Leibniz: truth, knowledge and metaphysics


Leibniz: truth, knowledge and metaphysics
Leibniz: truth, knowledge and metaphysics Nicholas Jolley Leibniz is in important respects the exception among the great philosophers of the seventeenth century. The major thinkers of the period characteristically proclaim the need to reject the philosophical tradition; in their different ways Descartes, Hobbes and Spinoza all insist that new foundations must be laid if philosophy is to achieve any sure and lasting results. Even Malebranche, who seeks to revive the teaching of Augustine, joins in the general chorus of condemnation of Aristotle and his legacy. Leibniz, by contrast, does not share in this revolutionary fervour. Although he is capable of criticizing the Aristotelian tradition, he is also careful to remark that much gold is buried in the dross.1 Leibniz of course is as enthusiastic as any of his contemporaries about the new mechanistic science; indeed, he is one of its most distinguished advocates and exponents. But by temperament Leibniz is not a revolutionary but a synthesizer; in philosophy, as in politics and religion, he deliberately sets out to mediate between opposing camps. As he himself said, ‘the majority of the sects are right in a large part of what they assert but not so much in what they deny’.2 The distinctive character of Leibniz’s reconciling project needs to be made a little clearer. Other philosophers in the period had of course also tried to show that the new science was compatible with natural theology. Descartes, for example, sought to find a place in his philosophy for such orthodox doctrines as the existence of a personal God and the immortality of the soul. But in contrast with Descartes, Leibniz sought to retain as much as possible of the Aristotelian framework and to combine it with the emerging scientific and philosophical ideas; we shall see, for example, that Leibniz seeks to fuse Aristotelian and Cartesian conceptions of the soul. The synthesizing spirit of Leibniz’s philosophy is one of its fascinations, but it is also a source of weakness; Leibniz sometimes seems to be trying to reconcile the irreconcilable. The structure of the present chapter is as follows. The first three sections are devoted to the analysis of Leibniz’s general metaphysics. In the first two sections we shall see how Leibniz formulates an Aristotelian theory of corporeal substance in his first mature work, the Discourse on Metaphysics (1686), and how he seemingly attempts to derive a number of metaphysical doctrines from purely logical considerations concerning truth. In the third section we shall see how in his later writings Leibniz abandons his theory of corporeal substance for a form of idealism; this is the famous doctrine of monads. In the fourth section we shall look at the anti-Newtonian theories of space and time which Leibniz formulated at the very end of his career. In the following section we shall study Leibniz’s somewhat ill-conceived attempt to apply his general theory of causality to the problem of the relationship between mind and body which Descartes bequeathed to his successors. Finally, in the last two sections we shall analyse Leibniz’s psychology and his theory of knowledge; here we shall see how Leibniz seeks to reinterpret some ideas deriving from Descartes and Spinoza. THE ARISTOTELIAN BACKGROUND: SUBSTANCE AND AGGREGATE The synthesizing spirit of Leibniz’s philosophy is clearly visible in Leibniz’s first mature work, the Discourse on Metaphysics, and in the correspondence with Arnauld which it precipitated. One way of looking at these works is to see that Leibniz is trying to revive Aristotelian doctrines about substance and to show that they are in conformity with the new science; indeed, they are largely free of the conceptual difficulties which plague the more recent Cartesian ideas. It is true that Leibniz thinks that Aristotle did not say the last word about substance. But it is still possible to see Leibniz as engaged in extending, rather than replacing, the Aristotelian project. We must begin by reminding ourselves of two very influential claims that Aristotle made about substance. First, for Aristotle, a substance is what may be termed an ‘ultimate subject of predication’. Thus, by this criterion Alexander is a substance because while we can predicate properties of Alexander—we can say, for instance, that he was a Macedonian—he himself is not predicable of anything else; there is nothing of which we can say that it is an Alexander. To put the point another way, the noun ‘Alexander’ can appear only in the subject position in a sentence and never in the predicate position. By contrast, honesty is a subject of predication but not an ultimate one; for though we can predicate properties of honesty, honesty itself is predicable of other things—for instance, a person who possesses the virtue.3 Second, in response to the characteristically Greek preoccupation with flux, Aristotle claims that substances are substrata of change: ‘The most distinctive mark of substance appears to be that while remaining numerically one and the same, it is capable of admitting contradictory qualities.’4 Thus, although he never instantiates both properties simultaneously, Alexander as an infant is two feet tall and as an adult, say, six feet tall. To say that Alexander is a substance is a way of drawing our attention to the fact that one and the same individual persists through the change in qualities. The relation between these two claims about substance is not entirely clear, but on the face of it, they do not seem to be equivalent; it seems that there could be items which are ultimate subjects of predication, even though they do not persist through time. A lightning flash, for example, is instantaneous, but it is a subject of predication which is not itself obviously predicable of anything else. Although Leibnizian substances characteristically satisfy the condition, in the Discourse on Metaphysics Leibniz is silent, at least officially, about the idea that substances are substrata of change. But early on in this work Leibniz approvingly cites Aristotle’s claim that substances are ultimate subjects of predication: ‘It is of course true that when several predicates are attributed to a single subject, and this subject is not attributed to any other, it is called an individual substance.’5 It is true that in the next breath Leibniz indicates that this definition is not fully satisfactory: ‘But this is not enough, and such an explanation is merely nominal.’6 Presumably Leibniz’s point is, not that the definition fails to capture necessary and sufficient conditions, but that it is somehow shallow compared with the one which, as we shall see, he goes on to propose. But in any case, whatever the grounds for his partial dissatisfaction, Leibniz seems to make fruitful use of the Aristotelian idea that substances are ultimate subjects of predication. In the Arnauld correspondence, in particular, Leibniz deploys this idea in order to reach anti-Cartesian conclusions about the status of bodies and at least to prepare the ground for the very Aristotelian thesis that the paradigm substances are organisms. In the correspondence with Arnauld Leibniz argues for a remarkable negative thesis; he seeks to show that most of the things which both the man in the street and the Cartesians take to be substances are not really substances at all. In general, Leibniz’s thesis is that no non-organic body is a substance. The argument in outline is as follows: 1 No aggregate is an ultimate subject of predication. 2 All non-organic bodies are aggregates. 3 Therefore, no non-organic body is an ultimate subject of predication (and hence not a substance). The basic idea behind the argument is that if the notion of an ultimate subject of predication is thought through, we shall see that it disqualifies tables, chairs and the like from counting as substances. Why does Leibniz think that an aggregate, such as an army, is not an ultimate subject of predication? An army of course is at least a subject of predication in the sense that we can ascribe various properties to it; we can say, for example, of a given army that it fought bravely. But it is not an ultimate subject of predication because in Leibniz’s words, ‘it seems…that what constitutes the essence of an entity through aggregation is only a state of being of its constituent entities; for example, what constitutes the essence of an army is only a state of being of the constituent men’.7 In the words of one recent commentator, an aggregate is a state of being of those entities that compose it in the sense that any truths about the aggregate can be expressed in propositions that ascribe modes and states to the composing entities without any need to refer to the aggregate itself.8 Thus, a proposition such as ‘The army fought bravely’ is reducible to propositions which ascribe various properties to the members of the aggregate, namely, the individual soldiers. Perhaps more controversial is the second premise of the argument. A nonorganic body such as a block of marble does not seem to be on a par with clearcut examples of aggregates such as an army or a flock of sheep. Leibniz must admit that a block of marble is more tightly bonded than these aggregates, but he would claim that this fact is not metaphysically significant; a block of marble is no less an entity by aggregation than a flock of sheep.9 But in that case what is a block of marble an aggregate of? At first sight it seems that Leibniz would say that a block of marble is an aggregate of physical parts which are themselves aggregates and so on ad infinitum. But though he shows some hesitancy on this issue, in the correspondence with Arnauld Leibniz suggests that a marble slab is an aggregate of organisms no less than a flock of sheep: ‘perhaps this marble block is merely a heap of an infinite number of living bodies, or is like a lake full of fish, although these animals are ordinarily visible only in half-rotten bodies.’10 This thesis draws support from the empirical discoveries made possible by the recent invention of the microscope. Thus Leibniz reaches an important negative conclusion which is in obvious conflict with Cartesian theses; no non-organic bodies are substances.11 But this conclusion still leaves open the question of Leibniz’s positive views on the issue of what items qualify as substances. Recent work has shown that around the time of the Discourse on Metaphysics Leibniz was remarkably hesitant on this issue; indeed, he flirted with a number of possible positions.12 He was perhaps particularly uncertain as to whether anything physical counted as a substance, but as we shall see, he also had doubts about the ontological status of souls. Despite his hesitations, the view to which he seems to have been most attracted is that organisms, and perhaps souls, are the only substances; organisms are what Leibniz calls ‘corporeal substances’. With regard to physical objects, then, Leibniz’s teaching is that every body is either itself a corporeal substance or an aggregate of corporeal substances. Leibniz’s somewhat tentative positive thesis raises an obvious question: why are organisms better candidates for substantiality than non-organic bodies? Leibniz’s short answer to this question is clear: organisms are not just aggregates but true unities, and every entity which is endowed with a true unity is a substance. For Leibniz, an organism is truly one by virtue of possessing a soul or principle of life which confers unity on it; in scholastic terminology the soul is said to inform the body. Indeed, Leibniz even goes so far as to revive the scholastic doctrine that the soul is the substantial form of the body; here he is drawing on the fact that in medieval philosophy it is the presence of a substantial form that makes a body a natural unity.13 The thesis that only the presence of a soul can confer unity on a body, and thus make it a genuine substance rather than an aggregate, obviously needs to be justified. Leibniz is not totally forthcoming on this subject, but he does throw out some suggestive hints which make it possible for us to see what he has in mind. In correspondence with Arnauld he explains that the unity of an aggregate is a matter of convention only.14 The unity of a university department, for example, is conventional in the sense that it depends on certain human interests; for teaching purposes, let us say, it is convenient to group a Leibniz specialist with a philosopher of language rather than with a seventeenth-century historian. But there is no metaphysical fact of the matter which determines this classification. The unity of a human body, however, is not at all like that. The fact that my hand and foot belong together, but not my hand and the table in front of me, is determined not by convention but by nature, or rather