Is Hume’s Principle Analytic?

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 Nq, 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. © 1999 by the University of Notre Dame. All rights reserved.