Leibniz and the Principle of Sufficient Reason

by

Owen Pikkert

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Philosophy University of Toronto

© Copyright by Owen Pikkert 2018

Abstract

Leibniz and the Principle of Sufficient Reason

Owen Pikkert

Doctor of Philosophy

Department of Philosophy

University of Toronto

2018

Leibniz’s principle of sufficient reason (PSR) is the claim that everything has an explanation.

It rules out brute facts, inexplicable primitives, and purely random events. On the usual view,

Leibniz grounds the PSR in purely descriptive truths. On my view, Leibniz grounds the PSR in this being the best of all possible worlds. God only creates the best, and a world in which the PSR is true is better than a world in which it is false. For the PSR ensures that the world has an explanatory structure, the investigation of which facilitates human happiness.

This way of grounding the PSR faces at least two problems. The first problem is that it presupposes that the PSR is a contingent principle, even though most commentators take it to be necessary. But I argue that Leibniz is indeed committed to the contingency of the PSR.

I demonstrate this by showing how, for Leibniz, PSR-violating entities such as vacua, atoms, and indiscernible bodies are possible but not actual. I also argue that the contingency of the

ii PSR does not conflict with Leibniz’s other modal commitments. In particular, it does not conflict with the modal status of his principle of the identity of indiscernibles, nor with the modal status of his theory of truth.

The second problem is that this way of grounding the PSR seems to be circular. For the PSR cannot be partially grounded in God’s choice of the best if God’s choice of the best is itself grounded in the PSR. I argue that Leibniz avoids this problem by grounding God’s choice of the best not in the PSR, but in God’s aim to maintain his own happiness. A suboptimal world would compromise God’s happiness, so he only creates the best. This constitutes a novel interpretation of Leibniz’s view that God has created the best of all possible worlds.

iii Acknowledgments

I am most grateful to Marleen Rozemond, an excellent and dedicated supervisor. I am also grateful to the other members of my supervisory committee: Donald Ainslie, Karolina

Hübner, William Seager, and, as external readers, Deborah Black and Martin Lin. Further thanks are due to the following persons for commenting on individual chapters: Christian

Barth, Sebastian Bender, Marc Bobro, Michael Della Rocca, Robert Mason, Jeff

McDonough, and Matthew Wurst. Michael Della Rocca deserves special mention for generously advising me while I spent a term at Yale during the early stages of this dissertation. Finally, I gratefully acknowledge funding from the Social Sciences and

Humanities Research Council of Canada, and from the Balzan Styles of Reasoning Project at the University of Toronto.

iv Table of contents

A note about citations vii

1. Introduction 1

1. Overview of the dissertation 3

2. What is Leibniz’s PSR? 5

2. The grounds of the PSR 19

1. Clarifying the question 19

2. The nature of necessary and sufficient conditions 21

3. The nature of truth 26

4. Harmony 29

5. God’s wisdom 32

3. The modal status of the PSR 40

1. Absolute possibility 41

2. The absolute possibility of indiscernibles 45

v 3. Indiscernibles and the PSR 50

4. Problems for indiscernibles as violations of the PSR 53

4. God’s choice of the best 68

1. The argument from the PSR 70

2. The argument from the will 73

3. Leibniz’s official argument 77

4. God’s happiness 80

5. The cosmological argument 93

1. Leibniz’s formulation of the cosmological argument 94

2. The mereological interpretation 99

3. The modal interpretation 104

4. The contrastive interpretation 111

Conclusion 119

References 122

vi A note about citations

Leibniz’s writings appear in many different volumes compiled by many different editors.

Matters are further complicated by the fact that the official Akademie edition of Leibniz’s works is far from complete. I have adopted the following conventions to keep things as straightforward as possible. Each time I mention or discuss one of Leibniz’s writings, I include both the title and the date either in the body of the text or in the corresponding footnote. Letters are dated to the nearest known day, whereas all other writings are dated to the nearest known year. Note that many titles are the creations of later editors. I have preserved these titles, however, for the purpose of comparing references and to stimulate the memory of the reader already used to such titles. In all cases I provide a citation both to the writing as it appears in its original language and as it appears in translation. The one exception is when a writing is cited from the Yale Leibniz Series (CP, DSR, LDB, LDV,

LoC). This is because the Yale editions provide both the original language and the translation on opposing pages. In such cases I tend only to cite the Yale edition.

vii 1. Introduction

Suppose someone comes across a house in a secluded area. There is much about this house that cries out for explanation: its strange location, the identity of its owner, and its current occupancy. But there is also much about this house that is perfectly normal: it has a front door, it is made out of bricks, and it has three bedrooms. Presumably, all of these facts have some explanation. And presumably, the explanation for these facts will appeal to other facts that themselves have an explanation. It will not do to say of any fact that it is absolutely brute, without any explanation whatsoever.

Anyone who feels the force of these intuitions feels the force of the principle of sufficient reason (PSR), the claim that everything has an explanation that is sufficient to explain why it is so and not otherwise. Indeed, for many the PSR seems obviously true – so obvious, in fact, that it is remarkable to them that anyone would question the PSR at all. Yet it is a controversial principle. Perhaps the most influential early challenge was advanced by

Hume, who, by allowing for the possibility of something to exist without a cause, thereby denied that the PSR is necessarily true.1 For if it is possible to have something without any cause, then there will be no explanation for why it occurs. More recently, a number of philosophers have denied that the PSR is true at all. They point to the fact that the PSR seems

1 Treatise 1.3.3.3. Della Rocca (2014: 7) reads this as “an argument against the PSR or, at least, against the necessity of the PSR.”

1 to imply some form of necessitarianism, and that it conflicts with certain interpretations of quantum mechanics.2

Possibly due to the influence of such objections, some philosophers now treat the

PSR as a purely pragmatic principle.3 They advocate that we should continue to assume the

PSR in our reasoning, though not because it must reflect the fundamental nature of reality. In fact, our investigations might uncover certain brute features of the world, and we should accept them as such. In their view, the PSR is a purely methodological principle: it can be violated in certain cases, and possibly abandoned altogether.

Other philosophers, however, see this retreat as premature. Some of them have questioned whether the objections from necessitarianism and from quantum mechanics are sound.4 And others have even attempted to defend versions of the PSR itself.5 In recent years exciting work has been done on both fronts. The time is therefore ripe to consider how the principle’s most famous historical proponent, Gottfried Wilhelm Leibniz (1646-1716), understood and employed his great principle. In this dissertation, that is what I shall attempt to do.

2 Necessitarianism: van Inwagen (1983: 202-204; 2015: 164-167), Bennett (1984: 115). Quantum mechanics: Grünbaum (2005: 151-152), van Inwagen (2015: 164). 3 Schlesinger (1995), Wiggins (1996). 4 Replies to the objection from necessitarianism: Lin (2012), Schnieder and Steinberg (2016), Levey (2016). Reply to the objection from quantum mechanics: Pruss (2006: 160-170). 5 Pruss (2006), Della Rocca (2010), Dasgupta (2016).

2 1. Overview of the dissertation

The dissertation is structured as follows. In the remainder of this introductory chapter I examine more closely what exactly Leibniz took the PSR to be. This is necessary to address more theoretical concerns regarding the PSR, concerns that are taken up in subsequent chapters.

In chapter 2 I examine the grounds of the PSR itself. In virtue of what does Leibniz think that the PSR is true? I consider and reject three answers: that the PSR is grounded in the nature of necessary and sufficient conditions; that it is grounded in the nature of truth; and that it is grounded in the world’s harmony. Instead, I suggest that the PSR is grounded in

God’s wisdom. A wise God always acts for the best, and so will create a world in which the

PSR is true. This is because a PSR world is one with an explanatory structure, the investigation of which increases the happiness of its creatures. Thus the PSR is really grounded in another principle, namely the principle of the best, as well as the way in which the truth of the PSR contributes to a world’s goodness.

In chapter 3 I consider whether the PSR is necessary or contingent. This is an important question for my account. For if the PSR is absolutely necessary in the same way that logical truths are absolutely necessary, then the truth of the PSR is overdetermined both by its value and by the fact that it cannot fail to obtain. I argue, however, that Leibniz is actually committed to the absolute possibility of violations of the PSR. These include indiscernible entities such as vacua, atoms, and indiscernible bodies generally. I also take up some concerns that this account raises. One concern is that indiscernibles are absolutely

3 impossible because Leibniz infers indiscernibility from his theory of complete concepts.

Another concern is that in one text Leibniz seems to describe the PSR as being metaphysically necessary. And yet another concern is that Leibniz’s inference of the PSR from his theory of truth commits him to the absolute necessity of the PSR. I argue that all of these concerns can be adequately addressed.

In chapter 4 I investigate why Leibniz thinks that God chooses the best possible world. While Leibniz is famous for holding such a view, the details are far from straightforward. It is sometimes thought that God’s choice of the best follows from the PSR.

Alternatively, it is sometimes thought that God’s choice of the best follows from his Socratic will. I argue that the former is false and that the latter only provides an incomplete account of

Leibniz’s view. On Leibniz’s official argument, God chooses the best because he is omnipotent, omniscient, and perfectly good. The key question, of course, is what Leibniz means by perfect goodness in this context. I argue that Leibniz does not have in mind God’s goodness to creatures, but rather God’s goodness to himself. For according to Leibniz, God seeks to maintain his own supreme happiness. Because the creation of a suboptimal world would conflict with God’s happiness, he only creates the best. I also address several texts that seem to pose a problem for such an account.

In chapter 5 I turn to what is probably Leibniz’s most famous application of the PSR.

This is to his cosmological argument for the existence of God. The argument is structurally quite simple: although each state of the world is explained by a prior state, the world itself lacks an explanation, which is only provided by God. However, it is difficult to determine what exactly Leibniz thinks God’s existence must explain. I consider and reject two answers: that God explains why a whole world exists over and above its parts, and that God explains

4 why the world is possible in the first place. With respect to the former, I argue that Leibniz does not even allow the world to constitute a mind-independent whole, must less a mind- independent whole that exists over and above its parts. With respect to the latter, I argue that the answer is subject to a dilemma. On my view, rather, God explains why this world exists rather than some other possible world. There are many infinite series that are merely possible, so we need God to explain why our particular series is the actual one. I argue that this works well as an interpretation both of Leibniz’s canonical formulations of the argument, and of some non-canonical formulations as well.

2. What is Leibniz’s PSR?

Before addressing these issues, however, we need to gain a better grasp of what Leibniz meant by the PSR. This can be accomplished either by examining Leibniz’s written formulations of the principle, or by examining how he used it. I shall adopt both approaches here.

2.1. Leibniz’s formulations of the PSR. It is important to note that Leibniz was hardly the first philosopher to adopt some sort of explanatory principle. As with so much in philosophy, antecedents can be found in Plato. In his opening speech of the Timaeus, the title character distinguishes between that which always is and that which comes to be. The former is unchanging and grasped by the understanding, whereas the latter is changing and grasped by

5 opinion. Timaeus then puts forward the following claim: “everything that comes to be must of necessity come to be by the agency of some cause, for it is impossible for anything to come to be without a cause.”6 Timaeus goes on to argue that the universe has come to be, for it is perceptible and therefore grasped by opinion. So, by the claim just advanced, the universe must have a cause. Timaeus concludes that this cause must be a divine craftsman, who created the most beautiful universe according to an eternal model. The model itself, however, has no cause.

Descartes advances a different explanatory principle. Unlike Plato, Descartes does not restrict his principle to that which comes to be. Instead, his principle ranges over everything that exists. As Descartes puts it in his First Set of Replies, “the light of nature does establish that if anything exists we may always ask why it exists; that is, we may inquire into its efficient cause, or, if it does not have one, we may demand why it does not need one.”7 The expansion of the explanatory demand to everything that exists is significant because it allows Descartes to argue that anything that objectively exists must also have an explanation. Thus Descartes argues in his Third Meditation that our objectively existing idea of God must have an explanation, which can only come from God himself.8 The expansion is also significant because it allows Descartes to argue that anything that eternally exists must have an explanation as well. Thus Descartes argues in his Fifth Meditation that God’s existence is explained by his own nature.9 This is in keeping with the qualification that

6 Timaeus 28a, Cooper 1234. 7 AT VII 108/CSM II 78. 8 AT VII 40-45/CSM II 28-31. 9 AT VII 65/CSM II 45.

6 Descartes puts on his explanatory principle: in at least one sense God lacks an efficient cause of his existence, but this does not mean that God’s existence is a brute fact.10

Spinoza advances an even stronger explanatory principle. According to Spinoza, not only must everything that exists have an explanation, but everything that does not exist must have an explanation for why it does not exist. As he writes in 1p11dem of his Ethics, “For each thing there must be assigned a cause, or reason, as much for its existence as for its nonexistence.”11 Spinoza immediately puts this claim to good work in 1p11dem by showing that God necessarily exists. For suppose that God does not exist. What could explain this?

According to Spinoza, if the explanation appeals to a substance of the same nature as God, then this is tantamount to conceding that God exists. If it appeals to a substance of a different nature than God, then this substance could not causally interact with God, and so could not prevent God from existing. But if the explanation appeals to God’s own nature, then God would have a contradictory nature, contrary to God’s perfection. Since these are the only options, Spinoza infers that God necessarily exists.

Leibniz would have been familiar with Descartes’ and Spinoza’s explanatory principles, though it is unclear whether he was familiar with Plato’s. Here are ten of

Leibniz’s own formulations of the PSR [principium rationis sufficientis, principe de la raison suffisante], drawn from both public and private writings, from all periods of his life:

10 I am using “efficient cause” in what Descartes calls the “literal and strict meaning” of the term (AT VII 109/CSM II 79). As Descartes observes, when we consider God’s power “in a sense he [God] stands in the same relation to himself as an efficient cause does to its effect” (AT VII 111/CSM II 80). How exactly Descartes understands these different senses of efficient causation will not be pursued here. 11 Geb II 52/Curley I 417.

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For it is necessary to refer everything to some reason, and we cannot stop until we have arrived at a first cause – or it must be admitted that something can exist without a sufficient reason for its existence, and this admission destroys the demonstration of God and of many philosophical theorems.12

The first principle of reasoning is this: nothing exists or comes about unless a reason can be given, at least by an omniscient being, why it exists rather than doesn’t, or why it is this way rather than otherwise. In a word, a reason can be given for everything.13

[N]othing at all happens without some reason, i.e. there is no proposition, except identical ones, in which the connexion between the subject and predicate cannot be displayed distinctly.14

[N]othing exists without a reason, or that every truth has its a priori proof, deduced from the concept of terms.15

[T]he Principle of Providing a Reason, which is that every true proposition which is not known through itself receives an a priori proof, i.e. that a reason can be provided for every truth, or as is commonly said, that nothing happens without a cause.16

[T]he received axiom that nothing is without reason, or there is no effect without a cause …17

12 Letter to Wedderkopf (May 1671), A.6.2.186/L 146. 13 Conversation with Steno (7 December 1677), CP 122-123. 14 An Introduction to a Secret Encyclopedia (1683-5?), A.6.4.529/MP 7-8. 15 Letter to Arnauld (4/14 July 1686), G II 62/M 71. 16 A Specimen of Discoveries (c. 1686?), A.6.4.1616/LoC 303-304. 17 Primary Truths (c. 1689), A.6.4.1645/AG 31, emphases removed.

8

[T]he other principle is that of the determinant reason: it states that nothing ever comes to pass without there being a cause or at least a reason determining it, that is, something to give an a priori reason why it is existent rather than non-existent, and in this wise rather than in any other.18

The fundamental principle of reasoning is that there is nothing without a reason; or, to explain the matter more distinctly, that there is no truth for which a reason does not subsist. The reason for a truth consists in the connexion of the predicate with the subject, that is, that the predicate is in the subject.19

And that [principle] 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, although most of the time these reasons cannot be known to us.20

[T]he principle of the need for a sufficient reason for anything to exist, for any event to happen, for any truth to take place.21

There are a number of things to note about how Leibniz formulates the PSR. The first concerns its scope. In some of these formulations, Leibniz restricts the PSR to certain types of entities. These include propositions [propositio], truths [verité, veritatis], facts [fait], assertions [enontiation], and events [événement].22 In other formulations he gives the principle broader scope, saying simply that everything has a reason, or that nothing is

18 Theodicy (1710), G VI 127/T §44. 19 Metaphysical Consequences of the Principle of Reason (c. 1712), C 11/MP 172. 20 Monadology (1714), G VI 612/AG 217. 21 Fifth Letter to Clarke (18 August 1716), G VII 419/LC L5.125. 22 In quoting from the original I have kept the same number and case.

9 without a reason. The scope of the explanans is broad as well. Leibniz does not in fact specify that only certain types of explanations are permitted, so long as those explanations are sufficient to explain the explanandum. He does not, for instance, say that only some of

Aristotle’s causes are permitted whereas others are not. Consider the case of Caesar crossing the Rubicon. Caesar’s crossing can be explained formally: it is part of Caesar’s essence to cross the Rubicon, so if he did not cross then he would not be Caesar. Caesar’s crossing can be explained finally: Caesar thought it best to cross the Rubicon, so he did. And Caesar’s crossing can be explained efficiently: the series of past states plus the laws of nature determine Caesar to cross.23

In addition to questions of scope, there are some other features of Leibniz’s PSR that are worth noting. One is that he sometimes describes it as a “principle of reasoning”.24 This might suggest that Leibniz sees the PSR as a law of thought, one that either describes how we should reason, or how we do in fact reason. Leibniz certainly thinks that the former is true. As for the latter, Leibniz suggests that it is often but not always true. As he writes in his

Fifth Letter to Clarke (18 August 1716), “Has not everybody made use of this principle [the

PSR] 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 …”25 But while the

PSR is indeed a law of thought, it is also a claim about the world itself. Even if no one assumed that everything that exists has a sufficient reason, everything that exists has a

23 I omit an example from material causation, as this depends on the degree to which Leibniz is an idealist, an issue that is well beyond the scope of this dissertation. 24 Conversation with Steno (7 December 1677), CP 122-123; Metaphysical Consequences of the Principle of Reason (c. 1712), C 11/MP 172. 25 G VII 419-420/LC L5.127.

10 sufficient reason nonetheless. This comes through in various non-epistemic formulations of the principle: “nothing is without reason, or there is no effect without a cause” and “the need for a sufficient reason for anything to exist, for any event to happen, for any truth to take place.”26

Leibniz also seems to conflate causes with reasons. In the formulation from the

Theodicy he is a bit more careful: “nothing ever comes to pass without there being a cause or at least a reason determining it”.27 Overall, though, the impression is that Leibniz does not sharply distinguish between them. But in The Elements of True Piety (1677-8?) he does draw a sharp distinction:

[T]here is nothing without a reason [ratione], but that does not mean that there is nothing without a cause [causa]. For a cause is the reason for a thing outside of the thing, or its reason of production, but it is possible that the reason for a thing is inside the thing itself. And this is the case in all those things which are necessary, like the truths of mathematics which contain their reason in themselves; likewise God, who alone is the actual reason for the existence of actual things.28

Leibniz treats causes as a subset of reasons. A reason is any type of explanation, and everything has a reason. These include things which contain their explanations in their own natures, such as the truths of mathematics and the truth that God exists. They also include things the explanations for which are outside of them; in this case the reasons in question are

26 Primary Truths (c. 1689), A.6.4.1645/AG 31; Fifth Letter to Clarke (18 August 1716), G VII 419/LC L5.125. 27 G VI 127/T §44. 28 A.6.4.1360/SLT 192.

11 causes. Leibniz is most likely thinking of efficient causes, though they could be final causes too, in the way that Aristotle’s unmoved mover imparts motion by being an object of desire.

At any rate, while everything has a reason, not everything has a cause.

The final thing to note about Leibniz’s formulations of the PSR is that he sometimes puts it in terms of giving an “a priori proof”. This is especially evident in the formulations after 1679 or so, although, as the formulations from the Monadology and the Fifth Letter to

Clarke attest, he did not always continue to put the PSR in such terms. By an “a priori proof”

Leibniz means a proof which analyzes the concepts of the subject or predicate (or both) of the truth to be proved; this analysis will continue until an identity statement is reached (in the case of necessary truths) or at least converged upon (in the case of contingent truths, given that their analysis is infinite).29 Such a method of a priori proof is thereby a way of identifying the sufficient reason for the truth in question. As Leibniz’s view that each truth has an a priori proof has a direct bearing on the grounds of the PSR, it will be further discussed in the next chapter.

2.2. Leibniz’s uses of the PSR. As with so much in philosophy, the PSR is most easily grasped when employed in the context of specific examples. In what follows I will provide four examples of arguments that Leibniz gives that rely on the PSR. Throughout the course of this dissertation we shall encounter a variety of other such arguments as well. These include arguments against vacua, atoms, and indiscernible bodies (chapter 3), as well as arguments for the existence of God (chapter 5).

29 See On Contingency (1686?), Grua 303-304/AG 28-29; Primary Truths (1689), A.6.4.1645/AG 31.

12 One way in which Leibniz employs the PSR is to conclude that certain things do not exist because they fail to explain what they are supposed to explain. The clearest example is that of gravity. Proponents of gravitational force, most notably Newton, had introduced gravity to explain how bodies attract other bodies. But as Leibniz argues in his Metaphysical

Consequences of the Principle of Reason (c. 1712), gravity in fact violates the PSR:

This principle [the PSR] disposes of all inexplicable occult qualities, and other similar figments. For as often as writers introduce some primitive occult quality they impinge on this principle. For example, suppose that someone thinks that there is in matter some attractive force which is primitive, and therefore not derivable from the intelligible notions of body (namely, magnitude, shape and motion). And suppose he wants it to happen that by this attractive force bodies tend towards some other body without being pushed, as some conceive gravity – namely, as if heavy things were attracted by the body of the earth, or as if they were attracted to it by some sympathy, in such a way that the ulterior reason of this cannot be given from the nature of bodies, and the method of attraction cannot be explained. Such a person admits that there is no reason for the truth that a stone tends towards the earth.30

According to Leibniz, gravity violates the PSR in two distinct ways. One is that “the ulterior reason of this [gravitational force] cannot be given from the nature of bodies”. It is the nature of bodies to be extended (and in particular to have magnitude, shape, and at least the possibility of motion). Barring a miracle, all modifications of bodies must be explained in terms of extension. But Leibniz denies that gravity can be explained from extension alone.

Given that gravity is not supposed to be miraculous either, there is simply no explanation for how gravity can exist in the first place. Gravity also violates the PSR in that “the method of

30 C 11-12/MP 172.

13 attraction cannot be explained”. Even if there is an explanation for why gravity exists, there is still no explanation for how it works. How can the attractive force of one body act on another body that is not adjacent to it? Barring any such explanation, the PSR is violated on that count as well.

This argument against gravity makes no mention of God. Leibniz is quite fond, however, of arguing that certain states of affairs imply a violation of the PSR by God, so the states of affairs in question do not obtain. In §340 of his Theodicy (1710) Leibniz gives such an argument against mind-body occasionalism. This is the view that a particular bodily state provides God with the occasion to cause a particular mental state. In the specific version that

Leibniz considers, which he attributes to Bayle, it is the view that particular movements in one’s body provide God with the occasion to cause one’s soul to have ideas of particular secondary qualities. Leibniz thinks that the basic problem with such a position is that, given the occasion provided by a particular bodily movement, God has no sufficient reason to cause the soul to have the idea of one secondary quality (or set of secondary qualities) rather than another. Leibniz elaborates as follows:

For he [Bayle] is persuaded, with the modern Cartesians, that the ideas of the perceptible qualities that God gives (according to them) to the soul, occasioned by movements of the body, have nothing representing these movements or resembling them. Accordingly it was a purely arbitrary act on God’s part to give us the ideas of heat, cold, light, and other qualities which we experience, rather than to give us quite different ideas occasioned in the same way. I have often wondered that people so talented should have been capable of relishing notions so unphilosophical and so contrary to the fundamental maxims of reason. For nothing gives clearer indication of the imperfections of a philosophy than the necessity experienced by the philosopher

14 to confess that something comes to pass, in accordance with his system, for which there is no reason.31

Leibniz here exploits the radical dissimilarity between the primary qualities of bodies and the ideas of secondary qualities in souls. Suppose, for instance, that when someone touches fire, this provides God with the occasion to cause that person’s soul to have an idea of heat. But why should this be so? Even if God’s action is in conformity with some general volition, there is nothing about the relation between primary qualities and ideas of secondary qualities that explains why God decreed this general volition. For instance, God could have decreed a general volition that each time someone touches fire, he or she has a secondary idea of coldness instead. It must have been a brute fact, then, that God decreed that he would act one way rather than another.

