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One of Leibniz’s fundamental philosophical commitments is the principle of sufficient reason (PSR). Yet Leibniz’s precise understanding of this principle is elusive. Leibniz provides several seemingly different formulations of its content, and Leibniz sometimes seems to require the PSR being metaphysically necessary and sometimes being metaphysically contingent. I argue that these puzzles can be solved by taking seriously Leibniz’s insistence that the PSR is a principle of reasoning. For Leibniz, I argue, to say that the PSR is a principle of reasoning is to say that it is a regulative principle of rational inquiry, a principle that settles some of the permissible and impermissible moves in the game of rationally inquiring into a fundamentally intelligible reality. According to this reading, there is a coherence between epistemology and metaphysics: for Leibniz, one is epistemologically justified in holding metaphysical doctrines precisely because they result from engaging in the type of rational inquiry structured by the PSR understood as a principle of reasoning.
Keywords: Leibniz, rational inquiry, metaphysics of modality, psr
How to Cite: Garcia Torres, J. (2026) “Leibniz on the PSR as a Regulative Principle of Rational Inquiry”, Journal of Modern Philosophy. 8(0). doi: https://doi.org/10.25894/jmp.2841
Undoubtedly, a fundamental commitment in Leibniz’s philosophy is the principle of sufficient reason (PSR). Yet Leibniz’s precise understanding of this principle is elusive, and, as we shall see below, his use of the PSR provides fertile ground for interpretative perplexities. The main goal of this paper is to offer a particular interpretation of Leibniz’s PSR. Furthermore, much of this paper’s project concerns philosophical methodology. In particular, I argue that Leibniz’s philosophical methodology for thinking about metaphysics and his version of the PSR are more closely related than is commonly acknowledged.
One way of introducing my main thesis is by briefly considering a criticism of Leibniz’s philosophical methodology. Kant, upon encountering Hume’s radical empiricist methodology, claims to have been awakened from his (Leibnizian) dogmatic slumber (AK 4:260). What Kant means by this is not as straightforward as one might like, but he is clearly chastising Leibniz for employing what he regards as a naïve and uncritical philosophical methodology when thinking about metaphysical matters. Robert Adams, who acknowledges his sympathies for Leibniz’s methodology in metaphysics, describes what he takes to be Leibniz’s methodology in the following way: ‘He was typically willing to begin an argument with whatever seemed true to him and might seem true to his audience, without worrying too much about whether epistemology would present it as something we can really know’ (Adams 1994: 3). As both Kant and Adams see it, then, a characteristic feature of Leibniz’s philosophical methodology is a kind of epistemological neglect: a lack of concern with whether the bold metaphysical theses Leibniz advocates are in fact knowable or supported by a tenable epistemological model. Kant finds great fault with such neglect, whereas Adams finds it acceptable because he thinks that it is not clear that epistemology deserves a place of priority in philosophical methodology (1994: 3–4). In either case, they agree that Leibniz divorces metaphysical thinking from epistemological considerations.
I think that characterizing Leibniz’s philosophical methodology in this fashion is distortive. As I read him, Leibniz’s thought embodies an admirable coherence or unity in its epistemological and metaphysical commitments. Leibniz’s PSR, I argue in this paper, is a case in point. It is common in the secondary literature to read Leibniz’s PSR as a mere metaphysical or logical principle.1 By contrast, I propose to take seriously Leibniz’s insistence that the PSR is one of the ‘two first principles of all our reasoning’ (G.7.309/MP 75).2 In particular, I propose that for Leibniz to say that the PSR is a principle of reasoning is to say that it is a regulative principle of rational inquiry, one that establishes normative constraints on proper reasoning when inquiring into the nature of reality. The PSR tells us what to expect and what not to expect, and it settles as permissible or impermissible several important types of moves in the game3 of rational inquiry into a fundamentally intelligible reality.
As I see it, there is a coherence between epistemology and metaphysics: for Leibniz, one is epistemologically justified in holding metaphysical doctrines precisely because they result from engaging in the type of rational inquiry structured by the PSR, understood as a principle of reasoning.4 My proposal is structurally analogous to that of modern proponents of a scientific stance—thinkers with the conviction that modern scientific methodology is an epistemologically credible, or the most epistemologically credible, form of inquiry. These thinkers endorse scientific theses because they result from engaging in modern scientific inquiry, and, according to these thinkers, they are epistemologically justified in holding them precisely because they are the results of modern scientific inquiry. Likewise, I suggest, Leibniz endorses many metaphysical theses—that no substances differ in number only, that there is no vacuum, that God exists, etc.—because they are the results of engaging in the form of inquiry structured by the PSR, and he takes himself to be epistemologically justified in holding these metaphysical theses precisely because they are the results of the form of inquiry structured by the PSR.
I offer a cumulative argument based on textual and philosophical considerations. My proposal is partly an interpretation of some texts, but it is also a general framework or lens that enables other texts to make sense. Some texts, I argue, would be perplexing without something like my proposal—for example, passages in which Leibniz explicitly refers to the PSR as a principle of reasoning, and passages in which Leibniz treats the PSR as a regulative principle of rational inquiry into a fundamentally intelligible reality. One significant advantage of my proposal, I argue, is its ability to solve two philosophical puzzles that emerge from thinking of Leibniz’s PSR as merely a metaphysical or logical principle. The first puzzle emerges because Leibniz articulates the PSR in seemingly distinct ways. I call this the ‘content’ puzzle, which can be articulated as a question: what is the content of Leibniz’s PSR? The second puzzle arises because Leibniz seems to treat the PSR sometimes as metaphysically contingent and sometimes as metaphysically necessary. I thus call it the ‘modal status’ puzzle, which can also be articulated as a question: what is the modal status of Leibniz’s PSR? At first sight, it seems that the content and modal status puzzles place Leibniz scholars in predicaments: an interpreter must choose which texts or arguments to give greater importance in her interpretation and thereby unavoidably compromise the seemingly conflicting texts and philosophical ideas.5 I argue that Leibniz scholars can escape these predicaments by reading Leibniz’s PSR as first and foremost a principle of reasoning.
