Date: Jan 30, 2013 4:03 AM
Author: Virgil
Subject: Re: WMytheology � 203

In article 
<e289d619-2f59-4f4d-82d9-0e81428830da@m12g2000yqp.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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!


He is not trying not to understand anywhere as strongly as you are.

>
> For a potentially infinite set



Outside of WMytheology sets are either finite or not finite (infinite)
with no middle ground.
> But a potentially infinite set

No such things exist in standard set theories.

> But "actually
> infinite" means a number larger than every n.


Not at all. Actually infinite means set that is bigger than any single
FISON, such as the union of all FISIONS.

Note that if one can discriminate a FISON from a non_FISON, then one can
have a set of all FISONS, which is easily provable not to be the
surjective image of any FISON, and thus must be infinite.


> It is easy to understand
> that this number can never be exhausted by finite numbers n.


Infiniteness of a set is not a number at all but a property possessed by
some sets, the property of being injectable to a proper subset of
itself, which property |N enjoys.

Does WM declare there is any natural number, n, such that n+1 is not
also a natural number? Unless WM can find some such natural number, the
the set of naturals injects into a proper subset of itself, and is thus
infinite.
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