 Okay, so hello. Good morning to each and every one of you, so welcome to this edition of Philosophy and What Matters, where we tackle what matters to us from a philosophical point of view. I'm J.J. Joaquin, a philosopher here at De La Salle University, and with us is our good friend Alan Hayek. Our first discussion will be on counterfactuals. So what are counterfactuals? So think of it this way, I might have, I would have been in Canberra right now if had it not been for the pandemic, you would have been in some other place had it not been for this Zoom interview. But what do we mean by those things? So may I present Alan Hayek, a professor of philosophy at the Australian National University. He will be a guide in tackling this particular question. Oh, by the way, Alan and I have been friends for 10 years now, so let's start. So what are counterfactuals, Al? Okay, now to start, think of them as sentences, and in English we typically express them using the subjunctive conditional form, you know, if it were the case that A, it would be the case that B, you know, Hillary Clinton nearly won the presidential election, but she didn't, you know, perhaps she would have won if there had been no Russian influence, okay? If there had been no Russian influence, she would have won. There's a counterfactual. She'd campaigned harder in certain states, she would have won. There's a counterfactual. And presumably, you know, her regret about the election is informed by such counterfactuals. So first think of counterfactuals as sentences that we typically express in English in the subjunctive. In fact, I want to ask you, the interviews going in both directions, whether Filipino has the subjunctive form, and do you express counterfactuals in a parallel way, the way we do in English? No, I think so, because our conditionals actually are in counterfactual forms. So our anti-seedant part are already in the negative formulation, and we're thinking about the consequence in terms of that, anti-seedent. So then that may be, good, thank you. So that maybe brings me to the second important thing to bring out, a distinction between counterfactuals and so-called indicative conditionals. And again, in English, it's easy to bring that out, and I'll ask whether the same is true for Filipino. Okay, here's the classic pair of cases. Counterfactual. If Oswald hadn't shot Kennedy, someone else would have. That seems false. Unless you think there was some conspiracy, and there was a backup gunman and something, that seems false. Okay, that's the subjunctive. Indicative. If Oswald didn't shoot Kennedy, someone else did. Now that seems clearly true, because we know someone did, and there's some controversy over whether it was Oswald. If Oswald didn't do it, then someone else did. That's the indicative. And notice how in English the mood changed. I switched from the subjunctive to the indicative to capture this different flavor of the conditional. And we sometimes say that the indicative corresponds to a sort of epistemic conditional. It's to do with your state of information. Counterfactual, by contrast, is supposed to be worldly. It's supposed to be about how things are in the world, maybe it's dispositions or it's laws of nature. It's a modal notion that we're attaching to the world itself. So that, I think, is the good setup. Okay, so there's a distinction between indicative, what we know so far about the world, then you have the counterfactuals, which are facts in the world, and we're playing around with those facts when we think about counterfactuals. Well, we're imagining, we keep fixed certain facts about the actual world, and then we're entertaining certain changes to the actual world. And what would ramify from that? And the game here is to try and work out, like, what do you hold fixed? Because we don't, it's not just like complete chaos reigns, you know, it's not like anything goes, you know, if Clinton had campaigned harder, she would have been a unicorn, you know, there's, we're constraining how you think about these hypothetical situations. But we do so in a different way to the way we do the indicative conditionals. Yeah, so that's the sort of setup. That's the sort of beast that we're trying to... To understand here. Okay. And it's quite a beast. I mean, there's been a history, like, going back to the ancient Greeks, they even worried about conditionals. And even the even the crows on the rooftops are crowing about which conditionals are true. That's what Calomacus said. And you had the old Stoics like Chrysippus and Diodorus worried about the truth conditions for... For conditionals, right, right. So this has been... This study has been going on for, well, millennia now. How about contemporary philosophers thinking about this? So who are the people here? Yeah, so interestingly, I would say there was really quite a long gap, like a couple of thousand years. It didn't work much on conditionals. And then there was a revival in the 40s with people like Goodman and Chisholm. And, for example, soon after that in the 50s, Goodman's fact fiction and forecast had a central chapter on counterfactuals and the problem of giving truth conditions for them. And then I would say that the heyday, well, first of possible worlds semantics came soon after that, especially in the 60s, thanks to especially Kripke's influence. And then I would say the golden era of study of conditionals. And now let's focus, especially on counterfactuals. That was starting in the late 60s, this classic debate between Stoenacker and Lewis. We'll talk about them more in a moment, I'm sure. And Stoenacker had a classic paper, a theory of conditionals. And then Lewis's classic book, Counterfactuals, offered a sort of rival theory to Stoenacker. And then that was the golden era of counterfactuals. Now, let me also add, as you know, Lewis was one of my PhD supervisors. I know, I know. Which was fantastic. He was told, okay, so, and I'll say something, go ahead. Yeah, so I remember you telling me a story about David Lewis once you were accepted in Princeton, right? He called you, he got home and he said that, hello, Al, Alan Hoyer. You've been accepted to Princeton. Is that the story? Did I get the story? Well, that is the story. Can you imagine this moment in my life, you know, I've been on applied to Princeton. And, you know, I was fast asleep. It was early in the morning for me on Saturday morning in Melbourne. He was in Princeton Friday night. And he called me and this was just a life changing moment. That's a long story, which we could tell later. But yeah, that was my first meeting with Lewis. And he was tremendously influential on me and, you know, a wonderful supervisor. And he told me regarding counterfactuals, the reason why he wrote that book, and he wrote these classic papers about counterfactuals, in a way it was not first, because he wanted to tell us about counterfactuals. He wanted to give an account of causation. Oh, right, right. He wanted to give a counterfactual analysis of causation. And he was concerned that people would think, well, hang on, counterfactuals are not on secure footing. That's a sort of shaky foundation for causation. So Lewis felt pressure to firm up the foundations, namely to give this rigorous analysis of counterfactuals. And then he felt free to go on and use them in the analysis of causation and other things. Very interesting. That was his order of thought. And that's what motivated him. So he's starting with causation first. He's starting to figure out what cause and effect relations are. Then he figured out that, oh, I could analyze this in terms of counterfactuals. Is that the thing? Yeah, yeah, that's right. He needed the notion of counterfactual dependence. You know, if the cause hadn't happened, the effect would not have happened. Would not have happened. Notice, that's how we use the counterfactual there. And they both happened. And causation involves chains of counterfactual dependence in his early account. So he needed to shore up the account of counterfactuals. And notice, by the way, and I'm sure we'll talk about this soon, in his analysis of counterfactuals, he talked about possible worlds that were key to understanding counterfactuals. And there were worries about possible worlds too. Even though they'd been appealed to in these very semantic theories, it wasn't clear what they were. And so he went on later to write this classic book on the plurality of worlds. Defend the possible world's view. Before we get into that, let's go back to counterfactuals again. So why do counterfactuals matter? Why should we think about them? Yeah, so many reasons. For a start, we as philosophers care about them. In a way, the analysis of causation from Lewis, that was just part of, again, this golden era of counterfactuals. And people just started analyzing all sorts of things. And they still do in terms of counterfactuals. So just think of how all the things that we hold dear that philosophers whip out the counterfactuals to understand. So I said causation, the perception, knowledge, personal identity, laws of nature, rational decision, like causal decision theory, confirmation, dispositions, free action, explanation, the direction of time, and so on. So counterfactuals keep on being implicated in these other things. So that's the first answer that we as philosophers care about them. It's not just philosophers. Science traffics in counterfactuals, sometimes explicitly, like in drawing out consequences of its theories. For example, I just looked up, there's a physics textbook problem. If you were to drill a hole all the way through the earth, and then jump in, how long would it take you to get to the other side of the earth? And what would happen? And the answer is you become this harmonic oscillator. But anyway, notice how I said it in terms of a counterfactual. You know, if you were to drill this hole, how fast would you travel? How long would it take? So science appeals to concepts that are maybe tacitly counterfactual, for example, dispositions. And then, you know, social sciences, counterfactuals are earning their keep in history. You know, what certain thing happened, what would have happened, you know, for subsequent history, if it had been