by the metaphysical truth that my soul animates my body. I can, for example, feel pain in my hand and foot, but I cannot feel pain in the table in front of me. Thus the presence of a soul provides a wholly non-conventional basis for classifying some physical parts together. Leibniz’s doctrine that organisms are true substances was the target of two shrewd objections from Arnauld. In the first place, Arnauld objected that Leibniz seemed to be smuggling in a merely stipulative definition of substance. As Arnauld sees it, Leibniz redefines substance as that which has a true unity, and on this basis he reaches the anti-Cartesian conclusion that no bodies except organisms are substances. But in that case he has covertly abandoned the traditional definition of substance as that which is neither a mode nor state; using more Aristotelian language, we could restate Arnauld’s point by saying that Leibniz has abandoned the definition of substance as an ultimate subject of predication.15 Leibniz is of course entitled to offer a stipulative definition of substance if he chooses, but he is not entitled to switch back and forth between such a definition and a more traditional one. Leibniz’s reply to this objection is important: he answers Arnauld by saying that far from abandoning Aristotle’s definition of substance he is simply drawing out a consequence of it: being a true unity is implied by being an ultimate subject of predication. Indeed, the concepts of a true unity and of an ultimate subject of predication are logically equivalent. ‘To be brief, I hold as axiomatic the identical proposition, which varies only in emphasis: that what is not truly one entity is not truly one entity either. It has always been thought that ‘one’ and ‘entity’ are interchangeable.’16 Arnauld also objected to Leibniz’s reintroduction of animal souls or substantial forms. As a good Cartesian, Arnauld made the familiar points against this doctrine; it is superfluous for the purposes of explaining animal behaviour, and it raises embarrassing difficulties concerning the status of animal souls after the destruction of their bodies. Arnauld cited the case of a worm both parts of which, when cut in two, continue to move as before, and challenged Leibniz as to what he would say about it.17 The serious philosophical point behind Arnauld’s raillery is that an animal is no more a genuine unity than a non-organic body such as a table. Thus the chopping up of a worm is in principle no different from the chopping up of a table; in both cases we are simply left with parts of the original body. In reply Leibniz seeks to reconcile the facts about the case of the worm with his thesis that animals are genuine substances which possess true unity by virtue of the souls which animate them. From the fact that both parts of the worm continue to move, it does not follow that we must postulate either two souls or none. The soul may continue to animate one of the parts, and it is this part which is strictly to be identified with the worm. In this sense the worm survives the division of its body.18 LOGIC AND METAPHYSICS The originally Aristotelian idea of substance as an ultimate subject of predication thus plays a major role in the Discourse on Metaphysics and the correspondence with Arnauld; it provides the basis for Leibniz’s persistent claim that substances are genuine unities. But as we have seen, Leibniz thinks that the Aristotelian doctrine does not go far enough. In the Discourse on Metaphysics Leibniz seeks a deeper understanding of what is involved in being a substance, and he finds it in what we may call the ‘complete concept theory’: this is the famous claim that ‘the nature of an individual substance or 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 the notion is attributed’.19 In the following sections of the Discourse Leibniz develops a train of thought which led Bertrand Russell and the French scholar, Couturat, to claim that Leibniz derived his metaphysics from his logic.20 As a general theory about the roots of Leibniz’s metaphysics, the Russell- Couturat thesis has come in for a good deal of criticism. For one thing, the thesis does not seem to apply to the writings of Leibniz’s later period; there purely logical theories seem to play little or no role in generating metaphysical doctrines. Even at the time of the Discourse, Leibniz appeals to non-logical considerations in support of his metaphysics. Leibniz invokes his physical theory that in collisions ‘bodies really recede from other bodies through the force of their own elasticity, and not through any alien force’.21 In this way Leibniz seeks to confirm his metaphysical doctrine that there is no causal interaction between substances. Moreover, at least as formulated by Russell, the so-called ‘logicist’ thesis suffers from a different kind of difficulty. According to Russell, Leibniz validly derived his metaphysics from his logic; against this, it has been remarked that there are in fact serious problems with the purported deduction. Considerations like these have led some writers to argue that Leibniz did not so much derive his metaphysics from his logic as tailor his logic to a metaphysics to which he is attracted for independent reasons.22 Nonetheless, there does seem to be some truth in the Russell-Couturat thesis. At least in the Discourse and other writings of the same period, Leibniz certainly seems to rely on logical premises in arguing for metaphysical conclusions. This is not to say that as it stands the deduction is watertight; at points Leibniz seems to be smuggling in certain unstated non-logical premises. The claim that Leibniz derived his metaphysics from his logic is more mysterious than it need be. When Russell and Couturat put forward this thesis, they had something quite specific in mind when they spoke of Leibniz’s ‘logic’: they were referring to his theory of truth. The theory of truth in question is explicitly stated, not in the Discourse on Metaphysics, but in the correspondence with Arnauld where it appears almost as an afterthought. However, the theory makes itself felt in the Discourse, for it seems to ground the deep analysis of the nature of substance which Leibniz offers as a supplement to Aristotle. Leibniz’s distinctive theory of truth can best be explained by way of contrast. Perhaps the most intuitive doctrine of truth is some version of the correspondence theory; in other words, truth consists in a relation of correspondence between propositions and states of affairs in the world. It is some version of the correspondence theory that Aristotle seems to have had in mind when he defined truth as saying of that which is that it is and of that which is not that it is not.23 Although he sometimes seems to suggest that he is simply following in Aristotle’s footsteps, Leibniz in fact advances a radically different theory. For Leibniz, truth consists not in a correspondence between propositions and states of affairs but in a relation between concepts. Leibniz provides a succinct summary of his theory in a letter to Arnauld: ‘In every true affirmative proposition, necessary or contingent, universal or particular, the concept of the predicate is in a sense included in that of the subject: praedicatum inest subjecto; or else I do not know what truth is.’24 Let us call this ‘the concept-containment theory of truth’. Leibniz’s theory of truth can be seen as a generalization of a more familiar and more limited claim. Consider the proposition: ‘Gold is a metal’. It is plausible to say that the proposition is true because the concept expressed by the predicate term is contained in the concept expressed by the subject term; in other words, an analysis of the concept of gold would reveal that the concept of metal is one of its constituent concepts. (Analysis is conceived of here as a matter of replacing a given term by its definitional equivalent.) As his comment to Arnauld shows, Leibniz wishes to extend this insight to all affirmative propositions, including singular ones such as ‘Julius Caesar crossed the Rubicon’. Thus Leibniz holds that the proper name ‘Julius Caesar’ is not simply an arbitrary label; it expresses a concept no less than the term ‘gold’ does. The proposition ‘Julius Caesar crossed the Rubicon’ is true because the concept of crossing the Rubicon is contained in the concept of Julius Caesar. From this general, conceptcontainment theory of truth Leibniz’s distinctive claim about the nature of individual substances follows as a special case; by virtue of the general theory, all the predicates which are true of an individual substance are contained in the concept of that substance.25 ‘From these considerations there follow a number of important paradoxes.’26 This remark in the Discourse is key evidence for the claim that Leibniz derived his metaphysics from his logic, and it is certainly true that Leibniz goes on to present a number of remarkable doctrines about the basic structure of the world. Commentators tend to come up with slightly different lists of the doctrines that are so derived, but there are five major doctrines which are generally included. 1 The identity of indiscernibles: there cannot be two substances which are exactly alike. 2 The expression thesis: every substance expresses or mirrors the whole universe. 3 The denial of causal interaction between (created) substances. 4 Every substance is the causal source of all its states. 5 The hypothesis of concomitance (or what is later termed by Leibniz ‘The pre-established harmony’): the states of substances are harmonized by God so that they give the appearance of causal interaction. (The phrase ‘preestablished harmony’ is also sometimes used by Leibniz and by commentators to refer to the conjunction of theses 3–5.) The relation of these doctrines to Leibniz’s logic is more problematic in some cases than in others. In the case of (at least one version of) the identity of indiscernibles, the derivation is relatively straightforward. The complete concept of an individual substance is presumably a concept under which no more than one individual can fall. Thus if there were two substances exactly alike there would be two substances with the same complete concept, which is impossible. It should be noted, however, that the complete concept theory seems to provide the basis for only a weak version of the identity of indiscernibles; for all the argument so far shows, this principle would be satisfied by two substances which differed solely in terms of their spatial relationships. However, for reasons which will become clearer, Leibniz in fact subscribes to a stronger version of the identity of indiscernibles to the effect that two substances cannot be exactly alike in terms of their intrinsic (i.e. non-relational) properties. Leibniz’s more popular statements about the identity of indiscernibles can be unhelpful. For example, Leibniz sometimes tries to provide a posteriori support for the principle by means of an anecdote; he tells how a courtier was challenged to find two leaves exactly alike, and how after a while he abandoned the search as fruitless.27 Picturesque as it is, this story is doubly misleading. First, in so far as it follows from the complete concept theory, the identity of indiscernibles is a thesis about substances. Strictly speaking, for Leibniz, dead leaves are not substances but aggregates of substances. Second, and more importantly, the identity of indiscernibles is not an empirical generalization but a necessary truth. The thesis is not that as a matter of contingent fact there are no two substances exactly alike, but that there could not be two such substances. More serious problems of derivation are presented by the other main metaphysical theses 2–5. Different commentators locate the main difficulties in different places, but they agree in the general diagnosis: Leibniz tends to slide from what is true at the level of concepts to claims about what is true at the level of substances in the world. Leibniz may have been unwittingly encouraged in this tendency by the imprecision of his terminology; as used by Leibniz, terms such as ‘subject’ and ‘predicate’ are dangerously ambiguous. The word ‘subject’ for example is ambiguous as between subject-concept and the substance in the world which instantiates the concept: mutatis mutandis, the term ‘predicate’ is similarly ambiguous.28 Bearing this ambiguity in mind, in the remainder of this section we shall, then, examine the problems presented by 2–4. Despite the unusual terminology, on one level at least the expression thesis is straightforward. Leibniz was pressed by Arnauld as to what he meant by ‘expression’, and in reply he made clear that it was a technical term which he explained as follows: ‘one thing expresses another (in my terminology) when there exists a constant and fixed relation between what can be said of one and of the other.’29 When Leibniz