note here that the more recentPeripatetics have, as I think, misunderstood the demonstration bywhich the Ancients tried to prove God’s existence. For as I findit in a certain Jew, called Rab Chasdai, it runs as follows: ifthere is an infinite regress of causes, then all things thatare will also have been caused; but it does not pertain to anythingwhich has been caused, to exist necessarily by the force of its ownnature; therefore, there is nothing in Nature to whose essence itpertains to exist necessarily; but the latter is absurd; therefore,the former is also. Hencethe force of this argument does not liein the impossibility of there being an actual infinite or an infiniteregress of causes, but only in the supposition that things which donot exist necessarily by their own nature are not determined to existby 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 philosopherHasdai Crescas in rejecting the Aristotelian ban on actual infinity(see Melamed 2014). For Spinoza (and Crescas) the existence of aninfinite regress of causes is perfectly legitimate. Yet, if all theitems 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 areason which explains its instantiation in reality. The ultimatereason for the instantiation of such an infinite chain of contingentbeings must, claims Spinoza, be a being whose existence is notcontingent (for otherwise, the chain will remain merely contingent andits instantiation in reality would not be sufficiently explained).Thus, Spinoza allows for an infinite regress of causes (orexplanations) as long as the entire infinite chain is grounded in abeing which exists by virtue of its mere essence.

3. Leibniz

No philosopher is more closely associated with the PSR than GottfriedWilhelm Leibniz (1646–1716). He was the first to call it by nameand to recognize it as a major principle of philosophy. Still, Leibnizwas well aware of the similarity between his principle andSpinoza’s claims. Thus, in a 1676 marginal note to his copy ofSpinoza’s “Letter on the Infinite” (which we havejust discussed at the end of §2), he writes: “This isrightly observed, and agrees with what I am accustomed to saying thatnothing exists but that for whose existence a sufficient reason can beprovided” (Leibniz,Labyrinth of the Continuum, 117/Aiii71). Leibniz’s treatment of the PSR is also noteworthy forits 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 theMonadology (1714) he writes:

31. Our reasonings are based on two great principles, that ofcontradiction, in virtue of which we judge that which involves acontradiction to be false, and that which is opposed or contradictoryto the false to be true.

32. And that of sufficient reason, by virtue of which we consider thatwe can find no true or existent fact [fait], no trueassertion [énonciation véritable], withoutthere 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 epistemicterms. They are principles of “our reasoning”. Theyconcern what we “judge” or “find”. And yet itis clear that Leibniz intends them to have metaphysical as well asepistemic import. In the case of the PSR, this will become moreevident when we discuss how Leibniz understands the notion of asufficient reason but it is already indicated in the passage quotedabove by the fact that Leibniz explicitly states that there aresufficient reasons for every truth or fact even if such reasons areunknowable by us. (The distinction between the epistemic andthe metaphysical collapses with respect to God because there canbe no gap between what an omniscient being knows and how thingsare.)

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

[T]he principle of sufficient reason, namely, that nothinghappens [rien n’arrive] without a reason. (GVII 356; LC L2; AG 321, our emphasis)

The PSR is here said to apply to what “happens”. Thissuggests a version of the PSR that applies not to truths or facts butrather events: Every event has a sufficient reason.

These vacillations in the formulation of the PSR are not typicallytaken to register indecision on Leibniz’s part as to the scopeof the PSR. Rather they are usually understood as indicating thatLeibniz views the scope of the PSR to be very wide, perhaps evenabsolutely 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 avariety of domains where each is especially important. For example,there are domains where the truths of the domaindepend onone of the two principles. These domains are characterized modally:The Principle of Contradiction rules over the domain of necessarytruths and the PSR rules over the domain of contingent truths (A 6 41616/MP 75; G VII 355–56/LC 15–16).

There are also domains that are characterized in terms of subjectmatter or areas of inquiry. The Principle of Contradiction allows usto study mathematics, whereas the PSR allows us to study metaphysics,natural theology, and physics (G VII, 355–6; LC L2; AG 321). Itis far from obvious that these two ways of assigning domains to thePrinciples are equivalent. For example, it would be natural to assumethat metaphysics and natural theology would include necessarypropositions and thus the PSR would encroach upon the territoryassigned to the Principle of Contradiction according to the modalcharacterization.

