How to make (mathematical) assertions with directives

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...

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Bibliographic Details
Published in:Synthese (Dordrecht) 2023-10, Vol.202 (5), p.127, Article 127
Main Authors: Caponetto, Laura, San Mauro, Luca, Venturi, Giorgio
Format: Article
Language:English
Subjects:
Directives
Education
Epistemology
Logic
Mathematics
Metaphysics
Original Research
Philosophy
Philosophy of Language
Philosophy of Science
Pragmatics
Theory
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Summary: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.
ISSN:1573-0964
0039-7857
1573-0964
DOI:10.1007/s11229-023-04360-7