says that every substance expresses the whole universe, at least part of what he wants to say is that, given a complete knowledge of the concept of any individual substance, say Alexander, it is possible in principle to read off the predicates (i.e. predicate-concepts) of every other substance. We can see that Leibniz must hold this by virtue of the fact that there are relational truths linking Alexander to everything else in the universe. It is a fact about Alexander, for example, that he was born so many years before Ronald Reagan became President of the United States. It follows, then, that all such relational predicates must be contained in the complete concept of Alexander, and so on for every other substance. Thus if one really knew the complete concept of Alexander, one would ipso facto also know everything there was to be known about the universe. When Leibniz says that every substance expresses the universe, he also wants to assert a more controversial and more metaphysical thesis. In the Discourse on Metaphysics Leibniz claims that ‘there are at all times in the soul of Alexander traces of everything that has happened to him and marks of everything that will happen to him, and even traces of everything that happens in the universe, even though God alone could recognize them all’.30 But of course it is not easy to see how from the fact that the concept of Alexander timelessly includes the predicate of dying in 323 BC, it follows that there must be marks of this event in Alexander’s soul even before it happens. It has been suggested that Leibniz is thinking along the following lines.31 Since it is a timeless fact about Alexander that he dies in 323 BC, throughout his history there must be something about Alexander himself by virtue of which this proposition is true; there must be some persistent structural modification of Alexander corresponding to the fact of his dying. This modification remains quiescent until the event when it bursts into activity; subsequently, it reverts to a state of quiescence. Commentators have similarly stressed the difficulty of seeing how theses 3 and 4 follow from Leibniz’s logic. From the fact that every individual substance has a complete concept Leibniz infers that all the states of a substance are a consequence of that concept; from this he concludes, apparently, that there is no causal interaction between created substances. But this argument seems fallacious.32 Consider the proposition: ‘Julius Caesar was killed by Brutus and Cassius.’ Here a causal relational predicate ‘killed by Brutus and Cassius’ is truly ascribed to Julius Caesar. This causal predicate must, then, be contained in the concept of Julius Caesar. But then it clearly does not follow from the complete concept theory that there is no causal interaction between created substances. Nor does it help matters to point out that, though in the Discourse Leibniz derives 4 from 3, he sometimes reverses the order of the derivation. For if it is difficult to see how 3 follows from the complete concept theory, it is no less difficult to see how 4 follows from that theory.33 One way of dealing with these problems is to suppose that the derivation of 3 from Leibniz’s logic is mediated by a doctrine that we have not so far discussed; this is the doctrine that ‘there are no purely extrinsic denominations’, which is itself a consequence of the ‘marks and traces’ version of the expression thesis.34 The claim that there are no purely extrinsic denominations is one of Leibniz’s more obscure doctrines, but is generally taken to assert the reducibility of relations; in other words, all relational truths about individual substances can be deduced from non-relational truths about those substances. For example, the relational proposition ‘Smith is taller than Jones’ is reducible in the sense that it can be derived from the non-relational propositions ‘Smith is six feet tall’, and ‘Jones is five feet ten inches tall’. Thus by virtue of his thesis that there are no purely extrinsic denominations, Leibniz would claim that the proposition ‘Julius Caesar was killed by Brutus and Cassius’ is reducible to propositions which ascribe only non-relational predicates to those individuals.35 But this approach does not really solve the problem. The thesis that there are no purely extrinsic denominations asserts at most that relational propositions are theoretically dispensable; it does not assert that such propositions are actually false. But it seems that it is the stronger thesis which is required if the claim that there are no purely extrinsic denominations is to provide a basis for 3; for Leibniz is committed by 3 to saying that propositions which assert causal relations between created substances are all of them, strictly speaking, false. An alternative way of dealing with these problems is to reinterpret Leibniz’s notion of a complete concept. One writer, in particular, has been impressed by those passages in which Leibniz tells Arnauld that the complete concept of an individual contains the laws of its world.36 On this basis it has been suggested that a Leibnizian complete concept is constituted by a combination of basic (i.e. non-relational) predicates and laws—the laws of its universe. These laws are taken to include a law of succession for the states of the substance; such a law would imply that a substance’s states causally depend only on itself. On this interpretation, then, there is no danger that the complete concept of Julius Caesar, say, will contain causal predicates such as being killed by Brutus or Cassius; such a predicate must be excluded because it suggests of course that a state of Julius Caesar causally depends on other created substances. We may still wonder, however, whether this interpretation can do justice to the expression thesis, given that relational predicates are excluded from complete concepts. But here again the crucial point is taken to be that laws are built into complete concepts. The idea is that the concept of an individual substance contains noncausal laws of coexistence with other substances; from this it follows, as the expression thesis requires, that the predicates of all other substances can be deduced from the concept of a given substance. It is in this sense, then, that ‘every individual substance involves the whole universe in its perfect concept’.37 This interpretation is attractive, for it frees Leibniz’s argument from its otherwise obvious invalidity. But as its proponent acknowledges, it does so at a heavy price; a complete concept turns out not to be a purely logical notion, for Leibniz has packed some of his metaphysics into it. Thus the difficulty now is not that Leibniz’s argument involves a non sequitur but that it is effectively questionbegging. Before we conclude this section, it is worth clarifying thesis 4— that every substance is the causal source of all its states. At a minimum Leibniz holds that every state of a substance is caused by an earlier state of that substance.38 But Leibniz seems to be committed to more than this when he claims, as he often does, that a substance gets all its states ‘out of its own depths’;39 this phrase suggests something crucial about the way in which the states of a substance are caused by its earlier states. In fact, Leibniz’s view of intra-substantial causality seems to draw on the ‘marks and traces’ version of the expression thesis. Remember that, according to that thesis, a substance bears within itself the marks of all its future states. Thus Leibniz holds that when an earlier state causes a later state, this later state was in a sense latent or dormant in the substance all along; when the state is caused, it emerges from quiescence and bursts into activity; subsequently, it reverts to a condition of quiescence. The causing of a state thus seems to be the activation of a ‘mark’ that was pre-existent in the substance throughout its previous history. THE DOCTRINE OF MONADS The metaphysical doctrines 1–5 which, in the Discourse on Metaphysics, Leibniz deduces from his logic all concern substances, and throughout his subsequent career Leibniz continues to assert these doctrines; they are some of the great constants of his philosophy. None the less, Leibniz’s metaphysics underwent a major development between the Discourse (1686) and the Monadology (1714). Although Leibniz never recants any of the five doctrines, he changes his mind about what sort of items really fall under the concept of substance. In the Discourse Leibniz holds, despite some hesitation, that all substances are either organisms or souls; in his later philosophy he comes to hold that, strictly speaking, there are no corporeal substances; rather, all substances are either souls or at least soul-like. The later philosophy is thus a form of idealism inasmuch as it maintains that the basic furniture of the universe is mental or spiritual in nature. This is the famous doctrine of monads.40 It may of course be questioned just how sharp this transition was, and it is true that there are times in his later writings when Leibniz speaks as if there really are corporeal substances. But the dominant character of Leibniz’s later metaphysics is well represented by his remark to De Volder: ‘Considering the matter carefully, it must be said that there is nothing in the world except simple substances and in them, perception and appetite.’41 Taken strictly, this claim implies that there are no corporeal substances. The term ‘monad’ derives from a Greek word for unity. The fact that Leibniz chose this term to denote the fundamental entities in his later metaphysics shows that there is continuity in his thought; as before in the Discourse and the correspondence with Arnauld, a substance is a genuine unity. But a monad, unlike a corporeal substance, is a unity in a quite straightforward sense; it has no parts, or, in other words, it is simple. Now the simplicity of monads is a clue to further aspects of their nature. Since they are simple, monads are immaterial —which, for Leibniz, means that they are spiritual, for everything material has parts. The simplicity of monads also entails, for Leibniz, that they are indestructible. Here the underlying idea is that destruction consists in decomposition, and that where there are no parts, there can be no decomposition. Hence, in the case of monads, ‘there is no dissolution to fear’.42 The fact that monads are immaterial and spiritual imposes a radical restriction on the properties of which they are capable; it rules out all such physical properties as size, shape and even position. As the quotation from the letter to De Volder bears out, the basic properties of monads are perception and appetite, or appetition. The notion of perception, which Leibniz defines as ‘the expression of the many in the one’,43 is central not just to Leibniz’s metaphysics but also to his psychology, and it will accordingly be discussed in the penultimate section of this chapter. But something may be said here about appetition. Appetition is the dynamic principle in the monad; it is that by virtue of which a monad changes its state. Yet, as one writer has suggested, it is possible that, for Leibniz, appetitions and perceptions are not two kinds of modifications but rather the same modification viewed differently. From one point of view every passing state is an expression of the many in the one and as such it is a perception. From the other point of view every passing state is a tendency to a succeeding state and as such it is an appetition.44 A possible parallel would be Spinoza’s doctrine that every finite mode of substance can be viewed under the attributes of both thought and extension. The doctrine of monads is not merely idealistic; it is also in a sense monistic. But the term ‘monism’ is a little misleading and needs clarification. Monadology is certainly not monistic in the sense in which Spinoza’s metaphysics is monistic; Leibniz is not asserting, as Spinoza does, that there is only one substance (Deus seu Natura). Rather, monadology is monistic in the sense that, according to Leibniz, there is only one kind of basic entities, namely souls. In this respect the contrast with Spinoza’s monism is at a maximum. Far from asserting that there is just one substance, Leibniz holds that there are infinitely many simple substances and that, by virtue of the identity of indiscernibles, no two are exactly alike. Monads are in fact hierarchically arranged. At the top of the hierarchy is God who seems to be the supreme monad;45 at the bottom of the hierarchy are what Leibniz calls ‘bare monads’ which provide the metaphysical foundation for inanimate matter. The basis for this hierarchical classification is quality of perception; borrowing Cartesian terminology, Leibniz says that monads differ in terms of the clarity and distinctness of their perceptions. For example, the minds of human beings are near