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

Vaughan Pratt pratt at cs.stanford.edu
Sat Oct 11 18:59:56 EDT 2008

Absent a generally accepted Theory of Everything it is premature to 
speculate on whether such a theory would meet all the conditions of 
Gödel's first incompleteness theorem.  But assuming it does, those 
finding such a theory useful will be no more handicapped than number 
theorists and computer scientists, some of whose most useful theories 
already do meet the condition of the theorem yet whose productivity 
seems none the worse for it.

None of Gödel's theorems would appear to have adversely impacted the 
productivity of either applied mathematicians or physicists, and I'm not 
aware of anyone else's theorems that have done so either.  Gödel's first 
incompleteness theorem can only be considered "alarming" as you put it 
by those who believe that the continued progress of pure and applied 
mathematics will ultimately depend on the eventual success of Hilbert's 
program of wir müssen wissen, wir werden wissen.  The proper reaction to 
Gödel's theorem by such believers should be the acknowledgment that 
their belief is a lost cause: for those theories meeting the conditions 
of the theorem, we will never know because we cannot know.  People 
should be allowed to nurse their lost causes in private but not so as to 
be a burden to others.

Vaughan Pratt

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?

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