Reference and Identity Over Time
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The purpose of this chapter is to discuss the thesis that the identity of particulars over time is relative and that this accounts for the consistency of the idea of change. The problem is nicely stated by the mathematician W. J. Reichmann. He says, “Heracleitus contended that nothing is stable… (it is impossible) to step into the same river once since it is changing as we step. It is the same, yet not the same. This goes far deeper than mathematics. It goes to the very root of existence, for how may we say that a thing is… if it is always changing into something else?” In other words we are normally inclined to accept what is conventionally called “Leibniz’s Law,” that (a = b) ≡ (∀ϕ) (ϕa ≡ ϕb). But this sort of case arises, suppose that ‘a’ and ‘b’ are names of the same object at different times, at 1 and at 2 and that a changes over time, so that at 1 has the property P and at 2 lacks this property, but that at all times a has the property S. Then Leibniz’s Law is apparently violated since we cannot, straight off at least, substitute P for ϕ. (The temporalization of predicates is discussed later.) Using the notation ‘a = b’ for, “‘a \(\mathop = \limits_\phi \) b’ relative to the concept o,” we also have the relativity of identity (that “two” particulars can be same object relative to one concept and yet not the same relative to another) for in the above case we have ‘at 1 = at 2’ but ‘at 1 = at 2’.
KeywordsModal Logic Object Language Relative Identity Chapter VIII Variable Predicate
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