During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in (...) the context of the later development of gauge theories. (shrink)

This essay revisits some classic problems in the philosophy of space and time concerning the counting of possibilities. I argue that we should think that two Newtonian worlds can differ only as to when or where things happen and that general relativistic worlds can differ in something like the same way—the first of these theses being quaintly heterodox, the second baldly heretical, according to the mores of contemporary philosophy of physics.