So, that's how Lewis defines time travel, divergences between personal time and external time. The classic objection to backwards time travel is usually referred to as the Grandfather Paradox. A big part of Lewis' paper is designed to defuse the argument that time travel must generate generally logically contradictory outcomes. Now I stress that Lewis is only defending the logical possibility of time travel. All Lewis' paper aims to show is that it's logically possible for someone to travel in time. Lewis isn't saying that time travel is physically possible. Still less is he saying that time travel actually occurs and time travellers walk among it. So the aim of the game is to defend the claim that it's logically possible to travel in time. But to put it another way, that some backward time journeys can be described without falling into contradiction. Well, why might someone think that a backward time journeys are logically problematic? Well, the classic argument appeals to grandfather paradoxes. And it goes something like this. If it was possible to travel in time, it would be possible to create contradictions. It's not possible to create contradictions, therefore, it's not possible to travel backwards in time. Now Lewis accepts some of that argument. He accepts that it's not possible to create a contradiction. Any real state of affairs, any real world had better be consistent. The world had better be logically possible. Or to put it another way, to establish that something is logically impossible is to establish that it just cannot possibly occur. So Lewis does accept that contradictions can't occur. But where he differs from the proponents of the grandfather paradox argument is that he thinks that backward time travel needn't necessarily involve the ability to generate paradoxes. Interpreted properly, backward time travel can be internally consistent. Well, why are they called grandfather paradoxes? Well, the standard example, popular from innumerable science fiction stories and films. Imagines a traveler going back in time and removing an essential cause of her or his existence. The standard example imagines that the traveler goes back in time and eliminates a grandparent, typically a grandfather, before grandfather has had a chance to father any children. So if you could travel back in time and eliminate your grandfather before grandfather had achieved parenthood, you would remove one of your parents from existence. If you remove one of your parents in existence, you presumably remove yourself. So, if your mission succeeds, your grandfather doesn't exist, one of your parents didn't exist and you don't exist. Well, if you don't exist, how do you travel back to carry out your mission in the first place? The mission seems to succeed [INAUDIBLE], if and only if it doesn't succeed. Which seems to have assumed many, a glaring logical contradiction. So the problem is that if you could travel back in time and eliminate the causes of your own existence, you could make yourself both exist and not exist at the same time. Which is surely logically impossible. Now as I say, Lewis thinks that logical contradictions can't occur. Where he thinks the grandfather paradox argument goes wrong is in assuming that time travel necessarily generates the ability to enact logical contradictions. I don't have a problem with either of my grandfathers. So for the sake of argument, I have assumed that my mission is to assassinate someone I do have a problem with, namely Adolf Hitler. So let's suppose that I get funding to develop a time machine. And my experimental launch takes place in January 2013. I've done my homework and I decide that the best place to strike at Hitler is in late 1908, during the so-called hunger years when Hitler was trying to eek out a living as an artist in Vienna. A reason that at this point Hitler doesn't have an army. He's not surrounded by security guards, he's a lone, private individual and therefore a safe target. So let's suppose that I arrive in Vienna in 1908, dressed and equipped and trained to pass myself of as a native Viennese of the period. I get Hitler in my sights, I try to pull the trigger and what happens? Well, something that can't happen is that I successfully assassinate in 1908 someone who doesn't in fact die until 1945. Assuming that death is a one short operation, one and the same person can not die in 1908 and die in 1945. So my successfully assassinated Hitler in 1908 would generate a grandfather paradox. I should just say at this point that people seem to think that paradoxes are okay, provided history is only changed a little bit. Well unfortunately, Logic doesn't recognize things being slightly contradictory. Something's either contradictory or it isn't. So I can't do anything in 1908 that hasn't already happened in the history whence I come. So if I get Hitler in my sights in 1908, there seems a guarantee of failure. But that failure might take any one of a number of forms. My gun could jam. I could sneeze. Hitler could duck to tie up his shoelaces. I could be run over by a tram. Or I could successfully shoot down somebody I believe is Hitler, only to discover I shot the wrong person. Now all of those outcomes are perfectly consistent with Hitler surviving until 1945. So my mere presence in the past is not necessarily contradictory. So certain outcomes are compatible with Hitler surviving until 1945. So my actions in the past seem to be restricted, but that's not the same as saying they're impossible. One thing to bear in mind is that in Lewis' analysis, each movement, each time happens only once. It's not that 1908 happens without my presence. And then I go back in my machine and somehow 1908 happens again, only this time I'm there. If Lewis is correct, each moment happens once and once only. And the course of history is consistent over time. So if I travel back from 2013 to 1908, the history whence I come contains anything that I get up to when I arrive at my destination in the past. So provided that the history that I come from in 2013 is consistent with the history that I arrive in the 1908, there's no paradox. So where does the appearance of paradox come from? Why does the grandfather paradox argument have such an appeal? And Lewis says it's because there's an ambiguity, a [INAUDIBLE] ambiguity in the argument's very first premise. If it was possible to travel backward in time, it would be possible to generate paradoxes. But what does possible mean? Lewis says that to answer this question properly, we need to the notion of someone being compossible. Now, compossibility means possible relative to a set of facts or certain states of affairs. Here's an example, adapted from Lewis. Is it possible for me to speak Gaelic? Well, in one sense, it is. I can speak one language, at least. I can master some basics syntax, I got a few lungs at my disposal, I got a larynx that functions. So in a sense, yes, I should be able to speak Gaelic but dont' ask me to recite any of Scotland's rich history of Gaelic poetry because as it happens I've never learned Gaelic. My education just hasn't stretched to picking up the words, the syntax and the grammar. So in one sense, it's possible for me to speak Gaelic relative to one set of facts. It's compossible with one set of states of affairs. But relative to another set of facts, a bigger, a more inclusive set is not possible. But there's no paradox here, because the set of facts according to which it's possible that I could speak Gaelic are not the same set of facts as the set of facts which mean that it's impossible for me to speak Gaelic. Apply this to time travel cases. Is it possible for me to assassinate Hitler in 1908? Well, relative to those one set of facts, it is possible. Unless, supposed that my gun is in good order, my eye is keen, I'm well-trained. This is perhaps the least plausible instance of the whole scenario, but let's just suppose that my training and my eyesight are up to the job. Let's suppose that Hitler isn't wearing a Kevlar vest or any kind of armor. Well relative to facts like that, then yes, my mission succeeding is possible. It's compossible with those facts. But the success of my mission is not compossible with a more inclusive set of facts, particularly not relative to the fact that in 1945 Hitler is still alive. So what's compossible relative to some facts about 1908 is not possible relative to a more inclusive set of facts. But there's no paradox here, because it's a feature of possibility, of compossibility. That what's possible relative to one set of facts may not be possible relative to another set of facts. So Lewis says, backward time travel can be logically consistent, provided you bear in mind that what's possible relative to one set of facts may not be possible relative to another set of facts.
