## Towards a theory of speech acts in mathematics: The case of naturalness

(Giorgio Venturi, UNICAMP)

In this talk we will offer a novel picture of mathematics, where the theory of speech acts ([4]) plays a constitutive role of mathematical reality. Our starting point consists in the analysis of the debate between mathematical realists and anti-realists; in particular the discussion whether or not mathematical objects exist, and if so in which sense. We will try to undermine the incompatibility of these two opposite positions, arguing that the goal of mathematics is not the study of abstract objects (but that they are only a useful means). Toward this end we will make use of the distinction between propositional content and forms of representation, arguing that what is commonly understood as a mathematical object is, only, part of a form of representation. The main argument for the application of a theory of speech acts to mathematics will be offered by the semantic homogeneity between mathematical and natural language (see [1]), sustained by the realists. Given this homogeneity it will therefore sufficient to show that the use of speech acts is a fundamental component of mathematical discourse. We will therefore offer a taxonomy of speech acts in mathematics ([2], [3]). In the end, as an application of the image of mathematics offered, we will offer a new definition of abstract object and we will outline a response to an indispensability argument `a la Quine-Putnam, showing the ontological indeterminateness of its outcome.

References:

[1] P. Benacerraf, Mathematical truth, The Journal of Philosophy, 70(19), pp. 661–679, 1973.

[2] L. San Mauro, G. Venturi, Towards a theory of speech acts in mathematics: the case of naturalness, submitted.

[3] L. San Mauro, G. Venturi, Speech acts in mathematics: a manifesto, in preparation.

[4] J. R. Searle, Speech acts: An essay in the philosophy of language, volume 626. Cambridge University Press, 1969.

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References:

[1] P. Benacerraf, Mathematical truth, The Journal of Philosophy, 70(19), pp. 661–679, 1973.

[2] L. San Mauro, G. Venturi, Towards a theory of speech acts in mathematics: the case of naturalness, submitted.

[3] L. San Mauro, G. Venturi, Speech acts in mathematics: a manifesto, in preparation.

[4] J. R. Searle, Speech acts: An essay in the philosophy of language, volume 626. Cambridge University Press, 1969.

Click for slides.