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

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herb z

Posts: 1,187
Registered: 8/26/06
Re: Mathematics as a language
Posted: Nov 4, 2010 2:40 AM
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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.

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

--
hz


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