(My apologies; I didn't fully understand what you were asking for.)
First, it doesn't claim that philosophy makes zero progress, just that science/AI research/etc. makes more. There were still broad swathes of knowledge (e.g. linguistics and psychology) that split off relatively late from philosophy, and in which philosophers were still making significant progress right up to the point where the point where they became sciences.
Second, philosophy has either been motivated by or freeriding off of science and math (e.g. to use your example, Frege's development of predicate logic was motivated by his desire to place math on a more secure foundation.) But the main examples (that are generally cited elsewhere, at least) of modern integration or intercourse between philosophy and science/math/AI (e.g. Dennett, Drescher,, Pearl, etc.) have already been considered, so it's reasonable to say that mainstream philosophy probably doesn't have very much more to offer, let alone a "centralized repository of reductionist-grade naturalistic cognitive philosophy" of the sort Yudkowsky et al. are looking for.
Third, the low-hanging fruit would have been taken first; because philosophy doesn't settle points and move on to entire new search spaces, it would get increasingly difficult to find new, unexplored ideas. While they could technically have moved on to explore new ideas anyways, it's more difficult than sticking to established debates, feels awkward, and often leads people to start studying things not considered part of philosophy (e.g. Noam Chomsky or, to an extent, Alonzo Church.) Therefore, innovation/research would slow down as time went on. (And where philosophers have been willing to go out ahead and do completely original thinking, even where they're not very influenced by science, LW has seemed to integrate their thinking; e.g. Parfit.)
(Btw, I don't think anybody is claiming that all progress in philosophy had stopped; indeed, I explicitly stated that I thought that it hadn't. I've already given four examples above of philosophers doing innovative work useful for LW.)
Yeah, I'm not sure we disagree on much. As you say, Less Wrong has already made use of some of the best of mainstream philosophy, though I think there's still more to be gleaned.
Part of the sequence: Rationality and Philosophy
Despite Yudkowsky's distaste for mainstream philosophy, Less Wrong is largely a philosophy blog. Major topics include epistemology, philosophy of language, free will, metaphysics, metaethics, normative ethics, machine ethics, axiology, philosophy of mind, and more.
Moreover, standard Less Wrong positions on philosophical matters have been standard positions in a movement within mainstream philosophy for half a century. That movement is sometimes called "Quinean naturalism" after Harvard's W.V. Quine, who articulated the Less Wrong approach to philosophy in the 1960s. Quine was one of the most influential philosophers of the last 200 years, so I'm not talking about an obscure movement in philosophy.
Let us survey the connections. Quine thought that philosophy was continuous with science - and where it wasn't, it was bad philosophy. He embraced empiricism and reductionism. He rejected the notion of libertarian free will. He regarded postmodernism as sophistry. Like Wittgenstein and Yudkowsky, Quine didn't try to straightforwardly solve traditional Big Questions as much as he either dissolved those questions or reframed them such that they could be solved. He dismissed endless semantic arguments about the meaning of vague terms like knowledge. He rejected a priori knowledge. He rejected the notion of privileged philosophical insight: knowledge comes from ordinary knowledge, as best refined by science. Eliezer once said that philosophy should be about cognitive science, and Quine would agree. Quine famously wrote:
But isn't this using science to justify science? Isn't that circular? Not quite, say Quine and Yudkowsky. It is merely "reflecting on your mind's degree of trustworthiness, using your current mind as opposed to something else." Luckily, the brain is the lens that sees its flaws. And thus, says Quine:
Yudkowsky once wrote, "If there's any centralized repository of reductionist-grade naturalistic cognitive philosophy, I've never heard mention of it."
When I read that I thought: What? That's Quinean naturalism! That's Kornblith and Stich and Bickle and the Churchlands and Thagard and Metzinger and Northoff! There are hundreds of philosophers who do that!
Non-Quinean philosophy
But I should also mention that LW philosophy / Quinean naturalism is not the largest strain of mainstream philosophy. Most philosophy is still done in relative ignorance (or ignoring) of cognitive science. Consider the preface to Rethinking Intuition:
Conclusion
So Less Wrong-style philosophy is part of a movement within mainstream philosophy to massively reform philosophy in light of recent cognitive science - a movement that has been active for at least two decades. Moreover, Less Wrong-style philosophy has its roots in Quinean naturalism from fifty years ago.
And I haven't even covered all the work in formal epistemology toward (1) mathematically formalizing concepts related to induction, belief, choice, and action, and (2) arguing about the foundations of probability, statistics, game theory, decision theory, and algorithmic learning theory.
So: Rationalists need not dismiss or avoid philosophy.
Update: To be clear, though, I don't recommend reading Quine. Most people should not spend their time reading even Quinean philosophy; learning statistics and AI and cognitive science will be far more useful. All I'm saying is that mainstream philosophy, especially Quinean philosophy, does make some useful contributions. I've listed more than 20 of mainstream philosophy's useful contributions here, including several instances of classic LW dissolution-to-algorithm.
But maybe it's a testament to the epistemic utility of Less Wrong-ian rationality training and thinking like an AI researcher that Less Wrong got so many things right without much interaction with Quinean naturalism. As Daniel Dennett (2006) said, "AI makes philosophy honest."
Next post: Philosophy: A Diseased Discipline
References
Dennett (2006). Computers as Prostheses for the Imagination. Talk presented at the International Computers and Philosophy Conference, Laval, France, May 3, 2006.
Kahneman, Slovic, & Tversky (1982). Judgment Under Uncertainty: Heuristics and Biases. Cambridge University Press.
Nisbett and Ross (1980). Human Inference: Strategies and Shortcomings of Social Judgment. Prentice-Hall.
Rips (1975). Inductive judgments about natural categories. Journal of Verbal Learning and Behavior, 12: 1-20.
Rosch (1978). Principles of categorization. In Rosch & Lloyd (eds.), Cognition and Categorization (pp. 27-48). Lawrence Erlbaum Associates.
Rosch & Mervis (1975). Family resemblances: studies in the internal structure of categories. Cognitive Psychology, 8: 382-439.
Smith & Medin (1981). Concepts and Categories. MIT Press.