Here is the plan. In section two, I provide some textual support for my interpretation of Leibniz’s PSR as a principle of reasoning. In section three, I present one significant advantage of my proposal, namely its ability to solve the content and modal status puzzles. In section four, I rely on Bas van Fraassen’s notion of a philosophical stance to elaborate on my interpretation of Leibniz’s PSR as a regulative principle of rational inquiry.
In this section, I offer some textual evidence for my proposal. This evidence, granted, is not definitive, but it is suggestive. Coupled with my proposal’s ability to solve the content and modal status puzzles, it provides good reason to take the proposal seriously in the literature on Leibniz’s PSR.
Leibniz characterizes the PSR, along with the Principle of Contradiction (PC), as one of the ‘two first principles of all our reasoning’ (G.7.309/MP 75; see also M 31–32; T 340; LC L.5.20; ‘Metaphysical Consequences of the Principle of Reason’, §1). What does Leibniz mean when he describes the PSR as a ‘principle of reasoning’? Sleigh (1983: 193f) argues that Leibniz cannot simply mean that the PSR is a permissible premise in argumentation, or mean what we mean by ‘rules of inference’, such as modus ponens. Leibniz’s meaning must be different from this. What exactly is it?
I propose that for Leibniz to say that the PSR is a principle of reasoning is to say that it is a regulative principle of rational inquiry, a principle that establishes normative constraints on proper reasoning when inquiring into the nature of reality. The PSR tells us what to expect and what not to expect, and, in particular, it settles as permissible or impermissible several important types of moves in the game of rational inquiry into a fundamentally intelligible reality.
I know of no text in which Leibniz states this explicitly. However, Leibniz repeatedly treats the PSR roughly along these lines. For example, in his correspondence with Clarke (1715–1716), Leibniz uses the PSR to argue against Newtonian absolute space. Newtonian space permits God to rearrange all bodies in the physical universe and yet keep all relations amongst bodies unchanged, by, say, flipping ‘east into west’ (LC L.5.5). But such flipping is absurd, something for which God would have no reason, Leibniz insists: ‘[I]n truth the one would exactly be the same thing as the other, they being absolutely indiscernible, and consequently there is no room to inquire after a reason for the preference of the one to the other’ (LC L.5.5, emphasis added). Leibniz’s point here is not merely about the nature of space but, importantly for our purposes, the nature of rational inquiry. The PSR imposes constraints on the normative space (i.e., ‘room’) of rational inquiry into reality. Similar observations can be made about other texts. For instance, in his important work the Monadology (1714), he writes: ‘Our reasonings are based on two great principles, that of contradiction [PC]… [a]nd that of sufficient reason, by virtue of which we consider that we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise’ (M 31–32/AG 217, emphases added). Here Leibniz treats the PSR as the guide for identifying what to expect in the process of rationally inquiring into reality. The PSR serves as an assurance that sufficient explanations can be found, and thus as a license to inquire into such explanations. Leibniz does something similar in his Principles of Nature and Grace (1718); in that work, after presenting the PSR, he writes: ‘Assuming this principle, the first question we have a right to ask will be, why is there something rather than nothing?’ (PNG 7/AG 210, emphasis added). Here, again, Leibniz is treating the PSR as a principle that structures rational inquiry into reality: it settles which questions ‘we have a right to ask’ and which questions constitute permissible questions to pursue in rational inquiry into a fundamentally intelligible reality.
More generally, Leibniz often complains about philosophers failing to ‘use’ the PSR in their metaphysical inquiry. For example: ‘The principle of the need for a sufficient reason does alone drive away all these specters of imagination. Men easily run into difficulties for lack of making right use of that great principle’ (LC L.5.48, emphasis added). It is tempting to think that by his talk of ‘using’ the PSR, Leibniz is merely encouraging philosophers to include the PSR as a premise in their arguments about metaphysical matters. However, this reading often obscures what Leibniz is doing in his recommendations to use the PSR. Leibniz, I suggest, is often inviting philosophers to participate in a particular form of inquiry structured by the PSR, a form of inquiry that avoids mere ‘specters of imagination’ (LC L.5.48), ‘indefensible opinions’ (LC L.5.20), ‘absurdities’ (LC L.5.113), ‘chimeras’ (T 45; T 175; LC L.5.127), ‘tales of fairies’ (LC L.5.114), ‘carelessness’ (LC L.5.127), ‘sophisms’ (T 307), etc. It is telling, I think, that these criticisms are not merely criticisms that opinions incompatible with the PSR are false (as we would expect if the PSR were a mere metaphysical principle), but that such opinions are ‘false and absurd, because one of the greatest principles of good sense is that nothing ever happens without a cause or determining reason’ (G 3.402/AG 194, emphasis added). These accusations, I suggest, are different ways of pointing out that people that fail to reason in accordance with the type of rational inquiry structured by the PSR are failing to reason properly. These philosophers are not merely failing to take advantage of appealing to a true premise in their arguments; rather, for Leibniz, they are failing to reason well in a deeper and more problematic way.
One interesting case of textual support for my proposal comes from the end of the Leibniz–Clarke correspondence. Much of the correspondence reads like an exchange of assertion and counter-assertion between largely incompatible physical and metaphysical systems. Towards the end of their correspondence, however, both Clarke and Leibniz conclude their cases in favor of their respective systems by making claims that can reasonably be read as appeals to the plausibility of their philosophical methodologies. For instance, one of the recurring themes of the correspondence is Leibniz’s objection that Newton’s notion of gravity, or attraction, introduces unintelligible or ‘occult’ qualities and is thus unacceptable (LC L.3.17; L.5.113; L.5.122–123). In the final part of Clarke’s final letter, Clarke responds to this objection thus: ‘The phenomenon itself, the attraction, gravitation, or tendency of bodies toward each other (or whatever other name you please to call it by), and the laws or proportions of that tendency, are now sufficiently known by observations and experiments’ (LC C.5.124–130, emphasis added). The phenomenon of gravitational pull is a ‘fact found by experience’ (LC C.5.118–123), and, as such, it should not be denied. Clarke continues: ‘That this phenomenon is not produced… without some cause capable of producing such an effect, is undoubtedly true. Philosophers therefore may search after and discover that cause, if they can, whether it is mechanical or not mechanical’ (LC C.5.118–123). Clarke is here clearly putting forth an empirical form of inquiry, according to which observation and experimentation take priority: for Clarke, fit with empirical data is a stronger theoretical virtue than explanatory power. Leibniz, by contrast, places greater value on explanatory power. This point comes clearly in the preface to his New Essays, where Leibniz contrasts his views with those of Locke. Therein, Leibniz writes: ‘I note, indeed, that I recognize that we are not allowed to deny what we do not understand, though I add that we have the right to deny (at least in the order of nature) what is absolutely unintelligible and inexplicable’ (NE 65). Leibniz thus thinks that a theory’s explanatory power is paramount. These disagreements about the relative importance of different theoretical virtues can be understood as disagreements about philosophical methodology and which form of rational inquiry is preferable.
