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Are there any good philosophical reasons for thinking that time travel is possible?

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Yes and no. Let me explain.

Some people think that is flat-out impossible. They appeal, for example, to puzzles like the Grandfather Paradox: if time travel were possible, the argument goes, I would be able to go back to 19xx and kill my Grandfather before he met my Grandmother. This would mean that I would never exist, and so the scenario requires both that I do and that I don't exist: contradiction. This is meant to show that time travel is impossible. Philosophers can help us sort through that sort of problem, and in fact some have. David Lewis's "The Paradoxes of Time Travel" (you can find it in his Philosophical Papers, volume II) is still a lucid and useful sorting of the issues. Lewis argues -- correctly, I think -- that the Grandfather Paradox doesn't show what it's meant to. Roughly, the idea is this: if I do someday travel back to 19xx gunning for Grandpa, then first, it's true even now in 2008 that there was a deranged philosopher lurking around in those days gunning for Earl Stairs. (You may dooubt that this is so; so do I. But do either of us know it beyond all doubt?) Second, however, we can say for sure that I failed. I didn't manage to kill Grandpa, because he did actually marry Grandma, and they did actually have a son who married my mother and became my father. Time travel stories have to be consistent, but consistent time travel stories are possible. So philosophers have offered reasons to think that time travel is possible in the broadest sense: it's not inherently incoherent -- it's logically possible or metaphysically possible.

If we take philosophers like Lewis to have done that part of the job correctly, however, there's another question that calls for a different sort of expertise: do the laws and conditions that hold in this universe allow for time travel? Roughly, is time travel physically possible? That's not something that philosophical reflection alone can tell us. General relativity, our best theory of space and time, apparently allows for "closed time-like curves," and following one of those would amount to time travelling. But "allows for" is pretty abstract. It doesn't follow that there's any way of arranging this that a human body could survive. And it also doesn't follow that the technology needed to generate those curves is within our capability. So on the most general question, yes: philosophers can give us reasons to think time travel is possible. But when it gets down to the nitty gritty, physicists and physiologists and engineers would have to weigh in.

(I've assumed, by the way, that you had travel into the past in mind. Ordinary "time travel" into the future is no problem; that's how we got from yesterday to today. And relativity straightforwardly allows for more interesting variants on future-oriented time travel. If you did it the right way, you could get from Times Square, Jan 1 2009 to Times Square, Jan 1 2010 in less than a year, by your reckoning. Hermann Bondi's Assumption and Myth in Physical Theory is still a friendly introduction to those ideas 40 years after it was written.)

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