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)

According to standard, pre-philosophical intuitions, there are many composite objects in the physical universe. There is, for example, my bicycle, which is composed of various parts - wheels, handlebars, molecules, atoms, etc. Recently, a growing body of philosophical literature has concerned itself with questions about the nature of composition.1 The main question that has been raised about composition is, roughly, this: Under what circumstances do some things compose, or add up to, or form, a single object? It turns out that (...) it is surprisingly difficult to give a satisfactory answer to this question that accords with standard, pre-philosophical intuitions about the universe's composite objects. In fact, the three rival views in response to this question that have received the most support in the literature are (i) that there are no objects composed of two or more parts (which means that there are no stars, chairs, humans, or bicycles);2 (ii) that the only objects composed of two or more parts are living organisms (which still means no stars. (shrink)

(1) Materialists hold that every real, concrete phenomenon in the universe is a wholly physical phenomenon. (2) Consciousness ('what-it's-likeness', etc.) is the most certainly existing real, concrete phenomenon there is. It follows that (3) all serious materialists must grant that consciousness is a wholly physical phenomenon. ‘How can consciousness possibly be physical, given what we know about the physical?’ To ask this question is already to have gone wrong. We have no good reason (as Priestley, Eddington, Russell and others observe) (...) to think that we know anything about the physical that gives us any reason to find any problem in the idea that consciousness is wholly physical. (shrink)

In the past fifteen years or so there has been a lot of attention paid to theories of “sparse” universals, particularly because of the work of D. M. Armstrong. These theories are of particular interest to those of us concerned with the distinction between natural and non-natural properties, since, as David Lewis has observed, it seems possible to analyze naturalness in terms of sparse universals. Moreover, Armstrong claims that we should conceive of universals as being “immanent” as opposed to “transcendent”, (...) and if universals are immanent then, as we will see, there is pressure to admit they are sparse as well. But I will argue that neither of these alleged reasons to accept a sparse conception of universals succeeds: the outlook for a fully general analysis of naturalness in terms of universals is not good, and the apparent advantages of immanence over transcendence are illusory. (shrink)

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

Alan Sidelle's Necessity, Essence, and Individuation is a sustained defense of empiricism—or, more generally, conventionalism—against recent attacks by realists. Sidelle focuses his attention on necessity a posteriori, a kind of necessity which contemporary realists have taken to support realism over empiricism. Turning the tables against the realists, Sidelle argues that if there are in fact truths necessary a posteriori, it is not realism, but rather empiricism which provides the best explanation for them.

Persistence through time is like extension through space. A road has spatial parts in the subregions of the region of space it occupies; likewise, an object that exists in time has temporal parts in the various subregions of the total region of time it occupies. This view — known variously as four dimensionalism, the doctrine of temporal parts, and the theory that objects “perdure” — is opposed to “three dimensionalism”, the doctrine that things “endure”, or are “wholly present”.1 I will (...) attempt to resolve this dispute in favor of four dimensionalism by means of a novel argument based on considerations of vagueness. But before argument in this area can be productive, I believe we must become much clearer than is customary about exactly what the dispute is, for the usual ways of formulating the dispute are flawed, especially where three dimensionalism is concerned. (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).

A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...) functions and those that do correspond to continuous functions. (shrink)

A bronze statue is a lump of bronze – or so it might appear. But appearances are not always to be trusted, and this one is notoriously problematic. To see why, imagine a bronze statue (perhaps a statue of David) and ask yourself: Which lump of bronze is the statue? Presumably, it is the lump that makes up the statue (or, as we say, the lump that constitutes the statue). After all, why should the statue be any other lump of (...) bronze? But if that is right, if the statue is the lump of bronze that constitutes it, then why can the lump of bronze survive being melted down whereas the statue it constitutes cannot? It seems that in fact the bronze statue is not the lump of bronze that constitutes it, since the statue and the lump of bronze have different persistence conditions. But then is it some other lump of bronze? Is it a lump of bronze at all? These questions are troubling; they appear to have no easy answers. (shrink)

Being conscious is intrinsic. Suppose P, a conscious human being, “shrinks” by losing an atom from her left index finger. Suppose that at the very first instant at which P has lost that atom, the atoms that then compose her remain just as they were immediately before “the loss.” This implies—assuming MS for reductio—that, just as those atoms compose a conscious object after the loss, so they composed a conscious object before the loss. Name that latter object ‘the atom-complement’.

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.

I argue that a solution to puzzles concerning the relationship ofobjects and their properties – a version of the `bundle' theory ofparticulars according to which ordinary objects are mereologicalfusions of monadic and relational tropes – is also a solution topuzzles of material constitution involving the allegedco-location of material objects. Additionally, two argumentsthat have played a prominent role in shaping the current debate,Mark Heller's argument for Four Dimensionalism and Peter vanInwagen's argument against Mereological Universalism, are shownto be unsound given this version (...) of the bundle theory. (shrink)

This is a defense of endurantism against an alleged paradox.

