Puryear develops an objection against a prominent attempt to show that the universe must have a temporal beginning. Here I formulate a reply.

We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed (...) with this account, we are ineluctably driven to introduce a highly constructive notion of (outer) measure based exclusively on the total magnitude of potentially infinite collections of line segments. The Paradox of Measure then consists in the proof that every finite or potentially infinite collection of points lacks magnitude with respect to this notion of measure. We observe that the Paradox of Measure, thus understood, troubled analysts into the 1880’s, despite their knowledge that the linear continuum is uncountable. The Paradox was ultimately resolved by Borel in his thesis of 1893, as a corollary to his celebrated result that every countable open cover of a closed line segment has a finite sub-cover, a result he later called the “First Fundamental Theorem of Measure Theory.” This achievement of Borel has not been sufficiently appreciated. We conclude with a metamathematical analysis of the resolution of the paradox made possible by recent results in reverse mathematics. (shrink)

The correspondence between Samuel Clarke and Anthony Collins of 1706–8, while not well known, is a spectacularly good debate between a dualist and a materialist over the possibility of giving a materialist account of consciousness and personal identity. This article puts the Clarke Collins Correspondence in a broader context in which it can be better appreciated, noting that it is really a debate between John Locke and Anthony Collins on one hand, and Samuel Clarke and Joseph Butler on the other. (...) Anthony Collins argues on behalf of John Locke's claim that it would be as easy for God to superadd the power of thinking to matter as for him to connect a soul to a body. Locke did not believe that matter could naturally produce thought or consciousness, but it was in God's power to make matter think. To defend Locke's claim Collins must defend the claim that there are emergent properties in the world – properties of a whole that are not possessed by the parts. Collins also defends a materialist version of Locke's account of personal identity against a variety of charges. Because the topics of debate in the correspondence are of such great interest to us, it deserves to be rescued from the neglect into which it fell and from which intellectual historians and philosophers have only recently and partially removed it. (shrink)

Ned Markosian argues (Australasian Journal of Philosophy 76:213-228, 1998a; Australasian Journal of Philosophy 82:332-340, 2004a, The Monist 87:405-428, 2004b) that simples are ‘maximally continuous’ entities. This leads him to conclude that there could be non-particular ‘stuff’ in addition to things. I first show how an ensuing debate on this issue McDaniel (Australasian Journal of Philosophy 81(2):265-275, 2003); Markosian (Australasian Journal of Philosophy 82:332-340, 2004a) ended in deadlock. I attempt to break the deadlock. Markosian’s view entails stuff-thing coincidence, which I show (...) is just as problematic as the more oft-discussed thing-thing coincidence. Also, the view entails that every particular is only contingently so. If there is a world W like our own, but with ether, then there would be only one object in W. But, since merely adding ether to a world does not destroy the entities in it, then W contains counterparts of all the entities in the actual world—they just are not things. Hence, if simples are maximally continuous, then every actual particular is only contingently so. This in turn entails the following disjunction: (i) identity is contingent or intransitive, or (ii) there are no things at all in the actual world, or (iii) the distinction between stuff and things is one without a difference. I recommend that we reject this stuff-thing dualism. (shrink)

This article investigates the problem of the identity of the parts of space in Newton’s natural philosophy, as well as the holistic or structuralist nature of Newton’s ontology of space. Additionally, this article relates the lessons reached in this historical and philosophical investigation to analogous debates in contemporary space-time ontology. While previous contributions, by Nerlich, Huggett, and others, have proven to be informative in evaluating Newton’s claims, it will be argued that the underlying goals of Newton’s views have largely eluded (...) prior analysis and that Newton’s approach is similar, and lends support, to several current structuralist trends in the conception of space-time ontology. (shrink)

In Metaphysical Themes: 1274–1671, Robert Pasnau compares the medieval and early modern approaches to the material-immaterial divide and suggests the medievals held the advantage on this issue. I argue for the opposite conclusion. I also argue against his suggestion that we should approach the divide through the notion of a special type of extension for immaterial entities, and propose that instead we should focus on their indivisibility.