otherwise. We mentioned regret with psychology. By the way, a bit of personal psychoanalysis. I think the reason why I'm so fascinated by counterfactuals, and one reason why I want them to come out mostly false, is I'm so prone to regret. You know, I'm prone to regret. And what informs regret are usually counterfactuals. You know, if only I hadn't done this blah blah thing, things would be better. You know, I would be happier or whatever. I regret that I did that thing. So you're psychologizing the thing here. Yeah, yeah. Counterfactuals are really important in our psychology in that respect. Regret, relief, relief likewise. You know, oh, I'm so glad that, you know, there were no problems with our Zoom connection now. You know, if we'd had troubles with the Zoom, this would not be going smoothly now, but here we are, it's going smoothly. That's relief expressed in terms of counterfactuals. So, you know, a lot of our mental economy is used up. Yeah, using counterfactuals. So that's why we should care about, so yes, as your nice slide says, why does this matter? I've given you several reasons why it matters. No, so let's go back to the sciences first. So we know we are in a pandemic. So modeling is some sort of counterfactual, if you think about it. So what would have happened if we have set the conditions in the following way? Is that the same thing? That's a good example. That's right. So I'm hearing a lot about these coronavirus models. You know, if we were to, you know, lock down things to this extent, what would be the effect if we went to not lock down at all, if we were to make no changes? For example, they said in Australia that if there had been no intervention, and notice the counterfactual, there would have been about 20,000 Australian deaths by now. In fact, there's been roughly 100. And so that's supposed to indicate the efficacy of government's interventions. You know, the lockdown is a good thing, is the claim, because things would have been so much worse if we hadn't intervened. Yeah. Okay. So yeah, so counterfactuals are involved in our reasoning about many things. So how do we understand counterfactuals? Let's go to the theories of counterfactuals. Excellent. Yes. So how do you analyze counterfactuals in a philosophical way? Great. So maybe I'll start by saying how not to analyze them. And then that'll give us a bit of motivation how we should do it instead. So here's the first thing you might try. Now, if your students have done a bit of logic, then they probably know about the so-called material conditional. So that's the analysis of if, then, which has a truth table. And the truth table is very simple. It's true on every line, except where the antecedent is true and the consequent is false. And by the way, I hope everyone's clear on this terminology. The first part of the conditional, if p, the first part is the antecedent, then q, q is the consequent. And I'll be using that terminology a lot. So the truth table for if p, then q, the so-called material conditional, is true in every case except where you have true antecedent almost consequent, p is true, q is false, and that line is false. Now, why am I saying this? It follows from that that counterfactuals, namely cases where the antecedent is false or presupposed to be false, the paradigm cases, would come out automatically true, all of them, on this analysis. And that seems wrong. If there had been no Russian influence, Clinton would have won true, because there was Russian influence, we're imagining that's the whole point. Maybe that one's okay to come out true. Maybe that's what one thing she's upset about. But if there'd been no Russian influence, she would have been a unicorn, true because it's false that there was Russian influence. And whatever you like, stick in the consequent, all of those things would come out true on the material conditional analysis. And that's crazy because counterfactuals presumably are more discriminating than that. They don't just vacuously go true just because their antecedents are false. So that would be a bad analysis. So we don't use material conditionals to analyze counterfactuals? Okay. That's right. Now, something else you might try. Now I'm going to introduce a bit of modal logic. You might say the material conditional, it mustn't just be true. It has to be necessarily true. And we symbolize that with a box to the operator out the front. So you might say the truth conditions are necessarily and then the material conditional. And I actually like that analysis. Maybe later on we'll talk about that. But anyway, the first worry that people have about that is now you have the opposite problem, it seems. Now most counterfactuals will come out false because it's very hard to make this necessity claim true. Basically, it's saying all of the P worlds are Q. All of the worlds where P is true are worlds where Q is true. And that's very demanding. Okay. That's the thought. Okay. So then now we finally get to the positive theories which are, you know, more orthodox where the conditional, the counterfactuals sort of somehow intermediate between those two things. It's not the material conditional. Supposedly it's not the strict conditional as well. Right. It's something in between. So we need to talk about that. Now, I need to say something about possible worlds. Is now the right time for me to do that? Yeah. Before that, I'll just summarize. We want to analyze counterfactuals. We need to understand them. So one bad suggestion, one bad analysis is in terms of material conditionals. Because counterfactuals would turn out true. True. Too easily. Yep. Too easily. Then another bad analysis is in terms of strict conditionals. So you have the modal operator in the conditional. Because, well, no counterfactual will be true in that. Very, very few. And that's the orthodoxy. I actually like that account. But yes, that is what people normally yes. So we want something in the middle that we could capture to some true counterfactuals. At least we, intuitively we suppose it's true counterfactuals. And we rule out some false counterfactuals as well. So we need that middle ground. Yeah. The sweet spot in the middle. Okay. So let's go to the analysis. The standard analysis of counterfactuals now. Good. That's right. And it is typically presented in terms of possible worlds. And I should just say a little bit about possible worlds. And then we can give the analysis Stornacker and then Lewis. Possible worlds, that's a topic in itself. We could go for hours just on them. But think of them as ways the world could be. Now, we know one way the world could be. It's the actual world. Here it is. But the world could have also gone some other way. Clinton could have won the election. She didn't. The actual world she lost. But in other worlds, we can imagine, she won. So think of possible worlds as ways the world could be. Could have been or could be. Now, you might sort of think of them. They're a little bit like lines of a truth table. You know, here are different combinations of truth values of the key components. Okay. But for various reasons, it seems worlds are richer things than that. People sometimes think of them as maximally consistent sets of sentences. I think I'll just fast forward to Lewis because we want to talk a lot about Lewis. His famous notorious account of possible worlds is that they're concrete. They're real. Just as real as the actual world. They're not just adding concrete things. They're not just abstract objects. But they're spatio-temporally isolated, causally isolated from each other. There is a world in which Clinton or, as he would say, a counterpart of Clinton won the election or the counterpart of the election. We can't get there from here. There's no access. No access. There's no spatio-temporal but it's out there, so to speak. It exists. It's just as real as the actual world. All that's special about the actual world is that we are in it. It's this sort of indexical analysis that it's like here and now. It's actual. But it could easily be different and for other people it is. So that's his modal realism, as it's called. And he defends this modal realism in a few ways. But the main way is he calls it philosophers' paradise. If you just spot him as plurality of worlds, then a lot of benefits, philosophical benefits, follows. Now you can give elegant analyses of various things like propositions or properties, mental content, as we will soon see counterfactuals, so he will claim. So he says that it's a little bit like believing in numbers in mathematics, cantors, paradise. You should believe in numbers because when you do, you get this beautiful theory and if you believe in possible worlds, you get this beautiful metaphysics. Right. You get beautiful metaphysics and it handles all sorts of problems. I'll quickly just mention a couple of or maybe three famous objections to Lewis's counterfactual realism. Okay. Then we'll move on. There's what he famously calls the incredulous stare. Like, what the hell are you talking about? What do you mean? In fact, just to emphasize how strong his modal realism is, it's not just that there's one or two other worlds. There are infinitely many other worlds that really exist. In fact, it's a big infinity too. That's another topic. It's like a huge ontological commitment. The incredulous stare is basically, come on, common sense doesn't countenance the reality of these other worlds. There's only one world. Here we are, the actual world, and this is just a way of speaking. Then there's sort of an epistemological problem. It resonates with a problem that Benaceriff raised about in mathematics. You might say, in order to know about something or to have rational beliefs about something, you need to be causally connected to it. But remember, I said a moment ago that Lewis individuates the worlds by their internal causal connection, but they're isolated from each other. You can't get there from here. You can't send signals to another world. You might say, hang on, how could we ever get to know about these worlds if they're causally isolated? Right. But here's a brilliant reply, I think, in another connection. That principle seems to overgeneralize. If you say you can only know about things if you're in