Second-order logic and logicism

Mind 99 (393):91-99 (1990)

Abstract
Some widely accepted arguments in the philosophy of mathematics are fallacious because they rest on results that are provable only by using assumptions that the con- clusions of these arguments seek to undercut. These results take the form of bicon- ditionals linking statements of logic with statements of mathematics. George Boolos has given an argument of this kind in support of the claim that certain facts about second-order logic support logicism, the view that mathematics—or at least part of it—reduces to logic. Hilary Putnam has offered a similar argument for the view that it is indifferent whether we take mathematics to be about objects or about what follows from certain postulates. In this paper I present and rebut these arguments
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DOI 10.1093/mind/XCIX.393.91
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