Leibniz argues that there must be a fundamental level of simple substances because composites borrow their reality from their constituents and not all reality can be borrowed. I contend that the underlying logic of this ‘borrowed reality argument’ has been misunderstood, particularly the rationale for the key premise that not all reality can be borrowed. Contrary to what has been suggested, the rationale turns neither on the alleged viciousness of an unending regress of reality borrowers nor on the Principle of (...) Sufficient Reason, but on the idea that composites are phenomena and thus can be real only insofar as they have a foundation in substances, from which they directly ‘borrow’ their reality. The claim that composites are phenomena rests in turn on Leibniz's conceptualism about relations. So understood, what initially looked like a disappointingly simple argument for simples turns out to be a rather rich and sophisticated one. (shrink)

This paper argues that all of the standard theories about the divisions of space and time can benefit from, and may need to rely on, parsimony considerations. More specifically, whether spacetime is discrete, gunky or pointy, there are wildly unparsimonious rivals to standard accounts that need to be resisted by proponents of those accounts, and only parsimony considerations offer a natural way of doing that resisting. Furthermore, quantitative parsimony considerations appear to be needed in many of these cases.

In this paper, I argue that Spinoza holds a perspectivalist view of mereological composition, a form of anti-realism. The paper has two parts: In the first half of the paper, I introduce interpretive puzzles for the standard realist reading of Spinoza’s mereology. In the second half of the paper, I discuss Spinoza’s positive view on mereological composition and present a perspectivalist reading that avoids the interpretive puzzles.

In Spinoza’s substance monism, radically different attributes constitute the essence of one and the same substance qua a strongly unified whole. Showing how this is possible poses a formidable Cartesian challenge to Spinoza’s metaphysics. In this paper I suggest a reconstruction of Spinoza’s notion of substance that meets this challenge and explains a major feature of this notion. I then show how this reconstruction can be used to resolve two fundamental problems of the Cartesian framework that pertain to Spinoza’s metaphysics. (...) On this basis, I then explain two further major features of Spinoza’s notion of substance. While my suggested reconstruction has all these advantages and accords well with Spinoza’s conceptual framework, it goes beyond what he explicitly says concerning substance monism. It is in the spirit of his metaphysical framework rather than in its letter. Thus, all I intend to show is that Spinoza has the conceptual resources for coming to terms with some of the deep problems that beset his metaphysics. (shrink)

The problem of the “identity of identity and nonidentity”, which haunted German idealism, has two closely related aspects. The first, epistemological aspect concerns the possibility of knowledge of an objective world. The second, transcendental aspect, concerns the question of how thoughts can be directed towards the world. Reconstructing McDowell’s Kantian account of intentionality as a purported resolution of the transcendental aspect of IINI, I pose the following dilemma for McDowell’s account: Either part ways with Kant’s purported resolution of IINI at (...) a crucial point, thereby being driven towards an approach that McDowell firmly opposes, indeed cannot accept, or follow Kant to the letter, and then face, head-on, a deep problem that Kant’s purported resolution of IINI faces. Parting ways, as I show, with Kant’s purported resolution of IINI, McDowell finds himself impaled upon the first horn of this dilemma. Were he, however, to respond by following Kant to the letter, McDowell would find himself impaled upon the second horn. Thus, I conclude, McDowell’s account of intentionality fails. (shrink)

When some objects are the parts of another object, they compose that object and that object is composite. This article is intended as an introduction to the central questions about composition and a highly selective overview of various answers to those questions. In §1, we review some formal features of parthood that are important for understanding the nature of composition. In §2, we consider some answers to the question: which pluralities of objects together compose something? As we will see, the (...) dominant answers are all of them and none of them. In §§3-4, we examine one of the main arguments that has driven philosophers to these extreme answers: the argument from vagueness. In §5, we turn to the question of whether composition is unique: is it sometimes the case that some things compose more than one thing? Finally, in §6, we turn from the question of which composites exist to the question of which composites exist fundamentally. (shrink)

