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

From: J.E. (troubled6man_at_yahoo.com)
Date: 09/19/04 

Date: 19 Sep 2004 10:29:43 -0700

> Yeah, the "no" fix. Ha ha ha. That was a funny joke.
>
> I agree with you.
>
> Do you ever read my writings and if so think that something I wrote
> can help you support your arguments? If so, I think I support your
> arguments.

How would I read your arguements? Do you know the subject names?
 
> Partially, that's because I agree with some of your arguments.

I think it stems from having completed infinities, which I didn't use
to have a problem with. But the problem seems to be that if we
pretend a (complete) list of all the reals exist, then someone can
present another one. Rather than say this means there are lots and
lots of reals, it seems to cast doubt as to whether the list could
really be made. Basically the axioms don't allow you to construct
that list as a complete list (infinite set), so there must be a
problem with finishing it. Maybe it's related to one of the posters
saying that some questions the list would answer (like what
computations give the same number) are "undecidable"? As a scientist
I'm interested in compressing many observations into universal
statements, maybe the list has "too much" information on it, and can't
be compressed and assuming one has it expands the universe enough to
describe another.

For instance, every turing machine source code is a string, so to
every positive integer you could assign a source code and if the code
ever halts execution, you can say assign that number to 1, otherwise
assign it to zero. Then you can make a real number that has it's nth
digit be the number associated with that halting problem. That real
number is a really weird irrational number because the halting problem
can't be solved recursively, so there isn't a rule to generate the
number. But yet it seems to exist in the "intended model" at least.

> If it's only one more, why not use f(x)=x+1?

If we put the new number at the beginning of the list, then they'd
just turn around and present another new number. And we'd just keep
repeating that game all day, which would get really tired, really
fast.
 
> Shall we call you... Dr. J.?

Nope, I'm broke. I don't have enough money to print my thesis and fly
a bunch of professors over to ask questions while I defend my thesis,
and if I don't publish my thesis and I don't defend it, then the only
way I can become a Dr. is to go to medical school. I have no interest
in doing that unless someone were to pay me enough money, and for
enough money, I'd publish and defend my thesis.

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