Speech acts in mathematics

We offer a novel picture of mathematical language from the perspective of speech act theory. There are distinct speech acts within mathematics (not just assertions), and, as we intend to show, distinct illocutionary force indicators as well. Even mathematics in its most formalized version cannot do without some such indicators. This goes against a certain orthodoxy both in contemporary philosophy of mathematics (which tends to see mathematics as a realm in which no pragmatic features of ordinary language are present) and in speech act theory (which tends to pay attention solely to communication in ordinary language but not to formal languages). As we will comment, the recognition of distinct illocutionary acts within logic and mathematics and the incorporation of illocutionary force indicators in the formal language for both goes back to Frege’s conception of these topics. We are, therefore, going back to a Fregean perspective. This paper is part of a larger project of applying contemporary speech act theory to the scientific language of mathematics in order to uncover the varieties and regular combinations of illocutionary acts (silently) present in it. For reasons of space, we here concentrate only on assertive and declarative acts within mathematics, leaving the investigation of other kinds of acts for a future occasion.