Abstract

The main thesis defended in this paper is that, interpreted in the light of reflections of Peirce and Poincaré, one can found in mathematical reasoning a non-logical symptom that may be aesthetic in Goodman’s sense. This symptom is called exemplification and serves to distinguish between only logically correct and even explanatory proofs. It broadens the scope of aesthetics to include all activities involving symbolic systems and blurs the boundaries between logic and aesthetics in mathematics. It gives a better understanding of Poincaré’s thesis that to affect aesthetic value to certain properties is not simply an added value, a bonus that somehow rewards the mathematician’s mechanical labor, but on the contrary, taking the aesthetic value into account can be helpful to mathematical practice. As an example, three proofs of the irrationality of √2 are compared for their aesthetic functioning.