How we understand Descartes’s physics rests on how we interpret his ontological commitment to individual bodies, and in particular on how we account for their individuation. However, Descartes’s contemporaries as well as contemporary philosophers have seen Descartes’s account of the individuation of bodies as deeply flawed. In the first part of this paper, I discuss how the various problems and puzzles involved in Descartes’s account of the individuation of bodies arise, and the relevance of these problems for his physics. With (...) an eye toward resolving these puzzles, I argue for an interpretation of the Cartesian ontology in which bodies are not individuated by motion but, instead, are mind-dependent. As part of this reading, I demonstrate the sense in which we can clearly and distinctly perceive bodies, and also the senses in which the real, conceptual, and modal distinctions apply to them. I conclude by explaining how this account of the mind-dependent individuation of bodies is consistent with Descartes’s definition of ‘motion’ and ‘a body’ in Principles, Part II, section 25—the very passage that prima facie entails the most troubling of the individuation puzzles. Finally, I show that this account is consistent with Descartes’s general goal in constructing his physics. (shrink)

Consider a circle and a pair of its semicircles. Which is prior, the whole or its parts? Are the semicircles dependent abstractions from their whole, or is the circle a derivative construction from its parts? Now in place of the circle consider the entire cosmos (the ultimate concrete whole), and in place of the pair of semicircles consider the myriad particles (the ultimate concrete parts). Which if either is ultimately prior, the one ultimate whole or its many ultimate parts?

The problem of qualitative heterogeneity is to explain how an extended simple can enjoy qualitative variation across its spatial or temporal axes, given that it lacks both spatial and temporal parts. I discuss how friends of extended simples should address the problem of qualitative heterogeneity. I present a series of arguments designed to show that rather than appealing to fundamental distributional properties one should appeal to tiny and short-lived tropes. Along the way, issues relevant to debates about material composition, persistence (...) over time and existence monism are discussed.  . (shrink)

Leibniz holds that nothing in nature strictly corresponds to any geometric curve or surface.Yet on Leibniz’s view, physicists are usually able to ignore any such lack of correspondence and to investigate nature using geometric representations. The primary goal of this essay is to elucidate Leibniz’s explanation of how physicists are able to investigate nature geometrically, focussing on two of his claims: (i) there can be things innature which approximate geometric objects to within any given margin of error; (ii) the truths (...) of geometry state laws by which the phenomena of nature are governed. A corollary of Leibniz’s explanation is that physical bodies do have boundaries with which geometric surfaces can be compared to very high levels of precision. I argue that the existence of these physical boundaries is mind-independent to such an extent as to pose a significant challenge to idealist interpretations of Leibniz. (shrink)

Leibniz holds that nothing in nature strictly corresponds to any geometric curve or surface.Yet on Leibniz’s view, physicists are usually able to ignore any such lack of correspondence and to investigate nature using geometric representations. The primary goal of this essay is to elucidate Leibniz’s explanation of how physicists are able to investigate nature geometrically, focussing on two of his claims: (i) there can be things innature which approximate geometric objects to within any given margin of error; (ii) the truths (...) of geometry state laws by which the phenomena of nature are governed. A corollary of Leibniz’s explanation is that physical bodies do have boundaries with which geometric surfaces can be compared to very high levels of precision. I argue that the existence of these physical boundaries is mind-independent to such an extent as to pose a significant challenge to idealist interpretations of Leibniz. (shrink)

In this paper I argue that what has been called Leibniz’s “aggregate argument” for unities in things in fact comprises three quite distinct lines of argument, with different concepts being advanced under the name ‘unity’ and meriting quite different conceptual treatment. Two of those arguments, what I call the Borrowed Reality Argument and the Multitude Argument, also appear in later writings to be further elaborated into arguments not just for unities but for simples. I consider the arguments in detail. I (...) suggest that one of the two, the Borrowed Reality Argument, is philosophically more promising and has the stronger evidence for being central in Leibniz’s thought as he argues for the existence of simple substances. (shrink)

Mathematician and philosopher Hermann Weyl had our subject dead to rights.