We must therefore distinguish distinct ways of associating theprinciples with various domains. The first way is to specify thedomain to which each principleapplies. Leibniz appears tobelieve that, according to this approach, there is a single universaldomain and it is associated equally with each principle. There are nocontradictory contingent facts or truths and so the Principle ofNoncontradictionapplies to all contingent truths as well asall necessary truths. Likewise, it is usually assumed that, forLeibniz, every necessary truth has a sufficient reason (see Broad1975: 12 and 34 and Rodriguez-Pererya 2018). For example, mathematicaltruths, might have sufficient reasons in the form of proofs that reston statements of identity. Thus the PSRapplies to allnecessary truths as well as all contingent truths.

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

The third way is to specify a domain of truths that can beinvestigated on the basis of each principle. For Leibniz, wecan know mathematical truths only on the basis of the Principle ofContradiction and only metaphysical, theological, and physical truthsrequire the PSR in order to be known. We will see in more detail inwhat way the PSR allows us to investigate these domains in the sectionon applications.

3.1 What is a Sufficient Reason?

When Leibniz insists that every truth or fact requires a sufficientreason, what does he mean by “sufficient reason?” In sometexts he suggests that sufficient reason is an “apriori proof”. This should not be understood in Kantianterms as a proof that doesn’t require any input from senseexperience. Rather, Leibniz uses the term “apriori” in its original pre-Kantian meaning, which means anargument from causes to effects. Ana priori proof is a proofthat reflects the causal order. Thus, a sufficient reason would be aproof that is both a demonstration—a set of premises and aconclusion such that the former necessitate the later–and acausal explanation—a statement of the causal antecedents of sometruth or event (see Adams 1994: 109).

In order to fully understand Leibniz’s conception of asufficient reason, we need to also understand his theory of truth andits relationship to his theory of modality. Let us begin with truth.To keep things simple, we will focus only on categorical propositionsof subject-predicate form. A proposition is true, according toLeibniz, just in case the concept of the predicate is contained in theconcept of the subject. Uncontroversially, the concept of thepredicateunmarried is contained in the conceptbachelor and it is this conceptual containment which explainsthe truth of the statementbachelors are unmarried. ButLeibniz makes the further highly controversial claim thatalltrue statements are true for this reason, even statements likeCaesar crossed the Rubicon. That is, this statement is truebecause the conceptcrossed the Rubicon is contained in theconcept of Caesar. This theory of truth is sometimes called theconceptual containment theory of truth. It has as aconsequence that all truths are analytic. But wouldn’t such atheory entail that all truths are necessary? After all, how could ananalytic truth be contingent?

In response to this worry, Leibniz develops an account of contingencyin terms ofinfinite analysis.^[8] Leibniz understands analysis as the process of replacing the terms ofa proposition with definitions or partial definitions. A demonstrationresults when an identity is obtained through the process of analysisin a finite number of steps. Leibniz claims that all and onlynecessary truths have a finite demonstration by analysis and all andonly contingent truths do not have a demonstration by analysis in afinite number of steps. In this way, he preserves the distinctionbetween necessary and contingent truths while also maintaining thatall truths are analytic, that is, true in virtue of the meaning of theconcepts involved.

This has led some commenters to think that Leibniz gave up the accountof sufficient reason as ana priori proof. If there were aproof or demonstration, it would reveal that the concept of thepredicate was contained in the concept of the subject in a finitenumber of steps and hence every proposition would be necessary.Leibniz is not a necessitarian in his late philosophy and thus hecould not have accepted this consequence. Instead, he must haveshifted from the conception of a sufficient reason as anapriori proof to that of ana priori proof sequence,where the latter notion is understood as an analysis that converges onan identity without reaching it in a finite number of steps (seeSleigh 1983: 200). What it means for an analysis to converge on anidentity is, unfortunately, obscure. Nevertheless, there is some clearsense in which every contingent truth has a sufficient reason on thisunderstanding. The sufficient reason why it is true that Caesarcrossed the Rubicon, for example, is that the conceptcrossing theRubicon is contained in the conceptCaesar. The truth ofthe proposition obtains in virtue of the concepts of the subject andthe predicate. Of course, this reason is undiscoverable by any finitehuman mind because it is buried too deeply in the concept of Caesar.Only God, in his omniscience sees the conceptual connection betweenthem. It is enough for there to be such a connection for there be asufficient reason.

Such a conception of the nature of a sufficient reason have led somecommentators to think that for Leibniz the PSR is a logical notion orthat it is a metaphysical notion that is ultimately reducible to logic(Couturat 1901: 123ff and Russell 1937: v). But the notion of asufficient reason as a non-terminating proof sequence is not the onlyconception of a sufficient reason to be found in Leibniz. And otherconceptions have a decidedly less logical and more metaphysicalflavor.

