Kripke's paradox and the Church-Turing thesis

Synthese 160 (2):285-295 (2008)
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
Keywords Church–Turing thesis  Kripke  Computational theory of mind  Extended cognition  Rule-following
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John R. Searle (1980). Minds, Brains and Programs. Behavioral and Brain Sciences 3 (3):417-57.
Hilary Putnam (1975). The Meaning of 'Meaning'. Minnesota Studies in the Philosophy of Science 7:131-193.

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