Can aesthetic considerations legitimately be linked to the empirical success of scientific theories? I suggest that a satisfactory answer to this question should account for the apparent attraction that aesthetic considerations seem to have for scientists, while also explaining the apparent instability of the link between the beauty of a theory and its success. I argue that two widespread tendencies in the literature, Pythagorean and subjectivist approaches, have difficulties meeting this challenge. I propose a Kantian conception of aesthetic judgments as second-order considerations, related to our own intellectual capacities for making sense of the world, and argue that it fares better.
Breitenbach deconstructs pythagoreanism (eg. Poincaré) and subjectivism as accounts of beauty in mathematics, and from the difficulties with these constructs the ‘desiderata’ that an account should satisfy. She then puts forward the Kantian beauty, adding in a footnote that Kant probably wouldn’t agree with this usage. Hm.