Theodore Sider

Eternalists say that non-present entities (for instance dinosaurs) exist; presentists say that they do not. But some sceptics deny that this debate is genuine, claiming that presentists simply represent eternalists' quantifiers over non-present entities in different notation. This scepticism may be refuted on purely logical grounds: one of the leading candidate ‘presentist quantifiers’ over non-present things has the inferential role of a quantifier. The dispute over whether non-present objects exist is as genuine and non-verbal as the dispute over whether there is life on other planets.

This note is to show that a well-known point about David Lewis’s (1986) modal realism applies to Timothy Williamson’s (1998; 2002) theory of necessary existents as well.1 Each theory, together with certain “recombination” principles, generates individuals too numerous to form a set. The simplest version of the argument comes from Daniel Nolan (1996).2 Assume the following recombination principle: for each cardinal number, ν, it’s possible that there exist ν nonsets. Then given Lewis’s modal realism it follows that there can be no set of all (that is, Absolutely All) the nonsets. For suppose for reductio that there were such a set, A; let ν be A’s cardinality; and let µ be any cardinal number larger than ν. By the recombination principle, it’s possible that there exist µ nonsets; by modal realism, there exists a possible world containing, as parts, µ nonsets; each of these nonsets is a member of A

While many are impressed with the utility of possible worlds in linguistics and philosophy, few can accept the modal realism of David Lewis, who regards possible worlds as sui generis entities of a kind with the concrete world we inhabit.1 Not all uses of possible worlds require exotic ontology. Consider, for instance, the use of Kripke models to establish formal results in modal logic. These models contain sets often regarded for heuristic reasons as sets of “possible worlds”. But the “worlds” in these sets can be anything at all; they can be numbers, or people, or sh. The set of worlds, together with the accessibility relation and the rest of the model, is used as a purely formal structure.2 One can even go beyond establishing results about formal systems and apply Kripke models to English, as Charles Chihara has recently argued.3 Chihara shows, for instance, how to use Kripke models (plus primitive modal notions) to give an account of validity for English modal sentences. In other cases worlds are not really needed at all. It is often vivid to give a counterexample thus: “There is a possible world in which P. Since your theory implies that in all worlds, not-P, your theory is wrong.” But the counterexample could just as easily be given using modal operators: “Possibly, P. Since your theory implies that it is necessary that not-P, your theory is wrong.”.

The intimate relationship between X and Y consists in the existence of (metaphysically) necessary truths correlating their occurrences/existences/instantiations. E would be in some sense “overdetermined” if caused by both X and Y.2 Some philosophers say this would be bad, that this cannot or does not happen, that we should construct theories ruling it out, at least in certain cases.3 But why? Given the necessary truths correlating objects and their parts, objects and events concerning those objects, physical and supervenient mental properties, and so on, X and Y do both seem to be causes of E. Should we say that a baseball..

Locke’s view that continuants are numerically distinct from their constituting hunks of matter is popular enough to be called the “standard account”.1 It was given its definitive contemporary statement by David Wiggins in Sameness and Substance2, and has been defended by many since. Baker’s interesting book contributes new arguments for this view, a new definition of ‘constitution’, and a sustained application to persons and human animals. Much of what she says develops this view in new and important ways. But in some cases she does not advance the position, and in others she takes steps backwards. According to Baker, a person is numerically distinct from her constituting animal. One of Baker’s leading arguments is surprisingly unconvincing. Persons differ in important ways from non-human animals. Only persons are moral agents, modify their goals, have wars, culture, etc. If persons were identical to animals—if we were “nothing but animals”, as she puts it—then the manifest discontinuity between humans and non-human animals would be located “within the domain of biology”. “But from a biological point of view, human animals…are biologically continuous with non-human animals.” (p. 17) The argument fails: why should identifying persons with animals preclude saying that these particular animals have radically distinctive features that are of little interest to biologists? The traditional case for non-identity (which Baker accepts) is more powerful: a person and her constituting animal differ by having different persistence conditions. If my memories were transferred to a new body and my old body destroyed, I the person might survive, but the human animal who constituted me would perish. Therefore, before the transfer, I and the animal that constituted me would be numerically distinct but extremely similar things located in exactly the same place. This consequence—the central thesis of the Wiggins view—is surprising: so surprising that some reject the Wiggins view on that basis..

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..