Reflection in set theory the Bernays-levy axiom system
pp. 137-169
in: Evandro Agazzi, György Darvas (eds), Philosophy of mathematics today, Berlin, Springer, 1997Abstract
It is a classical saying that mathematics is about numbers and space. Of course, in the last three centuries, the theory of movement and more important statistics also entered the scene. But still two other subjects of independent character became treatable by mathematical methods, namely infinity in the proper sense (Cantor) and a theory of coding (Gödel). These two themes are clearly related to philosophy in general and especially to epistemology ("Erkenntnistheorie"). This is evident in the case of any theory of coding. The relation of a code to what it is supposed to code — and many related questions — became treatable inside mathematics. The phenomena, results and observations may and will lead to a better and deeper understanding of the role and the merits or weaknesses of coding in the general sense of epistemology. Here I will not enter into this fascinating theme.