A Tale of Two Thinkers,One Meeting,and Three Degrees of Infinity: Leibniz and Spinoza (1675–8)

The article presents Leibniz's preoccupation (in 1675–6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ‘Leibniz's Problem’ and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ‘Spinoza's solution’ is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's solution is to distinguish between three kinds of infinity and, in particular, between one that applies to substance, and one that applies to numbers, seen as auxiliaries of the imagination. The rest of the paper examines the extent to which Spinoza's solution solves Leibniz's problem. The main thesis I advance is that, when Spinoza and Leibniz say that the divine substance is infinite, in most contexts it is to be understood in non-numerical and non-quantitative terms. Instead, for Spinoza and Leibniz, a substance is said to be infinite in a qualitative sense stressing that it is complete, perfect and indivisible. I argue that this approach solves one strand of Leibniz's problem and leaves another unsolved.     

Leibniz on Infinite Numbers,Infinite Wholes,and Composite Substances

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz's argument against the world soul relies on his rejection of infinite number, and, as such, Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz's rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’ – collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts.     

Mental Manipulations and the Problem of Causal Exclusion

Leibniz has long faced a challenge about the coherence of the distinction between necessary and contingent truths in his philosophy. In this paper, I propose and examine a new way to save genuine contingency within a Leibnizian framework. I conclude that it succeeds in formally solving the problem, but at unbearable cost. I present Leibniz's challenge by considering God's choice of the best possible world (Sect. 2). God necessarily exists and necessarily chooses to actualize the best possible world. The actual world therefore could not be different, for if it were different it would be a distinct and inferior world and hence would not be created. In Section 3, I defend Leibniz from this challenge. I argue that, while it is necessary for God to choose to create the best possible world, it is not necessary for any world to be the best possible. This is because the criterion for judging perfection can itself be contingent. Different criteria will judge different worlds as the best. Thus it is necessary for God to create the best, but not necessary which is the best. Distinguishing between possible worlds in Leibniz's sense and in the modern sense allows a fuller exposition of this position. There are worries that can arise with the claim that the criterion of perfection is contingent. I consider two of the most pressing (Sect. 4). The first argues that the criterion is in God's understanding and hence is necessary; the second alleges that a contingent criterion of perfection violates Leibniz's cherished Principle of Sufficient Reason. These worries are well grounded, and examining them reveals a deep incompatibility between this solution and Leibniz's metaphysical views. I conclude that there is a real solution available, but that it is unacceptable to Leibniz or a Leibnizian. The search for a genuine solution that is genuinely Leibnizian goes on.     

Leibniz's Two Realms Revisited

Leibniz speaks, in a variety of contexts, of there being two realms—a “kingdom of power or efficient causes” and “a kingdom of wisdom or final causes.” This essay explores an often overlooked application of Leibniz's famous “two realms doctrine.” The first part turns to Leibniz's work in optics for the roots of his view that nature can be seen as being governed by two complete sets of equipotent laws, with one set corresponding to the efficient causal order of the world, and the other to its teleological order. The second part offers an account of how this picture of lawful over‐determination is to be reconciled with Leibniz's mature metaphysics. The third addresses a line of objection proposed by David Hirschmann to the effect that Leibniz's doctrine undermines his stated commitment to an efficient, broadly mechanical account of the natural world. Finally, the fourth part suggests that Leibniz's thinking about the harmony of final and efficient causes in connection with corporeal nature may help to shed light on his understanding of the teleological unfolding of monads as well.     

