Date: Mar 20, 2013 9:02 PM
Subject: Re: Matheology § 224
On 3/20/2013 4:07 PM, WM wrote:
> On 20 Mrz., 22:01, fom <fomJ...@nyms.net> wrote:
>> Indeed, you have not even given an explanation
>> of *all* that is agreed upon.
> If you don't know the set theoretic meaning of "all natural numbers",
> then you should try to learn it. If you don't know the meaning of
> Cantor's "wohlunterscheidbar" (well-distinguishable) that has to be
> true for all elements of every set, then you should try to learn it.
You should learn what is required when you
make claims in academic discourse.
Cantor's theory is based on a presumption
of units that had been rejected in Frege's
writings on arithmetic and is not represented
in the mathematics of modern set theory.
What is meant by this is that Cantor rejected
the thought that Russell's paradox applied to
his meaning of set precisely because of how
he thought of "finished classes" and how this
thought differed from the Frege's"extension
of a concept".
Your remarks suggest that you know how to
reconcile the Cantorian notion with the
mathematics that has arisen in the sense of
the Frege-Russell paradigm.
Please explain to us how the two different
views are reconciled.
Discussion of these matters may be found
in Hallett's "Cantorian Set Theory and The
Limitation of Size"