Ethan Lowe

'Object' and 'criterion of identity' are philosophical terms of art whose application lies at a considerable theoretical remove from the surface phenomena of everyday linguistic usage. This partly explains their highly controversial status, for their point of application lies precisely where the concerns of linguists and philosophers of language merge with those of metaphysicians. This chapter explains the possession of determinate identity‐conditions. It argues that the distinction between 'abstract' and 'concrete' objects is itself a highly controversial one, and although it has indeed been argued that this distinction turns ultimately upon differences between the criteria of identity governing objects of these two broad categories. It examines the role which criteria of identity play in our talk about objects of the least controversial varieties. The chapter concerns the problem of identity over time and the paradoxes to which identity criteria often appear to give rise when time is brought into the picture.

Eric T. Olson has argued that those who hold that two material objects can exactly coincide at a moment of time, with one of these objects constituting the other, face an insuperable difficulty in accounting for the alleged differences between the objects, such as their being of different kinds and possessing different persistence-conditions. The differences, he suggests, are inexplicable, given that the objects in question are composed of the same particles related in precisely the same way. In response, I show that the differences are not at all inexplicable once it is recognized that the conditions for a persisting object to be composed by certain particles at a moment of time must involve facts concerning other moments of time, and that the relevant facts are different for persisting objects of different kinds. Philosophers who neglect this sort of constraint on composition principles may be said to be victims of the 'cinematographic fallacy'

I propose a fourfold categorisation of entities according to whether or not they possess determinate identity-conditions and whether or not they are determinately countable. Some entities – which I call ‘individual objects’ – have both determinate identity and determinate countability: for example, persons and animals. In the case of entities of a kind K belonging to this category, we are in principle always entitled to expect there to be determinate answers to such questions as ‘Is x the same K as y?’ and ’How many Ks are there satisfying condition C?’, even if we may sometimes be unable in practice to discover what these answers are. But other entities apparently lack either determinate identity, or determinate countability, or both. In these terms I try to explain certain important ontological differences between familiar macroscopic objects and various rather more esoteric entities, such as the ‘particles’ of quantum physics, quantities of material stuff, and tropes or property instances.

David Lewis, following in the tradition of Broad, Quine and Goodman, says that change in an object X consists in X's being temporally extended and having qualitatively different temporal parts. Analogously, change in a spatially extended object such as a road consists in its having different spatial parts . The alternative to this view is that ordinary objects undergo temporal change in virtue of having different intrinsic non-relational properties at different times. They endure, remaining the same object throughout change, whereas Lewis's temporally extended 4D objects perdure.It is impossible to come down on one side or the other of the endurance/perdurance debate without a clear and unambiguous understanding of what ‘endurance’ is. ‘Perdurance’ is clear enough. Every 4D object of non-zero temporal thickness perdures simply by having temporal extension, i.e. by having different temporal parts, or stages, at different times. But Lewis muddies the waters by giving a confused and ultimately untenable definition of endurance.His first step is to cover both perduring and enduring by offering the neutral word persist. ‘Let us say that something persists iff, somehow or other, it exists at various times’ . Something then perdures if it persists by having different temporal parts at different times, no one part being wholly present at more than one time. In contrast, a thing endures if it persists by being wholly present at more than one …

Substantial change occurs when a persisting object of some kind either begins or ceases to exist. Typically, this happens when one or more persisting objects of another kind or kinds are subjected to appropriate varieties of qualitative or relational change, as when the particles composing a lump of bronze are rearranged so as to create a statue. However, such transformations also seem to result, very often, in cases of spatiotemporal coincidence, in which two numerically distinct objects of different kinds exist in exactly the same place at the same time, such as a statue and a lump of bronze. Various attempts to resist this way of describing the results of such transformations are examined and found wanting and objections to the possibility of cases of spatiotemporal coincidence are rebutted

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