Date: Feb 26, 2013 7:11 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots
On Feb 26, 12:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
We both agree
There does not exist an m
such that the mth line
of L is coFIS with the diagonal
(here we interpret "There does
not exist" to mean "we cannot find").
So we agree any such m must be an
unfindable natural number.
I am not interested in arguments
about whether an unfindable number exists.
[I still do not understand why
WM rejects the obvious proof by contradiction
Suppose that P is a predicate such that
for every natural number m, P(m) is true.
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)
> Every natural number is findable.
Which, according to WM does
not mean that you can prove every
natural number is findable.