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There is a long tradition of regarding mathematical knowledge as a priori knowledge. But most detailed accounts in this tradition are not overtly platonistic and many are clearly not. In this chapter I examine three recent accounts that explicitly combine the claims that mathematical objects are platonic and that we can know a priori that they exist.
KeywordsAbstract Object Mathematical Knowledge Mathematical Object Singular Term Mathematical Truth
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- 1.My discussion draws on the criticism of Wright’s argument by Field (1989, ch. 5) and by Musgrave(1986).Google Scholar
- 2.Based on Hale’s version of the argument (1987, p. 11). It omits details concerning syntactic and semantic functioning, and Frege’s context principle, which I do not wish to dispute.Google Scholar
- 3.Janet Folina (2000, p. 327) makes a similar point.Google Scholar