While I agree that philosophy has the ability to ask good questions, unfortunately it does not seem to be able to answer those questions in any meaningful way. Science also has the ability to ask good questions, but it knows how to answer them in a meaningful way (at least good science does). By meaningful, I mean provably true. Philosophy is very happy to take untested opinion as true. Which is provably dangerous.
I get the sense from reading your post that you think of Philosophers as Philospher-Kings, who sit at the top of humanity and think about important things and their ideas eventually trickle down to the Plebeians at the bottom. And once everyone agrees with the Philosophers, there will no longer be a need for Philosophy. Give me Science any day.
This is unfortunately true of many species of philosophers, and in many ways they are responsible for their own growing public irrelevance. Growing, if not fully accomplished!
So, I agree with your post to the extent that it applies to much of the last hundred years of philosophy. We see the results of this disparity in guys like Lawrence Krauss, who says much the same thing.
It's a hard argument to counter, not because it's a good argument, but because culturally and educationally we lack the common philosophical vocabulary to identify its problems, without running aground on local political issues. We are all children of Descartes and we are catechized our whole lives to think in reductionist terms and anticipate reductionist answers to every facet of human experience.
I completely disagree with your hard distinction between Science and Philosophy, but I don't have a quick-and-dirty answer for you. I know why you see this distinction, and there's truth in it, but also, to my mind, deep error. I would suggest you look at the history of philosophy of science, its origins in Bacon and Descartes and a much older philosophical debate that transcends questions of whether "good answers" are given and dives deeper into the nature of answers themselves. Any honest appraisal of this history of ideas I think must identify a larger meta-debate, not between "Science" and "Philosophy" but between two opposing Philosophies, two opposing Sciences, in fact.
I got the sense that he thinks of philosophers more in the fashion of scientists doing basic research in universities and R&D departments. People don't know their names, and they rarely have much direct impact, but their work is foundational to a lot of practical things that come later.
Philosophy is very happy to take untested opinion as true.
This is demonstrably false. Philosophy, almost by definition, is a process of rationally testing "opinion". Your post reeks of scientism and nothing more.
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.
Can you name one modern rigorous and precise discipline that does not have philosophic roots? We don't know what science today's philosophy might produce in the future.
I think that kings ought to be philosophers, metaphorically speaking: I trust politicians who prove they have at least some understanding of philosophical inquiry much more than I trust the ones who are skeptical. But philosophers themselves shouldn't be kings: hell, how would you pick the one to rule over the rest of them? The best philosophers are frequently the most controversial: the controversy surrounds them because of how challenging and provocative their thoughts are.
Here's the thing with "provably true" that I find worrisome: the process of proving something as rigorously as scientific research demands it is so slow, so painstaking, that if we relied entirely on science to inform our knowledge, we'd lose out on literal millennia of human experience. Now, there are some things for which scientific rigor is absolutely necessary: don't get me wrong, I think science is one of the best things ever. But it's not enough. It's a tool in an arsenal which employs many different techniques to get at knowledge, and as far as techniques go, it's a highly specialized one.
Philosophy is a much, much broader technique; in fact, it specializes in finding ways to look at even broader questions in exquisite detail. That makes it a very impractical tool if you're trying to, say, build a space ship. But it makes it a far more useful tool if you're trying to understand things as complex and abstract and subtle as, say, questions of how we acquire knowledge, or what it means to think. "Meaning" is something which science deals with very practically, and as a result its meaning will usually go only as deep as is needed to achieve a practical result. Once science begins worrying about satisfying deeper curiosities, well, it's no longer practical and your argument is moot.
You think philosophy is provably dangerous. Well, I think that science left unchecked is dangerous as well – it's such a powerful method of inquiry that it can convince you it's the only sort of inquiry that has any meaning whatsoever, which is a seductive promise (it's so simple! it could explain everything!) but not a true one. There have been certain controversies involving very bright scientific minds saying some very stupid things, and then attempting to "prove" that there's a scientific justification for what they're saying. It's especially frustrating because these scientific thinkers, who are so humble and questioning when examining the universe from their lens, are incapable of the same humility when offered any other perspective on their thoughts – even well-reasoned and meaningful ones.
But I wouldn't argue that because of this, we ought to cut funding to science, or insist that science change its techniques. No: science should do what it's good at, period. But so should philosophy. And so should mathematics, or theology, or history, or whichever other method of inquiry might yield useful and important breakthroughs. The dangerous part of science is its claim that it ought to dominate other fields of study, which practically speaking I find no different from the claim made by fundamentalist Christians that their religion should dominate all fields of study. There's a similar belief that their worldview is so right, so all-pervasive, that no other argument could possibly suffice to dethrone it.
"Here's the thing with "provably true" that I find worrisome: the process of proving something as rigorously as scientific research demands it is so slow, so painstaking, that if we relied entirely on science to inform our knowledge, we'd lose out on literal millennia of human experience."
"Philosophy is a much, much broader technique; in fact, it specializes in finding ways to look at even broader questions in exquisite detail. That makes it a very impractical tool if you're trying to, say, build a space ship. But it makes it a far more useful tool if you're trying to understand things as complex and abstract and subtle as, say, questions of how we acquire knowledge, or what it means to think."
To be blunt: you need to read Pearl (and Kahneman), because it is clear you are not familiar with the ideas you are arguing against.
I get the sense from reading your post that you think of Philosophers as Philospher-Kings, who sit at the top of humanity and think about important things and their ideas eventually trickle down to the Plebeians at the bottom. And once everyone agrees with the Philosophers, there will no longer be a need for Philosophy. Give me Science any day.