Finitude and Hume’s Principle
- Richard G. HeckAffiliated withDepartment of Philosophy, Harvard University
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The paper formulates and proves a strengthening of ‘Frege’s Theorem’, which states that axioms for second-order arithmetic are derivable in second-order logic from Hume’s Principle, which itself says that the number of Fs is the same as the number ofGs just in case the Fs and Gs are equinumerous. The improvement consists in restricting this claim to finite concepts, so that nothing is claimed about the circumstances under which infinite concepts have the same number. ‘Finite Hume’s Principle’ also suffices for the derivation of axioms for arithmetic and, indeed, is equivalent to a version of them, in the presence of Frege’s definitions of the primitive expressions of the language of arithmetic. The philosophical significance of this result is also discussed.
- Finitude and Hume’s Principle
Journal of Philosophical Logic
Volume 26, Issue 6 , pp 589-617
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Richard G. Heck (1)
- Author Affiliations
- 1. Department of Philosophy, Harvard University, Cambridge, Ma, U.S.A.