76 | Ned Hall on Possible Worlds and the Laws of Nature

0:00:00 Sean Carroll: Hello, everyone, and welcome to the Mindscape Podcast. I'm your host, Sean Carroll. And you know, if you're a long-time listener, that I tend to mix things up from week to week. The episodes are not really related to each other, for the most part. But this week's episode can, in some sense, be thought of as a philosophical companion piece to last week's episode. Last week, we had Max Tegmark talking about the mathematical multiverse.

0:00:24 SC: Today, we have Ned Hall, who's a philosopher, in fact, chair of the Philosophy Department at Harvard University, who's done absolutely important work on causality, on the laws of nature and also on the idea of possible worlds. The philosopher David Lewis, who was very well-known in philosophy circles, although less well-known to the general public, examined this idea of all possible worlds and how they could be related to each other. Not physically, not sort of causally, but the different ways in which they differed from each other and how those ways entered into our analysis of counterfactual conditions, examining possibilities that didn't actually come true in our universe.

0:01:04 SC: So I talk with Ned about causation and the laws of physics, as I said, and how we analyze these ideas in the context of imagining all the different possible universes out there. Now, Lewis thought that all the different possible universes were actually real, that they actually existed. That's very close to Max Tegmark's idea of a mathematical universe, where every mathematical structure actually exists.

0:01:29 SC: But it's a little bit different. I think you can actually use the idea of possible worlds in a way that doesn't necessitate that you believe that they're all real. But whatever your position on that is, we're going to get there today. This is a wonderful conversation; Ned is just a true genius at taking esoteric, philosophical ideas and bringing them down to earth and making them very understandable. So, let's go.

[music]

0:02:09 SC: Ned Hall, thanks for being on the Mindscape Podcast.

0:02:11 Ned Hall: Oh, delighted.

0:02:12 SC: You're a real, honest philosopher, which I take it, in some sense, is it unfair to think of what philosophers do, as taking sort of the common sense questions we all have and then taking them super-duper seriously and digging into them?

0:02:25 NH: I think that's fair. I think that's fair. Sometimes, questions will arise along the way that you didn't anticipate and that don't have any clear common sense analog. So, some of these questions you know about. So, if we were talking about foundations of quantum mechanics, we could ask questions like, "How do you get a world of middle-sized dry goods that seem to have a kind of relatively clear geometrical arrangement in space, out of something as weird as a quantum mechanical wave function?"

0:02:51 SC: Yeah. I wish the physicists would take that question a lot more seriously than they do. But yeah, philosophers are definitely there. But it starts with looking at an object and going, "What's this?"

0:03:01 NH: That's right, yeah. So even that question, you could think, goes back to a question that I gather was very prominent in Aristotle. You pick something out in the world that's familiar and you ask, "What is it?" And there's a certain way of asking that question, where you have in mind a certain kind of answer. So, if I point to that book on the table and ask, "What is it?", it's... You're not answering the question appropriately if you say, "Oh, it's Ned's copy of this report," right.

0:03:29 SC: It doesn't capture the essence, somehow.

0:03:29 NH: Right. Right.

0:03:31 SC: Right, capturing the essence of things. So, there's many questions that we could start with. But I know the one that you've written about quite a bit, and also I am personally interested in, is the idea of causation or causality, cause and effect. What is your favorite word there, causation, causality?

0:03:47 NH: I'm ecumenical.

0:03:48 SC: Okay.

0:03:48 NH: I used to be, for some reason, I have no idea why, but I used to bristle when people said "causality," I don't know why.

[chuckle]

0:03:55 NH: It's like, "That's not the way I learned it." But it's the same thing.

0:03:57 SC: Yeah, okay, good. So, roughly speaking, in our everyday lives, in the folk image we have of the world, the manifest image, we are always talking about causes and effect.

0:04:07 NH: Yeah.

0:04:07 SC: "I got sick because I had bad sushi," or whatever. And, therefore, the philosophers like to analyze this. So why is it even hard? What are the mysteries that pop up when we try to ask, "What do you mean by causation?"

0:04:20 NH: Oh, boy, so there are mysteries, I think, along a number of different axes. So, one of them we might get to later, if we talk about laws of nature. But when we talk about cause and effect, that kind of talk goes along with other kind of talk, like talk of the powers of things. So, for example, suppose you have a headache and you take some ibuprofen and your headache goes away, and you say it went away because you took the ibuprofen. We would happily add, "Right, ibuprofen has the power or capacity to cure headaches." And that talk of powers and capacities seems to introduce a dimension to our sort of picture of the world that's different from the dimension we're focusing on when we simply give a kind of blow-by-blow account of what happened, where and when.

0:05:08 SC: It does seem to add something...

0:05:09 NH: Right. Right. Right.

0:05:09 SC: Over and above the stuff.

0:05:11 NH: Something that, in some sense, knits things together. And, for a philosopher, that's like, "No, that's like the candle to the moth."

0:05:19 SC: Knitting things together, yeah.

0:05:20 NH: Sometimes you get burned, you know. We want to understand, what is that knitting together? And you'll find, in the history of philosophy, radically different views about this. Some people think like, "Well, right. We just have to think of the world as really having two aspects." There's the kind of aspect, again, that we get at when we simply report what happens, where and when, when we fill out our encyclopedia of the occurrences that make up the world. And then there's the aspect we get at when we say things like, "What causes what?", or, "What has the power to do what?", or ultimately, if we translate this into the language of modern physics, "What are the fundamental laws that govern what happens?" So, there are some people, philosophers and non-philosophers alike, who think really you need a two-factor view of what reality is like. There's kind of the stuff that happens and then there are the necessities, the powers.

0:06:00 SC: Okay. Yeah.

0:06:00 NH: Or the necessary connections.

0:06:00 SC: Right, as a hard-boiled physicist... I will play the role today of the hard-boiled physicist, since you're the philosopher in the room. I think I can just get along with just the stuff doing things, and the rest is commentary, in some sense. Is that one fair attitude?

0:06:00 NH: Yeah. The question is whether you think the... How you think about that commentary. So, there is another kind of view, which has a long tradition, which says there's a kind of commentary on that stuff, which should be thought of as a kind of conceptual grid we impose on the way we think about the stuff that happens. But it's a kind of mistake to think that that conceptual grid is latching on to some structure that's out there.

0:06:50 SC: Right. It really is a little bit extra in some sense.

0:06:52 NH: Yeah, yeah, yeah.

0:06:53 SC: Yeah. But okay, but then there's another point of view which says, no, that there's a fundamental feature of the world, which are these powers, I guess.

0:07:00 NH: Right. Right, right, right. And sometimes, you can bring out the difference by... Fairly clearly, by thinking of, imagining really, really simple scenarios. So, imagine a scenario like this, like a "possible world" that looks like this. It's got two Newtonian particles in it, and they orbit around each other, 'cause things are... The initial conditions are set up just right. So they orbit around each other in perfect circular motion, thanks to the gravitational attraction between them. So they've got mass, no charge, the only force there is the gravitational force between them.

0:07:35 SC: And since we're Newtonian, there's not even gravitational waves, so they can do this forever.

0:07:39 NH: Right. Right, right, right. And it seems like I could describe that scenario in a very different way. I could ask you to imagine a world in which there are particles, and each particle just follows a very, very simple boring law that really permits no interaction between them. Every particle simply orbits in a circular motion. We'll have to imagine that there's something it's moving relative to, like absolute space. Let's just spot that, so that we can understand what it is to be moving...

0:08:11 SC: In a circular...

0:08:11 NH: In a circular orbit, without reference to other material objects. So here's this alternative way to describe this. There's one law, it governs every particle individually. Every particle just moves for all time in a circular orbit. And someone who thinks that talk of necessary connections, or powers, or causes, or laws is a kind of valuable, useful grid that we impose on the phenomena, will look at this, and say, "Well, these are two alternative ways you might have of describing exactly the same thing."

0:08:39 SC: Yeah.

0:08:39 NH: So there really is no factual difference between these two possible worlds at all. And, of course, there's not really any practical need served by describing things one way or another, because the world is so simple that...

0:08:50 SC: It's such a simple world, right?

0:08:51 NH: Right. Right. Yeah, there's no prospect of being in that world, and describing it. [chuckle]

0:08:55 SC: There are no people in there to think about it, right? Yeah.

0:08:57 NH: Right. Right, right, yeah. 'cause I didn't say these are smart particles.

[chuckle]

0:09:00 NH: And someone who's on the other side will say, "No, no, no. There's all the difference in the world, as it were, between these two scenarios." So, one the way they might try to bring that out is they might ask you to consider hypotheticals pertaining to the worlds. They might say, "Well, here's something that's true of the Newtonian world. If there were a third particle somehow introduced, the motions going forward would no longer be circular." Which is almost certainly right. You'd have to set... You're better at this than I am. You would have to set things up just right to still preserve circular motion.

0:09:34 SC: That's right.

