Date: Mar 2, 2013 7:17 AM
Subject: Re: Matheology § 222 Back to the roots
On 1 Mrz., 23:51, William Hughes <wpihug...@gmail.com> wrote:
> > The argument is not only time.
> m can change even though the time does not ?
The maximum depends on the personal environment, the capability to
abbreviate numbers, the wish to do so, and many more factors. It
invents relativity into mathematics.
> > But in general your description is
> > acceptable.
> > So what is your true opinion about this potential infinity which,
> > contrary to finished infinity, is not self-contradictory and allows
> > for all calculations required in analysis?
> "Potential infinity" does not differ in any
> essential way from "finished infinity".
> The language changes a bit, and at times you need more words
> but the behaviour is the same.
> With finished infinity you do not have a largest
> With potential infinity you do not have a largest
> non-variable natural
> With finished infinity there is no line of L
> that contains every FIS of d.
But there are all FIS of d, which must be in infinitely many different
lines of the complete list.
This is a contradiction, because the list, by definition cannot
fulfill this requirement.
Why do you refuse to consider this simple fact?
> With potential infinity there is no line of L
> that has a non-variable index and contains
> every FIS of d
> With finished infinity there are no balls
> in the vase.
And we have a contradiction with analysis. Compare "The Paradox of
Tristram Shandy", PlanetMathOrg (2012) http://planetmath.org/?op=getobj&from=objects&id=12607
Your argument that in analysis the set of digits would not go to
infinity with the values of the numbers n, is easily falsified by
Two proofs against actual infinity. In addition there is the Binary
Tree which has not more than infinitely (aleph_0) paths that can be
distinguished even by infinite strings (with aleph_0 bits each).