What is to believe in a mathematical assertion?

  • Luca San Mauro
  • Giorgio Venturi
Keywords: Mathematical language, Assertions, Mathematical beliefs, Naturalism in mathematics, Doxastic paradox


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.


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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.