causal connection to them or that they have causal effects on you. I see where it is going. Here's a great, I think, counter example. Think of the whole of history, like all of space-time and all events in it in the whole of history. We believe in that. There is such a thing as that, but it has no causal connection to us. No causal connection to anything. Right. It's entire you. All causation happens within it. So that's a good case or something that it seems we should believe in, but not because we're causally connected to it. One last problem, and then we can move on. Krypti had this famous argument from concern. His example concerned Hubert Humphrey losing his election, but we could make it Clinton just as easily. As I said, Clinton has a regret. She wishes she had campaigned harder in Michigan, blah, blah. Now, Krypti's objection is, well, but the object of Clinton's concern is not a counterpart in some other space show, temporarily, causally, distant, remote, unconnected possible world. What she cares about is here and now. Her concerns, yeah. In the actual world. So how bizarre that according to Lewis, the object of her concern is this causally remote individual that looks like her right exactly. But again, there's I think there's a really strong reply to that objection. Well, okay, that might be a worry for, for, you know, the modal realist account. It seems like it's even a bigger worry for the alternative accounts like, you know, where a possible world is some abstract object, like say a maximally consistent set of sentences. It's not like Hillary Clinton is concerned about some abstract object, you know, maximally consistent. That's a good one. Yeah, that's a good one. If this objection is any good against Lewis, it's even stronger, I would have thought. Against the absolute, those who really in abstract are right, right. Exactly. That's it. So, okay, that's the setup. So JJ, I think we've set up the sort of position nicely. Now we can finally give the analysis of counterfactual. Okay, so let's get into that. So just a summary. So counterfactuals, we want to understand them. And one way of thinking about them is in terms of possible worlds. Yeah. Yeah, you have given Lewis's position modal realism that, well, those possible worlds are concrete objects. They exist, but they're costly isolated from each other. Now, let's set aside the metaphysics, the metaphysical concerns about possible world. Now, let's use it in understanding counterfactuals. Let's start with Bob Solnaker's theory. Perfect. Yeah, excellent. So Al, do you know Bob personally? Yeah. Oh, yeah, sure. Yeah. Okay. Can you tell us something about him? Oh, terrific guy. I got to know him fairly well a couple of ways. I had a visiting position at MIT for a while. And he was, of course, there and, you know, a central figure in the department. And I especially got to know him better. I taught at this Budapest summer school on conditionals. And he was one of the professors there. And that was a wonderful time. One of the highlights of my academic life, actually. And various people were there. Jason Stanley and Barry Lowe organized it. There was Angelica Kratzer. The linguist. Yeah, sorry. The linguist, Angelica Kratzer. Yes, yes. That's right. And earlier, I should have probably mentioned her as well, you know, in the history of the study of counterfactuals and conditionals more generally. I talked about philosophers. But there's been an Edgington who I also just mentioned now in Budapest was also important. And we might come to her views later about no truth values and a probabilistic account. But linguists like Kratzer have been very important in the study of counterfactuals and conditionals generally as well. Von Fintel as well. Anyway, so Stolack, he was one of the people at this summer school. And it was great to get to know him better there too. Okay, so his account, I think we're ready. We've introduced possible worlds, but we need one other notion, a notion of closeness of worlds. And I'll maybe try and convey that intuitively, and then we can maybe get more rigorous about it. Intuitively. So take something that's true of the actual world. So my example is, I'm not really up to speed on, you know, who's cool in music these days. By my example will involve Britney Spears and, you know, she had this song Whoops I Did It Again. That's so 90s. It's so 90s. I'm sure that dates me, doesn't it? Oh, yeah. Britney Spears made famous this song Whoops I Did It Again in the actual world. That's true. Someone else could have. And we can imagine more and less sort of similar worlds accordingly. So for example, Madonna could have made that song famous. And that, so to speak, that doesn't involve a big departure from actual history. That's fairly similar. Frank Sinatra could have made it. That's not okay. How about me? Maybe I could have made it famous. Well, that's getting a bit more bizarre. You know, I'm not a great singer and I'm not a famous singer. But okay, yeah, I suppose I could have made that song famous. One of my dogs, you know, Laddy. Laddy could have made it famous. Hang on, that's getting pretty, pretty bizarre. You know, this desk that I'm sitting at could have made it famous knowing now we're really getting bizarre. You know, an electron could have made it famous. Okay. Number 17 could have made it as famous. So somewhere things started going pretty crazy. And eventually, I think we're shading off into impossibility. But along our route there, we were considering more and less similar ways to the actual world that these worlds could be. Okay. Now, so in that sequence, for example, I had, you know, Madonna making the song famous. That was a fairly close possible world. It wouldn't require much of a change to our world to have her making it famous. And Frank Sinatra, fairly close. And then it started shading off more and more bizarre. Okay. So we let's just start with this intuitive notion that we have a sort of ordering of worlds according to how similar they are to the actual world. Okay. Okay. Now. And finally, we can state intuitively Stolackers theory. If it were the case that A, it would be the case that C, A for antecedent, C for consequent. That's true if and only if C is true at the closest A world, the closest world where A is true, or as we might say, the nearest or as we might say, the most similar world where A is true. And now we can also relativize that to a particular starting world called it W. Okay. Now, it's always good to have a picture. I don't exactly have a whiteboard here, but I can, I can draw a picture. I don't know if you'll, you'll see this, but if I, if I draw like this, do you see me? That's meant to be a line. Yeah. Let's put the actual world, let's say there, and that's the little symbol for actual. And now we're imagining worlds ordered, as we might say linearly, according to how similar they are to the actual world. And so in my, in my example, you know, a fairly close world, say this one, Madonna, Madonna, and here's Frank Sinatra making it famous, and here's me, and, and it gets more and more crazy. So Stolack is basically saying, if you want to evaluate A, and here's the symbolism, box arrow C, I think you can see that. Yeah. Starting at the actual world, you go to the closest A world. And I mean, let's imagine it's here. And then ask, is C true at that closest A world? If the answer is yes, then the counter true. If it's false, then it's false. Okay. So you look at the closest world where the antecedent is true. Now, so that's, that's the view. Now I should quickly get to a couple of objections to it, but did you want to stop me? Yeah. So, yeah, my question is first. So I'm thinking about Stolnaker's theory. So there's a kind of ordering of worlds. Yep. The similarity relation or the nearness relation is determined by how close the possible world is to the index world or the actual world in our case, right? So the farther away the world is, it's not something that we should consider in our analysis, or it makes a counterfactual false under this analysis. Yeah. You always consider the closest world where the antecedent is true. Yeah, the antecedent is true. Right. If sometimes the counterfactual forces you to go a long way out because the antecedent itself is very far-fetched, but even then, you always try to stay as close as you can to the actual world. Or whatever the world we're considering is, right? So the index world. Exactly. And now Stolnaker does this formally in terms of what he calls a selection function, but I'm trying to convey the intuition. It's something about resemblance to the actual world that we're trying to maximize. Okay. And I want to not only talk to you about counterfactuals, but I also want to share with you some philosophical techniques. And some of them I learned from Lewis himself. And so right now, here's a good one, because I have this other project, what I call philosophical heuristics. Tools of the trade that we use for some reason, we rarely teach them. We teach logic, all these other techniques. Anyway, so here's a good one. In philosophy, if someone gives you an analysis of something, or you know, some claim that involves the word, see the word in neon lights, and watch out for a certain kind of problem. There are two, so the X typically comes with a presupposition. There's exactly one X, the X. Well, there are two ways that could go wrong. There could be multiple Xs, there could be two or three or many Xs. Or, other way, there could be zero Xs, just none at all. Okay, that's two things that you could try. So if someone hits you with an account of something that has the form blah, blah, blah, the X, blah, blah, blah, think, ah, does this account survive objections from these two sides, multiple Xs or none. Okay, so let's go back to the Stornacre analysis, and now I'm going to say it with a bit of emphasis. This will be my neon lights in my presentation. So again, if it were the case that A, it would be that C. That's true according to Stornacre, if and only if C is true at the... Nearest world, okay. Nearest, nearest A world, right. Right. Okay, well, he's presupposing that there's exactly one. There's a unique nearest A world. Okay, so what does Lewis do? He objects exactly, as