MALEBRANCHE AND LEIBNIZ ON THE BEST OF ALL POSSIBLE WORLDS

In this article I explore Leibniz's claim in the Theodicy that on the essential points Malebranche's theodicy “reduces to” his own view. This judgment may seem to be warranted given that both thinkers emphasize that evils are justified by the fact that they follow from the simple and uniform laws that govern that world which is worthy of divine creation. However, I argue that Leibniz's theodicy differs in several crucial respects from Malebranche's. I begin with a qualified endorsement of Charles Larmore's recent claim that remarks in Malebranche's correspondence with Leibniz indicate that their theodicies rely on incompatible conceptions of the moral rationality of divine action. I also attempt to go beyond Larmore's discussion in highlighting further differences concerning the sort of freedom involved in the divine act of creation. My conclusion is that these differing conceptions of divine morality and divine freedom reveal that in contrast to the case of Leibniz, Malebranche's theodicy not only does not require that God create anything at all, but also is compatible with the result that the world he decides to create is not uniquely the best possible.     

Disinterested Love: Understanding Leibniz's Reconciliation of Self- and Other-Regarding Motives

While he was in the employ of the Elector of Mainz, between 1668 and 1671, Leibniz produced a series of important studies in natural law. One of these, dated between 1670 and 1671, is especially noteworthy since it contains Leibniz's earliest sustained attempt to develop an account of justice. Central to this account is the notion of what Leibniz would later come to call `disinterested love', a notion that remained essentially unchanged in Leibniz's work from this period to the end of his life. Through his notion of disinterested love, Leibniz sought to resolve the supposed conflict between self- and other-regarding motives. For a variety of reasons, many commentators have failed to understand the basis of Leibniz's proposed resolution. My purpose in the present paper is to clarify the terms in which Leibniz effected this resolution, as well as to point out important developments in his later thought concerning the relation between pleasure, good, and happiness.     

Brandom's Leibniz

I discuss an objection by Margaret Wilson against Robert Brandom's interpretation of Leibniz's account of perceptual distinctness. According to Brandom, Leibniz holds that (i) the relative distinctness of a perception is a function of its inferentially articulated content and (ii) apperception, or awareness, is explicable in terms of degrees of perceptual distinctness. Wilson alleges that Brandom confuses ‘external deducibility’ from a perceptual state of a monad to the existence of properties in the world, with ‘internally accessible content’ for the monad in that state. Drawing on Leibniz, I develop a response to Wilson on Brandom's behalf.     

Leibniz on Memory and Consciousness

In this article, I develop a higher-order interpretation of Leibniz's theory of consciousness according to which memory is constitutive of consciousness. I offer an account of Leibniz's theory of memory on which his theory of consciousness may be based, and I then show that Leibniz could have developed a coherent higher-order account. However, it is not clear whether Leibniz held (or should have held) such an account of consciousness; I sketch an alternative that has at least as many advantages as the higher-order theory. This analysis provides an important antecedent to the contemporary discussions of higher-order theories of consciousness.     

Self-concern From Priestley To Hazlitt

This article argues that the Fourth and Fifth of John Toland's Letters to Serena are best understood as a creative confrontation of Spinoza and Leibniz – one in which crucial aspects of Leibniz's thought are extracted from their original context and made to serve a purpose that is ultimately Spinozistic. Accordingly, it suggests that the critique of Spinoza that takes up so much of the fourth Letter, in particular, should be read as a means of `perfecting' Spinoza (via Leibniz), rather than as the outright dismissal it might appear to be. In order to make its case, the article outlines: the supposed problems that Toland finds in Spinoza; what Toland takes from Leibniz, and what he discards, in order to solve these `problems'; and the imprint of Spinoza's naturalism on the eventual `solution' that Toland offers. The article concludes that, whatever the success of this `solution', Toland's speculative labours should still be treated as creative, perspicuous and intrinsically significant.     

German Idealism and the Concept of Punishment

This paper examines the Leibnizian background to Kant's critique of the ontological argument. I present Kant's claim that existence is not a real predicate, already formulated in his pre-critical essay of 1673, as a generalization of Leibniz's reasoning regarding the existence of created things. The first section studies Leibniz's equivocations on the notion of existence and shows that he employs two distinct notions of existence – one for God and another for created substances. The second section examines Kant's position in his early paper of 1763. My claim is that Kant's view of existence in 1763, namely that it is not a predicate, is strongly related to the logical notion of possibility, formulated by Leibniz and accepted by Kant.     