According to the Monist Interpretation of Descartes, there is really only one corporeal substance—the entire extended plenum. Evidence for this interpretation seems to be provided by Descartes in the Synopsis of the Meditations, where he claims that all substances are incorruptible. Finite bodies, being corruptible, would then fail to be substances. On the other hand, ‘body, taken in the general sense,’ being incorruptible, would be a corporeal substance. In this paper, I defend a Pluralist Interpretation of Descartes, according to which (...) there are many corporeal substances. In particular, I show that none of the claims in the Synopsis about incorruptibility and substance entail either that finite bodies are not substances, or that the only corporeal substance is the entire plenum. (shrink)

Leibniz argues that God doesn't create everything possible because not all possible things are compossible, that is, compatible with each other. Much recent debate has focused on Leibniz's conception of compossibility. One important aspect of this debate, which has not been examined directly, is the distinction between possible worlds and possible creations: the notion of possible world is more robust than simply whatever God can create. Many commentators have relied on this distinction without a clear formulation of it. I develop (...) the distinction between possible worlds and possible creations by looking at how Leibniz characterizes what God is capable of creating. I argue that possible creations must be both logically consistent and determinate. Possible creations differ from possible worlds insofar as possible creations fail to be either maximal or harmonious. I conclude, therefore, that focusing on the notion of determinateness offers a new approach to answering the question why doesn't God create everything possible? (shrink)

Leibniz argues that Cartesian extension lacks the unity required to be a substance. A key premise of Leibniz’s argument is that matter is a collection or aggregation. I consider an objection to this premise raised by Leibniz’s correspondent Burchard de Volder and consider a variety of ways that Leibniz might be able to respond to De Volder’s objection. I argue that it is not easy for Leibniz to provide a dialectically relevant response and, further, that the difficulty arises from Leibniz’s (...) commitment to part-whole priority in the case of material wholes, a commitment not shared by De Volder. One major implication is that Leibniz relies on a bottom-up conception of material things, which makes his argument vulnerable to objections stemming from certain types of monist positions. (shrink)

Adams presents an in-depth interpretation of three important parts of Leibniz's metaphysics, thoroughly grounded in the texts as well as in philosophical analysis and critique. The three areas discussed are the metaphysical part of Leibniz's philosophy of logic, his essentially theological treatment of the central issues of ontology, and his theory of substance. Adams' work helps make sense of one of the great classic systems of modern philosophy.

Monism is the view that there is only a single material object in existence: the world. According to this view, therefore, the ordinary objects of common sense—cats and hats, cars and stars, and so on—do not actually exist; there is only the world. Because of this, monism is routinely dismissed in the contemporary literature as being absurd and obviously false. It is simply obvious that there is a plurality of material things, thus it is simply obvious that monism is false, (...) or so the argument goes. I call this the common sense argument against monism and in this paper I offer a response. I argue that providing the monist can make his view consistent with the appearance that there is a multiplicity of material things, then it is not rationally acceptable to reject monism solely on the basis of that appearance. Through an appeal to a particular type of property—distributional properties—I sketch out a plausible story of how monism is perfectly consistent with the appearance of plurality, and thus nullify the common sense argument. There may be any number of arguments that serve to undermine monism, but the common sense argument is not one of them. Monism deserves to be taken more seriously than that. (shrink)

The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. Terence Horgan and Matjaz [hacek over z] Potrc [hacek over c] argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth and (...) ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc [hacek over c] consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. Terence E. Horgan is Professor of Philosophy at the University of Arizona. Matjaz [hacek over z] Potrc [hacek over c] is Professor of Philosophy at the University of Ljubljana. (shrink)

Few philosophers have left a legacy like that of Gottfried Wilhelm Leibniz. He has been credited not only with inventing the differential calculus, but also with anticipating the basic ideas of modern logic, information science, and fractal geometry. He made important contributions to such diverse fields as jurisprudence, geology and etymology, while sketching designs for calculating machines, wind pumps, and submarines. But the common presentation of his philosophy as a kind of unworldly idealism is at odds with all this bustling (...) practical activity. In this book Richard. T. W. Arthur offers a fresh reading of Leibniz’s philosophy, clearly situating it in its scientific, political and theological contexts. He argues that Leibniz aimed to provide an improved foundation for the mechanical philosophy based on a new kind of universal language. His contributions to natural philosophy are an integral part of this programme, which his metaphysics, dynamics and organic philosophy were designed to support. Rather than denying that substances really exist in space and time, as the idealist reading proposes, Leibniz sought to provide a deeper understanding of substance and body, and a correct understanding of space as an order of situations and time as an order of successive things. This lively and approachable book will appeal to students of philosophy, as well as anyone seeking a stimulating introduction to Leibniz's thought and its continuing relevance. (shrink)