Leibniz also gives other arguments that reject certain states of affairs because they imply a violation of the PSR by God. In his correspondence with Clarke, for instance,

Leibniz gives a theological twist to an ancient line of argument. The ancient line of argument is to claim that all possible options are qualitatively indiscernible; there is therefore no sufficient reason why one option should obtain rather than any of the others, so none of the options obtain. Thus Anaximander argued that because all points of space are qualitatively indiscernible, there is no reason for the earth to move to one point of space rather than another, so it remains still.32 Likewise Parmenides argued that because all points of time are

31 G VI 316/T §340. 32 This is admittedly a rational reconstruction of Anaximander’s argument, which is quite condensed. Here is how Aristotle describes it: “There are some who say, like Anaximander among the ancients, that it [the earth] stays still because of its equilibrium. For it behooves that which is established at the centre, and is equally related to the extremes, not to be borne one whit more either up or down or to

15 qualitatively indiscernible, there is no reason for ‘What Is’ to come into existence at a particular time, so it has always existed.33

Leibniz’s twist is to take this style of argument and use it to demonstrate a violation of the PSR by God. He gives two such arguments in his correspondence with Clarke. In his

Third Letter (25 February 1716) Leibniz argues against Newtonian absolute space by suggesting that God would have no sufficient reason to locate bodies in one point of space rather than another:

Space is something absolutely uniform, and without the things placed in it, one point of space absolutely does not differ in any respect whatsoever from another point of space. Now from this it follows (supposing space to be something in itself, besides the order of bodies among themselves) that it is impossible there should be a reason why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner and not otherwise – why everything was not placed the quite contrary way, for instance, by changing east into west.34 the sides; and it is impossible for it to move simultaneously in opposite directions, so that it stays fixed by necessity” (KRS no. 123). It is unclear how the fact that the earth is at the centre contributes to this argument, for even if it were not it might still be surrounded by qualitatively indiscernible points of space, in which case the argument might still go through. 33 Parmenides puts the point in typically Delphic fashion: “It never was nor will be, since it is now, all together, one, continuous. For what birth will you seek for it? How and whence did it grow? I shall not allow you to say nor to think from not being: for it is not to be said nor thought that it is not; and what need would have driven it later rather than earlier, beginning from nothing, to grow? Thus it must either be completely or not at all” (KRS no. 296). Note that there are several other claims and arguments in this passage against ‘What Is’ coming into existence at a particular time. One is that the means by which ‘What Is’ would come into being are obscure. And another is that we cannot even speak or think about what is not. 34 G VII 364/LC L3.5.

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This is a surprisingly tricky argument. Two points in particular are worth noting. First,

Leibniz’s argument does not rule out absolute space per se. It only rules out absolute space that contains bodies. In other words, God could create a completely empty absolute space.

Second, the problem is not simply that the points of absolute space are qualitatively indiscernible. Rather, the problem is that, being qualitatively indiscernible, the points of absolute space are such that God has no reason to locate bodies at one point rather than another. So Leibniz does not rule out absolute space because the qualitative indiscernibility of its points violates the principle of the identity of indiscernibles – even though that is in fact the case. Rather, Leibniz rules out absolute space because the qualitative indiscernibility of its points explains why God, in locating bodies in it, would violate the PSR.

In his Fourth Letter (2 June 1716), Leibniz gives a structurally similar argument against indiscernible bodies. The arguments are so similar, in fact, that there has been a tendency to conflate them.35 Leibniz’s argument in the Fourth Letter is as follows:

It is an indifferent thing to place three bodies, equal and perfectly alike, in any order whatsoever, and consequently they will never be placed in any order by him who does nothing without wisdom. But then, he being the author of things, no such things will be produced by him at all, and consequently there are no such things in nature.36

35 Parkinson (1965: 133) and Vinci (1974: 98-99) seem to conflate the arguments. Chernoff (1981: 128, 131) correctly distinguishes between them. 36 G VII 372/LC L4.3.

17 This argument differs from the preceding one in both its premises and in its conclusion. In his Third Letter Leibniz supposes for reductio that absolute space exists. He then goes on to conclude that it does not, a conclusion that is compatible with there being qualitatively indiscernible bodies. In his Fourth Letter, by contrast, Leibniz not make any assumption about the nature of space. In fact the argument goes through regardless of whether space is absolute or relational. He does, however, suppose for reductio that there are indiscernible bodies. The argument then proceeds by claiming that God lacks a sufficient reason to locate indiscernible bodies relative to each other regardless of whether space is absolute. It is rather like a curator trying to figure out which way to arrange three indiscernible pictures: the problem is not that the wall is blank (though that may be true), but that, being indiscernible, there is no reason why, say, one picture should be hung to the left of the others as opposed to the right. If the curator is governed by the PSR, then, according to Leibniz at least, the curator will not hang any indiscernible pictures at all.

We now have some sense of what Leibniz took the PSR to be. We are thus in a position to examine some more theoretical questions concerning this principle. These include questions concerning its grounds, modal status, and relation to God. In the next chapter we shall consider the first of these questions, namely the grounds of the PSR itself.

18 2. The grounds of the PSR

Leibniz evidently believed that the PSR is true. But why did he think so? More precisely, what are the grounds of Leibniz’s PSR? Commentators have offered a variety of answers to this question. As we shall see, these include alleged truths about the nature of necessary and sufficient conditions, the nature of truth itself, and the fact that our world is harmonious. In this chapter I will argue, however, that Leibniz does not ground the PSR in any of these ways. Instead, Leibniz grounds the PSR in God’s wisdom. A wise God will always act for the best, and so will create a world in which the PSR is true. This means that the PSR is in fact partially grounded in another principle, namely the principle of the best. Leibniz’s grounds for the PSR are thus not purely descriptive, but value-based. The PSR is true because it is good for it to be true.

1. Clarifying the question

What do I mean by identifying the grounds of Leibniz’s PSR? By “grounds” I mean that in virtue of which the PSR is true. The grounds of the PSR will be those truths that are explanatorily prior to the PSR, and are such that the PSR is true because of them. I will take the grounding relation to hold between truths, and to be characterized as a strict partial

19 order.37 That is, I will take the grounding relation to be irreflexive (no truth can ground itself), asymmetric (two truths cannot ground each other), and transitive (if one truth grounds a second truth and that second truth grounds a third, then the first truth grounds the third truth as well).

Notice that by “grounds” I do not mean that which justifies belief in the PSR.

Leibniz’s reason for why we are justified in believing in the PSR is in any case easy to identify. For in his Fifth Letter to Clarke (18 August 1716) Leibniz writes:

I have often defied people to advance an instance against that great principle [the PSR], 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 number of instances in which 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 …38

Leibniz’s argument is an inductive one. There are no uncontroversial counterexamples to the

PSR, and there are innumerable examples in its favour. Thus we are justified in believing that the PSR is true. But this does not tell us why the PSR is true, only that we are justified in believing it.

Before proceeding to identify these grounds, a word about chronology is in order. As with the scholarship of Plato, it has become commonplace in Leibniz scholarship to distinguish between Leibniz’s early period (1646-79), middle period (1679-95), and late

37 For opposing views on whether grounding is a strict partial order, see Raven (2013) and Rodriguez- Pereyra (2015). 38 G VII 420/LC L5.129.

20 period (1695-1716).39 Of the three rival proposals that I will consider, one appeals to a text from Leibniz’s early period, while the others appeal to texts from Leibniz’s middle and late periods. My own proposal appeals to an undated text and a text from Leibniz's late period to show that the PSR is grounded in God’s wisdom. However, to show how this inference goes through, I appeal to texts from Leibniz’s early and middle periods as well. It would be helpful if I could also appeal to texts from Leibniz’s late period to prove this latter point. At the same time, I know of no reason to think that Leibniz abandoned the views of these earlier texts.

2. The nature of necessary and sufficient conditions

In 1671 or 1672, while still a young man, Leibniz wrote the following proof of the PSR. It is found in some notes that he entitled Demonstration of Primary Propositions:

Proposition: Nothing exists without a reason or whatever exists has a sufficient reason.

39 I am dating the middle period as beginning with the 1679 series of logic papers and ending with the publication of A New System of Nature. Garber, to whose classic article the division of a middle period is generally attributed, does not give precise dates; he simply focusses on Leibniz’s writings in “the mid-1680’s and ‘90’s” (1985: 28). In his later book, he variously describes Leibniz’s middle period as “from the early 1680s to 1700 or so” and “from roughly the late 1670s to the mid- or late 1690s” (2009: v, xix).

21 Definition 1: A sufficient reason is something which having been posited, the thing exists.

Definition 2: A requisite is something which if not posited the thing does not exist.

Demonstration:

Whatever exists has all its requisites. For, if one is not posited, the thing does not exist per Definition 2. All requisites having been posited, the thing exists. For, if the thing does not exist, something will be lacking in virtue of which it does not exist, i.e., a requisite. Therefore, all the requisites constitute a sufficient reason per Definition 1. Therefore, whatever exists has a sufficient reason. Q. E. D.40

As others have noted, this proof is clearly influenced by Hobbes.41 In fact, Leibniz had been reading Hobbes’ De Corpore just a year or so earlier.42 There Hobbes uses the definitions of a “requisite” and a “sufficient reason” (which he calls an “entire cause [causa integra]”) to construct a proof of necessitarianism.43 Leibniz presumably read the proof, liked the definitions, and thought that he could use them to prove the PSR.

40 A.6.2.483/Sleigh (1983: 203-204). 41 Piro (2008: 466), Arthur (2014: 91, 175). I am grateful to Christian Barth for first pointing out Hobbes’ influence on the proof to me. 42 Goldenbaum (2008: 56) reports finding Leibniz’s marginalia on a copy of De Corpore; the marginalia are from 1669 or 1670. Beeley (2011: 34) claims that Leibniz was acquainted with De Corpore while still a student in Leipzig during the early 1660’s. 43 II.9.5/Molesworth I.121-123.

22 Now, as others have also noted, Leibniz’s proof is a bad one.44 The problem lies in the second premise: “All requisites having been posited, the thing exists.” While Leibniz does give a supporting premise in its favour, on closer inspection that premise is nothing but the contrapositive of the premise to be proved. Furthermore, the premise in question seems to presuppose the truth of the proof’s conclusion, namely the PSR. For if the PSR is false, then it would be possible for all the requisites (which are just necessary conditions) to be posited, yet for the thing not to exist. While the nonexistence of the thing would be a brute fact, that would not be a strike against it.

Despite such difficulties, Leibniz continued to advance informal versions of the proof throughout his youth:

Whatever exists, at any rate, will have all the requisites for existing; however, all the requisites for existing taken together at the same time are a sufficient reason for existing. Therefore, whatever exists has a sufficient reason for existing.45

There is nothing without a cause, since there is nothing without all the requisites for existing.46

For existence, it is necessary that the aggregate of all requisites is present. A requisite is that without which a thing cannot exist. The aggregate of all requisites is the full cause of a thing. There is nothing without a reason; for there is nothing without an aggregate of all requisites.47

44 Sleigh (1983: 204), Frankel (1986: 334), Adams (1994: 68), Blumenfeld (1995: 374), Piro (2008: 466), Look (2011: 204), and Rodriguez-Pereyra (2013: 10). 45 Philosopher’s Confession (1672-3), CP 33. 46 A Chain of Wonderful Demonstrations about the Universe (1676), DSR 107. 47 On Existence (1676), DSR 111-113.

23

Thus the youthful Leibniz clearly liked the proof. But the question is whether the more mature Leibniz came to see the problems with the proof, and hence to abandon it. Some notable interpreters of Leibniz, namely Sleigh and Adams, think that Leibniz continued to endorse the proof his whole life.48 They point to a sentence from Leibniz’s Fifth Letter to

Clarke (18 August 1716), written during his last year: “For the nature of things requires that every event should have beforehand its proper conditions, requirements, and dispositions, the existence of which makes the sufficient reason of such an event.”49 This sentence, according to Sleigh and Adams, shows that Leibniz did not abandon his early proof. After all, Leibniz does write it in response to Clarke’s request for a proof of the PSR. It therefore seems as if

Leibniz recalled his youthful proof, and produced this sentence in order to satisfy Clarke’s demand.

Now it is not immediately obvious whether Leibniz even intended to summarize his old proof of the PSR with this single sentence. But even if he did, there are reasons to doubt that Leibniz continued to endorse the proof himself. First, it would be remarkable if, after more than forty years, someone with Leibniz’s intelligence could have failed to see the basic problems that beset this simple proof – problems that are immediately obvious to almost all who comment upon it. Moreover, Leibniz elsewhere mentions the proof in a list of claims that he had come to abandon. This list is found in On Freedom (c. 1689), written some ten years after his informal versions of the proof, but some thirty years before his Fifth Letter to

Clarke:

48 Sleigh (1983: 203), Adams (1994: 68, 117). 49 G VII 393/LC L5.18.

24

For my part, I used to consider [Ego cum considerarem] that nothing happens by chance or by accident, except with respect to certain particular substances; that fortune, as distinct from fate, is an empty word; and that nothing exists unless its individual requisites are given, and that from all these taken together it follows that the thing exists. So I was not far from the view of those who think that all things are absolutely necessary …50

Here Leibniz provides a list of claims that he believed in his youth: that certain substances are subject to chance, that fatalism is true, and that his youthful proof of the PSR is valid.

These claims are not entirely consistent. For it is difficult to see how certain substances can be subject to chance if fatalism is unrestrictedly true, and if there is a valid proof of the PSR.

Nevertheless, we know both from the tense employed and from his subsequent denial of chance and fatalism that these are claims that Leibniz used to believe. This gives us good reason to think that Leibniz had come to abandon his youthful proof of the PSR as well.

One might wonder, however, why Leibniz wrote this sentence to Clarke in this first place. One option is that he temporarily forgot his prior concerns with the proof. This could be because he had not considered the proof in a long time, because he was writing in haste, or because he was frustrated with Clarke by this stage in the correspondence (or all of these at once). Another, less charitable option is that Leibniz strongly desired to bring the correspondence with Clarke to a close, so he tried to pacify Clarke with views that he knew faced problems. Given that Leibniz does not state his intentions explicitly, it is difficult to determine which of these options is correct. Whatever his intentions, however, we have seen

50 A.6.4.1653/MP 106.

25 that there are good reasons to deny that the mature, reflective Leibniz continued to endorse the proof.

3. The nature of truth

Another alleged ground for Leibniz’s PSR is his theory of truth.51 As was mentioned in the previous chapter, this is the theory that every true proposition is such that it can be reduced to an identity statement (in the case of necessary truths), or at least to approach convergence upon an identity statement (in the case of contingent truths). The reduction in question proceeds by analyzing the concepts of the subject or predicate (or both), a process which

Leibniz describes as giving an “a priori proof”. The most well-known example of Leibniz’s inference from his theory of truth to the PSR is found in Primary Truths (1689):

The primary truths are those which assert the same thing of itself or deny the opposite of its opposite ... Moreover, all remaining truths are reduced to primary truths with the help of definitions, that is, through the resolution of notions; in this consists a priori proof, proof independent of experience ...

51 Parkinson (1965: 66; 1995: 207-208; 1999: 203), Blumenfeld (1995: 373-374), and Look (2011: 205). Not everyone sees Leibniz’s theory of truth as grounding the PSR: Wiggins (1987: 264) sees the PSR as motivating Leibniz’s theory of truth, whereas Mondadori (1973: 90) sees the PSR as both motivating Leibniz’s theory of truth and being provable from it.

26 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, as Aristotle also observed ... Many things of great importance follow from these considerations, considerations insufficiently attended to because of their obviousness. For the received axiom that nothing is without reason, or there is no effect without a cause, directly follows from these considerations; otherwise there would be a truth which could not be proved a priori, that is, a truth which could not be resolved into identities, contrary to the nature of truth, which is always an explicit or implicit identity.52

Leibniz begins this text by stating his theory of truth. He then makes two inferences. The first is to Aristotle’s theory of truth, which is that for all truths the predicate is “in [inest]” the subject.53 The second inference is from Leibniz’s theory of truth to the PSR. For suppose that the PSR is false. Then there is at least one brute fact. But no a priori proof can be given of a brute fact. This is presumably because such a proof would identify the sufficient reason for the fact, when by hypothesis there is none. By Leibniz’s theory of truth, all truths have a priori proofs. So the PSR is true.

Thus Leibniz clearly takes his theory of truth to imply the PSR. But does this mean that Leibniz’s theory of truth grounds the PSR? I think that it does not. To see why, we will have to balance what Leibniz writes in Primary Truths with what he writes in other texts. For

52 A.6.4.1644-1645/AG 30-31. 53 Aristotle’s theory of truth is found in Categories 1a23-5, in Barnes I 3. There is some discussion over whether Leibniz’s interpretation of Aristotle is accurate; for opposing viewpoints, see Beck (1969: 208) and Brody (1977: 44-45).

27 elsewhere Leibniz proceeds in the opposite direction: he starts with the PSR, and then seems to infer his theory of truth:

[N]othing exists without a reason, or [ou] that every truth has its a priori proof, deduced from the concept of terms.54

[T]he Principle of Providing a Reason, which is that [quod scilicet] every true proposition which is not known through itself receives an a priori proof, i.e. [sive] that a reason can be provided for every truth, or [vel] as is commonly said, that nothing happens without a cause.55

The fundamental principle of reasoning is that there is nothing without a reason; or, to explain the matter more distinctly [vel ut rem distinctius explicemus], that there is no truth for which a reason does not subsist. The reason for a truth consists in the connexion of the predicate with the subject, that is, that the predicate is in the subject.56

In these texts Leibniz seems to treat his theory of truth as a version of the PSR. This is a point that has not been lost on Leibniz’s commentators.57 In fact Leibniz seems to think of the PSR and his theory of truth as being the same claim, though expressed in different words.

To say that everything has a reason is just to say that every truth has an a priori proof, which

54 Letter to Arnauld (4/14 July 1686), G II 62/M 71. 55 A Specimen of Discoveries (c. 1686?), LoC 303-304. 56 Metaphysical Consequences of the Principle of Reason (c. 1712), C 11/MP 172, emphasis in original. 57 Russell (1900: 32-33), Couturat (1901: 214-216; 1902: 1-2), Rescher (1952: 27; 1967: 25), Broad (1975: 11-12), Hanfling (1981: 67-68), Sleigh (1982: 234; 1983: 200-201), Piro (2008: 463), and Rodriguez-Pereyra (2013: 4).

28 can in theory be accomplished, if only by an infinite mind, by analyzing the concepts of the subject and of the predicate until an identity statement is reached or at least converged upon.

But if Leibniz takes the PSR and his theory of truth to ultimately come to the same thing, then it cannot be the case that the one is grounded in the other. What we need is some independent, logically prior truth that explains why the PSR is true. And this is not provided by Leibniz’s theory of truth itself.

4. Harmony

The preceding two proposals appeal to features that are generally thought to obtain in all possible worlds. Yet there is another proposal that appeals to a feature that obtains in the actual world, but not in all possible worlds. This is the fact that the actual world is, according to Leibniz, harmonious. The world’s harmony might be thought to ground the PSR. For surely a world containing brute facts cannot be a harmonious world. So what grounds the truth of the PSR is the fact that the actual world is a harmonious one.58

In response, it must be noted that Leibniz never actually infers the PSR from harmony. And, when we consider what he means by “harmony”, we can see why he does not. Let us distinguish between two types of Leibnizian harmony, namely proportional

58 I am grateful to Michael Della Rocca for suggesting this way of grounding Leibniz's PSR to me. Jorati (2016: 194-198) identifies the PSR as the principle that governs harmony, though she does not claim that the PSR is grounded in harmony.

29 harmony and perceptual harmony. Leibniz likes to characterize the former rather cryptically in terms of unity in variety:

Harmony is when many things are reduced to a kind of unity. For where there is no variety, there is no harmony, and the musician who always plays: you know the rest. In turn, where variety is without order, without proportion, without concord, there is no harmony.59

Order, proportions, harmony delight us; painting and music are samples of these.60

Perfection is the harmony of things, or the state where everything is worthy of being observed, that is, the state of agreement or identity in variety; you can even say it is the degree of contemplatibility. Indeed, order, regularity, and harmony come to the same thing.61

In these texts Leibniz thinks of harmony in terms of perfection and regularity. Such harmony seems to obtain when the right proportions are observed. To use Leibniz’s examples of music and painting, a proportionally harmonious piece of music will be one in which there are many notes of many kinds, all of them exhibiting the proper proportions. Likewise, a proportionally harmonious painting will be one in which there are many brushstrokes of many colours, balanced in a proportional way.

Now nothing about the way that Leibniz characterizes proportional harmony suggests that it implies the PSR. Consider again the examples of music and painting. Suppose that an

59 The Elements of True Piety (1677-8), A.6.4.1359/SLT 191, emphasis in original. 60 Theodicy (1710), G VI 27/T 51. 61 Letter to Wolff (18 May 1715), GLW 170-172/AG 233-234.

30 orchestra plays a proportionally harmonious piece of music, but as soon as they finish five further notes are heard. There is no explanation for why these notes are heard; they just popped into existence from nothing. Does this mean that the proportional harmony of the piece is thereby compromised? Not necessarily, assuming that the added notes contribute to the quantitative and qualitative variety of the piece, without detracting from its proper proportions. Or consider a painter who has just completed a proportionally harmonious painting. Right after she applies the last brushstroke, five other brushstrokes appear for no reason. This does not imply that the proportional harmony of the painting must be compromised. If anything, it could have been improved.

The case is similar when it comes to perceptual harmony. This is the type of harmony that obtains when different monads have the same perceptual content, albeit from different points of view. For instance, in §59 of the Monadology (1714) Leibniz writes of the

“universal harmony, which results in every substance expressing exactly all the others through the relations it has to them”.62 In §78 he goes on to describe the “harmony pre- established between all substances” as that of all substances being “representations of a single universe”.63

Here we can make a similar point as before: just because a collection of monads is perceptually harmonious does not imply that all of the monads’ states have sufficient reasons. For suppose that one monad has a perceptual state for which there is no sufficient reason. This does not mean that the perceptual harmony of the collection is compromised.

For the monad with the brute perceptual state may simply have gotten lucky: its brute

62 G VI 616/AG 220. 63 G VI 620/AG 223.

31 perceptual state may still be of the same universe, expressed by all the other monads, though possibly from a different point of view. Thus the perceptual harmony of the collection is preserved. Neither the world's proportional nor perceptual harmony, then, is sufficient to ground the PSR.

