Mathematics – History and Overview
Scientific paper
2004-09-30
Mathematics
History and Overview
19pp, the paper was written for a conference on the philosophy of F. Gonseth and 20th century science, organized by Eric Emery
Scientific paper
Here we review a kind of post-World-War-II "Nachtrag" to H. Weyl's philosophical comments on mathematics and the natural sciences published in the middle of the 1920s. In a talk given at Z\"urich in the late 1940s, Weyl discussed F.Gonseth's dialectical epistemology and considered it as being restricted too strictly to aspects of historical change. His own experiences with post-Kantian dialectical philosophy, in particular J.G. Fichte's derivation of the concept of space and matter, had been a stronger dialectical background for his own 1918 studies in purely infintitesimal geometry and the early geometrically unified field theory of matter (extending the Mie-Hilbert program). Although now Weyl distantiated himself from the speculative features of his youthful philosophizing and in particular from his earlier enthusiasm for Fichte, he again had deep doubts as to the cultural foundations of modern mathematical sciences and its role in material culture of high modernity. For Weyl, philosophical "reflection" was a cultural necessity; he now turned towards K. Jasper's and M. Heidegger's existentialism to find deeper grounds, similar to his turn towards Fichte's philosophy after World War I.
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