Importantly for my purposes, Leibniz concludes his final letter to Clarke with some remarks that I think are perplexing if one does not read the PSR as first and foremost a regulative principle of rational inquiry. Even though in the correspondence he appeals to the PSR as ‘my axiom’ (LC L.3.5; L.3.7) and even questions whether the PSR is ‘a principle that needs to be proven’ (LC L.5.125), Leibniz promises a defense of this principle: ‘I shall speak more largely at the conclusion of this paper concerning the solidity and importance of this great principle of the need for a sufficient reason for every event, the overthrowing of which principle would overthrow the best part of all philosophy’ (LC L.5.20). Here is what Leibniz presents as his defense of the PSR at the end of his fifth letter to Clarke:
Has not everybody made use of this principle on a thousand occasions? It is true that it has been neglected out of carelessness on many occasions, but that neglect has been the true cause of chimeras… and a thousand other fictions… (LC L.5.127, emphasis added)
I have often defied people to advance an instance against that great principle, to bring any one uncontested example in which it fails. But they have never done it, nor ever will. It is certain that there is an infinite numbers of instances in which it succeeds, <or rather it succeeds> in all the known cases in which it has been made use of. From this one may reasonably judge that it will succeed also in unknown cases or in such cases as can only by its means become known, according to the method of experimental philosophy. (LC L.5.129)
It is tempting to read Leibniz’s defense of the PSR here as an instance of reasoning by induction: the PSR has been successful in known cases; therefore, it is reasonable to think that the PSR will be successful in unknown cases. However, such a defense of the PSR would be quite weak, and not in tune with Leibniz’s insistence on treating the PSR as a fundamental principle, an axiom, the ground of all contingent truths, etc. Furthermore, Leibniz is quite aware of the limitations of inductive reasoning: ‘For example, even after having experienced a hundred thousand times that iron placed on the surface of water sinks to the bottom, we are not assured that this must always happen’ (G 6.505/AG 190). In fact, sometimes Leibniz contrasts induction with the type of understanding of causes attained by using reason: ‘This is why the wisest people do not rely on [induction] to such an extent that they do not try to probe into the reason for what happens’ (NE 50). It is thus unlikely that Leibniz is providing an inductive argument in support of the PSR at the end of his fifth letter to Clarke.
One of the advantages of my proposal is that it enables us to make sense of this otherwise puzzling defense of the PSR. So, what are we to make of Leibniz’s advertised defense of ‘the solidity and importance’ of the PSR, a principle without which ‘the best part of all philosophy’ would be overthrown (LC L.5.20)? On my view, Leibniz is providing a defense of the PSR that is structurally analogous to the kind of defense that proponents of the scientific stance offer in support of their stance (this topic takes center stage in section four below). Why trust the scientific method as a sound form of rational inquiry? Because it is a form of inquiry that reliably tracks truth.6 That a particular form of inquiry tracks truth is indeed a strong form of recommendation. On my reading, it is this type of defense of the PSR that Leibniz presents at the end of his fifth letter to Clarke.
Furthermore, my proposal also makes sense of the claim with which Leibniz begins this defense of the PSR. Leibniz writes that ‘I dare say that without this great principle one cannot prove the existence of God nor account for many other important truths’ (LC L.5.126). It is tempting to read this passage as claiming that for theists of Leibniz’s orientation, it would be useful to endorse the PSR to ‘prove’ doctrines that they want to hold on the basis of their religious commitments. This is likely not what Leibniz means, however. In fact, elsewhere Leibniz expresses caution regarding this type of argumentation:
But when someone has devised certain principles and wants to uphold them on the grounds that without them some accepted doctrines would collapse, the argument is not conclusive. Because what is necessary to uphold our knowledge must be distinguished from what serves as a foundation for our accepted doctrines or for our practices. (NE 492)
So what is Leibniz doing when he notes that without the PSR many important truths cannot be proven? Rodriguez-Pereyra reads in this claim the beginnings of a type of Aristotelian transcendental argument: the PSR is justified because it is a necessary presupposition in a type of discourse or inquiry (2013, 52–53). Rodriguez-Pereyra thinks, however, that this brief remark (in LC L.5.126) is insufficient to justify this ‘interesting interpretation’ (2013, 53). My proposal in this paper can be read as an elaboration of Rodriguez-Pereyra’s brief remarks. According to my interpretation, Leibniz thinks that propositions such as ‘God exists’, and many other important truths, can be known by engaging in the type of form of rational inquiry structured by the PSR, and that this fact is a mark of the reliability of such a method of inquiry. As I read it, this claim is part of Leibniz’s promised defense of the PSR at the end of his fifth letter to Clarke, a defense whose primary goal is to establish the reliability of the form of inquiry structured by the PSR as a regulative principle of rational inquiry into a fundamentally intelligible reality.
In contrast to an inductive argument for the PSR, this defense is not weak. If successful, it would show that one is epistemologically justified in holding metaphysical doctrines because they result from engaging in the form of rational inquiry structured by the PSR, for such epistemic justification is predicated upon the reliability of that form of inquiry in attaining truth. I will say more about this in section four of this paper. Before that, I wish to provide further justification for my interpretation: its ability to solve the content and modal status puzzles.
