Re: Godel's Theorem under Fuzzy Logic?

Christopher Reid Palmer (reid@newton.pconline.com)
Mon, 20 Apr 1998 13:30:02 +0200 (MET DST)

On Sat, 28 Mar 1998, Stan Rice wrote:

> This (below) is hardly a mathematical point, but is it not true?--
> Fuzzy gradations, no matter how fine the steps involved (let alone
> only 10 steps,) come down in the end to binary distinctions. I.e. in
> the end either "this degree" does or does not apply, is or is not
> adequate to these criteria, is or is not alowed to trigger an action.
> In other words, there is no distinction that is not bivalent, because
> any distinction whatever is bivalent.
> Can anyone show otherwise?

Take a statement like:

(1) I am tall.

Assume this statement is .7 true. How true is it that this statement is .7
true? Well, that's fuzzy too, contrary to what you seem to be suggesting.

> In other words, fuzzy is bivalent as long as it admits of distinction.

Not so. There are two extremes to the distinction, but the
evalation of the distinction need not fall on the extreme ends {0, 1}.

> A more profound question is whether the consciousness in which
> all distinctions appear actually supports them in the manner that
> we imagine. Penrose seems right to me.

Come again?

___________________________________________________________________________
Christopher Reid Palmer : reid@pconline.com : innerfire on IRC (EFNet)

Accept loss forever : Jack Kerouac