Critical Notice of Michael Dummett's Frege: Philosophy of Mathematics

Crispin Wright

in The Reason's Proper Study

Published in print March 2001 | ISBN: 9780198236399
Published online November 2003 | e-ISBN: 9780191597565 | DOI:
Critical Notice of Michael Dummett's Frege: Philosophy of Mathematics

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Though Michael Dummett's assessment of Frege's philosophy of mathematics in Frege: Philosophy of Mathematics (1991) is strikingly positive compared to the one given in Frege: Philosophy of Language (1973), he remains highly critical of Fregean approaches to arithmetic. In this critical study, Crispin Wright provides a brief overview of Frege: Philosophy of Mathematics and rehearses four Dummettian lines of argument against his neo‐Fregean programme (see also Chapter 8 of this volume); the main line of argument aimed to establish that the impredicativity of Hume's Principle prevents it from playing its intended explanatory role. Dummett favours a logicist approach to arithmetic, but believes that neither Frege nor neo‐Fregeans (Wright, in particular) have managed to develop such an approach satisfactorily. Wright formulates three requirements on logicist accounts of arithmetic and argues that, given Dummett's positive endorsement of a logicist account of arithmetic, these requirements leave Dummett as much in need of a solution to the objections presented as the Wrightian neo‐Fregean. The critical study concludes by questioning the plausibility of Dummett's proposal to the effect that the worry concerning impredicativity can be dealt with via the notion of indefinite extensibility.

Keywords: arithmetic; Dummett; Hume's Principle; impredicativity; indefinite extensibility; logicism; Wright

Chapter.  6257 words. 

Subjects: Philosophy of Mathematics and Logic

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