Leibniz repeatedly appeals to the PSR as a secure foundation for much of his philosophy. For example, responding to Clarke’s inquiries, Leibniz boldly presents many of his philosophical positions as firmly planted in the wide-ranging PSR: ‘But of what principle, I beseech you? Would to God less clear principles had never been laid down. The principle in question is the principle of the need for a sufficient reason for anything to exist, for any event to happen, and for any truth to take place’ (G 7.419/LC 5.125). However, despite Leibniz’s unqualified insistence on the clarity of his PSR, he often presents this fundamental principle differently. Sometimes Leibniz explicitly builds the demand for contrastive explanations into the wide-ranging principle: ‘[N]othing happens without a reason why it should be so rather than otherwise’ (LC 2.1; see also A 2.2.65; 6.4.1616; 6.4.1645; NE 179; G 6.127; 6.602; 6.612). On occasion Leibniz presents the PSR as a causal principle: ‘[N]othing is without reason, or there is no effect without a cause’7 (A 6.4.1645/AG 31, emphasis in original; see also A 6.4.1616; G 5.127). Yet other times Leibniz presents the PSR as an idiosyncratic logical principle: ‘[T]here is nothing without reason, that is, that there is no proposition in which there is no connection between the subject and the predicate, that is, no proposition which cannot be proved a priori’ (Grua 187/AG 19, emphasis in original; see also A 2.2.65; DM 13). One important interpretative puzzle thus pertains to the very content of Leibniz’s PSR. Are the different formulations of the PSR distinct enough to constitute independent PSRs? Is one formulation in some sense prior or more fundamental than the others?8 Alternatively, can those different formulations somehow ultimately be saying the same thing or referring to the same underlying reality?9 These are important exegetical questions regarding Leibniz’s PSR.
Another important interpretative controversy is about the modal status of Leibniz’s PSR. Is Leibniz’s PSR metaphysically necessary or metaphysically contingent? Commentators have argued for both positions,10 and their different readings have led them to diverging interpretations of other central elements in Leibniz’s metaphysics of modality.11 It is not too surprising that commentators disagree here given the various uses to which Leibniz subjects the PSR.
Some of the main considerations for both positions are the following. On the one hand, there are several considerations for reading Leibniz’s PSR as metaphysically contingent. First, Leibniz insists that the PSR is the ground of all contingent truths. He writes: ‘Our reasonings are based on two great principles, that of contradiction… And that of sufficient reason’ (M 31–32, emphasis in original). The principle of contradiction (PC) grounds ‘The truths of reasoning [that] are necessary and their opposite is impossible’ (M 33); whereas the PSR grounds ‘the truths of fact [that] are contingent’ (ibid). For Leibniz, then, ‘All truths contingent by their nature… rest on the latter principle [the PSR]’ (Grua 287/AG 19). Secondly, Leibniz provides arguments with the PSR as a premise and metaphysically contingent conclusions (see DM 13; Grua 303; C 519; LC 1.1; 3.5). A prominent example is Leibniz’s insistence that the PSR enables us to conclude that God chooses the best, but God does so contingently, because divine ‘motives’ or reasons for acting ‘incline but do not necessitate’ the divine choice (LC 5.9). From these claims it is not unreasonable to conclude that if the PSR were metaphysically necessary, then this necessity would transfer onto the truths that follow from it, or ‘rest’ upon it, contrary to Leibniz’s insistence that these are contingent truths. Third, Leibniz countenances the metaphysical possibility of entities—like qualitatively indiscernibles beings—that, he claims, violate the PSR (G 7.420; LC 5.127).12 Fourth, Leibniz insists that all metaphysical necessities in some sense reduce to the PC (Grua 302; M 31–3; LC 5.10), and that the PC and the PSR are independent; thus, making the PSR itself not metaphysically necessary.13 Thus, it seems reasonable to conclude that Leibniz is committed to thinking of the PSR as metaphysically contingent.
On the other hand, there are also several considerations for reading Leibniz’s PSR as metaphysically necessary. First, Leibniz attempts to derive the PSR from his account of the nature of truth itself. He writes: ‘Therefore, the predicate or consequent is always in the subject or antecedent, and the nature of truth in general or the connection between the terms of a statement, consists in this very thing’ (C 518/AG 31). This is Leibniz’s notorious predicate-in-subject notion of truth (PIN). Leibniz claims that the PSR follows from PIN: ‘that nothing is without reason, or there is no cause without effect, directly follows from these considerations; otherwise, there would be a truth which could not be proven a priori… contrary to the nature of truth’, (ibid). Arguably, the principle governing the nature of truth, PIN, is metaphysically necessary; and if PIN implies the PSR, then the metaphysical necessity of PIN transfers onto the PSR. Second, Leibniz also employs the PSR as a premise in arguments whose conclusions are clearly intended to be metaphysically necessary, like the existence of God. Given the PSR, there is a sufficient reason for everything that is, including the universe itself. Furthermore, ‘This sufficient reason for the existence of the universe cannot be found in the series of contingent things’ (PNG 8/AG 210), for this series is precisely what stands in need of explanation. ‘Thus the sufficient reason… must be outside this series of contingent things, and must be found in a substance which is its cause, and which is a necessary being… And this ultimate reason for things is called God’ (PNG 8/AG 210). Leibniz thus advances arguments with the PSR as a premise and with conclusions that are metaphysically necessary. Further, it is reasonable to think that the conclusion of an argument is metaphysically necessary only if the premises on which it rests are themselves metaphysically necessary.14 Thus, it seems that Leibniz’s PSR is metaphysically necessary.
Here are thus two important puzzles regarding Leibniz’s fundamental principle. Reading Leibniz’s PSR first and foremost as a principle of reasoning can help solve these puzzles, I argue. If so, this is a significant benefit of my proposal.
A comparison with Leibniz’s PC helps solve the content puzzle. As we have seen, Leibniz thinks that the PC and the PSR are the ‘two first principles of all our reasoning’ (G.7.309/MP 75). Like the PSR, Leibniz presents the PC in a multiplicity of seemingly distinct ways. Here are some presented by Rodriguez-Pereyra (2013, 46):
PC1: For any two contradictory propositions p and q, one is true and the other is false.
PC2: For any proposition p, p is either true or false.
