Forget Hawking's postulated time travel consistency principle, the principle of non-contradiction is all that's needed. If time really is much like a spatial dimension and arbitrarily traversable--if time travel is possible--no paradoxes will occur since there is no "first" run through of time. There is simply 12:24am June 24th 2011. Time paradoxes will not occur for the very same reason that a thrown ball doesn't go both left and right at the same time.
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