I said, on either side. He thinks there's a problem on the plurality of nearest A world. So an example of that. If Bisey was French, Verdi was Italian. If Bisey and Verdi had been compatriots, they would have, what, been Italian? Or French. It would have been French, right? Or maybe they could have been Swiss, like maybe they met, you know, in the middle or something. Anyway, so the worry is that there could be multiple closest A worlds, nearest A worlds. Okay, so then this presupposition of uniqueness would fail. Okay, so that's an objection on that side. Now the objection on the other side, remember, was maybe there are no closest A worlds. How could that happen? Lewis has this nice example. Maybe you've got an infinite sequence of closer and closer worlds, but none closest. And here's an example. If I were taller than seven feet, or maybe I need to make it metric, you know, these days. That's all right, that's all right. You can make it two metres. If I were taller than seven feet, how tall would I be? Well, would I be seven foot one inch? Well, that seems like a gratuitous departure from my actual height. A little bit closer would be more similar. You know, seven foot, half an inch would be closer. Seven foot, quarter an inch closer still, an eighth, like an infinite sequence of ever closer worlds, none closest. So there's no closest world, right? And that's the objection on the other side. Right, right. That's, that's pretty cool. So I'm trying to figure out the objection against Solnagor's theory. So Solnagor's theory implies that a hunter-factual is through if and only if the closest A-world is where the consequent is true. That's it. So that's the idea. So the nearest A-world. So the objection will be, again, either the uniqueness of the nearest A-world or the existence of the nearest A-world. Yeah. Yeah, okay. Yeah, that's right. You said it well. Okay. So we're thinking about Solnagor. Does Lewis offer an alternative to Solnagor's theory? Yes. Let's go there. Let's go to Lewis's theory. And it's supposed to take care of these objections. And probably, let's dive into it this way. Here's probably the fastest way to say it. Don't, don't presuppose that there's a unique closest or nearest A-world, antecedent world. Consider all of the closest A-worlds. Okay. If all of them are C, then the counterfactual A would C is true. In all those worlds. Yeah. Okay. That's right. So it's a kind of necessity. It's saying all of these closest antecedent worlds are consequent worlds. Maybe saying it's a little bit more carefully. I'll try drawing another picture. Now the picture is not the line. Let's make another picture. Think of it more like a bullseye. You've got the actual world. By the way, I talked about philosophical heuristics. A good heuristic is draw a diagram. Diagrams are always good for focusing the mind. Okay. Actual world. Now, imagine kind of rings like a bullseye diagram around the actual world, which represent similarity, similarities where there are ties. So for example, I imagined Bise and Verdi being compatriots. There's the Italian way and the French way. And they might be equally close to the actual world. So maybe I could draw it like this. Here is, they're both French. And here is they're both Italian. And what these spheres, these circles are supposed to convey is that they're equally distant from the actual world. Okay. So according to the Lewis analysis, you've got to make sure that all of the closest worlds are antecedent worlds are consequent worlds. And the way he says it, the way I would put it is start at the actual world and start heading out. And you're going to further and further more dissimilar worlds as you go out. As you go on this path, you hit A and C worlds earlier than you hit A and not C worlds. So you hit A and C worlds, like for example, maybe here, before you hit any A and not C worlds, then A would C is true. But that's a slightly harder way of saying that the way I did it earlier, just think of it as all of the closest A worlds are C. And that'll do. Yeah, I think the circles are helpful here. So instead of thinking about it in terms of a linear measure, we're looking at it for multiple dimensions, like from here's the actual world, so here are some other possible worlds. So if in those A worlds C is true, then the counterfactual would be true. Yeah, if in all of them, then the counterfactual is true. Right. So the idea will be we could have multiple candidates for the A world. Right. Yeah. Okay. So yeah, I think that's a nice way of putting it. So how does it apply to counterfactuals? Can we give an example? Okay. So let's revisit. How about we do the Bizet and Verdi one? If Bizet and Verdi had been compatriots, they would have been Italian. Think of that. Okay. Intuitively, that's false, I think, and Lewis thinks, because why Italian? You know, French would be just as live a possibility. Right. And so it is not true that starting at the actual world and going out to less and less similar worlds, it's not true that you hit compatriot worlds and Italian before you hit compatriot worlds and French. No. On the contrary, you hit them at the same time, you know, they're equally distance from the actual world. Okay. So it's not true that all of the closest compatriot worlds are Italian worlds, because some of them are French worlds. Okay. That's the key idea. Now, I don't know if I should start with some of the objections. That case seems to work out pretty well. Some other cases won't be so good for Lewis, I think. No, let's try to figure out first the Lewis idea. So I think there's a move from a wood counterfactual to a mite counterfactual. Excellent. Yeah. I wanted to bring that up. Okay. Okay. Remember, so wood behaves a bit like necessity. It means that all of the closest P worlds, that now P is the antecedent before it was A, RQ, all of the closest A worlds are C. Mite behaves like possibility. Right. And it's an existential quantifier. It says there exists a world with a certain property. In this case, it would be some of the closest A worlds are C. Some of the closest antecedent worlds are consequent worlds. Okay. Right. And then that's the dual of wood. It behaves very much like necessity and possibility in modal logic, you know, box and diamond. Okay. And in fact, Lewis explicitly interdefines them. Basically, wood is not might not. Right. So like necessities are not possible, not. Yeah. That's it. All right. Okay. So as long as there's at least one closest antecedent world where the consequent is true, then that's good enough for the truth of the mite counterfactual. So let's do it for Bizet and Verdi. If they'd been compatriots, they might have been French. That seems true. Right. Right. Which is to say, among the closest worlds where they're compatriots, there's at least one French world. They're both French. Right. Right. Right. Intuitively, that's right. There's also a closest world where they're both Italian. That's fine that they might have been Italian too. But we wanted to get right that they might have been French. So maybe a way of putting it simply is might counterfactuals are very easy to make true. Okay. And I say especially, woods are correspondingly hard to make true because they require all of them. They require this universality, this necessity. And that's more demanding. Anyway, so that's the Lewis, Lewis account. Yeah. So what we're still not thinking about counterfactuals in terms of strict conditionals, right? Right. So excellent. We noticed that we said all of the closest antecedent worlds, all of the closest A worlds, we didn't say all of them will stop. Okay. Now strict conditional, you know, remember that has the form of a box, a modal operator, then the way to understand that is all of the antecedent worlds are consequent worlds. I didn't say all of the closest. I just said all, right? So in that sense, it seems like the strict conditional is stronger because it's it's quantifying not just over the closest antecedent worlds, but over all of them. Now, you might say, well, we can, we can sort of talk of different strict conditionals like we could confine ourselves to just the most similar, the closest worlds. And then then it almost seems like a terminological point. You could say, well, I whenever I say all, I mean all closest. And then it sort of collapses to the strict conditional. The way Lewis put it was the counterfactual, the variably strict conditional. They're strict conditionals in a certain sense. They involve this kind of necessity, all of the relevant worlds, the consequent worlds. But it's variable because it depends on this notion of similarity. Okay. Yeah. Change the similarity relation. And you change which are the closest worlds. And you check which are the true counterfactuals. So, so his thought was that the counterfactual somehow intermediate in strength between the strict conditional. And notice it's definitely not the material conditional where that you only look at the actual world, you know, or all of the actual world to the only one. We have only one world. Is the con is the consequent world that that it's controversial whether that's a good analysis of the indicative, but it's not controversial that that would be a very bad analysis of the only look at the actual world. So Lewis, it has this sort of intermediate view that you look at a lot of worlds, but not all of them. Yes. Okay. So how about impossible antecedents? Excellent. So that's especially relevant here because remember, there was this presupposition was starting with Stornack theory that there was a unique closest antecedent world. And we, we worried about that in two ways. Now, another way that could fail is if there are just no antecedent worlds at all, we forget about closest antecedent worlds, there are none of them. Namely, the antecedents impossible. It's just not possible for A to be true. So there are no A worlds, period. Right. Of course, there are no closest ones. There aren't any. And this is an issue for both Stornack and Lewis. Now, when I gave the truth conditions for each of them, I, I elided over this extra clause that they need when there are no possible antecedent worlds at all. And they both say that the counterfactual just becomes vacuously