Crisis and return of intuition in Hans Hahn's philosophy of mathematics. (Q2702588)

The author underlines how radical an empiricist Hans Hahn was: space, time and number were, for example, ``superfluous entities'' for him. In his 1933 lecture ''The Crisis of Intuition'' Hahn used such counterintuitive examples as Peano's space-filling curve and Weierstrass's non-differentiable continuous function to illustrate what he took as the banishment of intuition from mathematics. The author points out that these very examples show a transformed or intellectualized use of intuition rather than an abandonment. Kant's arguments for the role of intuition are at the root of modern discussions. The author maintains that the weakness of those early arguments is due only to Kant's reliance on his knowledge of the mathematics of his time. As mathematics has developed ``thus Kantian epistemology should also be further developed in order to clarify the concept of `intuition' in relation to mathematical `intuition' and thereby find an explanation of the 'puzzling efficiency of mathematics' in the empirical sciences.''NEWLINENEWLINEFor the entire collection see [Zbl 0948.00029].