Date: Feb 24, 2013 9:56 AM Author: William Hughes Subject: Re:
Matheology § 222 Back to the roots So, when WM says that a
natural number m does not exist, he may mean that you can prove
it exists but you cannot find it. Suppose that P is a predicate
such that for every natural number m, P(m) is true. Let x be a
natural number such that P(x) is false. According to WM you
cannot prove that x does not exist. (WM rejects the obvious
proof by contradiction: Assume a natural number, x, such that
P(x) is false exists. call it k Then P(k) is both true and
false. Contradiction, Thus the original assumption is false and
no natural number, x, such that P(x) is false exists) We will
say that x is an unfindable natural It is interesting to note
that WM agrees with the usual results if you insert the term
findable. There is no findable last element of the potentially
infinite set |N. There is no findable index to a line of L that
There is no ball with a findable index in the vase. It does not
really matter if nonfindable n