Marshall
Posts:
1,928
Registered:
8/9/06
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Re: Mathematics as a language
Posted:
Nov 3, 2010 9:59 PM
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On Nov 3, 4:50 pm, Transfer Principle <lwal...@lausd.net> wrote:
> On Nov 3, 3:23 am, Herman Jurjus <hjm...@hetnet.nl> wrote:
>
> > On 11/3/2010 6:52 AM, herbzet wrote:
> > > 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.
>
> Corollary: CH is true.
> Proof: Since Goedel 1940 we know that it is logically consistent to
> assume that there exists f, a bijection between the set of countable
> ordinals (i.e., aleph_1) and P(N).
> By the principle above, f mathematically exists. Therefore CH is true.
> QED
>
> (Note: The above "corollary" stems from an earlier sci.math discussion
> regarding the relationship between CH and Pen Maddy's "MAXIMIZE".)
We have concluded that a consequence of herbzet's idea is
that there are systems in which CH is true and systems in which
CH is false.
So, we're all good ... right?
Marshall
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