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Physical boundaries and the earliest topologists. Topology has a relatively short history; but its 19th century roots are embedded in philosophical problems about the nature of extended substances and their boundaries which go back to Zeno and Aristotle. Although it seems that there have always been philosophers interested in these matters, questions about the boundaries of three-dimensional objects were closest to center stage during the later medieval and modern periods. Are the boundaries of an object actually existing, less-than-three-dimensional parts of (...) the object—that is, are solids bounded by two-dimensional surfaces, surfaces by one-dimensional “edges” or “physical lines”, edges by dimensionless “simples”? If not, how does a perfectly spherical object manage to touch a perfectly flat object—what part of the sphere is in immediate contact with the plane, if the sphere has no unextended parts? But if such parts be admitted, are we not then saddled with “actual infinities” of simples, lines, and surfaces spread throughout each continuous object—the boundaries of all the object’s internal parts? Does it help to say that these internal boundaries exist only “potentially”? (shrink)

Let us say that an extended object is “composed wholly of simples” just in case it is an aggregate of absolutely unextended parts spread throughout an extended region—that is, just in case there is a set S such that: every member is a point-sized part of the object, and for every x, x is part of the object if and only if it has a part in common with some member of S. Could a truly extended substance be composed entirely (...) of unextended parts? Reflection upon the fact that it must be at least possible for extended objects to touch one another suggests that the answer to this question is: No. (shrink)

The topic of this book is material objects. Like most interesting concepts, the concept of a material object is one without precise boundaries.

I would like to discuss the claim that the resources of plural reference and plural quantification are sufficient for the purpose of paraphrasing all ordinary statements apparently concerned with composite material objects into plural statements concerned exclusively with simples.

What are the necessary and jointly sufficient conditions for an object's being a simple (an object without proper parts)? According to one prominent view, The Pointy View of Simples, an object is a simple if and only if the region occupied by that object contains exactly one point in space. According to another prominent view, MaxCon, an object is a simple if and only if it is maximally continuous. In this paper, I argue that both of these views are inconsistent (...) with the possibility of discrete space. I then go on to formulate analogues to these two views that are consistent with this possibility, and argue that if we are willing to grant the possibility of discrete space, we should endorse the analogue to The Pointy View of Simples over the analogue to MaxCon. (shrink)

Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching consequences for (...) our understanding of a host of classical philosophical concepts. (shrink)

I argue that the assumptions that physically basic things are either mereologically atomic, or that they are continuous and there are no atoms, both face difficult conceptual problems. Both views tend to presuppose a largely unquestioned assumption, that things have parts corresponding to the geometric parts of the regions they occupy. To avoid these problems I propose a third view, that physically simple things occupy a finite volume without themselves having parts. This view is examined enough to tease out some (...) of its consequences and show that it withstands the obvious questions it faces. I conclude by mentioning some precedents for this view in Democritus, Kant, and Whitehead, with close variants in Boscovich, Harré, and Markosian. (shrink)

Many otherwise reasonable philosophers are impatient with ontology. These philosophers will probably have little time for Objects and Persons, which claims that while there do exist “atoms arranged statuewise”, there do not exist statues; while there do exist atoms arranged tablewise and atoms arranged chairwise, there exist no tables and chairs. Though I join these philosophers, at the end of the day, in rejecting Merricks’s claims, that day is long, whereas they want a quick verdict. But why? Do our impatient (...) friends think that Merricks’s claims are contradictory, analytically false, or otherwise conceptually incoherent? They may say that the conventional meaning of “there exists a statue” is “there exist atoms arranged statuewise”, but this does not stand up to scrutiny. Someone could, of course, just decide to mean such a thing by “there exists a statue”, but then her pronouncements would be irrelevant to Merricks, who intends to be using a.. (shrink)

‘‘Thus I believe that there is no part of matter which is not—I do not say divisible—but actually divided; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.’’ (Leibniz, letter to Foucher).

