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Why should anyone care what a philosopher thinks about a problem in mathematics? Would you give any weight to a mathematician's opinion about a new technique in brain surgery?
Most people think that logic is a perfect way to
understanding. Godel proved that logic has limitations.
In the 1930s, Austrian mathematician Godel
proved a theorem which became the "Godel
theorem" in cognition theory. It states that
any formalized 'logical' system in principle
cannot be complete in itself. It means that a
statement can always be found that can be
neither disproved nor proved using the means
of that particular system. To discuss about
such a statement, one must go beyond that
very logic system; otherwise nothing but a
vicious circle will result. Psychologists say
that any experience is contingent - it's
opposite is logically possible and hence
should not be treated as contradictory.
http://www.exploratorium.edu/complexity/CompLexicon/godel.html
Ask any experienced lawyer. He will tell the same
from his experience.
The implication of Godel's incompleteness theorem
is that the truth about anything in creation is
incomplete as far as human understanding is concerned.
Any symbolism that has evolved from man's desire to understand himself
and his function within the universe must invariably reflect the laws of
nature. Henri Bergson defined intuition as instinct that is capable of
reflecting upon its object and of enlarging it indefinitely. Only by
intuition, he declared, can the absolute be comprehended. The Upanisads
say that every thing in creation is unique. Even small things like
germs or sand particles are microcosms. No person can have the complete
knowledge to understand every aspect of even such simple things.
The Upanishads say that truth has infinite number of
dimentions. The more you know about something, the
more you will come to know that there is more to know.
For me Mathematics is no more than a language with its own limitations. To me Godel's incompleteness theorem was another indicator that mathematics is inadequate to describe life. The proof may be right or wrong. So what? Still mathematics is essentially inadequate to describe life.
More in my site
http://www.what-is-cancer.com/papers/contents/compFrame.htm
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