Frege's Definition of Numbers

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Date

1987-04

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Philosophical Papers

Abstract

In searching for a theory of number, one of the first and most fundamental decisions (or discoveries) to be made for Frege concerns the logical status of numbers: are they objects or functions? The route to the answer to this question in the Grundlagen is tortuous indeed. It does not immediately emerge that numbers are objects, and given a knowledge of Frege’s later work, one might not think that this view was forthcoming at all. In what follows I want to consider just what objects Frege thinks numbers are, and how and why his early account of this in the Grundlagen differs from his later Grundgesetze formulation.

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Edwin Martin, "Frege's Definition of Numbers," Philosophical Papers, Vol. XVI, No. 1, April, 1987.

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Article