One such characterization of a sufficient reason comes fromLeibniz’s conviction that in order to preserve the notion ofcausal activity, without which substances are not reallysubstances—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 oressence of the substance. Now according to Leibniz, substances donot causally interact with one another (see the entryLeibniz on causation). The changes that they undergo derive solely from their own natures orprimitive active force, which consequently determines the whole of itshistory. Many texts suggest that, for Leibniz, the sufficient reasonfor any state of a substance is its primitive active force (NE65–6; T 400/G VI, 354; Mon. 18/G VI, 609–610; G IV, 507; GIII, 72).

In many ways primitive active force plays the role of the concept ofthe subject in the logical version of the PSR. Just as on the logicalversion the PSR that \(a\) is \(F\) is explained by the factthat 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 asCouturat and Russell emphasize the logical notion of a sufficientreason to the detriment of the metaphysical notion, other commentatorssee the logical and the metaphysical as two equally fundamentalpresentations of the same datum (see Frankel 1994).

Another metaphysical characterization of a sufficient reason connectswith the Principle of the Best, which says that for any proposition\(p\), \(p\) is true just in case \(p\) holds in thebest 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 PSRor a rival to the PSR? It is, in fact, a consequence of the PSR inconjunction with three additional assumptions: (1) the sufficientreason for every choice is that the chooser perceives it to be thebest; (2) God chooses the actual world; (3) God perceives something tobe what is best just in case it is the best.

In some texts, Leibniz suggests that the sufficient reason forcontingent truths cannot be found in the concepts or natures ofthings. We must instead look to the Principle of the Best (Mon.36–38/G VI, 613). In other words the sufficient reason for anycontingent proposition of the form “\(a\) is\(F\)” is that \(a\) is \(F\) is true in the bestpossible word. This appears to be an entirely different sort of reasonthan the fact that “\(a\) is \(F\)” is analyticor that the nature of \(a\) determines that it is \(F\).Those latter reasons are to be found internal to the concept of thesubject or the nature of the substance. Reasons that advert to thePrinciple of the Best look outside the concept of the subject or thenature of the substance and make comparisons between worlds in termsof their relative perfections. It is possible that Leibniz thoughtthat these different conceptions of sufficient reasons were equivalentbut 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 theconcept 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 thatis derivable from the concepts of a sufficient reason and the conceptof a requisite (A VI, ii, 483; see also G VII 393, LC L5.18; AVI.iii.133). The concept of a requisite is that of a necessarycondition. In this context, Leibniz defines a sufficient reason as asufficient condition. If something exists, then all of its requisiteshave been posited. Leibniz then asserts that if all of a thingsrequisites have been posited, then it exists. Thus, all of athing’s requisites are a thing’s sufficient reason. Thequestion-begging assumption is that all the necessary conditions forsomething to exist are jointly sufficient for it to exist. Anybody whodenies the PSR will not agree with this assumption and it is clearlynot encoded in the definitions ofrequisite andsufficient reason provided by Leibniz (for furtherdiscussion, see Harrop 2020).

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

It is worth noting that Leibniz believed the PSR before he developedhis conceptual containment Theory of Truth. In fact, the PSR is one ofLeibniz’s earliest and most stable philosophical commitments(see, for example, Leibniz’s 1671 letter to Wedderkopf AII.ii.117f/L146). This observation has led some scholars to concludethat rather than deriving the PSR from the conceptual containmenttheory of truth, Leibniz was in fact led to the conceptual containmenttheory from his antecedent commitment to the PSR. The conceptualcontainment theory explains how there could be a sufficient reason forevery truth by guaranteeing that there will be an explanation in termsof conceptual relations (see Adams 1994: 69). Moreover, in at leastone text, it is not at all clear whether, for Leibniz, the conceptualcontainment theory of truth motivates the PSR, or rather it is the PSRwhich motivates the conceptual containment theory of truth: seeLeibniz,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 reasonand no cases where fact is known not to have a sufficient reason. Hethen says that it is reasonable to assume that the PSR holds in allcases where we do not know that sufficient reason. Leibniz describesthis as “the method of experimental philosophy, which proceedsa posteriori” (G VII 420; LC, L5.129).

