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Reference and Identity Over Time

  • T. Chapman
Chapter
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Part of the Synthese Library book series (SYLI, volume 159)

Abstract

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’.

Keywords

Modal Logic Object Language Relative Identity Chapter VIII Variable Predicate 
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References

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    P. T. Geach, Reference and Generality, Ithaca, New York: Cornell University Press, 1962.Google Scholar
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    David Wiggins, Identity and Spatio-Temporal Continuity, Oxford: Blackwells, 1967.Google Scholar
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    John Woods, “Essentialism, Self-Identity and Quantifying In” in Milton K. Munitz, ed., Identity and Individuation, New York: New York University Press, 1971, pp. 165–198.Google Scholar
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    W. Van Orman Quine, Word and Object, New York and London: John Wiley and Sons, Inc., 1960, p. 198. See also the papers by Quine and Ruth Barcan Marcus in I. M. Copi and J. A. Gould, eds., Contemporary Readings in Logical Theory, New York: Macmillan, 1967.Google Scholar
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    See, e.g., David Lewis, “Counterpart Theory and Quantified Modal Logic”, Journal of Philosophy 65 (1968), pp. 113–126 particularly Axiom 2 on p. 114.CrossRefGoogle Scholar
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    Nicholas Rescher and Alasdair Urquhart, Temporal Logic, New York and Vienna: Springer-Verlag, 1971, p. 242.Google Scholar
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    See G. H. Hughes and M. J. Cresswell, An Introduction to Modal Logic, London: Methuen, 1968, Chapter XI.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1982

Authors and Affiliations

  • T. Chapman
    • 1
  1. 1.Department of PhilosophyUniversity of GuelphCanada

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