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

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Marshall

Posts: 1,936
Registered: 8/9/06
Re: Mathematics as a language
Posted: Nov 3, 2010 9:59 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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



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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