Frege's theory of concepts and objects and the interpretation of second-order logic

Philosophia Mathematica 1 (2):139-156 (1993)
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Abstract

This paper casts doubt on a recent criticism of Frege's theory of concepts and extensions by showing that it misses one of Frege's most important contributions: the derivation of the infinity of the natural numbers. We show how this result may be incorporated into the conceptual structure of Zermelo- Fraenkel Set Theory. The paper clarifies the bearing of the development of the notion of a real-valued function on Frege's theory of concepts; it concludes with a brief discussion of the claim that the standard interpretation of second-order logic is necessary for the derivation of the Peano Postulates and the proof of their categoricity.

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Citations of this work

Frege's Other Program.Aldo Antonelli & Robert May - 2005 - Notre Dame Journal of Formal Logic 46 (1):1-17.
Critical Notice.William Demopoulos - 1993 - Canadian Journal of Philosophy 23 (3):477-497.

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