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Topic: Matheology § 300
Replies: 63   Last Post: Jul 18, 2013 2:23 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 300
Posted: Jul 13, 2013 3:29 PM

In article <krroho\$8mp\$1@dont-email.me>,
"Julio Di Egidio" <julio@diegidio.name> wrote:

> "Zeit Geist" <tucsondrew@me.com> wrote in message

> > On Friday, July 12, 2013 1:41:31 PM UTC-7, muec...@rz.fh-augsburg.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 non-sequitur, 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 finite-inductive 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.
--

Date Subject Author
7/13/13 LudovicoVan
7/13/13 Tucsondrew@me.com
7/13/13 LudovicoVan
7/13/13 Tucsondrew@me.com
7/13/13 LudovicoVan
7/13/13 Virgil
7/13/13 LudovicoVan
7/13/13 Virgil
7/13/13 Virgil
7/13/13 LudovicoVan
7/13/13 Virgil
7/13/13 Virgil
7/13/13 LudovicoVan
7/13/13 Virgil
7/13/13 Virgil
7/13/13 LudovicoVan
7/13/13 Virgil
7/15/13 albrecht
7/15/13 Virgil
7/15/13 mueckenh@rz.fh-augsburg.de
7/15/13 Virgil
7/15/13 Virgil
7/16/13 Virgil
7/16/13 albrecht
7/16/13 Virgil
7/16/13 LudovicoVan
7/16/13 Virgil
7/16/13 LudovicoVan
7/16/13 Virgil
7/17/13 Virgil
7/17/13 Virgil
7/17/13 Virgil
7/17/13 Tanu R.
7/18/13 Virgil
7/17/13 albrecht
7/17/13 Virgil
7/17/13 mueckenh@rz.fh-augsburg.de
7/17/13 Virgil
7/17/13 Virgil
7/17/13 Virgil
7/16/13 fom
7/15/13 Virgil
7/15/13 fom
7/13/13 Virgil
7/13/13 LudovicoVan
7/13/13 Virgil
7/14/13 Virgil
7/14/13 Virgil
7/15/13 Virgil
7/15/13 Virgil