Time and Causation

I had an extraordinary week because I decided I changed my mind about this quite early on. And I've virtually rewritten the whole lecture in the last week. But it's so enjoyable, the subject. I mean, you must be loving it. I hope you are. I am. Okay. So let's. If you remember, this is the fifth week of lectures. So we've done four weeks of looking at various theories of causation.

And we've considered three types of reductive analysis. So we've looked at the regularity theory, which comes from Hume. So he thinks causation is lawful regularity. And we've looked at the counterfactual theory, which comes from David Lewis. He thinks causation is counterfactual dependency of some kind. We saw that there are few accounts of counterfactual dependency that won't do.

But we saw one that maybe will do. And we've looked at singulars theories where causation is a set of perhaps or a physical process. We haven't considered primitivism the idea that causation is so fundamental and central to our thinking that we can't reduce it. So it's like truth. It's it is just suy generous one thing in itself. And nor have we considered illuminative ism and the idea that causation doesn't exist. More than briefly. We'll look at that very briefly today.

But I think somebody said to me last week that she thought this might be the case. Well well, we'll have a look at others who think this. So this week, we're going to be looking at the relation between causal asymmetry and temporal asymmetry. So we're no longer looking at a theory of causation. We're looking at theories of how the causal asymmetry is aligned with the temporal ASEM of God. I've probably done that the whole way through. Because, of course, these spellcheck doesn't pick that up.

No, not Cashel. Causal. Causal. Whenever you read Casualty, you should read it as causal. Okay. So the folk concept of causation. And you remember last week, I distinguish the folk concept and the scientific concept and said that any account of the scientific concept is only going to be interesting from our point of view, if it arguably is or can be seen to be the folk concept. Because what we're interested in is causation as we use it in our everyday lives.

So the folk concept of causation seems to be asymmetric causes come before their effects. If we see causes e e does not cause, see, they're asymmetric and this asymmetry seems to align with the direction of time. The fact that time itself seems to have a direction from past to future, it doesn't go from future to past. So it's interesting to ask how these two asymmetries are related. I mean, the fact that they are aligned so well makes it look as if they might be related.

Well, Hume has theories about this or views on this or other. He his views aren't very interesting on this. He thinks causation itself is symmetrical. So he thinks if A and B are constantly conjoined, then A is constantly conjoined with B and B is constantly conjoined to A. Of course, has to be. That's the relation of constant conjunction is a symmetrical relation. And Hume thinks that causation is constant conjunction. Therefore, Hume thinks the relation of causation is a symmetrical relation.

So he thinks there's no more to the causal arrow, to the fact that there appears to be an asymmetry of causation than the semantic convention that causes come before their effects. So cause is just defined in such a way that causes come before their effects. An effect is just defined in such a way that effects come off to their causes. This is surely not very interesting. I mean, one problem is lots of people have thought that simultaneous causation and backwards causation are possible.

But according to Hume or on Hume story, all these people are conceptually confused. So anyone who thinks that time travel really might be possible is conceptually confused. It couldn't be anyone who thinks that there are tachyons. Particles that move faster than speed of life light are conceptually confused. So they're there. The objection to them is not just that they're wrong empirically, but that they've got their concepts mixed up.

Same with precognition. And any suggestion that a cause could come at the same time as its effect or after its effect is confused on Hume's story. And that's got to be a problem for Hume's story, because there. It seems perfectly reasonable to consider the possibility of simultaneous backwards causation, even if we don't seem to see it very often or indeed at all.

So the second problem is that it doesn't explain the fact that fact of our practical reason, which is that we see the past as fixed and the future open. So when we deliberate to achieve goals. So we want to achieve some goal or other we deliberate about future goals. We do not deliberate about past goals because we can't change the past. So if we're thinking about what we can do, it's about how to change the future.

And again, a human can't explain this. He just says, well, if you think you can do anything else, you're conceptually confused. And surely we might think there's a bit more to it than that. There is a sense we think, don't we, in which the past really is fixed and the future really is open? Well, he can't explain that. So Hume's account of the alignment of the temporal symbols, a cemetery and the causeless cemetery is unsatisfactory, to say the least.

What we should like is an account of causal asymmetry that ensures the possibility, at least in principle, of simultaneous causation and backwards causation. And explains our deliberative practises. Preferably in terms of some objective asymmetry that ensures that the past is fixed and the future is open. And David Lewis attempts to offer such an account, the same chap just gave us the counterfactual theories. OK. Any questions about Hume's? And the problems with it?

No, it's pretty straightforward, I think. Okay, so let's have a look at David Louis'. Here he is. Lewis thinks that causal asymmetry depends upon the asymmetry of counterfactual dependence. Well, that won't surprise you. And that the asymmetry of counterfactual dependence depends on the asymmetry of over determination. What's that? Okay. So to evaluate this claim and to relate it to our hope of understanding the relation between the temporal asymmetry and the causal asymmetry,

we need to ask several questions. And here are the questions that we're going to be asked answering in this lecture. So first of all, you want to know, I assume, what they symmetry of over determination is. Okay. Secondly, you'll want to know how the asymmetry of counterfactual dependence depends on the aim at a cemetery of over determination. If if Lewis is using this asymmetry to explain that asymmetry, we've got to know how they're related.

And thirdly, does appeal to a symmetry of over determination. Explain the relation between the causal arrow and the temporal arrow. Because that's what we want to know. So those two are things that we've got to know in order to know this. But that's the important thing. And I've already said that we've got to desiderata of an account of the alignment of the symmetries.

Does louis' accounts give us the first one? I does it permit the possibility in principle of backwards and simultaneous causation? And you can imagine what the second one is. Does Louis' account Louis' account to explain are deliberative practises? And lastly, of course, is Louis' account correct? Are there any objections we can bring to it or should we just reject it and with it the explanation of the alignment between causal asymmetry and temporal asymmetry.

Okay. And you won't think of any other questions? I hope not. But if you can think of them afterwards. So what I'm going to do for the rest of this lecture is try and answer these questions. So let's start with the asymmetry of over determination. What is the asymmetry of over determination? Lewis says that in this world, though, not in every world. So we're talking about something contingent here. We're not talking about something necessary in this world.

