Structure and Categoricity: Determinacy of Reference and Truth-Value in the Philosophy of Mathematics

摘要

This article surveys recent literature by Parsons, McGee, Shapiro and otherson the significance of categoricity arguments in the philosophy of mathematics.After discussing whether categoricity arguments are sufficient to securereference to mathematical structures up to isomorphism, we assess what exactlyis achieved by recent `internal' renditions of the famous categoricityarguments for arithmetic and set theory.