true. It's like trivially true. If you can't quantify over any A worlds, A worlds, because there aren't there are none. Any, any counterfactual A would see comes out true, vacuously true. It's, it's so to speak true at all of the A worlds, all none of them, as Lewis used to love to say. So it's trivially true that for example, let's give an example. So if I say had two plus two been five, then I would have been in somewhere else. How would you analyze that kind of? So yeah, right. If two plus two had been five, then, well, some things that are intuitively true, maybe true, like mathematics would look a bit different to what we're used to. Right. If, you know, if, if, if two plus two equal five, then I guess two plus three would equal six or something like that. Two plus two's four, two plus two's five, two plus three, six. Maybe that doesn't sound so crazy. But if, if two plus two had equaled five, then, you know, Clinton Clinton would have been a unicorn. That's true. In Lewis's account, in Lewis's account, vacuously true, trivially true, because there are no worlds in which two plus two is five. So at all of them, all none of them, it's true that she's a unicorn and, and not a unicorn and whatever you like. So there's just no distinctions to be made. But, but then some people think that's the wrong answer, namely, it seems that there are intuitively false counterfactuals of that kind. And in fact, I think I've got an example or two here. Yes, Daniel Nolan. If three, if 323 were prime, it would be divisible by two, four, and 16. That seems false. It turns out that, that the antecedent's impossible. It's not possible for 323 to be prime. It's obvious, but it's true. And it seems the wrong answer, that that counterfactual should come out vacuously true. It seems non-vacuously false. Or here's an example of mine that I quite like. Remember Lewis believed that there are infinitely many possible worlds, and they're all real and they're concrete, infinitely many. And that, that's a key, key part of his, his book on the plurality of worlds, his whole metaphysical picture. Okay, consider this counterfactual. If there had, if there had been 17 possible worlds, Lewis would have been exactly right in his theory. That's surely false. The whole point, his theory is that there are infinitely many. He argued about that at some length, but he certainly didn't think there were exactly 17 possible worlds. And that seems, by his lights, that's an impossible antecedent. There's no possible world at which it's true that there are 17 total possible worlds. We don't want it to come out vacuously true. So we want it to come out false, right? Yeah, so how about case, we're thinking about counterfactuals the whole time right now, but we're supposing that the antecedent part is true, sorry, false. Yeah, right. Yeah, one of cases where in the antecedent is true. Excellent. Good. So in a way, this is so to speak, the opposite extreme. So far we've been talking about one extreme, there are no possible worlds at all where the antecedent is true. No matter how far out you go, you don't find any. The opposite extreme is you don't have to leave the actual world at all, because the antecedent is already true right here. Right. And that's, and by the way, this is another good philosophical heuristic, another good technique. Look at extreme cases. Okay. And when it comes to similarity, look at the most remote case, so to speak, which I'm imagining is impossible. And now look at the closest case, the least remote case, that's where the, that's the actual world. Okay, so now imagine the counterfactual has a true antecedent. So according to Lewis, you don't have to go anywhere else. You just look at the world is the antecedent is true. And it's just a matter of whether the consequent is true here in the actual world. So to put it simply, the counterfactual just becomes the material conditional. It becomes true in every key. Well, it comes true if the consequent is true, right? False if the consequence false in the actual world, and you don't have to look at any other possible worlds near or far. Okay. So, so there's the schema, you know, true would true gives you true. Right. Okay. Well, is that true? Is that is that plausible? And look, it is, I guess, somewhat plausible that the actual world is the most similar world to itself. And that's so-called strict centering that there's no other world that's as close to the actual world as itself. But that seems to yield certain puzzling results. Because there are some cases where you have true would true that are intuitively false. So for example, if there's no connection between the antecedent and the consequent or worst, if there's actually anti-correlation, if the antecedent is sort of bad news for the consequent, it's like counter evidence for the consequent, but they just both happen to be true, then that seems like the wrong result. So can you give an example of those cases here? Yes, yes, sure. Let's yeah, let's let's here's a good case. I looked up a bit of geography and I know what your latitude and longitude in in the Miller. Okay. Okay. So speaking to you, you're in the northern hemisphere. I know that. And you are at the longitude 120 degrees 58 minutes east. I didn't know that. Okay. So the following counterfactual is true. JJ, if you were in the northern hemisphere, somewhere or other, you would be at exactly 120 degrees 58 minutes east. Okay. Now, you might say, yeah, well, that's that's true, because there you are and there you are, you're in the northern hemisphere and you are at that longitude. But you might, I have the opposite intuition, namely, look, if I were anywhere at all in the northern hemisphere, I would be exactly at that longitude and nowhere else. I don't know, you know, so easily could be a little bit to the side, a little bit east, a little bit west. So the counterfactual is making this very strong claim, it seems to me, if you're anywhere in the northern hemisphere, you'd be exactly at that longitude. That comes out true, that's true would true. According to the Lewis analysis, that's just plain true on its own, because the closest world is the actual world. True, true. But I think there's an intuition that pulls the other way, that you shouldn't get such a specific counterfactual to be true. And we ought to come up with a case where where you have a counter support between the antecedent and the consequent. How about this, if Trump had been losing in the polls and he defended various people and, you know, scandals about things he had said emerged, he would have won the election. Well, he did and he did. The antecedent is true, all of those things actually happened. He did actually win the election. But you might say, hang on, that counterfactual seems funny, because the antecedent counter supports, he won the election despite all of those things. The counterfactual suggests some positive connection between the antecedent and the consequent, not a negative one. And in the actual world, there happened to be a negative connection, but both the antecedent and consequent were true. So you might say that's a worry also for this Louisian analysis. And Stornakatou, I would have the same issue about the true, would true yields a true counterfactual. Actually, the last case is interesting. What if the antecedent and the consequents are completely opposing each other, right? So the antecedent is a counter evidence or consequent. That's an interesting example. So anyway, you've got a spectrum of examples. You've got maybe the intuitively true ones are where the antecedent is positively correlated or it's good evidence for the consequent. You've got cases of just completely neutral, you know, the antecedent sort of militates neither way in favor of the consequent. Right. And then maybe the worst case is where it's actually negative. It's counter evidence, the antecedent and the consequent. And still, it comes out true according to this analysis. Okay. So we have seen Louisian analysis and Stornakatou's analysis. I've seen some upshots of that view. How about the logic of counterfactuals? How about the reasoning that we have? Would Modus ponens turn out valid in counterfactual? That's a good that's very relevant right here, isn't it? Modus ponens will come out valid according to Stornakatou and Louis because just for everyone to be clear, Modus ponens is the inference rule. If P then Q, P, therefore Q, that's meant to be valid. And so now consider the case where P is true in the actual world. You don't have to leave. You don't have to go to some other world. So right here and now, P is the case. And if P were the case, Q would be the case. So just check whether, you know, in the actual world, Q is true according to the analysis. According to our premises. It's true. So Q will be true in the actual world. I didn't maybe say that as well as I could have, but P is true in the actual world. So you don't need to go anywhere else to check. If P then Q is true according to one of the premises. So we only need to check the actual world. Okay. Forget your Q. And it's true. So we can directly conclude Q. Modus ponens comes out valid. And that seems to be a good thing because Modus ponens seems very intuitive. Another, I think, intuitive inference rule would be, let's call it agglomeration. Namely, P would Q. P would R. Therefore, P would Q and R. You can just conjoin the consequence. So let's see that. So if some antecedent condition implies a consequence, and the second, counterfactuality implies another Q as a consequence, then you have the same antecedent counterfactuality implying a different consequence. Then the inference will be from that antecedent, it counterfactually implies both those consequences. That's right. That's right. And you can see why that would fall out of the Stolnecker-Lewis analysis too. Namely, go to the closest P world. Q is true at them. Also, R is true at them. So Q and R is true at all of them because that's just closure under conjunction at those worlds. So that comes out valid and that seems good. And so far, the analysis is getting ticks. These are judgments of validity that we want upheld and they are upheld. That's good. How about cases where we think the argument