3.3 Applications

Leibniz says that PSR is needed if we are to go beyond mathematics tometaphysics and natural science. How does the PSR help in thosedomains of inquiry? There is a general pattern of argument thatLeibniz uses to establish conclusions using the PSR. First, he assumesthe falsity of what he wants to prove. Call the proposition to beproved \(p\). Then he tries to show that if \(p\) werefalse, there would be some fact or truth for which there could not besufficient reason. But by the PSR, there is no such fact or truth.Therefore, \(p\) is true. Leibniz uses this template to argue fora number of claims, including the indefinite extension of space(Labyrinth of the Continuum, 233), determinism(Leibniz-Stahl Controversy, 17), the impossibility of bareoccult qualities and bare faculties (Philosophical Writings,172–3), the identity of indiscernibles, relationalism withrespect to space and time, and the existence of God. Let us brieflylook at how Leibniz uses the PSR to argue for each of the last threetheses.

Leibniz presents arguments for the existence of God from the PSR in anumber of different places (for example,The Ultimate Originationof Things, G VII 302–3; L 486–8.Monadology§37). Suppose that God does not exist. If God does not exist,then the only things that exist are contingent beings. Would theentire series of contingent things have an explanation? Theexplanation of the entire series cannot be a member of the seriessince then it would explain itself and no contingent thing isself-explanatory. But the explanation cannot be outside of the seriesbecause 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 forGod’s existence Spinoza cites in the name of Crescas which wehave just discussed at the end of §2 above. In fact, this proofby Leibniz appears in a 1676 gloss to his copy of Spinoza’sletter discussing Crescas’ proof. See Leibniz,The Labyrinthof the Continuum, 117).

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

For similar reasons, Leibniz thinks that space and time cannot besubstances or anything else absolute and must ultimately be a systemof relations that obtain between bodies (e.g., LC, L, 3.5). This isbecause if space, for example, were absolute, then there would bespace points that were indiscernible from one another. God would treatthese space points differently from each other insofar as he orientshis creation in space one way rather than another. This would have tobe an arbitrary decision for the reasons outlined above. So, space andtime are not absolute (see Lin 2011).

Next to the PSR, Leibniz also holds a complimentary principleaccording to which nothing is without effects, or “nothing issterile” (see, for example, Monadology §69 and AG 38).

4. Émilie du Châtelet

At the beginning of this entry we have addressed briefly the questionof motivating the PSR. The PSR demands that all facts must have asufficient explanation, and were the PSR itself unmotivated, it wouldseem to simply refute itself. We have also seen that overallLeibniz’s attempts to justify the PSR were not particularlysuccessful (in Spinoza’s early works there is an attempt tojustify the PSR, but he deserted this path in his later works). Inthis section, we would like to discuss one of the most intriguingattempts to justify the PSR as an exceptionless methodologicalprinciple. The arguments we are about to discuss appear inÉmilie du Châtelet’s 1740Institutions dephysique (Foundations of Physics) “ostensibly atextbook in physics for her son, but in reality, a highly originalwork in natural philosophy” (Detlefsen 2018, §1). In thiswork, Du Châtelet attempts to provide a unified Newtoniannatural philosophy that is grounded in metaphysics. Just like Leibniz,du Châtelet views the principle of contradiction and theprinciple of sufficient reason as the two fundamental principles ofphilosophy.

Immediately after presenting the PSR, Du Châtelet turns tojustify the principle:

If we tried to deny this great principle, we would fall into strangecontradictions. For as soon as one accepts that something may happenwithout sufficient reason, one cannot be sure of anything, forexample, that a thing is the same as it was the moment before, sincethis thing could change at any moment into another of a differentkind; thus truths, for us, would exist only for an instant.

For example, I declare that all is still in my room in the state inwhich I left it, because I am certain that no one has entered since Ileft; but if the principle of sufficient reason does not apply, mycertainty becomes a chimera since everything could have been throwninto confusion in my room, without anyone having entered who was ableto turn it upside down (Foundations of Physics, §8| DuChâtelet 2009, 129)

Without the PSR, claims Du Châtelet, we cannot be certain thatthe unexperienced world has the continuity and unity we always assume.Were we not to assume the PSR, we should be seriously concerned aboutthe possibility of things appearing out of thin air and disappearinginto nothing. Without the PSR, we cannot assume the permanence ofanything. The very fact that we are not concerned about the suddenappearance or disappearance of things, seems to indicate that weactually assume the PSR. Moreover, claims Du Châtelet, our veryfoundational notions of equality and identity, seem to assume theprinciple:

