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Journal of Philosophical Logic

, Volume 26, Issue 6, pp 589–617 | Cite as

Finitude and Hume’s Principle

  • Richard G. Heck
Article

Abstract

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.

Keywords

Philosophical Significance Primitive Expression Number ofGs Infinite Concept 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Richard G. Heck
    • 1
  1. 1.Department of PhilosophyHarvard UniversityCambridgeU.S.A.

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