Abstract

Saul Kripke’s analysis of the concept of the natural numbers that we are taught in school yields a novel and axiomatically economical way of representing arithmetic in standard set theory—one that helps to answer Benacerraf’s objection from extraneous content as well as Wittgenstein’s objection from unsurveyability. After describing Kripke’s proposal in some detail, we examine it in the light of work by Quine, Steiner, Parsons, Boolos and Burgess. Although the primary aim of this paper is to present and explicate Kripke’s view, we conclude by discussing some of the issues that are faced by Kripke’s proposal, so that the reader can get a sense of the geography of these issues.