It's typically the case. In other words, it can happen in this world that it's not like this. But typically it is like this. And there are many more future determinants of events than past determinants of events.

I the put of events in there. Okay, so Lewis thinks that there is an asymmetry of over determination because it's typically the case in this world that events have many more future determinants than past determinants, and a determinant is a set of minimal conditions such that there are sufficient for the event. Okay, well, we'll say something more about that in a minute. Okay, so let's have a look at an example.

We say that the campus lighting his campfire started the forest fire because we believe that had the camper not lit his campfire, there would not have been a forest fire. Okay. Does that make sense? We think the nearest no camp far possible world to this world is the world in which the forest didn't burn down. OK, so if you remember, we evaluate counterfactuals by saying in the world where the antecedent history of, say, is there a world in which the antecedent and the consequence are true?

Is that world a world like that, nearer than any world in which the consequent the antecedent is true and the consequent false? So looking at had the camper, whereas it had the camp not it is camp father would not have been a forest fire. We're looking for whether there's a world in which the camper did light its campfire. Sorry, didn't light his campfire and there wasn't a forest fire. Is that nearer than any world where he did light his camp fire and there was a forest fire?

Have I got that right? Who is on the ball here? On let me just in case I've confused you. The come had the camper not lit his father, that would not have been a forest fire. OK. So we're looking. Which is NERA. Kamper didn't light fire and no fire or camper didn't light fire and far anyway. You with me? OK. So that's only true if that world is nearer than that world. Yep. OK. Sorry to confuse you there.

So we think the nearest no campfire possible worlds to this world is one in which the forest didn't burn down. We don't believe it's a world where there was another condition sufficient to burn the forest down. Overdetermined of outward determination of future events. By past events, it does happen in this world. So if you're facing a firing squad, you may end up with two bullets in your heart.

So if the first bullet hadn't killed you, the second would have done and your death is over determined. It undoubtedly happens in this world, but it doesn't happen very often. It would be very bad luck in this world. Once we discover there's a link between the camp highlighting the camp fire and the forest fire, it would be very unlucky if the camp hadn't lit is far and lightning were to strike.

And the FA start anyway. It's not usually the case in this world that the past over determines the future. But now consider that the forest fire happened a year ago. There'll be many traces of the forest fire and in principle, scientists, forensic scientists will be able to discover where and how it started. So there'll be many conditions a year off to the fire that could only have come about because the fire started when and how it did.

And that's what forensic science is all about. And what we're seeing when we see that is that there are many future determinants of the fire. There are many conditions, sets of minimal conditions such that they are sufficient for the fire having started when and how it did. So there's an asymmetry of past to future here. So typically, there's only one minimal set of conditions such that given the laws of nature as they are, they were sufficient for the forest fire starting when and how it did.

But again, typically there are many sets of minimal conditions such that given the laws of nature being as they are, again, they are sufficient for the forest. Forest fires having started having started, I should say, when and how it did. The future, says Lewis, typically over determines the past, but the past does not typically over determine the future. And this is the asymmetry of over determination. Okay, anyone want to ask any questions about that before I go on?

Basically, what does it mean when you say that the top line, the top paragraph differs from the second only word starting is that rather than having staff write. Starting in other words, there was only one minimal set of conditions before the fire that was sufficient for the fire. But there are many sets of milling pool conditions off to the fire for the fire. And it's those conditions that science, that lead science to say that that's where the fire started. Okay. How are things?

Joint. OK. Can you imagine a forensic scientist saying, ah, if this were not the case? If so, given that this is the case and that this is the case, it must be the case that the fire started here before. Those conditions there off to the fire. It's the fire that caused those conditions, but those conditions are sufficient for the fire having started. Then. Yeah. Okay. So. So there's one. This is typically the case. Condition sufficient for the fire starting.

And many, again, typically conditions sufficient for the fires having started. I should say then and there. That's the difference. That's the asymmetry. So if the camp hadn't lit his fire, the fire, the forest would not have burnt down. Is one sufficient condition, I should think that you will accept that happily. Okay. What. You're having trouble with, I assume, is this one. The idea that there are many conditions in the future sufficient for the fires having started.

Okay, but again, think about forensic science and think about the fact that a forensic scientists would be able to go into that forest and identify conditions that would only be there if the fire had started then and there. In other words, they are looking backwards. They determine that that's why the fire started. Yeah. Then exactly the same way. Uh. Sufficient evidence. Can I say that? I mean, will that make it easier for you?

So if I say this condition was sufficient, OK, that's got to be causal. I suppose it's it's causally sufficient for the fire having started. And here I can use Causley again, because if you're thinking and we are thinking maybe I should have said this before, that the laws of nature are deterministic in each direction. So the reason the forensic scientists can look at a crime scene.

Forget the far from the reason a forensic scientist can look at a crime scene and say this is the sort of weapon that you're looking for. This is the sort of height of the person who wielded the weapon. The person who wielded the weapon is probably right handed. The reason that the forensic scientists can say that is because there are lots of things about the crime scene that make it the case that this is what must have happened.

Well, you can write improbability if you like. Even if you add the words probability. That's that's not a problem. I think I'm worried about the determined cause of the fire because as I see it. There isn't any over determination of the cause of the fire. There's only one cause of the fire and that's the camper having litters, there could be others. Yep, you're absolutely right. There could be a lightning strike. Yeah, absolutely. So we looked back and we see that the fire did start that way.

But of course, it could have started. It could have been that had the camper not lit his campfire, the lightning would have struck. But in this case, that's not well, nor is it true often in this world, is it? So if the fire brigade tells us that the fire in the house started because there was a short circuit here, we tend to think that that was the only sufficient condition for the fire that was around at the time.

And of course, we might be wrong later on, the fire brigade might come to us and say, oh, hang on, we've also just discovered this oily rag of petrol covered rag. So maybe it was that. And now we seem to have two potentially sufficient conditions for the fire. And this is going to throw up. You know, this is really irritating because that's very uncommon. That would count as if there's more than one condition sufficient for starting something for causing something that's over determination.

