Decision Theory

Given Ludovicianism, strange things happen in time travel cases. Imagine my future self appears, dying of radiation sickness. Before dying, he (me?) reveals that a nuclear war will kill us all. Time cannot be changed, so war looks likely. But if you use excessive means (e.g. torture/hypnosis) to make me believe a war has taken place (when none had!), poison me with polonium, and send me back in time, we’d have a consistent scenario but everyone (expect myself) gets to live. Is it rational to use excessive means? This is a type of Newcomb case. The chapter argues that ‘one-boxers’ should use excessive means. ‘Two-boxers’ should also use excessive means, even though they should nevertheless two-box in standard Newcomb cases. The chapter ends with an Appendix about regular Newcomb cases, arguing that in ‘perfect predictor’ cases its reasoning means that the ‘two-boxer’ should instead select one-box.

The Grandfather Paradox

The Grandfather Paradox is as follows: time travel is possible; were time travel possible, I could go back in time and kill my grandfather before he met my grandmother; such an act of murder is impossible. Since we have a contradiction, we have to give up on one of the premises (with many presuming that we should give up on time travel’s possibility). This paradox is the focus of most of the book, so most of the chapter is spent explaining the details of the paradox and its different variations. Crucially, this chapter delivers a lengthy exposition of the most pressing version of the paradox; it is referred to frequently in the remainder of the book. The chapter ends by also sketching the proposed solutions that the rest of the book discusses.

Changing the Past

Here’s a paradox: time travel is possible; were it possible, you could change the past; it’s impossible to change the past. This chapter argues that we can resolve this paradox in two different ways. One way, the ‘Ludovician’ method, is to accept that changing the past is impossible but deny that time travel requires changing the past (and, as part of the chapter’s discussion, it argues both that Ludovicianism is incompatible with the future being open and that the ‘bilking’ argument isn’t problematic). Another way introduces ‘indexed worlds’—i.e. worlds with extra universes or extra-temporal dimensions—at which the past can be changed. The chapter argues for the metaphysical possibility of both Ludovician and indexed worlds.

The Bootstrapping Paradox

Bootstrapped things are things which are, at least partially, responsible for their own existence. For instance, a bootstrapped object might be someone who was their own mother whilst bootstrapped knowledge might exist because someone uses a time machine to go back in time and tell themselves how to make that time machine. The Bootstrapping Paradox is this: time travel is possible; were time travel possible, bootstrapped entities would be possible; such entities are impossible. This chapter investigates the different types of bootstrapped entity (objects, information, and causal loops). It then argues that you can avoid the paradox by denying that time travel necessitates bootstrapped objects and, more importantly, that there are also no good reasons to think bootstrapped entities are impossible.

Modes of Time Travel

This chapter discusses the ways in which one might travel back in time. Of course, there are no actual, known instances of time travel, so the different modes are drawn from fiction, historical thought, and speculative physics: perhaps we could ‘teleport’, discontinuously, back into the past; perhaps we could travel back into the past in the same way we persist forwards, traversing the intervening instants between ourselves and the past; perhaps we instead warp spacetime to allow us to come back to where we began. The chapter ends by discussing two things that are not technically time travel—cases of frozen time and time being an illusion—which are nevertheless closely connected.

Probability

How would probability work in a time travel scenario? This chapter offers answers for both the Ludovician and the non-Ludovician who believes the world is indexed. Given Ludovicianism (and impossability theory), metaphysical impossibilities can have a positive objective chance. Nevertheless, we should say our credence of these things coming about is zero. The chapter argues that the upshot of this is that we should never expect any time travel to happen. Indeed, the more likely it looks as if you can travel in time (and, e.g., build a working time machine), the more likely it is that some calamity affects you (or all of us!) to prevent that happening. At an indexed world, things work substantially differently. At an indexed world, credence and chance don’t come apart. The chapter argues that at an indexed world, we might expect time travel to occur.

The Double Occupancy Problem

Imagine a time machine travels back in time in the same way it persists into the future (i.e. by persisting backwards). For instance, this is how time machines move through time in H.G. Wells’s The Time Machine. Such a machine would have a problem: immediately upon moving back in time it would collide with its earlier self. This is the ‘Double Occupancy Problem’. Using the notions introduced in Chapters 1–3, this chapter explains how to avoid this ‘Double Occupancy Problem’: such time machines can travel back in time just as long as they are both in motion and move back in time bit by bit.

Impossability Theory

My preferred solution to the Grandfather Paradox is to say that time travellers have the ability to do the metaphysically impossible (and so I can kill my grandfather), even though they never will. This requires physical possibility to outstrip metaphysical possibility. This chapter argues that, given the dialectic one must be in when considering the Grandfather Paradox, it’s reasonable to assume just that. It then argues that, given that assumption, impossability theory follows. The rest of the chapter explains Jack Spencer’s argument for the same conclusion, before discussing how impossability theory can be applied to a selection of paradoxes other than the Grandfather Paradox, and which have nothing to do with time travel.

Incapacity Theory

We can solve the Grandfather Paradox by arguing that, when I go back to kill my grandfather, I lose the ability to kill him. Call this incapacity theory. I do not believe this theory is correct. This chapter argues that this is David Lewis’s view. His argument for it focuses on how we analyse the words ‘can’ and ‘could’. But if you take the Grandfather Paradox seriously, you should take contemporary advances in modality seriously and believe in impossible worlds and non-trivial counterpossibles. Once we do that, we can reconstruct a variant Grandfather Paradox which is immune to the incapacity theorist’s argument.

Inconsistency Theories

Some believe dialetheism, i.e. that there can be true contradictions. If there can be true contradictions, then we might take the moral of the Grandfather Paradox to just be that, when time travelling, some contradictions turn out to be true (e.g., it’s true that my grandfather is both dead and alive in 1930). There has been little attention paid to this possible line of response to the Grandfather Paradox. This chapter remedies that omission. However, it argues that even if you are comfortable with true contradictions, that does little to help with the Grandfather Paradox. You either end up with a theory of time travel which is simply bizarre or one which is indistinguishable from a theory saying that time travel necessitates that the world is indexed (e.g. is a world of hypertime).