The `problem of time' is a cluster of interpretational and formal issues in the foundations of general relativity relating to both the representation of time in the classical canonical formalism, and to the quantization of the theory. The purpose of this short chapter is to provide an accessible introduction to the problem.

In this paper I examine G. W. Leibniz’s view on the debate between occasionalists, mere conservationists, and concurrentists. Although commentators agree that Leibniz wants to reject occasionalism and mere conservationism, there is considerable disagreement about whether Leibniz is committed to a theory of divine concurrence that differs from occasionalism and mere conservationism in principled ways. I critically assess three interpretations of Leibniz’s theory in this paper. The first two (those of Robert Adams and Sukjae Lee) differ with respect to important (...) details, but they both assume that Leibniz straightforwardly affirms the continual creation doctrine. I argue that a coherent Leibnizian theory of divine concurrence cannot be constructed on the ontological framework that the continual creation doctrine provides. The third interpretation that I consider holds that Leibniz is willing to affirm the continual creation doctrine only to the extent that it provides an acceptable way of characterizing the dependence of finite substances on God at the level of appearances. It is suggested that Leibniz’s deep metaphysical view of creation and conservation is that in a single act God creates and conserves substances that are non‐spatial and atemporal at the deepest level of metaphysical rigor. I argue that this alternative account of creation and conservation provides a promising ontological framework that can support a coherent theory of creaturely activity that does not collapse into occasionalism or mere conservationism. (shrink)

This paper examines Leibniz’s views on the theistic doctrine of continual creation and considers their implications for his theory of finite substance. Three main theses are defended: (1) that Leibniz takes the traditional account of continual creation to involve the literal re-creation of all things in a successive series of instantaneous states, (2) that a straightforward commitment to the traditional account would give rise to serious problems within Leibniz’s theory of finite substance and his metaphysics more generally, and (3) that (...) Leibniz does not straightforwardly affirm the continual creation doctrine, despite certain texts that initially seem to suggest otherwise. I also present a more speculative interpretive hypothesis about what Leibniz’s considered view of creation might have been, namely that in a single act, God creates and conserves substances that are non-spatial and atemporal at the deepest level of reality. (shrink)

In the early twentieth century, a rare strain of British idealism emerged which took Leibniz's Monadology as its starting point. This paper discusses a variant of that strain, offered by Hilda Oakeley. I set Oakeley's monadology in its philosophical context and discuss a key point of conflict between Oakeley and her fellow monadologists: the unreality of time. Oakeley argues that time is fundamentally real, a thesis arguably denied by Leibniz and subsequent monadologists, and by all other British idealists. This paper (...) discusses Oakeley's argument for the reality of time, and Oakeley's attack on the most famous account of the unreality of time offered in her day: that of J. M. E. McTaggart. I show that Oakeley's critique of McTaggart can be extended to challenge all monadologists, including that of the great monad, Leibniz himself. (shrink)

This paper explores various metaphysical aspects of Leibniz’s concepts of space, motion, and matter, with the intention of demonstrating how the distinctive role of force in Leibnizian physics can be used to develop a theory of relational motion using privileged reference frames. Although numerous problems will remain for a consistent Leibnizian relationist account, the version developed within our investigation will advance the work of previous commentators by more accurately reflecting the specific details of Leibniz’s own natural philosophy, especially his handling (...) of the dynamical interactions of plenum bodies. (shrink)

En este artículo examinamos los aspectos más relevantes de la concepción del espacio de Leibniz. A través de un enfoque genético, nuestro propósito es mostrar que, en su desarrollo evolutivo, dicha concepción sufre dos transiciones destacables, las que separan y distinguen tres versiones teóricas. En su juventud, Leibniz defiende una concepción substancialista del espacio. Sin embargo, debido a la adopción del nominalismo, dicha concepción sufre un primer giro que decanta en un monismo substancialoide, el que se consolida en el período (...) medio de la filosofía de Leibniz. Ya en el período tardío, Leibniz reformula, en una segunda transición, su concepción del espacio, la que adopta la forma definitiva de -lo que llamamos- un relacionismo substancialoide. (shrink)

Anyone preparing to work through Catherine Wilson's important 1989 book, Leibniz's Metaphysics, would be well advised to go back for another look at Bertrand Russell's Critical Exposition of the Philosophy of Leibniz, for it is this book that provides the foil and the context for much that Wilson has to say. In particular, the preface to Russell's first edition stresses the very points regarding both methodology and content on which Wilson will disagree most vigorously with her predecessor.

