Geometry, admirably axiomatised
by Euclid, unexpectedly opened to non-Euclidean territories, indicating that the Euclidean set is a particular version among many possible geometries.
According to standard deontic logic, the system can be axiomatised
in more than one way; for instance:
(The Great Depression and the Cold War are mentioned as important, but only in passing and with no elaboration as to how and why they were important.) And few concessions are made to the reader's possibly imperfect knowledge of modern axiomatised economic theory or the mathematical theories from which it arose.
Such a methodology is a natural complement to fully axiomatised choice theory precisely because the concepts of such a theory are so abstract and therefore capable of many concrete applications.
I think that a lesson of the paradoxes is that we must go to an axiomatised
truth theory rather than defining "true", even inductively.
But, any physical theory that appeals to the real number continuum cannot be formally axiomatised
in the language of first order logic.
First, M can be axiomatised
. Secondly, as (viii) of [sections]1 tells us, any non-theorem of M can be shown in M to be a nontheorem.