So I'm. Yes, that's why the word typically is so important. Sometimes there's over determination from past to future, but typically in this world that isn't over determination from past future. There's only one sufficient condition for an effect. But when it comes to the forensic scientists checking out why it started, there are lots of things that lead back to the fire, to the campfire. Be instant before the fire starts. You might say one identifiable act is.

That is one of many. No, no. You looking the other way is the many factors that tell you. There was one. I think you could have an equal number of determinants. Going in each direction you go, you go with the fire. Yes, I see what you're saying. Okay. I did say, but I didn't make a lot of the fact that it has to be a minimal set of sufficient conditions.

There's so have I said it here? Okay. There's only one minimal set of conditions such that given the laws of nature, the camp fire was a necessary part of that minimal set of sufficient conditions. That being said, after a. The forced fall of camp for you would be a. Minimal sets of conditions looking backwards. Well. OK, so this is this what you're saying here is the campfire. And you're saying there are many things that lead to that, just as there are many things that lead away away.

The more you have. Yep. Okay. And we're saying that this is the cause because had this not occurred, the forest fire would not have occurred. So. I want the word necessary in there somewhere, don't I? Because it's the NSA's necessity of this one. That's important because it's the it's everything looks back at this one. Not at the others. Just before the fire.

So it's typically there's only one minimal set of conditions such that given the laws of nature, they were sufficient for the forest fires starting and the camp fire was what was a necessary part of those. I think you're quite right that that needs to be in the. But what happened in. Will that happen in the future is a necessary condition of the sufficiency of the condition with the one condition in the past five? I think so, yes. Sorry, I'm looking at that one person behind you.

Good past. Yes, I have already introduced explanation. Yes. And think of it like this. The camp fire, as you said, has many different causes and many different effects. But we explain it. We do remember when I talked about we we only learnt what the difference explanation is, is we talk about the cause. In other words, it's the one that makes it intelligible to us. Explanation. Well, because when we identify that condition, the forest fire makes sense to us.

So I could just as easily say, had the camper not been born, the forest fire would not have started. And that's true because the the campers birth was a necessary condition of the fire starting. But it doesn't give us an explanation, does it? It's it doesn't make the fire intelligible to us, whereas if I pick out this cause the camp fire. It's an explanation because it does make the fire intelligible. The normally intelligent person would choose and that would not be affected. But. I take it.

That's what I just said. So so there are lots of different causes, most of which wouldn't be cited in an explanation. The only causes that can be cited in an explanation are the ones that make intelligible to us the effect. There's no there there can be I mean, there are lots of conditions necessary for the minimal set of sufficient conditions, but some of them won't be cited in explanations. OK. I'm going to move on. You know, I mean, just the right direction.

Well, do you remember it's always the case that that's any one event has many things that contribute to the cause. But if we're wanting to explain it, we'll pick it will say had the camper not lit the campfire, the fire would not have started. It's also true that had the winds not been in the right direction, the fire would not have started. And we might use that as an explanation if we're particularly interested in why the fire went that way instead of that way or whatever.

So what we pick out is the explanation tends to be relevant to our interest in an explanation. What it is we want, if we only want to know whether it's why it started. The camp fire is the one. If we want to know the direction it went in, probably the wind's direction would be. But I want I just want to go back because I'd hate to lose you at this point.

So let's just. OK. Lewis says that the asymmetry of over determination is the result of its typically being the case, that events have more future determinants. There are more things in the future that determine that this fire started with a campfire that will tell us, if you like, that this thing started with the campfire. Then there are things in the past that ensure that the forest fires started. Good, this I'm good, think I'm getting myself confused here.

So we say that the campers lighting his campfire started the forest fire and we say that because we believe that had the camper not lit his campfire, there would not have been a forest fire. And that's because the possible worlds. So we ask, which is an era where the camper didn't like the fort, his campfire. And there was no forest fire or the one where he didn't lighter's camp fire and there was a fire anyway.

If that world's close closer than the forest fire is overdetermined, which it might be similar, more similar to. I know. I'll be looking at that in a minute. Okay. So we think that the nearest no camp fire possible world to this one is the one where the well, the forest didn't burn down. If the camp hadn't lost as far, the forest would not have burned down. And we don't believe there was another condition similar. We know that had the campfire not. Sorry, I can't put it that way.

If we see that there's a link between the camper lighting his fire and the forest fire, we tend to discount the possibility that there was another condition that was sufficient, although there might have been. And so, although overdetermined, a future event over determination of future events by past events does happen. So do you remember you might be shot and you have two bullets in your heart if one hadn't killed you.

The other would have done. And if the camp fire, if the camp hadn't lit his camp fire, the lightning would have struck. And the forest burned down any way might be true, but it's not true. Very often in this world, there tends to be one thing that will pick out as the minimally sufficient condition for the starting of a fire. And then I wanted you to get it OK, so that, I think should be fairly straightforward. But now I'm asking you to consider that it happened a year ago.

And I'm pointing to the truth that they are going to be many traces of the forest fire at this point. And scientists are in principle able to follow those back to identify the cause of the fire. The thing we're picking out is the cause of the fire. So many conditions that could only have come about because the fires started when and how it did. And what that is, says Lewis, is it shows us that there are many future determinants of the FA if we're looking backwards.

There are many ways of telling it that it was the FA. If we're looking forwards, the forest fire started because of the campfire. Okay, so that's the asymmetry of over determination, and I hope that they'll be a bit of time left at the end of the session. For those who who would still like to ask about this. But let's go on to look at how the asymmetry of counterfactual dependence depends on the asymmetry of over determination. My throat is not going to hold out. I think so.

Lewis says that when we evaluate counterfactuals, we rely on determining the overall similarities, said this, Lance, to the question that you wanted to ask. Just then, the overlap all similarity to the actual world. Various possible worlds, and in determining this, we've got two things that we've got to consider. Firstly, we've got to consider the laws of nature of that world and how, like the laws of nature of this world, they are.

And secondly, we've got to consider particular matters of fact at that world and how similar they are to the particular matters of fact at this world. So you might have world worlds where the particular matters. Well, where the laws of nature are very different from our world. I mean, perhaps these are worlds where things water looks like this and tastes like this and behaves like this, but is X, Y, Z. So they're not our world are our laws. They're very different from our laws.

