Do philosophers really think that the problems they discuss are important in themselves, or does thinking about the problems merely serve as practice in analytical thinking? How does philosophy differ from puzzle solving (besides the fact that puzzles actually tend to get solved)?
I think most philosophers think the problems are important. But there are lots of different views about why they are. One possible view is that worrying about such problems helps us to get clear about certain things we need to be clear about if we're to do science. See my response to a different question for elaboration: 30 .