## Notre Dame Journal of Formal Logic

### Speech Acts, Categoricity, and the Meanings of Logical Connectives

Ole Thomassen Hjortland

#### 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

https://projecteuclid.org/euclid.ndjfl/1415382951

Digital Object Identifier
doi:10.1215/00294527-2798700

Mathematical Reviews number (MathSciNet)
MR3276407

Zentralblatt MATH identifier
1342.03024

#### 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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