@cicerone imposter,
cicerone imposter wrote:They are "all" computable. Who cares what goes beyond infinity?
They are
not all computable, unless you hold
by definition that the only numbers which exist are those which are computable. This is known as
begging the question, and entails the rejection of classical mathematics. As science uses classical mathematics and denial of the present result still doesn't imply that free will is impossible in a nondetermined world, the free will denier is again cutting off his nose to spite his face.
Tomr's objection, that he can list all numbers, fails, for at least two reasons. First, if I tell you that I will choose a number between one and one hundred, and Tomr claims that he can compute what that number will be, nobody would agree that he had performed the claimed computation if he just listed all the possible numbers. That is just a statement of the set from which the number will be constructed, it is not a computation of the number. Yet, his claim to have shown how to compute the number amounts to exactly this. Also,
it is a matter of mathematical proof, that he cannot write out all the reals. He can at most write out a
countable infinity of numbers, but the whole point of my argument is that the probability of a real being in the set of countable numbers is zero.