What is to believe in a mathematical assertion?
Keywords:
Mathematical language, Assertions, Mathematical beliefs, Naturalism in mathematics, Doxastic paradox
Abstract
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.
References
Bach, Kent and Harnish, Robert (1979) Linguistic Communication and Speech Acts, MIT Press, Cambridge.
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.
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.
Published
2021-07-20
How to Cite
San Mauro, L. and Venturi, G. (2021) “What is to believe in a mathematical assertion?”, Rivista Italiana di Filosofia del Linguaggio, 15(1). doi: 10.4396/2021060V4.
Section
VARIA
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