the top of the hierarchy by virtue of their capacity for a very high grade of perception, namely reason. A striking feature of monadology, however, is that although monads differ enormously in terms of the quality of perception, in a sense they do not differ in terms of the objects they perceive; for giving a new twist to his expression thesis Leibniz holds that every monad perceives the whole universe according to its point of view. The qualification tacked on to this thesis is to be understood in terms of the doctrine that there are qualitative differences among perceptions. To say that two monads differ in their point of view is to say that they do not enjoy exactly the same distribution of clarity and distinctness over their perceptual states. In this way Leibniz can also explain how the identity of indiscernibles applies to monads in spite of the fact that they all perceive the whole universe. These are remarkable doctrines, and we may well wonder how Leibniz came to arrive at them. In fact, however, the basic argument for the fundamental principles of monadology is quite straightforward; it turns on two main assumptions: the infinite divisibility of matter and the thesis that there must be basic or ultimate entities. For Leibniz, it would be shocking to reason, or at least to divine wisdom, if everything in the universe were composed of compounds whose components were themselves compounds, and so on ad infinitum. The infinite divisibility of matter implies that these basic entities cannot be physical, for everything physical is a compound of the sort just described. Thus although physical atoms are a fiction, there can and must be ‘spiritual atoms’ or monads. A natural initial reaction to monadology is to wonder at Leibniz’s willingness to prefer it to the more down-to-earth metaphysics of the Discourse. But in response to the argument outlined above we may wonder why Leibniz was not in a position to advance it earlier. Certainly throughout his career Leibniz holds that the universe must consist of basic or ultimate entities. Moreover, in his earlier philosophy Leibniz also held a version of the thesis of the infinite divisibility of matter; matter, considered in abstraction from souls or substantial forms, is infinitely divisible ‘in innumerable possible ways but not actually divided in any’.46 So at the time of writing the Discourse Leibniz believed, as he continued to believe, that nothing purely material could be a basic entity. But the difference between Leibniz’s earlier and later views seems to be this. In the Discourse Leibniz held that, though in the abstract, matter is infinitely divisible, taken concretely it is composed of organisms which are material beings endowed with souls, and that these organisms are genuinely basic entities. In his later philosophy Leibniz may have continued to hold that matter is in some sense composed of organisms, but he gave up the thesis that organisms are genuinely basic entities or intrinsic natural unities. Why, then, did Leibniz give up the view that organisms are basic entities? A plausible answer is that he came to feel that some of the claims about substance which he had deduced from his logic did not clearly apply to organisms. According to the Discourse substances are indivisible but, as we saw earlier, in the correspondence with Arnauld Leibniz had difficulty defending the thesis that organisms are indivisible. Possibly Leibniz became dissatisfied with his answer to Arnauld’s puzzle about the worm that is cut in two. By contrast, monadology is largely free from these difficulties: as a simple, immaterial being a monad satisfies the indivisibility criterion much more clearly than an organism. Moreover, the earlier, Aristotelian metaphysics fares less well than monadology in accommodating the thesis that there is no causal interaction between substances. In the earlier metaphysics this thesis implies that no two organisms interact, but it has no such implications for other bodies; for instance, it does not entail that no two billiard balls interact. And this may well have come to seem arbitrary to Leibniz. By contrast, monadology suffers from no such problem. For one thing, it is perhaps fairly intuitive to say that souls cannot causally interact. But in any case, by restricting the thesis to souls or soul-like entities, Leibniz is at least able to escape the charge that he is simply drawing an arbitrary line through the physical world. An obvious problem for an idealist philosopher who holds that reality is ultimately spiritual is to determine the status of bodies. Leibniz’s idealism certainly implies that bodies cannot be substances, but beyond that it leaves their status unspecified. For one thing, idealism does not discriminate between eliminativist and reductionist approaches to this issue; in other words, it does not discriminate between the thesis that bodies do not exist and the thesis that, although bodies exist, they are to be reduced to something which is ontologically more basic. Fortunately, on this issue Leibniz leaves us in no doubt about his position: in a letter to De Volder he remarks: I do not really eliminate body, but I reduce it to what it is. For I show that corporeal mass, which is thought to have something over and above simple substance, is not a substance, but a phenomenon resulting from simple substances, which alone have unity and absolute reality.47 Leibniz is thus in some sense a reductionist about bodies; what is less clear is the nature of the reduction. Some writers have claimed that Leibniz anticipated Berkeley’s phenomenalism; they have thought that he came to espouse the thesis that bodies are sets of harmonized perceptions.48 Leibniz seems to have flirted with this thesis on occasion; in a very Berkeleian passage he tells Des Bosses: It is true that things which happen in the soul must agree with those which happen outside of it. But for this it is enough for the things taking place in one soul to correspond with each other as well as with those happening in any other soul, and it is not necessary to assume anything outside of all souls or monads. According to this hypothesis, we mean nothing else when we say that Socrates is sitting down than that what we understand by ‘Socrates’ and by ‘sitting down’ is appearing to us and to others who are concerned.49 Leibniz was certainly well placed to defend a version of phenomenalism. Other phenomenalists, such as Berkeley, who hold that the supply of souls or minds is finite are forced to analyse statements about the existence of physical objects in terms of statements about possible perceptions; they are forced to appeal to the perceptions which a mind would have in such and such circumstances. Leibniz, by contrast, does not have to take this line since he holds that the number of souls is infinite and that every possible point of view on the phenomena is actually occupied. Thus Leibniz can analyse all statements about the existence of physical objects in terms of other statements which are exclusively about the actual perceptions of monads.50 Phenomenalism, however, does not seem to be Leibniz’s considered view. Most characteristically Leibniz states that a physical object is, not a set of perceptions, but an aggregate of monads or simple substances. In saying this Leibniz is careful to point out that he does not mean that monads are parts of bodies; rather, any part of a body is itself physical, and since matter is infinitely divisible, there will be no part of matter which does not have parts which are themselves smaller bodies. Leibniz sometimes explains the relationship between bodies and monads by saying that bodies are ‘beings by aggregation’ which result from monads or simple substances.51 Bodies are also said to be ‘well-founded phenomena’;52 they are well-founded in the sense that they are appearances which are grounded in monads. Despite some differences in formulation, Leibniz’s main view seems to be that bodies are aggregates of monads. We may well wonder how this can be so; how can an aggregate of simple, unextended substances be identified with a physical object? It would seem that a physical object must have properties which no aggregate of monads could have. Certainly a physical object must have properties which no individual monad can have. Perhaps Leibniz would insist on the logical point that, from the fact that individual monads are unextended, it does not follow that an aggregate of monads is unextended; to suppose otherwise is to commit the fallacy of composition. This fits in well with Leibniz’s claim that ‘aggregates themselves are nothing but phenomena, since things other than the monads making them up are added by perception alone by virtue of the very fact that they are perceived at the same time’.53 In other words, to talk of aggregates is to go beyond the reality of the monads themselves and to make essential reference to the contribution of the perceiving mind. Alternatively Leibniz may hold, as he is traditionally interpreted as holding, that a body is not, strictly speaking, identical with an aggregate of monads; rather, an aggregate of monads is misperceived by us as a physical object having the properties of size, shape and position.54 According to Leibniz’s monadology, there is really nothing in the world but simple substances; strictly speaking, there are no corporeal substances. Leibniz makes only one concession to the privileged status which he had accorded organisms in his earlier philosophy: where organisms are concerned, in the corresponding aggregate of monads there is one monad which is dominant with respect to other members of the aggregate. The dominance relation is to be spelt out in terms of superior clarity and distinctness of perceptions. For example, in the case of human beings the mind is the dominant monad with respect to the aggregate of monads that constitute the body. But towards the end of his life Leibniz seems to have become dissatisfied with this theory; he appears to have felt that the ‘hypothesis of mere monads’ did not do justice to the unity possessed by organic bodies. In other words, the presence of a dominant monad was not enough to fill this role. Leibniz seems to suggest that, in addition, we must postulate something substantial which unifies the monads; this is what he came to call a ‘substantial bond’ (vinculum substantiale). Some scholars have expressed scepticism as to whether Leibniz ever committed himself to the theory of the vinculum substantiale.55 The basis for such scepticism is that Leibniz first proposed the theory in correspondence with the Jesuit Des Bosses who invited him to explain how monadology could accommodate the Catholic dogma of transubstantiation: this is the dogma that in the Eucharist the whole substance of the consecrated bread and wine is changed into the substance of the body and blood of Christ. It has thus been suggested that the doctrine of substantial bonds is merely the concession of a diplomat intent on accommodating Catholic dogma. But there are grounds for doubting this interpretation. In the first place, Des Bosses was not entirely happy with the theory of substantial bonds; he raised theological scruples against it. Second, and more importantly, the philosophical fit between the theory and the dogma of transubstantiation is not a very close one.56 The theory of substantial bonds is intended to account for the unity of organisms. The consecrated bread and wine, however, are not themselves organisms, but rather aggregates of them.57 Indeed the indications are that Leibniz was engaged in pursuing an independent train of thought about the unity of organisms which led him to the idea of substantial bonds, and that he then adapted this idea to meet the demands of the dogma of transubstantiation. SPACE AND TIME As we have seen, Leibniz speaks of monads as having points of view, but this expression is metaphorical; it must not be taken literally as implying that monads occupy positions in space. This is clearly not Leibniz’s view. Unfortunately, Leibniz never offers a detailed account of the relations between his doctrine of monads and his theory of space, but he seems to hold that spatial relations are logical constructions out of the perceptual states of monads. In other words, the claim that a certain body is in such and such a spatial position is to be ultimately analysed in terms of propositions about monads and their properties. Thus from his knowledge of the perceptual states of monads, God could read off all the facts about the spatial relations of bodies in the universe. Leibniz is committed, it seems, to the same view of time mutatis mutandis. Strictly speaking, monads are no more in time than they are in space, but the temporal relations of events can in principle be read off from the properties of monads. How consistently or rigorously Leibniz adhered to this view of time is