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The roots of contemporary Platonism. (English) Zbl 0706.03001

This is a review of philosophy of mathematics, written from within a parochial and somewhat old-fashioned Quinean perspective. The alternatives to Platonism are Intuitionism (and related constructivist approaches), Formalism (including attempts to rescue the program from Gödelian problems), and Logicism, with fairly full and discerning references to recent work on each. The objection to Intuitionism is that it requires revision of standard mathematics, and thus fails to meet Quine’s demand for a naturalised epistemology; to Formalism, that (as Frege said) it fails to account for mathematics’ applicability; and to Logicism, Quine’s rejection of the analytic/synthetic distinction. The Platonism defended is a blend of the reluctant Quinean and the more enthusiastic Gödelian versions. The author points to the need for an existentially neutral philosophy of mathematics, one which overcomes Quine’s dictum that to be is to be a value of a variable, but except for brief dismissive references to C. ParsonsMathematics in philosophy (Ithaca, NY; Cornell U.P., 1983), she does not engage with Meinongians [cf. R. Routley, Exploring Meinong’s jungle and beyond (Canberra; ANU, 1980)]; she also mentions the need for a philosophy which takes account of the history of mathematics, but without citing I. LakatosProofs and refutations (1976; Zbl 0334.00022).
Reviewer: J.Mackenzie

MSC:

03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics

Citations:

Zbl 0334.00022
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