5. God’s wisdom

I have so far examined three alleged grounds of Leibniz’s PSR. All have been found wanting. But Leibniz does provide grounds for the PSR, though these are quite different from those already considered. These grounds have to do with God’s wisdom. If God is perfectly wise, then God will always act for the best. If God always acts for the best, then the PSR is true. Given that God is perfectly wise, the PSR is true. We find Leibniz advancing such grounds in two texts, one from an undated text and the other from his Fifth Letter to Clarke

(18 August 1716). As both texts make the same point, I quote them together:

I cannot always explain myself fully, but I always try to speak accurately. I begin as a philosopher, but I end as a theologian. One of my great principles is that nothing happens without reason. That is a principle of philosophy. Nevertheless, at bottom it is nothing but an affirmation of the divine wisdom, though I do not speak of this at first.64

64 LH IV.I.39/Curley (1972: 96). I am grateful to Donald Rutherford for pointing this text out to me.

32 And God's perfection requires that all his actions should be agreeable to his wisdom and that it may not be said of him that he has acted without reason, or even preferred a weaker reason before a stronger.65

It may be objected, however, that these texts only support the first inference (from God’s wisdom to his acting for the best), not the second inference (from God’s acting for the best to the PSR). God's wisdom, when conjoined with his omnipotence and goodness, may entail that God always acts for the best. But that does not seem to entail that God must create a world in which the PSR is true. In fact a world with a few brute facts might be positively desirable. It might ensure, for instance, a certain level of epistemic humility among its inhabitants. So perhaps Leibniz is only offering a proof of the principle of the best (PB), the claim that God always acts for the best, not of the PSR itself.

I do not think that this objection is sound. In the undated text Leibniz describes the principle in question as "that nothing happens without a reason". That sounds a lot like the

PSR. Leibniz also describes it as his "great principle", a label that he tends only to apply to the PSR and to the principle of contradiction.66 And while Leibniz does not explicitly mention the PSR in the selection from the Fifth Letter to Clarke, the immediate context makes it clear that he is trying to prove the PSR. The selection is actually part of Leibniz's response to Clarke's demand for a proof. In the paragraph immediately preceding the selection Leibniz writes, "it is very strange to charge me with advancing my principle of the need for a sufficient reason without any proof drawn either from the nature of things or from the divine perfections." In the next sentence he gives his proof from the nature of things,

65 G VII 393/LC L5.19. 66 See §31-32 of the Monadology (1714), G VI 612/AG 217.

33 which is just that possible allusion to his old argument from the nature of necessary and sufficient conditions. Then Leibniz gives his proof from the divine perfections, which is the selection at hand. And he immediately goes on to write, "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". Such talk strongly suggests that Leibniz intended to prove the PSR, not simply the PB.

But if this was Leibniz's intention, then it seems as if we have a good philosopher making a bad argument. For even if we accept the inference from God's wisdom to the PB, how is the inference from the PB to the PSR supposed to follow? My suggestion is that we look to Leibniz's other writings, in order to see if he defends another premise that would allow the inference to go through. This is not an arbitrary move: as is well known, Leibniz often does not reveal all of his own views at once, especially in his correspondence with

Clarke. And it is a move which in the present case turns out to be rewarding. For in some of his other writings we find Leibniz endorsing the following premise: a world with an explanatory structure facilitates our happiness, and is in that respect superior to a world that lacks such a structure. Let us examine a couple of relevant texts, to see that this is so.

The first text is a rather scattershot writing from Of an Organum or Ars Magna of

Thinking (c. 1679):

The supreme happiness of man consists in the greatest possible increase of his perfection. … Just as disease consists in an impaired functioning of the faculties, so perfection consists in an increase of one’s power or faculties. The most powerful of human faculties is the power of thinking.

34 The power of thinking can be assisted either by remedies of the body or by remedies of the mind. … It is the greatest remedy for the mind if a few thoughts can be found from which infinite others arise in order, just as from the assumption of a few numbers, from one to ten, all the other numbers can be derived in order. Whatever is thought by us is either conceived through itself, or involves the concept of another. Whatever is involved in the concept of another is again either conceived through itself or involves the concept of another; and so on. So it must either proceed to infinity, or all thoughts are resolved into those which are conceived through themselves.67

I believe that Leibniz's order of exposition is the opposite of the order of logical priority. Let us therefore start at the end of the text and work our way backwards. Towards the end

Leibniz claims that whatever we think about is either conceived through itself or through another. This comes close to one of Spinoza's axioms in the first part of his Ethics: "What cannot be conceived through another, must be conceived through itself."68 Indeed, given that the conceived-through relation seems to be an explanatory one, some commentators see this axiom as a version of the PSR, or at least motivated by it.69 That Leibniz should put the PSR in such Spinozistic terms is not entirely surprising, for he had visited Spinoza some three years prior.

Working our way backwards, we see Leibniz claiming that the mind's power can be

67 A.6.4.156-157/MP 1, emphases in original. 68 Geb II 46/Curley I 410. 69 Della Rocca (2008: 4-5), Lin (2013: 137). As we saw in the previous chapter, Spinoza also puts the PSR in more familiar terms in 1p11dem: “For each thing there must be assigned a cause, or reason, as much for its existence as for its nonexistence” (Geb II 52/Curley I 417).

35 increased through certain "remedies". The greatest of these, he says, is to identify those thoughts "from which infinite others arise in order". Seeing as Leibniz immediately goes on to put the point in terms of thoughts being conceived through each other, I take "arise

[exurgant]" to be equivalent to the conceived-through relation. So Leibniz is saying that the best way to improve the power of one's mind is by identifing those few thoughts through which many others are conceived, but which are themselves not conceived through many others. That is, one can improve one's mind by identifying those thoughts through which many other thoughts are explained.

Now Leibniz puts all this in terms of thoughts, not things. This might suggest that

Leibniz thinks that the conceived-through relation only applies to thoughts. Such a suggestion is, however, mistaken. For shortly afterwards Leibniz writes that God himself

[Deus ipse] may be conceived through himself.70 Here the conceived-through relation obtains of a thing, not a thought. And Leibniz does say that investigating the explanatory structure of thoughts contributes to one's happiness. This takes us to the first sentence of our selection from the Organum: "The supreme happiness of man consists in the greatest possible increase of his perfection." Investigating the explanatory structure of thoughts perfects the mind, and the perfection of the mind brings happiness.

The Organum is not as clear a text as we might like. It reads like a list, it focuses primarily on the explanatory structure among thoughts, and it uses some rather Spinozistic language. However, there is another text that states the benefits of investigating the world's explanatory structure much more clearly. This text is from the slightly later Introduction to the Elements of Natural Science (1678-84):

70 A.6.4.158/MP 2.

36

The greatest usefulness of theoretical natural science, which deals with the causes and purposes of things, is for the perfection of the mind and the worship of God. … By understanding the laws or the mechanisms of divine invention, we shall perfect ourselves far more than by merely following the constructions invented by men. For what greater master can we find than God, the author of the universe? And what more beautiful hymn can we sing to him than one in which the witness of things themselves expresses his praise? But the more one can give reasons for his love, the more one loves God. To find joy in the perfection of another – this is the essence of love. Thus the highest function of our mind is the knowledge or what is here the same thing, the love of the most perfect being, and it is from this that the maximum or the most enduring joy, that is, happiness, must arise.71

Leibniz is concerned here with the benefits of "theoretical natural science [physicae rationalis]". This is not simply the science of inductive observation. Rather, it is the science which concerns “the causes and purposes of things [de rerum causis ac finibus]". The theoretical natural scientist seeks to probe as far as possible into the world's explanatory structure. In doing so he or she receives two benefits, namely the perfection of the mind and the worship of God. We have already seen that the former is accomplished by increasing the

71 A.6.4.1994-1945/L 280. Note that my dating of this text as being from 1678-84 is a composite between those suggested by the Akademie editors and those suggested by Loemker. The Akademie editors suggest 1678-9? (they include the question mark); Loemker suggests c. 1682-4. Note also that I have slightly altered Loemker’s translation as follows: (i) I have translated felicitatem as “happiness” in the final sentence, whereas Loemker translates it as “felicity”. (ii) Unlike Loemker, I have not included the following sentence right after the heading (the part in italics): “Of these two applications of this science, the former can be sought only in theoretical science, the latter in empirical science as well.” This is because the Akademie editors decided that this sentence occurs at the end of the paragraph right before the heading.

37 mind's power. With respect to the latter, Leibniz seems to suggest that the more we discover about the world's explanatory structure, the more we will appreciate God's perfection.

Unfortunately, Leibniz does not tell us which perfection he has in mind. Presumably it is the perfection of God's skill as a craftsman. The more we come to see the extraordinary intricacy and complexity of the world's explanatory structure, the more we come to be in awe of God's skill at bringing such a structure about. This increased recognition of God's perfection prompts us to love and worship him all the more. And from this "the maximum or the most enduring joy, that is, happiness, must arise." Not only does investigating the world's explanatory structure perfect the mind; it facilitates the worship of God, and this bring happiness too.

Let us now return to Leibniz's proof of the PSR from God's wisdom. Recall that the proof made two inferences: from God's wisdom to the PB, and from the PB to the PSR. By itself this second inference is problematic. However, we have seen that a world with an explanatory structure provides extra opportunities for creaturely happiness. All that remains is to show that Leibniz takes creaturely happiness to be a good-making feature of a world.

And this Leibniz definitely believes. For in both the Discourse on Metaphysics (1686) and in the Theodicy (1710) he claims that the happiness of minds is God's principal aim.72 What is more, in his Memoir for Enlightened Persons of Good Intention (mid 1690’s) Leibniz claims that God attempts to accomplish this aim in part by creating the universe in such a way that it facilitates creaturely happiness. As Leibniz puts it, "the entire universe is made for minds, such that it can contribute to their happiness as much as possible."73 How does the universe

72 A.6.4.1537/AG 38; G VI 168/T §118. 73 K X 9-10/R 105.

38 contribute to the happiness of minds? Certainly proportional harmony will make such a contribution.74 But what Leibniz writes in the Organum and the Introduction suggests that the universe's explanatory structure makes a contribution as well. The investigation of the world's explanatory structure increases the happiness of creaturely minds, thus making this world better than a world that lacks such a structure. This is the missing premise which, I think, allows Leibniz to infer the PSR from the PB.

In this chapter I have argued for both a negative and a positive point. The negative point is that Leibniz’s PSR is not grounded in the ways commonly invoked. It is not grounded in the nature of necessary and sufficient conditions, nor in the nature of truth, nor in the world’s harmony. Instead, Leibniz grounds the PSR in God’s wisdom. By his wisdom God chooses the best possible world, and the PSR contributes to a world’s goodness. For Leibniz, the PSR does not obtain simply because of some purely descriptive facts. Rather, the PSR obtains because of its value: all else being equal, a world in which the PSR obtains is better than a world in which it does not. Because this is the best of all possible worlds, the PSR must obtain in it.

74 This point is also observed, though not necessarily using the language of proportional harmony, by Blumenfeld (1995b: 384), Rutherford (1995: 51-4), Rescher (2013: 58-9) and Griffin (2013: 107-8).

39 3. The modal status of the PSR

In the last chapter we saw how Leibniz grounds the PSR in God’s wisdom. But this proposal faces a problem. If the PSR is a necessary truth, then it is trivially true in the actual world. In that case the PSR is true regardless of God’s choice. The fact that God wills the PSR to be true simply overdetermines it.

This problem is particularly acute, given that the great majority of Leibniz’s commentators think that, for Leibniz, the PSR is a necessary truth.75 Yet there are a few commentators who recognize that Leibniz’s position on the matter is not straightforward.

Adams, for instance, concedes that the modal status of Leibniz’s PSR is difficult to determine.76 Della Rocca goes further, arguing that the necessity of the PSR poses problems for divine freedom, and that Leibniz’s views on the modal status of the PSR merit further investigation.77 And Jorati goes further still, presupposing the contingency of the PSR in her account of Leibnizian compossibility.78

In this chapter I will take an even further step: I will argue that Leibniz is in fact committed to the contingency of the PSR. More precisely, Leibniz is committed to violations of the PSR being absolutely possible. While Leibniz does not explicitly state this claim, it is

75 Russell (1900: 35-36), Sleigh (1983: 202-203), Rutherford (1992: 43-44, 49), Adams (1994: 175), Savile (2000: 34-37), Jauernig (2018: 214), and Rodriguez-Pereyra (2014: 82). 76 Adams (1994: 175). 77 Della Rocca (2015). 78 Jorati (2016: 194-7).

40 implied by claims that he does explicitly state. Given both his intelligence and the systematic nature of his thought, there is a good chance that Leibniz realized that he was committed to the absolute possibility of violations of the PSR. But whether or not he actually realized this is not a question that I will attempt to answer.

Given that Leibniz employs a variety of modal notions, I will begin by briefly describing what Leibniz means by absolute possibility. I will then argue that Leibniz thought that qualitatively indiscernible things (indiscernibles) are absolutely possible. Next I will argue that, according to Leibniz, indiscernibles violate the PSR. Because indiscernibles are absolutely possible, violations of the PSR are therefore absolutely possible as well. I will conclude by considering three problems for my account. These include Leibniz’s alleged inference of qualitative discernibility from complete concepts, a text in which Leibniz seems to claim that the PSR is necessary, and the necessity of his theory of truth. I will argue that all of these problems can be satisfactorily resolved.79

1. Absolute possibility

My claim is that violations of the PSR are absolutely possible. What does this mean? Leibniz does not analyze absolute possibility in terms of possible worlds.80 Instead, he analyzes it in

79 I omit discussion of whether Leibniz’s argument for the PSR from necessary and sufficient conditions entails that the PSR is necessary. For, as we saw in the last chapter, Leibniz abandoned that argument. 80 See Adams (1994: 46-50) for an extended discussion of this point.

41 terms of the implication of contradictions. In his Conversation with Steno (7 December

1677), Leibniz describes the distinction between absolute necessity and hypothetical necessity as follows:

Absolute necessity is when a thing cannot even be understood to be otherwise, but it implies a contradiction in terms, e.g., three times three is ten. Hypothetical necessity is when a thing can be understood to be otherwise, in itself, but per accidens, because of other things already presupposed outside itself it is necessarily such and such.81

Something is absolutely necessary when its negation implies an internal contradiction.

Something is absolutely possible when its negation does not imply an internal contradiction.

Something is hypothetically necessary, by contrast, if its negation does not imply an internal contradiction, though it is nevertheless necessitated by something else. Notice that this allows for something to be both absolutely possible yet hypothetically necessary.

Leibniz maintained these modal distinctions his whole life. For instance, in the year of his death he wrote the following in his Fifth Letter to Clarke (18 August 1716):

For we must distinguish between absolute and hypothetical necessity. We must also distinguish between a necessity that takes place because the opposite implies a contradiction (which necessity is called logical, metaphysical, or mathematical) and a necessity which is moral, by which a wise being chooses the best and every mind follows the strongest inclination.82

81 CP 118-119, emphases removed. 82 G VII 389/LC L5.4.

42 Here again we have the distinction between absolute and hypothetical necessity. But then

Leibniz seems to invoke an entirely different type of necessity, which he calls “logical, metaphysical, or mathematical”. This difference is, however, only apparent. For Leibniz defines such necessity in the same terms as absolute necessity, namely that its negation implies a contradiction. And, a few sections later, Leibniz explicitly identifies absolute necessity with metaphysical necessity.83 Leibniz also goes on to contrast absolute necessity with moral necessity. Such moral necessity is not equivalent to hypothetical necessity, but is rather a species thereof. For something is morally necessary not when its negation implies an internal contradiction, but when it is necessitated by some being (usually God) thinking it good for what is morally necessitated to obtain.

As an example of how Leibniz applies these distinctions, consider what Leibniz has to say regarding whether God can create just a single monad. On the one hand, it seems as if

God can, for there is nothing logically inconsistent in the existence of such a monad. On the other hand, it seems as if God cannot, for the perceptions of the single monad would not correspond to any other monads. Leibniz describes both the problem and its solution in a

Letter to Des Bosses (29 April 1715):

The other objection is this: if all monads have their perceptions from their own states, so to speak, and without any physical influence of one on another, and, further, if the perceptions of each monad correspond precisely to all the other monads that God has already created or to their perceptions, then God could not have created any of those monads that now exist without having produced all the others, etc. The response is

83 G VII 391/LC L5.10.

43 easy and has already been given: he could absolutely, but not hypothetically, because he decided to act always most wisely and most harmoniously.84

Leibniz’s solution is to say that it is absolutely possible for God to create a single monad, but that it is hypothetically impossible. This is because God has decided to act in a wise manner.

And the existence of only a single monad conflicts with God’s wisdom. Although he does not say so explicitly, presumably the conflict here has to do with the fact that a wise God will create the best possible world, the goodness of which is at least partly a function of its plenitude. A world with a single monad would not be plenitudinous at all. Thus it is really moral necessity that is doing the work: the existence of the best possible world is morally necessitated by God’s wisdom and goodness, which makes the existence of a single monad hypothetically impossible.

On my view, violations of the PSR have precisely the same modal status in Leibniz’s philosophy as that of the single monad. They are absolutely possible, given that their negation does not imply an internal contradiction. Yet they are hypothetically impossible, given that the existence of the best possible world is morally necessitated. It is not part of my argument, however, that the absolute possibility of such violations implies that there are possible worlds in which they occur. While that may be the case, it depends on precisely what is required to count as a Leibnizian possible world. This is a difficult issue that I will not try to resolve here. Rather, the important point is that, were it not for his wisdom and goodness, God could have created violations of the PSR, regardless of whether they occur as part of possible worlds or not.

84 LDB 338-339.

44 2. The absolute possibility of indiscernibles

There is a great deal of disagreement over whether Leibniz was committed to the absolute possibility of indiscernibles.85 This is partly Leibniz’s own fault. For Leibniz sometimes claims that it is necessary that there are no indiscernibles in nature.86 But at other times he drops the “in nature” qualification, claiming only that it is necessary that there are no indiscernibles.87 Still, the necessity in question could just be moral necessity: it is morally necessary that there are no indiscernibles in the actual world given God’s wisdom and goodness. I believe that this is indeed what Leibniz has in mind, for in several texts Leibniz commits himself to the absolute possibility of indiscernibles. I will consider three such texts here.

The first text is from a Letter to Bernoulli (13/23 January 1699):

I don’t say that the vacuum, the atom, and other things of this sort are impossible, but only that they are not in agreement with divine wisdom. For even if God were to produce only that which is in accordance with the laws of wisdom, the objects of power and of wisdom are different, and should not be confused. From an infinity of

85 For those who think that Leibniz was committed to the absolute possibility of indiscernibles, see Russell (1900: 55-56), Vinci (1974: 100), McCrae (1976: 110), Chernoff (1981: 135), Carriero (1995: 21 nt. 68), Vailati (1997: 117, 125), Lodge (2010: 25), Lin (2016: 450), and Jorati (2017). For those who deny this, see Parkinson (1965: 132-133), Broad (1975: 40-41), Jolley (2005: 86), and Rodriguez-Pereyra (2014: 118-126). For a variety of interpretive options, see Jauernig (2008). 86 See, for example, Primary Truths (1689), A.6.4.1645/AG 32. 87 On the Principle of Indiscernibles (c. 1696), C 8/MP 133; Preface to the New Essays on Human Understanding (1704), G V 49/NE 57; Monadology §9 (1714), G VI 608/AG 214.

45 possibles, God chose, in accordance with his wisdom, that which is most appropriate. However, it is obvious that the vacuum (and likewise atoms) leaves sterile and uncultivated places, places in which something additional could have been produced, while preserving everything else. For such places to remain contradicts wisdom. I think that there is nothing sterile and uncultivated in nature, even if many things seem that way to us.88

Now it is generally agreed that Leibniz is here granting that vacua and atoms are possible.89

They are the sorts of things that are within God’s power to produce, though he did not produce them because they allow for “sterile and uncultivated places”. Yet there are some, particularly Rodriguez-Pereyra, who question whether Leibniz thought at the time of writing that vacua and atoms are cases of indiscernibles.90 After all, there is a long tradition, going back to Epicurus at least, according to which atoms have different shapes and sizes.91 And in the Letter to Bernoulli Leibniz does not rule out vacua and atoms on account of their indiscernibility. Rather, he rules them out on account of the restrictions they place on ontological plenitude.

Still, there is good reason to think that, at the time of writing to Bernoulli, Leibniz did believe that vacua and atoms are cases of indiscernibles. Ten years earlier he had written,

“There is no vacuum. For the different parts of empty space would then be perfectly similar and mutually congruent and could not be distinguished from one another. And so they would

88 GM III 565/AG 170. 89 Carriero (1995: 21), Lodge (2010: 34 nt. 7), and Brown (2016: 210). Note that Brown denies that this implies that there are possible worlds with vacua and atoms. 90 Rodriguez-Pereyra (2014: 119). 91 See §42 of the Letter to Herodotus, IG 7.

46 differ in number alone, which is absurd.”92 And only a year earlier he had written,

“[N]owhere are there things perfectly similar (which is among my new and more important axioms). Another consequence of this is that, in nature, there are neither corpuscles of maximal hardness …”93 Although Leibniz does not explicitly refer to atoms here, the use of the diminutive “corpuscles [corpuscula]” does suggest that he is thinking of bodies that are at least very small. And his claim that such corpuscles are maximally hard might suggest that he is thinking of atoms as well.

Some five years after writing to Bernoulli, Leibniz reiterates the possibility (but not actuality) of a vacuum in his New Essays on Human Understanding (1704):

[A]lthough I deny that there is any vacuum, I distinguish matter from extension, and I grant that if there were a vacuum inside a sphere the opposite poles within the hollow would still not touch. But I believe that divine perfection does not permit such a situation to occur.94

Leibniz here grants that if there were a vacuum inside a sphere, then the sphere would not collapse in on itself. But it might be objected that when Leibniz says “if there were a vacuum” he is referring to something that is counterpossible, not merely counterfactual. But

Leibniz goes on to make the same move as he did to Bernoulli: the reason why the vacuum does not exist is because it conflicts with God’s perfection. This suggests that the existence

92 Primary Truths (1689), A.6.4.1647/AG 33, emphasis removed. 93 On Nature Itself (1698), G IV 514/AG 164, emphasis removed. 94 II.xiii.21, G V 138/NE 151.

47 of the vacuum is not a counterpossible; if it were, then the conflict with God’s perfection would not be needed to explain why a vacuum does not exist.

The preceding texts concern the possibility of vacua and atoms. As we have seen,

Leibniz does take them to be cases of indiscernibles. In his Fifth Letter to Clarke (18 August

1716), however, Leibniz suggests that indiscernible bodies in general are possible but not actual:

This supposition of two indiscernibles, such as two pieces of matter perfectly alike, seems indeed to be possible in abstract terms, but it is not consistent with the order of things, nor with the divine wisdom by which nothing is admitted without reason. … When I deny that there are two drops of water perfectly alike, or any two other bodies indiscernible from each other, I do not say that it is absolutely impossible to suppose them, but that it is a thing contrary to the divine wisdom, and which consequently does not exist.95

This text has split commentators into two camps. Some think that it shows that Leibniz genuinely believed that indiscernibles are possible.96 Others think that Leibniz is simply conceding that they are possible for the sake of argument, without believing so himself.97 As

I see it, the chief interpretive difficulty lies in the fact that Leibniz does not say that indiscernibles are possible, but only that the supposition of indiscernibles is possible. That is, indiscernibles are supposable. This is a difficulty because Leibniz does not think that

95 G VII 394-5/LC L5.21,25. 96 Russell (1900: 55-56), Vinci (1974: 100), McCrae (1976: 110), Chernoff (1981: 135), Carriero (1995: 21 nt. 68), Lodge (2010: 25), Lin (2016: 450), and Jorati (2017: 912). 97 Parkinson (1965: 132-133), Broad (1975: 40-41), and Jolley (2005: 86).

48 supposability entails possibility. To use one of his own examples, a wheel turning with the fastest motion is supposable but not possible. This is because one can always extend one of the wheel’s spokes beyond its rim, such that any point on the spoke beyond the rim will be moving faster than the wheel itself.98

It is indeed difficult to adjudicate Leibniz’s precise intentions in writing this passage.