PC3: For any proposition p, p is not both true and false.
PC4: For any proposition p, if p implies a contradiction, then p is false.
PC5: For any proposition p, if p is false, then not-p is true.
PC6: For any proposition p, if p is an identical proposition, then p is true.
Some of these formulations are not unlike modern logical principles—the law of excluded middle (PC1) and the principle of bivalence (PC2), for example—but others are more distinctly Leibnizian (like PC6). Why does Leibniz present all these as ‘the principle of contradiction’? A similar ‘content’ puzzle arises here: what does Leibniz’s PC state or mean? Rodriguez-Pereyra offers an intriguing suggestion or ‘hypothesis’ (2013, 47): for Leibniz, the PC is ‘a name of whatever principle played a certain function in his theory—roughly, a principle that, in his view, excluded true contradictions and served to ground mathematical and necessary truths in general’ (2013: 47, emphasis added). This suggestion preserves ‘the meaning’ (2013, 47) of the PC, namely that of excluding true contradictions and grounding mathematical and necessary truths, while allowing different principles—PC1 through PC6—to play the role specified by this meaning, in different contexts of logical argumentation. The connection between Leibniz’s PC and the principles PC1 through PC6 is thus clear; the content puzzle is solved for Leibniz’s PC. Incidentally, this suggestion also helps make sense of Leibniz’s PC as a principle of reasoning: the PC guides or structures proper logical reasoning—by specifying the goal of logical reasoning, that of avoiding true contradictions and proving necessary truths, and by settling a multiplicity of more precise rules for permissible and impermissible logical moves—namely PC1 through PC6—which, for Leibniz, guide and structure proper logical reasoning itself.
This contrast with Leibniz’s PC helps us to solve the content puzzle for Leibniz’s PSR. For Leibniz, the PSR is the name of whatever explanatory principle plays the role of ensuring that reality is intelligible or that everything has an explanation; put differently, the meaning of the PSR is the theoretical role that ensures the permissibility of seeking explanations when inquiring into reality, and the different formulations of the PSR are the particular explanatory principles that play the role specified by the meaning of the PSR in different contexts of rational inquiry. The various formulations of the PSR, then, are different ways of specifying different explanation-relations holding between different explananda and explanantia. The causal version of the PSR specifies that causal relations are appropriate ways of making intelligible why some events happened and others did not. The logical version of the PSR specifies that a priori proofs are appropriate ways of making intelligible why some propositions are true and others are not. And so on.
The suggestion here is structurally analogous to Hilary Putman’s influential account that to be water is to be whatever it is that plays the semantic role provided by the meaning of the term ‘water’. It turns out that the thing that plays this role is the chemical compound H2O, so it turns out that water is H2O (Putnam 1975, vol. 2: 192ff). A similar move is made by Robert Adams, who argues that to be a moral obligation is to be whatever it is that plays the semantic role provided by the meaning of the expression ‘a moral obligation’. Adams further argues that it is God’s commands that are best suited to play this semantic role, so moral obligations are God’s commands (Adams 1999, ch. 11). The main difference with my proposal is that the meaning of Leibniz’s PSR is itself not settled by conventional use within a linguistic community, but rather by Leibniz’s theoretical commitment to treating reality as fundamentally intelligible. It is this theoretical role that provides the meaning of Leibniz’s PSR, and it is the multiplicity of formulations of the PSR, understood as particular explanatory principles, that play the role provided by the meaning of Leibniz’s PSR in different contexts of rational inquiry into fundamentally intelligible reality.
The content puzzle is solved.
Solving the modal status puzzle requires situating Leibniz’s PSR in his modal metaphysics. A good place to begin is to note that Leibnizian rationalism—or Leibniz’s conviction that reality is fundamentally intelligible—is attractive, at least to some extent. When a building burns down, a plane crashes, or a person dies, part of what it is to engage in rational inquiry into what happened is to seek a sufficient explanation, one that at least in principle makes it intelligible to the inquirer why things happened as they did and not otherwise. By contrast, insisting that ‘it just happened’ seems both a) an impermissible move in the game of rational inquiry and b) tantamount to giving up on treating reality as fundamentally intelligible. Leibnizian rationalism seems uncontroversial here.
Leibnizian rationalism, however, extends far beyond events like plane crashes and buildings burning down. As I read him, for Leibniz, all of reality—including all modal metaphysics—is within the purview of his rationalism. Leibniz’s demand for explanations applies to all truths, including all truths about modal metaphysics. For example, Leibniz accepts that God has knowledge of subjunctive conditionals of human freedom—proposition of the form ‘if agent S were in circumstance C, S would freely φ’. Leibniz writes, for example: ‘God knows what any free mind would choose if it were to find itself in any situation which nevertheless will not actually occur’ (Rationale of the Catholic Faith §7, A 6.4.2318/LGR 75; see also A 6.4.1374; T 103). Moreover, Leibniz confidently assures us that there must be explanations for the truth of these conditionals: ‘Let us assume that Paul is placed in the same circumstances in which Peter is also placed and with the same assistance [i.e., divine grace], and that God says to me that Peter is then going to reject grace, while Paul is going to accept it; it is certainly necessary that there is some reason for this difference’ (A 6.4.1374/SLT 105). Leibniz further insists that such explanations must in principle be within the reach of the understanding of finite minds: ‘But it is also necessary that this… choice is known to God, and if he deigned to explain it to me, I would understand, and so I would obtain full knowledge of a future conditional event a priori’ (ibid).
Furthermore, understanding Leibniz’s PSR as principle of reasoning has implications for understanding Leibniz’s account of the metaphysics of modality, for engaging in modal metaphysics is itself best understood as a particular type of rational inquiry into modal reality, an inquiry itself structured by Leibniz’s PSR. In this way of thinking about modal metaphysics, a central question is whether the types of explanations that meet the demands of Leibniz’s PSR require that explanantia necessitate explananda. We turn to this topic next.
