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The Reason's Proper StudyEssays towards a Neo-Fregean Philosophy of Mathematics$
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Bob Hale and Crispin Wright

Print publication date: 2001

Print ISBN-13: 9780198236399

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198236395.001.0001

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

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

Chapter:
(p.189) 8 Dummett's Critique of Wright's Attempt to Resuscitate Frege
Source:
The Reason's Proper Study
Author(s):

Bob Hale (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198236395.003.0009

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

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