Notre Dame Journal of Formal Logic

Wittgensteinian Predicate Logic

Kai F. Wehmeier


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.

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Notre Dame J. Formal Logic, Volume 45, Number 1 (2004), 1-11.

First available in Project Euclid: 2 September 2004

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Zentralblatt MATH identifier

Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30} 03B60: Other nonclassical logic 03F05: Cut-elimination and normal-form theorems

Wittgenstein variables cut-free calculi


Wehmeier, Kai F. Wittgensteinian Predicate Logic. Notre Dame J. Formal Logic 45 (2004), no. 1, 1--11. doi:10.1305/ndjfl/1094155275.

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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.
  • [3] Hintikka, J., "Identity, variables, and impredicative definitions", The Journal of Symbolic Logic, vol. 21 (1956), pp. 225--45.
  • [4] van Benthem, J., Exploring Logical Dynamics, Studies in Logic, Language and Information. CSLI Publications, Stanford, 1996.
  • [5] Wittgenstein, L., Tractatus Logico-Philosophicus, Harcourt, Brace & Co, New York, 1922. Translated by C. K. Ogden.