Why Frege Does not Deserve His Grain of Salt

Crispin Wright

in The Reason's Proper Study

Published in print March 2001 | ISBN: 9780198236399
Published online November 2003 | e-ISBN: 9780191597565 | DOI:
Why Frege Does not Deserve His Grain of Salt

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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

Chapter.  9401 words. 

Subjects: Philosophy of Mathematics and Logic

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