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Wittgensteinian predicate logic. (English) Zbl 1088.03027

Summary: We investigate a first-order predicate logic based on Wittgenstein’s suggestion to express identity of object by identity of sign and difference of objects by difference of signs. Hintikka has shown that predicate logic can indeed be set up in such a way; we show that it can be done nicely. More specifically, we provide a perspicuous cut-free sequent calculus, as well as a Hilbert-type calculus, for Wittgensteinian predicate logic and prove soundness and completeness theorems.

MSC:

03B60 Other nonclassical logic
03A05 Philosophical and critical aspects of logic and foundations
03F05 Cut-elimination and normal-form theorems
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[1] Carnap, R., The Logical Syntax of Language , Routledge and Kegan Paul, London, 1937.
[2] Floyd, J., ”Number and ascription of number in Wittgenstein’s Tractatus ”, pp. 145–91 in Future Pasts , edited by J. Floyd and S. Shieh, Oxford University Press, New York, 2001. · Zbl 1096.03001
[3] Hintikka, J., ”Identity, variables, and impredicative definitions”, The Journal of Symbolic Logic , vol. 21 (1956), pp. 225–45. JSTOR: · Zbl 0071.01101 · doi:10.2307/2269095
[4] van Benthem, J., Exploring Logical Dynamics , Studies in Logic, Language and Information. CSLI Publications, Stanford, 1996. · Zbl 0873.03001
[5] Wittgenstein, L., Tractatus Logico-Philosophicus , Harcourt, Brace & Co, New York, 1922. Translated by C. K. Ogden.
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