It seems to me that one of the things that philosophy does, at least for me, a beginner, is to expose mysteries where I thought there were none. Do any of you feel the same way, do you like that chill up your spine when you realize what you thought was self-evident might not be? Is the feeling that you have solved the problem more exciting than the feeling of wonder?

You have put it very well: exposing those mysteries is a deep pleasure of philosophy. That is one of the reasons that the great skeptical arguments -- arguments that seem to show that we have no reason to believe anything we have not seen, or anything outside ourselves, or even that our thoughts have any content -- are fascinating. They do cause a chill up the spine. The feeling of having solved the problem (a feeling I rarely have) is difficult to compare with the feeling of wonder at the problem. But if you are by disposition a philosopher you will not be inclined to wallow in the wonder; instead it will drive you to try to solve the problem.

If we built a computer that could analyse our minds, and it figured out how they work and explained it to us, would we be able to understand?

Maybe 'the true and complete theory of mind' would be too difficult for us to understand or to understand fully, but if so this is not because we would be using our minds to try to understand the theory of mind, but just because the theory was too difficult for us. Just as there is no paradox in using your eyes to look at your eyes (with the help of a mirror), there is no paradox in using your mind to understand your mind.

Does the future exist in any knowable fashion? If so, can it be known in any absolute way? If not, why do so many of us believe it can?

On one view of time, the future is as real now as the present or the past, much as other places are as real as the place you happen to be; on another view the future is not yet real but will be. Either way, many philosophers would say that we can know some things about it, though Hume's great sceptical argument against induction attacks this idea. But Hume's argument is not especially about the future: it applies to any inference from what we have observed to what we have not observed, whether what we have not observed is in the future, present or past. In any event, it's not very surprising that we believe we can know something about the future, since we have so often formed expectations that we have subsequently found to be satisfied.

We are often told time is like a river. Are there other useful analogies for time? For example: Time is like a bowl of jello with fruit: time is the jello and events are the fruit stuck in it. I guess what I'm really asking is does time have to flow? Is there another way of thinking about time?

One of my favourites is from Santayana, who says that the present is like a fire that runs along the fuse of time. That captures our sense of past, present and future each having a different ontological status, an intuitive view that philosophers have not found easy to defend or even to make very clear.

Do you believe that freedom is just being able to do what one wants without constraint? If so, why and how?

Sean Greenberg rightly says that the absence of physical constraint does not guarantee freedom. Moreover, as Harry Frankfurt has plausibly claimed, absence of physical constraint isn't even necessary for free will, though it is necessary for freedom. If I start out with free will, you don't take it away from me just by putting me in prison, though you do take away my freedom.

It has always struck me that philosophy is not a subject that has made any real progress. A lot of elaborate constructs of when we perceive certain things to be piles and so forth seem to be problems that can be dealt with (eventually) by sciences such as psychology and neurology. Why waste time constructing elaborate theories that are not scientifically provable? Things like inconsistencies in how people act may be a result of people just not being perfectly logical creatures. Why waste so much time pondering questions where 1. progress is hard to judge 2. the resulting ideas do not really change the world in any significant manner.

I share Richard Heck's sentiments on this matter, and I would add that there is an additional sense in which a lot of philosophy is 'before science'. I'm thinking primarily about epistemology and metaphysics in the philosophy of science, where we are trying to work out how science works and what attitude we ought to take towards scientific claims. Insofar as one takes science seriously, it is natural also to take seriously these 'before' questions, however incomplete and inconclusive our answers to them may be.

Should we philosophize about philosophy? Why?

Here is one reason. A central task of philosophy is to figure out how our knowledge-seeking activities work and what they achieve. That is epistemology and it is, for example, a big part of the philosophy of science. So if you think that philosophy is in the knowledge-seeking business, then it is natural to be interested also in how that activity works and what it achieves.

I am a postgraduate linguistics student engaged in a programme of research in which much of the theoretical apparatus proposed by the majority of language scientists ("Words and Rules" - à la Pinker) is dismissed as epiphenomena of exemplar-based cultural learning. Lately, however, I have been struggling with the definition of the word "epiphenomenon". Any thoughts?

An epiphenomenon is something that is real and has a cause, but does not in turn go on to cause other things. A common simile is that it is like the smoke coming out of the locomotive. Thus in the philosophy of mind epiphenomenalism is the view that experiences are caused by physical states of the brain, but do not in turn cause anything: they are just the smoke the brain gives off while it is working.