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A NOTE ON THE CUT-ELIMINATION PROOF IN “TRUTH WITHOUT CONTRA(DI)CTION”

  • ANDREAS FJELLSTAD (a1)

Abstract

This note shows that the permutation instructions presented by Zardini (2011) for eliminating cuts on universally quantified formulas in the sequent calculus for the noncontractive theory of truth IKTω are inadequate. To that purpose the note presents a derivation in the sequent calculus for IKTω ending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counterexample is of the kind that leaves open the question whether cut can be shown to be eliminable in the sequent calculus for IKTω with an alternative strategy.

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*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BERGEN PO BOX 7805, 5020 BERGEN NORWAY E-mail: andreas.fjellstad@uib.no

References

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Da Ré, B. & Rosenblatt, L. (2018). Contraction, infinitary quantifiers, and omega paradoxes. Journal of Philosophical Logic, 47 (4), 611629.
Fjellstad, A. (2018). Infinitary contraction-free revenge. Thought: A Journal of Philosophy, 7(3), 179189.
Gentzen, G. (1934). Untersuchungen über das logische Schliessen i, ii. Mathematische Zeitschrift, 39, 176210, 405–431.
Petersen, U. (2000). Logic without contraction as based on inclusion and unrestricted abstraction. Studia Logica, 64(3), 365403.
Zardini, E. (2011). Truth without contra(di)ction. Review of Symbolic Logic, 4(4), 498535.

Keywords

A NOTE ON THE CUT-ELIMINATION PROOF IN “TRUTH WITHOUT CONTRA(DI)CTION”

  • ANDREAS FJELLSTAD (a1)

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