There's nothing wrong with building on axioms if you understand that they are stipulated rather than foundational, and much philosophy has been done tearing dow

There's nothing wrong with building on axioms if you understand that they are stipulated rather than foundational, and much philosophy has been done tearing down exactly the beautiful structures you identify as problematic. That just is rationally testing "opinion", which I put in quotes because it's a loaded word you introduced in place of axiom to undermine the position of philosophy. I remind you that Goedl's incompleteness theorem, which gives analytical rigor to your point, came out of early 20th century logic, and was in direct response to the philosophical program of the Vienna Circle, which again is philosophers. How, do you suppose, you could establish Goedl's incompleteness theorem with the scientific method? Rational testing is analysis with logic and deconstruction and, to the applicable degree, empiricism.