Mathematics?

[Zuhair]

I did some reading into structuralism, all in all it does complicate
matters, yes in some aspects it revealed non trivial interesting
results, but the way how I see it is that it is not suitable as a
characterization or a definition of mathematics.

I think it is easier to see mathematics in the way I already posted to
this Usenet, here is a more complete statement:

"Mathematics is the study of properties and relations of objects that
are faithfully interpret-able in a consistent formal system extending
logic that is effectively axiomatized by simple laws of reason".

So mathematics is reducible to logic+laws of reason.

This call for a characterization of "reason", which is not that easy
subject at all. Many of the rules of reason are already implicit in
the metatheory of logic itself, however some are not, it is more
plausible that those rules be thought of being known priori, or quasi-
posteriori, and highly intuitive that skepticism in their truth is
negligible, some of those laws might be justified on the basis of
being beneficial assumptions. Primitives in those rules better be
those already encountered in the meta-theory of logic like "set
membership", "part-hood", "natural number" etc....

Now that some physical objects can behave in such a manner only
entails that their behavior is "mathematical" even though such
behavior would be of more interest to physicists who after all must
have good training in mathematics in order to deal with them!

Zuhair