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.