Without this principle there would not be identical things, for twothings are identical when one can substitute one for the other withoutany change to the properties which are being considered. Thisdefinition is accepted by everyone. Thus, for example, if I have aball made out of stone, and a ball of lead, and I am able to put theone in the place of the other in a basin of a pair of scales withoutthe balance changing, I say that the weight of these balls isidentical, that is the same, and that they are identical interms of weight. If something could happen without a sufficientreason, I would be unable to state that the weight of the balls isidentical, at the very instant when I find that it is identical, sincea change could happen in one and not the other for no reason at all(Foundations of Physics, §8| Du Châtelet 2009,129)

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

According to some commentators, Du Châtelet’s lastargument shows not only that everything must have a sufficient reason,but also that this reason must beaccessible to us (i.e.,humans, or finite cognizers), at least in principle (Amijee 2021 andWells 2021). Here is why. Consider the scales scenario in a world inwhich the PSR obtains strictly (and we are aware of this), but somereasons are in principle inaccessible to us. In such a world, we couldnot infer with certainty the equality of the balls from the horizontalstates of the scales, since we should consider the possibility ofinterfering causes that are inaccessible to us.

A version of the PSR which requires that all reasons must beaccessible to humans is not easy to accept: why should we assume thatthe nature of the world is such that it is cognitive accessible to anyspecific being? Of course, an anthropocentric version of the PSR mightbe warranted if one assumes that the world was created by a benevolentcreator who intentionally designed the world in such a manner that itwill always be accessible to human beings, but this cluster of heavypremises would be clearly rejected by many proponents of the PSR (suchas Spinoza).

Setting aside the question of whether Du Châtelet’s lastargument indeed requires that reasons must be accessible to humans, itseems she does offer a promising line of motivating the PSR as aregulative rather than a factive principle (see §1 above).

5. The PSR before Spinoza and Leibniz

The PSR is nearly as old as philosophy itself. Anaximander, one of theearliest of the pre-Socratics, is usually credited—on the basisof Aristotle’sde Caelo, (b12295b10–16)—with being the first to make use of it.Anaximander argues, we are told, that the Earth remains stationary inspace because it is located in the center of the universe and thus is“indifferently” related to any “extremepoint”. This indifference means that if it were to move in anydirection, it would do so without a reason. Since he concludes fromthis that it does not move, we can assume that Anaximander believesthat motion in the absence of a reason is impossible.

Parmenides, another pre-Socratic, implicitly appeals to the PSR whenhe claims that the world cannot have come into existence because thenit would have come from nothing (Fragment B8 9–10). It isagainst the later alternative that Parmenides appears to wield thePSR. 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 thanit actually did? Parmenides appears to think that if the world comesinto existence from nothing, then there is no possible answer to thisquestion. After all, prior to the coming-to-be of the world, there isnothing to explain its coming-to-be. Thus, its coming-to-be would bean arbitrary brute fact. There are no brute facts regardingcoming-to-be. So, the world did not come into existence fromnothing.

Another ancient source for the PSR is Archimedes who writes:

Equal weights at equal distances are in equilibrium, and equal weightsat unequal distances are not in equilibrium but incline towards theweight which is at the greater distance (On the Equilibrium ofPlanes, 189).

Archimedes assumes that if there is a balance such that there is nodifference between the weights and distances on either side, thenneither side of the balance can move up or down. This is sometimestaken to be an implicit application of the PSR and is cited byLeibniz in his correspondence with Clarke as a precedent for his ownprinciple.

In the Islamic world, Avicenna appears to assume a version of the PSRwhen he claims that the existence or nonexistence of any non-necessarypossible thing must have a cause outside itself. If it didn’t,then either the cause would be internal to the non-necessary possiblething (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 alternativeand thus he appears to be committed that all existence andnonexistence has a cause (Avicenna,Metaphysics 1.6 §1;Al-Shifa’:Al-Ilahiyyat, 37; See Richardson747).

In the medieval Latin West, Peter Abelard argues that God must createthe best of all possible worlds in a way that both appears topresuppose some version of the PSR and anticipates Leibniz’sreasoning on the subject. If God didn’t, Abelard argues, therewould have to be some reason for it. But what reason could that beexcept God’s injustice or jealousy? But God cannot be unjust orjealous. So there is no possible reason for God making anything lessthan the best. Everything has a reason. Thus God makes the bestpossible world (Op. cit. col. 1324b; McCallum 1948, 93).Abelard’s opinion was rejected as heresy and mainstream opinionof philosophers during the Middle Ages in the Latin West appears toreject the PSR. God, on the mainstream medieval view, enjoys freedomof indifference with respect to his creation. Thus there is nosufficient reason for why God created what he did and the PSR slipsfrom prominence until its early modern revival at the hands of Spinozaand Leibniz.