This essay proposes a new interpretation of a central, and yet overlooked, argument Leibniz offers against Descartes’s power-free ontology of the corporeal world. Appealing to considerations about the successiveness of motion, Leibniz attempts to show that the reality of motion requires force. It is often assumed that the argument is driven by concerns inspired by Zeno. Against such a reading, this essay contends that Leibniz’s argument is instead best understood against the background of an Aristotelian view of the priority of (...) real being over time. The essay also shows how this alternative interpretation can help to shed new light on the difference between Leibnizian forces and Aristotelian powers, as well as on Leibniz’s famous claim that accounting for force leads us beyond the mechanistic corporeal realm. (shrink)

As an idealist, Gottfried Wilhelm Leibniz could not recognize anything corporeal as substantial. However, under the influence of Cartesian terminology, he devoted considerable effort to analysing the corporeal world, while not recognizing its real substantiality of course. Leibniz took the concept of substance from Plato, Aristotle and the scholastics, but developed it in two ways. It is a well-known fact that Leibniz introduced the term ‘corporeal substance’ in his letter to Antoine Arnauld dated to October 1687. In the letter, Leibniz (...) understands an object of nature, like an animal or a plant, as ‘corporeal substance’. In the very same letter, Leibniz introduces the terms ‘indivisibility’ and ‘phenomenon’. Every corporeal substance can be real only as a unity, i.e. by being indivisible. Such entity must have a soul or at least an entelechy. In an opposite case, that entity would not be a real unity but just a phenomenon. No corporeal entity is indivisible and therefore not a substance. The paper aims at introducing Leibniz’s distinction between substances and phenomena and taking a closer look at the historicalphilosophical influences Leibniz experienced while developing his views of the corporeal world. Aristotle and Descartes will receive most of the attention, of course, as the concepts of ‘entelechy’ and ‘hylomorphism’ were introduced by the former, and the understanding of corporeal substance as determined by extension alone is part of the latter. The core of the original critique by Leibniz takes off from the properties of the continuum as well as the nature of shape, motion and extension. The case of continuum will receive special attention. It is analysed with the help of the novel approaches by Samuel Levey and Vassil Vidinsky. Leibniz was critical about our poor understanding of the continuum but his own interpretation of it was not fully consistent either. Although the new developments enable us to take a fresh look that has not been possible so far, the issue remains open for further study. (shrink)

Kant holds that the applicability of the moral ‘ought’ depends on a kind of agent-causal freedom that is incompatible with the deterministic structure of phenomenal nature. I argue that Kant understands this determinism to threaten not just morality but the very possibility of our status as rational beings. Rational beings exemplify “cognitive control” in all of their actions, including not just rational willing and the formation of doxastic attitudes, but also more basic cognitive acts such as judging, conceptualizing, and synthesizing.

This essay offers an account of the relationship between extended Leibnizian bodies and unextended Leibnizian monads, an account that shows why Leibniz was right to see intimate, explanatory connections between his studies in physics and his mature metaphysics. The first section sets the stage by introducing a case study from Leibniz's technical work on the strength of extended, rigid beams. The second section draws on that case study to introduce a model for understanding Leibniz's views on the relationship between derivative (...) and primitive forces. The third section draws on Leibniz's understanding of the relationship between derivative and primitive forces in order to shed light, in turn, on his understanding of the relationship between extended, material bodies and unextended, immaterial monads. The fourth section responds to a likely objection by arguing that Leibniz's monads may, in a perfectly reasonable sense, be spatially located. (shrink)

It is widely believed that relationism cannot make room for the possibility of intervals of time during which no changes occur. Benovsky has recently challenged this belief, arguing that relationists can account for the possibility of changeless time in much the same way as substantivalists do, thereby concluding that the two views are interchangeable for all theoretical purposes. This paper intends to defend the meaningfulness of the traditional dispute between substantivalists and relationists, by contending that the particular form of relationism (...) on which Benovsky has based his criticism is in fact alien to that debate. (shrink)

Between 1698 and 1706 Leibniz was engaged in one of his most interesting correspondences, with the Dutch philosopher and physicist Burcher de Volder. The two men were concerned primarily with the question of how the motion of bodies can be explained without appeal to the direct intervention of God. Leibniz presented a naturalistic account of motion to De Volder, but failed to convince him of its adequacy. I shall examine one reason for this failure - the disagreement that arose over (...) the issue of whether there is a substance whose nature is constituted by extension. (shrink)

Leibniz's widely influential account of time provides a significant puzzle for those seeking to locate this account within his hierarchical ontology. Leibniz follows his scholastic predecessors in supposing that there are different grades of being, with substances being the most real and all other things possessing their reality via their relationships to substance. Following this picture, Leibniz suggests that phenomenal bodies only possess the being that they derive from the substances (i.e., monads) that ground them. Some would argue that time (...) likewise only possesses its being based on the bodies that it relates. Contrary to this suggestion (i.e., that time is twice removed from substances), I will argue that time is derived directly from rational souls. Thus, I will argue that time is on an ontological par with the phenomenal world of bodies. (shrink)