And there are other worlds where I male. Let's say, actually, whether that is a possible world is a different, difficult question. So, OK, so we've got to determine we've got to look at the both these two things. And the counterfactual is going to be true or false, depending on how we weigh these two things with each other. And I'm going to illustrate this claim to you by bringing to Lewis's claim an objection called the future similarity.

Objection. That I think you might find interesting as well. OK, if Nick Nixon had pressed the button, they would have been a nuclear holocaust. OK, who believes that? If Nixon had pressed the button, that would have been a nuclear holocaust. And you will not believe it. Why? All right. Okay. But we sort of think that in this world, things were such in the Cold War that everything was set up in such a way that if either side had actually pressed the bloody button,

we would have been in trouble. Okay. So usually would consider that to be true. We'll just ignore Mike and anyone else who thinks that maybe not. Okay. But surely, says Kit Fine, who brought this objection originally. Any world in which a nuclear holocaust didn't happen should be nera taken as nearer to our world, more similar to closer to our world than any world in which a nuclear holocaust did happen. And you can see why says that, you know, a world in which a nuclear holocaust.

I mean, given that this is a world in which though there was so far no nuclear, I'm touching wood, no nuclear holocaust and any world, any other world in which there wasn't a nuclear holocaust is going to be more like this world than any world in which there was a nuclear holocaust. And so surely this is a problem for louis' accounts of counterfactuals. Whoops. I didn't realise that was going to. Do you see why that is a problem for Louis' account of counterfactuals?

Lewis says that what we look for is the worlds closest to our own and what we're thinking here is in the world in which Nixon did press the button, which is not our worlds, of course, because in our world, thankfully, he didn't press the button. But in the world in which he did press the button, there would have been a nuclear holocaust. Now, intuitively, we think that that's true.

But what Kit Fine is saying is it's actually not true if what we're looking for is the world that's more similar to ours. So this is a black mark for Louis' theory. Let me go on to how Lewis responds to this, and that might help you understand if you haven't understood the problem here.

So Lewis responds by taking us through the procedure of identifying possible worlds and judging their relative similarity to ours and their two things, we've got to note before considering this rebuttal of this objection. And this is the one that I should have said earlier, perhaps for ease of exposition. Lewis considers the laws of nature to be everywhere and always deterministic.

He explicitly says, and I put the reference in the notes for all these things, by the way, he is missing and says that this is necessary for his claim. But it does just make it a lot easier to think about. And he's going to talk about miracles in a minute. So you need to know what a miracle is and what a miracle is, is a violation in our laws of nature. But importantly, it expresses a relation between this world and another world.

So if we're thinking about a world in which Nixon did press the button. OK. There is a violation of our laws. There must be, because in this world, he didn't press the button. But it's not a violation of the will of the laws in that world. How could it be? There can't be violations of the laws of nature. So the laws of nature of this other world, the world where he didn't press the button, are not the same as ours. They may be like ours, but they're not the same as ours.

They couldn't be. Again, let me continue. Okay, so we surveyed the possible worlds. So we're looking for the nearest world where Nixon did press the button. Sorry, you're gonna have to put up with my stopping for. The nearest well, where Nixon did press the button. Well, there are worlds that we discount as being so dissimilar to ours where they're not even candidates.

So the world where Nixon presses the button and there is this great spray of confetti comes out or the missiles go off and shower Moscow and Leningrad and so on with with confetti. Okay. The confetti worlds are not worlds. This is similar to us. There are such worlds, but they're not ones that are going to be counted for the purpose of this. And another world which doesn't count is the world in which Nixon presses a button.

But where the laws are identical to our own. In other words, where particular matters of fact are so completely different to our own. But the laws determine that he presses the button. So that's what Lewis says, is that either laws are similar to our own or they're not. Sorry, either worlds are similar to our own or they're not. And this world just clearly isn't. We don't take any account of this world. So let's have a look at the worlds that we do count.

Firstly, we're going to look at worlds of type one and then lots of worlds here, not just one world. And so there are worlds that are just like ours until a tiny miracle. So tiny change in the laws of nature causes just enough divergence from our world for Nixon to press the button. And so what Lewis says, perhaps a couple of extra neurones fire in his brain or something like that. But anyway, you know, there he is. He's sitting there thinking about pressing the button in our world.

He doesn't press it. But in this world, he does. God, maybe it's an accident. But once he's pressed the button, worlds of type one evolve in accordance with their own laws. And we know that these laws are very like ours because up until the point of pressing the button, the worlds have been identical. All we've got is a tiny miracle. So they're a perfect match with respect to matters of fact, up until the divergence miracle. And they're an almost match with respect to the laws.

We only had a tiny, divergent miracle in order to get Nixon pressing the button. But the future of these worlds radically diverges from our own. There's a nuclear holocaust. So and this is why Fine thinks they can't be like our own. But what Lewis is arguing is that they can be, even though they're so unalike. So let's look at type two worlds. So these are worlds again, just like Harz, until there's a tiny divergence miracle which causes Nixon's press the button.

But then there a convergence miracle. And so he presses the button. But there's no nuclear holocaust. Okay. So they're a perfect match with respect to the past until the divergence miracle, which causes Nixon to press the button. And although the Holocaust didn't happen, it's because there was a little convergence. Miracle. A little miracle that brought the world back. So there wasn't a Holocaust. And 10 years at Lewis says, 10 years after this convergence miracle.

This world is going to be very different from our own. And that's because Nixon press the button. And the Holocaust didn't happen, so Nixon's, huh? Wiping the sweat from his brow is having a large gin. He's writing his memoirs. He gets the Nobel Peace prise. He, you know, et cetera, et cetera. And each of these little divergences of matters of fact, adds up to a big divergence. Ten years later. So, again, that world is like. So it's like [INAUDIBLE] up to the first miracle.

Nixon presses the button. Here's another miracle, and there's no Holocaust. And you might think that this world is more like ours than so world one. It's like Harz until there's a first miracle. And then Nixon presses a button. And then there's a Holocaust. So this is not like us. And this is like ours. But increasingly divergent. And then. We've got type three worlds, which, again, just like us, till there's a tiny, divergent miracle which causes him to press the button.