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)

We do not fully understand Hume’s account of space if we do not understand his view of determinations of extension, which is too much ignored a topic. In this paper, I argue for an interpretation that determinations of extension are unities in Hume’s view: single beings in addition to their components. This realist reading is reasonable on both textual and philosophical grounds. There is strong textual evidence for it and no textual reason to reject it. Realism makes perfect sense of (...) the metaphysics of determinations of extension along Humean lines and Hume’s view of spatial relations. (shrink)

The employment by seventeenth-century natural philosophers of stock theological notions like creation, immensity, and eternity in the articulation and justification of emerging physical programs disrupted a delicate but longstanding balance between transcendent and immanent conceptions of God. By playing a prominent (if not always leading) role in many of the major scientific developments of the period, God became more intimately involved with natural processes than at any time since antiquity. In this discussion, I am particularly concerned with the causal and (...) spatio-temporal relations between God and nature in the seventeenth century as recent scholarship has revealed how dramatically traditional conceptions of these relations were transformed by philosophers and scientists like Descartes, Malebranche, More, and Newton. (shrink)

The paper argues that digital ontology (the ultimate nature of reality is digital, and the universe is a computational system equivalent to a Turing Machine) should be carefully distinguished from informational ontology (the ultimate nature of reality is structural), in order to abandon the former and retain only the latter as a promising line of research. Digital vs. analogue is a Boolean dichotomy typical of our computational paradigm, but digital and analogue are only “modes of presentation” of Being (to paraphrase (...) Kant), that is, ways in which reality is experienced or conceptualised by an epistemic agent at a given level of abstraction. A preferable alternative is provided by an informational approach to structural realism, according to which knowledge of the world is knowledge of its structures. The most reasonable ontological commitment turns out to be in favour of an interpretation of reality as the totality of structures dynamically interacting with each other. The paper is the first part (the pars destruens) of a two-part piece of research. The pars construens, entitled “A Defence of Informational Structural Realism”, is developed in a separate article, also published in this journal. (shrink)

This paper aims to clarify Locke’s distinction between simple and complex ideas. I argue that Locke accepts what I call the “compositional criterion of simplicity.” According to this criterion, an idea is simple just in case it does not have another idea as a proper part. This criterion is prima facie inconsistent with Locke’s view that there are simple ideas of extension. This objection was presented to Locke by his French translator, Pierre Coste, on behalf of Jean Barbeyrac. Locke responded (...) to Barbeyrac’s objection, but his response, along with a passage from Chapter XV of Book II of the Essay, “Of Duration and Expansion, considered together,” has been taken to show that he did not accept the compositional criterion. I examine these passages and argue that they are not in tension with but rather affirm that criterion. (shrink)

Pan-dispositionalism is one of the major theories in current analytic metaphysics concerning dispositional properties and how they relate to categorical properties. According to pan-dispositionalists, all fundamental properties are dispositional in nature, such that any supposed categorical properties are either unreal or reducible in some way to the dispositional. I argue that if pan-dispositionalism is true then metaphysical naturalism is false. To the extent that one finds pan-dispositionalism a plausible theory, one ought to question the truth of metaphysical naturalism. On the (...) other hand, if one is a committed metaphysical naturalist, one ought to question the truth of pan-dispositionalism. Either way we get a significant result, of interest both to those working in metaphysics and to those working in philosophy of religion. (shrink)

Is there a fundamental layer of objects in nature? And if so what sorts of things populate it? Among those who answer ‘yes’ to the first question, a common answer to the second is ‘atoms,’ where an atom is understood in the original sense of an object that is spatially unextended, indivisible, and wholly lacking in proper parts. Here I explore some of the ontological consequences of atomism. First, if atoms are real, then whatever motion they appear to undergo must (...) be discrete. The link between atomism and discrete motion goes back at least to Aristotle and is admitted by some atomists, but the full significance of that admission has been neglected. I argue that a commitment to discrete motion in turn entails significant and sometimes counter-intuitive results. I also examine the implications of these results for the philosophy of mind and for discussions of metaphysical naturalism. (shrink)

