Speech Acts, Categoricity, and the Meanings of Logical Connectives

Hjortland, Ole T. (2013): Speech Acts, Categoricity, and the Meanings of Logical Connectives. In: Notre Dame Journal of Formal Logic

Abstract

In bilateral systems for classical logic, assertion and denial occur as primitive signs on formulae. 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 (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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 100 Philosophy and Psychology > 160 Logic
• Language: English