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2014 Speech Acts, Categoricity, and the Meanings of Logical Connectives
Ole Thomassen Hjortland
Notre Dame J. Formal Logic 55(4): 445-467 (2014). DOI: 10.1215/00294527-2798700

Abstract

In bilateral systems for classical logic, assertion and denial occur as primitive signs on formulas. Such systems lend themselves to an inferentialist story about how truth-conditional content of connectives can be determined by inference rules. In particular, for classical logic there is a bilateral proof system which has a property that Carnap in 1943 called categoricity. We show that categorical systems can be given for any finite many-valued logic using n-sided sequent calculus. These systems are understood as a further development of bilateralism—call it multilateralism. The overarching idea is that multilateral proof systems can incorporate the logic of a variety of denial speech acts. So against Frege we say that denial is not the negation of assertion and, with Mark Twain, that denial is more than a river in Egypt.

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Ole Thomassen Hjortland. "Speech Acts, Categoricity, and the Meanings of Logical Connectives." Notre Dame J. Formal Logic 55 (4) 445 - 467, 2014. https://doi.org/10.1215/00294527-2798700

Information

Published: 2014
First available in Project Euclid: 7 November 2014

zbMATH: 1342.03024
MathSciNet: MR3276407
Digital Object Identifier: 10.1215/00294527-2798700

Subjects:
Primary: 03B20, 03B50

Rights: Copyright © 2014 University of Notre Dame

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Vol.55 • No. 4 • 2014
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