Abstract
How are ‘every’,’ some’ and their like related to ‘the same as’? Is there any ground for saying that an understanding of the former—of expressions of generality—presupposes an understanding of the latter— of expressions of identity? Let us begin with formalised languages, those framed by use of the apparatus of predicate logic. In a second-order language, identity is definable, so no problem arises. If, in a first-order language, identity is taken as primitive, it is at least un-problematic that an interpretation of the language must involve a relation of identity over the domain. But suppose that a language is framed within first-order logic without identity: is there then any need to assume that an interpretation of the language will involve or invoke a relation of identity over the domain?
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Notes
W. V. Quine, review of P. T. Geach, Reference and Generality, Philosophical Review, 1964, 100-104.
The definition as stated is adapted for the case when the only non-logical constants of L are predicates. It will be obvious how it is to be modified for the general case in which L contains also function symbols.
P.T. Geach, ‘Ontological Relativity and Relative Identity’, in M.K. Munitz (ed.), Logic and Ontology, New York University Press, New York, 1973, pp. 287–302.
P.T. Geach, ‘Names and Identity’, in S. Guttenplan (ed.), Mind and Language, Clarendon Press, Oxford, p. 157.
Op. cit. pp. 156-157.
‘Ontological Relativity and Relative Identity’ (see note 3 above), p. 290.
Op. cit. p. 294.
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© 1991 Springer Science+Business Media Dordrecht
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Dummett, M. (1991). Does Quantification Involve Identity?. In: Lewis, H.A. (eds) Peter Geach: Philosophical Encounters. Synthese Library, vol 213. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7885-1_13
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DOI: https://doi.org/10.1007/978-94-015-7885-1_13
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