Paradoxes, Intuitionism, and Proof-Theoretic Semantics

In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 363-374 (2024)
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Abstract

In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame the underlying logic for the paradoxes, but has to take into account the particular concept formations. For proof-theoretic semantics, however, this comes with the challenge to block some forms of direct axiomatizations of the Liar. A proper answer to this challenge might be given by Schroeder-Heister’s definitional freedom.

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Author Profiles

Reinhard Kahle
University Tübingen
Paulo Guilherme Santos
Universidade Nova de Lisboa

References found in this work

Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.
The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.

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