What is to believe in a mathematical assertion?
In this brief article we present the following paradox: one cannot assume that mathematicians are trustworthy when they express their mathematical (dis)beliefs, while also maintaining four basic theses about natural and mathematical language. We carefully present the very natural hypotheses on which this paradox is based and then we show how to deduce the paradox from these assumptions. We end by presenting the possible ways in which one can reject the paradox, together with their conceptual implications.
Grice, Herbert P. (1957), «Meaning», in Philosophical Review, vol. 66, n. 3, pp. 377-388.
Hadamard, Jacques (1945), Essay on the Psychology of Invention in the Mathematical Field, Princeton University Press.
Pagin, Peter (2016), Assertion, in Zalta Edward N., The Stanford Encyclopedia of Philosophy, Metaphysics Research Lab editor, Stanford University, winter edition.
Ruffino, Marco, San Mauro, Luca and Venturi, Giorgio (2020), «Speech acts in mathematics», in Synthese, Online first, doi.org/10.1007/s11229-020-02702-3.
Searle, John (1969), Speech acts: An Essay in the Philosophy of Language, Cambridge University Press.
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