The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics

By Bob Hale; Crispin Wright | Go to book overview

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

Crispin Wright


I

Dummett's new book is the long-awaited sequel to his Frege: Philosophy of Language. 1 But anyone who has been expecting some seven hundred or so pages in which the central ideas of Frege's writings about mathematics, refurbished and extended, would form the basis for a treatise on all, or almost all issues of contemporary concern in the philosophy of mathematics, will be disappointed. Less than half the length of FPL, Frege: Philosophy of Mathematics (FPM) contrasts with its predecessor in its virtual confinement to Frege's actual agenda in the philosophy of mathematics—the problem of the status of the truths of number theory and analysis, and of our knowledge of them. One effect of this is that much of the book is given to the kind of critical analytical commentary on Frege's texts which was conspiciously absent from Frege: Philosophy of Language. It is no criticism of the former book to welcome this. In particular, the secondary literature on Frege has hitherto lacked anything to compare with the detailed account of the argumentation of the Introduction and first three sections (up to §55) of Grundlagen which Dummett offers over the first third of his book.

It ought to be no surprise that the two books should so contrast in scale, organization, and philosophical style. For in the Introduction of FPL Dummett wrote, recall, that

[Frege's] philosophy of mathematics is [now] a starting point only in a historical sense. It is not true that Frege's formulation of the problems of the philosophy of mathematics any longer strikes us as the most fruitful way to pose the questions that arise on the subject: on the contrary, certain questions which subsequent writers have caused to appear as constituting the central issues passed Frege by as if quite unproblematic. 2

And while 'Frege's work in philosophical logic remains fresh and relevant to the problems as we now see them', 3 the verdict must be that 'Frege, as a

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