[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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