Thursday, March 10, 2005

Gödel, Original Sin, and Sausage...

Jordan Ellenberg (he of the countably infinite reading list) has a nice Slate review of a new book about Gödel's theorem (Incompleteness, by Rebecca Goldstein). He makes the important point that the incompleteness theorem did not have the cataclysmic effect on modern mathematics that non-mathematicans were under the impression it does. All it does is destroy a
"Communist takeover of mathematics" in which individuality and intuition would be subjugated, for the common good, to logical rules.
This tidbit is funny.
Yet, Gödel is routinely deployed by people with antirationalist agendas as a stick to whack any offending piece of science that happens by. A typical recent article, "Why Evolutionary Theories Are Unbelievable," claims, "Basically, Gödel's theorems prove the Doctrine of Original Sin, the need for the sacrament of penance, and that there is a future eternity."
To that, I have only one response: the Sacred Sausage Invocation. Amen.



  1. The popular definition in the review goes something like Godel's=there exist true statements that are unproveable

    This "true but unproveable" seems to come up a lot. Does that make any sense? If something is unproveable in given system of axioms, how is it true? 

    Posted by Yaroslav Bulatov

  2. So the actual statement is more nuanced. The correct statement is that it is possible to construct a statement in a consistent system of logic that essentially says 'this statement cannot be proved'. Now if the system is consistent, it will not prove a false statement. If the statement could be proved, it would be false, which would violate consistency. The only other choice is that the statement is true, but then cannot be proved within the system.

    The trick is that "true" is relative to the logical system, and is not defined outside it. in fact what Godel basically showed is that there no absolute notion of truth (or no sound and complete logic system) 

    Posted by Suresh


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