This paper establishes that the occasional identity relation and the contingent identity relation are both non-transitive and as such are not properly classified as identity relations. This is achieved by appealing to cases where multiple fissions and fusions occur simultaneously. These cases show that the contingent and occasional identity relations do not even satisfy the time-indexed and world-indexed versions of the transitivity requirement and hence are non-transitive relations.

Here I propose a coherent way of preserving the identity of material objects with the matter that constitutes them. The presentation is formal, and intended for RSL. An informal presentation is in preliminary draft! -/- Relative-sameness relations—such as being the same person as—are like David Lewis's "counterpart" relations in the following respects: (i) they may hold between objects that aren't identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different (...) contexts. They differ from counterpart relations, however, in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis's Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). (shrink)

An alternative to the standard endurance/perdurance accounts of persistence has recently been developed: the stage theory (Sider, T. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press, 2001; Hawley, K. How Things Persist. Oxford: Oxford University Press, 2001). According to this theory, a persisting object is identical with an instantaneous stage (temporal part). On the basis of Leibniz's Law, I argue that stage theorists either have to deny the alleged identity (i.e., give up their central thesis) or hold (...) that stages are both instantaneous and continuants. I subsequently show that, although stage theory is flexible enough to accommodate the latter claim, the cost for accommodating it is an excessive proliferation of persistence concepts. (shrink)

André Gallois (1998) attempts to defend the occasional identity thesis (OIT), the thesis that objects which are distinct at one time may nonetheless be identical at another time, in the face of two influential lines of argument against it. One argument involves Kripke’s (1971) notion of rigid designation and the other, Leibniz’s law (affirming the indiscernibility of identicals). It is reasonable for advocates of (OIT) to question the picture of rigid designation and the version of Leibniz’s law that these arguments (...) employ, but, the problem is, some form of rigidity is required for one to affirm the occasional identity of objects, and some (restricted) version of Leibniz’s law must be conceded if identity really is involved. Gallois accordingly recommends an account of rigidity and a version of Leibniz’s law to this end.1 We find Gallois’ proposals entirely inadequate to their task. We aim in this paper is to explicate and defend an alternative approach for occasional identity theorists. We do not seek to defend (OIT) per se; our aim, rather, is simply to show that the arguments from rigid designation and Leibniz’s law are inconclusive. Let’s begin with an outline of these arguments. (shrink)

André Gallois (1998) attempts to defend the occasional identity thesis (OIT), the thesis that objects which are distinct at one time may nonetheless be identical at another time, in the face of two influential lines of argument against it. One argument involves Kripke’s (1971) notion of rigid designation and the other, Leibniz’s law (affirming the indiscernibility of identicals). It is reasonable for advocates of (OIT) to question the picture of rigid designation and the version of Leibniz’s law that these arguments (...) employ, but, the problem is, some form of rigidity is required for one to affirm the occasional identity of objects, and some (restricted) version of Leibniz’s law must be conceded if identity really is involved. Gallois accordingly recommends an account of rigidity and a version of Leibniz’s law to this end.1 We find Gallois’ proposals entirely inadequate to their task. We aim in this paper is to explicate and defend an alternative approach for occasional identity theorists. We do not seek to defend (OIT) per se; our aim, rather, is simply to show that the arguments from rigid designation and Leibniz’s law are inconclusive. Let’s begin with an outline of these arguments. (shrink)

André Gallois’s Occasions of Identity injects a refreshing new perspective into an old debate. Actually, what is new is the advocacy of the perspective: Gallois takes up a view that many consider a non-starter, and shows this reaction to be premature. The debate is over the right way to understand the traditional puzzles involving two things being in the same place at the same time; the perspective is that identity can hold temporarily (and contingently). Suppose an amoeba, name it AMOEBA, (...) divides in two. One of the resultant amoebas, POND, lives in a pond; the other, SLIDE, is examined on a slide in a laboratory. Does AMOEBA survive this process, and if so, does it survive as POND or SLIDE? If we stipulate that POND and SLIDE are symmetrically related to AMOEBA then it seems arbitrary to identify AMOEBA with exactly one of POND and SLIDE. But we cannot identify AMOEBA with each, for then by the transitivity and symmetry of identity we would wrongly identify POND and SLIDE. We are left with the conclusion that AMOEBA is identical to neither. But this seems wrong too; surely fission does not result in death. So just what does happen to AMOEBA? How to respond to this and related cases (involving statues and their constituting hunks of matter, cats and their undetached parts, and so on) has been much discussed.1 There are many proposals, each with distinctive strengths and weaknesses. To these Gallois adds his own, which runs as follows. After division, there are two amoebas, POND and SLIDE, each of which existed before division. But it does not follow that there were two amoebas before division. Though POND and SLIDE are numerically distinct after division, they were numerically identical before division. The identity relation can hold temporarily, or occasionally, as Gallois puts it. My sense is that this sort of claim is regarded by most metaphysicians as downright wacky. And yet there is something very natural about it. Why distinguish POND and SLIDE today because they will differ tomorrow? I suspect the “wackiness” reaction has two sources, one based on Leibniz’s Law.. (shrink)

An alternative to the standard endurance/perdurance accounts of persistence has recently been developed: the stage theory (Sider, T. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press, 2001; Hawley, K. How Things Persist. Oxford: Oxford University Press, 2001). According to this theory, a persisting object is identical with an instantaneous stage (temporal part). On the basis of Leibniz's Law, I argue that stage theorists either have to deny the alleged identity (i.e., give up their central thesis) or hold (...) that stages are both instantaneous and continuants. I subsequently show that, although stage theory is flexible enough to accommodate the latter claim, the cost for accommodating it is an excessive proliferation of persistence concepts. (shrink)