It has recently been suggested that, for Leibniz, temporal facts globally supervene on causal facts, with the result that worlds differing with respect to their causal facts can be indiscernible with respect to their temporal facts. Such an interpretation is at variance with more traditional readings of Leibniz’s causal theory of time, which hold that Leibniz reduces temporal facts to causal facts. In this article, I argue against the global supervenience construal of Leibniz’s philosophy of time. On the view of (...) Leibniz defended here, he adopts a non-modal reduction of time to events, a form of reductionism that entails a strong covariation between a world’s temporal facts and its causal facts. Consequently, worlds discernible with respect to their temporal facts must be discernible with respect to their causal facts, and worlds discernible with respect to their causal facts must be discernible with respect to their temporal facts. This position strongly favors the standard identificatory reduction of time to causation often imputed to Leibniz. (shrink)

The aim of this paper is to analyze Leibniz and Newton’s conception of space, and to point out where their agreements and disagreements lie with respect to its mode of existence. I shall offer a definite characterization of Leibniz and Newton’s conceptions of space. I will show that, according to their own concepts of substance, both Newtonian and Leibnizian spaces are not substantiva!. The reason of that consists in the fact that space is not capable of action. Moreover, there is (...) a sense in which space is relational, because their parts are individuated only by means of their mutual relations. (shrink)

This paper reexamines the historical debate between Leibniz and Newton on the nature of space. According to the traditional reading, Leibniz (in his correspondence with Clarke) produced metaphysical arguments (relying on the Principle of Sufficient Reason and the Principle of Identity of Indiscernibles) in favor of a relational account of space. Newton, according to the traditional account, refuted the metaphysical arguments with the help of an empirical argument based on the bucket experiment. The paper claims that Leibniz’s and Newton’s arguments (...) cannot be understood apart from the distinct dialectics of their respective positions vis-à-vis Descartes’ theory of space and physics. Against the traditional reading, the paper argues that Leibniz and Newton are operating within a different metaphysics and different conceptions of “place,” and that their respective arguments can largely remain intact without undermining the other philosopher’s conception of space. The paper also takes up the task of clarifying the distinction between true and absolute motion, and of explaining the relativity of motion implied by Leibniz’s account. The paper finally argues that the two philosophers have different conceptions of the relation between metaphysics and science, and that Leibniz’s attempt to base physical theory on an underlying metaphysical account of forces renders his account of physics unstable. (shrink)

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles (...) and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

This book presents an in-depth interpretation of three important parts of Leibniz's metaphysics: the metaphysical part of Leibniz's philosophy of logic, his essentially theological treatment of the central issues of ontology, and his theory of substance.

This anthology is about the signal change in Leibniz’s metaphysics with his explicit adoption of substantial forms in 1678-79. This change can either be seen as a moment of discontinuity with his metaphysics of maturity or as a moment of continuity, such as a passage to the metaphysics from his last years. Between the end of his sejour at Paris and the first part of the Hanover period, Leibniz reformed his dynamics and began to use the theory of corporeal substance. (...) This book explores a very important part of the philosophical work of the young Leibniz. Expertise from around the globe is collated here, including Daniel Garber’s work based on the recent publication of Leibniz's correspondence from the late 1690s, examining how the theory of monads developed during these crucial years. Richard Arthur argues that the introduction of substantial forms, reinterpreted as enduring primitive forces of action in each corporeal substance, allows Leibniz to found the reality of the phenomena of motion in force and thus avoid reducing motion to a mere appearance. Amongst other themes covered in this book, Pauline Phemister’s paper investigates Leibniz’s views on animals and plants, highlighting changes, modifications and elaborations over time of Leibniz’s views and supporting arguments and paying particular attention to his claim that the future is already contained in the seeds of living things. The editor, Adrian Nita, contributes a paper on the continuity or discontinuity of Leibniz’s work on the question of the unity and identity of substance from the perspective of the relation with soul and mind. (shrink)

Leibniz argues against Descartes’s conception of material substance based on considerations of unity. I examine a key premise of Leibniz’s argument, what I call the Plurality Thesis—the claim that matter (i.e. extension alone) is a plurality of parts. More specifically, I engage an objection to the Plurality Thesis stemming from what I call Material Monism—the claim that the physical world is a single material substance. I argue that Leibniz can productively engage this objection based on his view that matter is (...) discrete. The discreteness of matter provides two aspects of support for the Plurality Thesis. First, it indicates that the parts of matter do not share boundaries and are, therefore, independent in an important sense. Second, it indicates that the parts of matter are determinate and are, therefore, ontologically prior to the wholes they compose. (shrink)