For they must accept either that our reports of the cross-temporal number of cats are not always reports of the counting of cats as when I say, truly, that I have only ever owned three cats or that two cat-stages cats may be counted as one and the same cat, so that counting cats is not always counting in accordance with absolute identity.
An argument against the perdurance theory that has been the focus of interest is one presented in various guises by a number of writers, including Wiggins , Thomson and van Inwagen Applied to persons it can equally well be applied to other persisting things , it asserts that persons have different properties, in particular, different modal properties, from the summations of person-stages with which the perdurance theory identifies them.
To elaborate a little. I might have died when I was five years old. But that maximal summation of person-stages which, according to perdurance theory, is me and has a temporal extent of at least fifty years, could not have had a temporal extent of a mere five years. So I cannot be such a summation of stages. This argument illustrates the interdependence of the various topics discussed under the rubric of identity. This is the topic of the next section. However, though this is perhaps the most natural way to interpret de re modal statements once it has been accepted that the apparatus of possible worlds is to be used as an interpretative tool , there are well-known difficulties that make the approach problematic.
For example, it seems reasonable to suppose that a complex artefact like a bicycle could have been made of different parts. On the other hand, it does not seem right that the same bicycle could have been constructed out of completely different parts.
But now consider a series of possible worlds, beginning with the actual world, each containing a bicycle just slightly different from the one in the previous world, the last world in the sequence being one in which there is a bicycle composed of completely different parts from the one in the actual world. One cannot say that each bicycle is identical with the one in the neighbouring world, but not identical with the corresponding bicycle in distant worlds, since identity is transitive.
Hence it seems one must either adopt an extreme mereological essentialism, according to which no difference of parts is possible for an individual, or reject the interpretation of de re modal discourse as asserting identity across possible worlds. This and other problems with cross-world identity suggest that some other weaker relation, of similarity or what David Lewis calls counterparthood, should be employed in a possible world analysis of modal discourse. Since similarity is not transitive this allows us to say that the bicycle might have had some different parts without having to say that it might have been wholly different.
On the other hand, such a substitution does not seem unproblematic, for a claim about what I might have done hardly seems, at first sight, to be correctly interpretable as a claim about what someone else however similar to me does in another possible world Kripke [], note An assessment of the counterpart theoretic analysis is vital not just to understanding modal discourse, however, but also to getting to the correct account of identity over time.
For, as we saw, the argument against perdurance theory outlined at the end of the last section depends on the correct interpretation of modal discourse. In fact, it is invalid on a counterpart theoretic analysis which allows different counterpart relations different similarity relations to be invoked according to the sense of the singular term which is the subject of the de re modal predication Lewis , Ch. Since the two similarity relations in question are distinct the first modal statement may be true and the second false even if I am identical with the sum of stages in question.
Counterpart theory is also significant to the topic of identity over time in another way, since it provides the analogy to which the stage theorist who regards all everyday reference as reference to momentary stages rather than to perdurers appeals to explain de re temporal predication. The problem of identity over time for things of a kind, for stage theorists, is just the problem of characterizing the appropriate temporal counterpart relation for things of that kind. For a more detailed discussion of the topic, see the entry transworld identity.
Whether de re modal discourse is to be interpreted in terms of identity across possible worlds or counterpart theoretically or in some other way entirely is also relevant to our next topic, that of contingent identity. Kripke challenged this platitude, though, of course, he did not reject the possibility of contingent statements of identity. But he argued that when the terms flanking the sign of identity were what he called rigid designators, an identity statement, if true at all, had to be necessarily true, but need not be knowable a priori , as an analytic truth would be.
Connectedly, Kripke argued that identity and distinctness were themselves necessary relations: if an object is identical with itself it is necessarily so, and if it is distinct from another it is necessarily so. The debate over contingent identity is concerned with the assessment and proper analysis of these examples.
One of the earliest examples is provided by Gibbard Consider a statue, Goliath, and the clay, Lumpl, from which it is composed. Imagine that Lumpl and Goliath coincide in their spatiotemporal extent. It is tempting to conclude that they are identical. But they might not have been.
Goliath might have been rolled into a ball and destroyed; Lumpl would have continued to exist. The two would have been distinct. Thus it seems that the identity of Lumpl and Goliath, if admitted, must be acknowledged as merely contingent.
One reaction to this argument available to the convinced Kripkean is simply to deny that Lumpl and Goliath are identical. But to accept this is to accept that purely material entities, like statues and lumps of clay, of admittedly identical material constitution at all times, may nonetheless be distinct, though distinguished only by modal, dispositional or counterfactual properties.
To many, however, this seems highly implausible, which provides the strength of the argument for contingent identity. Another way of thinking of this matter is in terms of the failure of the supervenience of the macroscopic on the microscopic. He appeals to counterpart theory, modified to allow a variety of counterpart relations, to explain this.
