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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 3:45 PM

In article <krs3h3\$2sl\$1@dont-email.me>,
"Julio Di Egidio" <julio@diegidio.name> wrote:

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

> > On Saturday, July 13, 2013 7:40:24 AM UTC-7, Julio Di Egidio 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).

> >
> > The are numbers that are not Natural Numbers.
> > The number of Naturals Numbers is a number,
> > and it greater than any finite number, that is to say,
> > It is greater than any Natural Number.
> >
> > Here, number means Cardinality, of course.
> >
> > In most Mathematical circles the standard is ZF(C).
> > Yes, standard Set Theory is being questioned here.
> > And most who question it here have not come up with
> > a good reason to reject. Nor have they come up with
> > a suitable replacement.

>
> You still have this idea of the standard vs. the cranks, but the one with no
> arguments, the non-sequiturs and, in fact, no clue (e.g. as to the standard
> and the non-standard), here is still you.
>

> >> > 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_finiti
> >> sm>

> >
> > Those ideas in Finitism are assumptions.

>
> You just don't know what you are talking about.

All mathematics is based on assumptions, since every theorem is
ultimately an if-then statement, with much of the "if" clause very often
assumed rather than stated.

Without SOME assumptions, even the simplest of finitisms cannot get
started.
>
> > Although they may lead to consistent systems,
> > they are far less powerful than a system that assumes
> > an infinite set.

>
> Again, you don't know what you are talking about.

Sounds to me that he knows precisely what he is talking about, since it
is well know among non-finitists at least, that not every theorem in
standard analysis has a close analog within finitism.
>
> > I can count head of cattle or stones with a Strictly Finite system.
> > However, it is very difficult to define a Surface Integral and
> > most likely impossible to prove FLT in any form of Finitism.

>
> And, again, you just don't know what you are talking about...

Then lets see your finitist definition of a surface integral.
>
> So, no arguments, non-sequiturs, no clues: another dog of the empire? I
> Captain America somewhere else...

It seems clear that you are the one with your head inconveniently placed.

And until you can give a simple but finitist definition of a surface
integral, there it will remain.
--

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