But then there's a convergence miracle that doesn't just prevent the Holocaust happening, but it also wipes out all traces. Of Nixon having pressed the button. Okay, so here we've got this just like us. And then there's a small divergence miracle. Nixon presses a button. And then there's another miracle. But where is this miracle just wiped out? He's pressing the button and left everything else the same. This wipes out. Every trace of button pressing.

So he doesn't need a large gin. He doesn't write his memoirs. He doesn't know the light waves that would have gone from the button. Don't go. Everything goes back to how it was. So we've got this world like yours till Nixon presses the button. And then there's a holocaust. Not like ours at all after that. This one like ours till Nixon presses the button. And then, although there's a no holocaust, there have been a lot of little changes which will become bigger changes later on.

And then this world, which is like us, till Nixon presses a button. And then because of another miracle exactly like ours from then on. OK. Lewis says. That these worlds. OK. What I've just said, these are a perfect match with respect to matters of fact, until the divergence miracle. And then they're a perfect match again, because the convergence miracle wipes out all traces. But the miracle required here, says Lewis, is huge. It's huge and it's diverse and it's complex.

And that's because there are so many traces of Nixon pressing the button that have to be wiped out. And that you you can't just call that a small miracle. You can't just change a couple of neurones and have that. Do what you want. So the laws of nature in this world are very different from our own, and the need to postulate huge miracles means that these worlds are further from our world than the worlds in which we don't need to postulate a huge conversion miracle.

So here these worlds, which is the outcome we wanted. We think that it's true that had Nixon not pressed the button, there would have been a holocaust. What we've got to rule out is these two sets of worlds. But Lewis thinks it's quite easy to rule out these sets of worlds as being more similar to our own. This one, because actually, if everything had been up till then as it was. And you don't introduce any more miracles. But that tiny little divergence, miracle, you'd get the Holocaust.

You wouldn't get the no Holocaust world. Surely a free world. Is. I'd rather not introduce epistemological problems here. We're looking at it from a metaphysical point of view here. You're absolutely right. The only person who would know the difference. Well, actually, even Nixon wouldn't know the difference. Why is it because it's wiped out his memory? Exactly. So nobody would know the difference here. But but this is a this is a metaphysical thought experiment. It's not epistemological.

You're absolutely right that the epistemologically we couldn't tell the difference between Major. Plus, why what sorry? Why would you say that would have been against the laws of nature? If he had pressed the button. Well, remember that we're thinking of the laws as deterministic. So in this world, the laws determine him not to press the button. Therefore, if he did press the button, there must have been a different set of laws.

And or different matters of fact. So that's based on the idea that everything is. Yes. All these experiments are based on that, on the thought that they're determined into the future and indeed from the future into the past. OK, do you see why this is a rebuttal of the future similarities? Objection. Why we would choose that world as big.

So even a world in which a holocaust has happened is going to be more similar to our world than than these other worlds, because you've got to change the laws of nature just too much to get those other worlds as being similar to our own. And as Chris quite helpfully pointed out, this is not an epistemological thought experiment. It's a metaphysical one. We've got to adopt a God Sci. view of this. We can't look at how what we would have thought if we had been there.

Okay, so according to Lewis, there's an asymmetry of the miracles needed to change the past and those needed to change the future. So the four small, divergent miracles, those that change the future need only change a few neurones in Nixon's brain. But the huge convergent miracles, those that wipe out those that change the past, have got to wipe out the many diverse and widespread changes of the traces of Nixon's pressing the button.

So not just Nixon's neurones at Nixon's brain, but also his sweat on his finger has got to gather up from the button and leap back to his finger, and he stops looking at the gin bottle and and so on. And according to Lewis, this justifies our thinking that Type one worlds are closer to our worlds than type two or three worlds. And that's the end of the future. Similarity. Objection.

And the asymmetry of over determination explains the asymmetry of counterfactual dependence because it generates this asymmetry of miracles. So there'll always be an asymmetry of miracles that you need to change the future. And miracles, you need to change the past, says Lewis. And that asymmetry of miracles. Generates counterfactual. The asymmetry is some counterfactual dependence because it depends on that. Or maybe the other way round. I can't remember which way I'm thinking. Okay.

So let's just have a look. Justice explain the relation between the causal arrow and the temporal, Larry. Now, this is the place where the physicists in the audience can watch me and wonder if I get it right. So the asymmetry of over determination is a contingent empirical asymmetry. It's contingent. Nobody is saying it's an oh, sorry. Okay, it's an objective feature of the world. Okay. It's not something that we're projecting onto the world.

It's an objective feature of the world. And according to Lewis explains both the arrow of time and the causal arrow. And therefore, the fact that they're aligned with each other. And if the eight, he says at the end of his piece that I I'm using relying on quite heavily here. And which, of course, is referenced in your hand out. If the asymmetry of over to termination could be related to the asymmetry of entropy.

He says he doesn't know how to do this. It would ensure that his account is respectable from a physicalist point of view as well. But other people have done this. I mean, it was many years ago that he said he didn't know how to do this. So the laws of fundamental physics, as we saw, I think either last week, all the time before our time symmetric and they run forwards, they run backwards, symmetrical.

There's no a symmetry that couldn't come in there, except, I mean, apparently, I'm told there are a few particles which that might not be true, which I assume are tachyons. Okay. Well, so we might think if we think this that time can't be asymmetric and there are physicists who think that time can't be asymmetric because all that time doesn't exist because of this. But there is a part of physics that does permit temporal asymmetry. And it's Thurm Ajin thermodynamics. Okay.

It's that branch of physics. So this is physics one oh one. Right, for the rest of you. And for me, it's that branch of physics that is concerned with heat and temperature and their relation to energy and work. And therefore, laws of thermodynamics. And the one that concerns us. Oh, OK. So all these laws express constraints on macroscopic variables. OK. They're not the microscopic variables, but the macroscopic ones pressure entropy, an internal energy, the energy within a system.

And these are common to all materials rather than just particular to particular materials. It's the second law of thermodynamics that tells us that entropy always increases, that unconstrained energy and matter will spread. So if you look at the picture that's rather ghostly behind this here, you've got something being contained. But when you remove the constraints, it expands into the area that's available to it. So entropy always increases, is unconstrained energy and matto will spread.

