Mathematical practice and naturalist epistemology

structures with potential for interaction

Bart Van Kerkhove

Jean P. Van Bendegem

pp. 61-78

in: Gerhard Heinzmann, Manuel Rebuschi (eds), Aperçus philosophiques en logique et en mathématiques, Philosophia Scientiae 9 (2), 2005.

Abstract

In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and epistemology.