Frege's Other Program

Notre Dame Journal of Formal Logic 46 (1):1-17 (2005)
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Frege's logicist program requires that arithmetic be reduced to logic. Such a program has recently been revamped by the "neologicist" approach of Hale and Wright. Less attention has been given to Frege's extensionalist program, according to which arithmetic is to be reconstructed in terms of a theory of extensions of concepts. This paper deals just with such a theory. We present a system of second-order logic augmented with a predicate representing the fact that an object x is the extension of a concept C, together with extra-logical axioms governing such a predicate, and show that arithmetic can be obtained in such a framework. As a philosophical payoff, we investigate the status of the so-called Hume's Principle and its connections to the root of the contradiction in Frege's system.



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Author Profiles

G. Aldo Antonelli
University of California, Davis
Robert May
University of California, Davis

References found in this work

Logicism and the ontological commitments of arithmetic.Harold T. Hodes - 1984 - Journal of Philosophy 81 (3):123-149.
Frege’s Theorem: An Introduction.Richard G. Heck - 1999 - The Harvard Review of Philosophy 7 (1):56-73.
Is Hume's principle analytic?G. Boolos - 1998 - Logic, Logic, and Logic:301--314.
Is Hume's principle analytic?Crispin Wright - 2001 - Notre Dame Journal of Formal Logic 40 (1):307-333.

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