I give reasons to suggest that the various ‘homogeneous substance’ objections to perdurance theory should not be regarded as raising serious difficulties. The main strategy is to show that there are equally exotic possibilities involving extended mereological simples that may turn the tables on the endurance theorist, insofar as she will have difficulties with these cases analogous to those she raises for the perdurantist. I conclude that such exotic cases are less useful that we might suppose in adjudicating between these (...) competing doctrines of persistence. (shrink)

The following quotation, from Frank Jackson, is the beginning of a typical exposition of the debate between those metaphysicians who believe in temporal parts, and those who do not: The dispute between three-dimensionalism and four-dimensionalism, or more precisely, that part of the dispute we will be concerned with, concerns what persistence, and correllatively, what change, comes to. Three-dimensionalism holds that an object exists at a time by being wholly present at that time, and, accordingly, that it persists if it is (...) wholly present at more than one time. For short, it persists by enduring. Four-dimensionalism holds that an object exists at a time by having a temporal part at that time, and it persists if it has distinct temporal parts at more than one time. For short, it persists by perduring. In the light of these comments, some readers will perhaps find the question that forms the title of this paper a little puzzling. They may have learned to use the terms ‘fourdimensionalism’ ‘perdurantism’ and ‘belief in temporal parts’ interchangeably; or perhaps even to define one in terms of the other. Such a usage, however, is inapposite. We might imagine a Flatland-like world of two spatial dimensions and one temporal, whose philosophers are divided between a theory of persistence on which they persist by having temporal parts, and a theory on which they persist by being wholly located in each of several times. This is just the same issue we face, but at least the label ‘four-dimensionalism’ seems inapposite: the four-dimensionalist Flatlanders believe in only three dimensions! (shrink)

The surviving sources on the Stoic theory of division reveal that the Stoics, particularly Chrysippus, believed that bodies, places and times were such that all of their parts themselves had proper parts. That is, bodies, places and times were composed of gunk. This realisation helps solve some long-standing puzzles about the Stoic theory of mixture and the Stoic attitude to the present.

The question of what truths are necessary in the broadest possible sense is a difficult one to answer, as is the question of what the limits are to what is possible. (Most people would see these two questions as different sides of the same coin, of course, since many think the question of what is possible is just the question of what is not necessarily ruled out). We have three general sorts of strategies for determining whether something is necessary (or (...) possible). We can identify it in a class that we were previously sure was a class of things that are necessary – we might show it is a theorem of a logical system that we have confidence in, or that the sentence appears to be true simply in virtue of the meanings of the words, or that it is a true statement involving names or about natural kinds of the “necessary a posteriori” sort discussed by Kripke and Putnam, and there are perhaps other classes of claims which we are prepared to accept are necessary if true.1 Likewise, we might establish the possibility of something occurring by reference to a class of well-established or uncontroversial possibilities: e.g. we are inclined to think that it is possible (in the broadest sense) for an event to occur in the future if one of the same kind has occurred in the past. (shrink)

Objects and Persons presents an original theory about what kinds of things exist. Trenton Merricks argues that there are no non-living inanimate macrophysical objects -- no statues or rocks or chairs or stars -- because they would have no causal role over and above the causal role of their microphysical parts. Humans do exist: we have non-redundant causal powers. Along the way, Merricks has interesting things to say about mental causation, free will, and various philosophical puzzles. Anyone working in metaphysics (...) will enjoy this lucid and provocative book. (shrink)

Gareth Evans has argued influentially against vague identities. David Lewis and Theodore Sider have argued against vague parthood. Much of the distaste among philosophers for metaphysical vagueness is sourced in these arguments. I argue that even if the considerations adduced by Evans, Lewis and Sider are conclusive, metaphysical boundary vagueness remains possible.

In a recent paper titled ' Simples ', Ned Markosian asks and answers the Simple Question, which is, 'under what circumstances is it true of some object that it has no proper parts?' Markosian 's answer to the simple question is MaxCon, which states that an object is a simple if and only if it is a maximally continuous object. I present several arguments against MaxCon.

Here is a question about mereological simples that I raised in a recent paper.

I raised the following question in a recent paper: What are the necessary and jointly sufficient conditions for an object's being a simple? And I proposed and defended this answer (which I called 'MaxCon'): Necessarily, x is a simple iff x is a maximally continuous object. In a more recent paper, Kris McDaniel raises several objections to MaxCon, including, in particular, two objections based on a principle about the supervenience of constitution that he calls 'SoC'. The purpose of the present (...) paper is to address the main objections raised by McDaniel, and to show that none of them poses a serious threat to MaxCon. (shrink)

Since the publication of Peter van Inwagen's book, Material Beings,1 there has been a growing body of philosophical literature on the topic of composition. The main question addressed in both van Inwagen's book and subsequent discussions of the topic is a question that van Inwagen calls "the Special Composition Question." The Special Composition Question is, roughly, the question Under what circumstances do several things compose, or add up to, or form, a single object? For the purposes of formulating a more (...) precise version of the Special Composition Question, we can adopt the following technical terms. (shrink)

Introduction In the first four chapters of this book, I develop and defend a monistic account of human persons according to which human persons are highly ...

