Mathematical Definitions as Speech Acts

Marco Ruffino

In this paper my aim is to consider the special linguistic act involved in mathematical definitions. I shall first be concerned with the purely linguistic question of the semantic mechanism behind performative utterances, since these are, according to Austin’s (1962) original view on the topic, the instrument of doing things by means of language. Next, I shall consider the relation between performatives and directive speech acts since the latter are, according to Searle (1979), a way of making true a propositional content by the very utterance of a sentence with this propositional content. Finally, I shall examine how exactly definitions can be seen as a characteristically mathematical performative or a directive speech act. This discussion has its roots in Frege’s (1879) remark that definitions require an illocutionary force indicator distinct from the one of assertion. My ultimate goal is to carry on this discussion now using the machinery of contemporary speech act theory.