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

Alasdair Urquhart urquhart at cs.toronto.edu
Sat Oct 11 09:43:23 EDT 2008

On Thu, 9 Oct 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?  I know this suggestion of
> application of Godel's theorem was made decades ago but why didn't it
> make a bigger impact?  Is it because it is wrong or were there some
> sociological reasons for mainstream ignorance of it?

The basic problem with this idea is that it is consistent with
current knowledge (as far as I know) that there could be a Theory of 
Everything that is in some sense complete in its physical implications,
though remaining incomplete in its mathematical foundations.

Of course, it remains rather unclear what we mean by "complete in its
physical implications."  But I would guess that physicists would be
very happy with a fundamental theory that predicts all of the
basic properties of the elementary particles, including the
constants that currently have to be "put in by hand."
Of course, gravity would have to be included as well, and that
seems at the moment to be a very intractable problem.

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