0:09:35 NH: Whereas, in the other world, where there's just a simple law that applies to all particles separately, if you introduced a third particle, then, by stipulation, it too would move in a circular motion. And so, for people on this side of this divide that we're talking about, it will simply be obvious that there has to be a difference between these two worlds, because there's a difference in what would be the case were a certain thing to happen. And then, you might... You could probably predict how this will go. People on the other side will say, "Well, look, that conceptual grid that we're talking about imposing on reality is quite rich. It includes talk of laws and causes, and talk of hypotheticals."

0:10:16 SC: Yeah, possible worlds.

0:10:17 NH: That's another aspect of the grid.

0:10:18 SC: Yes. Yeah. Yes.

0:10:19 NH: And so, all you're doing is drawing attention to the fact that the grid we impose has this rich conceptual structure, but you haven't yet convinced me that that structure is answering to anything that's really out there in the world.

0:10:31 NH: It's a little bit difficult even to think too deeply at this level about this very simple example, simply because it's so simple, and we inevitably think about those two particles as if they were part of our much richer world, and that it enables us in some sense to ask these hypothetical questions, whereas the particles themselves could never ask these. [chuckle]

0:10:52 NH: Right, right, right, right, right. So there's a different kind of example you could think about that connects much more to our world as we experience it. Although, to motivate the example, I have to take sides on debates in the foundations of quantum mechanics, in particular...

0:11:07 SC: Go ahead.

0:11:07 NH: No. And...

0:11:07 SC: I'm used to that.

[laughter]

0:11:09 NH: In particular, how we should think about probability. So you're... As I know, you're very familiar with... There are approaches to the foundations of quantum mechanics that say that the fundamental dynamical laws are stochastic, as it were, if we write down the equations that govern how things evolve, those equations have probabilities written right into them. And you can't explain away those probabilities as a reflection of our ignorance about initial conditions or anything like that. So, let's just grant, for the sake of argument, that...

0:11:44 SC: Let's imagine.

0:11:45 NH: Yeah. Or imagine that that's the correct description of our world. Obviously, we know quantum mechanics has to be fixed, but we imagine any way of fixing it up is going to preserve this irreducibly probabilistic component. So then you could ask, "Well, how do you think about that probabilistic component if you're on one side or the other of this divide?" So, for people who think that the world has this extra dimension, many of them are just happy to include a probabilistic dimension as well. And that will... That stance will have certain concrete ramifications. For example, if I'm on that side of this divide, I think, "Right, there's just this... In addition to the facts about what happens where and when, there are these facts, among other things, about probabilities." I will think that while it's likely that those probabilities are reflected in observable frequencies, there's no guarantee of that.

0:12:39 SC: You could get lucky/unlucky, right.

0:12:40 NH: Yeah, we could get unlucky. We might be unlucky. Whereas, if I think that, no, talk of probabilities is just another component of this conceptual grid, I have no particular reason to grant that possibility. It's not even clear what it could mean for me to say we could be unlucky.

0:12:56 SC: In the sense that the probability is nothing other than the frequency with which...

0:13:00 NH: Yeah, yeah, yeah. And you have to be careful about how you spell out that idea, because, you know, we could ask embarrassing questions like which frequencies determine the probabilities. I think those kinds of questions ultimately can be answered. But the overall approach would be one that said talk of probabilities is a way to kind of encapsulate in a mathematically elegant form a whole ton of information about frequencies. Or it might be information that we don't yet have. So we could say our current best guess about what those frequencies will be.

0:13:39 SC: So I'm getting the impression, my plan was to start with causality and go to other places. But I'm getting the impression that there are so many other things we need to think about before we really do causality right, that maybe we should finish with causality and talk more about things like the nature of the laws of physics. When you talk about laws, you've introduced these concepts of powers or propensities. As a physicist, I hear philosophers talking about these, but they're not our language as physicists. So what are the different ways that we have of thinking about what you mean by a law of nature or a law of physics?

0:14:15 NH: Good. So there's one approach that's squarely in the conceptual grid camp that sees talk of laws as earning its keep because of the way that concept of law helps us organize our view of the world.

0:14:34 SC: So can I just rephrase that as, there's a bunch of things happening, we perceive patterns within it, and it's a way of encapsulating everything.

0:14:41 NH: Yes, yes. And let me try to give an analogy that may be kind of familiar and easier to get a handle on. Imagine you're a mathematician and you do number theory. And what are you trying to do when you do number theory? Well, prove interesting results about the numbers. We have some background view that certain results would be interesting to prove and certain other ones not so interesting to prove. It's not clear where those judgments come from.

0:15:08 SC: Why you think that, that's right.

0:15:09 NH: Yes. But that's okay. We can just say, we tend to agree on what's interesting and what's not. Like Fermat's theorem is interesting. Like how many 7s are in the decimal expansion of 2 by 2 by 2 by 2 by 2 by 2 is not interesting. And we also tend to agree on which statements about arithmetic are obvious, maybe obvious enough that we would not feel ourselves to be any more confident of them just because we prove them from other statements. They're kind of starting point obvious, as it were. And over time, we hit upon a small set of those obvious statements that seem to do a very effective job for us of organizing our mathematical practice. What do I mean by organizing our mathematical practice? Well, when I claim to have a proof of something you can say, "Ned, can you show me how to get that proof from our small set of starting point statements?"

0:16:04 SC: Yeah.

0:16:05 NH: And maybe we would ask other things of those statements as well. We want them to be powerful enough that we think it's plausible, or it's at least a reasonable hypothesis, working hypothesis, to think that we can use them to establish or refute interesting...

0:16:21 SC: Okay. So these statements are axioms or assumptions?

0:16:23 NH: Yup, yup, yup.

0:16:24 SC: I didn't want to to leap ahead, but...

0:16:25 NH: So that was why... I was being sneaky about it. That was the reveal. That this is this...

0:16:30 SC: Sorry. I gave it up, sorry.

0:16:31 NH: No, no. That's fine. You gave it up at the right, just the right moment. This is a view about what it is for something to be an axiom.

0:16:38 SC: Okay.

0:16:38 NH: And it's a view that's anthropocentric in a certain way, 'cause it's we who find these things obvious or epistemically powerful, powerful with respect to their ability to establish or refute the claims we care about. Maybe there are other desiderata we have as well. But it's not out there in the mathematical universe. If we imagine like we're Platonists and we think there's a universe of mathematical truths, it's not that some of them somehow shine more brightly as like being the fundamental truths.

0:17:08 SC: Yeah, okay. That makes sense. As long as you're a truth, you're a truth.

0:17:09 NH: Yeah, yeah. So this is a little capsule story about the rationale for us humans who are interested in number theory to single out certain statements as axioms. And it can be used to justify a choice of axioms and we could all agree that in certain senses, it's objective what the axioms are. What do I mean by that? Well, I mean we find ourselves agreeing on what's a good choice. Things could have turned out differently. You could imagine a race of creatures who can think about numbers, but there's vast disparity between those creatures as to which statements about the numbers they find obvious.

0:17:50 SC: But...

0:17:53 NH: They're like, "Do you think 2 + 2 = 4 is obvious?" What are you thinking, Sean?

0:17:53 SC: But maybe you can. Maybe you think you can imagine those people, but maybe really every set of rational people would agree.

0:17:58 NH: Yeah, yeah. And that... Which is an interesting conjecture. Maybe, now we're getting into really deep waters.

0:18:03 SC: Yeah.

0:18:03 NH: Maybe there's something about the nature of rational thought itself that it grounds or explains why we find some obvious or some not, and that would be very cool if someone could establish that.

0:18:14 SC: Yeah.

0:18:16 NH: But even if that's not the case, that doesn't need to be a threat. We could still say, look, it's enough for us to have an agreed upon way of organizing our view of the world. And I like that as an analogy for the way that this one camp... I might as well give them a label. I'll call them Humeans, after David Hume.

0:18:35 SC: Good.

0:18:35 NH: 'Cause he was this Scottish philosopher who famously denied that there are any real necessary connections in the world.

0:18:41 SC: So Hume is on the side like there's a bunch of stuff happening.

0:18:44 NH: Yeah.

0:18:44 SC: And we impose some way of talking about it.

0:18:47 NH: Yeah, yeah, yeah.

0:18:47 SC: Love it. [chuckle]

0:18:48 NH: Yeah, yeah, yeah. And so that's one way to go. And then a number of interesting questions arise. What is the best way to organize our view of the world? The example of axioms is, is maybe overly simple in some respects 'cause it's a little too easy to spot the interests of ours that are served by singling out axioms. Whereas when it comes to laws of nature, there are all sorts of interests that might be served. Now, there's lot of things that people on the, we'll call them the anti-Humean side, would say in response, but I think one place to focus, which is a place that many of them will want to put pressure, is on a particular use that we put concepts like the law of nature to, which is in explanations of phenomena, not just predictions, but explanations. And here you can see that the analogy with mathematics is beginning to weaken and maybe break down.

