Why did Leibniz fail to complete his dynamics?

Leibniz’s ‘new science of dynamics’ is typically taken to have been completed in the late monadological metaphysics. On this view, stemming from Martial Gueroult and continuing in the recent interpretations of Robert Adams and Pauline Phemister, Leibniz accomplished his dynamics in his later account of physical forces as merely phenomenal modifications of monadic, metaphysical forces. This paper argues, by contrast, that Leibniz considered the dynamics to be an unfinished project: this is evident in statements from throughout his mature period until his final months. Two possible reasons for the non-completion of the dynamics are discussed. The first is that his encounter with the superior physics of Newton’s Principia caused Leibniz to continually defer his own contribution. I argue, however, in favour of a second reason: that there are philosophical difficulties inherent in the science of dynamics that prevented its completion. These difficulties are found in the relation of dynamics to metaphysics, and in the more fundamental split within dynamics, into the doctrine of primitive and derivative forces. Through three late exchanges with de Volder, Wolff and Des Bosses, I show that the relation of primitive and derivative forces remained an unsolved – although not in principle unsolvable – problem for Leibniz.     

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.     

Essence and Possibility in the Leibniz‐Arnauld Correspondence

In the 1680s, Gottfried Leibniz and Antoine Arnauld engaged in a philosophically rich correspondence. One issue they discuss is modal metaphysics – questions concerning necessity, possibility, and essence. While Arnauld's contributions to the correspondence are considered generally astute, his contributions on this issue have not always received a warm treatment. I argue that Arnauld's criticisms of Leibniz are sophisticated and that Arnauld offers his own Cartesian account in its place. In particular, I argue that Arnauld offers an account of possibility that is actualist (only actual things exist), modal actualist (modality is irreducible) and essence‐based (essences ground de re counterfactuals).     

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.     

Leibniz on Concurrence and Efficient Causation

Leibniz defends concurrentism, the view that both God and created substances are causally responsible for changes in the states of created substances. Interpretive problems, however, arise in determining just what causal role each plays. Some recent work has been revisionist, greatly downplaying the causal role played by created substances—arguing instead that according to Leibniz only God has productive causal power. Though bearing some causal responsibility for changes in their perceptual states, created substances are not efficient causes of such changes. This paper argues against such revisionism; not only was Leibniz a consistent advocate of concurrentism (at least in his “mature” years), but also his account of concurrentism involves both God and created substances as efficient causes of the changes in the states of created substances.     

Metaphysics of quantity and the limit of phenomenal concepts

Quantities like mass and temperature are properties that come in degrees. And those degrees (e.g. 5 kg) are properties that are called the magnitudes of the quantities. Some philosophers talk about magnitudes of phenomenal qualities as if some of our phenomenal qualities are quantities. The goal of this essay is to explore the anti-physicalist implication of this apparently innocent way of conceptualizing phenomenal quantities. I will first argue for a metaphysical thesis about the nature of magnitudes based on Yablo’s proportionality requirement of causation. Then, I will show that, if some phenomenal qualities are indeed quantities, there can be no demonstrative concepts about some of our phenomenal feelings. That presents a significant restriction on the way physicalists can account for the epistemic gap between the phenomenal and the physical. I’ll illustrate the restriction by showing how that rules out a popular physicalist response to the Knowledge Argument.     

The ontomystical argument revisited

I argue that Alexander Pruss’s ontomystical arguments should not be endorsed without further argumentative support of their premises. My specific targets are his claims that (i) Śamkara’s principle is true and (ii) the high mystics had phenomenal experiences of radical dependence and as of a maximally great being. Against (i), I urge a host of counterexamples. The only ways I can see for Pruss to respond to these counterexamples end up falsifying (ii). The key problem which leads to this conclusion is that Pruss needs a criterion for distinguishing phenomenal experiences from non-phenomenal experiences according to which the experiences of the high mystics were phenomenal experiences while the experiences of those persons I discuss in my counterexamples to Śamkara’s principle are not. There appears to be no such criterion. I suggest that the future of the ontomystical arguments lies in developing them as inductive rather than deductive arguments.     