Extended simples are physical objects that, while spatially extended, possess no actual proper parts. The theory that physical reality bottoms out at extended simples is one of the principal competing views concerning the fundamental composition of matter, the others being atomism and the theory of gunk. Among advocates of extended simples, Markosian’s ‘MaxCon’ version of the theory has justly achieved particular prominence. On the assumption of causal realism, I argue here that the reality of MaxCon simples would entail the reality (...) of irreducible, intrinsic dispositional properties. The existence of dispositional properties in turn has important implications for another central debate in metaphysics, namely that between two major competing views concerning the ontology of laws: dispositionalism versus nomological necessitarianism. (shrink)

There are four main theories concerning the ultimate constitution of matter: atomism version 1, atomism version 2, the theory of gunk, and the theory of extended simples. These four theories are usually seen as diametrically opposed. Here I take a stab at ecumenism, and argue that atomism version 1 and the theory of extended simples can be reconciled and rendered compatible by reference to the reality of dispositions.

Hume’s discussion of space, time, and mathematics at T 1.2 appeared to many earlier commentators as one of the weakest parts of his philosophy. From the point of view of pure mathematics, for example, Hume’s assumptions about the infinite may appear as crude misunderstandings of the continuum and infinite divisibility. I shall argue, on the contrary, that Hume’s views on this topic are deeply connected with his radically empiricist reliance on phenomenologically given sensory images. He insightfully shows that, working within (...) this epistemological model, we cannot attain complete certainty about the continuum but only at most about discrete quantity. Geometry, in contrast to arithmetic, cannot be a fully exact science. A number of more recent commentators have offered sympathetic interpretations of Hume’s discussion aiming to correct the older tendency to dismiss this part of the Treatise as weak and confused. Most of these commentators interpret Hume as anticipating the contemporary idea of a finite or discrete geometry. They view Hume’s conception that space is composed of simple indivisible minima as a forerunner of the conception that space is a discretely (rather than continuously) ordered set. This approach, in my view, is helpful as far as it goes, but there are several important features of Hume’s discussion that are not sufficiently appreciated. I go beyond these recent commentators by emphasizing three of Hume’s most original contributions. First, Hume’s epistemological model invokes the “confounding” of indivisible minima to explain the appearance of spatial continuity. Second, Hume’s sharp contrast between the perfect exactitude of arithmetic and the irremediable inexactitude of geometry reverses the more familiar conception of the early modern tradition in pure mathematics, according to which geometry (the science of continuous quantity) has its own standard of equality that is independent from and more exact than any corresponding standard supplied by algebra and arithmetic (the sciences of discrete quantity). Third, Hume has a developed explanation of how geometry (traditional Euclidean geometry) is nonetheless possible as an axiomatic demonstrative science possessing considerably more exactitude and certainty that the “loose judgements” of the vulgar. (shrink)

This paper distinguishes in Maxwell’s thought between “atomic molecules” and “ultimate atoms,” and arrives at a set of properties that characterize each type of atom. It concludes that Maxwell is a mathematical atomist, an approach that entails the notion that although it is impossible to observe the ultimate atoms as free particles, we can nevertheless study them as mathematical observables, on the caveat that mathematical formalism remains tied to phenomenalism and to theoretical interpretations of such phenomena as, for example, mass (...) and force variations, gravitational pull, gas diffusion and viscosity, and heat conduction. (shrink)

Is it possible for an individual that has gone out of being to come back into being again? The English Aristotelian, Thomas White, argued that it is not. Thomas Hobbes disagreed, and used the case of the Ship of Theseus to argue that individuals that have gone out of being may come back into being again. This paper provides the first systematic account of their arguments. It is doubtful that Hobbes has a consistent case against White. Still his criticism may (...) have prompted White to clarify his views on identity over time in his later work. (shrink)