What is crucial to making sense of contingent identity is an acceptance that modal predicates are inconstant in denotation that is, stand for different properties when attached to different singular terms or different quantifying expressions. Counterpart theory provides one way of explaining this inconstancy, but is not necessarily the only way Gibbard , Noonan , However, whether the examples of contingent identity in the literature are persuasive enough to make it reasonable to accept the certainly initially surprising idea that modal predications are inconstant in denotation is still a matter of considerable controversy.
Finally, in this section, it is worth noting explicitly the interdependence of the topics under discussion: only if the possibility of contingent identity is secured, by counterpart theory or some other account of de re modality which does not straightforwardly analyse de re modal predication in terms of identity across possible worlds, can perdurance theory or stage theory as an account of identity across time be sustained against the modal arguments of Wiggins, Thomson and van Inwagen.
The thesis comes in a weak and a strong form. In its weak form the thesis is that the mereological composition relation is analogous in a number of important ways to the identity relation and so deserves to be called a kind of identity. In its strong form the thesis is that the composition relation is strictly identical with the identity relation, viz. The strong thesis was considered by Plato in Parmenides and versions of the thesis have been discussed by many historical figures since Harte , Normore and Brown The progenitor of the modern version of the thesis is Baxter a, b, but it is most often discussed under the formulation of it given by Lewis , who first considers the strong thesis before rejecting it in favour of the weak thesis.
Lewis 85 makes five likeness claims:. Anyone who denies unrestricted mereological composition, for example, will deny 2. And the defender of strong pluralism in the material constitution debate i. And some endurantists who think that ordinary material objects can have distinct parts at distinct times will deny 5. But there is a more general problem with 1, as van Inwagen has made clear Consider a world w1 that contains just two simples s1 and s2.
Now consider the difference between someone p1 who believes that s1 and s2 compose something and someone p2 who does not. Ask: how many objects do p1 and p2 believe there to be in w1? The answer, it seems, is that p1 believes that there are three things and p2 only two. So how can a commitment to the existence of fusions be ontologically innocent? One recent suggestion is that although a commitment to the existence of fusions is not ontologically innocent, it almost is: to commit oneself to fusions is to commit oneself to further entities, but because they are not fundamental entities they are not ones that matter for the purpose of theory choice Cameron , Schaffer , Williams , and see also Hawley If composition is a type of identity this gives some kind of explanation of why the parallels between the two hold.
But the strong thesis, that the composition relation is the identity relation, gives a fuller explanation. So why not hold the strong thesis? Because, many think, there are additional challenges that face anyone who wishes to defend the strong thesis. If we adopt a language that allows the formation of plural terms we can unproblematically define a plural identity relation that holds between pluralities of objects too.
But, according to the strong Composition as Identity thesis, there can also be true hybrid identity statements that relate pluralities and single objects. The first challenge facing the defender of the strong thesis is the least troublesome. It is the syntactic problem that hybrid identity statements are ungrammatical in English Van Inwagen, However, there is in fact some doubt about whether hybrid identity statements are ungrammatical in English, and some have pointed out that this is anyway a mere grammatical artefact of English that is not present in other languages e.
Norwegian and Hungarian. So it seems that the most this challenge calls for is a mild form of grammatical revisionism. And we have, at any rate, formal languages that allow hybrid constructions to be made in which to express the claims made by the defender of the strong Composition as Identity thesis.
The second challenge is more troublesome. It is the semantic problem of providing coherent truth-conditions for hybrid identity statements. But this account clearly does not work for hybrid identity statements, for there is no single referent for a plural term.
Moreover, the standard way of giving the truth-conditions for plural identity statements mentioned above does not work for hybrid identity statements either. The third challenge is the most troublesome of all. But it seems that the defender of strong Composition as Identity must deny this.
After all, the bricks are many, but the wall is one. The second and the third challenges have been thought by many to be insurmountable Lewis, for example, rejects strong Composition as Identity on the basis of them.
But, in recent semantic work in this area, accounts have emerged that promise to answer both challenges. Wallace a, b, Cotnoir Whether they do so, however, remains to be seen. Like the impossibility of contingent identity, the impossibility of vague identity appears to be a straightforward consequence of the classical concept of identity Evans , see also Salmon Relatedly, it appears to follow that identity itself must be a determinate relation.
But some examples suggest that this conclusion is too sweeping — that even identity statements containing precise designators may be, in some sense, indeterminate. Consider Everest and some precisely defined hunk of rock, ice and snow, Rock, of which it is indeterminate whether its boundaries coincide with those of Everest. There is no space to go into these matters here, but one particular variant of the Evans argument worth briefly noting is given by Hawley Download all slides.
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