This post has grown to ridiculous proportions. I've divided up this too-long discussion into a part 1 and part 2. Part 1 deals with the supposed entailment of determinism from the possibility of time travel. Part 2 deals with the possibility that closed causal loops undermine determinism.
It's something of a staple of the literature on time travel that if it's possible, then we must be determined. But I'm not really sure this is the case. David Lewis made this claim in his "The Paradoxes of Time Travel," and it recently appeared in a nice piece in discover by Sean Carroll.
Here's the basic idea: Suppose that I go back in time to prevent the assassination of Abraham Lincoln in 1865. Since Lincoln was assassinated in 1865, it must be that I failed to prevent the assassination. Therefore, it is not possible for me to prevent the assassination, therefore I am determined not to prevent the assassination.
However, it doesn't follow that I am determined to fail or Lincoln is determined to be assassinated just because it in fact happened that he was assassinated. From the triviality, "Que sera, sera," it doesn't follow that what will be necessarily will be. Lewis's and Carroll's conclusion that we are determined does not follow from the fact that some particular thing will happen and even that we know it will happen. I'll explain a couple of terms and try to show why the possibility of time travel does not entail determinism. (Carroll puts this in terms of undermining free will, but that overlooks the compatibilist position that we can be free and determined at the same time.)
Philosophers distinguish de dicto from de re modal claims. Modal claims are claims having to do with possibility or necessity. The claim that I might have been taller is a modal since it is a claim not about what is but about what might be. De dicto modal claims are only about the words and do not involve the essential nature of the thing. Necessarily, bachelors are unmarried, but it is not true that bachelors are necessarily married. It is a matter of definition that for something to count as a bachelor, it cannot be married. But individual bachelors (people who currently meet the definition) are not necessarily bachelors in that they can get married. De re modal claims are claims about the thing and necessary facts about the thing or its essential nature. De re claims have a different scope. There are fewer clear examples of de re modal claims, perhaps none that apply to our ordinary space-time world. The number 2 is necessarily even. Given the nature of the number 2, there is no possibility that it be other than even. It might be that humans are necessarily physical beings if, for example, it is impossible (in some sense) for humans to exist without a physical body.
Given these terms, the determinist position is that our actions are de re necessitated, not de dicto necessitated. The determinist says that necessarily Lincoln dies in 1865, and necessarily, I will not prevent Lincoln's assassination in 1865. However, all we are really justified in saying is that Lincoln was assassinated in 1865, so, necessarily, given that fact, Lincoln was assassinated in 1865. Necessarily, Lincoln, who was assassinated in 1865, was assassinated in 1865. But it is not true that Lincoln, who was assassinated in 1865, was necessarily assassinated in 1865.
This really shouldn't be a surprising result. The present is the future's past, and we don't think it follows that now, on June 29, 2010 I am typing means that necessarily on June 29, 2010 I will be typing. The fact is that Lincoln was assassinated in 1865, but he might not have been.
Or to give a similar example, if I know that I will pass my exam tomorrow, then it is a fact that I will pass it. But it does not follow that necessarily I will pass it. I will but I might not.
Lewis points out that one's preventing Lincoln's assassination in 1865 is not compossible with (possible given the fact that) Lincoln was assassinated in 1865. Thus, I cannot prevent the assassination given that it occurred. But compossibility with all facts is not what determinism requires. Determinism requires that an event's not occurring is not compossible with all prior facts. And that does not render Lincoln's assassination determined, only necessitated by the fact that it actually occurred. And that's a relatively trivial claim. (Although if Lincoln's assassination occurred both in my past as part of my history and my present as I travel to the past, this notion of determinism gets more complicated. I'll try to sort this out below.)
Were I to try to prevent Lincoln's assassination by hiding out in the Ford Theater and leaping on Booth when he attempted to sneak in and assassinate the president, I would fail. Since Booth succeeded, doesn't it follow that I necessarily fail to prevent the assassination? No, it follows that I will fail--in fact, if I attempted to save the President, then I did fail--but it does not follow that I necessarily fail.
It may seem that the philosophical distinction above represents a distinction without a difference. If nothing I try prevents the assassination of Lincoln, then how is that different from my not being able to prevent the assassination at all? More generally, how can all this talk of de re necessity and possibility make sense when the only world we have available to us is the actual world, the world in which Lincoln was assassinated and in which I failed to prevent it? What is the point of possibility and necessity talk at all if the only thing we can talk about is the actual world?