Leibniz was uncharacteristically frustrated by this stage in the correspondence, and may therefore have tried to bring it to a close by conceding claims that he did not believe himself.

Nevertheless, I think that this text does point in favour of Leibniz holding indiscernibles to be absolutely possible. For we have already seen that Leibniz thought that vacua and atoms are absolutely possible, and that he held these to be cases of indiscernibles. Thus there is good precedent in Leibniz’s own writings to interpret this passage as expressing a genuine belief that indiscernibles are absolutely possible. Moreover, in this passage Leibniz gives precisely the same reason for the nonexistence of indiscernibles as he did for vacua and atoms. This is not that they are absolutely impossible, but that they conflict with God’s wisdom. It would be odd to give this as a reason for the nonexistence of indiscernibles, if in fact they are absolutely impossible.

98 Meditations on Knowledge, Truth, and Ideas (1684), G IV 424/AG 25. Leibniz makes a similar point about perpetual mechanical motion in his New Essays on Human Understanding (1704), IV.x.7, G V 419/NE 438.

49 3. Indiscernibles and the PSR

So far I have argued that, according to Leibniz, indiscernibles are absolutely possible. In this section I will argue that, according to Leibniz, indiscernibles violate the PSR. There are two lines of evidence for this claim. The first is from Primary Truths, in which Leibniz argues that indiscernibles in general violate the PSR. The second is from his correspondence with

Clarke, in which Leibniz argues that vacua and atoms in particular violate the PSR as well.

Let us first consider what Leibniz writes in Primary Truths (1689):

From these considerations it also follows that, in nature, there cannot be two individual things that differ in number alone. For it certainly must be possible to explain why they are different, and that explanation must derive from some difference they contain. And so what St. Thomas recognized concerning separated intelligences, which, he said, never differ by number alone, must also be said of other things, for never do we find two eggs or two leaves or two blades of grass in a garden that are perfectly similar.99

Leibniz begins this text by appealing to certain “considerations”. This clearly refers to the preceding part of Primary Truths, in which Leibniz infers the PSR from his theory of truth

(we considered this inference in chapter 2). That Leibniz is relying on the PSR is also confirmed by the way in which the argument proceeds. For suppose that there are two indiscernible individuals. There must be an explanation for their numerical distinction: “For

99 A.6.4.1645/AG 32, emphasis in original.

50 it certainly must be possible to explain why they are different [Utique enim oportet rationem reddi posse cur sint diversae]”. According to Leibniz, the explanation must appeal to some difference in their intrinsic qualities. But by hypothesis there is no such difference. So, given that the PSR is true, there are no indiscernibles in nature. As Leibniz also claims, this conclusion is confirmed by empirical investigation as well.

Indiscernibles therefore violate the PSR by lacking a sufficient reason for their numerical distinction. Yet Leibniz does not conclude from this that indiscernibles are absolutely impossible. He only concludes that indiscernibles are impossible “in nature [in natura]”. To use Leibniz’s examples, this allows for indiscernible eggs, leaves, or blades of grass to be absolutely possible. It is just that there is no sufficient reason for why they are numerically distinct. So, if the PSR is true in the actual world, the actual world will lack such indiscernible entities.

In his correspondence with Clarke, Leibniz focuses on vacua and atoms as violations of the PSR. Leibniz actually gives a list of violations of the PSR in his Fifth Letter (18

August 1716). These include “an absolute real time or space, a vacuum, atoms, attraction in the scholastic sense, a physical influence of the soul over the body , and a thousand other fictions either derived from erroneous opinions of the ancients or lately invented by modern philosophers.”100 We already know one reason why vacua and atoms might appear on this list: they are cases of indiscernibles, which by the argument in

Primary Truths means that there is no sufficient reason for their numerical diversity. But there are other possible reasons as well. In the postscript to his Fourth Letter (2 June 1716), for example, Leibniz argues that vacua and atoms violate the PSR in a different way:

100 G VII 420/LC L5.127, emphasis added.

51

I shall add another argument grounded on the necessity of a sufficient reason. It is impossible that there should be any principle to determine what proportion of matter there ought to be, out of all the possible degrees from a plenum to a vacuum, or from a vacuum to a plenum. Perhaps it will be said that the one should be equal to the other, but, because matter is more perfect than a vacuum, reason requires that a geometrical proportion should be observed and that there should be as much more matter than vacuum, as the former deserves to be preferred. But then, there must be no vacuum at all, for the perfection of matter is to that of a vacuum as something to nothing. And the case is the same with atoms: what reason can anyone assign for confining nature in the progression of subdivision?101

This is a slippery text, which I interpret as follows. Leibniz first gives an argument against vacua. For let us suppose some particular ratio of matter to vacua. This ratio is no better than any other particular ratio. So God would violate the PSR by picking one ratio rather than another. Leibniz then considers an objection: there is a best ratio, namely that of one to one.

He responds by saying that matter is better than vacua, so really the best ratio is one to zero.

This response is puzzling because it undercuts the argument it was supposed to save. That argument had relied on all the ratios being equally good, but Leibniz’s response denies this.

At any rate, in the last sentence of the text Leibniz goes on to claim that atoms violate the PSR as well. But the problem is not with the ratio of atoms to non-atoms. Rather, the problem is that there is no non-arbitrary stopping point for the division of matter. To expand on what Leibniz says, suppose that a piece of matter is divided in half, and that one of those halves is itself divided into half. Now suppose that this process is repeated a thousand times.

101 G VII 378/LC L4.PS.

52 By the thousandth division there will be only a tiny piece of matter left. Yet it would be arbitrary for this piece of matter to count as an atom, for presumably it too can be divided into even smaller parts. Given that matter is in fact infinitely divisible, any point at which it is said to be an atom would in fact be arbitrary. So atoms violate the PSR as well.

4. Problems for indiscernibles as violations of the PSR

4.1. Complete concepts and indiscernibles. I have argued that, according to Leibniz, indiscernibles are both absolutely possible and violate the PSR. But Leibniz is often thought to have inferred qualitative discernibility from his theory of complete concepts.102 More precisely, his inference seems to be from the claim that each individual has a complete concept to the claim that no two individuals are perfectly alike. Now if it is a necessary truth that each individual has a complete concept, and if the inference from complete concepts to qualitative discernibility is itself necessary, then it follows that individuals must be qualitatively discernible. This would pose a serious challenge to the view that indiscernibles are absolutely possible.

The text which is invariably invoked is from §8 and §9 of the Discourse on

Metaphysics (1686). Consider the following selection:

102 Russell (1900: 57-58), Parkinson (1965: 130), Adams (1979: 12), and Look (2011b: 94-95).

53 [W]e can say that the nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is attributed. … Several notable paradoxes follow from this; among others, it follows that it is not true that two substances can resemble each other completely and differ only in number …103

This selection would certainly suggest that Leibniz infers the qualitative discernibility of individual substances from the fact that they have complete concepts. The selection is, however, deeply misleading. For it omits a great deal of context, especially the part between

Leibniz’s claims about complete concepts and his inference to qualitative discernibility.

When that context is included, we can see that Leibniz does not make any such inference at all. Instead, he infers qualitative discernibility from an entirely different set of claims, ones which allow such qualitative discernibility to be a merely contingent fact.

Let us consider the selection from §8 and §9 of the Discourse in its full context (the letter divisions are my own):

[A] [W]e can say that the nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is attributed. … [B] Also when we consider carefully the connection of things, we can say that from all time in Alexander’s soul there are vestiges of everything that has happened to him and even traces of everything that happens in the universe, even though God alone could recognize them all.

103 A.6.4.1540-1541/AG 41.

54 [C] 9.That each singular substance expresses the whole universe in its own way, and that all its events, together with all their circumstances and the whole sequence of external things, are included in its notion.

[D] Several notable paradoxes follow from this; among others, it follows that it is not true that two substances can resemble each other completely and differ only in number … It also follows that a substance can begin only by creation and end only by annihilation; that a substance is not divisible into two … [E] Moreover, every substance is like a complete world and like a mirror of God or of the whole universe, which each one expresses in its own way, somewhat as the same city is variously represented depending upon the different positions from which it is viewed. Thus the universe is in some way multiplied as many times as there are substances, and the glory of God is likewise multiplied by as many entirely different representations of his work.104

This is a long and difficult text, which I interpret as follows. In [A] Leibniz claims that it is the nature of an individual substance to have a complete concept. In [B] Leibniz claims that, because everything is connected, there is contained in Alexander’s soul traces of everything that happens in the universe. In [C], which is the title of §9, Leibniz generalizes the claim about Alexander’s soul to all substances, suggesting that they each express the entire

104 A.6.4.1540-1542/AG 41-42. I have replaced Ariew and Garber’s translation in [B] of “Thus when we consider carefully the connection of things” with “Also when we consider carefully the connection of things”. This is because the sentence begins with Aussi. While Aussi can be translated as “Thus”, I prefer “Also” because Leibniz’s inference in [B] to the marks and traces found in Alexander’s soul is from the fact that everything is connected, not from the fact that each thing has a complete concept (though by grasping a thing’s complete concept, one would know all the ways in which it is connected to all other things). Also note that Ariew and Garber provide headline capitalization and italics for [C].

55 universe; he also repeats his claim that the concepts (or notions) of substances are complete.

In [D] Leibniz infers three features of substances: they are qualitatively discernible; they can only begin by creation and end by annihilation; and they are indivisible. In [E] Leibniz repeats his claim that substances express the whole universe, and adds that the diversity of such expressions multiplies the glory of God.

Our concern is obviously with Leibniz’s inference to the qualitative discernibility of substances in [D]. But in [A] and [B] respectively, as well as in [C], Leibniz presents two claims about substances: they have complete concepts, and they express the entire universe.

The usual reading takes Leibniz to infer the qualitative discernibility of substances from the first claim, namely that they have complete concepts. But this reading faces the following problem. While Leibniz does indeed infer the qualitative discernibility of substances, he also infers that substances only begin by creation and only end by annihilation, and that substances are indivisible. Yet how could the existence of a complete concept prevent a substance from naturally ceasing to exist, or from having parts?

This difficulty is avoided on my interpretation. For as I interpret the text, Leibniz indirectly infers the qualitative discernibility of substances from the second claim, namely that they express the entire universe. I say “indirectly” because he uses this second claim to draw an implicit inference: if substances express the entire universe, then substances must be like souls. This is because the type of expression that Leibniz has in mind is that of perceptual representation, as is suggested by his analogy in [E] of different people variously

56 representing the same city from different viewpoints.105 This is also why Leibniz speaks of

Alexander’s soul as that which is doing the expressing. His body, being a purely material entity, is not able to perceive anything at all, much less the entire universe. Elsewhere

Leibniz provides various arguments against matter being naturally able to perceive, such as his famous mill argument. How exactly these arguments work is not my concern here.106 All that matters for our purposes is that Leibniz denies that bodies can naturally perceive.

It is from the conclusion of this implicit inference that Leibniz goes on to infer the three features of substances in [D]. But this time, his inferences make sense. For souls are mereologically simple. Unlike bodies, they cannot be divided into parts. Therefore they cannot cease to be of themselves, as that would require the dissolution of their parts. Nor can they be divided into two, for the same reason.

What about the inference to the qualitative discernibility of substances? Here the inference seems less obvious. For even if substances are like souls, it does not seem to follow that they cannot express the universe in precisely the same way. There is, however, a solution to this problem. For in [E] Leibniz suggests that God is more glorified by substances having

“entirely different [toutes differentes]” expressions of his work. So the fact that substances are qualitatively discernible follows both from the fact that they are like souls (this being a necessary condition for them to express the entire universe), and from the fact that God is more glorified by a variety of different expressions.

105 Leibniz claims that expression is a genus of which perception is a species in a Letter to Arnauld (9 October 1687), G II 112/M 144. For more on Leibniz’s views on expression, see Sleigh (1990: 173- 176). 106 For a detailed discussion of Leibniz’s mill argument, see Rozemond (2014).

57 What Leibniz writes in §8 and §9 of the Discourse, then, does not commit him to the absolute impossibility of indiscernibles. For while such indiscernibles do not exist, the reason why they do not exist is that they do not maximize God’s glory. It is not because they are absolutely impossible. This fits very well with the persistent theme of the texts that we have considered: indiscernibles are absolutely possible, but inconsistent with the perfection of

God.

4.2. The Letter to De Volder and the PSR. The absolute possibility of violations of the PSR appears to conflict, however, with what Leibniz writes in a Letter to De Volder (24 March/3

April 1699). There Leibniz seems to claim that the PSR is “metaphysically necessary”:

I admit that each and every thing remains in its state until there is a reason for change; this is a principle of metaphysical necessity.107

As we have seen, Leibniz equates metaphysical necessity with absolute necessity. And this text does initially seem to indicate that the PSR is metaphysically necessary. But, as with our discussion of the Discourse on Metaphysics, context is key. In fact when the text is considered in context, it becomes clear that what is metaphysically necessary is not the PSR at all, but rather some other claim:

But even if there is a force in matter for preserving its state, that force certainly cannot in any way be derived from extension alone. I admit that each and every thing remains in its state until there is a reason for change; this is a principle of

107 LDV 73-75/AG 172.

58 metaphysical necessity. But it is one thing to retain a state until something changes it, which even something intrinsically indifferent to both states does, and quite another thing, much more significant, for a thing not to be indifferent, but to have a force and, as it were, an inclination to retain its state, and so resist changing.108

Leibniz is clearly concerned with bodies and forces. He begins by stating his well-known view that force cannot be derived from mere extension. He then concedes that it is indeed metaphysically necessary that “each and every thing remains in its state until there is a reason for change”. To which things and to which states does Leibniz refer? I suggest that

Leibniz is referring to the states of motion and rest of bodies. This becomes clear from considering the distinction that he draws in the subsequent sentence. The distinction is between the retention of a state until it is changed by some external thing, and the force of resistance to resist changes by an external thing. Leibniz thinks that the former can be derived from mere extension, but that the latter cannot. So what Leibniz concedes as being metaphysically necessary is that extended bodies retain their states of motion and rest unless those states are changed by some external thing.

But notice that this is not a concession of the metaphysical necessity of the PSR.

Instead, it is just a concession of the metaphysical necessity of Descartes’ first law of motion.109 As Descartes formulates the law in his Principles of Philosophy, “each and every thing, in so far as it can, always continues in the same state; and thus what is once in motion always continues to move.”110 It makes sense why Leibniz would concede Descartes’ first

108 LDV 73-75/AG 172. 109 Garber (2009: 136) also interprets the concession this way. 110 II.37, AT VIIIA 62/CSM I 240.

59 law. For De Volder is himself a Cartesian, and Leibniz is trying to concede as much

Cartesian physics as possible. Thus he concedes the metaphysical necessity of Descartes’ first law, but not of the PSR.

Yet why would Leibniz claim that Descartes’ first law is metaphysically necessary?

One answer might be that he simply infers Descartes’ first law from the PSR, and claims that it is metaphysically necessary because the PSR is metaphysically necessary. That would present a problem for the interpretation that I have developed. But there is a better answer, one that is explicitly rooted in Leibniz’s writings. The answer is that matter is essentially passive, and therefore incapable of producing changes in its own states of motion or rest.

Leibniz makes this point in his Conversation of Philarète and Ariste (1715):

I consider that matter includes only what is passive. … For, not only extension, but also the antitypy attributed to bodies are purely passive things, and consequently, action cannot originate from a modification of matter. Therefore, both motion and thought must come from something else.111

Here Leibniz appeals to the view that all natural modifications of matter must be explicable modifications of matter’s nature (more on this shortly). Now it is the nature of matter to be extended. This, Leibniz thinks, implies that matter is passive. So passivity is also part of the nature of matter, or is at least a proprium thereof. But Leibniz denies that motion can be a naturally explicable modification of something essentially passive. It would have to be a modification of something endowed with force, which in turn could cause passive bodies to

111 G VI 587/AG 263. For more on Leibniz’s invocation of the passivity of matter to deny that matter can think (or perceive), see Rozemond (2014).

60 move from one place to another. The explanation, then, for why Descartes’ first law of motion is metaphysically necessary is that it concerns bodies, and bodies are essentially passive entities.

4.3. The modal status of the theory of truth. In the last chapter we saw how Leibniz infers the

PSR from his theory of truth. While this theory may not be sufficient to ground the PSR, one might think that it is sufficient to show that the PSR is absolutely necessary. For if Leibniz’s theory of truth is absolutely necessary, and if this theory entails the PSR, then the PSR must be absolutely necessary as well. Leibniz makes this inference from his theory of truth to the

PSR in Primary Truths (1689), a passage that we considered in the last chapter as well:

For the received axiom that nothing is without reason, or there is no effect without a cause, directly follows from these considerations; otherwise there would be a truth which could not be proved a priori, that is, a truth which could not be resolved into identities, contrary to the nature of truth, which is always an explicit or implicit identity.112

Several commentators think that such passages support the absolute necessity of Leibniz’s theory of truth, and therefore of the PSR as well.113 Other commentators, however, have expressed doubts over whether Leibniz’s theory of truth, as it is expressed in such passages, is indeed absolute necessary.114 I take it that the key issue is whether Leibniz’s use of the term “nature [naturam]” in “the nature of truth” implies that his theory of truth is absolutely

112 A.6.4.1645/AG 31, emphasis in original. 113 Couturat (1901: 208-210), Jauernig (2008: 214), and Rodriguez-Pereyra (2014: 82). 114 Carriero (1995: 21 nt. 68, 23-26), Jorati (2017: 921 nt. 53).

61 necessary. To address this issue I will first discuss some of Leibniz’s views on the nature of matter. This will show that Leibniz uses the term “nature” in a couple of different ways. I will then consider which of these ways best fits Leibniz’s claims about the nature of truth.

In his Preface to the New Essays on Human Understanding (1703-5), Leibniz considers whether gravity and curved motion can be modifications of matter. He suggests that they can, but only by a miracle. This is because such modifications cannot be explained in terms of the nature of matter, namely extension, alone. Given that God’s wisdom precludes him from doing many miracles, we can therefore expect matter not to have such modifications. As Leibniz puts it:

And every time we find some quality in a subject, we ought to think that, if we understood the nature [la nature] of this subject and of this quality, we would understand how this quality could result from that nature. Thus in the order of nature (setting miracles aside) God does not arbitrarily give these or those qualities indifferently to substances; he never gives them any but those which are natural to them, that is to say, those that can be derived from their nature [nature] as explicable modifications. Thus we can judge that matter does not naturally have the attraction mentioned above [gravity], and does not of itself move on a curved path …115

Let us say that it is the absolute nature of matter to be extended. It is absolute in that to deny extension of matter entails a contradiction. Not even God can produce unextended matter. As

Leibniz suggests, the nature of matter admits of two kinds of modifications. Explicable modifications are modifications that are explicable in terms of the absolute nature of matter, such as shape. Miracles, by contrast, are modifications that are only explicable in terms of

115 G V 59/AG 304.

62 God’s action after creation. These would include gravity, curved motion, and, as Leibniz goes on to write, thought as well.116

But this taxonomy creates a problem. The problem is that there are modifications of matter which are not explicable modifications of the absolute nature of matter, but which

Leibniz would not want to count as miracles. For given that they are always true of matter, they would require constant miracles, contrary to the wisdom of God. Leibniz’s solution is to introduce a new category, which we may call the decreed nature of matter. These are properties that can be denied of matter without contradiction, so are not part of its absolute nature; they cannot be explained simply in terms of its absolute nature, so are not explicable modifications; yet they are not the result of God decreeing that matter has these modifications after creation, so are not miracles. Instead, they are properties of matter that

God decreed at creation that matter should always possess, barring a miracle in which God would revoke his initial decree.

This is all rather abstract, so let us consider an example of a decreed nature. Such an example is found in the fact that, as we have seen, matter always resists motion upon impact

– it pushes back, so to speak. This force of resistance is not an explicable modification of matter, for no force can be explained in terms of extension alone. Nor is it a miracle, for if it were then God would be doing miracles all the time. Yet the fact that matter always resists motion might make us think that it is the nature of matter to do so. Leibniz agrees: it is the nature of matter to have a force of resistance, and this is because of God’s decree. Leibniz

116 Leibniz also claims that curved or circular motion would be miraculous in the Theodicy (1710), G VI 326/T §355.

63 makes this claim in the same Letter to De Volder (24 March/3 April 1699) in which he claims that Descartes’ first law is metaphysically necessary:

Such a world, at any rate possible, in which matter at rest obeys that which puts it in motion without any resistance can indeed be imagined, but such a world would be merely chaos. And so, two things on which I always rely here, success in experience and the principle of order, brought it about that I later came to see that God created matter in such a way that it contains a certain repugnance to motion, and, in a word, a certain resistance, by which a body opposes motion per se. … And so the resistance of matter contains two things, impenetrability or antitypy and resistance or inertia, and since they are everywhere equal in body or proportional to its extension, it is in these things that I locate the nature [naturam] of the passive principle or matter.117

Notice that Leibniz immediately concedes that there is a possible world in which matter lacks the force of resistance. Thus it cannot be the absolute nature of matter to have such a force.

However, Leibniz also knows that in the actual world matter does have such a force. He knows this both from repeated observation (“success in experience”) and from the fact that

God has created the best possible world (“the principle of order”). As Leibniz writes, a world in which bodies do not resist motion at all would be totally chaotic. So why does matter in the actual world have such a force? Leibniz’s answer is that God created matter so as to have a force of resistance. And because matter always exhibits such a force, we may say that it is the nature of matter to do so. It is the decreed nature of matter to always resist motion upon impact.

117 LDV 73-75/AG 172-173.

64 Now it is tempting to think that this use of the term “nature” is a mere aberration.

Leibniz wrote an awful lot, and he used the word “nature” a lot. So it would not be surprising if he occasionally used the word in strange ways. I think that this concern can be blunted by considering what Leibniz writes in the Discourse on Metaphysics (1686). As is well known, the Discourse is a carefully written, organized work. In §7 we find Leibniz discussing what it means to say that an operation of the actual world is “natural”. His view is that an operation is natural if it agrees with a thing’s nature. This is hardly illuminating. But what is illuminating is what he says next. For Leibniz suggests that natures are only God’s “maxims” or “customs”, which God can discard or violate if he so desires:

[Natural operations] are called natural because they are in conformity with certain subordinate maxims that we call the nature of things [la nature des choses]. For one can say that this nature [nature] is only God’s custom, with which he can dispense for any stronger reason than the one which moved him to make use of these maxims.118

I take it that Leibniz does not mean that the nature of a thing is identical to a divine maxim, but only that it is the way it is because of a divine maxim. I also take Leibniz to be claiming that only some features of a nature are due to a divine maxim, not all of them. What is important for our purposes, however, is that Leibniz thinks that not all natures are absolute, but that some are decreed. They are the result of God’s decree for how things should be in the actual world.

Let us now bring all of this back to Leibniz’s theory of truth. As we have seen, there is division as to whether Leibniz’s theory of truth is absolutely necessary. The key point

118 A.6.4.1538-1539/AG 40.

65 concerns what Leibniz means by describing his theory of truth as the “nature” of truth. But as we have also seen, there is a distinction in Leibniz’s philosophy between absolute natures and decreed natures. If it is the absolute nature of truth to have a priori proofs, then indeed the PSR is absolutely necessary. If, on the other hand, this is only the decreed nature of truth, then the PSR obtains in the actual world but is not absolutely necessary. Which one is it?

It would be rash, I think, to come down hard on this issue. Leibniz uses the term

“nature” in both senses, and it is difficult to know which sense he had in mind while writing texts such as Primary Truths. However, there are several considerations in favour of reading the nature of truth as a decreed nature. First, if it were an absolute nature then it would be a logical contradiction to say that a truth lacks an a priori proof. This is a very strong claim, and I know of no text in which Leibniz makes such a claim. Second, reading the nature of truth as a decreed nature fits nicely with Leibniz’s grounding of the PSR in God’s wisdom.