0:19:39 SC: Yeah, this is a more science-based question.

0:19:40 NH: Yeah, right, right. 'Cause I think there is such a thing as explanation in mathematics. Presumably mathematicians in your audience are going to be nodding vigorously here, but it's not the same as scientific explanation. In scientific explanation it actually looks like one thing that we do routinely in giving scientific explanations is talk about not just what happens, but what would have happened if things had been different in certain ways. So, here's a nice example, and you can correct me if I've got the physics wrong on this, but my understanding of Newton is that in the Principia when he argued for the 1/r squared, force law for gravity.

0:20:17 SC: Gravity in [0:20:18] ____, yeah.

0:20:19 NH: Right. The argument was not that it was this law, as opposed to alternatives, like maybe the force varies directly with r, or with 1/r cubed or something else. The argument was not, "Well, look, 1/r squared gives you elliptical motion." It's true that it does and it's true that other forces don't, but, and this is, I have this on the authority of my spies, it's not... I've not read the Principia, so, audience, go and check. At the time that Newton was writing the empirical data was not precise enough to distinguish an ellipse from the other sorts of curves that would have been given by other force laws.

0:21:03 SC: Well, I'm pretty sure that it was good enough to distinguish between that and 1/r cubed.

0:21:10 NH: Yeah, it might be right. Yeah.

0:21:10 SC: But there are others, but I think you're right, there are things that would have done just as good a job empirically, yeah.

0:21:15 NH: Yeah. However, the 1/r squared law gives you a different prediction if you've got other planets in the solar system besides the Earth, which is that the axis of the ellipse, as a planet goes around the sun, you just focus on the long axis of the ellipse there it traces out, that axis itself rotates over time, which it wouldn't if the other planets weren't there. Now, notice what I just said, there would be no precession of these orbits, I think that's the right term, if there weren't other planets. Now, so I'll say it again, Newton puts us in a position to evaluate a hypothetical; if there had been no other planets then this orbit would not have precessed. And that actually looks like it's an explanation of the precession of the orbits, and it looks like an explanation that cites, not just facts about what does happen, but facts about what would have happened, and how do we make sense of that?

0:22:14 NH: Well, thankfully, according to these anti-Humeans, we've got laws to appeal to, and those laws actually dictate not just facts about what happens, 'cause they're sort of more ontologically robust than that, they dictate facts about what would have happened. And they are what allow us to kind of use these counterfactuals in a rigorous and controlled fashion, and we need to use them because otherwise we can't explain anything. And I think behind this is a much sort of more fundamental, so maybe fundamental in the sense of slightly murky thought, which is that to explain phenomena in the world, it's not enough simply to add to your description of them, your kinda blow-by-blow description of their surroundings, say. But to explain why something is the case you have to give information about what it constrains it to be that way.

0:23:04 SC: And so I think that you're building up to or maybe you've already achieved the motivation of the anti-Humean viewpoint, but as a Humean, should I really be bothered by any of this? I could contemplate subjunctive situations, counterfactual, I can ask like what would have happen under other circumstances. So in other words, as a Humean, I think I can look at the actual world, distill laws from it, and then use those laws to say what would have happened in other circumstances. So, what am I gaining by this anti-Humean addition?

0:23:39 NH: Well, you can do that, you might think that you could if you wanted to, describe those hypothetical situations with reference to any of a number of candidate laws. As long as those laws agree on the facts, on what actually happens, they're all as far as the world is concerned, equally good, in the same way that different axiomatizations of arithmetic are equally good as far as the mathematical truths are concerned, like you don't want to include in an axiom a mathematical falsehood, but as long as you got truths, math doesn't care. The only constraint on the choice in the case of mathematics seems to be that we care about using some more than others, because it suits our purposes, but it can sound awkward to think that which explanatory counterfactuals are true is somehow relative to our purposes and interests in marking out certain claims as the laws rather than others.

0:24:33 SC: Okay, I think I'm getting it, actually, so remarkably in real time. But test me on this, so if I'm a true Humean, and I think that the so-called laws of nature are just convenient encapsulations of what actually happens in our actual world, that makes it harder to talk about other possible worlds, right? How do I know which features of our world to extend to those worlds?

0:24:57 NH: Yeah. And you can stipulate that, you can say, "For my present purposes, I'm going to stipulate that the possible worlds I'm going to consider are all worlds in which the following statements are true." And now we sort of write down the things that we're treating as laws. And if you've got a stipulation like that, then you're okay, right. The worry that the anti-Humean has with this approach is that the stipulation seems like it's governed by questions about what's useful to us, whereas what's explanatory, what's genuinely explanatory shouldn't be governed by those questions. I can give you another example, I'm sort of curious what you think about this, but it's another example that we could think, see as like an intuition pump, this is a phrase philosophers like to use, to try and sort of tempt you over to the dark side of anti-Humeanism.

0:25:48 NH: So, imagine that some number of years from now, we're imagining kind of a utopian future where there's world harmony, and we've solved global warming, and we're... All human resources are now devoted to doing fundamental physics, 'cause we've all realized what a great pastime that is. So no wars, but just like lots of fundamental physics.

0:26:16 SC: Everyone gets a job.

0:26:16 NH: Yeah.

[laughter]

0:26:17 SC: All the postdocs you want, yeah.

0:26:19 NH: And we've reached the point where we realize that in order to test the two sort of remaining candidates for what the correct theory of fundamental physics is like, we need to build this super collider that rings the equator so that we can achieve high enough energies and so on. And we built it, and we've got the test set up, and we realized that the experiment we're going to run is going to achieve conditions that, we can plausibly say, have never been achieved in the history of the cosmos and absent our intervention on this case will never be achieved, unless there's some other intelligence out there who does this. So these are unique conditions. And now, someone sort of comes rushing in as we're about to fire up the experiment and says like, "Wait, wait, wait, wait, stop everything. I've just done some calculations. We've got these two theories, A and B. If theory A is correct, the test will go beautifully, and in fact, will give us results that will show us that theory A is correct, but we haven't been careful enough in working out the ramifications of theory B. If theory B is correct, this test will set off a new Big Bang."

0:27:29 SC: This is uncomfortably close to arguments people actually had when we turned on the Large Hadron Collider.

[laughter]

0:27:35 SC: So this is not such a thought experiment, yeah.

0:27:39 NH: Right. Okay. Now, if you're an anti-Humean, here's how you will think about the practical situation we face. You will think, "There is just a fact of the matter about which laws are correct." Of course, we could have gotten everything wrong. We could have been unlucky and deceived, and it's really theory C that's correct. But we've done our job well, and so we have entitlement to think that the true fundamental laws are either A or B, and that's just a fact that's like, you know, given independently of what happens as long as what happens is consistent with them. It's a kind of behind the scenes. The rules of the game are either the A rules or the B rules, and we simply don't know which are the correct rules yet. And so we can reason if they are the B rules. For all we know, they are the B rules, and so maybe we want to be cautious and not run the experiment, 'cause for all we know, we might destroy the world or at least start it over without us in it.

0:28:38 SC: Something like that. Right.

0:28:38 NH: Yeah. If you're a Humean, and you think that what laws are are simply something like highly useful summaries of what happens, it's really hard to know how to think about this, 'cause if we don't do the experiments, then the... Remember, I said that the experiment is going to achieve conditions that are unique in the history of the world. If we don't run the experiment, then there will be no such conditions to, as it were, include in the summary.

0:29:04 SC: There's no facts to discern irregularity about.

0:29:07 NH: Right, right. So it looks like you ought to say, "If we don't do the experiment, then it's simply indeterminate whether the laws are the A laws or the B laws." But that's not the way we would actually think about this. So a Humean could say, "Well, right. Our thinking is infected by a kind of certain anti-Humean elements." And some Humeans will actually point to history here. They'll say if you look at how physics arose in say that 17th and 18th century, it was against the kind of theological background. So someone like Newton would have happily said, "In writing down the laws, I'm literally seeing into the mind of God, like laws are God's commandments." And if you had that view, that's a very anti-Humean view.

0:29:50 SC: Oh, that's the most anti-Humean you can get, I presume, yes.

0:29:53 NH: Yeah, yeah. [chuckle] But the Humean might say, "Look, we should have outgrown that." So in offering this thought experiment, partly I'm offering it just 'cause I think it's fun to think about. You get to do that as a philosopher.

[laughter]

0:30:11 NH: But I don't mean to be suggesting it's somehow decisive in favor of the anti-Humean, but it does show, I think, that there's a kind of deep-seated component in the way we think about the world that the anti-Humean is latching on to.

0:30:25 SC: Yeah. Isn't it evidence against the anti-Humean view that there is no famous champion whose name we can attach to this view like we can for the Humean view?

[laughter]

0:30:37 NH: Maybe that's right. I suppose an anti-Humean might say, "Well, that's just because it's... "

0:30:41 SC: Every smart person agrees, I guess.

