Response to Dummett

Crispin Wright

in The Reason's Proper Study

Published in print March 2001 | ISBN: 9780198236399
Published online November 2003 | e-ISBN: 9780191597565 | DOI:
Response to Dummett

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Crispin Wright's neo‐Fregean approach to arithmetic––centred around Hume's Principle (N=)––involves two claims to the effect that (i) being informed that Hume's Principle is analytic of the cardinality operator, someone competent in a suitable higher‐order language to which this operator was added would understand everything needed to comprehend new statements containing the operator, and (ii) Hume's Principle can be stipulated without significant epistemological commitment, i.e. it can adequately explain the meaning of statements of numerical identity without any requirement to the effect that there be an independent assurance that there are objects satisfying the principle. In his paper ”Neo‐Fregeans in Bad Company?” (1998)––which responds to Crispin Wright's ”On the Harmless Impredicativity of N= (Hume's Principle)” (Chapter 10 in this volume) ––Michael Dummett can be read as advancing the dilemma that the claims (i) and (ii) cannot be jointly satisfied. In his response, Wright explores various interpretations of how exactly Dummett's dilemma is supposed to arise––arguing first that the dilemma does not engage the neo‐Fregean if it is taken to evolve around the issue of how the stipulation of Hume's Principle can lead to the recognition of a denumerable domain; and second that another interpretation of the objection––mediated by the Caesar Problem––leads to an unqualified rejection of (ii). Wright then goes on to touch on the Bad Company objection, and––provoked by a comment made by Dummett––concludes by discussing and elaborating the account of understanding of numerical terms offered in ”On the Harmless Impredicativity of N= (Hume's Principle).”

Keywords: Bad Company; Dummett; Frege; Hume's Principle; impredicativity; numerical terms; Wright

Chapter.  7905 words. 

Subjects: Philosophy of Mathematics and Logic

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