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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:

**********************************

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.

*********************************


Copyright© 2002 Principia Cybernetica - Referencing this page

Author
Don Stockbauer (donstockbauer[ at ]hotmail.com)

Date
Aug 24, 2002

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