Speech acts in mathematics

Synthese 198 (10):10063-10087 (2020)
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Abstract

We offer a novel picture of mathematical language from the perspective of speech act theory. There are distinct speech acts within mathematics, 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 and in speech act theory. 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 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.

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Author Profiles

Marco Ruffino
University of Campinas
Luca San Mauro
Università degli Studi di Roma La Sapienza
Giorgio Venturi
University of Campinas

References found in this work

How to do things with words.John Langshaw Austin - 1962 - Oxford [Eng.]: Clarendon Press. Edited by Marina Sbisá & J. O. Urmson.
Logical foundations of probability.Rudolf Carnap - 1950 - Chicago]: Chicago University of Chicago Press.
Speech Acts: An Essay in the Philosophy of Language.John Rogers Searle - 1969 - Cambridge, England: Cambridge University Press.
Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..

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