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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:
> 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).
> By your principle above, S mathematically exists. Therefore CH is false.


Sure.

Our conception of "sets", as codified in ZF(C), if consistent is an incomplete
notion that may be extended and sharpened in various directions. All of the
resulting structures (we could call them "set universes") have mathematical
existence.

--
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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