Leibniz's Twofold Gap Between Moral Knowledge and Motivation

Moral rationalists and sentimentalists traditionally disagree on at least two counts, namely regarding the source of moral knowledge or moral judgements and regarding the source of moral motivation. I will argue that even though Leibniz's moral epistemology is very much in line with that of mainstream moral rationalists, his account of moral motivation is better characterized as sentimentalist. Just like Hume, Leibniz denies that there is a necessary connection between knowing that something is right and the motivation to act accordingly. Instead, he believes that certain affections are necessary for moral motivation. On my interpretation, then, Leibniz is an externalist about judgements and motivation: he is committed to a gap between the judgement that something is morally right and the motivation to act accordingly. As a matter of fact, I will argue that there are two gaps. The first and less controversial one has to do with the fact that Leibniz reconciles his psychological egoism with ethical altruism through his account of love. The second gap between moral judgements and motivation is a more fundamental one: Leibniz denies that there are any necessary connections between beliefs and motivation, or even more generally, between perceptions and appetitions.     

Tense And Temporal Semantics

Tenseless theories of time entail that earlierthan, later than and simultaneous with (i.e.,McTaggart's `B-series') are the only temporalproperties exemplified by events. Such theories oftencome under attack for being unable to satisfactorilyaccount for tensed language. In this essay I arguethat tenseless theories of time are capable of twofeats that critics, such as Quentin Smith, argue arebeyond their grasp: (1) They can coherently explainthe impossibility of translating all tensed sentencesby tenseless counterparts; (2) They can account forcertain obviously valid entailment relations betweentensed sentence types. In analyzing tensed entailmentrelations tenselessly, I favor a date analysis oftensed language over a token-reflexive theory. Theupshot is that tenseless theories of time are notundermined by the linguistic facts.     

A REAPPRAISAL OF LEIBNIZ'S VIEWS ON SPACE, TIME, AND MOTION

Leibniz has been widely praised for maintaining against the Newtonians of his day the view that space and time are relative. At the same time, he has been roundly criticized for allowing that we can distinguish absolute from merely relative motion. This distribution of applause and criticism, I will argue, is in a measure unjustified. For on the one hand, those arguments, found in his correspondence with Clarke, by which Leibniz seeks to reject the view that space and time are "something absolute" are for the most part unsatisfactory, and on the other hand, Leibniz was not so naive as his critics have supposed in allowing absolute motions. Sections I - V of this essay will be concerned with the former issue; Leibniz's views on motion will be taken up in Section VI. The chief interest in all of this for present-day philosophers may lie, not so much in the historical issues concerning Leibniz and the Newtonians, but in a meta-philosophical question which inevitably arises from the historical issues, namely, the question whether developments in science can undermine the soundness of philosophical arguments which appeal to ordinary usage.     

Monads at the bottom,monads at the top,monads all over

This paper examines a widely accepted reading of monads as the most fundamental elements of reality. Garber [Leibniz – Body, Substance, Monad, Oxford: Oxford University Press, 2009] argues that simple monads – seen as mind-like atoms without parts and extension – replace the corporeal substance of Leibniz’s middle period. Phemister [Leibniz and the Natural World – Activity, Passivity and Corporeal Substances in Leibniz’s Philosophy, Dordrecht: Springer, 2005] argues that monads figure also at the top as complete corporeal substances. Building on Fichant [‘L’invention métaphysique’ in G.W. Leibniz, Discours de métaphysique suivi de Monadologie et autres textes, edited by Michel Fichant, Paris: Gallimard, 2004], I argue that, for Leibniz, monads function not only as building blocks at the bottom level of composition (for aggregates) but also at the top, as grounding the unity and hence the being of complete substances and organic unities. Since organic unities or living beings are seen by Leibniz as natural machines with a nested structure, and since monads are likened to living beings, this would imply that the use of the concept ‘monad’ holds not only at the bottom, and not only at the top, but all over the range between them.     

Kant's Argument that Existence is not a Determination

In this paper, I examine Kant's famous objection to the ontological argument: existence is not a determination. Previous commentators have not adequately explained what this claim means, how it undermines the ontological argument, or how Kant argues for it. I argue that the claim that existence is not a determination means that it is not possible for there to be non‐existent objects; necessarily, there are only existent objects. I argue further that Kant's target is not merely ontological arguments as such but the larger ‘ontotheist’ metaphysics they presuppose: the view that God necessarily exists in virtue of his essence being contained in, or logically entailed by, his essence. I show that the ontotheist explanation of divine necessity requires the assumption that existence is a determination, and I show that Descartes and Leibniz are implicitly committed to this in their published versions of the ontological argument. I consider the philosophical motivations for the claim that existence is a determination and then I examine Kant's arguments in the Critique of Pure Reason against it.     