0:30:42 NH: Exactly, yeah.

0:30:43 SC: Why are we calling it the Humean view? What does David Hume have to say about this?

0:30:47 NH: Well, so, famously, Hume, as you mentioned before, did deny that there are any real necessities in nature. And for reasons I don't fully understand, he's now kind of the historical standard bearer for that view. I say that, because usually in philosophy, when you find some philosopher who's famous for advocating some interesting idea, you can find some predecessor.

0:31:10 SC: Yeah. No, yeah. [chuckle]

0:31:10 NH: Hume too. It has to stop somewhere.

0:31:12 SC: Right.

0:31:13 NH: But Hume was relatively late in the day. But Hume's own approach was kind of interesting and detailed and well thought-out enough to have a lasting impact. He added something to the mix that we haven't really talked about, which is a kind of view that we humans naturally tend to project kind of features of our psychology out into the world. So one example that might be familiar or be kind of easy to grasp is color. We see the world as colored. Maybe it is, but maybe it isn't. Maybe it's just like atoms and electrons moving around reflecting light in a certain way.

0:31:53 SC: Yeah, I mean, let's... Sorry, let's explain a little bit more what it would mean for it not to be colored. I mean, we... Like you said, we experience color, but you're saying not to be colored in the sense that it's just an illusion, or it's just an emergent phenomenon, or what do you mean?

0:32:13 NH: The view I'm imagining here, which I don't mean to be endorsing, but just have it on the table is that it is an illusion, although unlike other illusions, like seeing a stick in water that looks bent or something like that, a highly serviceable and useful illusion.

0:32:28 SC: Right. Okay.

0:32:29 NH: So if you had to design a human being with a visual system in a way that where that visual system would help the human being survive, and [0:32:39] ____ environment.

0:32:39 SC: Color is very useful.

0:32:40 NH: Yeah.

0:32:40 SC: Yeah, right.

0:32:41 NH: But it's not really there. That's the thought.

0:32:42 SC: Okay.

0:32:45 NH: So we could use that as an example. It's very hard not to see the world as genuinely colored. But someone who thinks it's an illusion will be like, "Well, the way our visual system works, we're kind of projecting." When we take the world to be colored we're kind of projecting something that's properly understood as a feature of the way we respond.

0:33:02 SC: Well, sorry, when we're having this conversation, what mindset should we be in? Do we know that there are things called frequencies of light that correspond to different colors or are we sort of in a pre that perspective?

0:33:13 NH: Right. So this view got going pre that perspective, but where advances in physics had gotten to the point where the so-called natural philosophers who took this view about color were confident that the material world was just material objects in space.

0:33:32 SC: Yeah, okay.

0:33:33 NH: Yeah. And when you bring in a more complex view of material objects where they have charge, and where they... You know, they come in different fundamental varieties in their photons and the electrical properties of matter can make a difference to how that matter interacts with photons, it opens up space for reintroducing colors into the world as real elements.

0:33:53 SC: But for purposes of this thought experiment, we're honestly asking whether or not colors are fundamental real things or just illusions. Okay, good.

0:34:01 NH: And so you might think like that's an example of a projection. It actually occurs to me as we're talking, a much less controversial one might be our judgments about what foods are disgusting.

0:34:13 SC: Yeah, okay, good.

0:34:13 NH: So I have a constant argument with my family members about beets, 'cause I'm very ecumenical when it comes to food, I like almost everything except beets. It's as if all of my childhood food aversions coalesce somewhere around age 18 into beets.

0:34:30 SC: Well, you know, this might be exactly analogous to color, because it turns out that a lot of people's visceral reaction against certain foods can be traced to different taste receptors in their tongues.

0:34:41 NH: Interesting.

0:34:41 SC: Something like 20% of people really can't stand raw tomatoes.

0:34:47 NH: Oh, interesting!

0:34:48 SC: This is something that is so...

0:34:50 NH: I feel so sorry for them.

0:34:51 SC: Well, yeah, number one, you feel sorry for them, but not only do they not enjoy tomatoes, but they get social approbation because of it, like they're somehow flawed, because they don't enjoy tomatoes as much as they could, but it's honestly just physiological difference.

0:35:03 NH: Right, right. Whereas fortunately for me, beets are enough of a fringe food that I don't suffer their approbation. Right, but I enjoy getting these arguments where I will say, "Look, most people just don't understand how disgusting beets are." Like, I perceive the truth about beets, but other people don't. And of course, it's a joke. Right?

0:35:21 SC: Sure.

0:35:23 NH: And it's, for our purposes, an illuminating joke, because if I were being serious, I would be committing what you might call a projective error. I would be taking my reaction to beets and somehow projecting it out into the beets as if what I'm doing is simply passively picking up on this feature, disgustingness.

0:35:46 SC: Yeah, that beets have, right.

0:35:48 NH: Yeah, yeah.

0:35:48 SC: Okay and so, sorry, that is what Hume accuses us of doing?

0:35:51 NH: Yes, with our talk of necessity in particular.

0:35:54 SC: Okay.

0:35:55 NH: And here, the reaction is our own psychological habit of expecting things. So if you're walking along and oh, suppose you walk over a clear glass pane and there's a 20-foot gap underneath it, you will have a very strong psychological reaction to that.

0:36:18 SC: Yeah.

0:36:18 NH: Yeah. So that's just a vivid case. But he thinks these reactions to the world, these expectations that we build up over time are legion and of course they are. Normally when I walk along, I don't think about whether the ground will remain stable under my feet, I'm just habituated into automatically expecting it will.

0:36:39 SC: Okay, and good. And so the connection to the laws of physics is that these habituations are sort of our fault, they're not there in the world.

0:36:47 NH: Yeah, yeah, yeah. And like the example of color, Hume thinks it's good for us that we become habituated in this way.

0:36:56 SC: Right. He didn't know about evolution, but still... So, it wasn't selected Darwinianly but he could at least say, yeah, there's clearly a purpose being served by understanding that are colors and patterns in the world, more broadly. Okay, does this connect to... Okay, well, this is definitely food for thought for me, because I tend to be a proud Humean on most things, but I think it could give me a good reason to wonder whether or not I'm cheating when I talk about possible worlds in counterfactual situations. This must be closely related to Hume's famous problem of induction, how we go from seeing n things to assuming that it's true for n+1 as well.

0:37:36 NH: Yeah, yeah, that's right. And in the context of which he was raising this point about our... As he saw it, our tendency to project our expectations, our habits of expectations out onto the world as if we're just passively picking up the necessary connections that are out there. He was very concerned to try to show that, as he would put it, induction, this kind of thing we do routinely, or indeed any kind of inference where we take some limited data about the world and extrapolate it. It could be towards the future, could be towards the past, could be towards the small scale, could be towards the large scale. Any kind of extrapolation like that was for Hume not rational.

0:38:16 NH: For Hume, this point about projecting expectations was part of a longer kind of investigation in which he was trying to argue, I should say, in a way that was not received well by his contemporaries, that our, the kind of psychological processes we go through when we extrapolate are not really an instance of reasoning.

0:38:43 SC: Oh, okay, that's what he said.

0:38:43 NH: And that's going to sound crazy to any scientist. You're saying that I'm not engaging in reasoning when I take in data and spend days or weeks or months analyzing it.

0:38:43 SC: So let's bring it down to earth, what is an example of the kind of induction that he has in mind that we are not reasoning about?

0:38:43 NH: So a simple case might be, we could go back to something like Galileo's experiments involving freely falling or rolling objects. Hume thinks that we shouldn't feel guilty about the fact that after conducting those experiments we all find ourselves endorsing Galileo's conclusion, say that objects fall with a constant acceleration near the surface of the earth. But he thinks that we can't see that as a species of reasoning. And the argument is clever and frustrating and to try to encapsulate it, the key idea is that in extrapolating in a case like that, we seem to need to have as a background assumption some statement to the effect that nature as a whole behaves in a uniform manner. So before I go fill out the argument, let me give a different illustration. So imagine that Newton had a lesser-known brother. We'll call him, Newton was Isaac, we'll call him Schmisaac.

0:40:14 SC: Okay.

0:40:14 NH: Right. That's what philosophers do when they want to introduce a character, they just add "schm" to the front. And Schmisaac Newton published his own version of the Principia, complete with a gravitational force law which had the feature that it said that the force between any two massive objects is a constant times the product of their masses, divided by the square of the distance between them until the year, say, 2020. And then it just drops to zero. And understandably, nobody paid attention to this.

0:40:50 SC: Yeah. [chuckle]

0:40:52 NH: Right. You can see the trick here. This is a way of fashioning a force law that by design gives you the same predictions for any phenomena that we're presently in a position to look at or test, but differs outside the range that we have direct access.

0:41:07 SC: Falsifiable. It's a good scientific theory.

