[FOM] Godel's First Incompleteness Theorem as it possibly relates to Physics

Timothy Y. Chow tchow at alum.mit.edu
Tue Oct 14 17:11:55 EDT 2008

Brian Hart wrote:
> Why doesn't Godel's 1st Incompleteness Theorem imply the incompleteness 
> of any theory of physics T, assuming that T is consistent and uses 
> arithmetic?  Shouldn't the constructors of the Theory of Everything be 
> alarmed?

Others have responded to this question, but perhaps the best response is 
to answer the question with another question: Why *should* a constructor 
of a Theory of Everything be alarmed?

For example, should a physicist be alarmed that current physical theories 
cannot predict whether a computer-controlled nuclear bomb that is 
programmed to blow up the world if its search for a counterexample to the 
Riemann hypothesis succeeds, will in fact blow up the world?  Is it a 
necessary condition for the "completeness" of a TOE to be able to predict 
the behavior of such a bomb?

Without some explanation of what kind of "completeness" you think a TOE 
should have, the invocation of Goedel's theorem is simply fuzzy thinking.


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