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Winter 1999 Is Hume's Principle Analytic?
Crispin Wright
Notre Dame J. Formal Logic 40(1): 6-30 (Winter 1999). DOI: 10.1305/ndjfl/1039096303

Abstract

One recent `neologicist' claim is that what has come to be known as "Frege's Theorem"–the result that Hume's Principle, plus second-order logic, suffices for a proof of the Dedekind-Peano postulate–reinstates Frege's contention that arithmetic is analytic. This claim naturally depends upon the analyticity of Hume's Principle itself. The present paper reviews five misgivings that developed in various of George Boolos's writings. It observes that each of them really concerns not `analyticity' but either the truth of Hume's Principle or our entitlement to accept it and reviews possible neologicist replies. A two-part Appendix explores recent developments of the fifth of Boolos's objections–the problem of Bad Company–and outlines a proof of the principle $N^q$, an important part of the defense of the claim that what follows from Hume's Principle is not merely a theory which allows of interpretation as arithmetic but arithmetic itself.

Citation

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Crispin Wright. "Is Hume's Principle Analytic?." Notre Dame J. Formal Logic 40 (1) 6 - 30, Winter 1999. https://doi.org/10.1305/ndjfl/1039096303

Information

Published: Winter 1999
First available in Project Euclid: 5 December 2002

zbMATH: 0968.03009
MathSciNet: MR1811201
Digital Object Identifier: 10.1305/ndjfl/1039096303

Subjects:
Primary: 03A05
Secondary: 03-03, 03F35

Rights: Copyright © 1999 University of Notre Dame

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Vol.40 • No. 1 • Winter 1999
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