0:41:11 NH: Right. But, of course, this wouldn't be taken seriously. Now, as a side note, I will say when I bring up this example in philosophy of science classes, there are always a certain percentage of students who want to say, "Well, we just have to wait and see." Right.

0:41:28 SC: Really? They honestly do that?

0:41:29 NH: Yes, honestly. Yeah, yeah. They think, "Well, we don't know that... "

0:41:32 SC: They're just as good.

0:41:33 NH: "That gravity doesn't work that way. But we can wait until 2020 and find out."

0:41:39 SC: Arguably, Karl Popper thought that way, right? You just list every single possible thing that can happen and you chop them off one by one.

0:41:45 NH: Right. Right, right. And I think Hume would have been fairly impatient with this, because he would have correctly pointed out that we need to make these inferences, these extrapolations in order to act, in order to know how to act. So if you were designing a probe to send to Mars, you would design it under the assumption that gravity is going to continue to operate in the way it has in the past.

0:42:08 SC: Not all of these hypotheses are equally plausible.

0:42:10 NH: Right, right, right. But Hume would ask, how do we...

0:42:13 SC: So, sorry. So on the one hand, Hume is pointing out that it's a bit of a unsupported extrapolation. On the other hand, he's saying, "But we gotta do it."

0:42:21 NH: Right, right, right. So there's an aspect of Hume's view that's unusual here, which is that he thinks human reason... I'm going to go out on a limb here, 'cause hopefully, there are no Hume scholars in the audience. But the way I read Hume, he thinks of human reason as sort of like digestion. It's something that serves us in a certain way. And it can serve us better or worse. But it's a mistake to over-inflate it. So he's quite comfortable with saying, you can't form a rational argument to extrapolate one way rather than another. However, you will find yourself inevitably extrapolating one way rather than another. And certain ways of extrapolating are better for you than others.

0:43:09 SC: A typical scientist not philosophically trained would just say, "Well, but look, the gravity is the same tomorrow as it is today. Theory is just simpler. Therefore, I have greater credence in it." What's wrong with that?

0:43:20 NH: Yes, yes. So the question that will now arise is, how do we know? On what basis are we confident that the world operates according to simple principles? And here's where Hume's argument becomes clever, 'cause he observes that that very claim, the world operates according to simple principles or, as he would put it, nature is uniform, that looks like an empirical claim. And if you have the background attitude that any empirical claim about the world has to be substantiated by empirical data, but you also think that the very process of substantiation, in order for that to get off the ground, we need to pre-suppose that nature operates according to simple principles or is uniform, then it looks like you're running in a circle here.

0:44:04 SC: Yeah. A little bit.

0:44:05 NH: That's Hume's famous presentation, the argument for, of the problem of induction, rather.

0:44:10 SC: So, but the conclusion of it, just to be very clear, 'cause some people get this a little bit wrong, it's not that you can't do induction. It's not that you can't extrapolate. It's that the ground beneath you is shakier than you thought, but you gotta do it anyway.

0:44:23 NH: Right. Right. And the way I like to think about it is, you might have thought that you could endorse with a clear conscience this principle that any empirical claim about the world should only be believed if there's empirical evidence to back it up. But if Hume's right, we have to abandon that. We have to say something like, there's certain empirical claims about the world that we can't give up on pain of just not knowing how to extrapolate it all.

0:44:49 SC: And arguably, in some sense, this line of reasoning... I must be getting this wrong. But somehow, this line of reasoning seems to be feeding into the argument you gave for being anti-Humean. Because in some sense, we would have more justification for doing these extrapolations if we attributed to the laws of nature some extra property over and above mere regularity as an idea.

0:45:09 NH: That's a really interesting... That's a really interesting suggestion. And there's a lot of dispute within philosophy about that very question. So there are some people in philosophy, you can... In recent decades, you could find this argument very clearly presented in the work of, say, David Armstrong, who's... He's deceased now, but he was a very influential Australian philosopher, who argued that unless we see laws as having some genuine power or force, induction is irrational. It's not, Hume would say it's non-rational. He wouldn't say it was irrational with all the negative connotations that word has. But these philosophers will say, "No. We need real necessities in nature. Otherwise, if we take seriously the alternative, we should not expect anything about the future, except beyond the bland statement, 'Something will happen.'"

0:45:44 SC: Yeah, okay. Go ahead.

0:45:44 NH: The tricky question here is whether Hume's problem is just going to re-arise. So one way to bring this out is against a theological background. So it would be one thing if we could say to ourselves, "Look, we have independent reason to think that the cosmos was created by a benevolent, all-powerful being." And back in, say, Newton's day, a lot of people did think they had independent reason for that, believing that. At that rate, it was probably not a good idea to deny that in public.

[laughter]

0:46:36 NH: But if you had that view, then you could say, okay, the laws of nature, this goes back to what you were saying, the ultimate anti-Humean view is this kind of theistic view, you say there are these laws of nature, they're genuine rules and furthermore, we should be confident that those rules are intelligible to us, that as where the rules were built with us at least somewhat in mind. And that would give you a positive argument for thinking that the world is uniform or uniform enough for us to discover its principles, because the alternative is that God has this very kind of malicious or at least mischievous attitude.

0:47:12 NH: Subtle and also malicious, yes, right. But doesn't the flip side work too? In the modern perspective. Us being designed to understand the rules seems less plausible than... Well, sorry, the rules being designed for us to understand them seems less plausible than us being designed to map onto the rules since we obey the rules, right? We're part of this world.

0:47:33 NH: Yeah.

0:47:33 NH: So, discovering things about it is maybe not completely wildly implausible.

0:47:38 NH: Yeah, yeah. Though there's an interesting question how far that kind of perspective can take you. If you have a theistic perspective, you might be quite optimistic. You might think, "We can discover all the rules, even the rules that govern phenomena at incredibly small scale or at energy scales that are incredibly large. And so not the sort of thing we would ever encounter." Whereas there is a worry that if you think that we are designed, our cognitive equipment is the sort of equipment that will get us around well in the world. Well, that's fine for catching causal relations and regularities at our scale, but you might start to get uneasy, like, great, why should we think that the cognitive equipment that evolution's bequeathed us with, is going to let us do quantum gravity?

[chuckle]

0:48:26 SC: Well, as someone who tries to plump for the many worlds interpretation of quantum mechanics, I see the resistance because it's so different than what our intuition is. And I try to make the argument that, at some level, some point in the history of evolution we became too [0:48:42] ____ incomplete and we can do logic and then we can just put aside our... Not put aside our intuitions entirely, but not rely on them entirely either, and do a little bit better.

0:48:51 NH: Right. And so this brings us back to Hume's observation, at least if it's correct, that we seem to need to operate in the empirical domain with some background presumption that nature is uniform, 'cause that's not going to fall out just from logic.

0:49:06 SC: No, absolutely not, yeah. Okay.

0:49:09 NH: And so if we ask, well, suppose we posit these anti-Humean laws, but suppose, just to continue with the theological metaphor, that we imagine there are rules laid down by a god, but a god whose intentions we have no idea about at all. Like zero idea about.

0:49:24 SC: Plenty of people think that they're really tuned into God's intentions. [chuckle]

[laughter]

0:49:29 SC: But okay.

0:49:30 NH: So this would be a much more humble perspective like, yes, there is a God, but who knows what she wants, no idea whatsoever. Then Hume's question looks like it's going to re-arise, why would we expect those rules to be what we would consider simple? And is it actually... I've been doing a lot of the talking, but I'm just very curious of what your take is on what theoretical physicists think about standards of simplicity.

0:49:53 SC: Well, I was going to mention, it's been taken for granted in most circles that beauty, simplicity, elegance, are guiding principles when looking for new theories of nature, it's come under a bit of criticism lately. Most notably by Sabine Hossenfelder, who is a physicist, who has been saying it for a while, but has said more loudly recently that we've been tricked by looking too much or trusting too much in elegance and simplicity. And we do have this looming empirical fact about the world that we turned on the Large Hadron Collider, we had what I thought and what most people thought were very good reasons to think that we would discover not only the Higgs boson, but a proliferation of new particles. All of those arguments were based on considerations of elegance and simplicity and they were clearly wrong.

0:50:49 SC: And so, there's two ways to go. Either elegance and simplicity aren't as important as you thought or we got the elegance and simplicity wrong. That's always a possibility. So I think it's still most people, including myself, think that elegance and simplicity are extremely helpful. Of course, the data have the final say, but when you're extrapolating, as you say, into realms where you haven't actually done the empirical tests yet, of course you put the highest probability on the simplest thing going on.

0:51:17 NH: Right, right, and that's a very interesting observation, 'cause one of the things that I think is really fascinating about standards of elegance and simplicity is that they don't wear their content on their face. It's pretty clear what sorts of things would count as inelegant on any reasonable way of understanding that, like my Schmisaac Newton's law. But that may leave a fair amount of room within the things that could reasonably be viewed as elegant and simple. Presumably there's a fair amount of room for maneuver.

