"I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction." (Gauss)
"I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there." (Kronecker)
"...classical logic was abstracted from the mathematics of finite sets and their subsets...Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. This is the Fall and original sin of [Cantor's] set theory ..." (Weyl)
The topic of this lecture is causality - namely, our awareness of what causes what in the world and why it matters. Though it is basic to human thought, Causality is a notion shrouded in mystery, controversy, and caution, because scientists and philosophers have had difficulties defining when one event TRULY CAUSES another. We all understand that the rooster's crow does not cause the sun to rise, but even this simple fact cannot easily be translated into a mathematical equation.