Gottfried Wilhelm Leibniz was one of the central figures of seventeenth-century philosophy, and a huge intellectual figure in his age. This book from Glenn A. Hartz is an advanced study of Leibniz's metaphysics. Hartz analyzes a very complicated topic, widely discussed in contemporary commentaries on Leibniz, namely the question of whether Leibniz was a metaphysical idealist, realist, or whether he tried to reconcile both trends in his mature philosophy. Because Leibniz is notoriously unclear about this, much has been written on (...) the subject. In recent years, the debate has centered on whether it is possible to maintain compatibility between the two trends. In this controversial book, Hartz demonstrates that it is not possible to maintain compatibility of idealist and realist views - they must be understood as completely separate theories. As the first major work on realism in Leibniz's metaphysics, this key text will interest international Leibniz scholars, as well as students at the graduate level. (shrink)

A provocative ontological-cum-semantic position asserting that the right ontology is austere in its exclusion of numerous common-sense and scientific posits and that many statements employing such posits are nonetheless true. The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. Terence (...) Horgan and Matjaz Potrc argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth and ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. (shrink)

Daniel Garber presents a study of Leibniz's conception of the physical world, elucidating his puzzling metaphysics of monads, mind-like simple substances.

Thomas Holden presents a fascinating study of theories of matter in the seventeenth and eighteenth centuries. These theories were plagued by a complex of interrelated problems concerning matter's divisibility, composition, and internal architecture. Is any material body infinitely divisible? Must we posit atoms or elemental minima from which bodies are ultimately composed? Are the parts of material bodies themselves material concreta? Or are they merely potentialities or possible existents? Questions such as these -- and the press of subtler questions hidden (...) in their amibiguities -- deeply unsettled philosophers of the early modern period. They seemed to expose serious paradoxes in the new world view pioneered by Galileo, Descartes, and Newton. The new science's account of a fundamentally geometrical Creation, mathematicizable and intelligible to the human inquirer, seemed to be under threat. This was a great scandal, and the philosophers of the period accordingly made various attempts to disarm the paradoxes. All the great figures address the issue: most famously Leibniz and Kant, but also Galileo, Hobbes, Newton, Hume, and Reid, in addition to a crowd of lesser figures. Thomas Holden offers a brilliant synthesis of these discussions and presents his own overarching interpretation of the controversy, locating the underlying problem in the tension between the early moderns' account of material parts on the one hand and the program of the geometrization of nature on the other. (shrink)

Contemporary philosophers commonly suppose that any fundamental entities there may be are maximally determinate. More generally, they commonly suppose that, whether or not there are fundamental entities, any determinable entities there may be are grounded in, hence less fundamental than, more determinate entities. So, for example, Armstrong takes the physical objects constituting the presumed fundamental base to be “determinate in all respects” (1961, 59), and Lewis takes the properties characterizing things “completely and without redundancy” to be “highly specific” (1986, 60). (...) Here I look at the usually cited reasons for these suppositions as directed against the case of determinable properties, in particular, and argue that none is compelling (Sections 1 to 3). The discussion in Section 3 moreover identifies positive reason for taking some determinable properties to be part of a fundamental (or relatively fundamental) base. I close (Section 4) by noting certain questions arising from the possibility of fundamental determinables, as directions for future research. (shrink)

Mereological nihilism says that there do not exist (in the fundamental sense) any objects with proper parts. A reason to accept it is that we can thereby eliminate 'part' from fundamental ideology. Many purported reasons to reject it - based on common sense, perception, and the possibility of gunk, for example - are weak. A more powerful reason is that composite objects seem needed for spacetime physics; but sets suffice instead.

Leibniz’s correspondence with Antoine Arnauld is one of the clearest and most comprehensive expressions of Leibniz’s philosophy in the so-called middle period. This chapter will explore the philosophical content of this correspondence. It will concentrate on four of the most central topics: (a) complete concepts and contingency, (b) substance and body, (c) causation, and (d) the special status of rational souls in God’s plan.