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Teorema di Frege
Frege's Theorem
Conti, Ludovica
University School for Advanced Studies (IUSS) - Pavia
Zanetti, Luca
University School for Advanced Studies (IUSS) - Pavia
2023
Abstract
Frege’s Theorem (FT) states that the axioms of Peano Arithmetic (PA) can be derived, in second-order logic, from Hume’s Principle (HP), which asserts that the cardinal number of the concept F is identical to the cardinal number of G if and only if F and G can be put into one-to-one correspondence. This theorem lies at the heart of the abstractionist program in the philosophy of mathematics, whose goal is to provide a foundation for mathematical theories on the basis of principles with the same form as HP. This paper aims to provide an introduction to FT. Section 2 summarises the main steps in the proof of FT. Section 3 discusses the philosophical significance of FT, focusing on Hale’s and Wright’s neo-Fregean program. Finally, Section 4 highlights some limitations and possible developments of abstractionism.
Journal
Source
Ludovica Conti e Luca Zanetti , "Teorema di Frege", in "APhEx 27", 2023, pp. 36-74
Languages
it
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