Engaging in modal metaphysics understood as engaging in rational inquiry into modal reality naturally gives rise to questions like: What types of explanations meet the demands of Leibniz’s PSR in modal metaphysics? Are there sufficient explanations, explanations that meet the demands of the PSR, that do not necessitate that which they explain? Or are the demands of the PSR met only by necessitating sufficient explanations, explanations that make necessary that which they explain?15 Leibniz explicitly acknowledges the existence of both types of explanations: ‘In my view it is common to every truth that one can always give a reason… in necessary propositions, that reason necessitates; in contingent propositions, it inclines’ (Grua 302/AG 28). What does Leibniz mean here?
Leibniz defines necessary truths as those that can be demonstrated: ‘For, by definition a necessary proposition is one whose truth can be demonstrated with geometrical rigor’ (Grua 306/AG 30). For Leibniz, this definition is not merely nominal; rather, the explanation for the necessity of a given truth is its demonstration: ‘When a truth is necessary, its reason can be found by analysis, resolving it into simpler ideas and simpler truths until we reach the primitives’ (M 33/AG 217, emphasis added). ‘Analysis’ for Leibniz is a technical term. It is a particular proof structure that begins with a complex proposition, and after a series of permissible substitutions of definitions or parts of definitions of the terms in the proposition, the proof terminates in what Leibniz calls ‘identical propositions’. For Leibniz, an identical proposition is any proposition ‘which assert[s] the same thing of itself or deny the opposite of the opposite. For example, “A is A”, “A is not not-A”’ (C 518/AG 30). With this account of analyses at hand, Leibniz makes a distinction between two kinds of a priori proofs: finite and infinite analyses:
And with this secret the distinction between necessary and contingent truths is revealed… For in necessary propositions, when the analysis is continued indefinitely, it arrives at an equation that is an identity; this is what it is to demonstrate a truth with geometrical rigor. But in contingent propositions one continues the analysis to infinity through reasons for reasons, so that one never has a complete demonstration, though there is always, underneath, a reason for the truth, but the reason is understood completely only by God, who alone traverses the infinite series in one stroke of mind. (Grua 302/AG 28)
So, for Leibniz, necessary truths have finite analyses, and contingent truths have infinite analyses. All truths must have a priori proofs, which are their sufficient explanations. Finite analyses are the necessitating sufficient explanations of necessary truths, and infinite analyses are the non-necessitating sufficient explanations of contingent truths.
All of this applies only to what I have called ‘the logical version’ of the PSR. Leibniz, as we have seen, puts forth different formulations of the PSR, and thus countenances various other kinds of explanations. For example, when explaining events or facts ‘within the order of nature’ (NE 65), or in created reality, Leibniz thinks that the natures of things provide the ultimate level of explanation. For example, rejecting Locke’s suggestion that God can ‘superadd’ thought to bodies, Leibniz writes:
Whenever we find some quality in a subject, we ought to believe that if we understood the nature of both the subject and the quality we would conceive how the quality could arise from it. So within the order of nature (miracles apart) it is not at God’s arbitrary discretion to attach this or that quality haphazardly to substances. He will never give them any which are not natural to them, that is, which cannot arise from their nature as explicable modifications. (NE 65)
Leibniz here insists that, within the order of nature, explanations of events or facts must cite the natures of the things in question. Leibniz further divides such explanations into those provided by general natures and those provided by individual natures. In a letter to de Volder, from January 21st 1704, for example, Leibniz writes: ‘from universal natures there follow eternal consequences, from singular natures also temporal ones’ (G 2.263/L 534). It is reasonable to read Leibniz here as insisting that general natures provide necessitating sufficient explanations of the eternal consequences that follow from them, and individual natures provide non-necessitating sufficient explanations of the merely temporal consequences that follow from them (see Rutherford 1992).
These details need not detain us, however; what matters most for our purposes is that the PSR itself is not part of any of these sufficient explanations. For truths, it is analyses, both finite and infinite, that serve as the explanantia; and within the order of nature, it is natures, both general and individual, that serve as the explanantia. The PSR itself need not be cited for any of these explanations to be adequate. The PSR is rather an expression of the conviction that such sufficient explanations can, at least in principle, be found. What makes truths and beings metaphysically necessary, in this story, is precisely that they have necessitating sufficient explanations, and what makes truths and beings metaphysically contingent is precisely that they have non-necessitating sufficient explanations (and not necessitating sufficient explanations). The PSR is central in forming Leibniz’s modal metaphysics, but not because it is a metaphysical principle; rather, it is central because engaging in modal metaphysics is best understood as a particular type of rational inquiry, an inquiry into modal reality that, like all rational inquiry, is structured by the PSR.
We can finally solve the modal status puzzle. Most of the puzzle arises from the fact that Leibniz uses the PSR as a premise in arguments with conclusions that are sometimes metaphysically necessary and sometimes metaphysically contingent, and, in accordance with standard modern modal logic, a necessary conclusion only follows in an argument if the premises upon which it rests are themselves necessary.16 The main move in solving the modal status puzzle is to argue that Leibniz is not playing by the standards of modern modal logic in his use of the PSR in the various arguments in which it appears as a premise or conclusion.
As we have seen, Leibnizian modal metaphysics is structured by the PSR as a principle of rational inquiry, but establishing the necessity or contingency of some truth or being does not itself require citing the PSR itself: the PSR is not a premise in finite or infinite analyses of propositions. Rather, for Leibniz, what makes truths and beings metaphysically necessary is that they have necessitating sufficient explanations, and what makes truths and beings metaphysically contingent is that they have non-necessitating sufficient explanations (and not necessitating sufficient explanations). This means, I think, that it is a mistake to read Leibniz as trying to establish the necessity or contingency of propositions in arguments in which the PSR appears as a premise. Leibniz is simply not engaging in modal metaphysics, as he understands it, when he is presenting these sorts of arguments. Instead, what Leibniz is doing in these types of arguments—with the PSR as a premise and with conclusions with different modal status—is simply reminding interlocutors of what it is to engage in proper rational inquiry into a fundamentally intelligible reality (see subsection 4.3 for more details).
