People forget that Boolean algebra comes from a work called "The Laws of Thought," where Boole tries to describe the algebraic operations underlying thought. If you think that isn't something "philosophers do," this is an ancient goal stretching back to Aristotle's logic, up through Descartes, and into figures such as Leibniz (who independently invented calculus and played an important role in giving us the binary number system), Chomsky, and Jerry Fodor. Philosophy is one of the disciplines in the interdisciplinary field of Cognitive Science.
Much of the most important work on the foundations of mathematics was done by philosophers with a mathematical bent (or mathematicians with a philosophical bent, depending on how you want to look at it). Set theory. Incompleteness. First-order logic was invented by Frege.
A lot of the technology we're using right now is traceable back to the work of philosophers.
I've always found that the best way to think of philosophy is simply as inquiry. As a line of inquiry progresses, it may bud off into a field in its own right. Physicists today would have been called Natural Philosophers in Newton's time. In fact, before Newton it was Descartes' physics that reigned supreme in the academy. Some lines of inquiry might not bud off despite significant advancements, such as logic.
Of course, I don't mean to say that philosophy and inquiry are purely synonymous. There's something vague about what the discipline of philosophy exactly is. But I don't think that's too terribly important. The question is what philosophers do. Some of the stuff philosophers "do" would probably strike some readers here as very "heads in the clouds" type stuff. But some of the other stuff, I think HN would find interesting. Check out work by Hillary Putnam. Or Jerry Fodor, if you're interested in "language of thought" type stuff that bears some similarity to Boole's project in The Laws of Thought. Chomsky recently published a newish collection of essays called What "Kind of Creatures Are We?", which is worth a look too.