For if it were an absolute nature, then God’s wisdom would be unnecessary in ensuring that the PSR obtains in the actual world. Third, we have already seen that Leibniz is committed to the absolute possibility of truths that violate the PSR: the truth that two indiscernible bodies are in fact two, the truth that there is a particular ratio of vacua to matter, and the truth that a particular body, allegedly an atom, cannot be further divided. Leibniz thinks that these would all be brute truths, and no a priori proof can be given of a brute truth. Given that Leibniz also thinks that such entities are absolutely possible, this reading preserves the coherence of his philosophy.

66 In this chapter I have argued that Leibniz is committed to the absolute possibility of violations of the PSR. When God chose a PSR world, it is not because he lacked other options. Rather, it is because God chose to create the best possible world, and that will be a world in which the PSR obtains. But we have not yet examined why God chooses the best. Is it because God is beholden to the PSR, or is it because of some other set of truths? That question is the topic of the next chapter.

67 4. God's choice of the best

God’s choice of the best possible world is the supreme application of Leibniz’s principle of the best (PB). In chapter 2 I argued that the PSR is grounded in the PB plus the fact that the

PSR contributes to the goodness of a world. But why is the PB true? As we shall see, commentators have given several reasons for why Leibniz's God chooses the best. However, they tend to do so only in passing. This lack of extended discussion is surprising, for two reasons. First, although Leibniz’s optimism does find precedents in Plato and the Stoics, it stands in stark contrast to the views of Descartes, Malebranche, and Spinoza.119 So it cannot be assumed that Leibniz was an optimist simply because that was the received view of his day. Second, Leibniz's optimism affects almost every aspect of his philosophy. This is true of his metaphysics, theology, science, and ethics. Metaphysics: the world's optimality entails that it is quantitatively and qualitatively plenitudinous.120 Theology: the world's optimality provides a response to the problem of evil.121 Science: the world's optimality entails that

119 Plato, Timaeus 29a-30b, Cooper 1235-1236; Cicero, On the Nature of the Gods, 2.86-87, IG 154; Descartes, Sixth Replies, AT VII 431-432/CSM II 291; Malebranche, Treatise on Nature and Grace, I.xiv, Nadler 260; Spinoza, Ethics 1app, Geb II 77-81/Curley I 439-443. Note that both Malebranche and Leibniz think that the simplicity of natural laws is very valuable; it is just that, given his occasionalism, Malebranche does not count the value of simple laws as part of the value of the world itself. For further comparison between the theodicies of Malebranche and Leibniz, see Nadler (1994) and Schmaltz (2010). 120 A Résumé of Metaphysics (c. 1697), G VII 290/MP 146. 121 On the Ultimate Origination of Things (1697), G VII 306/AG 153.

68 comparatively simple laws of nature obtain, such as Snell's law of refraction.122 Ethics: the world's optimality entails that justice will be served, whether in this life or the next.123 While such applications may seem extraordinary to the contemporary mind, for Leibniz they are serious applications of a serious view.

I will begin by considering two arguments that commentators have attributed to

Leibniz. These are that God's choice of the best follows from the PSR, and that it follows from the Socratic nature of God's will. I will argue that Leibniz does not endorse the argument from the PSR. For my purposes this is a good thing: if Leibniz grounds the PSR in the PB but then grounds the PB in the PSR, then he would have a circular series of grounds.

Moreover, I will also argue that the argument from the Socratic nature of the will, though accurate as far as it goes, only provides an incomplete account of Leibniz's optimism. What is missing from both arguments is reference to God's goodness. On Leibniz's official argument, God chooses the best because he is perfectly wise, powerful, and good. The question, of course, is what Leibniz means by God's goodness. I will argue that Leibniz does not mean that God chooses the best in order to be good to creatures. Rather, he chooses the best in order to be good to himself. This is because God seeks to maintain his own supreme happiness. If God were to create a suboptimal world, then his own happiness would be compromised. Or so I shall argue.

122 Discourse on Metaphysics (1686), A.6.4.1565/AG 55. 123 Monadology (1714), G VI 622/AG 224.

69 1. The argument from the PSR

It is sometimes thought that Leibniz infers the PB from the PSR itself. There are two views on the relation between these principles, such that it would allow for this inference to go through. One view is that the PSR and the PB are in fact identical. This seems to be the position of Couturat, who uses "principe de raison" and "principe du meilleur" interchangeably.124 Couturat’s view receives some support from the fact that Leibniz’s definitions of the PB are not always as clear as we might like. For example, Leibniz describes the PB in §48 of the Monadology (1714) as follows: “God has power, which is the source of everything, knowledge, which contains the diversity of ideas, and finally will, which brings about changes or products in accordance with the principle of the best.”125

Leibniz had already introduced the PSR in §32, but here he only mentions the PB without defining it. So it might be thought that the PSR and the PB are one and the same.

Yet Couturat's position is too strong. For in other places Leibniz clearly distinguishes between the two principles. Consider, for instance, what Leibniz writes in a Letter to Des

Bosses (19 August 1715). There Leibniz gives two arguments, one from the PB and one from the PSR, for the claim that beings other than ourselves exist:

We conclude with the highest probability that we are not the only existents, not only from the principle of the divine wisdom, but also from that common principle which I have frequently urged – that nothing happens without a reason; for there appears to be

124 Couturat (1901: 220, 224). 125 G VI 615/AG 219.

70 no reason why we alone should be preferred above all other possible beings.126

Leibniz uses two principles to give two arguments for the same conclusion. The first principle is “the principle of the divine wisdom”. This is almost certainly a reference to the

PB, in that Leibniz often claims that God chooses the best because he is wise. For instance,

Leibniz writes in §1 of the Discourse on Metaphysics (1686) that “God, possessing supreme and infinite wisdom, acts in the most perfect manner, not only metaphysically, but also morally speaking.”127 Likewise, he writes in a Letter to Coste (19 December 1707) that “God or a perfectly wise person will always choose the best they know of.”128 The second principle is “that nothing happens without a reason”. This is clearly a reference to the PSR. Using these two principles, Leibniz concludes that there are other possible beings. While he does not spell out how exactly such arguments are supposed to go, Leibniz does make it clear that they rely on different principles. For we can conclude that we are not the only existents not only [non tantum] from the PB, but also [sed etiam] from the PSR.

The other view on the relation between the PSR and the PB is that the PSR entails the

PB. This seems to be the position of Adams, though he mentions it only in passing.129 One possible reason in its favour might be that Leibniz implicitly presupposes such an inference in those arguments, considered in chapter 1, according to which certain states of affairs imply

126 G II 502/L 613. 127 A.6.4.1531/AG 35. 128 G III 401/AG 194. Note that in these texts Leibniz implicitly presupposes that God is omnipotent and perfectly good as well. 129 Adams (1994: 175) writes that God’s choice of the best is “an obvious and crucial corollary of [the] PSR”. Note that Rescher (1952: 32; 1967: 33), Curley (1972: 90-91), and Ishiguro (1990: 197) also deny, as I do, that the PB follows from the PSR.

71 a violation of the PSR by God. Perhaps God does not choose between equally good options because he always acts for the best, which in turn is a consequence of the fact that he is governed by the PSR. This suggestion, however, faces a couple of difficulties. First, the inference from the PSR to the PB is simply invalid. The PSR demands that everything have an explanation; it does not demand that everything that God does must be explained in terms of his choice of the best. Spinoza's God, for instance, satisfies the PSR but not the PB.

Second, Leibniz does not even need to make this inference in order for such arguments to go through. For not only are both options equally good; they are also equally bad. So even if

God were not governed by the PB, he would still be stuck in deciding which option to create.

There is simply no reason in favour of one option that is not shared by the other option too.

What then is the relation between the PSR and the PB, if not one of identity or entailment? I believe that the relation is one of satisfaction: the PB satisfies the PSR, in that if the PB is true, then the explanatory demand posed by the PSR is satisfied in the case of

God. The PSR demands a sufficient reason for everything; the PB fulfills that demand in the case of God by claiming that the sufficient reason for all of God's actions is that he thought them best. But the PSR does not entail the PB. Consequently, we do not yet have the grounds of the PB itself.

72 2. The argument from the will

As already noted, Leibniz sometimes says that God chooses the best because he is wise.130 I shall assume that wisdom is a property of the intellect, namely the property of omniscience.

Now let us suppose that the will is Socratic: it always chooses what the intellect judges to be best. Let us also suppose that “best” here means what is best for the agent, not what is best for all agents or what is best metaphysically speaking (though of course something can be best in all these senses at once). This gives us a simple argument for why God chooses the best. By his omniscient intellect, God knows which world is best. And by his Socratic will,

God will choose the best. Therefore, assuming that God is also omnipotent, he will create the best possible world. As Mates puts it:

Leibniz accepts the Socratic principle that nobody desires what he really considers to be bad for himself, or, more generally, that everyone desires only what he deems to be best. Applying this to God, of whom it can be said that (1) if he deems something to be best, then it is the best, and (2) if he desires that something happen, then it does happen, we infer that the actual world, which God created, is the best of all possible worlds.131

Now everything about this view is correct as it stands. Leibniz's God is indeed omniscient

130 Discourse on Metaphysics (1686), A.6.4.1531/AG 35; Letter to Coste (19 December 1707), G III 401/AG 194; Fifth Letter to Clarke (18 August 1716), G VII 393/LC L5.18-19. 131 Mates (1986: 166-167), emphases in original. A similar view seems to be suggested by Rutherford (1995: 12), and Lin (2011: 202), though they do not put the point as explicitly as Mates.

73 and omnipotent. And Leibniz's God also has a Socratic will. As Leibniz writes in §45 of the

Theodicy (1710), "The will is never prompted to action save by the representation of the good, which prevails over the opposite representations. This is admitted even in relation to

God ..."132 But my interest is not in whether Leibniz believes that God's will is Socratic, but in why he believes this. As we shall see, this issue is not as straightforward as one might think.

The most obvious thing to think is that Leibniz simply defines the will in Socratic terms. Any will that does not choose the apparent best is no will at all. Leibniz does seem to provide such a definition of the will in The Elements of True Piety (1677-8?):

The will is the judgement concerning good and evil. That men understand this definition of 'will' is apparent from their modes of expression, in which if the definition is substituted for the thing defined then the sense will be evident to them. Hence we say everyone seeks the good and avoids the bad. No one wants evil on the grounds that it is evil. We will what we think is good, and conversely what we think is good is what we will.133

Here Leibniz claims that it is part of the definition of the will that it act on the apparent best reason. But elsewhere Leibniz seems to soften his definition of the will, suggesting that the will must only act on some reason or other. Consider what Leibniz writes in his Fourth

Letter to Clarke (2 June 1716):

A simple will without any motive is a fiction, not only contrary to God's perfection,

132 G VI 128/T §45. 133 A.6.4.1360/SLT 192.

74 but also chimerical and contradictory, inconsistent with the definition of the will ...134

Of course, if the will must always act on the best reason, then it will always be acting on some reason or other. So perhaps what Leibniz writes in his Fourth Letter does not represent a softening of what he writes in the Elements. However, I do think that Leibniz's considered position is only that of the softened definition. This is because, some time after writing the

Elements, Leibniz claims that God decreed that the will be Socratic. He claims this in §30 of the Discourse on Metaphysics (1686):

Moreover, in virtue of his decree that the will always tend toward the apparent good, expressing or imitating his will in certain particular respects (so that this apparent good always has some truth in it), God determines our will to choose what seems better, without, however, necessitating it.135

Leibniz is here focusing on the wills of creatures, not of God. In fact, he suggests that by decreeing that the wills of creatures be Socratic, their wills thereby imitate God's will. This does not, however, imply that God's will is essentially Socratic. For if it did then the nature of God’s will would be different from that of creatures, and there is no indication that

Leibniz thought this. It is better to think that God really made two decrees: first that his own will be Socratic, and then that the wills of creatures be Socratic too. And this is precisely what Leibniz claims earlier in §13 of the Discourse:

[The sequence of things that constitutes our world is] based on God's first free decree

134 G VII 371-372/LC L4.2. 135 A.6.4.1575/AG 61.

75 always to do what is most perfect and God's decree with respect to human nature, following out of the first decree, that man will always do (although freely) that which appears to be best.136

God first decrees that he will always act for the best. I take this to mean that God decrees that his will be Socratic. For Leibniz immediately goes on to write that God also decrees “that man will always do (although freely) that which appears to be best.” It would be strange if

Leibniz were using “decree [decret]” in one sense with respect to God, and in a different sense with respect to creatures. Rather, in both cases God is making a decree that the will, whether his own or that of creatures, be Socratic.

If this is so, then we might wonder whether Leibniz had changed his mind on the nature of the will by the time he wrote the Discourse. It is possible that he did. Perhaps he thought that the will is essentially Socratic while writing the Elements (1677-8?), changed his mind by the time of the Discourse (1686), and thereafter was careful only to say that the nature of the will requires that it act on some reason or other, as in the Fourth Letter to

Clarke (1716). Yet there is another interpretive option. Recall from the last chapter that we made a distinction between absolute natures and decreed natures. If it is part of the absolute nature of the will that it act on the apparent best, then not even God could decree otherwise.

But perhaps Leibniz only intended his definition of the will in the Elements to pick out the decreed nature of the will, namely that it act on the apparent best. In that case Leibniz did not change his mind at all; what he writes in the Discourse is just a more explicit formulation of a view that he always held.

We might also wonder why Leibniz held such a view in the first place. Why would

136 A.6.4.1548/AG 46.

76 God decree to himself that he always act for the best? If God did so for no reason at all, then he would violate the PSR. But if God did so because he judged it best, then it seems as if he already has a Socratic will. This dilemma seems decisive to me, in that I know of no plausible way to save Leibniz from it. Thus I do not think that Leibniz should have claimed what he did in the Discourse. In fact it seems that Leibniz is trying to preserve God’s freedom (“God’s first free decree”) by making claims that he should not have made.

What is clear, however, is that the argument from the nature of the will does not give us a complete explanation for why God chooses the best possible world. It is an argument the premises of which Leibniz would have endorsed, in that he believed God to be omniscient and in possession of a Socratic will. But if the reason why God has a Socratic will is because of God’s own decree, then ultimately the argument only tells us that God chose the best because he had decreed to always choose the best. This is not particularly informative. I suggest that we look instead to a different argument, one explicitly given by Leibniz himself.

3. Leibniz's official argument

Like the preceding arguments, Leibniz's official argument for God's choice of the best is a simple one. It invokes three properties, and then infers that God, possessing these properties, chooses the best. These three properties are those of supreme power [puissance], wisdom

[sagesse], and goodness [bonté]. We find Leibniz advancing this argument in §7 and §8 of the Theodicy (1710), as well as in §55 of the Monadology (1714):

77

And this intelligent cause ought to be infinite in all ways, and absolutely perfect in power, in wisdom and in goodness, since it relates to all that which is possible. ... Now this supreme wisdom, united to a goodness that is no less infinite, cannot but have chosen the best.137

And this is the cause of the existence of the best, which wisdom makes known to God, which his goodness makes him choose, and which his power makes him produce.138

As Sleigh observes, this argument is remarkably perfunctory.139 This is all the more surprising given how much of Leibniz’s philosophy hangs upon it. I take it that what Leibniz means by God’s power and wisdom in these texts is straightforward. God’s power is just his omnipotence, which allows him to bring any possible world into existence. And God’s wisdom is just his omniscience, which allows him to compare all possible worlds and to determine which one is best. The real question concerns what Leibniz means by God’s goodness.

One possibility is that by “goodness” Leibniz means God’s goodness to creatures. By creating a suboptimal world, God would violate creaturely rights. But God would never violate creaturely rights, so he only creates the best world. The problems with this suggestion are twofold: there is not, to the best of my knowledge, any textual evidence in its favour, and it faces a powerful objection by Robert Adams. Adams asks us to consider whose rights,

137 G VI 107/T §7-8, emphases in original. 138 G VI 616/AG 220. 139 Sleigh (2001: 171).

78 exactly, would be violated by God’s creation of a suboptimal world. Surely it is not the rights of creatures in the non-actualized best world. For it is difficult to see how merely possible creatures can have any rights at all, especially when those merely possible creatures will never be actualized. Their modal status will always remain that of non-actualized possibles.

It must therefore be the rights of creatures in the actualized suboptimal world that are violated. But according to Adams, there are certain criteria which, if satisfied, seem to allow

God to be morally justified in creating a suboptimal world. These are that, for each creature in the actualized suboptimal world, none would have existed in the best possible world; each creature is at least as happy on the whole as in any other world in which it could exist; and none would have a life so miserable on the whole that it would have been better for the creature never to have existed. If a world meets these criteria, then God would be morally justified in creating it.140

This objection is particularly powerful when directed against Leibniz. For on

Leibniz’s metaphysics, the first two criteria are trivially satisfied by his denial of counterfactual identity. According to Leibniz, if any individual had even slightly different properties from the ones it actually has, then it would no longer be the same individual.141

This means that no creature can exist in any other possible world while still retaining its identity as that creature. So no creature in the suboptimal world would have existed in the best possible world (satisfying the first criterion), and each creature in the suboptimal world is at least as happy on the whole as in any other world in which it could exist (satisfying the

140 Adams (1972: 319-321). For ease of exposition I have presented Adams’ criteria in a different order from the order in which he presents them. 141 Remarks on Arnauld’s Letter (May 1686), G II 42/AG 73.

79 second criterion). This is because no creature could exist in any other world at all.

What about the third criterion, that no creature would have a life so miserable on the whole that it would have been better for the creature never to have existed? Unlike the first two criteria, this makes no mention of counterfactual identity. Yet surely Leibniz would grant that, in the infinite realm of possible worlds, there is at least one world that fits this criterion. All we need is a world consisting of only a few creatures that are not hopelessly miserable. Of course, such a world will not be the best, if only because it is not plenitudinous. But while God would therefore not create it, this is not because he would thereby be violating any creaturely rights.

4. God’s happiness

What then does Leibniz mean by God’s goodness, if not goodness to creatures? I suggest that

Leibniz means God’s goodness to himself. In particular, the creation of a suboptimal world would decrease God’s own supreme happiness, so he only creates the best. In this section I will first provide reasons to think that Leibniz believed that God is in fact a happy being.

Then I will argue that Leibniz saw God’s happiness as explaining why God chooses the best possible world. Finally, I will consider a couple of texts that seem to pose problems for such an account.

4.1. The fact of God’s happiness. Let us begin by examining what exactly Leibniz means by

80 “happiness”. Leibniz was fond of defining value-laden concepts such as happiness, pleasure, and perfection in terms of each other.142 Happiness is simply enduring pleasure. This means that it is impossible for someone who only occasionally experiences pleasure to be happy.

Pleasure, which Leibniz tends to treat as equivalent to joy, is the sense [sensus, sentiment] of perfection (I will henceforth treat pleasure and joy as equivalent as well). The bearer of this perfection does not matter: it could be oneself, another person, an artifact, or something in nature. Unfortunately, Leibniz does not, in these lists of definitions at least, define perfection itself. But we have already seen plenty of examples of things that would count as perfections: proportional and perceptual harmony, minds increasing in their power, the divine attributes themselves, and so on.

Now Leibniz thinks that God is himself a happy being. I have found nine separate texts in which Leibniz claims as much.143 Sometimes these come as short statements or as rhetorical questions. For instance, in §191 of the Theodicy (1710) Leibniz asks rhetorically,

“Is it to be desired that God should not be bound to be perfect and happy?”144 And in §16 of the Principles of Nature and of Grace (1714) Leibniz asserts, “God is the most perfect and

142 See Aphorisms Concerning Happiness, Wisdom, Charity, and Justice (1678/9?), A.6.4.2798/LGR 138-139; Happiness (1694-8), Grua 579-584/SLT 167-170; A Dialogue (after 1695?), Grua 589/SLT 171-172. The definitions following this note are based on these texts. 143 Aphorisms Concerning Happiness, Wisdom, Charity, and Justice (1678/9?), A.6.4.2799- 2800/LGR 138-139; Dialogue between Theophile and Polidore (1679?), A.6.4.2237/LGR 134; Preface to the Diplomatic Code of People’s Rights (1693), G III 387/SLT 149-150; Letter to Nicaise (1697), A.2.3.369/LGR 159-160; Reflections on the Common Concept of Justice (c. 1702), Mollat 60/L 569; Letter to Hansch (1710), Dutens II 224-225/L 594; Theodicy (1710), G VI 230/T §191; Theodicy (1710), G VI 236-237/T §201; Principles of Nature and Grace (1714), G VI 605/AG 212. 144 G VI 230/T §191.

81 happiest.”145 At other times these statements come as premises in arguments. The value of these arguments is that they confirm that Leibniz does not take his talk of God’s happiness to be mere anthropomorphism – if he did, then the arguments would not go through. One such argument is directed against Cartesian divine voluntarism. In an appendix to the Theodicy entitled A Vindication of God’s Justice (1710) Leibniz writes:

Nor must the cause of the fall be sought in a certain indifference of God to good and evil, justice and injustice, as though these qualifications depended upon his arbitrary will. For if this were so it would follow that anything could have been constituted by him to bear these characters, and with equal justice and reason, that is to say, with none. This again would reduce all glory of his justice and his wisdom to naught, since he could find no joy [delectum] in his actions nor any reason for joy.146

Suppose, says Leibniz, that the standards of perfection depend upon God’s will. If he willed that perfection consists in chaos, then it is so. Or if he willed that perfection consists in harmony, then it is so as well. Leibniz then observes that God could find no joy in his actions. I take it that the actions Leibniz has in mind are not all of God’s actions, but only the actions of determining the standards of perfection. Given his definition of “joy”, we can see why Leibniz is right. For joy is the sense of perfection. But the actions of determining the standards of perfection cannot themselves be adjudicated as perfect or imperfect, since the standards of perfection have not yet been set. So God cannot receive joy from those actions when they cannot even be considered perfect in the first place. If one thinks that God must be perfectly joyful at all times, then this presents a problem for the divine voluntarist.

145 G VI 605/AG 212. 146 G VI 450/S 130-131, emphasis added.

82 We get another argument invoking God’s happiness in Leibniz’s Preface to the

Diplomatic Code of People’s Rights (1693). There Leibniz appeals to both God’s happiness and his formal definition of “love” to argue that we have good reason to love God:

But to love or to esteem is to be delighted by the happiness of another, or what amounts to the same, to make the happiness of another into one’s own. … The divine love, however, surpasses other loves, because God can be loved with the greatest result, since nothing is happier than God and also nothing can be understood as being more beautiful or more worthy of happiness. And since he also possesses supreme power and supreme wisdom, his happiness does not merely enter into ours (if we are wise, that is, if we love him), but even constitutes it.147

Love is a less primitive concept than both pleasure and happiness, as it is defined in terms of them. To love someone is simply to receive pleasure from their happiness. Notice that this makes it impossible to love an inanimate object. Strictly speaking, only persons can be loved.

While love can be directed at both happy and unhappy persons, one will receive more pleasure from loving someone who is happy. This allows for a simple argument as to why one should love God. For since God is perfect, he is the most worthy of happiness, and indeed he is supremely happy. So loving God will provide one with more pleasure than loving anyone else. If we love God continually, then we will have enduring joy, which is just

Leibniz’s definition of happiness. That is why Leibniz can write that if we love God, then his happiness becomes our own.

4.2. God’s happiness and God’s choice of the best. We have seen that Leibniz thinks of God

147 G III 387/SLT 149-150, emphasis in original.

83 as a happy being. God experiences enduring joy by having a constant sense of perfection.

