Lauener Foundation for Analytical Philosophy
Thursday 27 May 2010
4th International Lauener Symposium
on Analytical Philosophy
In Honour of Professor Sir Michael Dummett
Prof. Dr. Crispin Wright
Whence the Paradox? Axiom V and Indefinite Extensibility
In the last chapter of Frege: Philosophy of Mathematics Michael Dummett suggests that Frege's major mistake – the key to the collapse of the 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 of the existence of indefinitely extensible concepts" (page 317). I will try to say what I think is right about this particular diagnostic suggestion of Dummett's: to propose a characterization of indefinite extensibility, and to explain the connection of the notion so characterized with paradox.