I don't know where the idea that philsophy doesn't involve rigor and maths comes from. Leibniz came up with the entscheidung's problem, for god's sake! If you take the most basic interest in logic, maths, or even computers, you can't swing a cat without hitting a philosopher.
I am referring to computation, not abstractions. What's the trade-off between X and Y is the kind of place where having some specific numbers is very helpful.
EX: At what point if any can you say testing theories on public data produces more value than noise.
I'm having trouble seeing how any of that relates to your original comment or the responses to it. You said "[reasoning about what science is and does is part of philosophy] only if you approach Philosophy with a lot more rigor and math than what people have historically done." That comes across as a broad comment about levels of rigor in philosophy, not a comment on the usefulness of quantitative data in making trade-offs.
"reasoning about what science is and does is part of philosophy."
I am saying some of that analysis benefits from real hard data. So, if your saying all of that analysis falls under philosophy, then I don't think that's what most people mean when the use the term.
I actually think 'hard data' is typically about as relevant to philosophy as it is to maths. Not everything is reducible to stats.
I just find it weird to be using a machine that's a recognizable descendant of the work of philosophers, as much as engineers or mathematicians, then to be saying casually that philosophy isn't rigorous.
You could argue using hard data is less rigorous. But, in practice people make mistakes so without verification Philosophy and math is again arguably less rigorous, depending on what you mean by that word.
