How high the sky? Rumfitt on the (putative) indeterminacy of the set-theoretic universe

Abstract

This comment focuses on Chapter 9 of The Boundary Stones of Thought and the argument, due to William Tait, that Ian Rumfitt there sustains for the indeterminacy of set. I argue that Michael Dummett’s argument, based on the notion of indefinite extensibility and set aside by Rumfitt, provides a more powerful basis for the same conclusion. In addition, I outline two difficulties for the way Rumfitt attempts to save classical logic from acknowledged failures of the principle of bivalence, one specifically for his treatment of the set-theoretic case, the other of more general bearing but especially germane to the case of vagueness.