Date: Feb 27, 2013 7:04 AM
Subject: Re: Matheology § 222 Back to the roots

On 26 Feb., 22:54, William Hughes <> wrote:
> On Feb 26, 6:11 pm, WM <> wrote:

> > On 26 Feb., 13:11, William Hughes <> wrote:> On Feb 26, 12:47 pm, WM <> 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.

> > It is a variable that can take any natural number.
> OK, so we have constant natural numbers
> and variable natural numbers.

No. We have a "limit" (not an infinite limit however) of the list and
of the FIS of the d (which both are the same) that assumes a natural
number which however cannot be known.
> We agree that any such m cannot be
> a constant natural number but must
> be a variable natural number.

The "limit" is a variable, yes.
> Now, in standard terminology (where there
> is no such thing as a variable
> natural number) we have
> a natural number valued function of time
> (or of the number of FISs of d that "actually
> exist", an increasing function of time)
> m(t). It is trivial to see that there
> is an m(t) such that the "actually existing"
> line with index m(t), contains all
> "actually existing" FISs of d.


> However, calling m(t) "the index of the line
> that contains every FIS of d"
> strains language beyond the breaking point.

> Similarly, it follows by definition
> of "actually existing", that
> there is a time varying function max(t),
> such that at any time max(t) is the maximum
> of the "actually existing" natural numbers.
> However, calling the function max(t)
> the largest element of the potentially
> infinite set |N, is silly.

Wo does that? Note, there is no "set |N" in potential infinity. The
"set |N" is an actual, i.e., completed infinity. But this assumption
is contradicted (see below).
> Now no one can stop you using whatever
> terminology you want. However, do not
> expect that you can use idiotic terminology
> without being considered an idiot.

But one can use such arguing without being considered as such?
Remember: Your point of view requires, what you often have emphasized:
There are all FIS of d in the list, but there is no line containing
them. This implies that they are distributed among several lines and
contradicts the plain fact, according to which the list is

Do you have any explanation for that point of view?

Regards, WM