Kripke on Logicism, Wittgenstein, and De Re Beliefs about Numbers

Abstract

This chapter discusses the evolution of Saul Kripke's thinking about Wittgenstein. Philosophy is a struggle for clarity, and both Wittgenstein and Kripke have the power to get to the absolute nub of a problem, taking nothing for granted, especially the orthodoxies of academic philosophy. More significantly, the concept of a "buckstopper" takes account of the Wittgensteinian intuition that mathematical notation must be perspicuous to be mathematical. It is internal to the concept of a calculation that the calculation should have the power to persuade us to accept the result. Kripke notes himself that his proposal implies that the identity of the numbers is culturally dependent. Even a culture that recognized decimal numbers, but did not use our system of positional notation for the numbers would be using different numbers, and not just different numerals.

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