Date: Jan 30, 2013 3:28 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203
On 30 Jan., 00:16, William Hughes <wpihug...@gmail.com> wrote:

> On Jan 29, 10:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > On 29 Jan., 21:28, William Hughes <wpihug...@gmail.com> wrote:

>

> <snip>

>

> > > It does, however, imply that d in not one

> > > of the lines of the list L

>

> > For that sake you must check all lines. Can you check what is not

> > existing?

>

> So now your claim is

>

> We can know

>

> There does not exist a natural number n

> such that d is equal to the nth line

> of L

>

> but we cannot know

>

> d is not one of the lines of L

You are trying hard to misunderstand!

For a potentially infinite set L we can know: d is not in line number

n.

But a potentially infinite set is not actually infinite. And without

actually infinite sets, you have no uncountability. For instance, all

finite subsets of |N make up a countable power set. Only the actually

infinite subsets make up an uncountable power set. But "actually

infinite" means a number larger than every n. It is easy to understand

that this number can never be exhausted by finite numbers n. Therefore

we cannot prove that d is missing in the actually infinity list from

"for every n in |N, there is no line n that contains d".

We will never know something for all lines as we will never be able to

know all lines, since beyond every line n there are infinitely many

following.

Regards, WM