[Marxism] godel etc (was ...)
Charles Brown
cbrown at michiganlegal.org
Thu Mar 17 07:02:17 MST 2005
Scott Palmer
(( So we can say that Godel et al, do for Enlighment mathematics and
logic what Marx et al did to philosophy? ))
Gödel's work was important but not as generally applicable as one might
think.
In the early years of the 20th century, Bertrand Russell, Alfred North
Whitehead, Gottlob Frege and others had worked to derive all of
mathematics from a few fundamental logical ideas and axioms. They
intended that the system thus derived would be both (a) /complete/, in
that it included all mathematical truths, and (b) /consistent,/ in that
it included no contradictions. The pinnacle of this enterprise was
/Principia Mathematica,/ which Russell and Whitehead co-wrote and
published in 1914.
Just as Heisenberg showed in physics that one could determine the
position or the velocity of a subatomic particle but not both
simultaneously, Gödel showed that axiomatic systems like /Principia
Mathematica/ could be either complete or consistent, but not both. It
was bad news for Russell and his followers, and in its way, it was a
remarkable achievement. However, Gödel's work applies neither to
non-axiomatic mathematical systems nor to human knowledge in general.
^^^^^
CB: This is , for me, a clear and clarifying summary of the Principia
Mathematica project and its relationship to Goedel. ( And I have consider
them many times over the years)
I wonder whether since Goedel's work impacts fundamental mathematics, it
might have impact in areas of human knowledge, such as physics or economics,
which are heavily mathematical.
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