unclear. At the very end of his life the nature of space and time was the subject of a fierce controversy between Leibniz and Newton’s disciple, Samuel Clarke; the exchange thus took place at a point in Leibniz’s career when the doctrine of monads was securely in position. Despite this, in the controversy with Clarke Leibniz does not seek to reveal the idealist groundfloor of his metaphysics. Throughout this exchange Leibniz argues at an intermediate level of philosophical rigour;58 for the sake of argument he assumes that the phenomenal world of bodies in space is ontologically basic. We should also note that while the nature of space and time is the dominant topic in the correspondence with Clarke, it is by no means the only issue that divides Leibniz and Newton; Newton’s theory of universal gravitation is also one of Leibniz’s chief targets. Indeed, in his later years, Leibniz was engaged in a full-scale assault on the foundations of Newtonian science. According to Leibniz, Newtonian science was not only philosophically inept; it was a direct threat to natural religion.59 In the correspondence with Clarke Leibniz puts forward two positive theories about the nature of space and time. In the first place, Leibniz argues that space and time are not substances or attributes but relations. ‘Space is the order of coexistences; time is the order of successive existences.’60 Thus Leibniz directly opposes the Newtonian absolute theory according to which space and time are entities which exist independently of bodies and events. For Leibniz, by contrast, bodies are logically prior to space and events are logically prior to time; in other words, there would be no space if there were no bodies and there would be no time if there were no events.61 Second, Leibniz argues that space and time are ideal. This thesis follows from the relational theory in conjunction with Leibniz’s oft-repeated claim that substances alone are fully real, everything else being a mere ens rationis or mental construct. The claim that space and time are ideal might lead one to suppose that it is intimately tied in with the doctrines of the monadology, but in fact it is not; although it is fully consistent with those doctrines, it does not depend on them. We can see that this is so by reflecting that Leibniz would still subscribe to the ideality thesis if he held, as he earlier did, that there are genuinely corporeal substances. For the ideality thesis, the crucial point is that space and time are relations and are therefore merely mental constructs. In his letters to Clarke Leibniz offers two main arguments against the Newtonian theory. The first argument is from the principle of sufficient reason. Notoriously, this principle takes many different forms in Leibniz’s philosophy, but here it can be understood to mean simply that there must be a reason for God’s choice. The argument can be put in the form of a reductio ad absurdum. Suppose that the Newtonian theory of absolute space is true. Now the parts of this space are indiscernible, and so if God created a world he could have no reason for creating it at one point in space rather than some other. But we know both that God has created a world and that he never acts without a reason. The argument thus leads to a contradiction: God both does, and does not, act without a reason. It follows, then, that the theory of absolute space is false. Mutatis mutandis the argument can also be directed against the theory of absolute time.62 Leibniz’s second argument has proved to be of greater philosophical interest in our own time. This argument depends on a version of the identity of indiscernibles which, as various writers have noted, is really tantamount to the modern verificationist principle.63 According to Leibniz, the Newtonians are committed to saying that it makes sense to suppose that God could, for example, move the universe a few miles to the west while keeping its internal structure unchanged. Leibniz has no patience with such suppositions. If God were to do such things, no change would be observable even in principle. In a remarkable passage Leibniz then states the verificationist objection: Motion does not indeed depend on being observed; but it does depend on its being possible to be observed. There is no motion when there is no change that can be observed. And when there is change that can be observed, there is no change at all.64 The supposition in question can thus be dismissed as meaningless or, as Leibniz sometimes says, an impossible fiction. Ever since Clarke Leibniz’s readers have been bothered by a seeming inconsistency in his position. The first argument seems to assume that, though absolute space and time are contrary to the divine wisdom, they are at least logically possible; the second argument, by contrast, seeks to establish a stronger claim: the theory of absolute space and time is an impossible fiction. Relatedly, there seems to be an inconsistency in Leibniz’s claims about the identity of indiscernibles. Sometimes he says that to suppose two indiscernible entities or states of affairs is to suppose two things under the same name;65 at other times he says that, though logically possible, the existence of two indiscernible entities would be contrary to the divine wisdom.66 The problem of interpretation, however, is not really a serious one; it can be solved by assuming that Leibniz is mounting a two-pronged attack on the Newtonian position. Leibniz’s main argument turns on the claim that the identity of indiscernibles is a necessary truth: on this argument the supposition of two indiscernible entities is indeed an impossible fiction. But Leibniz is also prepared to argue in a more concessive vein: even if it is granted that two indiscernible entities are logically possible, it can still be shown that they would never obtain because they are contrary to the divine wisdom. CAUSALITY, PRE-ESTABLISHED HARMONY, AND THE MIND-BODY PROBLEM The seventeenth and eighteenth centuries were a period of intense interest in the nature of causality. Indeed, in this period the whole concept of causality was going through a process of transformation which was to culminate with Hume. But though early modern philosophers, such as Malebranche and Leibniz, anticipated some of Hume’s insights, at least officially they tended to cling to traditional, Aristotelian ideas about the nature of causality which Hume himself was to discard; as a result they often seem to occupy half-way positions on the road to Hume. In general we can say that seventeenth-century philosophers tended to operate with a stronger concept of causality than is current today. This fact is something which needs to be borne in mind when interpreting their metaphysical doctrines about causal relations. Rationalist philosophers, in particular, often seem to be announcing surprising news about the world, but to some extent they can be read as doing something rather different; they are insisting that a certain strong concept of causality is not satisfied by certain events and processes which we might take to be causal. Malebranche and Leibniz illustrate these points very clearly. In the case of Malebranche his occasionalism arises from his insistence that there must be a logically necessary connection between cause and effect; on this basis he concludes that no creature is a genuine cause.67 Anticipating Hume he insists that it is not logically necessary, for instance, that the kettle should boil soon after I light a fire under it or that my arm should go up when I will to raise it.68 Unlike Malebranche, Leibniz is not so wedded to the idea that necessary connection is a requirement for true causality; rather, he accepts the scholastic assumption that genuine causality involves a kind of contagion whereby properties are literally passed on from the cause to the effect. It is true that Leibniz’s position is not free from tensions. For instance, he criticizes the scholastic Suarez’s definition of ‘cause’ as ‘what flows being into something else’ on the grounds that it is barbarous and obscure.69 Yet Leibniz famously denies that monads causally interact on the ground that they have no windows through which anything could enter or depart.70 In other words, no properties can be literally transmitted from one simple substance to another. Yet if this is his ground for denying that substances causally interact, then Leibniz must be assuming something like the ‘contagion’ view of causality. And it is surely this concept of causality which Suarez was trying to capture, however clumsily, in his definition in terms of influx. Thus, rather than abandon traditional assumptions about causality, both Leibniz and Malebranche choose the heroic course of denying the existence of genuine causal relations between finite substances. In other words, they stop short of Hume’s revolutionary rethinking of the nature of causality. Leibniz’s doctrine of pre-established harmony, like Malebranche’s occasionalism, has been seriously misunderstood. It has been assumed that both doctrines are merely more or less ad hoc solutions to the mind-body problem which Descartes is supposed to have bequeathed to his successors. But this assumption is mistaken. Recall that on pp. 393–5 we saw how Leibniz tried to deduce his doctrine of the preestablished harmony (understood as the package of metaphysical theses 3–5) from purely logical considerations; in particular, he tried to deduce it from his complete concept theory. The doctrine of the preestablished harmony is thus not simply an ad hoc solution to the mind-body problem; it is a general theory about the relations between finite, created substances. In this respect it resembles Malebranche’s occasionalism. But in another respect there is an important relevant difference between the two theories. Because of his Cartesian assumptions, Malebranche is able to offer an occasionalist solution of the mind-body problem as a special case of a more general theory; it is not clear, however, whether Leibniz is really in a position to do the same. Indeed, at points in his philosophical career it is not even clear whether the mind-body problem really arises in his philosophy. We see, then, that Leibniz pays a price for his attempt to retain Aristotelian ideas while addressing characteristically Cartesian concerns. To understand the force of these observations it is useful to compare the positions of Descartes and Leibniz. In Descartes’s philosophy the mind-body problem is traditionally taken to arise from the fact that he holds that mind and body are both substances and that they are completely heterogeneous; the nature of mind consists wholly in thinking and the nature of body consists wholly in being extended. It has thus seemed difficult to Descartes’s readers to see how there could be any union or interaction between two such different substances. By contrast, at no point in his philosophical career did Leibniz accept all the assumptions which generate the mind-body problem in its pure Cartesian form. In the first place, although in his later philosophy Leibniz insists that the soul is a substance, he is much less certain about its status around the time of writing the Discourse on Metaphysics. Using scholastic terminology Leibniz notes: ‘the soul, properly and accurately speaking, is not a substance, but a substantial form, or the primitive form existing in substance, the first act, the first active faculty.’71 But if the soul is only an element of substance, then it is not clear that it makes sense to speak of a mind-body problem. Second, throughout his career Leibniz holds that the human body is not a substance but an aggregate of substances. It is true that the nature of the aggregate changes as his metaphysics develops: in the Discourse the body is an aggregate of organisms; in the Monadology it is an aggregate of monads. But at no time does Leibniz regard the human body as a substance in its own right. Finally, at least in his later philosophy, mind and body, for Leibniz, are not fundamentally heterogeneous, for the body is an aggregate of entities that are themselves soul-like. Now there may well be a case for saying that monads cannot causally interact, but it clearly has nothing to do with considerations of heterogeneity. As we have seen, it has rather to do with the fact that monads have no windows. In other words, causal interaction requires the literal transmission of properties, and in the case of monads this requirement cannot be met. In its classical form, then, the mind-body problem is a puzzle about the relations between two heterogeneous substances, and in this form the problem cannot arise in Leibniz’s philosophy. At most Leibniz faces a problem concerning the relation between a substance (mind) and an aggregate of substances (body). But in that case a solution to this problem cannot be straightforwardly derived from the general doctrine