Chapter

Dummett's Critique of Wright's Attempt to Resuscitate Frege

Bob Hale

in The Reason's Proper Study

Published in print March 2001 | ISBN: 9780198236399
Published online November 2003 | e-ISBN: 9780191597565 | DOI: http://dx.doi.org/10.1093/0198236395.003.0009
Dummett's Critique of Wright's Attempt to Resuscitate Frege

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In Frege: Philosophy of Mathematics (1991), Michael Dummett argues that the neo‐Fregean programme––championed by Crispin Wright––is destined to fail for four reasons: (i) no satisfactory solution has been given to the Caesar Problem, (ii) contextual definitions, like Hume's Principle (N=), are incapable of securing a notion of reference (for the singular terms introduced) robust enough for realism, (iii) the collapse of realism into ontological reductionism, and––the main worry––(iv) the impredicative character of Hume's Principle (N=). In this essay, Bob Hale responds to these objections in turn––arguing that Dummett misses a crucial point in his critique of Wright's solution to the Caesar Problem; that ”tolerant reductionism”––Dummett's alternative to Wright's realism––faces a dilemma; that, in his discussion of ontological reductionism, Dummett assumes that Wright must adhere to the view that the left‐ and right‐hand side of Hume's Principle have the same sense, while Wright only holds that the two sides have the same content; and lastly, that none of three worries concerning impredicativity has any decisive force against Wright's position.

Keywords: Caesar Problem; contextual definition; Dummett; Hume's Principle; impredicativity; reductionism; reference; Wright

Chapter.  13353 words. 

Subjects: Philosophy of Mathematics and Logic

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