And entropy is the only quantity in physics, the measurement of which requires us to postulate a particular direction of time as we go forward in time. The entropy of an unconstrained system will increase. And that's why if you don't drink your coffee quickly enough, it'll go cold. The heat will disperse.

So if we can if we can link the asymmetry of over determination with the asymmetry of entropy, we'll have a contingent empirically and physical, distinctly respectable asymmetry that in underlying the temporal and causal asymmetries explains why the two asymmetries align. I'm going to say sorry. I'm going to say something later about whether this is possible, because there are people who think that this isn't possible.

And there are other people who think that it is possible, but only under certain conditions. And I'll say something about that in a minute. But at the moment, I just want to say that this the link between entropy and the asymmetry of over determination would give us just what we want as long as it solves the two problems that we looked at earlier. So let's look at the first problem. Does it permit the possible permit, the possibility in principle of simultaneous and backwards causation?

Well. It's it is a contingent, a cemetery. There is nothing necessary about it. So that allows that they're all worlds. Not this world maybe, but there are worlds in which causation is simultaneous or backwards or both. And it also allows that there might even this world be cases of simultaneous or backwards causation. So it is just saying this is typically the case. It's typically the case in this world and it's a contentions matter.

So it allows there to be in this world simultaneous and backwards causation. And it allows there to be plenty of other worlds in which they're similar to. So it certainly meets that constraint. And. OK. Does it explain our deliberative practises? Well, it explains our common refusal to backtrack. So imagine that Joanna and Jayne had a really bad quarrel yesterday. Lewis has Jim and Jack, but I think that it's quite important to knowledge that there are women in the world.

So imagine that Joanna and Jane had a quarrel yesterday. You might think that if John asked Jane for help today, Jane would say no. Would you usually think that that's the counterfactual that would tell us what would happen if John asked Jane for help. But why don't we reason that if John asked Jane for help today, it would be because there hadn't been a quarrel yesterday. So she'd say yes. Well, we don't not reason like that.

And one of the reasons we don't reason like that, according to Lewis, is because of the asymmetry of over determination, because of our belief that we can't change the past. So it explains are reluctance to backtrack. Actually, we will backtrack.

I mean, if if we were talking about Johna and Jane's quarrel and you suggest, well, if John asked Jane for help, Jane would say no. I might jokingly say, well, actually, if John Ross Jane felt today, it would be because there hadn't been a quarrel and you would laugh, wouldn't you? But you wouldn't take it seriously, because we can all imagine situations where it was true that despite the quarrel, Joanna had asked Jane for help.

But they all involve situations that are so emotionally tearing or, you know, if something had happened that meant that John's child was her life was hanging on a thread and the only person who could help would be Jane. She would ask John the fact, Jane, for help, wouldn't she? Despite the quarrel. But so none of these situations involve the quarrels not having happened. But others have asked why?

The fact of a asymmetry of over determination should lead to our determining it's not rational to act with past ends in mind. So I thought you'd like to do this little Newcome problem. Some of you may know it, but the rest of you, OK. There are two boxes and this one is transparent. I know it doesn't look it, but it is. And that's why you can see that inside it. There's a thousand dollars. This one is opaque. You can't see what's inside that. But luckily, I can tell you that.

In a minute, you're going to be asked to choose whether to take just one of these boxes or to take both of them. And that and an infallible predictor. Somebody who knew which you were, which choice you are going to make has put either nothing in that box. If he reckons you were going to choose both boxes or a million dollars, if you thought you were just going to choose that box. So which is going to choose. Both boxes. Put your hand up if you're going to choose.

Both boxes. So shall I go over that again or is it clear? Yes, I will. OK. So you've got two boxes, one transparent. You can see there's a thousand dollars in it, one opaque, which is either empty or half a million dollars in it, depending on weather and into an infallible predictor. Reckons you would choose just this box or the two boxes. And he thought, okay. So looking at Mike, isn't it? Mike's going to choose one box that just this box.

I'm going to put a million pounds in it. But what's your name? Adrian is going to choose both boxes. I'm going to put nothing in here. Okay, who's going to pick both boxes? Hands up so I can see. OK, who's going to pick just the one box? Just the opaque box. I'm the one box or two. OK. So, so relatively easily, evenly divided. Those who would pick the two boxes. Why would you pick the two? What's your justification for picking the two? Can anyone tell me. Mm hmm.

OK. So you're going to if you buy picking two, you get a thousand dollars, whatever happens. And if there's a million pounds in here, you're doing even better. OK, minus. So you take my money. No, no. That one's going to have a thousand dollars in it, whatever you do. Say that was that you must pay about. No, no, that's not. In this one, there's either nothing or there's a million pounds. Oh, I see. You're changing the experiment. I'd have to think about that.

OK. Those of you who say that, you would only pick one. What's your reason there? Because I notice that if I it must be predicted. It's okay, because you your what do you want to do is provide evidence to yourself that the infallible predictor didn't predict that you would pick the only one. In which case they'll be a million pounds in it. Why the two boxes? Why didn't you go along with that? What makes you think that in picking both.

There might be a million pounds in there rather than nothing. Oh, right. Well, forget you. Are you saying the invalid. If you want a million dollars. If he thought you would pick only that box, he would have put a million pounds in that box. Whereas if he thought that you'd pick both, he would put you trust the concept. Yes. Because, I mean, the interesting thing about this is, that's all. So you'd you'd have both. Okay, so you have both boxes, your two Bokser.

Okay. The thought is here that when you're actually making your choice, it's too late, isn't it, that whatever has happened has already happened. So you should. If we're right that we never think of doing anything to affect the past, there's nothing we can do at this point, in which case we may as well take both. That's the thinking. And that's why Lewis says he would take both.

But the rest of us, those of us who won boxes, have a slight sneaking suspicion that actually by taking this box, we can make it to have been the case, that the infallible predictor will have predicted that we would choose that one. And so he would have put a million pounds in it anyway. Possibly you might. So you're free. I don't need to bring free will into it. Yes, she took up the whole point of. My prediction is infallible. And there's probably 10 pounds in there.