form is invalid? We think an argument of a certain schema has counter-instances. And there are a number of cases of this. Actually, we didn't talk about it too much. Now is a good time to talk about strengthening the antecedent. That's valid, right? That's valid in classical logic. So it is for the horseshoe, you know, the material conditional. It's true of entailment. The thought is that it fails for counterfactuals. Now, I actually disagree with what I'm about to say. I'm now channeling the orthodoxy and the literature. Certainly, Lewis and certainly Stolnecker. So they would say the following inference rule is invalid. There will be counter-instances. P would R, therefore P and Q would R. So what I just did was I strengthened the antecedent. I started with P, that would R, we're imagining. That's the premise. Now I strengthen it. P and Q. That would R, that seems to be false. So here's an example. I've got a fragile glass. If I were to drop the glass, it would break. True. That seems true. Right. If I were to drop the glass and have it land on a soft bed of feathers, it would break. Well, no, maybe not. You know, soft feathers cushion the fall. It would survive, let's imagine. Right. So that seems to be a counter example. Now, this brings us to what are so-called Sobel sequences. Namely, if you repeatedly strengthen the antecedent of a counterfactual, you get this sort of flip-flop pattern that the counterfactual seems maybe true initially. Strengthen the antecedent. It goes false. Strengthen again. It becomes true. Strengthen yet again. It becomes false. And you get this sort of alternation. When I was a child in primary school, we sometimes played this little game. I never realized how philosophically profound it was. Someone would begin a story with what seemed like bad news, and then the next person in the game had to add an extra detail to make it good news. Okay. So, oh, a guy falls out of a plane. That's bad news. That's bad. Okay. Next kid has to add an extra detail. Oh, it's okay. He's got a parachute. That's good news. Okay. Next kid. Nice to make it bad news again. The parachute's got a hole in it. That's bad. Okay. Next kid. He's got a second parachute. That's good. The second parachute's got a hole in it. That's bad. Blah, blah, blah. So you get the idea. We're sort of alternating. Good news, bad news, good news, bad news. Now, what you might say that's displaying is the so-called sequence structure of counterfactuals that if you keep on... Adding. Strengthening the antecedent, you will get this sort of flip-flop pattern. If someone were to fall out of a plane, that would be bad. Yes, of course. If you would fall out of the plane and have a parachute, that's good. If you would have fallen out of the plane and have a parachute and have a hole in the parachute, that would be bad, blah, blah, blah. So you get this alternating sequence. Notice this is right there, an argument against the strict conditional, against counterfactuals being analyzed as strict conditionals, because strict conditionals obey strengthening the antecedent. So if you start with a true counterfactual and then you add a bit of extra detail to the consequence, sorry, to the antecedent, you'll get another true one. That's pretty obvious. If all of the P-worlds are Q, then all of the P and R-worlds are also Q. So does all the more. Not only have you got all the P-worlds being Q, but if you've got particular P-worlds, the ones that are also R, of course, they're Q. They're just a subset of the original ones, and you said that all of them were Q. So the upshot there is strict conditionals obey strengthening of the antecedent. Yeah, they obey strengthening as a valid inference rule for counterfactuals, if you're imagining that analysis. And allegedly, sobel sequences teach us that counterfactuals do not behave that way, because they have this sort of alternating structure where when you add extra detail to the antecedent, you can turn a true counterfactual into a false one. And this was, I would say, this was Lewis's number one reason for rejecting the strict conditional analysis, because he liked this alternation of true false, true false, as you successively strengthened the antecedent. Strict conditionals don't deliver that. Counterfactuals there can't be strict conditionals according to Lewis. Now, for me, they are, but I don't want to get ahead of myself. So just to summarize where we're at, I've given you some inference patterns, which intuitively are valid, like motor's ponens, agglomeration, and the similarity account of Lewis and Stornacker delivers those verdicts. So tick, tick. Now we've been considering what seems to be an invalid inference rule that was strengthening the antecedent, and it'll come out invalid according to Lewis and Stornacker. So you might say there's another tick, because you don't want it to come out valid, and that's what the similarity account predicts. You could easily draw a diagram to convince yourself, and Lewis does in his book. Just a couple of others. We won't go into the same detail on them, but transitivity, A would be, B will see, therefore, A would see. Transitivity. It seems that that's invalid, that there are counter examples to that, and Stornacker had some famous ones. And again, that is vindicated by the similarity semantics. That will come out invalid according to Lewis, according to Stornacker. One last one. Contraposition. A would see. Therefore, not C would not A. So what happened there? I flipped the counterfactual and I negated. That's contraposition. By the contraposition holds for the material conditional. It holds for the strict conditional. And you might say here's yet another argument against those analyses, because intuitively, contraposition fails for counterfactuals. And again, Lewis and Stornacker predict that it fails with their similarity accounts. And so again, they'll give themselves ticks that they're delivering the right verdicts. Now again, the sort of heterodox guy that I am, I disagree with that orthodoxy. But let's set that aside. That is, that's the sort of received view. The logic of counterfactuals. The logic of counterfactuals. Here are the valid ones, valid inferences. Here are the invalid ones and the similarity accounts are getting them all correct. They're classifying them as intuition would have it. So I'll just go back to the strengthening idea. I'm thinking about monotonicity and non-monotonicity here. Lewis's counterfactual logic, a kind of non-monotonic logic. You could say it that way. That's right. So normally, strengthening a premise should deliver the conclusion all the more, so to speak. But counterfactuals have this allegedly non-monotonic feature that strengthening an antecedent can turn a true counterfactual into a false one. So non-monotonicity is a good word for that. So far, we discussed Lewis's account and Stollnaker's account and we have seen the upshots of the view. Let's go to some objections against the theory. There's an objection given by Kit Fein. It focuses on the crucial element in both theories. It asks us about how do you distinguish what worlds are similar and what worlds are not similar? I think that the objection was something about Nixon. So here's the counterfactual. If Nixon had pushed the button, so we are in the Cold War scenario. If he had pushed the button, then there would be nuclear holocaust. So I think that the objection is, so how would we distinguish between worlds that are antecedent worlds that are closer to that? That's right. So far, we've had this crucial notion of similarity or closeness or nearness as we've put it. And so far, we haven't said too much about what it involves to the extent that I did. I was assuming a sort of intuitive notion of similarity. For example, I used that and Lewis used it in the seven foot example. Remember, the example was if I were taller than seven feet, how tall would I be? Would I be seven foot one? Well, it'd be a bit more similar to my actual height to bring me down to seven foot, half an inch, seven foot quarter of an inch. That was more similar. So that was a kind of, you might say, intuitive notion of similarity that's picking up on this quantitative notion of height. And then more generally, you might say, in the early days of this theorizing about counterfactuals, people like Stolnacker and Lewis were thinking of a kind of intuitive resemblance notion. And the folk are very familiar with the notion of resemblance. It's hard to give a philosophical account of resemblance, like witness the grew paradox. But at least we do have a pretty good idea of when things are similar to each other or less similar. And I remember I did the Britney Spears and so on example. Intuitively, things were getting less and less similar. Okay. That's the setup. And now Fine has what seems to be a killer objection to thinking of similarity intuitively like that for counterfactuals. So let's just go through the Nixon. You're quite right. It's a Nixon example. And yeah, the Cold War, there's this button hooked up to the nuclear bomb. Nixon, thank God, never pressed the button. But if he had pressed the button, there would have been a holocaust. We want that to come out true. Okay. That's that's the intuitive answer. And Fine's objection is it seems to come out false according to Lewis. Let me just read Fine. And then I'll say it in my words. He says, if Nixon had pressed the button there would have been a nuclear holocaust is true. Or can be imagined to be so. Now suppose that there never will be a nuclear holocaust. Then that counterfactual is on Lewis's analysis very likely false. So that's why it's a good counter example. Given any world in which antecedent and consequent are both true, it will be easy to imagine a closer world in which the antecedent is true, but the consequent false. For we need only imagine a change that prevents the holocaust, but that does not require such a great divergence from reality. Okay, that's fine. Let me say it in my words. Say it in my words. World, holocausts make a big difference. Of course. You know, a world where there's a holocaust is not at all similar to the actual world where there is is no holocaust, right? Holocausts make huge changes. Alright, so imagine Nixon