Re: virus: Godel vs. Axiom of Choice Re. Freewill
Wed, 18 Dec 1996 15:48:20 -0600 (CST)

In less than 25 minutes, I will be introduced to *FINALS* week for real.

On Wed, 18 Dec 1996, Dave Pape wrote:


> > The highly controversial Axiom of Choice [from Set/class theory] is
> >much more interesting as a loophole--or possibly outright assertion.
> >Several schools of mathematics outright forbid its use, not including
> > the more common ones.
> > Woah.
> > A "proof" using the Axiom of Choice explicitly (and critically, no
> >rewriting to avoid it possible) is the ultimate in nonconstructive
> >proofs: not only does it fail to explicitly construct the
> >example, the proof *cannot* be patched to allow explicit construction.
> I really wish I understood this technical vocab. What field is this? Formal
> logic? Where do I look to learn this language?

It's close to formal logic. A technical source would be "Axiomatic Set
Theory", Bernays [a Dover reprint].

However, "construct" above means the same thing as in mechanics. It
would be like having a blueprint for making a car that required an
arbitrary choice that could not be found by *any* algorithm.

/ Towards the conversion of data into information....
/ Kenneth Boyd