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)

In his note "can there be vague objects?" ("analysis", 1978), Gareth evans presents a purported proof that there can be no vague identity statements. Some readers think that evans endorses the proof and its false conclusion. Not so. His point is that those who put vagueness in the world, Rather than in language, Will have no way to fault the proof and no way to escape the false conclusion.

A solution to the problem of intrinsic change for enduring things should meet three conditions. It should not replace monadic intrinsic properties by relations. It should not replace the having simpliciter of properties by standing in some relation to them. It should not rely on an unexplained notion of having an intrinsic property at a time. Johnston's solution satisfies the first condition at the expense of the second. Haslanger's solution satisfies the first and second at the expense of the third.

How do things persist? Are material objects spread out through time just as they are spread out through space? Or is temporal persistence quite different from spatial extension? This key question lies at the heart of any metaphysical exploration of the material world, and it plays a crucial part in debates about personal identity and survival. This book explores and compares three theories of persistence — endurance, perdurance, and stage theories — investigating the ways in which they attempt to account (...) for the world around us. Having provided valuable clarification of its two main rivals, the book concludes by advocating stage theory. Such a basic issue about the nature of the physical world naturally has close ties with other central philosophical problems. This book includes discussions of change and parthood, of how we refer to material objects at different times, of the doctrine of Humean supervenience, and of the modal features of material things. In particular, it contains new accounts of the nature of worldly vagueness, and of what binds material things together over time, distinguishing the career of a natural object from an arbitrary sequence of events. Each chapter concludes with a reflection about the impact of these metaphysical debates upon questions about our personal identity and survival. (shrink)

Think of “locations” very abstractly, as positions in a space, any space. Temporal locations are positions in time; spatial locations are positions in (physical) space; particulars are locations in quality space. Should we reify locations? Are locations entities? Spatiotemporal relation- alists say there are no such things as spatiotemporal locations; the fundamental spatial and temporal facts involve no locations as objects, only the instantiation of spatial and temporal relations. The denial of locations in quality space is the bundle theory, according (...) to which particulars do not exist; facts apparently about particulars really concern relations between universals. A “space”, in our abstract sense, consists of a set of objects, together with properties and relations defined on those objects. The objects are the locations of the space, and the distribution of the properties and relations over the locations defines the space’s structure. All spaces are thus quality spaces; when the relations are thought of as spatiotemporal then the space is also a spatiotemporal space. By not reifying locations one denies that these abstract spaces isomorphically represent the real world. The real world does in some sense have a structure that can be non-isomorphically represented by a space (or, more likely, a class of spaces), but the locations in those spaces do not correspond to anything real. We will examine modal considerations on reifying locations. Denying the existence of spatiotemporal locations excludes certain possibilities for spatiotemporal reality. Denying the existence of qualitative locations excludes certain possibilities for qualitative space. In each case the excluded possibilities are pre-analytically possible. Some of the possibilities can be reinstated by modifying the locationless theories, but at the cost of an unattractive holism. Do these modal considerations mandate postulating locations? That depends on whether modal intuition can teach us about the actual world.. (shrink)

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 formulate, elucidate, and defend a version of modal realism with overlap, the view that objects are literally present at more than one possible world. The version that I defend has several interesting features: (i) it is committed to an ontological distinction between regions of spacetime and material objects; (ii) it is committed to compositional pluralism, which is the doctrine that there is more than one fundamental part-whole relation; and (iii) it is the modal analogue of endurantism, (...) which is the doctrine that objects persist through time by being wholly present at each moment they are located. (shrink)

It follows from Humean principles of plenitude, I argue, that island universes are possible: physical reality might have 'absolutely isolated' parts. This makes trouble for Lewis's modal realism; but the realist has a way out. First, accept absolute actuality, which is defensible, I argue, on independent grounds. Second, revise the standard analysis of modality: modal operators are 'plural', not 'individual', quantifiers over possible worlds. This solves the problem of island universes and confers three additional benefits: an 'unqualified' principle of compossibility (...) can be accepted; the possibility of nothing can be accommodated; and the identity of indiscernible worlds can be decisively refuted. (shrink)

ONE KIND OF PHILOSOPHICAL PUZZLEMENT arises when we have an apparent conflict of intuitions. If we are philosophers, we then try to show that the apparent conflict of intuitions is only an apparent conflict and not a real one. If we fail, we may have to say that what we took to be an apparent conflict of intuitions was in fact a conflict of apparent intuitions, and then we must decide which of the conflicting apparent intuitions is only an apparent (...) intuition. But if we succeed, then both of the intuitions will be preserved. Since there was an apparent conflict, we will have to conclude that the formulation of at least one of the intuitions was defective. And though the formulation may be imbedded in our ordinary language, we will have to say that, strictly and philosophically, a different formulation is to be preferred. But to make it clear that we are not rejecting the intuition we are reformulating, we must show systematically how to interpret the ordinary formulation into the philosophical one. The extent to which we can show this will be one mark of our success in dealing with the philosophical puzzle. Another will be the extent to which our proposed solution contributes to the solution of still other philosophical puzzles. (shrink)