Nice posting. As a complete outsider/dilettante, I suppose I am allowed to make suggestions ...
How do we tell the difference between a discipline that doesn't really seek answers and a discipline which honestly seeks answers but just can't agree within itself?
First, I would ask whether the discipline has an agreed set of criteria which it uses to distinguish correct proposed answers from incorrect ones. Then, if the answer to that question is "no", I would ask whether the discipline is devoting the bulk of its effort toward coming up with such a set of criteria. If the answer to the second question is "no" as well, then I fear my view on the question of whether philosophy really seeks answers should be obvious.
And how can philosophy do something about its level of internal disagreement without having to apply the "kick out everyone who disagrees with [us]" solution?
Well, one approach suggested by my answer to the first question would be to embark on a crash program to find that set of criteria for correctness (and then kick out everyone who disagrees with the choices).
A better approach might be to abandon the pose that philosophers seek correct answers to precisely formulated questions. Instead take an approach which is both more holistic and more pluralistic (an approach which, incidentally, is actually not too far from what philosophy really does.) Instead of trying to systematically generate true facts about the world, philosophers should instead generate competing coherent systems of assumptions - systems which provide fruitful viewpoints toward the world. "Let a hundred flowers bloom; let a hundred schools of thought contend". That is, it is not the philosopher's role to find truth, it is instead his role to suggest methodology.
As I see it, there can be no universally good set of criteria for correctness of philosophical answers. The reason being that both questions and answers are inevitably theory-laden. So, abandon the conceit that good answers exist to good questions simpliciter. Accept the fact that both questions and answers grow out of theories, and that there is no such thing as a correct theory - only more and less fruitful theories.
This thread has produced some interesting commentary around whether philosophers actually want to answer their own questions, or whether they enjoy sounding profound by debating big questions but don't want to lose that opportunity for profundity by finding single correct answers to them.
I don't quite disagree with the latter theory: the main reason I quit academic philosophy was exasperation that people were still debating questions where the right answer seemed obvious to me (like theism vs. atheism, or whether there was a universally compelling morality/aesthetics of pure reason), and worry that my philosophical career would involve continuing to debate these issues ad nauseum rather than helping to solve them and move on to the next problem.
But when I explained this to a particularly sarcastic friend, he summarized it as "So you think philosophy is useless because not everyone agrees with you?"
The problem isn't that philosophers never come up with solutions. The problem is that they come up with too many different solutions.
Science has solved many scientific problems, and anyone wondering what the solution is can look it up in a book or on Wikipedia. Philosophers have also solved many philosophical problems, but it is full of so many distractions and false solutions that anyone wondering which proposed solution is correct will have to become nearly as good a philosopher as the person who solved it in the first place. It's much easier for science to settle its disputes via experiment than for philosophy to settle its disputes via debate.
I am wary of criticizing the discipline of philosophy simply on the grounds that not everyone in it agrees with me. But I also don't want to let it off and say it's okay that they've managed to go so long without coming to any answers, when it seems to me that settling at least some of the easier problems is not that difficult.
How do we tell the difference between a discipline that doesn't really seek answers and a discipline which honestly seeks answers but just can't agree within itself? And how can philosophy do something about its level of internal disagreement without having to apply the "kick out everyone who disagrees with Less Wrong" solution?