Frege's Theorem: An Introduction
The Harvard Review of Philosophy 7 (1):56-73 (1999)
| Abstract | A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence | |||||||||
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Øystein Linnebo (2004). Predicative Fragments of Frege Arithmetic. Bulletin of Symbolic Logic 10 (2):153-174.
Richard G. Heck Jr (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.
Edward N. Zalta, Frege's Logic, Theorem, and Foundations for Arithmetic. Stanford Encyclopedia of Philosophy.
William Demopoulos (1994). The Contemporary Interest of an Old Doctrine. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:209 - 216.
Tyler Burge (1998). Frege on Knowing the Foundation. Mind 107 (426):305-347.
Richard Heck (2011). A Logic for Frege's Theorem. In Frege's Theorem. Oxford University Press.
Matthias Schirn (2011). On Translating Frege's Die Grundlagen der Arithmetik. History and Philosophy of Logic 31 (1):47-72.
Richard Heck (2011). Ramified Frege Arithmetic. Journal of Philosophical Logic 40 (6):715-735.
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