Notre Dame Journal of Formal Logic

Speech Acts, Categoricity, and the Meanings of Logical Connectives

Ole Thomassen Hjortland

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 55, Number 4 (2014), 445-467.

Dates
First available in Project Euclid: 7 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1415382951

Digital Object Identifier
doi:10.1215/00294527-2798700

Mathematical Reviews number (MathSciNet)
MR3276407

Zentralblatt MATH identifier
1342.03024

Subjects
Primary: 03B50: Many-valued logic 03B20: Subsystems of classical logic (including intuitionistic logic)

Keywords
logical inferentialism logical constants categoricity proof theory sequent calculus

Citation

Thomassen Hjortland, Ole. Speech Acts, Categoricity, and the Meanings of Logical Connectives. Notre Dame J. Formal Logic 55 (2014), no. 4, 445--467. doi:10.1215/00294527-2798700. https://projecteuclid.org/euclid.ndjfl/1415382951


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