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

 Messages: [ Previous | Next ]
 herb z Posts: 1,187 Registered: 8/26/06
Re: Mathematics as a language
Posted: Nov 5, 2010 1:33 AM

Daryl McCullough wrote:
> herbzet says...
> >Daryl McCullough wrote:
> >> herbzet says...
> >> >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.

> >>
> >> The problem with this is that there could be two different
> >> mathematical objects, A and B, such that neither is inherently
> >> existence of B. They can't, therefore, both exist.

> >
> >Hard to answer in the absence of a concrete example.

>
> Well, the existence of a set that cannot be well-ordered contradicts
> the existence of a well-ordering of the universe of sets. Both are
> consistent, but they can't both exist.

You mean if the universe of sets is well-ordered, then every set is
well-ordered?

What does "a well ordering of the universe of sets" mean, anyway?

--
hz

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