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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 2:38 AM
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Marshall wrote:
> Transfer Principle wrote:
> > Herman Jurjus wrote:
> > > 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


there exist

> systems in which CH is true and systems in which CH is false.
>
> So, we're all good ... right?


Pretty much.

--
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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