Well to be fair most of those paradoxes have solutions
I vote that we don't derail this thread further by turning this into a "faster-than-light" debate, since in my experience it becomes more an issue of semantics than anything else, and really who wants that?
Oooooh! a faster then light debate? Isn't saying not to let one start, almost encouraging one?
Simple proof that faster then light IS possible. All models of the big bang theory pretty much require an inflation period in which space-time itself expands faster then light, allowing for mass from point a, to get to point b quicker then light. However the mass never really moves faster then light, in any frame of reference, as it is space-time that is moving. So technically mass didn't move from point a to point b at all, and no laws of physics were violated, in any way, shape or form. and the laws of physics most certainly didn't feel the need to file a formal complaint with their HR department about being violated, as they never really felt violated or something like that.
Assuming it has happened once, then space-time can in fact be moved, or expanded, or something like that. Assuming it once expanded faster then light, and the distance between mass expanded faster then light, then it could be made to do so again.
Assuming it could be made to do so, then one could in theory move away from mass faster then light. The catch is, none of this requires that it can be compressed, which would need to happen in order to approach other mass. i.e. you could expand the space between you and the earth by a distance of 1 light year, moving yourself 1 light year away from earth, but this wouldn't get you closer to any other star, it would simply create a lot of empty space between you and the earth, stranding you 1 light year away from the nearest pizza hut. I'm quite certain that is probably out of where they will deliver too. *sigh* suddenly this whole FTL stuff doesn't sound as appetizing.
Of course if space-time can be both expanded AND compressed, or even needs to be both. then essentially a "warp drive" is possible. where you create a bubble of space-time around yourself, and compress space in front of it, and expand it again behind you. thereby moving space-time itself, while you stay still. But then other problems come into play. Like those damn klingons come and try to steal your pizza hut meat lovers pan pizza.... *sigh* ok maybe a debate ISN'T a good idea.
EDIT: what can I say. I got bored and was reading this thread again