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ANNOTATION: Robin Craig's Observation that Godel's Theorem is not Limitative
Dr. Robin Craig has written an excellent article in which he
states that Godel's theorem does not so much limit us as instead
forces us to accept self-referential paradoxes, which imply
lying. Given this, it allows us to acquire any and all
knowledge. Thus it may not so much be the case of us evolving
to a state where lying is impossible as us having to accept
lying as part of life. But cybernetics may have the answer, as
its forte is navigating around obstacles and solving problems.
Learning to deal with lies hones our overall cognitive abilities.
The link to the entire article is
http://www.thoughtware.com.au/philosophy/philref/PHILOS.04.html
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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