Whence the Paradox? Axiom V and lndeiinite Extensibility


Συγγραφέας: Crispin Wright


Crispin Wright: Whence the Paradox? Axiom V and lndeiinite Extensibility (pdf, 270K)
In a well-known passage in the last chapter of Frege: Philosophy of Mathematics Michael Dummett suggests that Frege’s major "mistake"—the key to the collapse ofthe project of Grundgesetze—consisted in “his supposing there to be a totality containing the extension of every concept defined over it; more generally [the mistake] lay in his not having the glimmering of a suspicion ofthe existence of indefinitely extensible concepts" (Dummett [1991, 317]). Now, claims ofthe form, Frege fell into paradox because. are notoriously difficult to assess even when what replaces the dots is relatively straightforward. Offerings have included, for instance, that...