nietzsche wrote:okokok that's why I said assume for the sake of discussion that premonitions are possible!
Try again.
In a deterministic universe a possible solution to the causality thing is that precognitions were considered all along for the line of causality. That is, knowing about events in the future do influence the future therefore we could say the future influences the past, but somehow, that perception of an event in the future was always included in the line of causality and never jumped (if you picture causality in a line from past to future).
Another possible solution, is that time is not linear at all.
Essentially, true premonitions that are really predictable are only possible in 2 cases.
1. events entirely outside the person's direct ability to change. A small example might be a child, worried about a future trip that is already set, that the child cannot change, having a "vision" of something from that trip. A bigger example might be something like seeing that a prominent individual, far away, might do something.
2. If there is no real free will, no real variability.
Most people prefer not to accept #2, don't really consider it accurate. (if we did, we would all be fatalists). Therefore, most of us basically think of situations like #1.
I would say scenario #1 is about the only type of scenario I would really see. Anything else would be science fiction, and you instantly have a series of paradoxes, usually that the person seeing the vision is somehow either going to cause the event because of the premonition or is somehow going to be steered toward that end in ways utterly beyond the person's ability to control.