Some great epistemological rationalists, such as Plato and Descartes,appear to endorse the unrestricted PSR but in fact do not. Forexample, in theTimaeus Plato writes,

[E]verything that comes to be must of necessity come to be by theagency of some cause, for it is impossible for anything to come to bewithout a cause. (28a4–5)

This passage appears to assert the unrestricted PSR. But Platobelieves that there are things that are not among the things that“come to be,” and some of these things have no causeor reason. For example, the Demiurge creates the world by imposingorder on disorderly motion. The disorderly motion preexists the workof the Demiurge. It is uncaused and there is no reason for it.

At times, Descartes appears to endorse the unrestricted PSR. Forexample, he argues for the existence of God in the thirdMediation on the basis of the principle that there must be atleast as much reality in the cause as in the effect. And he justifiesthis causal principle by claiming that “Nothing comes fromnothing”. This appears to make him as much an adherent of theunrestricted PSR as Parmenides who, as we have seen, argues for hisconclusions on the same basis. But elsewhere Descartes claims that Godcreates the eternal truths, such as mathematical and metaphysicaltruths (Letters to Mersenne, April 15, May 6, and 27, 1630;FifthReplies, AT 7:380, CSM 2:261). Moreover, he claims that Godcreates 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. Ifmathematical and metaphysical truths are contingent and yet have nosufficient reason according to Descartes, then his philosophy imposesserious restrictions on any PSR.

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

Hume’s critique of causation presents an important challenge tothe PSR. In hisTreatise of Human Nature (I, 3, 3) Humeconsiders several arguments which attempt to prove the “generalmaxim in philosophy, thatwhatever begins to exist, must have acause” and finds all of them wanting. Hume argues thatsince the ideas of cause and its effect are evidently distinct, we canclearly conceive or imagine an object without its cause. He takes theseparability of the two ideas to show that there is no necessaryconceptual relation between the ideas of cause and effect insofar asconceiving the one without the other does not imply any contradictionor absurdity.

Christian Wolff (1679–1754), the most influential Germanphilosopher of the first half of the eighteenth century, was afollower of Leibniz and developed the latter’s system. LikeLeibniz, Wolff assigned to the PSR a central role in his system whileattempting to avoid necessitarianism (or “fatalism”). LikeSpinoza and Leibniz, Wolff demanded a reason for both the possibilityof things [ratio essendi] (i.e., coherence of essence) andfor the actualization, or coming to be, of essences [ratiofiendi]. Wolff mildly criticized Leibniz for allegedly groundingthe PSR merely in experience and attempted to marshal several proofsfor the principle (Rational Thoughts on God, the World, and theSoul of Human Beings, §§30–31, 143;Ontologia, §§56–78; cf. Look 2001,210–214). One of these proofs attempts to prove the PSR relyingon the principle of the Identity of Indiscernibles (RationalThoughts on God, the World, and the Soul of Human Beings§31), while the most famous proof attempts to derive the PSR fromthe Law of Non-Contradiction. According to the latter, if a thing\(A\) is assumed to exist without reason, than “nothing isposited that explains why \(A\) exists”. This, according toWolff, would mean that \(A\) exists because of nothing(Ontologia, §70), which Wolff claims to be absurd.(Wolff seems to be assuming here theex nihilo nihi fitmaxim.) Kant criticized the proof claiming that it is based on anequivocal use of the term “nothing” (AK 1:398).

Leonhard Euler, the great Swiss mathematician and a contemporary ofWolff, warned against the “wretched abuse” of the PSR bythose who

employ it so dexterously that by means of it they are in a conditionto demonstrate whatever suits their purpose, and to demolish whateveris raised against them. (Letters to German Princess, LetterXIII)

According to Euler, many of the proofs which rely on the PSR amount tonothing over and above apetitio principii, while othersderive carelessly the impossibility of things from our ignorance ofthe causes of these things.

In theCritique of Pure Reason (1781, 1787), Kant claims toprovide a proof for the PSR by showing that

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

Relying on his transcendental method Kant argues in the “SecondAnalogy of Experience” that a certain version of the PSR is acondition for the possibility of experience, and as a result also acondition for the possibility of objects of experience. Yet, thisargument also restricts the validity of the PSR to human experience,i.e., to things which appear in space and time. Any use of the PSRthat transgresses the boundaries of human experience is bound togenerate antinomies.

