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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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Why Frege Does not Deserve His Grain of Salt

Why Frege Does not Deserve His Grain of Salt

A Note on the Paradox of ‘The Concept Horse’ and the Ascription of Bedeutungen to Predicates

Chapter:
(p.72) 3 Why Frege Does not Deserve His Grain of Salt
Source:
The Reason's Proper Study
Author(s):

Crispin Wright (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198236395.003.0004

This paper offers a new solution to the concept horse paradox, which arises within a Fregean semantics. First, an explication of the well‐known paradox is given and five constraints on a satisfactory solution of this paradox are imposed. Second, it discusses and rejects on the basis of these five constraints Dummett's solution to the paradox, as well as the more recently offered alternative approach of Wiggins. In the following, the source of the paradox is identified with the intuitive sounding Reference Principle, i.e. that sameness of reference should ensure sameness of semantic role, which suffices to develop the paradox on a standard Fregean semantics. Lastly, a resolution is offered by distinguishing two kinds of semantic relations, reference for singular terms and ascription for predicates, which resolves the paradox, while retaining the Reference Principle, however it seems subject to other well‐known problems such as the intensional version of Russell's Paradox.

Keywords:   Ascription, Concept horse, Dummett, Frege, reference, Reference Principle, semantics, Wiggins

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