If this is right, this solves most of the modal status puzzle. It does away with all the cited considerations for thinking that Leibniz’s PSR must be understood as metaphysically necessary, and it also does away with several of the cited considerations for thinking that Leibniz’s PSR must be understood as metaphysically contingent. I find convincing the remaining considerations for thinking that Leibniz’s PSR is metaphysically contingent, especially those advanced by Pikkert (2021) and Bender (2022). However, these considerations are no longer part of a puzzle but are now simply persuasive considerations for thinking that the relevant particular principles playing the theoretical role specified by Leibniz’s PSR in different contexts of inquiry are themselves metaphysically contingent.
My proposal is that Leibniz’s PSR is a regulative principle of rational inquiry into a fundamentally intelligible reality. This means that the PSR provides the theoretical role of treating reality as fundamentally intelligible, a theoretical role that can be played by different principles in different contexts of rational inquiry, and that the PSR settles at least some of the permissible and impermissible moves in rational inquiry into a fundamentally intelligible reality. Further light on this interpretation can be shed from an unexpected quarter, namely, from a philosopher who is, in many ways, radically opposed to Leibniz’s own rationalism.17 That philosopher is Bas van Fraassen, and his take on what it is to be an empiricist (Van Fraassen 2002). I argue that Leibniz’s rationalism has remarkable structural similarities to van Fraassen’s empiricism.
Bas van Fraassen argues that deep within the empiricist philosophical tradition lie two essential attitudes: i) its rejection of metaphysics, or a fundamental conviction that there are no a priori factual statements; and ii) its openness to disagreement, or its rejection of dogmatism: no factual statement is immune from criticism or fails to stand in need of justification. He contends that these features make empiricism a philosophical stance: ‘A philosophical position can consist in a stance (attitude, commitment, approach, a cluster of such—possibly including some propositional attitudes such as beliefs as well)’ (2002: 47–8). To be an empiricist is to hold the aforementioned anti-metaphysics and anti-dogmatist attitudes. Accordingly, taking an empirical stance involves taking an ‘attitude toward empirical investigation and exploration’ (2002: 49). Van Fraassen’s empirical stance structures or guides rational inquiry into reality by settling permissible and impermissible moves in such inquiry: it is permissible to empirically falsify a particular scientific hypothesis, but impermissible to engage in discussions regarding the first principles of philosophy, etc. He elaborates:
Empiricism may also be approached through reflection on its positive attitude towards science. But this admiring attitude is not directed so much to the content of the sciences as to their forms and practices of inquiry. Science is a paradigm of rational inquiry… science as practice, as search, as rational form of inquiry par excellence. (2002: 63)
I wish to expand on van Fraassen’s ideas by distinguishing two ways of taking a philosophical stance. Thin stances leave open the viability of taking alternative and incompatible stances; they are pluralistic and permissive. Thick stances include the conviction that alternative stances lack important epistemic goods (truth, reliability, justification, warrant, etc.); they are exclusivist and critical of competing stances. A proponent of a thick philosophical stance X would find it legitimate to distinguish between ‘respectable thinkers’, who reason on the basis of the normative constraints imposed on rational inquiry by X, and ‘cranks’, who reason on the basis of alternative philosophical stances (Van Fraassen 2002: 48f).
An example can help. Call the ‘scientific stance’ the conviction that ‘science is a paradigm of rational inquiry’ (Van Fraassen 2002: 63). Accordingly, a thick scientific stance involves the conviction that other forms of inquiry lack important epistemic goods (truth, reliability, justification, warrant, etc.); a thin scientific stance lacks this second conviction. It is telling, I think, to consider the different responses to a transgression of scientific methodology by thinkers taking one or the other of these scientific stances. The scientific stance involves methodological naturalism: the conviction that supernatural explanations are not permissible in scientific inquiry. One recent scientific discovery is the fact that the possibility of carbon-based life depends upon a series of fundamental physical constants having values within a narrow range of possibilities, call this the ‘weak anthropic principle’ (Carter 1974). Proponents of the fine-tuned universe argument insist that the weak anthropic principle is best explained by the existence of an intelligent designer.
Thinkers that take a scientific stance can respond to the intelligent design proponent thus:
The weak anthropic principle is part of our best understanding of the universe.
Scientific stance: supernatural explanations are not permitted in scientific inquiry.
Therefore, postulating an intelligent designer as an explanation of the weak anthropic principle is unscientific.
Premises 1 and 2 in this argument are significantly different. Premise 1 is meant to articulate a fact in the world, and premise 2 is meant to articulate a particular element in rational inquiry. The main point of this argument, then, is to show a transgression on the normative constraints of the type of rational inquiry that is specified by the scientific stance. For the thinker that takes a thin scientific stance this argument shows that a plausible form of inquiry, namely scientific inquiry, fails to support the view of the intelligent design proponent. For the thinker that takes the thick scientific stance, this argument is devastating: it shows, she thinks, that there is something fundamentally mistaken about the position of the intelligent design proponent; in violating scientific methodology she has ceased to play the game of inquiring into reality properly. In transgressing scientific methodology, the intelligent design proponent cannot be taken seriously by ‘respectable thinkers’, the proponent of the thick scientific stance concludes.
This brief excursion into philosophical stances helps us further understand what it is to read Leibniz’s PSR as a regulative principle of rational inquiry. I think it is illuminating to read Leibnizian rationalism as a thick philosophical stance. After all, Leibniz often dismisses the epistemic credibility of reasonings not structured by the PSR: ‘The reasons advanced for a vacuum are mere sophisms’ (LC L.4.PS, emphasis added); ‘the denial of [the PSR] would have appeared too unreasonable’ (LC L.5.125, emphasis added); failure to use the PSR is due to ‘neglect out of carelessness’ (LC L.5.127); and to accept opinions contrary to the PSR ‘would renounce philosophy and reason’ (NE 65), etc. More generally, Leibniz accepts a distinction roughly along the lines of ‘respectable thinkers’ and ‘cranks’, tracking those that use the PSR and those that fail to do so. For example, he concludes his defense of the PSR at the end of his fifth letter to Clarke with the following remark: ‘And I believe reasonable and impartial men will grant me that having forced an adversary to deny that principle [the PSR] is reducing him ad absurdum’ (LC L.5.130). And, as we have seen, Leibniz repeatedly chastises opinions contrary to the PSR not merely as false but also as mere ‘specters of imagination’ (LC L.5.48), ‘indefensible opinions’ (LC L.5.20), ‘chimeras’ (T 45; T 175; LC L.5.127), ‘tales of fairies’ (LC L.5.114), ‘fictions’ (LC L.4.PS), ‘sophisms’ (T 307), ‘absurdities’ (LC L.5.113), and even ‘monstrosities’ (G 2.249/AG 175). These accusations target not merely the falsity of these opinions, but also their epistemic credibility; these opinions are ‘inexplicable, unintelligible, precarious, [and] groundless’ (LC L.5.120). This is the sort of thing a proponent of a thick philosophical stance would think of the opinions of those who fail to reason in accordance with the form of rational inquiry structured by such a stance.
