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

Tero Tulenheimo tero.tulenheimo at helsinki.fi
Fri Oct 10 18:45:03 EDT 2008

> 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?

If the goal of the constructors of the Theory of Everything is to  
obtain a recursive enumeration of all truths about the universe, they  
should be alarmed. But perhaps they should rather be seen as aiming at  
formulating a categorical higher-order theory (hence "descriptively  
complete" w.r.t. the universe). (Certainly the theory should also meet  
various more specialized criteria.) The impression that Goedel's  
theorem would have crucial relevance here may stem from two sources:  
(i) thinking that all decent theorizing should be carried out in  
first-order terms; (ii) thinking that scientific theories must be  
associated with a (complete) mechanical procedure for symbol  
manipulation, yielding precisely the true sentences as outputs.

   Tero Tulenheimo

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