Abstract

As was noted by Frege, the criteria of identity for abstract objects of certain sorts can be formulated in the following form: f(x) = f(y) iffφ(x, y). I argue that the criterion of identity for persons can be formulated in the same form, and that reference to persons hinges on a conceptual operation analogous to the characterization of a function f by the formulation of such a criterion. This account suggests that a certain puzzle about personal identity over time has no determinate answer, owing to the semantic indeterminacy in the singular terms in terms of which the puzzle is posed. I present a semantic solution to the puzzle along these lines, within the framework of supervaluation semantics.