Yes, that's why you would choose two boxes, presumably, so you don't lose anything by choosing two boxes through your speech. Yeah, but I assumed that's what you were thinking because that's what a two boxes would think. Assuming your table say sorry. So Soskin experiments are. No, I don't think they're grounded in reality, it's. Yes, actually, I have one.

I mean, you there's some description's is this experiment to have an almost infallible predictor and others have an infallible predictor, but almost infallible is probably better for the reason that you're saying. OK. Because if it's infallible, he would have known that you would choose only that one. Yep. OK. So. Oh, sorry. Got not done that. So Lewis says that you should take both boxes. And then he believes that our rational deliberations are determined by the asymmetry of over determination.

But if we realise the infallible predictor would have known that we would choose the single box, then. Those of us who would choose the one box would say it's not irrational to choose the one box, there's a good reason for doing so. So all rational deliberations are not guided solely by the asymmetry of over determination. Now, I'm happy if you ask lots of questions about that later, because I'm not sure I entirely understand how the how it works here.

And I'm still I'd like to have given a lot more thought to that before doing the essays. So if you want to ask questions about that, we can work it out together. But let's go on to the sixth question, which is, should we accept Lewis's account?

So we've looked at what Lewis's account is. So he says that the reason, the causal asymmetry and the temporal symmetry are aligned is because both are determined by the asymmetry of over determination and that the asymmetry of over determination is a contingent empirical asymmetry, possibly relatable to the asymmetry of entropy, which is an objective fact about the world in which we live. And it's quite consistent with there being simultaneous and backwards causation.

And it's it explains at least some of our rational choices. So. Well, Adam Elgar and all the references are, again, on your handouts. Where are your handouts? Are they. Have you gotten Doug? Oh, no, well, wait until the end. So Adam Elga thinks that convergence miracles needn't be large and diverse. So if you remember, Lewis's account depends upon an asymmetry of miracles. It depends upon the idea that miracles that caused a divergence can be small, very small.

Whereas miracles that cause a convergence must be big and diverse and wide spread. Well, Adam Algorithm, in a rather very interesting paper, argues that actually they needn't be large and diverse at all. It depends upon the boundary conditions. And if the boundary if the boundary conditions change just slightly, you could actually get a reconversion miracle. That's very small as well. I recommend you to read that paper.

If you're a physicist and really want to know what I'm talking about here, because that will tell you what I'm talking about. But Price and Westlake show that that just needs to shows that we need to set boundary conditions.

If we relate the asymmetry of over determination with the asymmetry of entropy, and we need to say that we should only consider those possible worlds in which the boundary conditions are as we think the boundary conditions must be in this world, i.e., we started off many, many years ago at the beginning of our universe with a state of very low entropy. And this is called the past hypothesis. And.

According to Price in Westlake, if you assume that the asymmetry of over determination is constrained by the past hypothesis, as the asymmetry of entropy must be constrained by the half past hypothesis, if it's to deliver our experiences, then you get a very nice link between entropy and over determination. They also think, however, that unless we build in the asymmetry for a rational of rational deliberation from the beginning,

we'll never succeed in getting it. They actually think that all these asymmetries are subjective. In fact, that fundamental physics is absolutely right. There is no asymmetry at a fundamental level in the world. And the symmetry sorry, the asymmetry at the macro level is entirely subjective. And there are physicists. This is for you. There are physicists and philosophers and there are references on the sheet who believe that time isn't real and perhaps at the micro level it isn't.

What does this tell us about its reality at the micro level? Perhaps these two are right to think that actually all these asymmetries are entirely the result of our perspective as rational agents on the world. Okay. Oh, sorry. There's someone else. So Matthias Frist, Fresh, believes that temporal asymmetry depends on causal asymmetry rather than the other way round. So, again, you can have a look at that. I haven't considered his view at all.

So. We've got courtroom now, which you can tell me what you think. And just to say we've examined the alignment of the course, Laro and the Temporal Arrow. Next week is the last week of these lectures. And we're going to be looking at mental causation and whether causation when it comes to mental states is different from causation in the physical world. Oh, I still give voice. Just. Bob. Right. I'm go back to the forest for better.

I can see the good lighting, the camper, lighting the fire, causes the forest fire and causes loads of pieces of evidence to be around a year later. Yeah. Which are caused by those we might call the effects. I can see the forensic scientists will be able to focus on any number of events independently without the others and say this effect shows conclusively that the fire started when and where it did. But I don't think anybody in normal English. Would say that those effects.

Were the cause? No, nobody's saying that the cause, see? In that case, let me say. Well, that's a purely yes. OK. Well, perhaps you could say they were the. I why wouldn't you say it's the cause. Answer because you think causes come before effects. Because I think it's just not the use of the word cause. We would say that there is. There's absolutely no doubt that you wouldn't say cause you'd say that they are they are the reason why I believe.

Whereas the writing was. Was the reason why it happened, not the reasons the police. And it's not only because the word cause you you would use cause here. So. Sorry, I should have two things here. I'm going to run out of paper. Crosswords getting. Hang on, let me just draw things as I want to draw them. OK. The camp fire cause is a sufficient condition of the forest fire caused the forest fire and the forest fire caused the traces that the forensic scientist is able to trace back.

And what you're saying is that you're happy to use the word cause here and indeed here. Yeah, but what you won't use is cause here. Not. I mean, so the traces of the fire didn't cause the fire. And you you assume that that's what I'm saying. Bearing in mind that the laws are deterministic. You could say this caused it to be the case that that. But I agree we wouldn't usually do that. But can I say that Trace A is a necessary part of a minimal sufficient condition for there having been a far.

So I'm not using the word cause. It's a minimal a sufficient condition for there to have been a fire. Sorry. It's. Who should have put is a necessary part of a minimal sufficient condition for there to have been a fire. None. What, it's a minimum, yes, it is. It's a minimal whatever you just said. Compassion for empathy for our believing that there was a fight. Well, possibly FXE. It's. I mean, I'm trying to keep our beliefs out of this, if you like.

I mean. I'm looking at the relation between this trace trace, a underfire, and I'm saying that trace is a necessary part of a minimal sufficient condition for there having been the fire or for that to have been the fire. So I agree that we are using the word cause here. It feels all wrong. One condition. Well, can I leave you to think about that? Because obviously you don't find nothis as worrying. And you might ask yourself, why is the secondary?

