David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 26 (6):589 - 617 (1997)
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 of Gs 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||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Richard Heck (1997). Finitude and Hume's Principle. Journal of Philosophical Logic 26 (6):589-617.
Richard Heck (1993). The Development of Arithmetic in Frege's Grundgesetze der Arithmetik. Journal of Symbolic Logic 58 (2):579-601.
Richard Heck (1999). Frege's Theorem: An Introduction. The Harvard Review of Philosophy 7 (1):56-73.
Øystein Linnebo (2004). Predicative Fragments of Frege Arithmetic. Bulletin of Symbolic Logic 10 (2):153-174.
Bird Alexander (1997). The Logic in Logicism. Dialogue 36:341�60.
Alexander Bird (1997). The Logic in Logicism. Dialogue 36 (02):341--60.
Fraser Macbride (2000). On Finite Humet. Philosophia Mathematica 8 (2):150-159.
Crispin Wright (2001). Is Hume's Principle Analytic? In Bob Hale & Crispin Wright (eds.), Notre Dame Journal of Formal Logic. Oxford University Press 307-333.
Edward N. Zalta, Frege's Logic, Theorem, and Foundations for Arithmetic. Stanford Encyclopedia of Philosophy.
Robert May (2005). Frege's Other Program. Notre Dame Journal of Formal Logic 46 (1):1-17.
Stewart Shapiro (2000). Frege Meets Dedekind: A Neologicist Treatment of Real Analysis. Notre Dame Journal of Formal Logic 41 (4):335--364.
Jeffrey Ketland (2002). Hume = Small Hume. Analysis 62 (1):92–93.
Added to index2011-05-29
Total downloads15 ( #175,574 of 1,726,249 )
Recent downloads (6 months)5 ( #147,227 of 1,726,249 )
How can I increase my downloads?