A Scrabble on Cantor, Hilbert, and Zermelo (5)

やっぱ飽きてきた。あと、バラバラになってきた。そろそろやめよう。

I think this attitude is natural one (or one might say, naive one). More curious is Hilbert's view. He tried to stand between two views. One views goes that mathematics really deals with infinities, and we are mere finite beings, thus we cannot capture all of mathematics. Another view goes that we are mere finite beings, and mathematics is our practice, so there does not exist any infinity (which we cannot treat) in mathematics (especially Kronecker's view). Hilbert went just the middle way: we are dealing infinities in mathematics with finite means. But it was a cry for moon.

I said that Cantor did not even try to show the consistency of his set theory. Surely, it is because the conception of mathematical proof of consistency does not exist at his days. But even were it the case, Cantor would not try, I think. His cold attitude to logic shows that. And Zermelo, a decendant of Cantor, kept his track in this respect.