Theodore Sider

Statues and lumps of clay are said by some to coincide - to be numerically distinct despite being made up of the same parts. They are said to be numerically distinct because they differ modally. Coincident objects would be non-modally indiscernible, and thus appear to violate the supervenience of modal properties on nonmodal properties. But coincidence and supervenience are in fact consistent if the most fundamental modal features are not properties, but are rather relations that are symmetric as between coincident entities, relations such as "opposite-possibly surviving being squashed"

Michael Jubien’s Ontology, Modality, and the Fallacy of Reference is an interesting and lively discussion of those three topics. In ontology, Jubien defends, to a first approximation, a Quinean conception: a world of objects that may be arbitrarily sliced or summed. Slicing yields temporal parts; summing yields aggregates, or fusions. Jubien is very unQuinean in his explicit Platonism regarding properties and propositions, but concerns about abstracta are peripheral to much of the argumentation in the book.1 His version of the doctrine that arbitrary mereological sums exist is nonstandard in that he views it as a convention (albeit a useful one) that we treat sums of objects as themselves being objects. Indeed, he views the concept of objecthood itself as being conventional. The world consists fundamentally of stuff, which we divide into things in any way that suits our purposes. In modality, Jubien’s views are to a first approximation Chisholmian: he holds the doctrine of mereological essentialism, according to which anything..

An introduction to temporal parts theory. Most of us believe in spatial parts: hands are spatial parts of people, an electron is a spatial part of a hydrogen atom, the earth is a spatial part of the solar system. Why are these parts "spatial" parts? Because they are spatially smaller: the hand is spatially smaller than the person, the electron is spatially smaller than the atom, the earth is spatially smaller than the solar system. Temporal parts, then, are parts that are temporally smaller. My current temporal part, "me-today", we might call it, is temporally smaller than me, since it exists today and only today. Temporal parts theory says that objects are made up of temporal as well as spatial parts.

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

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

In my book Four-dimensionalism (chapter 4, section 9), I argued that fourdimensionalism – the doctrine of temporal parts – follows from several other premises, chief among which is the premise that existence is never vague. Kathrin Koslicki (preceding article) claims that the argument fails since its crucial premise is unsupported, and is dialectically inappropriate to assume in the context of arguing for four-dimensionalism. Since the relationship between four-dimensionalism and the non-vagueness of existence is not perfectly transparent, I think the argument would retain some interest even if the premise were wholly unsupported; it would show that anyone who accepts that premise (which seems reasonable enough to me though perhaps not to others) must accept four-dimensionalism. Still, Koslicki is right that my defense of the premise was thin. So I will now try to do better. The new defense will have further premises, which could ultimately be rejected by opponents of four-dimensionalism, and so the argument retains the form: anyone who thinks certain things (which seem reasonable enough to me though perhaps not to others) must believe four-dimensionalism. But that’s metaphysics for you. I should also say that, in addition to the material on vague existence, there is more in Koslicki’s excellent paper which I cannot discuss here. I agree with much of it;1 and where we disagree there are formidable challenges, some of which I hope to address in the future

According to four dimensionalism, the material world is divided into momentary stages. In a four-dimensional world, which objects are the ordinary things, the things we normally name and quantify over? Aggregates of stages, according to most four-dimensionalists, but according to stage theorists (or exdurantists), ordinary objects are instead to be identified with the stages themselves. (A temporal counterpart theoretic account of de re temporal predication is then given.) This paper argues that a stage theorist is best positioned to accept David Lewis's argument from temporary intrinsics for four-dimensionalism, since stage theorists are the only four-dimensionalists who attribute monadic temporary intrinsic properties to ordinary things.