But Leibniz does not think that God’s joy is simply a descriptive fact about God. Rather, God also aims to maintain his joy. Leibniz puts the point succinctly in his Aphorisms Concerning

Happiness, Wisdom, Charity, and Justice (1678-9?): “The end or aim of God is his own joy, or love of himself [Dei finis sive scopus est laetitia propria seu amor sui].” Leibniz presumably does not mean that God aims to increase his joy – that would suggest that God is not already supremely happy, contrary to both the texts that we have considered and the general conception of God as a perfect being. Instead, God aims to maintain the supreme joy that he has always possessed. Given this aim, God will never do anything to compromise his happiness.

Unfortunately, in the Aphorisms Leibniz does not tell us why God has this aim in the first place. One possibility is that God aims to maintain his own joy because he is morally obliged to do so. Leibniz does say that this is true of creatures. In the New Essays on Human

Understanding (1704), Leibniz writes that “morality has indemonstrable principles, of which one of the first and most practical is that we should pursue joy and avoid sorrow”.148 And in a Letter to Wolff (18 May 1715) he writes that “in morals I set up our happiness as an end; this I define as a state of enduring joy.”149 However, Leibniz does not say that God is under the same obligation. So perhaps God only aims to maintain his supreme happiness because happiness is itself desirable, regardless of whether God is obliged to do so or not.

Either way, we need to consider the sources of God’s joy. If joy is the sense of perfection, which perfections does God sense? Leibniz’s answer is that God senses both his

148 I.ii.1, G V 81/NE 88. 149 GLW 170/AG 233, emphasis in original.

84 own perfections and the perfections of the world. Around the same time that he wrote the

Aphorisms, Leibniz also wrote the following in his Dialogue between Theophile and

Polidore (1679?):

For since God is a mind, and the most perfect of all, I see that he will be the happiest and the most satisfied. But I also see that he will have commerce with other minds, and that he will have much more pleasure, if I am permitted to speak in this way, in his kingdom over minds than in his power over bodies.150

Leibniz puts this text in the mouth of Polidore, not Theophile, Leibniz’s spokesperson.

However, Leibniz seems to intend Polidore’s speech at this point to represent Polidore coming to the realization that certain Leibnizian views are correct (immediately before this text Polidore states “I understand the force of your arguments very well”). Working with

Leibniz’s definition of pleasure, Polidore quickly realizes that God will receive constant pleasure simply by sensing his own perfection. But Polidore also goes on to observe that God will receive pleasure from the world that he has created. In fact he will receive more pleasure from certain things in the world than from others: minds in particular provide God with more pleasure than bodies. Still, Polidore does express some hesitation. For he hedges his claim that God will receive more pleasure with “if I am permitted to speak in this way”. This could simply be a narrative device, representing the fact that, while Polidore has come to basically accept Theophile’s views, he has yet to fully digest them. Or it might express a genuine reservation on Leibniz’s part. If so, it is an anomaly. For we have seen that there are plenty of texts in which Leibniz expresses no such reservation at all.

150 A.6.4.2237/LGR 134.

85 We find Leibniz advancing similar claims in his Reflections on the Common Concept of Justice (c. 1702):

One cannot envisage any other motive in God than that of perfection or if you like, of his pleasure. Assuming, according to my definition, that pleasure is nothing but the feeling of perfection, he has nothing to consider outside of himself; on the contrary, everything depends on him. But his happiness would not be supreme if he did not aim at as much good and perfection as possible.151

Here we find Leibniz repeating some of his earlier claims. God is motivated by his own pleasure (as in the Aphorisms), though this time Leibniz adds that this is God’s only motive.

And God’s perfection provides him with a source of pleasure (as in the Dialogue). But

Leibniz goes on to add that for God to maintain his supreme happiness, he must always aim at the greatest perfection. This makes sense: if God’s only aim is his own pleasure, then he must aim at maximal perfection, for pleasure just is the sense of perfection. While it is true that God can maintain his supreme happiness simply by sensing himself, if God is to create at all then his happiness can only be maintained by creating the most perfect world. As I read this text, then, Leibniz alludes to the perfection of the world as a necessary condition for

God’s happiness.

The best text for our purposes, however, is from §201 of the Theodicy (1710):

Yet God is bound by a moral necessity, to make things in such a manner that there can be nothing better: otherwise not only would others have cause to criticize what he makes, but, more than that, he would not himself be satisfied with his work, he would

151 Mollat 60/L 569.

86 blame himself for its imperfection; and that conflicts with the supreme happiness of the divine nature. This perpetual sense of his own fault or imperfection would be to him an inevitable source of grief, as M. Bayle says on another occasion.152

Leibniz begins by claiming that God is morally necessitated to create the best. This is something that we already know: in virtue of his goodness, God must create the best possible world. The significance of this text is that Leibniz goes on to explain why God is thus morally necessitated. And the answer is precisely that to which all the other texts have been alluding. The answer is that if God chose a suboptimal world, then the two sources of his pleasure would be compromised. God would not receive maximal pleasure from the world that he had created, for pleasure is just the sense of perfection, and the suboptimal world is by definition not maximally perfect. Nor would God receive maximal pleasure from himself.

For an inferior product suggests an inferior craftsman. God would in fact receive grief

[chagrins] not only from the inferior world, but also from himself as the creator of this world. All this compromises God’s supreme happiness. Seeing as God’s only aim is his own joy, God will therefore choose the best possible world.

4.3. Textual evidence to the contrary. We have examined a variety of texts in which Leibniz claims that God is supremely happy, that God aims to maintain his supreme happiness, and that he does so by creating the best possible world. Yet in a couple of places Leibniz seems to qualify or even reject his view that God experiences pleasure, joy, or happiness. For

152 G VI 236-237/T §201. Huggard translates “felicité” as “felicity”, which I have translated as “happiness” in keeping with the other texts.

87 instance, in On the Continuous Increase in the Perfection of the World (1689-90?) Leibniz writes:

All things considered, I believe that the world continuously increases in perfection and does not go around in a circle as if by a revolution, for thus there would be no final cause. And although in God there is no pleasure, there is still in him something analogous to pleasure, so that he rejoices in the continuous advance of his plans.153

In a way this text supports the interpretation that I have offered. Leibniz observes that the world continues to increase in its perfection, and that this provides God with something similar to pleasure. However, Leibniz also denies that God experiences pleasure itself: the pleasure that God receives from the world’s progress is simply “something analogous to pleasure”. What does Leibniz mean by this?

I suggest that we distinguish between two types of pleasure, and attribute to Leibniz the view that God lacks one type but possesses the other. There is in fact a rich history of distinguishing between different types of pleasure. Consider, for instance, Descartes’ distinction between different types of joy in The Passions of the Soul:

Joy is a delightful excitation of the soul, wherein consists the enjoyment it has of the good which the impressions of the brain represent to it as its own. ... I should also add that it is of the good which the impressions of the brain represent to it as its own, in order not to confuse this joy, which is a passion, with the purely intellectual joy which comes into the soul by the action of the soul alone, and which can be said to be

153 A.6.4.1642/SLT 196.

88 a delightful excitation, excited in it by itself, wherein consists the enjoyment it has of the good which its understanding represents to it as its own.154

Descartes distinguishes between two different types of joy, namely sensory joy (my term), and intellectual joy. The distinction is based on their respective sources. While all joy occurs in the soul, sensory joy also requires a brain, whereas intellectual joy does not. Sensory joy requires a brain because it is “the enjoyment it [the soul] has of the good which the impressions of the brain represent to it as its own.” These impressions are, in turn, presumably produced as a result of sensory stimuli. Intellectual joy, by contrast, requires no senses or brain at all. It only requires a soul with the faculty of understanding, which represents a particular good to the soul as its own.

It would be useful for our purposes if Leibniz endorsed something like Descartes’ distinction between sensory and intellectual joy. And, in A Dialogue (after 1695?), he does precisely that:

However, pleasantness lies in the feeling [sensu] of perfection, and this feeling is no doubt involved in every pleasure, but pleasures whose reason is not sufficiently understood, such as those that are perceived by the external senses, can conceal greater evils in the future, like a pleasant-tasting poison. Therefore we must strive for those clear and pure pleasures, whose perfection lies not only in the sense, but also in the intellect, and these we call pleasures of the mind [quae non tantum in sensu, sed etiam in intellectu perfectionum consistunt, quas voluptates animi appellamus], in which it is clear that evils cannot lie hidden. These pleasures eventually arise safe and

154 II.91, in Voss 69-70.

89 sound, and are able to bring forth enduring joy; through these pleasures there is a direct road to happiness.155

Like Descartes, Leibniz also distinguishes between types of pleasure according to their source. There is sensory pleasure, which is produced by the senses identifying some perfection, as well as intellectual pleasure, which presumably does not require the senses. As

Leibniz goes on to observe, the road to happiness is not through sensory pleasure, but through intellectual pleasure. This is because something can produce a short-term sensory pleasure while concealing an imperfection that leads to long-term displeasure. To use

Leibniz’s example, one might receive immediate pleasure by tasting something that turns out to be poisonous. It is better, then, to achieve happiness through intellectual pleasure.

With this distinction in hand, we can now see what Leibniz might mean when he says that “although in God there is no pleasure, there is still in him something analogous to pleasure”. What he is saying is that although in God there is no sensory pleasure (for he lacks the necessary senses), there is nevertheless in him something analogous to sensory pleasure, namely intellectual pleasure. They are analogous in that while their sources are different, both are produced by encountering some perfection. In the context at hand, God receives intellectual pleasure by considering the continual increase in the perfection of his own creation.

The other challenge for my interpretation comes from a comment that Leibniz makes on one of Bayle’s maxims. This comment is found in §116 of the Theodicy (1710) (note that the first sentence is a quotation from Bayle):

155 Grua 589/SLT 171-172.

90

‘As the infinitely perfect Being finds in himself a glory and a bliss [une beatitude] that can never either diminish or increase, his goodness alone has determined him to create this universe: neither the ambition to be praised, nor any interested motive of preserving or augmenting his bliss and glory, has had any part therein.’ This maxim is very good: praises of God do him no service, but they are of service to the men who praise him, and he desired their good.156

Bayle suggests that God’s glory and bliss cannot ever be increased or decreased. So God’s choice of the actual world could not have been motivated by the desire to maintain such glory and bliss, for he cannot lose such properties anyways. Therefore God must have had some other motive, which Bayle rather vaguely suggests is simply God’s goodness.

The problem for us is not with what Bayle writes, but with Leibniz’s response.

Although Bayle concedes that God is supremely happy, he denies that the desire to maintain his happiness had any part in God’s choice of world. Leibniz, however, describes Bayle’s maxim as “very good”. This seems odd, given the passages that we have considered

(including one from the Theodicy itself) in which Leibniz does seem to think that God’s choice of a world is determined by God’s desire to maintain his own happiness.

The way to remove the oddity is, I think, to consider what Leibniz writes after claiming that Bayle’s maxim is very good. For Leibniz tells us what it is about the maxim that prompts him to declare it good: praising God benefits creatures but not God himself, and

God desired the good of creatures. Both of these claims are in fact compatible with the interpretation that I have developed. While God’s happiness is maintained by creating the

156 G VI 167/T §116.

91 best possible world, it is not part of my interpretation that God’s happiness is maintained by the praises of creatures in particular. Moreover, Leibniz does not claim that God desired the good of creatures for their sake. Rather, Leibniz could be claiming that God desired the good of creatures for his own sake. In short, I suggest that when Leibniz declares Bayle’s maxim to be very good, he is not declaring the entire maxim to be very good. He is only referring to those parts of the maxim that he actually lists.

In this chapter we considered two inadequate arguments for why Leibniz’s God chooses the best. These are that such a choice follows from the PSR, and that it follows from the nature of the will. We also considered Leibniz’s official argument, which crucially invokes God’s goodness. I argued that the goodness in question should be understood as God’s goodness to himself. A suboptimal world would compromise God’s supreme happiness, so he only chooses the best.

92 5. The cosmological argument

In the previous chapter we considered the application of the PSR to God’s choice of a world.

In this final chapter we shall consider the application of the PSR to the existence of God. In particular, we shall consider Leibniz’s cosmological argument. The cosmological argument has a long tradition, going back at least to medieval philosophers such as Avicenna and

Aquinas, and arguably back to Plato himself.157 But Leibniz’s version is particularly well known. His argument has in fact reached canonical status: it is simply referred to as the

“Leibnizian cosmological argument” in the contemporary literature, and its soundness remains the subject of vigorous debate.158

Yet despite reaching canonical status, Leibniz’s own formulations of the argument tend only to be treated in passing, or as part of general summaries of his philosophy of religion.159 His formulations are, in fact, surprisingly difficult to interpret. They are

157 Avicenna gives his argument in many places, such as in his Remarks and Admonitions III.11-12, Inati 123-124. Aquinas’ versions of the cosmological argument are found in his Summa Theologiae I.2.3, HP 53-54, and are discussed more fully in Kenny (1980). Plato’s version is found in the Timaeus 28a-29a, Cooper 1234-1235. 158 For a detailed overview of this debate, see Pruss (2012). Well-known discussions of the argument are found in Mackie (1982: 82-87) and Taylor (1992: 100-108), as well as in the popular debate between Russell and Copleston (printed in Russell 1967: 138-159). 159 See Russell (1900: 175-177), Rescher (1967: 150-151), Broad (1975: 153-156), Craig (1980: 257- 281), Blumenfeld (1995: 364-376), Savile (2000: 43-49), Lin (2011: 198-200), Woolhouse (2010: 115), Arthur (2014: 187-188), Look (2014: 9-11), and Lascano (2018: 517-519). Exceptions include

93 surprisingly difficult because the argument itself seems so simple: no matter how far back we go in the series of contingent things, a sufficient reason for the existence of the entire series cannot be found in the series itself; we must therefore appeal to a being outside the series, which will necessarily exist and is ultimately identified as God.

The chief interpretive difficulty, I think, stems from the fact that it is not clear what exactly God is supposed to explain. In this chapter I will consider three interpretations that seek to address this difficulty. The first, which I shall call the mereological interpretation, suggests that God explains why the whole series exists, where the whole is something over and above its parts. The second, which I shall call the modal interpretation, suggests that

God explains why the series is possible. And the third, which I shall call the contrastive interpretation, suggests that God explains why this series exists rather than another. I will argue that the mereological and modal interpretations fail, and that the contrastive interpretation is correct. First, though, we must examine Leibniz’s formulation of the argument itself.

1. Leibniz’s formulation of the cosmological argument

Grünbaum (2005), though he is more interested in the validity of Leibniz’s argument than matters of interpretation, and Laerke (2011), whose interpretation I will discuss in §3.

94 Leibniz advances his cosmological argument in a great many places, starting from his youth to the end of his life.160 Yet the formulation that has received by far the most attention is found in On the Ultimate Origination of Things (1697). I will follow this trend and focus my discussion on this text. In §4, however, I will show how my interpretation fits with earlier and later formulations of the argument as well.

Leibniz’s cosmological argument in On the Ultimate Origination of Things is as follows:

For we cannot find in any of the individual things, or even in the entire collection and series of things, a sufficient reason for why they exist. Let us suppose that a book on the elements of geometry has always existed, one copy always made from another. It is obvious that although we can explain a present copy of the book from the previous book from which it was copied, this will never lead us to a complete explanation, no matter how many books back we go, since we can always wonder why there have always been such books, why these books were written, and why they were written the way they were. What is true of these books is also true of the different states of the world, for the state which follows is, in a sense, copied from the preceding state, though in accordance with certain laws of change. And so, however far back we might go into previous states, we will never find in those states a complete explanation for why, indeed, there is any world at all, and why it is the way it is. I certainly grant that you can imagine that the world is eternal. However, since you assume only a succession of states, and since no reason for the world can be found in any one of them whatsoever (indeed, assuming as many of them as you like won’t in any way help you to find a reason), it is obvious that the reason must be found elsewhere. For in eternal things, even if there is no cause, we must still

160 Conversation with Steno (1677), CP 113; On the Ultimate Origination of Things (1697), G VII 302-303/AG 149-150; Theodicy (1710), G VI 106/T §7; Principles of Nature and of Grace (1714), G VI 602/AG 209-210.

95 understand there to be a reason. … From this it follows that even if we assume the eternity of the world, we cannot escape the ultimate and extramundane reason for things, God.161

There are at least two features of this particular formulation of the argument that are worth noting. One concerns just how much Leibniz is willing to concede. He concedes whichever ontology of the world one prefers, so long as it consists of a series of contingent, dependent beings. It does not matter if these beings are bodies, souls, or both. Leibniz also concedes that the series may be eternal and that it consists of an infinite number of members. These concessions are significant because previous philosophers had used precisely the opposite claims in their own cosmological arguments. Al-Kindī, for example, had argued that the world must have a beginning in time, and that God must have caused this beginning.162

Aquinas had also argued that an infinite regress of states is impossible, and that God must be invoked to stop this regress.163 By conceding these claims, Leibniz has, as it were, given God less work to do. Indeed, what is left for God to explain?

The other feature worth noting concerns Leibniz’s use of the phrase “complete explanation” [rationem plenam]: “It is obvious that although we can explain a present copy of the book from the previous book from which it was copied, this will never lead to a complete explanation, no matter how many books back we go …”. This might suggest that

Leibniz’s argument relies on a contrast between partial explanations on the one hand, and complete explanations on the other. Perhaps each book is only partially explained by the one

161 G VII 302-303/AG 149-150. 162 §12 and §13 of On Divine Unity and the Finitude of the World’s Body, MR 21. 163 Summa Theologiae I.2.3, HP 53-54.

96 prior to it, for no complete explanation of a book can be given when it has an infinite number of causal antecedents. So there is something about each individual book that remains unexplained, and God is invoked to fill that explanatory gap. This is a tempting thought, and

Leibniz does seem to endorse it in at least one text. Consider what he writes in The

Confession of Nature Against Atheists (1669):

But there remains a doubt as to why it [a body] fills this much space and this particular space rather than another; for example, why it should be three feet long rather than two, or why square rather than round. … [I]f you say that it was made square by the motion of another body, there remains the question of why it should have had any determinate figure before such motion acted upon it. And if you refer the reason for this, in turn, to the motion of another body as cause, and so to infinity, each of your replies will again be followed by a question through all infinity, and it will become apparent that this basis for asking about the reason for each reason will never be removed, so that no full reason for the figure will ever be given.164

Leibniz supposes an infinite regress of bodies. The shape of any particular body is explained by the impact of another body, and so on to infinity. Leibniz seems to conclude from this that the explanation of the original body’s shape is nevertheless incomplete, for due to the infinite regress “no full reason for the figure will ever be given.”

What Leibniz writes in the Confession of Nature, however, does not give us the key to what Leibniz means by “complete explanation” in On the Ultimate Origination of Things.

There are three reasons for this. First, the Confession of Nature is a very early text, written when Leibniz was only twenty-three. While this does not mean that it should be dismissed

164 A.6.1.490-492/L 110-111.

97 out of hand, it does mean that the text should be handled with caution in attempting to interpret another text written some thirty years later. Second, Leibniz’s concern in the

Confession of Nature is only with explaining a feature of something in the world. He is not concerned with explaining some general feature of the world itself. So the two texts are not analogous in their purpose. Third, if the problem that Leibniz identifies in On the Ultimate

Origination of Things really was the same as that identified in the Confession of Nature, then we might wonder how God is supposed to solve it. Using the analogy of the books, it would seem that God would have to make a direct causal contribution to the book so that it goes from being partially explained to being completely explained. But this cannot be right. For given that each book in the series has an infinite number of causal antecedents, God would have to make a direct causal contribution to each and every book in the series, in addition to his usual acts of conservation and concurrence. This would make God far too causally involved in the world by Leibniz’s standards. After all, one of the chief features of Leibniz’s philosophy is that God does not directly interfere in the world’s activity, aside from the occasional miracle.

My own view is that Leibniz’s argument is not relying on a contrast between partial and complete explanations. When he says that each book is explained by a prior book, he means that it is completely explained by the prior book. Everything about the one book is explained by the one prior to it. And when he says that this still does not give us a complete explanation, he does not mean that there is something about an individual book that is unexplained. Rather, it is something about the series of books that is unexplained. Let us now consider some options as to what that unexplained feature might be.

98 2. The mereological interpretation

Perhaps the most obvious option is that God explains why the series as a whole exists. While each part of the series is explained by a prior part, there exists something over and above the parts, namely the whole itself, which remains unexplained. This is the sort of cosmological argument that Clarke advances in his A Demonstration of the Being and Attributes of God

(1705). Clarke considers whether an infinite series of “dependent beings” could exist without anything else existing. He dismisses this as absurd:

But, if we consider such an infinite progression as one entire endless series of dependent beings, it is plain this whole series of beings can have no cause from without of its existence because in it are supposed to be included all things that are, or ever were, in the universe. And it is plain it can have no reason within itself for its existence because no one being in this infinite succession is supposed to be self- existent or necessary (which is the only ground or reason of existence of anything that can be imagined within the thing itself, as will presently more fully appear), but every one dependent on the foregoing. And, where no part is necessary, it is manifest the whole cannot be necessary – absolute necessity of existence not being an extrinsic, relative, and accidental denomination but an inward and essential property of the nature of the thing which so exists.165

Clarke clearly assumes that there must be an explanation for the series itself. Yet what could that explanation be? It cannot appeal to a being outside of the series, for by hypothesis only

165 Dem II, p. 10.

99 the series exists. But it cannot appeal to a being within the series either, for none of them are necessary in themselves. Now according to Clarke, the beings stand to the series as parts to a whole. And the modal properties of the whole depend on those of its parts. So if the parts are not absolutely necessary, then neither is the whole. This means that there is no sufficient reason for why the whole exists. The existence of nothing but an infinite series would be a brute fact.

Clarke’s argument is the target of a famous objection by Hume. In his Dialogues

Concerning Natural Religion (1779), Hume observes that each part is explained by the one prior to it. This is an observation with which Clarke would agree. But Hume goes on to deny that there is a whole that exists over and above its parts. By excising the whole, Hume excises the brute fact that afflicts it (though Hume himself would be more willing to tolerate brute facts than Clarke). So the existence of an infinite series of dependent beings is not a brute fact after all. Hume has his character Cleanthes put the point as follows:

In such a chain too, or succession of objects, each part is caused by that which preceded it, and causes that which succeeds it. Where then is the difficulty? But the WHOLE, you say, wants a cause. I answer, that the uniting of these parts into a whole, like the uniting of several distinct counties into one kingdom, or several distinct members into one body, is performed merely by an arbitrary act of the mind, and has no influence on the nature of things. Did I show you the particular causes of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me, what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts.166

166 Dialogues IX, p. 92-93.

100 Hume’s point is that there is no whole out there in the world. It is simply the product of a mental act, one which unites the various parts for the sake of convenience.

Now which side would Leibniz have endorsed: Clarke’s argument or Hume’s objection? In On the Ultimate Origination of Things Leibniz does seem to distinguish between “individual things [singulorum]” and “the entire collection and series of things [toto aggregato serieque rerum]”. This might seem to suggest that Leibniz saw the collection or series as a whole existing over and above its parts. In that case Leibniz’s cosmological argument would be an appropriate target for Hume’s objection. But this cannot be right. For

Leibniz explicitly denies that an infinite series forms a whole at all. Consider what Leibniz writes in a Letter to Des Bosses (1 September 1706):

I maintain, strictly speaking, that an infinite composed from parts is neither one nor a whole, and it is not conceived as a quantity except through a fiction of the mind. The indivisible infinite alone is one, but it is not a whole; that infinite is God.167

In this text Leibniz distinguishes between being a unity (or one) [unum], and being a whole

[totum]. Following Harmer, let us characterize this distinction as follows: a unity is an entity that lacks parts, whereas a whole is a collection of parts considered at the same time.168 Now

Leibniz denies that an infinite collection is either a unity or a whole. It is easy to see why he would deny that it is a unity, for unities lack parts. It is less easy to see why he would deny that it is a whole (Harmer suggests that it has to do with Leibniz’s denial of infinite

167 LDB 53. 168 Harmer (2014: 247). For more on Leibniz’s views on wholes and aggregates, see Lodge (2001).

101 number).169 What is clear, however, is that the only thing that exists in addition to the parts is a mental fiction that considers the infinite collection as a whole. But this is very far from what is required by the mereological interpretation. The mereological interpretation requires that there exist a real, mind-independent whole that exists over and above the parts. That is something that Leibniz simply denies.

