Marco Ruffino

University of Campinas

Illocutionary Acts in Mathematics

24 June 2019, 11:00

Faculdade de Letras de Lisboa

Sala Mattos Romão (Departamento de Filosofia)

Abstract: Contemporary speech act theory was originally developed by Austin (1962) and further elaborated by Searle (1969, 1975, 1979) as an account of the illocutionary aspects of utterances in ordinary language. In particular, this theory searched for a foundational account of the linguistic dimension of human action. Later it found widespread application in the philosophy of mind, philosophy of law and, more recently, in the foundation of social sciences. However, in the philosophy of mathematics and of logic very little attention has been paid to pragmatic phenomena; indeed, pragmatic aspects of mathematical language are almost universally ignored. The purpose of this paper is to apply the machinery of contemporary speech act theory (especially Searle and Vanderveken (1985)) to the essential aspects of mathematics as a science. This hypothesis should not be understood as a defense of an anti-realist ontology of mathematical entities or propositions. Indeed, as I shall argue, this hypothesis is largely independent of any such ontology. Even if one adopts a strict realist view of mathematical entities, the discovery of these entities and of their structure depends largely on some illocutionary acts. It should also not be confounded with the trivial claim that communication among mathematicians is done in part using natural language and, as such, it is impregnated with illocutionary acts (questions, assertions, promises, praises, invitations, etc.).; the working hypothesis is that even at the level of highly abstract and formalized language there are some essential illocutionary acts as well as some illocutionary force indicators.