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Topic: Mathematics as a language
Replies: 35   Last Post: Nov 8, 2010 1:53 AM

 Messages: [ Previous | Next ]
 Marshall Posts: 1,936 Registered: 8/9/06
Re: Mathematics as a language
Posted: Nov 4, 2010 11:10 AM

On Nov 3, 11:40 pm, herbzet <herb...@gmail.com> wrote:
> Herman Jurjus wrote:
> > Marshall wrote:
> > > Herman Jurjus wrote:
> > >> herbzet wrote:
> > >>> Aatu Koskensilta wrote:
> > >>>> herbzet writes:
> > >>>>> Bill Taylor wrote:
>
> > >>>>>> Or whether the number 6 really exists.  Does it?
>
> > >>>>> It *could* exist -- therefore, mathematically, it *does* exist.
>
> > >>>> This is a traditional and appealing idea. But just what is meant by
> > >>>> "could" here? What sort of possibility is involved?

>
> > >>> For rhetorical punch, I purposely left out the modifier, which is "logical".
>
> > >>> What logically could exist -- that is, what is not inherently self-
> > >>> contradictory -- has mathematical existence.

>
> > >> Corollary: CH is false.
> > >> Proof: Since Cohen 1963 we know that it is logically consistent to
> > >> assume that there exists S, subset of P(N), equipollent neither to N nor
> > >> to P(N).

>
> > > Consistent with what? In what theory?
>
> > Co-consistent with ordinary mathematics, of course.
> > (I.e. with ZFC, and then also with any weaker theory.)

>
> Right -- the assumption here is that ordinary mathematics
> (i.e. ZFC, more or less) is itself consistent -- the ordinary
> and unremarkable gentleman's agreement.

Ok. But again, all the "counterexamples" just amount to saying
that (most) theories have undecidable sentences, right?

> (Excuse me for belaboring the point, but Marshall is, after all,
>  a programmer.)

Yay!

Marshall

Date Subject Author
11/2/10 Aatu Koskensilta
11/3/10 herb z
11/3/10 Herman Jurjus
11/3/10 Marshall
11/3/10 Herman Jurjus
11/4/10 herb z
11/4/10 Marshall
11/5/10 herb z
11/5/10 Herman Jurjus
11/6/10 herb z
11/6/10 James Dolan
11/6/10 Tim Little
11/6/10 Daryl McCullough
11/6/10 Marshall
11/6/10 Brian Chandler
11/6/10 Tim Little
11/7/10 lwalke3@lausd.net
11/8/10 Brian Chandler
11/7/10 herb z
11/7/10 Daryl McCullough
11/8/10 herb z
11/3/10 lwalke3@lausd.net
11/3/10 Marshall
11/4/10 herb z
11/4/10 herb z
11/4/10 herb z
11/3/10 Daryl McCullough
11/4/10 Bill Taylor
11/4/10 Daryl McCullough
11/5/10 herb z
11/4/10 herb z
11/4/10 Daryl McCullough
11/5/10 herb z
11/5/10 Daryl McCullough
11/4/10 VK