Date: Feb 28, 2013 2:03 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Feb 28, 12:03 pm, WM <> wrote:
> On 27 Feb., 21:28, William Hughes <> wrote:

> > On Feb 27, 8:21 pm, WM <> wrote:
> > > Do you prefer your argument?
> > There is no disagreement over the facts.
> > We both agree that there is a natural number
> > valued function of time, m(t), such that
> > at any time t, m(t) is the index of an existing
> > line which contains all existing FIS of d.
> > We both agree that m(t) is not constant.

> Until now I was of the opinion that you accept completed infinity.
> There is no m(t).

Well, I was of the opinion we agree. Looks like
I was wrong. I misinterpreted

> 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.

WM: Exactly!

I still do not understand why I cannot
take a simple natural number valued
function of time, say a(t) and set it
equal to m.