Kant’s view of space and time as exhibitingbrutedifference (i.e., the non-identity of locations in space and timecannot be reduced to conceptual explanation) stands in sharp contrastto the Principle of the Identity of Indiscernibles, and thereby alsoto the PSR. Salomon Maimon, Kant’s rationalist critic, attemptedto enforce rationalist strictures on Kant’s philosophy byarguing that Kant is unable to explain the necessary agreement ofintuitions and concepts. According to Kant, intuitions and conceptscome from entirely different sources: sensibility and understanding.But if this were the case, claims Maimon, we could not explain theconstant agreement between intuitions and concepts, which is necessaryfor the possibility of experience. This agreement can be explained ifwe reject the radical heterogeneity of intuitions and concepts, andview intuitions as disguised concepts. Thus, any difference exhibitedin space and time must have its ground in the universal forms of ourthought in general (Maimon,Essay on TranscendentalPhilosophy, Ch. 1, p. 13). Maimon also argued that we must seekan explanation for the fact that we havetwo forms ofintuition rather than one, and suggested that it is only the interplaybetween the two forms of intuition which allows us to exhibitdifference, by using a unity in one form to exhibit difference in theother form, i.e., conceive different times by concentrating on thechange occurring at the same location in space, or conceive differentlocations in space at the same point in time (Essay, Ch. 1, 13–14).

Maimon was probably the strictest adherer to an unrestricted versionof the PSR among the German Idealists. For Maimon, satisfying thedemands of the PSR isthe infinite task of both philosophyand science. Thus, in response to Maimonides’ claim that crucialastronomical 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 beexplainable through the principle of sufficient reason. How farwe can actually get in achieving this is beside the point. Thosethings that Maimonides, working with the astronomy of his day,regarded as inexplicable, new discoveries (particularly Newton’ssystem) equip us to explain quite well. The highest order in thearrangement of the world’s structure is for us a necessary ideaof reason, which, through the use of reason with regard to objects ofexperience,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 inHegel’s Logic. For Hegel, the demand for ground provides a majorsource of transition from one thing to another. It is, Hegel says,“the expulsion of itself from itself” (EncyclopediaLogic, §121A). Ground, for Hegel, is the unity of identityand difference: the ground of \(x\) has to explain all featuresof \(x\), and in sense duplicates it, yet it must also bedifferent from \(x\) in order to have explanatory value and notbe a merepetitio principii.

The PSR is the subject of Schopenhauer’s 1813 doctoraldissertation:The Fourfold Root of the Principle of SufficientReason. In this work, Schopenhauer provides a brief history ofthe PSR, and then raises the questions of the justification for thePSR and the proper scope of the principle. Schopenhauer follows Wolffin distinguishing among four kinds of reasons, corresponding to fourkinds of objects, and charges that much philosophical confusion arisesfrom attempts to explain objects of one kind by reasoning that belongsto the other kind. These four kinds of explanation, or four variantsof the PSR, share the very same ground. Along Kantian linesSchopenhauer suggests that it is the subject’s activity inregularly connecting representations that is the ground of the PSR(The Fourfold Root, §16).

7. The PSR in Contemporary Philosophy

It has recently been proposed by Dasgupta that a version of the PSRcould be formulated in terms of grounds. Grounding is said to be akind of explanation distinct from causal explanation. It is ametaphysical or constitutive explanation. It is generally taken to beasymmetric, irreflexive, and transitive. Alleged examples of groundingrelations are: dispositions (e.g., fragility) are grounded incategorical features (e.g., molecular structure); semantic facts(e.g., Jones meansaddition by “+”) are groundedby non-semantic facts (e.g., Jones is disposed to draw certaininferences); mental properties (e.g., pain) are grounded by physicalproperties (e.g., c-fibers firing; see Rosen 2010 and Fine 2012). Theproposal 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)

Heresubstantive means apt for grounding andautonomous means not apt for grounding. For example, perhapsessentialist facts are autonomous where essentialist facts are factsof the form: it is essential to \(x\) that \(\phi\). Theidea is that just as definitions are not apt for proof, essentialistfacts are not apt for grounding explanations, that is, they areautonomous (Dasgupta 2016: 6–9). The notion of an autonomousfact allows the adherent of this version of the PSR to avoid theAgrippan Trilemma without allowing for self-explanatory facts orinfinite regresses. Chains of explanation terminate with autonomousfacts, which are not brute because they are not apt forexplanation.

