I feel (as a non-philosopher who only casually reads) as though the question of empirical methods in philosophy comes down in large part to critiques of positiv

I feel (as a non-philosopher who only casually reads) as though the question of empirical methods in philosophy comes down in large part to critiques of positivism, operationalism and therefore also the Frankfurt School's aim to synthesise the social, economic, historical, philosophical (if you'll bear with me) and juristic sciences in a total approach rather than restricting to one area. It seems that one could avoid the onus to pursue quantitative methodology by rephrasing the question not as an empirical one. Your example of the twenty texts seems to call for an empirical analysis, but perhaps identifying "common themes in the genre" might not, depending on how the point is elaborated. It's another discussion as to whether such a question should be answered with empirical methods. To me it's a mistake to conflate rigor with empirical analysis, but you seem to agree when you talk about mathematics. Philosophical arguments can be rigorous, but a lot of what counts as some flavor of philosophy (the synthesis mentioned above) is critical and some really does make the claim to be rigorous. So it seems there's now a choice: either to say philosophy is not a science because it is not rigorous (due to some of its elements), or to say that philosophy can be scientific, just as information theory or theoretical physics, or theoretical computer science can be scientific. Many philosophers don't consider themselves scientists but I think this is at least in part because the mainstream conception of science really is empirical rather than rigorous analysis. In fact, even non-rigorous empirical analysis can pass for science. Depending on the area, I think that qualitative methodology can capture what quantitative can't, or where quantitative would be unreliable or impossible to use without changing the result significantly. In a nutshell, philosophy can be scientific if a method is pursued rigorously, but a lot of what is called philosophy is critical theory which is important if not scientific (despite using qualitative and quantitative analyses where appropriate). I have a feeling that critical theorists would question the separation we're erecting between science and non-science, especially those who view critical theory as in part an artistic endeavor too.