of pre-established harmony. For from the fact that no two substances can interact it does not follow that a substance cannot interact with an aggregate of substances. Despite these anomalies, Leibniz often writes as if he were in a position to solve the mind-body problem which Descartes bequeathed to his successors; he boasts, for instance, that his doctrine of preestablished harmony solves ‘the great mystery of the union of the soul and the body’.72 In passages like these Leibniz tends to downplay the extent of his Aristotelian-scholastic commitments; he suggests that he shares the dualist assumptions that generate the mind-body problem, and refuses to follow Descartes only in his commitment to interactionism. Leibniz then exploits his doctrine of the pre-established harmony in the following way. Although mind and body appear to interact, the metaphysical truth of the matter is that each is simply following its own laws: the body is acting in accordance with the laws of mechanism, the mind is acting in accordance with the laws of psychology. In the former case the causality involved is efficient, in the latter it is teleological.73 Thus, for example, my mind and my body have been so programmed by God that, when I form the volition to raise my hat, my arm is ready to execute the appropriate movement. PSYCHOLOGY: EXPRESSION, PERCEPTION, AND PETITES PERCEPTIONS Leibniz’s solution to the mind-body problem struck many of his contemporaries as remarkably similar to Malebranche’s occasionalism—a comparison which Leibniz resisted.74 In fact, however, Leibniz’s position is in some ways more reminiscent of Spinoza’s. Like Spinoza, Leibniz insists on the autonomy of the physical and mental realms; every physical event has a physical cause, and every mental event has a mental cause. There are of course also important differences between their views. Unlike Spinoza, Leibniz subscribes to the traditional Christian conception of a personal God and he holds, at least in his later philosophy, that the mind is a naturally immortal, immaterial substance. But these very differences suggest a way of viewing Leibniz’s project, at least with regard to the mind-body problem; he is seeking to do justice to some of Spinoza’s key ideas within the framework of traditional Christian theology. There is indeed much that is Spinozistic in Leibniz’s psychology. Consider, for instance, how Leibniz applies his concept of expression to the relationship between mind and body. According to Leibniz, the mind does not interact with the body, but it expresses it in the technical sense of the term which he explained for Arnauld’s benefit. Indeed, Leibniz tells Arnauld that the mind expresses its own body better than it expresses anything else in the universe.75 In response to Arnauld’s query Leibniz explains that he does not mean by this that our mind has clearer thoughts of, say, the activity of its lymphatic glands than of the satellites of Jupiter; he means rather that given a complete knowledge of my mental states a supermind would find it easier to read off truths about my physical states than about the celestial bodies.76 As Spinoza wrote, ‘the ideas that we have of external bodies indicate the constitution of our own body more than the nature of external bodies’.77 Leibniz might have stopped at this point, but in fact he goes further; he claims that the mind expresses its body by perceiving it, perception being a species of expression; indeed the mind perceives everything that happens in its body.78 Here again Leibniz seems to be following in Spinoza’s footsteps, for Spinoza had similarly written that ‘whatever happens in the object [i.e. the body] of the idea constituting the human mind is bound to be perceived by the human mind’.79 But whereas Spinoza does little to dispel the mystery surrounding this claim, Leibniz offers a body of theory which plugs the gaps in Spinoza’s account. This is the famous doctrine of unconscious perceptions. Here it is helpful to recall Leibniz’s hierarchical arrangement of monads. All monads perceive, but they differ vastly in terms of the quality of their perceptions. Human minds or spirits are distinguished not only by reason but also by ‘apperception’ which means consciousness or perhaps even selfconsciousness. But though Leibniz holds that human minds are set apart from lower monads by their capacity for (self)-conscious awareness, he further believes that they also have unconscious or little perceptions (petites perceptions); such perceptions are little because they are low in intensity. Not merely do large stretches of our mental life consist wholly in little perceptions, but even conscious mental states are composed of such perceptions. The doctrine of unconscious perceptions is perhaps Leibniz’s principal innovation in psychology, and it is of course profoundly anti-Cartesian in its implications. For Descartes subscribes to the view that the mind is transparent to itself; he is explicit that there is nothing in the mind of which we are not conscious.80 In the New Essays on Human Understanding, his reply to Locke, Leibniz remarks that there are ‘thousands of indications’ in favour of unconscious perceptions.81 Obviously there is an element of hyperbole in this claim, but even so, Leibniz certainly has a battery of arguments for his doctrine. Some of these arguments are based on a priori principles such as the identity of indiscernibles which requires that any two minds must be qualitatively, not just numerically, different. Although Leibniz is not quite explicit about this, another assumption of the argument seems to be that minds at or before birth have no conscious experiences; thus the individuating characteristics required by the identity of indiscernibles must occur below the threshold of consciousness.82 Other arguments are less tied to the distinctive principles of Leibniz’s metaphysics, but not all of them are more cogent. Leibniz is fond of arguing that, in order to hear the waves breaking on the shore, we must hear the noise of each individual wave.83 This argument has been criticized as being as dubious as arguing, from the fact that we feel the weight of a stone, that we must have an unconscious perception of each of the molecules that make it up.84 Perhaps more interesting is what we may call Leibniz’s ‘attention argument’ which may be illustrated by the following scenario.85 Suppose that two people, Smith and Jones, are having a conversation and that, throughout, a drill has been operating in the background; Smith has not been conscious of the noise, but he now suddenly has his attention drawn to it by Jones. Leibniz argues that in the act of attention Smith is really remembering a past perception of the noise. But ex hypothesi this earlier perception was not a conscious one and must therefore have been ‘little’ or unconscious. This argument clearly depends on the premise that attention involves memory, and one might wonder why one should accept this. If it is supposed to be true by definition, then the definition seems merely stipulative. Nonetheless, there is something attractive about the suggestion that cases like this force us to recognize the existence of unconscious perceptions, and Leibniz can support his conclusion in other ways. For example, it was implicitly assumed in our description of the case that Smith’s sense organs are equally stimulated by the drilling both before and during the act of attention. Now Leibniz cannot of course strictly ascribe any psychological effects to a physical stimulus, but by virtue of his theory of expression he can and does insist that some state of the soul must correspond to any such stimulation;86 and by hypothesis, as we have seen, the mental state which precedes the act of attention is not a conscious awareness of the noise. Leibniz can also fall back on an appeal to the law of continuity;87 there would be a flagrant breach of this law if the stimulus which ‘produced’ a conscious perception of the noise during the act of attention ‘produced’ no perception at all in the mind before the act. The doctrine of unconscious perceptions is a key element in Leibniz’s attack on the Cartesian view that mentality is all or nothing. For Leibniz, by contrast, mentality is a continuum which extends below the threshold of consciousness. Sometimes, as we should expect, Leibniz’s rejection of Descartes’s view of the mental life provides the basis for the rejection of other Cartesian doctrines. Leibniz sides with common sense against the notorious Cartesian thesis that animals are mere automata. He argues that the Cartesians were led astray by their failure to distinguish between thought and perception; in other words, the Cartesians have made the mistake of confusing a species with its corresponding genus.88 Thus even if animals have no thought (cogitatio), it does not follow that they have no perceptions. Leibniz is clear, then, that animals have a mental life, but he is less clear about its precise nature. He seems to have believed that, unlike humans, animals have no capacity for self-consciousness, but whether he believed that they could consciously feel pain is less certain. Unfortunately, the issue is complicated by an obscurity in Leibniz’s concept of apperception which, as we have suggested, is ambiguous between consciousness and selfconsciousness. 89 Somewhat curiously, however, at other times Leibniz uses his theory of perception to defend Cartesian theses, although often in a seriously modified form. Here too the doctrine of unconscious perceptions plays a key role. As against Locke, for example, Leibniz exploits the doctrine in order to defend, or rather re-work, the Cartesian thesis that the mind always thinks. For Leibniz, the mind always thinks, not in the sense of being always conscious, but rather in the sense of never being without some perceptions; for example, even in dreamless sleep or a coma the mind has its petites perceptions. It is thoroughly characteristic of Leibniz’s concerns that his defence of this Cartesian thesis is in the service of a larger goal—the vindication of an immaterialist theory of mind against what he sees as Locke’s subversive attack on this doctrine. For Leibniz, the immateriality of the mind entails that it is naturally immortal, and this in turn entails that it always perceives.90 KNOWLEDGE AND IDEAS In contrast with Locke and the other British empiricists, Leibniz has traditionally been classified as a rationalist, and this classification is fundamentally an epistemological one: a rationalist philosopher is one who believes that it is possible to know substantive truths about the world a priori, by reason alone. We might expect, then, that in his full-length reply to Locke, the New Essays, Leibniz would seize the opportunity to provide a systematic defence of the rationalist position in epistemology. Yet on the whole this expectation is disappointed. On the contrary, as I have already indicated, Leibniz’s main purpose in this work is not epistemological at all: it is metaphysical. Leibniz told a correspondent that in writing this work he was above all concerned to defend the immateriality of the soul.91 This fact about the work is remarkably suggestive of Leibniz’s overall philosophical orientation. Unlike Descartes and the British empiricists, Leibniz was not greatly interested in what have since come to be regarded as the central issues in epistemology; the problem of our knowledge of the external world, for instance, was never at the forefront of his philosophical concerns. As we have seen, Leibniz sometimes toys with phenomenalism, and in the hands of Berkeley phenomenalism serves as an answer to the challenge of scepticism. Leibniz, however, does not seem to have been primarily attracted to phenomenalism for this reason. On occasion, of course, Leibniz can make some shrewd criticisms of the attempts of other philosophers to solve epistemological questions. Leibniz is rightly suspicious of Descartes’s appeal to clear and distinct ideas, and he ruthlessly exposes the weaknesses of Descartes’s proof of the existence of the external world; he remarks with some justice that Descartes’s proof is so feeble that it would have been better not to try.92 But some of Leibniz’s criticisms of Descartes indicate a lack of deep engagement with the issues. Leibniz states that Varia a me cogitantur (‘Various things are thought by me’) has as strong a claim as the Cogito, ergo sum to be regarded as a first principle of knowledge.93 But this comment suggests a blindness to the peculiarly self-verifying character of the cogito. Perhaps Leibniz’s chief interest in the theory of knowledge lies in defending a version of the Cartesian, and ultimately Platonic, doctrine of innate ideas. Not surprisingly, Leibniz’s main defence of this doctrine is to be found in the New Essays; indeed, it constitutes the single most substantive treatment of