As an approach to a Theory of Everything a framework for developing a
coherent theory of mathematics and physics together is described. The main
characteristic of such a theory is discussed: the theory must be valid and and
sufficiently strong, and it must maximally describe its own validity and
sufficient strength. The mathematical logical definition of validity is used,
and sufficient strength is seen to be a necessary and useful concept. The
requirement of maximal description of its own validity and sufficient strength
may be useful to reject candidate coherent theories for which the description
is less than maximal. Other aspects of a coherent theory discussed include
universal applicability, the relation to the anthropic principle, and possible
uniqueness. It is suggested that the basic properties of the physical and
mathematical universes are entwined with and emerge with a coherent theory.
Support for this includes the indirect reality status of properties of very
small or very large far away systems compared to moderate sized nearby systems.
Discussion of the necessary physical nature of language includes physical
models of language and a proof that the meaning content of expressions of any
axiomatizable theory seems to be independent of the algorithmic complexity of
the theory. G\"{o}del maps seem to be less useful for a coherent theory than
for purely mathematical theories because all symbols and words of any language
musthave representations as states of physical systems already in the domain of
a coherent theory.Comment: 38 pages, earlier version extensively revised and clarified. Accepted
for publication in Foundations of Physic
