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"