Thomas Kuhn, Modern Mathematics and the Dynamics of Reason

It is now 30 years since a group of philosophers and historians published a collection of articles (Gillies D, Revolutions in mathematics, Oxford University Press, Oxford, 1992) which took as their central question the usefulness for the philosophy of mathematics of Kuhn’s constructions in the philosophy of science. Important work was done to see whether the concepts of ‘revolution’ and ‘paradigm’ made sense there. However, a feature of the collection which should raise doubts about the universality of its findings was the restriction, except in a single case, to work done prior to 1900. In this article I discuss what form a historically-oriented philosophy of modern mathematics should take, and the role it could play in developing Michael Friedman’s post-Kuhnian theory as described in his ‘Dynamics of Reason’ (2001) and later publications.