Abstract

In the Grundlagen Frege says that "line a is parallel to line b" differs from "the direction of a = the direction of b" in that "we carve up the content in a way different from the original way". It seems that such recarving is crucial to Frege's logicist program of defining numbers, but it also seems incompatible with his later theory of sense and reference. I formulate a restriction on recarving, in particular, that no names may be introduced that introduce new possibilities of reference failure, which is observed by Frege's examples. This restriction discriminates between various relatives of the "slingshot" argument which rely on a step of recarving. I offer an argument for the restriction based on Fregean principles, which I formalize in Church's "Logic of Sense and Denotation", and briefly discuss various axioms of his "Alternative (0)" which are incompatible with recarving.