They would call these the initial and secondary causes, it could have caused the initial cause and those others going to traces as the secondary causes of the campfire. Yes. The fire, not the. Oh. Would have been the initial cause. But if my should be more low to have the camp fire not spread to, say, containers of, I don't know, butane gas that he got for cooking, that would then have blown the thing much wider and actually caused the total forest.

So forensic scientist would look at them as initial primary causes. This is where they were caused. And then second coastline, but maybe yes. But but that doesn't response to Bob's point because he is happy to allow that causes can be in the past and have effects in the future. That causes in the past can have effects in the future. What he's unhappy about is what he saw as my surge, suggesting that there are causes in the in the future of things in the past.

And I hope that I've put in slightly at ease by saying that we don't have to use the word causes here. We. It's certainly true that the camp fire would have itself had lots of effect that combines to produce the forest fire. And those would be secondary causes on your yeah, because the ninety five with the primary indignation. Yeah. Yeah. But then several other things happened. Yeah. And the fire was no longer contained. It went wider and went into a forest fire.

Yeah. The fire started. It was just a campfire. Yeah, yeah, yeah, no, I see exactly what I mean. But something you just say. Yeah. I mean, what's your job? The secondary causes are in here, aren't they? Yeah. Well, the camp fire caused the secondary causes. And then the secondary causes combines to to cause the forest fire. Yes. Sorry, say again this. The secondary causes your meaning. The factors that contributed. Oh, OK. So things like the butane gasping there.

Okay. So so they were just okay. There was a whole context within which the campfire led to the forest fire. I mean, that doesn't go against anything I've said here. I mean, we've always allowed that when you strike the match. The match only causes the lighting of the flame if there is oxygen around. There's always a context within which, of course, has its effect. The tree friendly fire also means many conditions.

Yeah. I guess you can say asymmetrical because there are trees not just to the fire. Okay. There's no easy. Well, if you don't think there's any asymmetry, then you will agree with Elgar and you might read his paper because he he also disagrees with Lewis that there is an asymmetry of well, that there's an asymmetry in miracles and therefore an asymmetry of over determination. Chris, very. In fact, physics may well require as a condition.

Quantum mechanics, however, are much less happy about the suggestion that, as I understand, the effects occurred before the cause. But could causation? Well, nobody's saying that it can. All we're doing is is leaving the possibility open. If we. So if I'm going to tell me. But the man in the street believes that can't happen. We need to take and Louis' Count does take account of that, what what he's saying is that there typically. So if I go back to the slides where I'm considering that.

OK. So does he permit the possibility in principle of simultaneous and backwards causation? All he's saying is that it's typically the case that causes come before their effects. There might be cases in this world. He's not saying there are cases in this world. There might be cases of simultaneous and backwards causation in this world and there might not. And there are worlds in which there is cases of simultaneous causation.

There are also worlds in which there are cases of backwards causation right from the very beginning. It is human that's given us the idea that the word cause means comes before in effect. Well, well, no, because the thing is you do. It's certainly true that our experience tells us the causes come before effects, but that's consistent with everything that everybody said. But we do wonder about time travel. We do wonder about.

And I'm wondering about time travel, where we're postulating backwards causation. But I'm right. I'm not like a philosophical argument that denies. Backward causation. You're not getting this you could all this argument is saying is that in principle then might be worlds out there and it might not be this one in which there is backwards causation in which an an egg might sort of uncork itself and leap back into its shell.

But they're not saying it's this world. Do you see, I mean, there's a very it's a very important point here where what Lewis is doing, I think, is making sense of the eye of why lots of people have thought the backwards causation might be possible. Another people of thought, simultaneous causation might be possible. And he's allowed us to do that, whereas Hume doesn't. Hume just rules it out a priori. David, we see lots of things niggled me about it. Gone is the verdict rational?

Was he just omniscient? What presumably is rational as well. Because he said he was acting for reasons, isn't he? He's easy. He's just the sort of peculiar machine whose actions are determined by the position of it goes through the slit. Well, we've got to right into the thought experiment that he puts a thousand pounds of sorry, a million pounds into the opaque box.

If he believes that you're going to choose. Just so he's acting for a reason, he's put the thousand million pounds in there because he believes that you're going to choose that box only applies to charities. You. I'm not sure I'd call it a principle of charity. He has views on the choices that you will make in the future. He believes that you will choose two boxes, but you will choose only one.

And on the basis of his belief that you will choose two boxes, he's going gonna put nothing in the second box. And on the basis of the fact that you against choose both boxes, No. One box, he's going to put a million pounds in there. Is he generous? Was he trying to make it? He's trying to confound you all on me. He's probably quite predictable on an individual basis, but he's making this individual prediction.

Oh, it would have to you know, it would have to be for for one particular person, one choice and one choice of that person. Because, I mean, you might having chosen one way the first time might think something solid. Going to choose the other way the next time. Because I know. Do got it. Oh I see what you mean. I'm sorry. I shouldn't either. By choosing the box I'm trying. You can't influence sets. No, you can't influence it.

It's already done. The choices already be made as to whether there's a million pounds in there or nothing. But what you're trying to do is provide evidence for his having chosen. Yes. To put a million pounds in there. Doesn't your rationality determine how he's going? Yes. Yep. Yep. I mean, that's why it's a game theory problem. But he knew what you were going to choose.

I mean, when you write that in, you've immediately got a situation that isn't like any situation you're actually going to have. Well, he's omniscient and rational, isn't he? I'm not convinced he's not just on this. OK, so you think it's what? I'm just not convinced that it isn't a case of an exercise in risk on both sides. Well, it is your risk. I mean, if you choose one box, you're risking losing the thousand pounds thousand pounds.

If you choose both boxes, you're risking losing a million pounds. I. I mean, how can he. Sad. Oh, I see. Well we've just written that in the game. Well yes, of course. Because you're allowed to do that. The thought experiment. I said there is a question of whether he is infallible or almost infallible. I'm saying that I think it's a risk assessment. So why I don't think we'll have to assume that it's not his million pounds.

Unlike your assumption that it is his million pounds, maybe he's spending other people's money.