It might be objected, however, that the infinite series that Leibniz considers in his

Letter to Des Bosses is not analogous to the infinite series that he considers in On the

Ultimate Origination of Things. In the former Leibniz is concerned with an infinite composed from parts [ex partibus], whereas in the latter Leibniz is concerned with an infinite collection of individual things [singulorum] or states [status]. I think that this objection can be met by observing that Leibniz elsewhere makes the same point with respect to different kinds of entities. In his Rationale of the Catholic Faith (mid 1680’s?), Leibniz puts the point in terms of bodies: “even if it were granted that there is a greater number of bodies than any assignable number, a single infinite whole still cannot be constructed from them.”170 And in

§195 of his Theodicy (1710), Leibniz puts the point in terms of substances: “infinity, that is to say, the accumulation of an infinite number of substances, is, properly speaking, not a whole any more than the infinite number itself.”171 Indeed, if the reason why an infinite collection cannot form a whole is simply because it lacks a definite quantity, then the point will hold regardless of the type of entities in question.

169 Harmer (2014: 250). 170 A.6.4.2316/LGR 73. 171 G VI 232/T §195.

102 It might also be objected that in his Letter to Des Bosses Leibniz says nothing about whether the members of the series are causally dependent, whereas in On the Ultimate

Origination of Things he is explicitly concerned with members each of which is dependent on some prior member(s). Perhaps such dependency is sufficient to produce a real whole that exists over and above its parts, thus vindicating the mereological interpretation. We can see that this is not so, however, by considering what Leibniz writes in a Letter to Arnauld (28

November/8 December 1686):

I hold that a block of marble is not a complete single substance, any more than the water in a pond together with all the fish it contains would be, even if all the water and all the fish were frozen, or any more than a flock of sheep would be, even if these sheep were tied together so that they could only walk in step and so that one could not be touched without all the others crying out. There is as much difference between a substance and such a being as there is between a man and a community, such as a people, an army, a society, or a college; these are moral beings, beings in which there is something imaginary and dependent on the fabrication of our mind.172

Leibniz makes a negative point followed by a positive point. His negative point is that a variety of proposed conditions on parts are insufficient for substancehood. These include having each part touch at least one other part (like a frozen pond of fish), having all the parts move in the same direction (like a flock of sheep tied together), and having all the parts causally connected (like a flock of sheep that all bleat if one of them is touched). But this negative point is not our concern, in that being a substance is not the same as being a whole.

For according to Leibniz substances are unities, and we have already seen that unities lack

172 G II 76/AG 79.

103 parts. Our concern, rather, is with Leibniz’s positive point. His positive point is that even if all these conditions obtain (including causal dependence), the only being that results is a fictional being. As Leibniz puts it, such collections are “beings in which there is something imaginary and dependent on the fabrication of our mind [ou il y a quelque chose d’imaginaire et de dependant de la fiction de nostre esprit].” Not only does the causal connection of parts fail to give us a substance; it fails to give us a real, mind-independent whole as well.

We are now in a position to return to the question of whether Leibniz would have endorsed Clarke’s argument or Hume’s objection. What is striking is that, in the relevant respects at least, Leibniz’s mereological commitments are very similar to those of Hume’s.

In fact Hume’s claim that “the uniting of these parts into a whole … is performed merely by an arbitrary act of the mind, and has no influence on the nature of things” could have been written by Leibniz himself. Far from endorsing Clarke’s claim that God must explain a whole over and above its parts, Leibniz would have agreed with Hume’s objection. Wholes do not exist outside of minds. Instead, they exist as products of minds, and are to be explained as such.

3. The modal interpretation

104 The failure of the mereological interpretation suggests that we look elsewhere for what God is supposed to explain. Mogens Laerke advances a highly original alternative.173 According to Laerke, what God explains is not why the series exists, but why the series is possible. As

Laerke puts it, “the cosmological argument [in On the Ultimate Origination of Things] derives the existence of God, not from the experience of the existence of actual things, but rather from the conceivability or possibility of these things whose existence we experience.”174 While our experience of the world shows us that it exists, it also shows us that the world is possible. It is this possibility that God is supposed to explain.

It may seem as if this suggestion flies in the face of what Leibniz actually says. For, when it comes to the series of things, Leibniz claims that we cannot find among them “a sufficient reason for why they exist [sufficiens ratio existendi].”175 In On the Ultimate

Origination of Things, Leibniz seems concerned with existence, not possibility. But Laerke has a response to this worry. According to Laerke, Leibniz claims that the series exists to show that the series is possible. This is an a posteriori proof of possibility. Leibniz distinguishes this from an a priori proof of possibility in his Meditations on Knowledge,

Truth, and Ideas (1684):

Moreover, we can know the possibility of a thing either a priori or a posteriori. The possibility of a thing is known a priori when we resolve a notion into its requisites, that is, into other notions known to be possible, and we know that there is nothing incompatible among them. This happens, among other cases, when we understand the way in which a thing can be produced, whence causal definitions are more useful

173 Laerke (2011: 77-82). 174 Laerke (2011: 77-78), emphases in original. 175 G VII 302/AG 149, emphasis added.

105 than others. The possibility of a thing is known a posteriori when we know through experience that a thing actually exists, for what actually exists or existed is at very least possible. And, indeed, whenever we have adequate knowledge, we also have a priori knowledge of possibility, for having carried an analysis to completion, if no contradiction appears, then certainly the notion is at least possible. I won’t now venture to determine whether people can ever produce a perfect analysis of their notions or whether they can ever reduce their thoughts to primitive possibilities or to irresolvable notions or (what comes to the same thing) to the absolute attributes of God, indeed to the first causes and the ultimate reason for things.176

To give an a priori proof of possibility is extremely difficult. It requires providing a complete analysis of the thing in question. Such an analysis will not simply analyze the notion of the thing into its more primitive notions; it will also analyze those more primitive notions into even more primitive notions, all the way to “irresolvable notions [notiones irresolubiles]”. As Leibniz suggests, such irresolvable notions are notions of the divine attributes. It is not surprising that Leibniz expresses hesitancy over whether any finite person could ever provide such an a priori proof. It would require an incredibly long analysis, tracing the relevant notions back to God himself.

It is much easier, then, to give an a posteriori proof of possibility. This only requires that one know by experience that the thing in question exists. For if the thing exists, then it is clearly possible. Now Laerke thinks that Leibniz’s talk of the series of things existing is just an a posteriori proof of their possibility, as an a priori proof is much too difficult.177 Laerke also observes that there would be something circular or redundant about giving an a priori

176 G IV 425/AG 26, emphases in original. 177 Laerke (2011: 78-79).

106 proof as part of a cosmological argument. For if an a priori proof requires analyzing the notion of a thing back to the notions of the divine attributes, then the completion of such a proof would by itself show that God exists.178

Laerke’s interpretation is a novel one, and it does provide an answer to what God is supposed to explain. It suffers, however, from the following dilemma. The dilemma exploits the fact that Laerke’s answer is ambiguous. What exactly does Laerke mean when he says that Leibniz’s cosmological argument derives God’s existence from the “possibility of these things whose existence we experience”?179 Does it mean that God explains why actual things are possible? Or does it mean that God explains why, when actual things were merely possible, they were nevertheless real?

Suppose it is the former: God explains why actual things are possible. Now for

Leibniz, if something is possible, it is because its essence is not self-contradictory. Given that what is not self-contradictory cannot become self-contradictory at some point in time, it is an eternal truth whether or not something is possible. But Leibniz emphatically rejects the

Cartesian view that God explains why the eternal truths have the content that they do.180 This means that he cannot hold that God explains why actual things are possible.

178 Laerke (2011: 79-80). 179 Laerke (2011: 77-78), emphasis in original. 180 Leibniz provides objections to the Cartesian view in his Letter to Eckhard (1677), G I 253/L 181; in his Letter to Philipp (1680), G IV 285/D 4; in §2 of the Discourse on Metaphysics (1686), A.6.4.1532-1533/AG 36; and in §176 of his Theodicy (1710), G VI 219/T §176. These objections are all different: in the Letter to Eckhard Leibniz objects that the Cartesian view implies a self- contradiction in God; in the Letter to Philipp he objects that it cannot make sense of God’s faculties; in the Discourse on Metaphysics he objects that such a God is not praiseworthy; and in the Theodicy he objects that such a God is not to be trusted. Note also that the difference between Descartes and Leibniz here concerns the role of God’s will in determining the content of eternal truths, not in God’s

107 But suppose it is the latter: God explains why, when actual things were merely possible, they were nevertheless real. Unlike the first suggestion, this is an argument that

Leibniz endorses. So Laerke would be right to that extent. The problem, however, is that

Leibniz thinks that this is a different argument for God’s existence than his cosmological argument. To show this I will first provide a rational reconstruction of this argument, and then consider it in Leibniz’s own words.181

Let us first distinguish between two kinds of eternal truths. A universal eternal truth is an eternal truth that has a universal as its subject, such as the eternal truth that a triangle has three sides. An individual eternal truth, by contrast, is an eternal truth that has an individual as its subject, such as the eternal truth that Alexander defeats Darius. Now let us concede the following controversial premises. First, there are both universal eternal truths and individual eternal truths. Second, there must be something in virtue of which eternal truths are true – eternal truths must have a ground. Third, the ground of an eternal truth must itself be eternal. The question, of course, is what could possibly ground eternal truths.

Leibniz’s answer is that such truths are grounded in eternal essences. For example, the universal eternal truth that a triangle has three sides is grounded in the universal eternal essence of triangularity, whereas the individual eternal truth that Alexander defeats Darius is grounded in the individual eternal essence of Alexander. The latter type of essence can also be called a possible, for it can be instantiated as an actually existing substance, namely as

Alexander himself.

intellect as that in which eternal truths have their being. For such a reading of Descartes’ view of the ontology of eternal truths, see Rozemond (2008). For more on the Cartesian view, see Kaufman (2005). 181 For extensive discussion of the argument, see Adams (1994: 177-191) and Newlands (2013).

108 Now let us consider the ground of essences. Although the essences that we are considering do not actually exist, an individual eternal essence could exist as the essence of an actual substance. However, such essences are not nothing either. Instead, they have an intermediate degree of existence, which Leibniz calls “reality [realité]”. Now for another controversial premise: if something is real, then its reality depends on something that actually exists. Because eternal essences are real, they must depend on something that actually exists.

And because eternal essences are eternal, they must depend on something that is also eternal.

Only God both actually exists and is eternal. So we have the following chain of grounds: eternal truths are grounded in eternal essences, which are grounded in an eternal God. As

Leibniz goes on to argue, the way in which they are grounded is by being ideas in God’s mind. Essences, then, are simply ideas, though ideas that are both eternal and real.

This is only a sketch of Leibniz’s argument, one which skates over much controversial territory. It is, however, more precise than Leibniz’s own formulations of the argument. These formulations tend to be brief, sometimes convoluted, and individually inadequate to give a full sense of the argument. My own reconstruction is based on combining what Leibniz writes in On the Reality of Truth (1677), Specimen of Discoveries

(1686?), On the Ultimate Origination of Things (1697), and the Monadology (1714).182

Leibniz gives the argument in §43 and §44 of the Monadology as follows:

43. It is also true that God is not only the source of existences, but also that of essences insofar as they are real, that is, or the source of that which is real in possibility. This is because God’s understanding is the realm of eternal truths or that

182 A.6.4.18-19/SLT 181; A.6.4.1618/LoC 307; G VII 304-305/AG 151-152; G VI 614/AG 218.

109 of the ideas on which they depend; without him there would be nothing real in possibles, and not only would nothing exist, but also nothing would be possible. 44. For if there is reality in essences or possibles, or indeed, in eternal truths, this reality must be grounded in something existent and actual, and consequently, it must be grounded in the existence of the necessary being, in whom essence involves existence, that is, in whom possible being is sufficient for actual being.183

Leibniz does distinguish in this text between reality and existence, and between eternal truths and ideas. In both cases, Leibniz observes that the there is some kind of dependency of the former on the latter. By contrast, he treats essences, possibles, and ideas as equivalent. I take it that Leibniz’s concern is with individual eternal truths and the individual eternal essences on which they depend. As we have seen, these can indeed be called possibles. And, as

Leibniz observes, “if there is reality in essences or possibles, or indeed, in eternal truths, this reality must be grounded in something existent and actual [il faut bien que s’il y a une realité dans les Essences ou possibilités, ou bien dans les verités éternelles, cette realité soit fondée en quelque chose d’Existant et d’Actuel]”. As the capitalization in the original French indicates, this being is God.

What all this shows is that God does explain why, when actual things were merely possible, they were nevertheless real. But notice that this is a different argument for God’s existence than the cosmological argument. Regardless of what exactly God is supposed to explain, Leibniz’s cosmological argument is clearly concerned with states of the actual world, not with the status of mere possibles. He also makes no mention of eternal truths, the essences on which they depend, the distinction between reality and existence, or that the

183 G VI 614/AG 218.

110 former must depend on the latter. Moreover, Leibniz himself takes them to be different arguments. We can see this in the selection from the Monadology just considered. Leibniz had given his cosmological argument right beforehand. He then writes, “It is also true [Il est vray aussi] that God is not only the source of existences, but also [mais encore] that of essences insofar as they are real, that is, or the source of that which is real in possibility.”184

On this way of understanding Laerke’s view, however, they are actually the same argument.

I take this as reason not to endorse Laerke’s interpretation.

4. The contrastive interpretation

We are so far at a loss as to what exactly Leibniz’s God is supposed to explain. But let us look again at On the Ultimate Origination of Things. There Leibniz begins by saying that we cannot find in the series of individual things “a sufficient reason for why they exist

[sufficiens ratio existendi].”185 By itself, this is not particularly informative. And it seems open to Hume’s objection which, as we have seen, Leibniz would have endorsed. For if each state in the series is explained by a prior state, and if there is no whole over and above the

184 G VI 614/AG 218, emphases added. 185 G VII 302/AG 149.

111 states, then what is left to explain? The answer, I suggest, is that there is no explanation for why this infinite series exists rather than another.186

We can see that this is Leibniz’s intention by reconsidering his book analogy. Leibniz writes: “we can always wonder why there have always been such books, why these books were written, and why they were written the way they were [cum semper mirari liceat, cur ab omni tempore libri tales extiterint, cur libri scilicet et cur sic scripti].”187 Even if we grant that an infinite series of books on geometry has always existed, that each book is explained by a prior book, and that there is no whole over and above the books themselves, we can always ask why there are all these books on geometry. Why not an infinite series of books on, say, botany instead? Likewise for the states of the world: “we will never find in those states a complete explanation for why, indeed, there is any world at all, and why it is the way it is [nunquam in statibus rationem plenam repereris, cur scilicet aliquis sit potius Mundus, et cur talis].”188 For even if each state of the world is explained by a prior state, there are lots of other possible worlds the states of which are also explained by an infinite series of prior states. Why then this particular infinite series rather than another?

This contrastive interpretation makes the best sense, I think, of On the Ultimate

Origination of Things. It also makes the best sense of some of Leibniz’s other formulations of the argument. In what follows I will examine three of Leibniz’s other formulations. One of these comes from a text written twenty years before On the Ultimate Origination of Things;

186 Lascano (2018: 518-519) also seems to endorse this interpretation. However, she does so in half a paragraph of a survey article on seventeenth century arguments for God’s existence. I take my discussion to be much more extensive than her understandably brief discussion of the argument. 187 G VII 302/AG 149. 188 G VII 302/AG 149.

112 the other two come from texts written at least ten years after it. As we shall see, the contrastive interpretation works for these other texts as well.

In his early Conversation with Steno (1677), Leibniz writes:

The series of things could have been otherwise, absolutely speaking (i.e., its being otherwise does not imply a contradiction). For this reason, even if one cause is resolved into another to infinity, e.g., I am such because of such and such a cause, which in turn is such because of such and such a cause, and so on to infinity; nevertheless, however far we proceed a new question always remains, and a sufficient reason cannot be found in the series. Hence, it must be outside the series.189

Leibniz begins by observing that the series of things could have been otherwise. Given his denial of counterfactual identity, I take him to mean that it is absolutely possible for a different series to exist, not that it is absolutely possible for the same series to be different than it is. Leibniz then claims that if the series consists of an infinite number of dependent states, “a new question always remains, and a sufficient reason cannot be found in the series”. One option as to the identity of this new question is that, for each state of the series, there will be a new question as to why that state is the way it is. This is tempting but, I believe, mistaken. For notice that Leibniz claims that “For this reason … a new question always remains …”. The reason to which Leibniz refers is just the claim that a different series could have existed. So while the question “why is this particular state the way it is?” can always be answered by appealing to a prior state, there is always the new question of why this series of states exists when another series of states is also possible. That new

189 CP 113.

113 question cannot be answered by appealing to a state within the series, but must appeal to something outside of it.

Leibniz provides a better-known presentation of his cosmological argument in §7 of the Theodicy (1710):

God is the first reason of things: for such things as are bounded, as all that which we see and experience, are contingent and have nothing in them to render their existence necessary, it being plain that time, space and matter, united and uniform in themselves and indifferent to everything, might have received entirely other motions and shapes, and in another order. Therefore one must seek the reason for the existence of the world, which is the whole assemblage of contingent things, and seek it in the substance which carries with it the reason for its existence, and which in consequence is necessary and eternal. Moreover, this cause must be intelligent: for this existing world being contingent and an infinity of other worlds being equally possible, and holding, so to say, equal claim to existence with it, the cause of the world must needs have had regard or reference to all these possible worlds in order to fix upon one of them.190

We have here the same argument as the one found in the much earlier Conversation with

Steno. We have the claim that the world is contingent, for a different world could have existed with different motions and shapes, and those in a different order. We also have an inference to the claim that the sufficient reason for the world cannot be found in the world itself. Again, because the inference proceeds from the fact that a different world could have existed, what must be explained is why this world exists rather than another. This is further supported by Leibniz’s observation that the necessary being must be intelligent. For there is

190 G VI 106/T §7, emphases in original.

114 an infinity of other possible worlds that the necessary being must have cognized before actualizing one of them.

The most explicit support for the contrastive interpretation, however, comes from the

Principles of Nature and of Grace (1714):

7. So far we have just spoken as simple physicists; now we must rise to metaphysics, by making use of the great principle, little used, commonly, that nothing takes place without sufficient reason, that is, that nothing happens without it being possible for someone who knows enough things to give a reason sufficient to determine why it is so and not otherwise. Assuming this principle, the first question we have the right to ask will be, why is there something rather than nothing? For nothing is simpler and easier than something. Furthermore, assuming things must exist, we must be able to give a reason for why they must exist in this way, and not otherwise. 8. This sufficient reason for the existence of the universe cannot be found in the series of contingent things, that is, in the series of bodies and their representations in souls; for, since matter is in itself indifferent to motion and rest, and to one motion rather than another, we cannot find in matter the reason for motion, still less the reason for a particular motion. And although the present motion found in matter comes from the preceding motion, and it, in turn, comes from a preceding motion, we will not make any progress in this way, however far back we go, for the same question always remains.191

One of the more striking features of this text is that Leibniz explicitly invokes a contrastive version of the PSR, demanding “a reason sufficient to determine why it is so and not otherwise [une Raison qui suffise pour determiner, pourquoy il en est ainsi, et non pas autrement].” This version of the PSR demands that there are answers to two contrastive

191 G VI 602/AG 209-210, emphases in original.

115 questions: why is there something rather than nothing, and why these things rather than others? Leibniz then continues in §8 to advance the familiar claim that the sufficient reason for the universe’s existence cannot be found in the universe itself. This is ambiguous between the sufficient reason for the universe existing rather than not (the first question), and this universe existing rather than another (the second question). What Leibniz goes on to write suggests that he is primarily concerned with the second question. For he goes on to write that there is nothing about the nature of matter that can explain motion, much less a particular motion. What then can explain the motion of matter in our world? The explanation cannot simply appeal to the nature of matter itself. But while the motion of any particular body can be explained by the motion of some other body, “we will not make any progress in this way, however far back we go, for the same question always remains.”

What is this same question? Again, one option is just that it is the question of why a particular body has the motion that it does, where the particular body is one that has been invoked to explain the motion of some other body. Another option is that it is the question of why there is motion at all, given that motion cannot be explained by appealing to matter itself. This could constitute another argument for the existence of God, and indeed Leibniz gives such an argument elsewhere:

The principle of motion is one of the ways of leading us to the divinity. It is true that every body which is in motion is pushed by another body which, being in motion itself, is also pushed by another. And it always continues like this to infinity, or rather until a first motion is reached. But this first motion could not have its origin in bodies, since a body only ever pushes after having been pushed. We must therefore have recourse to a higher cause. But even if there was no first motion, and even if it were supposed that the chain of causes, or of bodies which push each other, continues to

116 infinity, we would still be obliged to look for the true cause of motion in something incorporeal, which must be found outside the infinite sequence of bodies.192

While the motion of a particular body can be explained by the motion of another body, either this will end in a finite regress or it will continue in an infinite regress. If the former, then there is a first body which did not receive its motion from another body. If the latter, then we still need an explanation for why there is motion in the universe at all. Either way we need to appeal to an incorporeal giver of motion. While that could be a non-divine incorporeal being,

Leibniz seems to think that we are well on the way to proving the existence of God.

I believe that both of these options are incorrect, for the same reason. For notice that

Leibniz introduces all this talk of motion in the Principles of Nature and of Grace to make a larger point. The point is that such facts about motion give us reason to believe that “[the] sufficient reason for the existence of the universe cannot be found in the series of contingent things”. My suggestion is that we read Leibniz as claiming that the sufficient reason for the existence of this universe rather than another cannot be found in the universe alone. This is because we know that the universe consists at least partly of matter, and we also know that there is nothing about matter that demands that it have some particular motion, or even motion at all. So while our world does have an infinite series of bodies in motion, there is another possible world with an infinite series of bodies with different motions. In fact, there is another possible world with an infinite series of bodies with no motion at all. Therefore there must be a sufficient reason for why our world exists rather than any of these others.

That is, we need an answer to Leibniz’s second contrastive question.

192 God is the Sufficient Reason for the World (1692-3), A.1.9.15/LGR 64.

117

In this chapter I have examined Leibniz’s deceptively simple cosmological argument. I considered three different interpretations that try to make sense of what exactly God is supposed to explain. The mereological interpretation has God explain the whole series, where the whole is something over and above its parts. The modal interpretation has God explain why the series is possible. And the contrastive interpretation has God explain why this series exists rather than another. I defended the contrastive interpretation, which makes the best sense, I think, of both On the Ultimate Origination of Things and of other texts.

118 Conclusion

We have come to the end of this dissertation. Given that a chapter-by-chapter summary was already provided in the Introduction, I will not repeat such a summary here. Instead, I will briefly summarize the dissertation’s main results, and then conclude by identifying some topics for further investigation.

