FOM: misuse of G"odel's theorem

Graham Solomon gsolomon at
Mon Feb 15 22:24:32 EST 1999

Here are a couple of examples of nonspecialist uses of the incompleteness 

In 1931, a brilliant research scientist by the name of Kurt Godel proved 
that no mathematical system can be entirely without internal 
contradictions. In this, he succeeded, once and for all, in turning on 
its head the deeply held conviction that mathematics alone can deliver us 
from the quagmire of inconsistency. Since this is quite beyond even the 
most refined logicians, how then can we expect to solve the 
ever-increasing ethical contradictions by a simple axiomatic system?
  It's time to bid farewell to these fantasies of omnipotence. In the 
long run no one -- no country and no individual -- can avoid coming to 
terms with the limits of his own responsibility, and setting priorities. 
Hans Magnus Enzensberger, _Civil Wars: From L.A. to Bosnia_  (New 
York: The New Press, 1994)  p. 66. Enzensberger's book was a New York 
Times Notable Book of the Year. He argues in the section in which Godel 
is cited that "our scope for action [in resolving conflicts] should be 
both finite and relative ... deep inside, we all know that our foremost 
concerns must be for our children, our neighbours, our immediate 
surroundings. ... Whether it is famine aid, political and military 
intervention, forced expulsions or mass migrations driven by the urge to 
escape from misery, the fact is that all imaginable options end in the 
logic of triage, whether we admit it or not."

In 1931 Kurt Godel was able to show that the _Principia Mathematica_ was 
capable of proving neither its own consistency nor _all_ of its 
constituent propositions: carefully though the _Principia_ had been put 
together, out of interdependent, accurately-fitted parts. A system of 
logic, a perfectly logical machine, is so far from wholly predictable 
that it cannot, Turing showed, even predict what it can or cannot do, and 
this when it is functioning perfectly. This truth, which the great 
comedians [like Buster Keaton] seem to have known intuitively, belies the 
Romantic notion that machines are models of tragic implacability,
Hugh Kenner, _The Counterfeiters: An Historical Comedy_ (New York: 
Anchor Books, 1973), p.138. Kenner's book is an engaging historical  
study of literary and other responses to the idea of simulations like 
clockwork ducks and other automaton devices, computer models of mind, etc.

Graham Solomon
Philosophy Department
Wilfrid Laurier University

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