Leibniz on the Metaphysics of Color

Drawing on remarks scattered through his writings, I argue that Leibniz has a highly distinctive and interesting theory of color. The central feature of the theory is the way in which it combines a nuanced subjectivism about color with a reductive approach of a sort usually associated with objectivist theories of color. After reconstructing Leibniz's theory and calling attention to some of its most notable attractions, I turn to the apparent incompatibility of its subjective and reductive components. I argue that this apparent tension vanishes in light of his rejection of a widely accepted doctrine concerning the nature of bodies and their geometrical qualities.     

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.     

The Cogito and the Metaphysics of Mind

Descartes used the cogito to make two points the epistemological point that introspection affords us absolute certainty of our existence, and the metaphysical point that subjects are thinking things logically distinct from bodies. Most philosophers accept Descartes’s epistemological claim but reject his metaphysical claim. I argue that we cannot do this if the cogito works, then subjects are non-physical. Although I refrain from endorsing an argument for dualism based on this conditional, I discuss how such an argument would differ from the conceivability arguments pursued by Descartes in the Sixth Meditation and by contemporary philosophers. Unlike those arguments, this argument would not be refuted by the discovery of a posteriori identities between physical and phenomenological properties. In other words, it is possible to argue for substance dualism even if phenomenal properties are physical properties.     

NAGEL VS. NAGEL ON THE NATURE OF PHENOMENAL CONCEPTS

In a footnote to his ‘What is it Like to be a Bat?’, Thomas Nagel sketches a promising account of phenomenal concepts that purports to explain why mind‐body identity statements, even if necessary, will always seem contingent. Christopher Hill and Brian McLaughlin have recently developed this sketch into a more robust theory. In Nagel's more recent work, however, he suggests that the only adequate theory of phenomenal concepts is one that makes the relation between phenomenal and physical states intelligible, or ‘transparent’. Developing such a theory, however, appears to be no easy task. In this paper I argue that the Nagel‐Hill‐McLaughlin proposal is preferable – and that a serious problem with it, noticed by Stephen Yablo, can be avoided by revising the proposal according to some further suggestions made by Nagel himself.     

The relationship between space and mutual interaction: Kant contra Newton and Leibniz

Kant claims that we cannot cognize the mutual interaction of substances without their being in space; he also claims that we cannot cognize a ‘spatial community’ among substances without their being in mutual interaction. I situate these theses in their historical context and consider Kant’s reasons for accepting them. I argue that they rest on commitments regarding the metaphysical grounding of, first, the possibility of mutual interaction among substances-as-appearances and, second, the actuality of specific distance-relations among such substances. By illuminating these commitments, I shed light on Kant’s metaphysics of space and its relation to Newton and Leibniz’s views.     

Restrictions on Representationalism

Strong representationalism claims that the qualitative character of our phenomenal mental states consists in the intentional content of such states. Although strong representationalism has greatly increased in popularity over the last decade, I find the view deeply implausible. In this paper, I attempt to argue against strong representationalism by a two-step argument. First, I suggest that strong representationalism must be unrestricted in order to serve as an adequate theory of qualia, i.e., it must apply to all qualitative mental states. Second, I present considerations – deriving largely from nonperceptual states – to show that an unrestricted form of strong representationalism is problematic.     

Leibniz and the Square: A Deontic Logic for the Vir Bonus

Seventeenth century philosopher Gottfried Leibniz's contributions to metaphysics, mathematics, and logic are well known. Lesser known is his ‘invention’ of deontic logic, and that his invention derives from the alethic logic of the Aristotelian square of opposition. In this paper, I show how Leibniz developed this ‘logic of duties’, which designates actions as ‘possible, necessary, impossible, and omissible’ for a ‘vir bonus’ (good person). I show that for Leibniz, deontic logic can determine whether a given action, e.g. as permitted, is therefore obligatory or prohibited (impossible). Secondly, since the deontic modes are derived from what is possible, necessary, etc., for a good person to do, and that ‘right and obligation’ are the ‘moral qualities’ of a good person, we can see how Leibniz derives deontic logic from these moral qualities. Finally, I show how Leibniz grounds a central deontic concept, namely obligation, in the human capacity for freedom.