In other words, fuzzy is bivalent as long as it admits of distinction.
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.
Cheers, Stan R
--------------------------
greenrd@hotmail.com wrote:
>
> Can Godel's Incompleteness Theorem be extended to formal systems based on
> fuzzy logic?
>
> This is a crucial question, IMO, with regard to Artificial Intelligence,
> because as I understand it, Roger Penrose's whole argument in his book
> "Shadows of the Mind" that convincingly attempts to show that AI is
> in principle unachievable on any algorithmic computer, assumes that the
> posited machine intelligence thinks in terms of either-or (Aristotlean) logic
> rather than fuzzy logic. Surely fuzzy logic would invalidate Godel's Theorem
> and hence his whole argument? - therefore AI might in fact be possible after
> all.
>
> However, I wonder whether Godel's Theorem can be extended to formal systems
> based on fuzzy logic. In this case, Penrose might be correct after all!
>
> I am only a first-year mathematics student, so please try to keep your replies
> as simple as possible.
>
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