epistemological issues in that work. But Leibniz’s case for innate ideas does not stand on its own; it is an application of a theory of ideas in general, and it is best to begin by taking a brief look at this theory. Leibniz’s theory of ideas can be understood against the background of a famous controversy between Malebranche and Arnauld.94 There are a number of issues in this controversy, but for our purposes the central problem is the ontological status of ideas. As an orthodox Cartesian Arnauld argued that ideas or concepts—e.g. the concept of a triangle—are mind-dependent entities; indeed, they are modifications of the mind.95 Malebranche, by contrast, argued that ideas are not in human minds at all; rather, they are in God.96 By thus locating ideas in God, Malebranche is self-consciously reviving the Augustinian doctrine of divine illumination; in order to achieve genuine knowledge of the world, our minds must be illuminated by the light of God’s ideas. But Malebranche’s philosophical point can perhaps be explained by removing the theological trappings; in contrast with Arnauld and orthodox Cartesians, he argues that ideas (concepts) are not psychological but abstract entities. Leibniz approves of Malebranche’s revival of the doctrine of divine illumination, and like Malebranche he speaks of God as the region of ideas.97 But despite his tendency to echo Malebranche’s language, Leibniz does not really follow him in regarding ideas as irreducibly abstract entities. Unlike Malebranche, Leibniz is a nominalist who cannot countenance such entities as basic items of ontology.98 Certainly Leibniz’s official definition of the term ‘idea’ is uncompromisingly psychological; ideas are ‘in the mind’ and they are ‘faculties’—that is, dispositions to think in certain ways.99 For Leibniz, then, since it is a psychological disposition, an idea is a persistent property of the mind. Thus, unlike Arnauld, Leibniz does not simply identify ideas with particular mental episodes. This definition of ‘idea’ does justice to something which Descartes recognized, if less explicitly and only intermittently: a person can have an idea of x even if at that moment he is not actually thinking of x. On such a theory of ideas it is not hard to see what is involved in a commitment to innate ideas. For if ideas are themselves mental dispositions, then innate ideas are innate mental dispositions; they are dispositions which we have had at least since birth. This is the form of the doctrine which Leibniz has primarily in mind when he defends the innateness of mathematical and metaphysical concepts against Locke. In his polemic Locke had adopted a twopronged strategy of attack on innate ideas. According to Locke, the thesis of innate ideas is either empirically false—it ascribes highly abstract concepts to infants — or it is condemned to triviality.100 In reply Leibniz seeks to show that his own dispositional theory of innate ideas constitutes a third option which is not caught in the mesh of Locke’s polemic. To claim that the mind has an innate idea of x is not just to say, as Locke supposes, that it is capable of thinking of x; a distinction must be drawn between dispositions and ‘bare faculties’.101 That Leibniz is right to draw such a distinction can be shown by reference to the case of a physical disposition such as fragility. When we call an object fragile, we are not just saying that it is capable of breaking; otherwise any object which breaks is fragile. Leibniz’s theory of innate ideas thus implies at least that the mind is differentially predisposed to form certain thoughts rather than others. Here Leibniz seems to be reviving Descartes’s thesis that ideas are innate in the same sense as that in which we say that generosity is ‘innate’ in certain families, or that certain diseases such as gout or stones are innate in others; it is not so much that the babies of such families suffer from these diseases in their mother’s womb, but simply that they are born with a certain ‘faculty’ or tendency to contract them.102 In one way, however, Leibniz’s dispositional theory of innate ideas seems to differ from Descartes’s. Unlike Descartes, Leibniz seems to hold that mental dispositions cannot be basic properties; they need to be grounded in fully actual, non-dispositional properties of the mind. Here Leibniz may be responding to Malebranche’s criticism that the Cartesians inconsistently countenanced basic powers in psychology, while rightly banishing them from physics.103 But while it is obvious how, say, fragility can be grounded in structural properties of the glass, it is less clear what could serve to ground mental dispositions. In order to meet this requirement, it seems that Leibniz once again appeals to his doctrine of unconscious perceptions. My innate disposition to think of a triangle, for example, would be grounded in an unconscious perception which has triangle content. It is this doctrine which Leibniz appears to have in mind when he writes in the New Essays that ‘ideas and truths are innate in us—as inclinations, dispositions, tendencies, or natural virtualities, and not as actions; although these virtualities are always accompanied by certain actions, often insensible ones, which correspond to them.’104 The dispositional theory is Leibniz’s main theory of innate ideas, but it is not the only one. Leibniz also advances what we may call the ‘reflection account’. According to this account, the idea of substance, for example, is innate in the sense that we can acquire it by turning our mental gaze inward and reflecting on the fact that our minds are substances. Leibniz seems to have been pleased with this theory, and it inspires some of his best-known remarks about innate ideas; it underlies such claims as ‘We are innate to ourselves’ and ‘There is nothing in the intellect which was not previously in the senses, except the intellect itself’.105 None the less, for all Leibniz’s evident pride in the doctrine, it does not seem very satisfactory. For one thing, on this account ideas turn out to be innate only in the minimal sense that they are not acquired through the senses. Moreover, the theory faces obvious difficulties in explaining our acquisition of mathematical concepts, and these are generally numbered among the explananda for any theory of innate ideas. We may perhaps acquire the idea of substance by reflecting on the fact that our minds are substances, but we can hardly acquire the concept of a triangle by reflecting on the fact that our minds are triangular. So far we have been chiefly concerned with Leibniz’s defence of a theory of innate ideas against the Lockean objection that it must reduce to triviality. But what positive arguments does Leibniz offer in favour of the innatist doctrine? In the New Essays Leibniz is much more forthcoming on this score in connection with innate propositions than with innate concepts. In part this fact reflects the emphasis of Locke’s own discussion, but it also testifies to Leibniz’s concern with a problem which has exercised philosophers at least since Plato: this is the problem of explaining how we can have a priori knowledge of necessary truths, as we do in the case of mathematics. Leibniz follows the Platonic tradition by arguing that it is impossible to explain such knowledge except on the assumption that it is innate in our minds.106 Through the senses, for example, we may perhaps come to believe that the Pythagorean theorem is true of all observed right-angled triangles, but we would never come to believe that this theorem expresses a necessary truth about such triangles. Leibniz’s case for innate knowledge has a distinguished ancestry, but it seems to be in danger of running together two separate issues.107 In the first place, there is a causal question: how do we acquire beliefs to the effect that necessarily p? Second, there is a question of justification: how do we justify our claim to know that necessarily p? Leibniz sometimes seems to say that both questions can be answered in terms of an appeal to innateness, but this claim is distinctly dubious. The hypothesis of innateness may be a plausible answer to the first question, but it is more difficult to see how it helps with the second, normative issue; on the face of it, it seems entirely possible that our innate beliefs should all be false. It is true that the innatist hypothesis would help to answer the second question on the further assumption of divine benevolence; a good God can be trusted not to inscribe a pack of lies on our minds. Unlike Descartes, however, Leibniz is reluctant to appeal to divine benevolence in order to solve epistemological questions. Leibniz’s philosophy, and his metaphysics in particular, is an extraordinarily ambitious work of synthesis. His system seeks, for example, to combine Aristotelian and Cartesian insights within a framework of Christian theology. Sometimes Leibniz’s attempts at synthesis seem overambitious and even misguided; on occasion Leibniz seeks to address issues—such as the mind-body problem—without indicating how far he has departed from the assumptions which initially gave rise to them. Leibniz may well have been aware of such stresses in his system, and it may have been because of this awareness that he never ceased to develop as a philosopher; he continued to seek new ways of assembling the materials of his philosophy into a coherent whole. Indeed, in some ways, despite its strangeness, his later idealism is more coherent than the earlier, Aristotelian metaphysics. But though Leibniz had to struggle to achieve overall coherence, in the process he made major contributions to philosophical thought about the issues he discussed; his theories of substance, identity, causality, space and time, and innate ideas are illuminating and historically influential. For all its internal tensions and unresolved problems, his system in its various forms remains one of the most impressive examples of speculative metaphysics. ABBREVIATIONS A German Academy of Sciences (ed.) G.W.Leibniz: Sämtliche Schriften und Briefe (Darmstadt, 1923–). References are to series and volume. AG R.Ariew and D.Garber (ed. and trans.), Leibniz: Philosophical Essays (Indianapolis, Ind., and Cambridge, Mass., 1989) AT C.Adam and P.Tannery (eds) Oeuvres de Descartes, 12 vols (Paris, 1897–1913; reprinted Paris, 1964–76) CSM J.Cottingham, R.Stoothoff and D.Murdoch (trans.), The Philosophical Writings of Descartes, 2 vols (Cambridge, 1985) F de C A.Foucher de Careil (ed.) Nouvelles Lettres et Opuscules Inédits de Leibniz (Paris, 1857) G C.I.Gerhardt (ed.) Die Philosophischen Schriften von G.W.Leibniz (Berlin, 1875–90) Grua G.Grua (ed.) G.W.Leibniz: Textes Inédits, 2 vols (Paris, 1948) L L.E.Loemker (ed.) G.W.Leibniz: Philosophical Papers and Letters (Dordrecht, 2nd edn, 1969) MP H.T.Mason (ed. and trans.) and G.H.R.Parkinson (intro.) The Leibniz-Arnauld Correspondence (Manchester, 1967) NE New Essays on Human Understanding (Nouveaux Essais sur l’Entendement Humain). References are to series VI, volume 6, of the Academy edition and to the Remnant and Bennett translation. The pagination of Remnant and Bennett is identical with that of the Academy text; one page number thus serves for both RB P.Remnant and J.Bennett (trans. and eds) G.W.Leibniz: New Essays on Human Understanding (Cambridge, 1981) I have generally followed the cited translations; any significant modifications are indicated in the notes. NOTES 1 See, for example, NE IV.viii, A VI.vi, RB 431. 2 Leibniz to Remond, 10 January 1714, G III 607. 3 See J.Bennett, A Study of Spinoza’s Ethics (Cambridge, Cambridge University Press, 1984), pp. 55–6. 4 Aristotle, Categories, ch. 5, 43. 5 Discourse on Metaphysics 8, G IV 432, L 307. 6 ibid., G IV 433, L 307. 7 Leibniz to Arnauld, 30 April 1687, G II 96–7, MP 121. 8 Sleigh [11.27], 123. 9 cf. Bennett, op. cit., p. 58. 10 Leibniz to Arnauld, 30 April 1687, G II 100–1, MP 126. 11 Strictly speaking, for Descartes, there is only one body or extended substance: the entire physical universe. 12 See Sleigh [11.27], 98–101. 13 See Broad [11.29], 49–51. 14 Leibniz to Arnauld, 30 April 1687, G II 101, MP 126. 15 Arnauld to Leibniz, 4 March 1687, G II 86, MP 107. 16 Leibniz to Arnauld, 30 April 1687, G II 97, MP 121. 17 Arnauld to Leibniz, 4 March 1687, G II 87–8, MP 109. 18 Leibniz to Arnauld, 30 April 1687, G II 100, MP 125–6. 19 Discourse on Metaphysics 8, G IV 433, L 307. 20 Russell [11.38]; Couturat [11.43]; Couturat [11.44], 21 ‘First Truths’, C 521, L 269. (Translation modified.) 22 See, for example, M.Ayers, ‘Analytical Philosophy and the History of Philosophy’, in J.Rée, M.Ayers and A.Westoby, Philosophy and its Past (Brighton, Harvester, 1978), p. 45. See also B.Brody, ‘Leibniz’s Metaphysical Logic’, in Kulstad [11. 34], 43–55. 23 Aristotle, Metaphysics 1011 b 27. 24 Leibniz to Arnauld, 14 July 1686, G II 56, MP 63. 