Postulate: Mathematics is constructed. We construct the syntax, grammar and assign semantics to mathematical statements artificially.
Lemma: There is no constraint on what constructed mathematical truths should look like. We could define true, false, para-consistent states, real numbers...you name it, and we could define axiomatic systems arbitrarily that would produce different solutions to the same equations.
What makes one axiomatic system yield physically consistent results, but not another? If I could define mathematical systems arbitrarily, what makes one axiomatic system yield the correct equations of motion of a particle and not another?
Are some mathematical systems inherent in nature? Could the necessity of mathematical truths be proved or disproved within a formal self-consistent system?
Do we need to invoke mathematical isomorphism to solve this (kind of) paradox?