LudovicoVan
Posts:
4,064
From:
London
Registered:
2/8/08


Re: Matheology § 300
Posted:
Jul 13, 2013 10:40 AM


"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

