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In a message dated 2/4/2002 10:02:47 PM Central Standard Time, Joe Dees
> >OK, for the moment, let's assume he will have no idea what the Godelian
> >threshold is- could you send me a nicely phrased, quickly asserted,
> >question I could rehearse and learn?
> >All the while realizing that I will be among a group of remarkable
> >miscellany, as I'm sure you're aware.
> Godel's Incompleteness Theorems I and II are the most important in 20th
> century mathematics. It is asserted that beyond a certain level of
> complexity, that any axiomatic system contains undecideable statements; the
> reason for this is the emergence of self-reference in complex systems.
> postulate axiomatic system A, and state that all true statements, and only
> true statements, are inside A. Now let us construct statement B. B is
> recursive and self-referential; that is, it refers to its own relation with
> axiomatic system A, and what it contends is that "B is not an axiom of A".
> What has happened here? If we include B in A, then B contains the false
> statement that B is not an axiom of A, and thus does not contain only true
> statements, but if we exclude B from A, then A does not contain all true
> statements, for it does not include the true statement that B is not an
> of A. To put it plainly, B either belongs BOTH inside and outside A, or
> NEITHER inside nor outsi!
> de A, and the dilemma is unresolveable within system A. B is undecideable
> with reference to A. The bottom drops out; mathematics is revealed as a
> But in reference to the universe A, WE are B, for we are within a universe
> that we nevertheless entertain a perspectival (point of) view upon; in
> words, Krishnamurti notwithstanding, as far as self-conscious awareness
> within our environs goes, we are at once NOT and NOT-NOT the world ("Neti,
> neti." (Not this, not that). Mind and world are not one, not two, not
> but are components od a dynamic and recursive interrelational system.
> hope this helps.
It would help a lot more if Douglas Hofstadter were giving the talk!
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