25 As Arnauld noted (Arnauld to Leibniz, 13 March 1686, G II 15, MP 9), these remarkable doctrines of Leibniz’s logic raise a number of puzzles concerning freedom and contingency. On these see, for example, Sleigh [11.27]. 26 Discourse on Metaphysics 9, G IV 433, L 308. 27 Leibniz’s Fourth Paper to Clarke, G VII 372, L 687. 28 See Parkinson [11.58], 6–8. 29 Leibniz to Arnauld, 9 October 1687, G II 112, MP 144. 30 Discourse on Metaphysics 8, G IV 433, L 308. (Translation modified.) 31 See Broad [11.29], 24–5. 32 See Loeb [11.55], 279. 33 It is worth noting here that, strictly speaking, there is a logical gap between 3 and 4 themselves. If 4 is derived from 3, then it is tacitly assumed that every state of a substance must have a cause. If, on the other hand, 3 is derived from 4, then it is tacitly assumed that there is no causal overdetermination. Both these assumptions would be congenial to Leibniz. 34 Parkinson [11.58], 147. 35 ibid., p. 151. 36 Loeb [11.55], 286. 37 ‘First Truths’, C 521, L 269. See Loeb [11.55], 286. 38 See Sleigh [11.27], 11. 39 See, for example, New System, G IV 484, L 457. 40 On the development of Leibniz’s philosophy, see Broad [11.29], 87; D.Garber, ‘Leibniz and the Foundations of Physics: The Middle Years’, in K.Okruhlik and J.R.Brown (eds) The Natural Philosophy of Leibniz (Dordrecht, Reidel, 1985), pp. 27–130. 41 Leibniz to De Volder, 30 June 1704, G II 270, L 537. 42 Monadology 4, G VII 607, L 643. 43 Revision note of 1697–1700 to ‘A New Method for Learning and Teaching Jurisprudence’, A VI.i p. 286, L 91n. 44 R.McRae [11.69], 60. 45 Whether God is a monad is not entirely clear. However, there are places where Leibniz seems to say that God is a monad—for example, Grua II 558. 46 See Broad [11.29], 75, for a helpful discussion of these issues. 47 Leibniz to De Volder, undated, G II 275, AG 181. 48 M.Furth, ‘Monadology’, in Frankfurt [11.32], 99–135, esp. p. 122; Loeb [11.55], 304–5. 49 Leibniz to Des Bosses, 16 June 1712, G II 451–2, L 605. 50 Furth, in [11.32], 118–19. 51 See, for example, Leibniz to Des Bosses, 31 July 1709, G II 379; Leibniz to Des Bosses, January 1710, G II 399. 52 See, for example, Leibniz to Arnauld, 9 October 1687, G II 118–19, MP 152. 53 Leibniz to Des Bosses, 29 May 1716, GP II 517, AG 203. 54 See, for example, Broad [11.29], 91. For criticisms of the ‘misperception’ interpretation, see Rutherford [11.59], 11–28. 55 ‘Nowhere does Leibniz himself assert that he believes it…. Thus the vinculum substantiale is rather the concession of a diplomatist than the creed of a philosopher’ (Russell [11.38], 152; cf. Broad [11.29], 124–5). 56 cf. Broad [11.29], 127. 57 Leibniz to Des Bosses, 20 September 1712, G II 459, L 607. 58 C.D.Broad, ‘Leibniz’s Last Controversy with the Newtonians’, in Woolhouse [11. 62], 171. 59 Leibniz’s First Paper to Clarke, G VII 352, L 675. 60 Leibniz’s Third Paper to Clarke, G VII 363, L 682. 61 cf. Broad, in [11.62], 158–9. 62 Leibniz’s Third Paper to Clarke, G VII 364, L 682–3. 63 Alexander [11.12], xxiii; Broad, in [11.62], 166. 64 Leibniz’s Fifth Paper to Clarke, G VII 403–4, L 705. 65 Leibniz’s Fourth Paper to Clarke, G VII 372, L 687. 66 Leibniz’s Fifth Paper to Clarke, G VII 395, L 700. 67 N.Malebranche, The Search After Truth, 6.2.3. 68 ibid. 69 See the Preface to an edition of Nizolius, G IV 148. For an illuminating discussion of these issues, see H.Ishiguro, ‘Pre-established Harmony versus Constant Conjunction’, in A.Kenny (ed.) Rationalism, Empiricism, and Idealism (Oxford, Oxford University Press, 1986), pp. 61–85. 70 Monadology 7, G VII 607; L 643. 71 ‘Notes on Some Comments by Michel Angelo Fardella’, AG 105; F de C 323. 72 Discourse on Metaphysics 33, G IV 458, L 324. 73 Monadology 33, G VI 620, L 651; Principles of Nature and of Grace 3, G VI 599, L 637. 74 See Chapter 10 for a discussion of Leibniz’s attitude towards Malebranche’s occasionalism. See also Sleigh [11.27], 150–70. 75 See Leibniz to Arnauld, 28 November/8 December 1686, G II 74, MP 92; cf. Leibniz to Arnauld, 30 April 1687, G II 90, MP 113. 76 See Leibniz to Arnauld, 9 October 1687, G II 112, MP 143–4. 77 Ethics Part 2, Proposition 16, Corollary 2. 78 Leibniz to Arnauld, 9 October 1687, G II 112, MP 144. 79 Ethics Part 2, Proposition 12. 80 First Set of Replies, AT VII 107, CSM II 77. 81 NE Preface, A VI.vi, RB 53. (Translation modified.) 82 ibid., p. 58. 83 ibid., p. 54. 84 J.Cottingham, The Rationalists (Oxford, Oxford University Press, 1988), p. 152. 85 NE Preface, A VI.vi, RB 54. 86 ibid. 87 See Leibniz’s appeal to the law of continuity, ibid., p. 56. 88 Leibniz to Treuer, 21 May 1708; see Jolley [11.22], 117; cf. Principles of Nature and of Grace 4, G VI 600, L 637. 89 McRae argues that Leibniz’s position on the issue of whether animals have sensation is contradictory. ‘On the one hand what distinguishes animals from lower forms of life is sensation or feeling, but on the other hand apperception is a necessary condition of sensation, and apperception distinguishes human beings from animals’ (McRae [11.69], 30). Leibniz certainly holds that self-consciousness distinguishes man from other animals, but whether he consistently equates selfconsciousness with apperception is less clear. 90 See Jolley [11.22], 104. 91 Leibniz to Jaquelot, 28 April 1704, G III 473. 92 ‘Critical Thoughts on the General Part of Descartes’s Principles’, G IV 360, L 391. 93 ibid., G IV 357, L 385. 94 This controversy was initiated by Arnauld’s On True and False Ideas (1683) which attacked Malebranche’s theory of ideas. On this controversy see S. Nadler, Arnauld and the Cartesian Philosophy of Ideas (Princeton, N.J., Princeton University Press, 1989); Jolley [11.65]. 95 On True and False Ideas, ch. 5, Definition 3. 96 Search After Truth 3.2.6. 97 ‘On the Radical Origination of Things’, G VII 305, L 488. 98 The case for Leibniz’s nominalism is well argued in Mates [11.57], ch. 10. 99 ‘What is an Idea?’, G VII 263, L 207. 100 J.Locke, Essay Concerning Human Understanding I.ii. 101 NE I.i., A VI.vi, RB 79–80. 102 Comments on a Certain Broadsheet, AT VIII-B 358, CSM I 304. 103 Elucidation Ten, Search After Truth. 104 NE Preface, A VI.vi, RB 52. 105 NE Preface, A VI.vi, RB 51; ibid., II.i, III. Strictly speaking, even the reflection account involves a dispositional component, since it is a theory of how we acquire ideas, and ideas are mental dispositions. 106 ibid., Preface, p. 49. 107 For this line of criticism see S.Stich (ed.) Innate Ideas (Berkeley and Los Angeles, Calif., University of California Press, 1975), Introduction, pp. 17–18. BIBLIOGRAPHY Original language editions 11.1 G.W.Leibniz: Sämtliche Schriften und Briefe, ed. German Academy of Sciences, Berlin and Darmstadt, Akademie Verlag, 6 series, 1923–. 11.2 Die Philosophischen Schriften von G.W.Leibniz, ed. C.I.Gerhardt, Berlin, Weidmann, 7 vols, 1875–90. 11.3 Opuscules et fragments inédits de Leibniz, ed. L.Couturat, Paris, Alcan, 1903. 11.4 G.W.Leibniz: Textes Inédits, ed. G.Grua, Paris, Presses Universitaires de France, 2 vols, 1948. English translations Collections and selected works 11.5 G.W.Leibniz: Philosophical Essays, trans. R.Ariew and D.Garber, Indianapolis, Ind., Hackett, 1989. 11.6 G.W.Leibniz: Philosophical Papers and Letters, trans. L.E.Loemker, Dordrecht, Reidel, 2nd edn, 1969. 11.7 Leibniz: Philosophical Writings, trans. M.Morris and G.H.R.Parkinson, London, Dent, 1973. 11.8 G.W.Leibniz: Logical Papers: A Selection, trans. G.H.R.Parkinson, Oxford, Clarendon, 1966. 11.9 Leibniz: Political Writings, trans. P.Riley, Cambridge, Cambridge University Press, 2nd edn, 1988. Separate works 11.10 Leibniz: Discourse on Metaphysics, trans. P.G.Lucas and L.Grint, Manchester, Manchester University Press, 1953. 11.11 The Leibniz-Arnauld Correspondence, trans. H.T.Mason with an introduction by G.H.R.Parkinson, Manchester, Manchester University Press, 1967. 11.12 The Leibniz-Clarke Correspondence, ed. H.G.Alexander, Manchester, Manchester University Press, 1956. 11.13 G.W.Leibniz: Theodicy, trans. E.M.Huggard, London, Routledge & Kegan Paul, 1952. Bibliographies and concordances Bibliographies 11.14 Ravier, E. Bibliographie des Oeuvres de Leibniz, Paris, Alcan, 1937. 11.15 Schrecker, P. ‘Une Bibliographie de Leibniz’, Revue philosophique de la France et de l’étranger 63 (1938) 324–46. 11.16 Heinekamp, A. (ed.) Leibniz Bibliographie: die Literatur über Leibniz bis 1980, Frankfurt, Klosterman, 2nd edn, 1984. 11.17 Totok, W. ‘Leibniz Bibliographie’, in Handbuch der Geschichte der Philosophie, vol. 14, Frankfurt, Klosterman, 1981, 297–374. Each volume of Studia Leibnitiana—from vol. 1 (1969) onwards—contains a bibliographical survey of the year’s work in Leibniz studies. Concordances 11.18 Finster, R., Hunter, G., McRae, R.F., Miles, M. and Seager, W.E. (eds) Leibniz Lexicon: a Dual Concordance to Leibniz’s ‘Philosophische Schriften’. Concordance I: Printed Philosophical Register with Large Contexts. Concordance II: Microfiche Key-Word-in-Context Concordance. Hildesheim, Olms-Weidmann, 1988. (Concordance to Die Philosophischen Schriften von G.W.Leibniz, ed. C.I.Gerhardt, Berlin, Weidmann, 7 vols, 1875–90). Leibniz’s relations to other philosophers 11.19 Belaval, Y. Leibniz, critique de Descartes, Paris, Gallimard, 1960. 11.20 Friedmann, G. Leibniz et Spinoza, Paris, Gallimard, 1946. 11.21 Hall, A.R. Philosophers at War: The Quarrel between Newton and Leibniz, Cambridge, Cambridge University Press, 1980. 11.22 Jolley, N. Leibniz and Locke: A Study of the New Essays on Human Understanding, Oxford, Clarendon, 1984. 11.23 Loemker, L.E. Struggle for Synthesis: The Seventeenth-Century Background to Leibniz’s Synthesis of Order and Freedom, Cambridge, Mass., Harvard University Press, 1972. 11.24 Mates, B. ‘Leibniz and the Phaedo’, Studia Leibnitiana Supplementa 12 (1973) 135–48. 11.25 Popkin, R. ‘Leibniz and the French Sceptics’, Revue internationale de philosophie 20 (1966) 228–48. 11.26 Schrecker, P. ‘Leibniz and the Timaeus’, Review of Metaphysics 4 (1950–1) 495–505. 11.27 Sleigh, R.C., Jr, Leibniz and Arnauld: A Commentary on their Correspondence, New Haven, Conn., Yale University Press, 1990. The philosophy of Leibniz: general surveys 11.28 Belaval, Y. Leibniz: Initiation à sa philosophie, Paris, Vrin, 1962. 11.29 Broad, C.D. Leibniz: An Introduction, Cambridge, Cambridge University Press, 1975. 11.30 Brown, S. Leibniz, Brighton, Harvester, 1984. 11.31 Cassirer, E. Leibniz’ System in seinen wissenschaftlichen Grundlagen, Marburg, Elwert, 1902. 11.32 Frankfurt, H.G. (ed.) Leibniz: A Collection of Critical Essays, New York, Doubleday, 1972. 11.33 Hooker, M. (ed.) Leibniz: Critical and Interpretive Essays, Minneapolis, Minn., Minnesota University Press, 1982. 11.34 Kulstad, M. (ed.) Essays on the Philosophy of Leibniz, Rice University Studies 63, Houston, Tex., Rice University Press, 1977. 11.35 MacDonald Ross, G. Leibniz, Oxford, Oxford University Press, 1984. 11.36 Rescher, N. The Philosophy of Leibniz, Englewood Cliffs, N.J., Prentice Hall, 1967. 11.37 Rescher, N. Leibniz: An Introduction to his Philosophy, Oxford, Blackwell, 1979. 11.38 Russell, B. A Critical Exposition of the Philosophy of Leibniz, London, Allen & Unwin, 1900. 11.39 Van Peursen, C.A. Leibniz, trans. H.Hoskins, London, Faber & Faber, 1969. Logic and metaphysics 11.40 Adams, R.M. ‘Phenomenalism and Corporeal Substance in Leibniz’, in P. A.French, T.E.Uehling and H.K.Wettstein (eds) Contemporary Perspectives on the History of Philosophy, Midwest Studies in Philosophy 8, 1983, 217–57. 11.41 Broad, C.D. ‘Leibniz’s Last Controversy with the Newtonians’, in [11.62], 157–74. 11.42 Brody, B. ‘Leibniz’s Metaphysical Logic’, in M.Kulstad (ed.) Essays on the Philosophy of Leibniz, Rice University Studies 63, Houston, Tex., Rice University Press , 1977, 43–55. 11.43 Couturat, L. La logique de Leibniz, Paris, Alcan, 1901. 11.44 Couturat, L. ‘Sur la métaphysique de Leibniz’, Revue de métaphysique et de morale 10 (1902) 1–25; English translation by R.Ryan in H.G.Frankfurt (ed.) 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Leibniz: Perception, Apperception, and Thought, Toronto, University of Toronto Press, 1976. 11.70 Parkinson, G.H.R. ‘The Intellectualization of Appearances: Aspects of Leibniz’s Theory of Sensation and Thought’, in M.Hooker (ed.) Leibniz: Critical and Interpretive Essays, Minneapolis, Minn., Minnesota University Press, 1982, 3–20. 11.71 Savile, A. ‘Leibniz’s Contribution to the Theory of Innate Ideas’, Philosophy 47 (1972) 113–24. 11.72 Wilson, M.D. ‘Leibniz and Materialism’, Canadian Journal of Philosophy 3 (1974) 495–513. 11.73 Wilson, M.D. ‘Leibniz: Self-Consciousness and Immortality: in the Paris Notes and After’, Archiv für Geschichte der Philosophie 58 (1976) 335–52. 11.74 Wilson, M.D. ‘Confused Ideas’, in M.Kulstad (ed.) Essays on the Philosophy of Leibniz, Rice University Studies 63, Houston, Tex., Rice University Press, 1977, 123–37.

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