Leibniz on Conatus, Causation, and Freedom

Abstract: In this paper, I address the topic of free will in Leibniz with particular attention to Leibniz's concept of volition, and its analogue in his physics – his concept of force. I argue against recent commentators that Leibniz was a causal determinist, and thus a compatibilist, and I suggest that logical consistency required him to adopt compatibilism given some of the concepts at work in his physics. I conclude by pointing out that the pressures to adopt causal determinism in Leibniz's system are perhaps more severe than those facing the contemporary libertarian, pressures that stem from empirical considerations about the behavior of bodies in the physical world, and the “well‐founding” of those bodies in simple substances.     

Judgment in a dynamic task: Microburst forecasting

The major goals of this research are to (a) study professionals engaging in dynamic, representative task conditions, (b) apply lens model theory to these conditions, (c) learn how judgments are changed in response to changing conditions, and (d) utilize a hierarchical judgment model to investigate the judgment process from perception of data to final judgment. The results indicate that (a) agreement regarding inferred cue values is modest, not because of differences in perception of proximal, directly observed cue values but because of differences in inferences drawn from them, (b) agreement in probability judgments is higher when inferred cue values are specified, (c) little change in judgments occurred over time, and (d) confidence increased over time. The results regarding agreement and accuracy over time were ambiguous.     

Aristotle on Modality: Nicholas DenyerNever Will and Cannot

In De Caelo 1: 11-12 Aristotle argued that whatever is and always will be true is necessarily true. His argument works, once we grant him the highly plausible principle that if something is true, then it can be false if and only if it can come to be false. For example, assume it true that the sun is and always will be hot. No proposition of this form can ever will be hot. No proposition of this form can ever come to be false. Hence this proposition cannot be false. Hence it is necessarily true, and so too is anything that follows from it. In particular, it is necessarily true that the sun is hot. Moreover, if the sun not only is and always will be hot, but also always has been, then it follows by similar reasoning that the sun not only cannot now fail to be hot, but also never could have failed. Anything everlastingly true is therefore, in the strictest sense of the term, necessarily true.     

Leibniz's Concept of Substance and his Reception of John Calvin's Doctrine of the Eucharist

Leibniz saw the question of the eucharist as a crucial stumbling block to the agreement between Lutherans and Calvinists. Mandated together with Daniel Ernst Jablonsky to prepare working documents for the negotiations between Hanover and Brandenburg in 1697, Leibniz carefully read through the Calvinist Confessions of faith and the works of Calvin in their 1671 edition. He made an extensive collection of excerpts from the Confessions of faith and from Calvin's Institutes all intended to show that Calvinists admitted the substantial presence of Christ's body in the eucharist. (This collection of excerpts is analysed here for the first time and compared with another little-known document, the Unvorgreiffliches Bedencken). L. had argued previously in 1691/92 that, contrary to the assertions of Pellisson-Fontanier, his own conception of substance and of Christ's presence in the eucharist was completely different from Calvin's. However, by 1697, it was clear to Leibniz that Calvin's concept of substance, which was broadly speaking Aristotelian, was never defined clearly by the reformer, and could be made to coincide with Leibniz's own notion of substance as force rather than substance in its dimensional sense. At the same time L. dissociated Ubiquitarianism (doctrine characteristic of late sixteenth century Lutheranism, which defended the dimensional presence of Christ's body in heaven and in the eucharist, by arguing that Christ in his divine nature could cause his physical body to be present in several places at the same time) from Lutheranism. He also drove a wedge between the doctrines of Zwingli and Calvin. L. thus attempted to find religious union on a common ontology and he might well have succeeded if it were not for complex political circumstances, which ultimately caused the failure of the negotiations.     