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

Jonathan Schaffer has relied on the notion of ground to revive anAristotelian, structured metaphysics, i.e., a metaphysics which isordered by priority relations (Schaffer 2009), and to defend PriorityMonism (see the entry onmonism). In response, Michael Della Rocca (2014) has argued that strictadherence to the PSR—and to Ockham’s Razor (see the entryonsimplicity)—undermines Schaffer’s structured metaphysics (and Priority Monism), sinceinsofar as all the features of the grounded are already present in theground, the existence of the grounded is just redundant. (See also theentry onmetaphysical grounding). More recently, in his audacious 2020 book, Della Rocca expanded hisargument. Relying on what he takes to be a strict adherence to thePSR, and assisted by F.H. Bradley’s critique of the reality ofrelation, Della Rocca argues that we are entitled to assert only theexistence of undifferentiated being that stands in no relations ofdistinction. According to Della Rocca, our major philosophicalconcepts – substance, action, knowledge, meaning, andexplanation – fail to meet the strict requirements of the PSR.Toward the end of the book, Della Rocca launches a powerful attack onthe widespread reliance on intuitions among analytic philosophers(Della Rocca, 2020, 260–290).

The question of the justification for the employment of the PSR hasbeen addressed in some recent literature (see, for example, DellaRocca (2010)). Fatema Amijee has argued that from a practical point ofview, participants in structural inquiry (i.e., an inquiry whichattempts to explain why a given fact obtains) must assume the PSR aslong as they do not discover that any fact is brute. Since structuralinquiry is intrinsically valuable (and assists us in discovering newtruths), it is rationally non-optional for us, and consequently, wemust be committed to the PSR (Amijee 2022).

Implications for the PSR might also be discerned in recent discussionsofsurprisingness orstrikingness, (although suchimplications are not typically stated explicitly). These discussions,which cut across such diverse subfields as epistemology, philosophy ofscience, metaethics, and philosophy of religion, have their origin inPaul Horwich’s observation that there is an intuitive differencebetween an event or fact beingunlikely and its beingsurprising (Horwich 1982). For example, it is equallyunlikely that, on a given occasion, a monkey typing randomly on atypewriter will type the string ‘sdlek93 91’ and that itwill type ‘I want a banana.’ But although theprobabilities of both events are the same, the latter string issurprising in a way that the former is not. The difference betweensurprising events or facts and unlikely fact is sometimes thought tomap onto the distinction between events or facts that call out forexplanation and those that do not. How can we account for thedifference between the merely improbable—which some believe doesnot call out for explanation—and the surprising—whichdoes? Often it is said that the surprising requires us to challengeour background beliefs and confirms hypotheses that are alternativesto those beliefs. Alternatively, that a theory T treats somethingsurprising as inexplicable is a reason to disbelieve T (White 2007;Schechter 2013). Thus, such inquiry is guided by the presumption thatthe surprising is explicable. Principles such as these have ledphilosophers to substantive conclusions as diverse as: (1) theuniverse was designed by an intelligent agent (White 2017; van Inwagen1993); (2) moral realism is false (Street 2006; Enoch 2011); (3) thereexists a multiverse (Leslie 1989; Parfit 1998); and Platonism aboutmathematics is false (Field 1989, 2005). Unfortunately, we cannotdiscuss the details of the arguments from the improbable/surprisingdistinction to these claims here. Nevertheless, this methodologicalassumption has interesting repercussions for the PSR. First of all,those who advocate the distinction tend to suggest that, if the PSR istrue, then it is so only in a restricted form. After all, the point ofthe distinction is that some things call out for explanation andothers do not. But it also suggests that something like a restrictedPSR is true. A principle that says that we have an epistemicreason to believe a hypothesis that would transform a surprising eventof fact into an unsurprising one would only be truth conducive if welived in a world in which events and facts are—at least for themost part—explicable. Why this is so can be illuminated byanalogy with induction. As Hume observed, induction is truth conduciveonly if nature is uniform (T. 1.3.6.4). So, by committing ourselves tothe method of induction, we thereby presuppose the truth of theprinciple of the uniformity of nature. Similarly, by takingourselves to have an epistemic reason to believe a theory because itrenders explicable what is otherwise surprising, we thereby presupposethe truth of a restricted PSR.

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

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