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 Freges Theorem, which states that axioms for second-order arithmetic are derivable in second-order logic from Humes 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 Humes Principle also suffices for the derivation of axioms for arithmetic and, indeed, is equivalent to a version of them, in the presence of Freges definitions of the primitive expressions of the language of arithmetic. The philosophical significance of this result is also discussed.
|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
Sean Walsh (2014). Logicism, Interpretability, and Knowledge of Arithmetic. Review of Symbolic Logic 7 (1):84-119.
Richard Heck (2011). Ramified Frege Arithmetic. Journal of Philosophical Logic 40 (6):715-735.
Bob Hale & Crispin Wright (2009). Focus Restored: Comments on John MacFarlane. Synthese 170 (3):457 - 482.
John MacFarlane (2009). Double Vision: Two Questions About the Neo-Fregean Program. Synthese 170 (3):443 - 456.
Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.
Similar books and articles
Fraser Macbride (2000). On Finite Humet. Philosophia Mathematica 8 (2):150-159.
Alexander Bird (1997). The Logic in Logicism. Dialogue 36 (02):341--60.
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.
Richard Heck (1999). Frege's Theorem: An Introduction. The Harvard Review of Philosophy 7 (1):56-73.
Richard Heck (1993). The Development of Arithmetic in Frege's Grundgesetze der Arithmetik. Journal of Symbolic Logic 58 (2):579-601.
Richard G. Heck Jr (1997). Finitude and Hume's Principle. Journal of Philosophical Logic 26 (6):589 - 617.
Added to index2009-01-28
Total downloads19 ( #102,742 of 1,679,365 )
Recent downloads (6 months)5 ( #48,400 of 1,679,365 )
How can I increase my downloads?