Not the least admirable of the late David Lewis’s attributes was his disdain for technical terminology and jargon. His writings are a model demonstrating that, with skill and care, it is possible to discuss even the most mathematical aspects of logic and semantics in clear English prose, and with only a minimum of symbolism. The main text of Parts of Classes [1, hereafter: PoC], a 120-page essay on the foundations of set theory, follows Aristotle in using letters as variables, and (...) has a few dashes and ellipses where it mentions schemata, but is otherwise free of logical notation. The essential advantages of what Church called “the logistic method” do not depend on its typographical accidents!) It is only natural that writers following him have taken one of his expressive words and turned it into a technical term: he allowed ‘atomless gunk’ as a possible complication in the mereological analysis of things, and ‘gunk’ is now a technical term in mereology. Gunk is stuff every part of which contains further parts, stuff which can be divided endlessly without ever arriving at an indivisible atom. (shrink)

Let us say that a thing is gunky just in case every part of that thing has proper parts. The idea that all physical objects are gunky seems sufficiently sweeping, interesting, and plausible that it is worth examining. However, there is a difficulty. The features of an extended object can surely vary continuously. If an object is gunky then it cannot have point-sized parts which have no further parts. But how can one conceive of a continuous variation in features other (...) than as the obtaining of different features at different point sized locations? (shrink)

We show that someone who believes in both gunk and the possibility of supertasks has to give up either a plausible principle about where gunk can be located, or plausible conservation principles.

In his Material Beings, Peter van Inwagen distinguishes two questions about parthood. What are the conditions necessary and sufficient for some things jointly to compose a whole? What are the conditions necessary and sufficient for a thing to have proper parts? The first of these, the Special Composition Question (SCQ), has been widely discussed, and David Lewis has argued that an important constraint on any answer to the SCQ is that it should not permit borderline cases of composition. This is (...) a far-reaching claim, since many plausible-seeming accounts of composition do permit borderline cases. Ned Markosian has recently directed our attention to the second, the neglected Inverse Special Composition Question (ISCQ). I will argue that those who accept Lewis’s constraint on answers to the SCQ should accept an analogous constraint on answers to the ISCQ, and I will discuss the effects of such a constraint. (shrink)

In this paper I present the Discrete Space-Time Thesis, in a way which enables me to defend it against various well-known objections, and which extends to the discrete versions of Special and General Relativity with only minor difficulties. The point of this presentation is not to convince readers that space-time really is discrete but rather to convince them that we do not yet know whether or not it is. Having argued that it is an open question whether or not space-time (...) is discrete, I then turn to some possible empirical evidence, which we do not yet have. This evidence is based on some slight differences between commonly occurring differential equations and their discrete analogs. (shrink)

This paper concerns the structure of any spatially extended things, including regions of space or spacetime. I shall use intuitions about the quantity of extended things to argue for a dichotomy: either a given finite extended thing is point-free gunk, that is, it has no points as parts, or it is made of grit, that is there are only finitely many points.

My enquiry will be within the scope of two suppositions. The first is that Space is continuous, not discrete. The second is that we are to adopt realism about either points or regions or both. That does not, however, preclude a choice of categories—substance or property—for these entities. Thus we could think of either regions or points as properties of the things in those regions or at those points. Alternatively, we could think of regions or points as substances which themselves (...) have properties. (shrink)

Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments based (...) on time travel, the debate between spacetime substantivalists and relationalists, and vagueness. Also included is a comprehensive discussion of the paradoxes of coinciding material objects, and a novel resolution of those paradoxes based on temporal counterpart theory. In conclusion Sider replies to prominent objections to four- dimensionalism, including discussion of the problem of the rotating homogenous disk. (shrink)

Hud Hudson offers a fascinating examination of philosophical reasons to believe in hyperspace. He explores non-theistic reasons in the first chapter and theistic ones towards the end; in the intervening sections he inquires into a variety of puzzles in the metaphysics of material objects that are either generated by the hypothesis of hyperspace or else informed by it, with discussions of receptacles, boundaries, contact, occupation, and superluminal motion. Anyone engaged with contemporary metaphysics, and many philosophers of religion, will find much (...) to stimulate them here. (shrink)

A substantial and in-depth study of the history of the atomic theory of matter between the time of Democritus and that of Newton. It is the first to emphasize the continuity of the atomic debate and the debt owed by the seventeenth-century "moderns" to the medieval critique of Aristotle.