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How to make (mathematical) assertions with directives

Accepted version
Peer-reviewed

Type

Article

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Authors

San Mauro, Luca 
Venturi, Giorgio 

Abstract

It is prima facie uncontroversial that the justi cation 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 out 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.

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Keywords

Journal Title

Synthese

Conference Name

Journal ISSN

0039-7857
1573-0964

Volume Title

Publisher

Springer
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