0:51:49 SC: Well, certainly comparing Newtonian gravity and absolute space-time to Einstein's general relativity, the beauty is in the eye of the beholder a little bit, and to someone who is not up on tensor calculus, general relativity can seem very far from elegant.

0:52:03 NH: Right, right, right. So there's another aspect to this discussion which is, you may need to have a certain amount of training...

0:52:09 SC: That's relevant to your background knowledge.

0:52:09 NH: This is a biased way to put it, but you may need to have a certain amount of training to appreciate elegance and simplicity that's there.

0:52:15 SC: I think that many worlds is very elegant and simple. Not everyone agrees. [chuckle]

0:52:19 NH: Oh, it is, it's quite elegant and simple.

0:52:21 SC: But well, to be fair to them, the connections we are forced to draw between the underlying formalism and the world of experience are not very elegant and simple. And so if that's part of the theoretical framework, then, granted, it's a mess.

0:52:37 NH: Yeah, and that's a good point. My only instinct, I think I have kind of old-fashioned rationalist instincts, I would have been very comfortable in that humanistic setting. And my own instinct is to think that the principles of elegance and simplicity should be seen as good guides if you're down at the level of fundamental physics, and then from then on up things get messier and messier. We might come back to this when we talk about causation, 'cause that's part of what makes causation such a vexed topic is that as you scale up, the kinds of relationships you can cleanly track become fewer and far between, I think.

0:53:08 SC: Well, yeah, let's start moving in that direction for the argument in favor of taking anti-Humeanism seriously, it relied on various hypothetical counterfactual situations, and we tossed around the phrase "possible worlds," and probably Hume didn't toss around that phrase or Newton, but it's become very popular in recent decades in philosophy. And was David Lewis your advisor, were you related to him somehow, academically?

0:53:38 NH: He was one of my mentors.

0:53:39 SC: Mentor, okay.

0:53:39 NH: He was not officially an advisor, but he's someone that I worked very closely with.

0:53:43 SC: So, explain to the audience why philosophers love to talk about possible worlds.

0:53:48 NH: Oh, okay. That's a complicated question. There are all sorts of different reasons. Let me highlight a couple very different reasons. One reason is that possible worlds just seem like an interesting topic in their own right. How did they become an interesting topic? Well, by a connection to something that we could already recognize if we go back to your original comments as part of our basic way of thinking about the world, that we seem to draw distinctions between what could be the case and what has to be the case. And for a philosopher that's just puzzling. What is that distinction?

0:54:25 SC: Yeah, 'cause we draw it all the time without interrogating what we mean.

0:54:29 NH: That's right. And, over the course of the 20th century, probably starting somewhere in the '40s, I'm a little hazy on the history here, it came to seem that we could clarify that question if we talked, not directly in terms of possibility and necessity, just using those words, but in terms of possible worlds, where the intuitive conception of what a possible world is, is it's a way that reality, as a whole, could have been. Another way to put it, which is a little more illuminating, is a possible world is something like a complete consistent story about the world.

0:55:10 SC: And just as a footnote, it's very different than the many worlds of quantum mechanics, which are all just different pieces of the same world, so we're using world to mean all of reality in one example thereof.

0:55:18 NH: That's right, that's right, that's right. So many worlds interpretations of quantum mechanics would describe one possible way for reality as a whole to be, and on that way of describing it, reality as a whole contains multiple cosmoi, if that's, whatever the plural of cosmos is, whereas for philosophers who are talking about possible worlds, there's no connection between possible worlds in the way that there's a connection between different branches of the multiverse. So, so far, so good. We can say, look, here's a kind of convenient way to clarify and regiment our talk of possibility and necessity. We'll talk about what is the case according to a complete and consistent description of reality as a whole.

0:56:02 SC: Which includes, just to make it perfectly clear, not only the purported laws of that world, but the individual events that happened in it, right, like, if I had not crossed the street denotes a possible world.

0:56:13 NH: Now, why would you want to talk this way? There are a number of different motivations, and I'm definitely not going to do justice to them all. Some of them come from analyzing language, you want a kind of systematic analysis of logical connections between statements about what could have been the case and what is the case and what must have been the case. Or you simply want to have a way of clarifying what I mean when I say something like this, I could have been taller than I am.

0:56:41 SC: Right.

0:56:42 NH: So, let's just pause over that example. We can all hear that there's an ambiguity there. On one way of hearing that, it's obviously false.

0:56:50 SC: It wouldn't be you if you were taller. Yeah.

0:56:52 NH: And another way of hearing it, it's plausible. And if you embrace talk of possible worlds, you can clarify the difference. You can say on one way of hearing it, I am asserting that there's a possible world according to which Ned, as Ned is in that world, is taller than Ned as he is in that world, and there is no such possible world. In any world in which I exist, I'm as tall as I am.

0:57:15 SC: That makes sense. [chuckle]

0:57:16 NH: On another way of understanding it, I'm saying there's a world in which Ned, as he is in that world, has a height greater than Ned as he is in the actual world. And so we see this just in microcosm here how talk of possible worlds can help clarify distinctions that ordinary language can blur.

0:57:34 SC: Yeah, okay, and I want to mention the name David Lewis, 'cause I think he's probably the greatest ratio of importance to modern philosophy versus public recognition. Most people on this feed have never heard of him in the way that they've heard of Wittgenstein or Sartre, and he took this... He did a lot of the spade work in making sense of this notion of possible worlds and he went so far as to say they're all real in some sense, right, modal realism.

0:58:00 NH: That's right. And it's hard to overstate how dramatic this move is. So, so far, if you're hearing the way I'm talking about possible worlds, you might think, alright, that seems like a useful device.

0:58:13 SC: Yeah, exactly, a tool.

0:58:15 NH: Lewis wanted to say, it's not just a useful device. He wanted... Well, he didn't just want to say, he did say that, in order for us to use this talk of possible worlds with a kind of clean, intellectual conscience, we need to answer the question, a version of the question that we started this podcast with, which is, "What are they?" And it's not enough just to say they're stories, because Lewis would say, okay, stories in what language exactly? Are these stories that are graspable? Are they written in a language that could be understood by a human? A little awkwardly, if they're stories, they can't just be any stories 'cause they have to be consistent on the usual way of understanding it, and they have to be complete in that the story, as it were, answers any question we might pose of it.

0:59:11 SC: The whole world, yeah, right.

0:59:12 NH: And that notion of completeness is actually related to consistency through the back door 'cause part of what we mean by saying a story is complete is that any addition to it would render it inconsistent. It's so full in what it says about the world that it couldn't say anything more without collapsing into inconsistency.

0:59:15 SC: There's some answer to every question you could allow to be asked.

0:59:15 NH: But, just focus on this demand of consistency. Lewis would want to know, what do we mean by consistent there? And for him it was very important to give an answer to that that didn't just reintroduce notions of possibility and necessity. So, there's a move he's making here that for people who are coming at this from outside philosophy is going to seem strange, and cards on the table, rightly so, I think. But the move is to say, it's not enough to use this notion of possible worlds to clarify our talk of possibility and necessity. We need to use it to analyze that talk into some other terms.

1:00:16 NH: So, what do we mean by analyzing talk into other terms? Well, it's helpful to draw on mathematics here. So in number theory, we don't think of the notion of a prime number as a primitive notion where it's like jazz. If you have to ask what a prime number is, you obviously never worked with one or something like that. We think we can define precisely what a prime number is in other terms. And in philosophy and indeed in the sciences and mathematics, we very often face this question, "When should we take some term as needing to be defined?" When should we think there's a... If we're going to use this term with a good conscience, we really need a story about how to understand it in other terms. I for example think our talk of causality is like that. I think there's... As a matter of good intellectual hygiene, we really need to explain our talk of causation, cause and effect in some other terms. Fiendishly difficult to do that.

1:01:13 NH: Lewis thought we had to do that with our notions of possibility and necessity. And he thought he could do that in a two-step process. So first step, to say that something is possible is to say that there's a possible world in which it's true. Second step, a possible world is literally a concrete chunk of reality as a whole. How is it related to the chunk that we're in? It bears no space-time relation to our chunk at all. It is in that sense a completely separate chunk of reality. Now, notice something fast just happened. I said it's a chunk of reality. That is, reality as a whole includes the actual world and it includes other concrete material chunks that are other possible worlds. But didn't I say before that a possible world was a way that reality as a whole could be?

1:02:10 SC: Yeah.

1:02:11 NH: Well, you can't say both of those are the same.

1:02:13 SC: The words are failing us a little bit.

1:02:15 NH: Yes. Yeah, yeah. And so, Lewis recognized that and he said, "When I say, just to sort of lodge the basic idea into your head, that a possible world is a way reality as a whole could be, I didn't really mean reality as a whole. I meant our corner."

1:02:30 SC: Yeah. Okay. That makes sense.

1:02:32 NH: So that's sort of the whole package there.

