It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical assertion (e.g. a theorem) is to provide a proof—and proofs are sequences of directives. The claim is backed up by linguistic data on the use of imperatives in proofs, and by a pragmatic analysis of theorems and their proofs. Proofs, we argue, are sequences of instructions whose performance inevitably gets one to truth. It follows that a felicitous theorem, i.e. a theorem that has been correctly proven, is a persuasive theorem. When it comes to mathematical assertions, there is no sharp distinction between illocutionary and perlocutionary success.

How to make (mathematical) assertions with directives / L. Caponetto, L. San Mauro, G. Venturi. - In: SYNTHESE. - ISSN 0039-7857. - 202:5(2023), pp. 127.1-127.16. [10.1007/s11229-023-04360-7]

How to make (mathematical) assertions with directives

L. Caponetto
Co-primo
;
2023

Abstract

It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical assertion (e.g. a theorem) is to provide a proof—and proofs are sequences of directives. The claim is backed up by linguistic data on the use of imperatives in proofs, and by a pragmatic analysis of theorems and their proofs. Proofs, we argue, are sequences of instructions whose performance inevitably gets one to truth. It follows that a felicitous theorem, i.e. a theorem that has been correctly proven, is a persuasive theorem. When it comes to mathematical assertions, there is no sharp distinction between illocutionary and perlocutionary success.
Proofs; Mathematics; Speech Acts; Assertives; Directives
Settore M-FIL/05 - Filosofia e Teoria dei Linguaggi
Settore M-FIL/02 - Logica e Filosofia della Scienza
Settore PHIL-04/B - Filosofia e teoria dei linguaggi
Settore PHIL-02/A - Logica e filosofia della scienza
2023
https://link.springer.com/article/10.1007/s11229-023-04360-7
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1117957
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