D. Z. Phillips and Wittgenstein's On Certainty

I start from Phillips' discussion of Rhees's dissatisfaction with the idea of a language‐game. Then, from a rereading of Moore, I go on to exemplify interconnected uses of the expressions “language‐game,”“recurrent procedure,”“world‐picture,”“formal procedure,”“agreement in judgment,”“genre picture” and “form of life.” The discussion is related to sense perception, our knowledge of time and space, and the picture‐theory. These topics connect with Wittgenstein's earlier treatment of the will – which changed markedly later. The subtext (in footnotes) confronts (i) the sceptical methods of Descartes and Hume with the grammatical methods of Leibniz, Kant and Wittgenstein, and (ii) the realism of Leibniz and the Tractatus with the transcendental idealism of Kant. My conclusion is that, although the method of Wittgenstein's later work remains in a sense grammatical, (i) in its new form it can free us from the conviction that the intellect can and must resolve one way or the other the conflicts that arise in the course of the latter confrontation, and that (ii), although release from such a conviction is to be seen as the aim of philosophical discourse in general, it allows philosophy to retain its overriding significance. A positive element in that lies in the respect the method demands for that in a human life which is transcendental to the activity of scientific theorising: respect, therefore, for the unique perspective of the individual historical agent.     

Kant's Modalities of Judgment

Abstract: This paper proposes a way to understand Kant's modalities of judgment—problematic, assertoric, and apodeictic—in terms of the location of a judgment in an inference. Other interpretations have tended to understand these modalities of judgment in terms of one or other conventional notion of modality. For example, Mattey (1986) argues that we should take them to be connected to notions of epistemic or doxastic modality. I shall argue that this is wrong, and that these kinds of interpretation of the modality of judgments cannot be reconciled with a key claim made by Kant, namely, that the modality of a judgment does not contribute to its content, and has nothing to do with the matter that is judged. I offer an alternative interpretation based upon Kant's explicating these modalities in terms of the location of a judgment in an inference, whereby the modality of a judgment is determined by the role a judgment plays in a given course of reasoning. If I am right, then Kant in fact presents an intriguing thesis pertaining to the inferential status and potential of all our judgments.     

Monadic Interaction

Leibniz has almost universally been represented as denying that created substances, including human minds and the souls of animals, can causally interact either with one another or with bodies. Yet he frequently claims that such substances are capable of interacting in the special sense of what he calls ‘ideal’ interaction. In order to reconcile these claims with their favored interpretation, proponents of the traditional reading often suppose that ideal action is not in fact a genuine form of causation but instead a merely apparent influence which serves to ‘save the appearances.’ I argue that this traditional reading distorts Leibniz's thought and that he actually considers ideal action a genuine (though non-standard) form of causation.     

Epistemic Principles and Epistemic Circularity

Can we show that our senses are reliable sources of information about the world? To show this, we need to establish that most of our perceptual judgments have been true. But we cannot determine these inductive instances without relying upon sense perception. Thus, it seems, we cannot establish the reliability of sense perception by means of an argument without falling into epistemic circularity. In this paper, I argue that this consequence is not an epistemological disaster. For this purpose, I defend a normative claim that it is reasonable to accept the general reliability of our perceptual judgments, instead of a factual claim that our perceptual judgments are generally reliable. More specifically, I offer a normative practical argument which explains why it is reasonable to accept the general reliability of our perceptual judgments, even though we cannot establish the general reliability of our perceptual judgments by means of theoretical reasoning.     

From the Flos Substantiae to the Vortex: A Shift in Leibniz's Early Philosophy

In February 1676, one of Leibniz's main concerns is with the problem of the seat of the soul and its relationship with the body, to which, in two very short papers, he provides two different solutions: the doctrine of the flos substantiae and the vortex theory. By analyzing the former, I suggest that, despite what other scholars claim, it is far from being an earlier exposition of the notion of monad. I argue that this doctrine is entertained by Leibniz only for a period, but is rejected later on and excluded from the final monadic system. This hypothesis seems to be supported by the shift to the notion of a vortex, which – despite having some evident pantheistic and monistic implications – offers a different solution to the problem of mind‐body union, by identifying the soul as the only cement of matter. In this article, by following the progress of such a shift, we discover some fascinating nuances in the young Leibniz's development.