The answer to this question is really too long to take up here. The short answer is that it makes sense of statements such as "I might have been taller," since some such statements are true, whereas others such as "I might have been an octopus," or "I might have been the number 1," are false. Without modality -- talk of possibility and necessity -- there's really no way to distinguish true from false claims of these sorts. Talk of unactualized possibles (things that might occur but do not) is a bit iffy for the empiricists among us, but it is nonetheless coherent. A golden mountain is an unactualized possible--it could exist but doesn't, but a round square is an unactualized impossible--it does not exist because it couldn't. Leaving aside theories of what unactualized possibles are, they have uses and truth conditions in our language.
If we admit that Lincoln was assassinated in 1865 and nothing I do or have done prevented it, then how does my supposed freedom--here taken to mean that it is possible that I save him--make any difference? Well, it doesn't make any causal difference to things that occur (that's partly why unactualized possibles are so puzzling), but such talk still makes sense. When Terry Malloy says, "I coulda been a contender," he regrets not actualizing a possibility even though it's a fact that he never was a contender. Had he said, "I couldn'ta been a contender," there would be nothing to regret.
But in cases in which there is a possibility of success, and in which I do not know the outcome, I can still attempt to act. There may be multiple possible things I can do this afternoon, and it makes sense for me to decide which of them to do even though necessarily whichever one I do is the one that I do. My actions render some possibility actual, and leave others as unactualized possibles, but the fact that that fact is not enough to render me unfree.
Note that I am not arguing for the existence of free will or the ability to do otherwise than we do even though I had to make some of my points hypothetically by supposing that I might have acted differently. I do not necessarily think we have free will or are not determined; I'm merely pointing out that such possibilities are consistent with time travel. I'm just claiming that the argument from the possibility of time travel does not establish that we are not free and cannot do otherwise. To say that necessarily we will do as we do, does not entail determinism, that we will necessarily do as we do. To put my point more succinctly: determinism cannot follow from the trivial logical point that necessarily everything that happens happens, and that's all that the possibility of time travel really shows.
Carroll talks about closed time-like curves or what Lewis calls closed causal loops. (The classic example is Robert Heinlein's "All You Zombies.") Carroll thinks if these are possible then determinism is not true.
Here's an example of a closed causal loop. One day (call it time t1) I receive a mysterious visitor who gives me instructions for how to build a time machine. I build the time machine (completed at time t2) and go back in time to give myself instructions on how to build it. (In fact, if I'd been lazy, I would have just left it around for myself to find so I wouldn't even have to bother building it as long as I remembered to leave it for myself in the past when I was done with it.) Now, everything in this story is consistent and potentially deterministic. We can suppose that everything in my brain is determined, and there is a complete causal story governing my acquiring the plans, building the time machine, and using it to give myself the plans at t1.
Carroll thinks, however, that if this sort of thing were possible, it would undermine determinism. Determinism, on his view, is the idea that everything that occurs at some time is necessitated by the state of the universe before that time, so that necessarily, if the state of the universe is such and such at time t0, necessarily so and so will occur at time t1. The problem I, the time traveler, create for determinism is that my receiving the plans at t1 (and all my work after that) are not determined by the state of the world at t0 but by the state of the world at t2 when I (deterministically) decide to travel back in time to give the instructions to myself. Thus, causation backwards in time occurs and determinism is undermined.
This kind of causation does violate our ordinary sense of causation and determinism. However, I'm not sure we should conclude that this alone could undermine determinism. Here's an admittedly imprecise analogy: Two particles P1 and P2 exist in two systems S1 and S2. P1 and P2 interact within these systems according to deterministic laws. However, P2 now comes into contact with P1, and P1's movement suddenly is no longer determined simply by the laws and the other parts of S1, it is also determined by P2 (and I suppose by its interactions with S2). It doesn't follow that P1's movements are not determined, just that they are not completely determined by system S1. In ordinary terms, we could just describe S1 and S2 as being part of a bigger system, and so that system would determine P1's motion. In the time travel case we have a system S2 that is in the future, so it cannot be described as part of the same system at the same time with S1. I think all this means is that we have to expand our concept of the system that determines P1 to include future events provided there is a time-line connecting P2 from the future to P1 at an earlier time.
David Lewis talks about personal time-lines as a way of making sense of the backwards causation we would get in time travel. The causation along the time-line is not backwards even though it is backwards from outside the time traveler's time-line. Just as special relativity made us give up the concept of absolute simultaneity, time travel would require that we give up absolute past, present and future. And as long as all personal time-lines are deterministic, then the system as a whole could still be counted as deterministic even though we could no longer define an event as determined in the intuitive way as "necessitated by everything that happened before time t1". We would have to modify it to something like "necessitated by everything that happened before time t1 on all time-lines causally interacting with that event."
So, again, I'm not sure that the possibility of time travel by itself entails or contradicts determinism.