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8 - Structural Realism and Contextual Individuality

Published online by Cambridge University Press:  08 January 2010

By
John Stachel
Edited by
Yemima Ben-Menahem
John Stachel
Affiliation:
Professor emeritus of physics and Director of the Center for Einstein Studies, Boston University
Yemima Ben-Menahem
Affiliation:
Hebrew University of Jerusalem
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Summary

ANOTHER PROBLEM OF REFERENCE

Hilary Putnam's “A Problem of Reference” poses the question: “how representations can enable us to refer to what is outside the mind” (Putnam 1981, p. 27). His approach is based upon “giv[ing] up the idea that … words stand in some sort of one-one relation to (discourse-independent) things and sets of things,” and facing the fact that “nature does not single out any one correspondence between our terms and external things” (ibid., p. 41).

Hallett (1994, p. 69) points out that “Putnam has used essentially two different arguments” to prove this, which Hallett calls “the Löwenheim-Skolem argument … and … the permutation argument.” Putnam 1981 focuses on the permutation argument, stating and proving the following theorem:

Let L be a language with predicates F1, F2, …, Fk (not necessarily monadic). Let I be an interpretation, in the sense of an assignment of an intension to every predicate of L. Then if I is non-trivial in the sense that at least one predicate has an extension which is neither empty or universal in at least one possible world, there exists a second interpretation J which disagrees with I, but which makes the same sentences true in every possible world as I does.

(Putnam 1981, pp. 216–217)

His proof is based on the existence of permutations of the individuals and the relations between them in all such possible worlds that preserve all truth values.

Type
Chapter
Information
Hilary Putnam , pp. 203 - 219
Publisher: Cambridge University Press
Print publication year: 2005

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References

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