pressing the button and let's let's imagine two different scenarios. In one version, there's a holocaust. Huge difference, very dissimilar from the actual world. Another scenario, he presses the button and it just malfunctions. You know, it sort of fizzles out and nothing happens. And then things go on very much like before, you know, very much as normal, you know, Nixon's maybe slightly surprised, but you know, the world looks very much like the actual world from then on. Let's picture it that way. So the big challenge to Lewis is that he seems to be making the wrong prediction. He seems to be saying that the Nixon counterfactual comes out false. Namely, if Nixon had pressed the button, there would not have been a holocaust. Rather, there would have been a malfunction. That would have been more similar. The holocaust world is very dissimilar. It's a huge change from the actual world. Okay, so that's a very nice problem. It's a good challenge that Nixon lays before Lewis. So I think we just have to agree straight away. Similarity cannot be the intuitive thing because I think that the fine is giving the correct ordering of judgments according to intuitive similarity. Intuitively, it's more similar that the button fizzles, malfunctions, and then things go on more or less as before. That's more similar than huge changes from a holocaust. Okay, all right, so then Lewis responds and he takes that on board. He says, right, similarity is not just the intuitive thing. Okay, so he has to do some well, contortions to make sure that he comes out with the right answer for the Nixon counterfactual, that it comes out true. It would be a little bit complicated here, you know, just, you know, an interview to go through all of those details, but I can summarize where he gets to. He says similarity for counterfactuals is not the familiar intuitive thing. It's related to that, but it's not exactly that. Rather, it obeys this certain order of priorities of what matters, and then he tells us, we could read it properly in a moment, but basically avoid miracles, big miracles, avoid big violations of the laws of nature, and then that's the first priority, then as much as possible, maximize agreement with particular facts. Okay, and then minimize miracles at all, even small miracles, which are violations of laws of nature, and then when it comes to approximate match of particular facts, well, he's not completely clear on whether that matters or not. It's of little or no importance, he says. So on the handout, if your students have it, I quoted him where he gives this system of priorities, one, two, three, four, you know, above all, as he says, it is of the first importance to avoid big, widespread, diverse violations of law, said succinctly, avoid big miracles, and then it is of the second importance to maximize the spatiotemporal region throughout which perfect match of particular fact prevails. So it's of the second importance to get the facts the same, right? And then the third is avoid small miracles, and then the fourth is it's of little or no importance to get the facts approximately right. Okay, now that Lewis argues that if you follow that priority system, he'll get the right result on the Nixon counterfactual. It'll come out true. Again, as I say, it's somewhat complicated to sort of talk through it about, you know, bigger and smaller miracles, but we can trust him that he gets the right answer on the Nixon case. But I want to make a couple of points. His whole system of priorities is calculated to fit the Nixon case, you know, because he's really concerned about whether, you know, the button fizzles or with the past to be different and blah, blah, blah. So he's taking that as a data point. And then he's trying to fit his theory to it. But then he moves on. It's actually, I find this rather funny in that paper. It's called Time Counterfactual Dependence and Time's Arrow, where he does this similarity ordering. He goes through the Nixon example, and he gives his system of priorities like straight away. He's done. It seems a little odd. He's looking at one data point, you know, the Nixon case, and then he fashions his whole system around it. You're kind of expecting, well, surely, there's a further paragraph where he says, oh, and the Nixon example is typical, you know, throw your favorite example at me, and the same system of ordering will do the job. He never says that. Maybe it was so obvious he didn't need to say it. He felt he didn't need to say it. But I feel like saying, well, hang on. Now, maybe you got the Nixon case right, but there'll be all these other cases that will go wrong to you, that similarity ordering. Let me give you one. And then, sorry, I've talked a lot. I'll let you, we'll go back to you. Consider this counterfactual. I didn't scratch my finger yesterday. That's true. If I'd scratched my finger yesterday, I would have done so at midnight, you know, as late as possible in the day. Not earlier. I would have scratched my finger at midnight. Now, that, I hope, sounds false to you. Why midnight? What's so specific? What's so specific? Why specifically midnight? Right. That seems to come out true on the Lewis ordering. Why is that? Now, we don't need any big miracles to have me scratch my finger yesterday. So, so then the second priority kicks in, namely, he says maximize the spatial temporal region. It's a perfect, perfect match. What that's going to mean in this case is that we, we want to maximize all of the perfect match of the actual world. And it'll turn out we get that by delaying my scratch as late as possible. Remember, I did not scratch yesterday. So, if we make my scratch earlier in the day, you know, that's not as big a match of perfect, perfect match of history as if we postpone it, you know, to as late as possible. Ah, in fact, let's make it midnight. But let that be the last moment of yesterday. That way, we will get the most perfect match of history. Nothing changed until right at the end. And then I scratched. That'll come out true, it seems on Lewis' account. And I think that's a bad result. In fact, to make it even worse, let's suppose that I'm more likely to scratch early in the day, you know, like I wake up itchy. And so that's when I tend to scratch, you know. And then as the day progresses, I become less and less likely to scratch. And in fact, midnight is the most unlikely time for me to scratch my finger. Okay. But still, according to Lewis, it seems, it's true that that's when I would have scratched. I would have scratched at midnight. I would have scratched at the most unlikely time. Because that's the time that would maximize the perfect match of history. And that seems to me like a very bad result. Okay, so JJ, I've talked a bit too much. I should go back to you. But this was to convey to you a couple of things. This was how Lewis responds to Fine's objection. Similarity is not just intuitive. It's this slightly, you know, quasi-technical notion involving miracles and so on with ordering of what matters. And then I claim he fashioned that to handle the Nixon case. But that's just one data point. And I think I can come up with other cases where that ordering goes wrong. Right. So, yeah, I'm thinking about the Fine objection. And I think the main objection is how do we distinguish between what's similar the worlds, the antecedent worlds that we need to consider in our analysis. Now Lewis would come in and say, well, the similarity relation could be cashed out in terms of here's our policy for that. So don't look at worlds which are deviating from our actual world too much, like no big miracles, no violations of loss of nature and so on. So that guarantees that if I follow these principles or policies for checking my eight worlds, I would get the correct analysis. I think that that's right. But you're saying that even if we follow Lewis's policy of checking the worlds, we will get into some commonsensical bad results, like the stretching of the finger and so on. That's a fine objection, by the way. How about your claim? You've been doing this for almost, I don't know how long, but you have been claiming that most counterfactuals are false. How can you give us just a background of what's going on there? Any opportunity. And by the way, just for a bit of fun, remember much earlier I talked about regret and I said how I'm prone to regret. And when I psychoanalyze myself, sometimes I think this is why I want most counterfactuals to come out false because those counterfactuals that inform my regret, if they were false I could make them go away. That's partially a joke. But I am serious, I do think most counterfactuals are false and let me go through a couple of my main reasons. Now in a way this involves me taking back almost everything I've said up to now because what I was presenting was orthodoxy. It's what the Stoenacker Lewis tradition thinks and what has become the received view about counterfactuals. So I'm flying in the face of all of that, but here's what I think. Maybe this is the easiest way to make the point. Consider, say a toss of a coin. Start with a coin toss. Oh, I will never toss the coin. Oh, but if I were to toss the coin, it would land heads, right? It would land heads, not tails, it would land heads. No, that was a joke. Why heads? It's a little bit like Bizet and Verli would be French, not Italian. Okay, actually maybe we'll do that in a moment. But yeah, look, I think it's a chancey coin and the counterfactual was second guessing the outcome of this chancey process. This chancey process would have wound up the heads way, not the tails way. No, I think that's misunderstanding chance. The whole point of chance is that it's open which way things would go. So you don't want to have a counterfactual telling you it would go one way, not the other. That's false. Okay, you were probably imagining a fair coin. Doesn't have to be a fair coin. Now make it highly biased. Highly biased to heads. 