  Response 4. All of the previous discussion completely misses the point. So far we have been taking the space-time structure as given, and asked the question whether a given time travel space-time structure imposes constraints on states on (parts of) space-like surfaces. However, space-time and matter interact. Suppose that one is in a space-time with closed time-like lines, such that certain counterfactual distributions of matter on some neighborhood of a point p are ruled out if one holds that space-time structure fixed. One might then ask “Why does the actual state near p in fact satisfy these constraints? By what divine luck or plan is this local state compatible with the global space-time structure? What if conditions near p had been slightly different?” And one might take it that the lack of normal answers to these questions indicates that it is very implausible that our world, or any remotely like it, is such a time travel universe. However the proper response to these question is the following. There are no constraints in any significant sense. If they hold they hold as a matter of accidental fact, not of law. There is no more explanation of them possible than there is of any contingent fact. Had conditions in a neighborhood of p been otherwise, the global structure of space-time would have been different. So what? The only question relevant to the issue of constraints is whether an arbitrary state on an arbitrary spatial surface S can always be embedded into a space-time such that that state on S consistently extends to a solution on the entire space-time.