1:02:34 SC: Parenthetically, Max Tegmark has reinvented and re-introduced this idea from a cosmological point of view saying that every mathematical structure corresponds to a real existing world.

1:02:44 NH: Is it corresponds to or is?

1:02:46 SC: Is.

[laughter]

1:02:48 SC: I'm not sure there's a difference, but if I'm channeling Max, then he would say is. And so, this is going to get us appealed, but I'm going to say it anyway.

[laughter]

1:02:56 SC: There's a measure problem in that case.

1:03:00 NH: Yes, yes, yes.

1:03:00 SC: If all the possible worlds exist, one exists where gravity is the inverse square law up until 2020.

1:03:06 NH: That's right.

1:03:06 SC: And why can we therefore say it probably isn't in our world?

1:03:13 NH: Awkward.

[laughter]

1:03:16 NH: So Lewis himself didn't have a lot to say about the problem of induction. I think, and I say this just from conversations I had with him, not from my knowledge of what he's written. I've read a lot of what he's written but I may have missed something. I think he thought it was just unavoidable that we have to spot ourselves something like a rational entitlement to believe that the corner of reality that we're in, the actual world, is simple and elegant.

1:03:44 SC: Good. So Max would like to say... So I think he's actually improved that a little bit. He's saying there is some measure of simplicity in the sense of algorithmic simplicity, the way the shortest descriptions of the entire universe get more weight somehow than longer ones. And I think that he's just pulled that out of nothing but at least it would help with the puzzle.

1:04:08 NH: Yeah, that's interesting. So it would be interesting to know how he would answer the following question, shortest descriptions in what language?

1:04:16 SC: Well, there you go. But I do think that's an answerable question. I think computer scientists think about that. There's some universality. There's some in the studies of Kolmogorov complexity, there's some wiggle room but not infinite wiggle room in answering that question.

1:04:30 NH: Right, right, right. So that would be interesting to dig into. There's a kind of famous variant on the problem of induction here due to Nelson Goodman that involves using weird predicates to describe a pattern. This is the grue and bleen problem which you may have heard of which arises here. 'Cause the kind of example Goodman had in mind is very simple, much simpler than the kind that Max is thinking about. But if you imagine that you go out into your garden every day and you look at your tomatoes and you notice that the young ones, the unripe ones are green and the ripe ones are red. You can describe the pattern you've observed in two different vocabularies. You can use the familiar vocabulary of green and red or you could use a kind of bent vocabulary where you say something is... I'm going to change... For Goodman it was blue and green were the things. Now it's going to be red and green. I'd say something is like reen if it's green up until 2020 or red and it's after 2020, and I say something is gred, if it's red, up until 2020 or green thereafter. The clever move here is that green and red are inter-definable with reen and gred.

1:05:45 NH: And so now we can ask, which is the right way to describe this? WE might say, "Well, look, a world in which the colors flipped on that date, 2020, would be a less simple world." We should believe our world is less simple. Well, it looks less simple if you describe it using the green/red vocabulary, but using the reen/gred vocabulary, it'll look simpler. It's the world in which you know very young tomatoes are reen, and ripe tomatoes are gred, always.

1:06:15 SC: This seems to be a problem that could, in principle, be overcome because of the fact that these concepts do not exist in isolation, right?

1:06:21 NH: Yes. Yes.

1:06:21 SC: There are photons, there is the universe, and maybe there's not as much free play, labels as we might imagine.

1:06:28 NH: That's right. You'd want to look at how things appear when you're down at the level of fundamental physical details. Is there still the same flexibility available?

1:06:38 SC: I think there's some flexibility there, like if there's Hamiltonian versus Lagrangian mechanics, but it's not infinite. Okay. Okay, and just because we have to cover so many centuries of knowledge in such a little time, so Lewis sets out this idea of possible worlds. He supposes that they're real. Do we have on the table the best argument that we should think of them as real?

1:07:05 NH: I can give you what I think is the best argument, but it really demands a crucial premise, which is that an account of possibility and necessity that doesn't analyze those terms in other terms that have no modal character to them, is distinctively inferior to an account that does analyze them in non-modal terms. And I don't know how to argue for that premise. Lewis in this famous work called On the Plurality of Worlds employs that premise very cleverly. And I indicated some of the ways, I guess I didn't give him proper credit, but it was from reading that book that I learned this point about the best complete stories that to make that account of possible worlds work, you really do need a modal notion, a notion of consistency, down at rock bottom, that you don't analyze away. And for Lewis, that was an incredibly serious cost. Now, what I again don't know how to make plausible is why that was a serious cost.

1:08:10 SC: Okay.

1:08:10 NH: And it may be that at heart, there was this deep Humean sympathies he had, he was a Humean about laws of nature. But it may be that that ran much deeper, that a notion, an unanalyzed notion of possibility or necessity is just anathema, like there's something just profoundly mysterious about that.

1:08:29 SC: I'm certain he's personally skeptical about the reality of other possible worlds, but I think I could sympathize with the feeling that it would make life easier, like if we have to keep using these in our talk, just believing in them, it takes a burden off of our shoulders, right?

1:08:45 NH: That's right. And it is true that philosophers often talk the way Lewis would recommend that they talk.

1:08:49 SC: Yeah.

1:08:50 NH: We routinely say things like, "Well, there is a possible world in which... "

[chuckle]

1:08:55 NH: And we're not careful about this. We don't say, "There is a consistent story about the world according to which," we just say, "No, there's this thing."

1:09:03 SC: That's right. And philosophers, of all people, are supposed to be careful, but the fact they have trouble with it maybe means something. Good. So I think this is bringing us back to what it means to be the cause of something, because when we say, "I got sick because I had bad sushi," we're comparing the world we live in to another possible world in which I didn't have sushi, is that right?

1:09:25 NH: Right. Yeah, yeah, yeah.

1:09:26 SC: But that's not quite enough.

1:09:28 NH: Right. Right. 'Cause not just any possible world. Here's a possible world, in which you didn't have bad sushi, you had bad chicken wings instead.

1:09:38 SC: Still would have gotten sick, right, yeah. So that's where all the fun lies. It's like comparing, how do we compare the possible worlds?

1:09:45 NH: Yes. Yes. And there's been a lot of thought put into this recently, by philosophers and non-philosophers alike. And a little back story there, why are non-philosophers involved in this debate? Well, there are lot of non-philosophers who worry quite a lot about how we can draw conclusions about what causes and what forms statistical data.

1:10:02 SC: From data, yeah.

1:10:02 NH: Yeah. And, again, this is a scenario where I'm no expert on the history, but I'm pretty sure that statistics as a field started out in the early 20th century fairly hostile to the notion of causation. You can find, I've actually checked one important work, I think it was Pearson, a book-length treatment of statistics early in the 20th century, where there's a whole chapter on why the notion of causality should be banished from good science.

1:10:27 SC: Well, Judea Pearl, who is leading the counter-attack there, certainly is very vocal about the fact that statistics as a field does not take causation seriously, let's put it that way.

1:10:38 NH: Right, right, right. But the early statisticians did have a point in the sense that, if you compare our ordinary way of talking about cause and effect to the ways of talking that they were recommending in terms of precisely definable notions of correlation, it looks like, with respect to scientific rigor, it's no contest. The notions of correlation are so much more rigorous.

1:11:04 SC: And again, it's reminiscent of the Humean versus anti-Humean argument. If you know what all the correlations are, what extra do you get by saying that something causes something?

1:11:12 NH: Yes, yes, yes, absolutely. Absolutely. So that's a deep, foundational question, I think. And, if I had to say what the prevailing view of that question is, among people like Pearl, who are fans of causal talk, it's that you get the kind of knowledge you need to help you decide how to intervene. 'Cause when we're deciding how to intervene on...

1:11:40 SC: Which, by the way, is another sort of hypothetical possible world kind of discussion, right?

1:11:45 NH: That's right.

1:11:45 SC: If I do intervene, if I don't.

1:11:46 NH: That's right. That's right. Yeah. In fact, we probably should have brought that up earlier, 'cause that's, in a way, the most immediately intuitive way in which we in our encounter with the world are up to our ears in hypotheticals. We're constantly thinking about, "What would happen if I were to do this, or to do that?" Or retrospectively, we might think like, "Oh, if only I had done that." And someone like Pearl takes that kind of talk very seriously, and rightly so.

1:11:46 SC: Sure, yeah. Whatever our philosophical stances are, we do talk that way, and we kind of have to. [chuckle]

1:11:46 NH: Right, right, right. And I suppose, in a way, I was getting at with that wild thought experiment about the two theories. 'Cause that evokes the same sort of thought that like, "Well, there's a structure to the possibilities that's pre-set, and when we're reasoning about what to do, we're sort of wondering what that structure is like." No. So for fans of what has come to be called an interventionist approach to causation, it has lots of different labels, the core thought that is that causal relations are relations that, at least in principle, are exploitable for purposes of manipulation. Like they...

