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ANNOTATION:
Robin Craig's Article that Godel's Theorem need not be Limitative (correction)
Dr. Robin Craig has written an excellent article in which he
states that Godel's theorem does not so much limit us as instead
it forces us to accept self-referential paradoxes as baggage
accompanying the state of ultimately acquiring all knowledge.
But cybernetics may have the answer, as its forte is navigating
around obstacles and solving problems. Learning to deal with
paradoxes hones our overall cognitive abilities.
Also, we need to cleanse all traces of evil from our
civilization if we wish it to be long-lived. Douglas Hofstadter
makes some good points in the final chapters of Metamagical
Themas that any residual evil in a system will contribute to its
extinction. Frank Drake has speculated that we may be able to
survive many billions of years around Sol without ever needing
to develop interstellar travel (and why do so when we can
communicate instead)? We would colonize outwards when the Sun
goes into its red giant phase, and huddle inward for the
billions and billions of years that the Sun remains a white
dwarf. To survive over these lengths of time we would need to
have present absolutely no malfeasance at all within us. And if
we do, then the Universe has 10**22 other shots at getting it
right.
The link to the entire article is
Robin Craig's Holes in the Heart of Reason
The pertinent section concerning Godel's theorem not being
limitative is reprinted below by permission:
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Gödel's theorem proves no more than its derivation proves: that
any system powerful enough to refer to itself, can make self-
referential paradoxes. I am a human being: conscious of the
world, conscious of my own existence, conscious of truth and
falsehood. Therefore, I can say "I cannot consistently make this
statement", or more simply, "this sentence is false", or more
simply still, "I am lying". So my ability to be "complete" makes
me "inconsistent": if I'm telling the truth I'm lying, and if
I'm lying I'm telling the truth.
Make no mistake: Gödel's theorem imposes no other limit. I can
know every fact about the universe, every physical law, all
chemistry, all biology, all psychology: it denies me none of it.
By its nature, by its own phraseology, Gödel's theorem allows a
rational being or even a formal system to have complete
understanding of absolutely everything: provided it pays
the "price" of being able to articulate self-referential
paradoxes. That price, I for one am happy to pay.
So this is the great truth which lies forever beyond the grasp
of logic, mathematics and science. This is the liberating
insight, the holistic grasp of reality, which only mysticism can
reach. The ability to say, "I am lying", and mean it.
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Copyright© 2002 Principia Cybernetica -
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