21st-century readers are no doubt aware that this "self-fulfilling prophesy" approach has been done quite literally to death over the course of 2500 years. All that remains to be innovated there is "how to trick the protagonist into creating the future he seeks to prevent, while preventing the reader from seeing this as a rehash of Oedipus Rex." Have you ever read one of these stories, or seen one of these films, and wanted to poke your eyes out? Now you know why.
Another approach at preserving causality in the face of paradox is the "multiple universes" approach. Here the universe protects itself by shooing would-be meddlers off into ANOTHER universe where the future they seek to prevent hasn't happened yet. One of the best examples of this is The Proteus Operation by James P. Hogan, which features no fewer than THREE different universes, two of which are sending time-travellers back to a third... and that third is, surprise! the one the reader grew up in.
These discussions are amusing to 31st-century wormhole physicists and wormspace theoreticians, because observational paradoxes occur all the time for them. You know that experiment where you take your car up to the speed of light, and then flash the headlights at oncoming traffic? They've done that. Near-light-speed vehicular travel and instantaneous hypernet communications result in all kinds of little quirks in "observed" and "actual" simultaneity, but none of the quirks are large enough or long enough to allow physicists and theoreticians to make a killing in the stock market. This is a good thing: rich scientists become lazy scientists. If good science always resulted in immediate wealth, progress would slow to a luxuriously decadent crawl.
Now, however, the single universe inhabited by Kevyn Andreyasn has given rise to conditions in which its own history can be re-written. Mathematically, Kevyn could show us all why it works, and why paradoxical causality doesn't require anybody to believe in it, but since he and a half-dozen Gav-clones invented 75% of the mathematics involved in the proof, most of us would have a hard time following it. If imaginary numbers like "i" (the square root of negative one) give you a headache, Kevyn's math would give you and everybody in a 10-kilometer radius fatal aneurisms.
Which brings us to today's installment of Schlock Mercenary: anyone who has ever "cheated" at Warcraft by reverting to a previously-saved game in order to be able to perfectly anticipate enemy troop movements knows full-well how this kind of time travel works. From the perspective of those in the "overwritten future," it's like bathing in the Fountain of Youth, and then drinking some some milk-of-amnesia. And from the perspective of those consciously traversing the path between the future-that-ceases and the past-that-is-the-now, it's the sort of second chance that most of us wish for longingly, but would probably just screw up if we were actually given it.