Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 300
Posted:
Jul 13, 2013 3:29 PM


In article <krroho$8mp$1@dontemail.me>, "Julio Di Egidio" <julio@diegidio.name> wrote:
> "Zeit Geist" <tucsondrew@me.com> wrote in message > news:41be4197cc38420fa4edb90e196ddc2b@googlegroups.com... > > On Friday, July 12, 2013 1:41:31 PM UTC7, muec...@rz.fhaugsburg.de > > wrote: > >> On Friday, 12 July 2013 19:13:19 UTC+2, Zeit Geist wrote: > >> > >> > It is rather silly to expect the process that creates each of the > >> > Naturals would produce the set of all Naturals, as that set is, > >> > itself, not a Natural. > >> > >> Each natural belongs to a finite initial segment. None of them > >> requires a number that is larger than every natural number. In > >> fact the contrary. If you do not talk about the set, then there is > >> no reason to talk about alephs. > > > > Yes, but for every Natural there is a larger natural, hence the number > > of Naturals is larger than any Natural. > > Since the number of natural numbers is not itself a natural number, that is > a nonsequitur, despite standardly the conclusive statement is correct: > indeed, a fallacy of relevance. Plus, the standard here is in question, so > one should rather qualify statements as well as objections (not that WM ever > does it, of course). > > > Why wouldn't I talk about the set of Naturals? > > That there is no such thing as a _set_ N (i.e. a finiteinductive set, an > "unfinished set") is a thesis of *strict finitism* already: > <http://en.wikipedia.org/wiki/Finitism#Classical_finitism_vs._strict_finitism> > > Julio >
"Strict finitism" is purely a matter of faith, not necessity, as people have been talking about "the set of naturals" for many years without the world collapsing. 