1:12:53 SC: Okay.

1:12:53 NH: So another way to put it is our interest in causation is an interest in facts about the world that we can use to settle what would happen if, what would happen if you do one thing or another. And you can easily think of examples where manipulation is about humans as off the table. We might wonder what would have happened to the dinosaurs if no asteroid had struck at a certain point. And for people who take this interventionist approach, I think you're supposed to see that as a kind of natural extrapolation of a kind of way of thinking about the world that really has its home in human agency.

1:13:26 SC: And when you say it that way, it just seems so sweetly reasonable that how can there... So isn't that just right, but what are the other possible ways of thinking about causation?

1:13:35 NH: I think that that is an open question, and I find myself in a rhetorically awkward situation here, because I think there's severe limitations on the interventionist approach, which I can explain, but it would be much better for my purposes if I could say, "Oh, and here's a nice alternative," but it's actually hard to think of an alternative.

1:13:53 SC: It's like string theory and quantum gravity, like it's the leading candidate and many... Or the multiverse is even a better example in explaining cosmological fine-tuning. When I had Leonard Susskind on the podcast, and he's a fan of the multiverse, and how it explains why various parameters in our observable universe have the numbers that they do, and he gets a lot of pushback for that, and he says, "Just tell me what else it could be. I don't want it to be this, but I have a theory that predicts it, it seems to work, I'm going to go with that until you can do better."

1:14:23 NH: Yeah, yeah. Which I think is a reasonable attitude, especially if you're a working scientist.

1:14:27 SC: Yeah.

1:14:28 NH: I think you have to be careful, though, not to throw too many babies out with the bathwater. So just to indicate where some of the difficulties arise, in the social sciences, we might want to attribute effects to features of the world where they're... It's not just that we can't manipulate them, it's not even clear what we would have in mind by manipulating them. So, maybe your social class has effects, downstream effects on the kind of opportunities available to you, we think. How do you manipulate someone's social class directly? And it's important to recognize that the background idea here is that causal relations are the kinds of relations that would be manifested in an ideal controlled experiment.

1:15:17 SC: Yeah, exactly.

1:15:19 NH: So what would be a controlled experiment?

1:15:20 SC: And in the possible world language, that corresponds to something like a minimal change from one world to another.

1:15:25 NH: That's right. That's right. In fact, the cleanest change would be you have a god-like power to swoop in on the cosmos at some localized place and time, tweak it while holding everything else at that time fixed and then see how things evolve forward.

1:15:38 SC: And in some sense, that's what Pearl tries to formalize in his causal calculus theory.

1:15:41 NH: Yeah, yeah, yeah. Though he's a little quietist, I think, about what the background is. Here for me, I come at this against the background of all the stuff we've been talking about about laws of nature where I say like, well, if you've already got in place, however you think about them, Humean or anti-Humean, things that you're going to treat us laws that tell you how to extrapolate forward from any given complete state of the world, then we can kind of get some control over counterfactuals that involve like localized changes to a state.

1:16:15 SC: Yeah.

1:16:15 NH: But Pearl doesn't say much about that. He doesn't... As I would put it, this is a place where I would want the counterfactuals that he describes in his causal diagrams, I would want them to be analyzed in terms of something else.

1:16:29 SC: Yeah, okay, that's fair.

1:16:30 NH: And that may... Who knows? Maybe that's just an aesthetic preference on my part where he's happy to treat that notion really as a kind of primitive and build a formal system around it.

1:16:38 SC: Okay. But you were giving us reasons to be skeptical of interventionist accounts?

1:16:41 NH: Right, right. So if you think of social features, like class is one, but here's one, race. You might think that what race you have has effects on your prospects, but that is a little awkward if you're an interventionist to try to answer the question, "What would be a perfectly controlled experiment in this case?" Or there are much more mundane examples too. There are everyday examples. So you're right now wearing a kind of... Sort of blue-gray shirt, here's a question we could ask, "How would this conversation have gone differently or be going differently right now if your shirt were some wild Hawaiian print?"

1:17:21 SC: Right.

1:17:22 NH: Maybe it wouldn't go differently. Maybe I'd be...

1:17:23 SC: You'd have lost respect for me.

1:17:24 NH: Exactly, yeah.

1:17:25 SC: But it would have been a much better...

[overlapping conversation]

1:17:27 NH: I'm so distracted, "What was that question?"

1:17:27 SC: Yeah.

1:17:27 NH: Right. Here's a way not to clarify that question about the influence the color of your shirt may or may not be having on the course of this conversation right now at this moment. We should not clarify that question by seeing it as the question: How would this conversation go from this point forward if your shirt, as a result of a localized intervention, were a Hawaiian print like a loud Hawaiian print, rather than this nice blue-gray, right?

1:17:54 SC: Yeah, okay.

1:17:55 NH: 'Cause the hypothetical situation we're imagining here is one where, as it were, God swoops in, makes a localized change to the pattern on your shirt, and then we see how our conversation goes forward from there. Here's how the conversation would go, "Oh, my God, Sean, what happened to your shirt?"

[laughter]

1:18:10 SC: Exactly. Right, yeah. I see, it violates the laws of physics as we understand them.

1:18:13 NH: Yeah, yeah. And once you notice this, this problem ramifies in the social and psychological realms. There's actually a student of mine, Alex Prescott-Couch, who's now a philosophy professor at Oxford, who really pointed this out, to me at least, quite clearly how widespread this issue is. He imagines a case where, oh, there's a... Joey is a student at a school, and Joey is a child of a single parent and gets teased a lot at school for being a child of a single parent, 'cause his classmates are kind of jerks and Joey is stressed out. And you might... You might think it's a good question how the teasing is interacting with the fact that he's just got a single parent in producing his stress.

1:19:01 NH: And for an interventionist, the natural way to approach this question is to ask a bunch of hypotheticals. There's the actual situation where the variable, the parent variable is set at 1 and the teasing variable is set at 1 and what we should do is contrast that with hypothetical situations in which those variables have the other possible values. And that works okay for some settings of those alternative variables. We could meaningfully ask how stressed out he would be if he weren't teased, but still had just one parent, or how stressed out he would be if he had two parents and weren't teased. Here's the weird one. How stressed out would he be if he had two parents and were systematically teased at school for having one? And as Alex points out, he would be in some Kafkaesque scenario.

1:19:49 SC: Yeah, he's like, "Dudes, why are you doing this?" [chuckle]

1:19:52 NH: And whatever our answer to that question is, it simply does not seem to be illuminating the causal question we were asking in the first place. It seems like the wrong way to think about it.

1:20:03 SC: That's kind of the minimal change.

1:20:05 NH: Yeah, that's right, it's the minimal change. And there are other things too, if we think about protracted events, like maybe Randolph, for example, smoked heavily in his 20s and he got cancer in his 50s, and we're curious about whether his decade-long history of heavy smoking caused his cancer. Notice we're not curious about whether that puff on that occasion caused his cancer. We really feel like in order to track the causal relations we're interested in, we need to zoom out to a longer time scale. So what would it be to intervene on that history in a localized way that doesn't introduce potentially confounding variables. That's the crucial thing.

1:20:48 SC: So, very roughly and perhaps unsatisfyingly, the situation we seem to be in is talk of causation or whatever it means to talk of it, does involve a comparison of different possible worlds; what is not completely clear is how to do the comparison, which world to include.

1:21:05 NH: I think that's a very good way to put it.

1:21:07 SC: It's interesting to me, especially because in science over and over again, we reach situations where we're asking and caring about different questions because of advances in technology, like quantum computing, for example, now that we can do it. But in some sense, this is an example where, maybe not within philosophy, but in the rest of the world, we're asking this philosophical question because of advances in technology. Now that we're in the big data era and we can see some correlations...

1:21:33 NH: Yeah, that's right.

1:21:34 SC: The idea of pointing them and being a good inductor or whatever, seeing some pattern and attaching some emerging reality to it, is becoming more important.

1:21:43 NH: Yeah. And I think some social scientists who are fans of this interventionist approach would really emphasize this kind of point. They would say we're now in a position to do causal investigation or causal inquiry better. And this interventionist approach provides us the right conceptual tool. We now have the ability to use that tool, 'cause we can either do randomized control trials or, like the best social scientists are incredibly clever at finding ways in which nature has done that for us. And that will give us insight in a kind of rigorous grounded way that we didn't have before just by going and talking to people or living with them and so on. But there is ongoing uncertainty, I think, within that field, or even outright dispute about whether we're losing something if we just set aside as kind of unscientific or un-rigorous those more "qualitative methods" that have historically been very important.

1:22:41 SC: But it sounds like there's plenty of room for a useful productive interaction between philosophers and social scientists here, maybe.

1:22:46 NH: Yes. That's the hope.

1:22:47 SC: Alright, that's always a good lesson to end on. So Ned Hall, thanks so much for being on the podcast.

1:22:54 NH: Oh, you're welcome, it's been a delight.

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