Kripke’s paradox and the Church–Turing thesis

Abstract

Kripke (1982, Wittgenstein on rules and private language. Cambridge, MA: MIT Press) presents a rule-following paradox in terms of what we meant by our past use of “plus”, but the same paradox can be applied to any other term in natural language. Many responses to the paradox concentrate on fixing determinate meaning for “plus”, or for a small class of other natural language terms. This raises a problem: how can these particular responses be generalised to the whole of natural language? In this paper, I propose a solution. I argue that if natural language is computable in a sense defined below, and the Church–Turing thesis is accepted, then this auxiliary problem can be solved.