## Notre Dame Journal of Formal Logic

### Frege's Other Program

#### Abstract

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.

#### Article information

Source
Notre Dame J. Formal Logic Volume 46, Number 1 (2005), 1-17.

Dates
First available in Project Euclid: 31 January 2005

http://projecteuclid.org/euclid.ndjfl/1107220671

Digital Object Identifier
doi:10.1305/ndjfl/1107220671

Zentralblatt MATH identifier
02186748

Mathematical Reviews number (MathSciNet)
MR2131544

#### Citation

Antonelli, Aldo; May, Robert. Frege's Other Program. Notre Dame Journal of Formal Logic 46 (2005), no. 1, 1--17. doi:10.1305/ndjfl/1107220671. http://projecteuclid.org/euclid.ndjfl/1107220671.

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