By the way, to clarify an earlier point: although I think some philosophy addresses important questions, that does not always translate into producing important results. Of course, the same could be said about science. Some research leads nowhere.
Also, the fact that it is possible to think about a question does not mean the question is worth thinking about, or at least not for any length of time. This applies even if the question is deep and profound. If it is fundamentally intractable, then devoting a lot of time and energy to pondering it is simply dumb. The same time and energy could be better spent on other questions.
I read a paper this year about how far grasshoppers can kick their poo. Clearly it's a not a problem peculiar to philosophy.
Take just one notorious example: the old "how do we know that we know?" stuff. You can very easily push that line of questioning to the point where it becomes obviously intractable and obviously futile. Even if you do manage to answer that question, at least for certain contexts, the obvious next stage would be "how do we know that we know that we know?", and this can go on ad infinitum. However, each stage would not appear to be futile just in terms of formal abstract thought. You need to apply common sense to put the brakes on.
Oh you'd be hard pressed to find someone with more disdain for the great game of epistemology than I do. It has it's place and it's a necessary question, but the way every amateur philosopher thinks he's armed in every argument because he's read Godel's second incompleteness theorem or similar... is fricking annoying. Thankfully there is more to philosophy than epistemology.
Another one would be something like "why does 1+1=2?". If you could really elucidate a solid answer to that it would be instant Nobel Prize material.
Well no, because there is no Nobel prize for mathematics or philosophy.
The advantage that science and mathematics have is an empirical basis to thoroughly ground them. This makes them simpler in some ways, because there are some directions in which you simply cannot go. Reality wont allow it. Philosophy lacks this, or at least doesn't have it to anything like that same extent. If you're going to indulge in philosophy, what you really need is a rough map with areas marked as "Here be idiots".
Undoubtedly there is less room for ambiguity in the sciences. We just have to have be smart enough to spot the bad philosophy from the good philosophy and the bad science from the good science. It just grates me that philosophy is often dismissed because it does not involve men in white coats in labs. I don't see philosophy as an alternative to science. And I don't think most scientists do either. I'm a physics student, and my lecturers regularly make a point of pointing out the philosophical implications of physical phenomena, like the superposition principle for instance. Also gives me an opportunity to be smug when Professor Evans mixes up the weak and strong anthropic principles.
Topic: Objective morality