David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Notre Dame Journal of Formal Logic 46 (1):1-17 (2005)
Frege’s logicist program requires that arithmetic be reduced to logic. Such a program has recently been revamped by the “neologicist” approach of Hale & Wright. Less attention has been given to Frege’s extensionalist program, according to which arithmetic is to be reconstructed in terms of a theory of extensions of concepts. This paper deals just with such a theory. We present a system of second-order logic augmented with a predicate representing the fact that an object x is the extension of a concept C, together with extra-logical axioms governing such a predicate, and show that arithmetic can be obtained in such a framework. As a philosophical payoff, we investigate the status of the so-called Hume’s Principle and its connections to the root of the contradiction in Frege’s system.
|Keywords||Frege arithmetic logicism neologicism Hume's Principle|
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