The world is a large and complicated place. While there is much that we do not know, we do know that the PSR is true in our world. We can then demand an explanation for why this world exists rather than another. The only possible explanation is that it was actualized by a necessary being. This necessary being, which we may call “God”, possesses an intellect

(for it cognizes the various options), as well as a will (for it chooses between them). By virtue of desiring to maintain his own supreme happiness, God chooses the best possible world. While it is tempting to think that the PSR is absolutely necessary, violations of the

PSR are in fact absolutely possible. Nevertheless, all else being equal a world in which the

PSR is true is better than a world in which it is false. For the investigation of the world’s explanatory structure allows creatures to perfect their minds and facilitates their worship of

God. This increases their happiness, which contributes to the perfection of their world. And the perfection of the world ensures that God’s own happiness is maintained. So God will create a world in which the PSR is true.

That, in a nutshell, is the view that I attribute to Leibniz. There are, however, some related topics that I have not addressed in this dissertation. The first concerns Leibniz’s uses

119 of the PSR. I have tried to give a fair sense of the chief ways in which Leibniz employs his great principle. These include arguments against gravity, mind-body occasionalism, absolute space, indiscernible bodies, vacua, atoms, as well as arguments for the existence of God.

However, I have not attempted to describe or even canvas all of the uses to which Leibniz puts the PSR. In particular, I have not discussed Leibniz’s PSR-based arguments against mind-body interaction, random atomic swerves, and tipping yet fully balanced scales.193 As these are all arguments in which Leibniz invokes the PSR, a complete treatment would discuss them as well.

Second, I have not examined how Leibniz’s own ontology satisfies the PSR. This is because the outcome of such an examination obviously depends on what we take Leibniz’s ontology to be. If it is an ontology of hylomorphic compounds, then it may be that the PSR is satisfied through a combination of formal, final, efficient, and material explanations. But if it is an ontology of completely immaterial substances, then the PSR might be satisfied through formal, final, and efficient explanations, but not through material explanations. It is well beyond the scope of this dissertation to answer the vexed question of whether Leibniz should be understood as some type of hylomorphist or as some type of idealist. Consequently, I have not attempted to answer the question of how Leibniz’s ontology satisfies the PSR.

Finally, I have not considered the history of the PSR after Leibniz.194 A simple narrative has it that the PSR was enthusiastically taken up by Wolff and Baumgarten, demolished by Hume, relegated to the realm of appearances by Kant, and further demolished

193 Mind-body interaction: Theodicy (1710), G VI 136/T §60. Atomic swerves: Theodicy (1710), G VI 316/T §340. Tipping scales: Second Letter to Clarke (December 1715), G VII 356/LC L2.1. 194 Such a history is briefly given by Rescher (1995: 1-23).

120 by twentieth-century physics. This simple narrative raises both a historical and a philosophical question. The historical question is whether the narrative is more of a contemporary retelling than one told by earlier philosophers. The philosophical question is whether the demolitions alleged by this narrative are as severe as the narrative suggests.

These are large and interesting questions. Their answers, however, will have to be pursued elsewhere.

121 References

Leibniz sources

A Sämtliche Schriften und Briefe. Berlin: Akademie Verlag, 1923-.

AG Philosophical Essays, edited and translated by Roger Ariew and Daniel

Garber. Indianapolis and Cambridge: Hackett, 1989.

C Opuscules et fragments inédits de Leibniz, edited by Louis Couturat. Paris:

Félix Alcan, 1903.

CP Confessio philosophi: Papers Concerning the Problem of Evil, 1671-1678,

translated and edited by Robert C. Sleigh, Jr.. New Haven: Yale University

Press, 2005.

D The Philosophical Works of Leibnitz, translated by George Martin Duncan.

New Haven: Tuttle, Morehouse & Taylor, 1890.

DSR De Summa Rerum: Metaphysical Papers, 1675-76, translated by G. H. R.

Parkinson. New Haven: Yale University Press, 1992.

Dutens Opera Omnia, edited by Ludovici Dutens. Geneva: Fratres De Tournes, 1768.

G Die philosophischen Schriften von Gottfried Wilhelm Leibniz, edited by C. I.

Gerhardt. Berlin: Weidmann, 1875-90.

122 GLW Briefwechsel zwischen Leibniz und Christian Wolff, edited by C. I. Gerhardt.

Halle: H. W. Schmidt, 1860.

GM Die mathematische Schriften von Gottfried Wilhelm Leibniz, edited by C. I.

Gerhardt. Halle: H. W. Schmidt, 1855.

Grua Textes inédits, edited by Gaston Grua. Paris: Presses Universitaires de France,

1948.

K Die Werke von Leibniz, edited by Onno Klopp. Hannover: Klindworth Verlag,

1864-84.

L Philosophical Papers and Letters, second edition, edited by Leroy E.

Loemker. Dordrecht: D. Reidel, 1969.

LC The Leibniz-Clarke Correspondence, edited by Roger Ariew. Indianapolis and

Cambridge: Hackett, 2000.

LDB The Leibniz-Des Bosses Correspondence, translated and edited by Brandon C.

Look and Donald Rutherford. New Haven: Yale University Press, 2007.

LDV The Leibniz-De Volder Correspondence, edited and translated by Paul Lodge.

New Haven: Yale University Press, 2013.

LGR Leibniz on God and Religion: A Reader, translated and edited by Lloyd

Strickland. London: Bloomsbury, 2016.

LH Die Leibniz-Handschriften der Königlichen Öffentlichen Bibliothek zu

Hannover. Edited by Eduard Bodemann. 1895.

LoC The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672-

1686, edited and translated by Richard T. W. Arthur. New Haven: Yale

University Press, 2002.

123 M The Leibniz-Arnauld Correspondence, translated by H. T. Mason.

Manchester: Manchester University Press, 1967.

Mollat Mittheilungen ans Leibnizens ungedruckten Schriften, edited by Georg Mollat.

Leipzig: H. Haessel, 1893.

MP Philosophical Writings, edited by G. H. R. Parkinson, translated by Mary

Morris and G. H. R. Parkinson. London: J. M. Dent, 1973.

NE New Essays on Human Understanding, translated and edited by Peter

Remnant and Jonathan Bennett. Cambridge: Cambridge University Press,

1996.

R Leibniz: Political Writings, edited and translated by Patrick Riley. Cambridge:

Cambridge University Press, 1988.

S Monadology and Other Philosophical Essays. Translated by Paul Schrecker

and Anne Martin Schrecker. New York: Macmillan, 1965.

SLT Leibniz: The Shorter Leibniz Texts, translated by Lloyd Strickland. London:

Continuum, 2006.

T Theodicy, translated by E. M. Huggard. La Salle: Open Court, 1985.

Other primary sources

AT Oeuvres de Descartes, edited by Charles Adam and Paul Tannery. Paris: J.

Vrin, 1969.

124 Barnes The Complete Works of Aristotle, edited by Jonathan Barnes. Princeton:

Princeton University Press, 1984.

Cooper Plato: Complete Works, edited by John M. Cooper and D. S. Hutchinson.

Indianapolis: Hackett, 1997.

CSM The Philosophical Writings of Descartes, translated by John Cottingham,

Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University

Press, 1984.

Curley The Collected Works of Spinoza, edited and translated by Edwin Curley.

Princeton: Princeton University Press, 1985, 2016.

Dem Samuel Clarke, A Demonstration of the Being and Attributes of God and

Other Writings, edited by Ezio Vailati. Cambridge: Cambridge University

Press, 1998.

Dialogues David Hume, “Dialogues Concerning Natural Religion.” In Dialogues

Concerning Natural Religion and The Natural History of Religion, edited by

J. C. A. Gaskin. Oxford: Oxford University Press, 1993.

Geb Spinoza Opera, edited by Carl Gebhardt. Heidelberg: C. Winter, 1925.

HP Thomas Aquinas, Basic Works, edited by Jeffrey Hause and Robert Pasnau.

Indianapolis: Hackett, 2014.

IG Hellenistic Philosophy: Introductory Readings, second edition, translated by

Brad Inwood and L. P. Gerson. Indianapolis: Hackett, 1997.

KRS The Presocratic Philosophers, second edition, edited by G. S. Kirk, J. E.

Raven, and M. Schofield. Cambridge: Cambridge University Press, 1983.

125 Molesworth The English Works of Thomas Hobbes of Malmesbury, edited by William

Molesworth. Aalen: Scientia Aalen, 1962.

MR Classical Arabic Philosophy: An Anthology of Sources, translated by Jon

McGinnis and David C. Reisman. Indianapolis: Hackett, 2007.

Nadler Nicolas Malebranche, Philosophical Selections, edited by Steven Nadler.

Indianapolis: Hackett, 1992.

Inati Ibn Sina, Remarks and Admonitions: Physics and Metaphysics, translated by

Shams C. Inati. New York: Columbia University Press, 2014.

Treatise David Hume, A Treatise of Human Nature, edited by David Fate Norton and

Mary J. Norton. Oxford: Clarendon Press, 2007.

Voss René Descartes, The Passions of the Soul, translated by Stephen H. Voss.

Indianapolis: Hackett, 1989.

Secondary sources

Adams, Robert Merrihew. “Must God Create the Best?” The Philosophical Review 81, no. 3

(1972): 317-332.

Adams, Robert Merrihew. “Primitive Thisness and Primitive Identity.” The Journal of

Philosophy 76, no. 1 (1979): 5-26.

Adams, Robert Merrihew. Leibniz: Determinist, Theist, Idealist. New York and Oxford:

Oxford University Press, 1994.

126 Arthur, Richard T. W. Leibniz. Cambridge: Polity, 2014.

Beck, Lewis White. Early German Philosophy: Kant and His Predecessors. Harvard:

Belknap Press, 1969.

Beeley, Philip. “Leibniz and Hobbes.” In The Continuum Companion to Leibniz, edited by

Brandon Look, 32-50. London: Continuum, 2011.

Bennett, Jonathan. A Study of Spinoza’s Ethics. Indianapolis: Hackett, 1984.

Blumenfeld, David. “Leibniz’s ontological and cosmological arguments.” In The Cambridge

Companion to Leibniz, edited by Nicholas Jolley, 353-381. Cambridge: Cambridge

University Press, 1995.

Blumenfeld, David. “Perfection and happiness in the best possible world.” In The Cambridge

Companion to Leibniz, edited by Nicholas Jolley, 382-410. Cambridge: Cambridge

University Press, 1995b.

Broad, C. D. Leibniz: An Introduction. Cambridge: Cambridge University Press, 1975.

Brody, Baruch. “Leibniz’s Metaphysical Logic.” Rice University Studies 63 (1977): 43-55.

Brown, Gregory. “Leibniz on the Possibility of a Spatial Vacuum, the Connectedness

Condition on Possible Worlds, and Miracles.” In Leibniz on Compossibility and

Possible Worlds, edited by Gregory Brown and Yual Chiek, 201-226. Springer, 2016.

Carriero, John. “Leibniz on Infinite Resolution and Intra-mundane Contingency: Part Two:

Necessity, Contingency, and the Divine Faculties.” Studia Leibnitiana 27 (1995): 1-

30.

Chernoff, Fred. “Leibniz’s Principle of the Identity of Indiscernibles.” The Philosophical

Quarterly 31, no. 123 (1981): 126-138.

Couturat, Louis. La Logique de Leibniz. Paris: Félix Alcan, 1901.

127 Couturat, Louis. “Sur la Métaphysique de Leibniz.” Revue Métaphysique et de Morale 10

(1902): 1-25.

Craig, William Lane. The Cosmological Argument from Plato to Leibniz. London:

Macmillan, 1980.

Curley, E. M. “The Root of Contingency.” In Leibniz: A Collection of Critical Essays, edited

by Harry G. Frankfurt, 69-97. Garden City: Anchor, 1972.

Dasgupta, Shamik. “Metaphysical Rationalism.” Noûs 50 (2016): 379-418.

Della Rocca, Michael. Spinoza. New York: Routledge, 2008.

Della Rocca, Michael. “PSR.” Philosophers’ Imprint 10 (2010): 1-13.

Della Rocca, Michael. “Playing with Fire: Hume, Rationalism, and a Little Bit of Spinoza.”

In The Oxford Handbook of Spinoza, edited by Michael Della Rocca. Oxford: Oxford

University Press, 2014. DOI: 10.1093/oxfordhb/9780195335828.013.019.

Della Rocca, Michael. “Review of Gonzalo Rodriguez-Pereyra, Leibniz’s Principle of

Identity of Indiscernibles.” Notre Dame Philosophical Reviews, 2015.

Frankel, Lois. “From a Metaphysical Point of View: Leibniz and the Principle of Sufficient

Reason.” The Southern Journal of Philosophy 24 (1986): 321-334.

Garber, Daniel. “Leibniz and the Foundations of Physics: The Middle Years.” In The Natural

Philosophy of Leibniz, edited by Kathleen Okruhlik and James Robert Brown, 27-

130. Dordrecht: D. Reidel, 1985.

Garber, Daniel. Leibniz: Body, Substance, Monad. Oxford: Oxford University Press, 2009.

Goldenbaum, Ursula. “Indivisibilia Vera – How Leibniz Came to Love Mathematics.” In

Infinitesimal Differences: Controversies between Leibniz and his Contemporaries,

edited by Ursula Goldenbaum and Douglas Jesseph, 53-94. Berlin: De Gruyter, 2008.

128 Griffin, Michael V. Leibniz, God and Necessity. Cambridge: Cambridge University Press,

2013.

Grünbaum, Adolf. “Does Leibniz’s Principle of Sufficient Reason License His Primordial

Existential Question “Why Is There Something Contingent, Rather Than Nothing?”

In Homo Sapiens und Homo Faber, edited by Gereon Wolters and Martin Carrier,

147-156. Berlin: De Gruyter, 2005.

Hanfling, Oswald. “Leibniz’s Principle of Reason.” Studia Leibnitiana 9 (1981): 67-73.

Harmer, Adam. “Leibniz on Infinite Numbers, Infinite Wholes, and Composite Substances.”

British Journal for the History of Philosophy 22, no. 2 (2014): 236-259.

Ishiguro, Hidé. Leibniz’s Philosophy of Logic and Language, second edition. Cambridge:

Cambridge University Press, 1990.

Jauernig, Anja. “The Modal Strength of Leibniz’s Principle of the Identity of Indiscernibles.”

Oxford Studies in Early Modern Philosophy (2008): 191-225.

Jolley, Nicholas. Leibniz. London and New York: Routledge, 2005.

Jorati, Julia. “Divine Faculties and the Puzzle of Incompossibility.” In Leibniz on

Compossibility and Possible Worlds, edited by Gregory Brown and Yual Chiek, 175-

199. Springer, 2016.

Jorati, Julia. “The Contingency of Leibniz’s Principle of the Identity of Indiscernibles.” Ergo

4, no. 31 (2017): 899-929.

Kaufman, Dan. “God’s Immutability and the Necessity of Descartes’ Eternal Truths.”

Journal of the History of Philosophy 43, no. 1 (2005): 1-19.

Kenny, Anthony. The Five Ways: St. Thomas Aquinas’ Proofs of God’s Existence. Notre

Dame: University of Notre Dame Press, 1980.

129 Laerke, Mogens. “Leibniz’s Cosmological Argument for the Existence of God.” Archiv für

Geschichte der Philosophie 93 (2011): 58-84.

Lascano, Marcy P. “Arguments for the existence of God.” In The Routledge Companion to

Seventeenth Century Philosophy, edited by Dan Kaufman, 505-535. Abingdon and

New York: Routledge, 2018.

Levey, Samuel. “The Paradox of Sufficient Reason.” Philosophical Review 125, no. 3

(2016): 397-430.

Lin, Martin. “Leibniz’s Philosophical Theology.” In The Continuum Companion to Leibniz,

edited by Brandon Look, 192-207. London: Continuum, 2011.

Lin, Martin. “Rationalism and Necessitarianism.” Noûs 46, no. 3 (2012): 418-448.

Lin, Martin. “The Principle of Sufficient Reason in Spinoza.” In The Oxford Handbook of

Spinoza, edited by Michael Della Rocca, 133-154. Oxford: Oxford University Press,

2013. DOI: 10.1093/oxfordhb/9780195335828.013.011.

Lin, Martin. “Leibniz on the Modal Status of Absolute Space and Time.” Noûs 50, no. 3

(2016): 447-464.

Lodge, Paul. “Leibniz’s Notion of an Aggregate.” British Journal for the History of

Philosophy 9, no. 3 (2001): 467-486.

Lodge, Paul. “The Empirical Grounds for Leibniz’s ‘Real Metaphysics’.” The Leibniz

Review 20 (2010): 13-36.

Look, Brandon. “Grounding the Principle of Sufficient Reason: Leibnizian Rationalism

and the Humean Challenge.” In The Rationalists: Between Tradition and Innovation,

edited by Carlos Fraenkel, Dario Perinetti, and Justin E. H. Smith, 201-219. New

York: Springer, 2011.

130 Look, Brandon. “Leibniz’s Metaphysics: The Path to the Monadology.” In The Continuum

Companion to Leibniz, edited by Brandon Look, 89-109. London: Continuum, 2011b.

Look, Brandon. “Leibniz’s Arguments for the Existence of God.” In The Oxford Handbook

of Leibniz, edited by Maria Rosa Antognazza. Oxford: Oxford University Press,

2014. DOI: 10.1093/oxfordhb/9780199744725.013.010.

Mackie, J. L. The Miracle of Theism: Arguments for and against the Existence of God.

Oxford: Clarendon, 1982.

Mates, Benson. The Philosophy of Leibniz: Metaphysics and Language. New York: Oxford

University Press, 1986.

McCrae, Robert. Leibniz: Perception, Apperception, and Thought. Toronto: University of

Toronto Press, 1976.

Mondadori, Fabrizio. “Reference, Essentialism, and Modality in Leibniz’s Metaphysics.”

Studia Leibnitiana 5 (1973): 74-101.

Nadler, Steven. “Choosing a Theodicy: The Leibniz-Malebranche-Arnauld Connection.”

Journal of the History of Ideas 55, no. 4 (1994): 573-589.

Newlands, Samuel. “Leibniz and the Ground of Possibility.” Philosophical Review 122, no. 2

(2013): 155-187.

Parkinson, G. H. R. Logic and Reality in Leibniz’s Metaphysics. Oxford: Clarendon Press,

1965.

Parkinson, G. H. R. “Philosophy and Logic.” In The Cambridge Companion to Leibniz,

edited by Nicholas Jolley, 199-223. Cambridge: Cambridge University Press, 1995.

131 Parkinson, G. H. R. “Sufficient Reason and Human Freedom in the Confessio Philosophi.” In

The Young Leibniz and his Philosophy, edited by Stuart Brown, 199-222. Dordrecht:

Kluwer, 1999.

Piro, Francesco. “For a History of Leibniz’s Principle of Sufficient Reason. First

Formulations and Their Historical Background.” In Leibniz: What Kind of

Rationalist?, edited by Marcelo Dascal, 463-478. Dordrecht: Springer, 2008.

Pruss, Alexander R. The Principle of Sufficient Reason: A Reassessment. Cambridge:

Cambridge University Press, 2006.

Pruss, Alexander R. “The Leibnizian Cosmological Argument.” In The Blackwell

Companion to Natural Theology, edited by William Lane Craig and J. P. Moreland,

24-100. Malden, MA: Blackwell, 2012.

Raven, Michael J. “Is Ground a Strict Partial Order?” American Philosophical Quarterly 50

(2013): 193-201.

Rescher, Nicholas. “Contingence in the Philosophy of Leibniz.” The Philosophical Review

61, no. 1 (1952): 26-39.

Rescher, Nicholas. The Philosophy of Leibniz. Englewood Cliffs: Prentice-Hall, 1967.

Rescher, Nicholas. Satisfying Reason: Studies in the Theory of Knowledge. Dordrecht:

Kluwer, 1995.

Rescher, Nicholas. On Leibniz: Expanded Edition. Pittsburgh: University of Pittsburgh Press,

2013.

Rodriguez-Pereyra, Gonzalo. “The Principles of Contradiction, Sufficient Reason, and

Identity of Indiscernibles.” In The Oxford Handbook of Leibniz, edited by Maria Rosa

132 Antognazza. Oxford: Oxford University Press, 2013. DOI:

10.1093/oxfordhb/9780199744725.013.002.

Rodriguez-Pereyra, Gonzalo. Leibniz’s Principle of Identity of Indiscernibles. Oxford:

Oxford University Press, 2014.

Rodriguez-Pereyra, Gonzalo. “Grounding is not a Strict Order.” Journal of the American

Philosophical Association 1 (2015): 517-534.

Rozemond, Marleen. “Descartes’s Ontology of the Eternal Truths.” In Contemporary

Perspectives on Early Modern Philosophy: Essays in Honor of Vere Chappell, edited

by Paul Hoffman, David Owen, and Gideon Yaffe, 41-63. Peterborough: Broadview,

2008.

Rozemond, Marleen. “Mills Can’t Think: Leibniz’s Approach to the Mind-Body Problem.”

Res Philosophica 91, no. 1 (2014): 1-28.

Russell, Bertrand. A Critical Exposition of the Philosophy of Leibniz. Cambridge: Cambridge

University Press, 1900.

Russell, Bertrand. Why I am not a Christian. London: Unwin, 1967.

Rutherford, Donald. “Leibniz’s Principle of Intelligibility.” History of Philosophy Quarterly

9, no. 1 (1992): 35-49.

Rutherford, Donald. Leibniz and the Rational Order of Nature. Cambridge: Cambridge

University Press, 1995.

Savile, Anthony. Routledge Philosophy GuideBook to Leibniz and the Monadology. London:

Routledge, 2000.

Schlesinger, George N. “A Pragmatic Version of the Principle of Sufficient Reason.” The

Philosophical Quarterly 45 (1995): 439-459.

133 Schmaltz, Tad M. “Malebranche and Leibniz on the Best of all Possible Worlds.” The

Southern Journal of Philosophy 48, no. 1 (2010): 28-48.

Schnieder, Benjamin and Alex Steinberg. “Without Reason?” Pacific Philosophical

Quarterly 97 (2016): 523-541.

Sleigh, Robert. “Truth and Sufficient Reason in the Philosophy of Leibniz.” In Leibniz:

Critical and Interpretive Essays, edited by Michael Hooker, 209-242. Minneapolis:

University of Minnesota Press, 1982.

Sleigh, Robert. “Leibniz on the Two Great Principles of All Our Reasonings.” Midwest

Studies in Philosophy 8 (1983): 193-216.

Sleigh, Robert. Leibniz & Arnauld: A Commentary on their Correspondence. New Haven

and London: Yale University Press, 1990.

Sleigh, Robert. “Remarks on Leibniz’s Treatment of the Problem of Evil.” In The Problem of

Evil in Early Modern Philosophy, edited by Elmar J. Kremer and Michael J. Latzer,

165-179. Toronto: University of Toronto Press, 2001.

Taylor, Richard. Metaphysics, fourth edition. Englewood Cliffs: Prentice Hall, 1992.

Vailati, Ezio. Leibniz and Clarke: A Study of Their Correspondence. New York and Oxford:

Oxford University Press, 1997. van Inwagen, Peter. An Essay on Free Will. Oxford: Clarendon Press, 1983. van Inwagen, Peter. Metaphysics, fourth edition. Boulder: Westview, 2015.

Vinci, Thomas C. “What is the Ground for the Principle of the Identity of Indiscernibles in

Leibniz’s Correspondence with Clarke?” Journal of the History of Philosophy 12, no.

1 (1974): 95-101.

134 Wiggins, David. “The Concept of the Subject Contains the Concept of the Predicate.” In On

Being and Saying: Essays for Richard Cartwright, edited by Judith Jarvis Thomson,

263-284. Cambridge, MA: The MIT Press, 1987.

Wiggins, David. “Sufficient Reason: a principle in diverse guises, both ancient and modern.”

Acta Philosophica Fennica 61 (1996): 117-132.

Woolhouse, Roger. Starting with Leibniz. London: Continuum, 2010.

135