Enlighten me. What is the process of "rationally testing opinion"? (More opinion is not the right answer.)
Philosophy can make large, beautiful, perfectly logical structures of thought. But they necessarily must begin with an axiom, some foundation on which to build. If the axiom is wrong, the whole structure falls. No matter how beautiful it is. I submit that the problem with Philosophy is that it is only too happy to build on untested axioms.
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.
Philosophy can make large, beautiful, perfectly logical structures of thought. But they necessarily must begin with an axiom, some foundation on which to build. If the axiom is wrong, the whole structure falls. No matter how beautiful it is. I submit that the problem with Philosophy is that it is only too happy to build on untested axioms.