Kripke's Paradox and the Church-Turing Thesis

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 of "plus", but the same paradox can be applied to any other term in natural language. Many responses to the paradox concen...

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Bibliographic Details
Published in:Synthese (Dordrecht) 2008-01, Vol.160 (2), p.285-295
Main Author: Sprevak, Mark D.
Format: Article
Language:English
Subjects:
Algorithms
Architecture
Computability
Computationalism
Determinacy
Education
Epistemology
Epistemology. Philosophy of science. Theory of knowledge
Input output
Language
Logic
Metaphysics
Natural kinds
Natural language
Original Paper
Paradoxes
Philosophy
Philosophy of Language
Philosophy of Science
Private language
Semantics
Skepticism
Terminology
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Summary: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 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.
ISSN:0039-7857
1573-0964
DOI:10.1007/s11229-006-9120-2