We think of a boundary whenever we think of an entity demarcated from its surroundings. There is a boundary (a line) separating Maryland and Pennsylvania. There is a boundary (a circle) isolating the interior of a disc from its exterior. There is a boundary (a surface) enclosing the bulk of this apple. Sometimes the exact location of a boundary is unclear or otherwise controversial (as when you try to trace out the margins of Mount Everest, or even the boundary of (...) your own body). Sometimes the boundary lies skew to any physical discontinuity or qualitative differentiation (as with the border of Wyoming, or the boundary between the upper and lower halves of a homogeneous sphere). But whether sharp or blurry, natural or artificial, for every object there appears to be a boundary that marks it off from the rest of the world. Events, too, have boundaries — at least temporal boundaries. Our lives are bounded by our births and by our deaths; the soccer game began at 3pm sharp and ended with the referee's final whistle at 4:45pm. It is sometimes suggested that even abstract entities, such as concepts or sets, have boundaries of their own, and Wittgenstein could emphatically proclaim that the boundaries of our language are the boundaries of our world. Whether all this boundary talk is coherent, however, and whether it reflects the structure of the world or simply the organizing activity of our mind, are matters of deep philosophical controversy. (shrink)

An encyclopedia entry which covers various revisionary conceptions of which macroscopic objects there are, and the puzzles and arguments that motivate these conceptions: sorites arguments, the argument from vagueness, the puzzles of material constitution, arguments against indeterminate identity, arguments from arbitrariness, debunking arguments, the overdetermination argument, and the problem of the many.

Deferential Monadic Panpsychism is a view that accepts that physical science is capable of discovering the basic structure of reality. However, it denies that reality is fully and exhaustively de- scribed purely in terms of physical science. Consciousness is missing from the physical description and cannot be reduced to it. DMP explores the idea that the physically fundamental features of the world possess some intrinsic mental aspect. It thereby faces a se- vere problem of understanding how more complex mental states (...) emerge from the mental features of the fundamental features. Here I explore the idea that a new form of aggregative emergence, which I call 'combinatorial infusion', could shed light on this problem and bolster the prospects for this form of panpsychism. (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)

Ci imbattiamo in un confine ogni volta che pensiamo a un’entità demarcata rispetto a ciò che la circonda. C’è un confine (una superficie) che delimita l’interno di una sfera dal suo esterno; c’è un confine (una frontiera) che separa il Maryland dalla Pennsylvania. Talvolta la collocazione esatta di un confine non è chiara o è in qualche modo controversa (come quando si cerchi di tracciare i limiti del monte Everest, o il confine del nostro corpo). Talaltra il confine non corrisponde (...) a una discontinuità fisica o a una differenziazione qualitativa (come nel caso dei confini del Wyoming, o della demarcazione tra la metà superiore e la metà inferiore di una sfera omogenea). Ma, che sia netto o confuso, naturale o artificiale, sembra esservi per ogni oggetto un confine che lo separa dal resto del mondo. Anche gli eventi hanno confini, quantomeno confini temporali. Le nostre vite sono delimitate dalle nostre nascite e morti; una partita di calcio comincia alle quindici in punto e termina col fischio finale dell’arbitro alle sedici e quarantacinque. E a volte si dice che anche le entità astratte, come i concetti o gli insiemi, hanno dei propri confini. Se tutto questo parlare di confini abbia davvero un senso, e se rifletta la struttura del mondo o solo l’attività organizzatrice del nostro intelletto, è però oggetto di profonda controversia filosofica. (shrink)

I offer a diagnosis of the parallelism between the Doctrine of Potential Parts and the Doctrine of Potential Wholes and briefly examine its bearing on Johansson’s account of the Tibbles-Tib Problem.

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

This essay demonstrates the inadequacy of contemporary substantivalist and relationist interpretations of quantum gravity hypotheses via an historical investigation of the debate on the underlying ontology of space in the seventeenth century. Viewed in the proper context, there are crucial similarities between seventeenth century theories of space and contemporary work on the ontological foundations of spacetime theories, and these similarities challenge the utility of the substantival/relational dichotomy by revealing a host of underlying conceptual issues that do not naturally align with (...) that distinction. (shrink)