I suggest that Leibniz’s PSR as a regulative principle of rational inquiry is predicated upon Leibnizian rationalism understood as a thick philosophical stance. Much like van Fraassen’s empirical stance, Leibnizian rationalism is not reducible to a mere factual statement (or metaphysical principle). Part of what makes it a philosophical stance is precisely that essential to it are attitudes, convictions, and commitments that are themselves not reducible to mere factual beliefs, and that help guide and structure a particular form of rational inquiry into reality.
Part of my solution to the modal status puzzle is the claim that when Leibniz uses the PSR as a premise in an argument, he is not engaging in modal metaphysics, and thus the modal status of the PSR is strictly orthogonal to the modal status of the other premises and conclusions of these arguments. I also argue that Leibniz’s recommendations to ‘use’ the PSR are not mere recommendations to use it as a premise in an argument. This raises an important question: what is Leibniz doing when he uses the PSR as a premise in an argument? My proposal offers an interpretation of what is going on in these cases.
Let the following ‘cosmological argument’ be a representative argument in which Leibniz’s PSR appears a premise (taken from PNG 8 and simplified):
The PSR holds.
The universe is a series of finite beings.
A series of finite beings cannot be an explanation for itself.
Therefore, the explanation for the universe’s existence comes from without (i.e., God).
On my reading, the main function of the PSR in this argument is structurally analogous to the function of the scientific stance in the argument against the intelligent design proponent outlined earlier. Just as the main goal of that argument was to illustrate a type of transgression in the game of rational inquiry into reality, so the main goal of arguments such as this cosmological argument is for Leibniz to convince interlocutors that their commitment to the fundamental intelligibility of reality (together with the non-PSR premises) requires that they also endorse the relevant conclusion. Put differently, for Leibniz, many arguments in which the PSR appears as a premise are intended to show his interlocutors that failing to endorse the conclusion of the argument (while holding onto the non-PSR premises) is tantamount to abandoning their commitment to the ultimate intelligibility of reality. What Leibniz is doing in these arguments, I suggest, is showing cases in which endorsing certain propositions—such as the existence of brute facts or indiscernible entities—constitutes transgressions of the rules of rational inquiry structured by the PSR. The PSR in these arguments thus does not function as a premise stating a metaphysical principle, or stating another fact about the world, but rather as a reminder of what rational inquiry into a fundamentally intelligible reality demands—again, this is a function structurally analogous to the function of the scientific stance in the argument previously sketched.
On my reading, it is these convictions about rational inquiry that lead Leibniz to insist that ‘science becomes real and demonstrative by means of these principles [PSR and PII], whereas before it did generally consist in empty words’ (LC 4.5, emphasis added). For Leibniz, to countenance brute facts or unintelligible aspects of reality is to abandon proper rational inquiry; it is to be content with ‘sophisms’, with ‘fictions, merely arbitrary and unworthy of true philosophy’ (LC 4.46).
Undoubtedly, a fundamental commitment in Leibniz’s philosophy is the principle of sufficient reason (PSR). Yet Leibniz’s precise understanding of this principle is elusive, since he provides several formulations that appear to be distinct. I call this the ‘content puzzle.’ Another important puzzle pertains to the modal status of the PSR. There are several considerations for reading Leibniz’s PSR as metaphysically necessary: Leibniz often uses it to derive conclusions, or derives it from premises, that he takes to be metaphysically necessary. There are also several considerations for reading Leibniz’s PSR as metaphysically contingent: Leibniz claims that it is the ground of all contingent truths, uses it in arguments whose conclusions are contingent, permits the metaphysical possibilities of entities that violate the PSR, and seems to think that the PSR does not reduce to the PC.
I have argued that these puzzles can be solved by taking seriously Leibniz’s insistence that the PSR is a principle of reasoning. I argue that, for Leibniz, to say that the PSR is a principle of reasoning is to say that it is a regulative principle of rational inquiry, a principle that settles some of the permissible and impermissible moves in the game of rationally inquiring into a fundamentally intelligible reality. According to this reading, there is a coherence between epistemology and metaphysics: for Leibniz, one is epistemologically justified in holding metaphysical doctrines precisely because they result from engaging in the type of rational inquiry structured by the PSR understood as a principle of reasoning. My proposal is structurally analogous to that of modern proponents of a scientific stance—thinkers with the conviction that modern scientific methodology is an epistemologically credible, or even the most epistemologically credible, form of inquiry. These thinkers endorse scientific theses because they result from engaging in modern scientific inquiry, and regard their views as epistemologically justified precisely because they result from modern scientific inquiry. Likewise, I suggest, Leibniz endorses many metaphysical theses—that no substances differ in number only, that there is no vacuum, that God exists, etc.—because they result from engaging in the form of inquiry structured by the PSR, and Leibniz takes himself to be epistemologically justified in holding these metaphysical theses precisely because they are the results of such a form of inquiry.
I offer a cumulative argument for my proposal based on textual and philosophical considerations. My proposal is partly an interpretation of some texts, but it is also a general framework or lens that enables other texts to be made intelligible. Most relevantly are the passages in which Leibniz states that the PSR is a principle of reasoning, and the passages in which Leibniz treats the PSR as a regulative principle of rational inquiry into a fundamentally intelligible reality. Furthermore, a major benefit of my proposal is its ability to solve the content and modal status puzzles. This cumulative case is not conclusive, I grant; but, all in all, it makes my proposal worthy of consideration in the secondary literature on Leibniz’s PSR.
The author has no competing interests to declare.
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