99% chance of heads, 1% chance of tails. If I were to toss the coin, it would land heads. No, I still say no. Because there's a 1% chance. The coin might land tails. So another way of my putting the same point is remember Lewis had this duality between might and would. Remember, might not entailed not would. Okay, it was a lot like necessity and possibility. So I said back then might counterfactuals are very easy to make true. Well, they render false the corresponding woods. Let's do it. If I were to toss the coin, it might land tails. I think that's obviously true. But I say that contradicts. It would land heads. So I feel like saying make up your mind. If you say the coin would land heads, they don't say it might not. It might land tails. Okay, so this is very much in keeping with that Lewis' opposition between might and would. Okay, so Lewis would have to deny that the might conditional is true in this case. But I say, of course, it's true because there's a positive chance. Okay, so that was the coin, which I've now made a biased coin. And now to finish the argument, because remember, it isn't just most counterfactuals about coins or something. It's about in general. Oh, it's counterfactuals, generally. Most counterfactuals are false, in general. Well, it's because they're chancy, most of them. Physics teaches us that our world is a chancy place. Start with quantum mechanics, but it sort of percolates up from that. So what we normally think of as deterministic or guaranteed outcomes are not really. They're really, I say, chancy. We learn that from physics. Okay, so take something that you think is deterministic and not chancy. Here, here go. I've got my iPhone. I will not drop the phone. In fact, I'll put it away. But if I were to drop the phone, it would fall. That seems to be true. That's about as true as they get. Counterfactuals aren't much more intuitively true than that. I say, no, it's still false. There's a chance of the phone not falling. Various weird things could happen. There could be a sudden updraft of wind that lifts the phone. It doesn't fall. We could go crazier still. Quantum mechanics tells us, it seems, there's some chance of the phone doing some really weird thing, like quantum tunneling to China. Very unlikely. I know that. But there's a chance of it happening. So I think of these normal processes as really being like lotteries. We don't think of them that way normally, but it's actually a lottery. What happens to the phone if I let go of it? It's very probable that it falls. Almost every ticket in the lottery has it falling. But there are some anomalous tickets in the lottery where it gets blown upwards by an updraft or some crazy quantum event happens. It vaporizes spontaneously. I know that's unlikely. It's extremely unlikely that still it might happen. Consider a lottery, a huge lottery. Let's say it's got a billion tickets or a trillion tickets or a Google number of tickets. If that lottery were played, ticket number one would lose. I say, well, no. It might win. It's very unlikely, but it might win. In fact, you'd better not say that ticket number one would lose. If you say that, then you'd better say, well, ticket number two would lose. It's got the same chance. Ticket number three would lose has the same chance. Therefore, every ticket would lose. If the lottery were played, every ticket would lose. But hang on, that's wrong. We know that's wrong. Some ticket would win. There would be a winning ticket in the lottery. You've contradicted yourself. The lottery paradox. It's very much like the lottery paradox. It's like a paradox for conditionals. In this case, it's agglomeration, what I called agglomeration earlier. All I did was agglomerate the consequence. If I were to, if the lottery were played, ticket number one would lose and ticket number two would lose and three would lose and and and all the way to the last ticket. No. No one thinks that because some ticket would win. Okay. So I'm appealing to a couple of things. I'm appealing to the logic. Like I like agglomeration. I'm appealing to might nots contradict woods. And I say that the ticket might win. Okay. So that's how I handle the really huge lottery. I say it's fault that the ticket number one would lose. It's false. The ticket number two would lose. They might win. And so it is with the phone. It's like a lottery with a huge number of tickets. Most of them correspond to the phone falling normally. I know that. But there's a small number of tickets. It's a lottery where something weird happens. That's why it's false that the phone would fall if it were dropped. It might not. I have to say this, but I think that you're appealing to another principle, a kind of regularity principle, right? So if something's possible or it might be the case, then there's a likelihood that it will be the case. I am making a connection between positive probability and might. If something is positive chance, then it might happen. But that seems to me very intuitive. Forget about counterfactuals. Just think about, say, lotteries in the future. I have bought a ticket in this huge lottery. My ticket might win, I say. That seems just true. And it's true even though I know it's extremely improbable. But the point is it has some positive probability. I have some chance of winning. I claim it follows from that that I might win. And this is might in the sort of deep metaphysical sense. It's not just my aesthetic. The world is such that it's true of my ticket that it might win because it has a positive chance of winning. So I think that's a very plausible principle too. And then I appeal to a counterpart of that for the would might counterfactuals. Okay. So finally, so what's your advice to our students who are working on some topics in philosophy? Why should they be interested in counterfactuals? And how would... Oh yeah. Yeah. Look at the people who are interested in it. Me. No. That gets the order of explanation the wrong way around. Why were these people and why so many philosophers interested in counterfactuals? Remember that long list I gave you more or less at the beginning of how counterfactuals are implicated in so much other stuff. Here's how I would put it. You can often think of philosophical topics like stations on a subway network. You certainly have a rail network. Do you have a subway network in Manila? No, just a train system. So it doesn't have to be subway. There you go. You've got a train system and think of a map of the train stations and you've got a sort of grand central station. I don't know what you call it in Manila. You've got a main station and lots of railway lines come out of that station. I sometimes think you can picture philosophy a bit that way but there are all these philosophical topics but there are certain central stations and then there are connections easily made from these central stations. Now it depends on your philosophical inclination what your grand central station or stations will be. For some people it might be consciousness for example. That might be a central station. Well for me my central stations are probability and conditionals. I reckon from both of those topics you very quickly get to so many other topics with very few transfers as we might say. I've said a bit about probability but let's focus on the conditionals. I gave you all of these other topics. Dispositions, explanations, laws of nature, causation, rational decision, blah blah blah. So to speak they're all just one stop away from conditionals and in particular in this case counterfactuals. So many people analyse these other things directly in terms of counterfactuals so you'd better understand counterfactuals pretty well if you want to understand these other things in terms of them. Actually this raises an interesting issue. I finished with saying I think most counterfactuals are false and now I'm saying there are all of these analyses in terms of counterfactuals. We talked about Lewis on causation that's what started that whole enterprise for him earlier. And so now there's a bit of a dilemma maybe a dilemma for me. So do I think that there is no such thing as causation or very little causation in the world because I think the counterfactuals he uses are false or do I think no one ever made a rational decision because the counterfactuals involved in rational decision making are false or do I think there's no such thing as knowledge because people analyse knowledge in terms of counterfactuals. There are no dispositions. Nothing was fragile for example because people analyse dispositions in terms of counterfactuals. Lewis also did by the way and so on. So now I'm sounding even crazier perhaps you know not only do I think all of these counterfactuals that common sense regards as true I regard as false but now I'm eliminating from the world causation and dispositions and knowledge and blah blah blah well no I think that tells us there's something wrong with these analyses. You shouldn't just analyse counterfactuals sorry it shouldn't analyse causation or knowledge or dispositions blah blah blah in terms of bear counterfactuals you know just P would Q things of that form. The truth I think is something sort of in the neighbourhood but it's a little different it's like probabilified counterfactuals like would probably that they could come out true if I were to let go of the phone it would probably form that's true but that's not what I originally said I said it would fall and that's false so adding the probably makes all the difference so I think these analyses might come out correct if you just probabilify them you get rid of the bear would counterfactuals and you replace them with something like would probably that that's a whole longer story for another day but but that's that's that I sort of more considered opinion about how to handle these counterfactuals but to just to repeat my answer to your question you asked why why should students care about counterfactuals because they're Grand Central Station right for me and for a lot of people that they they figure so centrally in so much of philosophy whether or not you agree with these analyses you you really need to understand counterfactuals and their interrelations with these all these various topics uh to have a good handle on so much of these areas of philosophy okay so thanks for your answer and that answer interview uh thank you Al nice nice to see you JJ nice to continue the friendship for 10 years yeah I look forward to the day when it won't have to be at such a distance really see you