Re: chaos <=> paradox. Prove me wrong. A challenge.

From: Lefty (Ye_at_h.Right)
Date: 09/23/04 

Date: Thu, 23 Sep 2004 02:51:04 GMT

> > Consider this.
> > Math may be an abstraction, but it still exists somehow in this
> > universe. If there are real paradoxes in math, this may suggest their
> > existence in the physical universe. No, it dosent prove anything, but
it's
> > certainly odd to think about.
> > Also, if the physical universe were "paradox free", then we might
have a
> > mathematics where Russel's Paradox (for example) does not exist.
>
> We do. The key was in using a formal rather than an informal approach
> to defining what counts as a mathematical statement. Paradoxes arise
> when you are not careful with your definitions and what system you are
> working in. If a system is consistent, it will not contain a paradox.
> If a system legitimately contains a paradox, it is actually an
> inconsistent system, and you can prove any kind of silliness.

I really need to know more about this to convince myself of these things. Do
you have any suggested readfings ? Godel ? I'm breaking new ground here
personally.

I am still having a hard time reconciling that the argument which you
described above can possibly be divorced from the universe in which it was
concieved. I really need to understand more about this. Please advise. Any
recommended readings ?

Thanks & I'm on my way -

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