>How do these finitists handle things like the real numbers? You may enjoy "Meta Math" by Gregory Chaitin (jump to Chapter 5 for the impatient): http://arxiv.

>How do these finitists handle things like the real numbers? You may enjoy "Meta Math" by Gregory Chaitin (jump to Chapter 5 for the impatient): http://arxiv.org/abs/math/0404335 http://arxiv.org/abs/math/0404335 "Finally, and perhaps even more devastatingly, it turns out that the set of all reals that can be individually named or specified or even defined or referred to—constructively or not—within a formal language or within an individual FAS, has probability zero. Summary: reals are unnameable with probability one. So the set of real numbers, while natural—indeed, immediately given—geometrically, nevertheless remains quite elusive: Why should I believe in a real number if I can’t calculate it, if I can’t prove what its bits are, and if I can’t even refer to it? And each of these things happens with probability one!" You might also want to take a look at some of Norman Wildbergers work, like: "Set Theory: Should You Believe?" web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf