Re: Skolem's Paradox and why is math the way it is?

From: J.E. (troubled6man_at_yahoo.com)
Date: 10/01/04 

Date: 30 Sep 2004 21:03:02 -0700

> > Like what happened with the big
> >bang and expanding spacetime.
>
> Can you provide the connection between Skolem and big bang theories?

I think that Skolem was touching on incompleteness, and that touches
on undecidability, which puts a shadow over all complicated equations
that haven't been solved, because if a solution (like a closed time
like curve) is hard to find but we haven't yet proven that they can't
be made, then we wonder if the reason we can't prove it, is because
they exist in some models of ZF and not others of ZF, i.e. the
existance of a solution is independant of ZF. Do I have a proof of
independance? No, I was hoping to make a model where such proofs were
easier, so that it wouldn't be so hard to do so.

> > Transfinite cardinal theory LOOKS like
> >something with baggage,
>
> Then don't waste your time on transfinite cardinal theory. Treat it
> as insider's mathematical art.

The transfinite arguements come up by using the axioms (and their
logical consequences) to prove that (mathematical) things exist or
don't exist. We have mathematical things in our models and it make
sense to ask if they (the mathematical things) exist. For instance,
it appears that physics could be done while ignoring sets of measure
zero, but is there an easy way to include just the sets with positive
measure, I don't know that.