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Wittgenstein and Ramsey on Identity

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From Dedekind to Gödel

Part of the book series: Synthese Library ((SYLI,volume 251))

Abstract

Jaakko Hintikka has recently proposed that the distinction between the standard and nonstandard interpretations of higher-order quantifiers be used as a new tool for investigations in the history of the foundations of mathematics.1 This distinction can be described succinctly as follows: let us take a second-order quantifier involving a one-place class variable X, whose values are classes of individuals of a domain do(M). Those adopting the standard interpretation would claim that the range of this quantifier is the entire power set P(do(M)), i.e. some values of X are arbitrary extensionally possible classes, while those adopting the nonstandard interpretation would consider only some such classes as constituting the range of the quantifier. (The same reasoning applies if X is a predicate variable or for function variables.)

Identity is the very Devil and immensely important; very much more so than I thought. It hangs — like everything else — directly together with the most fundamental questions.

L. Wittgenstein to B. Russell, 29.10.1913.

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Authors and Affiliations

  1. University of Ottawa, Canada

    Mathieu Marion

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  1. Mathieu Marion
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Editors and Affiliations

  1. Boston University, USA

    Jaakko Hintikka

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Marion, M. (1995). Wittgenstein and Ramsey on Identity. In: Hintikka, J. (eds) From Dedekind to Gödel. Synthese Library, vol 251. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8478-4_14

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  • DOI: https://doi.org/10.1007/978-94-015-8478-4_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4554-6

  • Online ISBN: 978-94-015-8478-4

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