## Notre Dame Journal of Formal Logic

- Notre Dame J. Formal Logic
- Volume 40, Number 1 (1999), 6-30.

### 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 $N^q$, 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.

#### Article information

**Source**

Notre Dame J. Formal Logic, Volume 40, Number 1 (1999), 6-30.

**Dates**

First available in Project Euclid: 5 December 2002

**Permanent link to this document**

https://projecteuclid.org/euclid.ndjfl/1039096303

**Digital Object Identifier**

doi:10.1305/ndjfl/1039096303

**Mathematical Reviews number (MathSciNet)**

MR1811201

**Zentralblatt MATH identifier**

0968.03009

**Subjects**

Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}

Secondary: 03-03: Historical (must also be assigned at least one classification number from Section 01) 03F35: Second- and higher-order arithmetic and fragments [See also 03B30]

#### Citation

Wright, Crispin. Is Hume's Principle Analytic?. Notre Dame J. Formal Logic 40 (1999), no. 1, 6--30. doi:10.1305/ndjfl/1039096303. https://projecteuclid.org/euclid.ndjfl/1039096303