- 46
- 0
I am an avid student of philosophy, not mathematics. I was more interested in these topics for there philosophical implications. It seems to me that Zeno showed the uncountable infinity of space long before Cantor, and that that infinity alone leads directly to Banach-Tarski. I don't know why one's a paradox but not the other. Pierre Bayle (his 1696 article on Zeno), Kant, Hegel and others thought these arguments show that reality is contradictory in the sense that Escher's "Ascending, Descending" picture is. Mathematicians don't always understand the shock waves they send through the field of philosophy. The Zenonian box: half of it stacked progressively on top of the other half, one fraction at a time, first blue then green, then blue again ect. When the box is whole again, will the top be blue or green? If traditional philosophy is true, there must be one color left on top. Period. But this is definitely a discussion for a different forum. Thanks