Episode 90: Bayesianism for Critical Rationalists!?
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Transcript
[00:00:06] Blue: Hello out there. Today, our guest Ivan Phillips methodically explains what Bayesianism is and is not. Along the way, we discuss the validity of critiques made by critical rationalists of the worldview that is derived from Bayes’s 1763 theorem. I came away with a new appreciation for this rationalist tradition and I hope someone else out there gets something out of this. I also want to mention that unlike most of our podcasts, there is a video of Ivan’s PowerPoint to supplement this one. So if you are on Spotify or another platform that supports video, you will get the full experience. But it should be okay with just the audio as well.
[00:00:52] Red: Alright, welcome to the Three of Anything podcast. Hey everybody.
[00:00:57] Blue: Hello Bruce.
[00:00:59] Red: And Ivan. We have Ivan here with us again. Hey Ivan. Hi
[00:01:03] Green: Bruce. Hi PC.
[00:01:05] Red: Hello. So we decided to do the unthinkable. We decided to invite Ivan, who last time if you don’t recall, he was on the podcast to talk about subjective values. So Ivan’s kind of our, what do we want to call it, heretical voice here? He follows the many worlds of David Deutsch page and comments a lot. He’s a top commenter. And he knows critical rationalism and David Deutsch’s stuff really well, but he’s kind of thinks in different ways on all of these questions. And he’s a Bayesian. So I thought, but he’s a Bayesian that has read logic of scientific discovery. So he knows critical rationalism too. So I wanted to invite him onto the show to do Bayesian epistemology for critical rationalists. And this is a video podcast. So he’s going to be sharing a screen because obviously there’s some formulas that it’s probably going to be easier if you can see it. But we’ll try to keep it so that it’s still, you’re able to listen to it. If you just want to listen to it, we’ll kind of discuss what we see on the screen and what the point is and try to make sure we give you the gist. But I have been very excited about having Ivan come back and talk with us and explain to me a Bayesian epistemology that I keep hearing about, but I feel like I don’t really understand. I think that’s our niche, isn’t it, Bruce?
[00:02:32] Blue: It’s just to, we want to piss everyone off in the nicest way possible. The nicest guy imaginable is going to just cause a firestorm here, maybe.
[00:02:44] Red: That’s what we’re hoping. It’s very polite firestorm. And Bayden and Ben will be listening very carefully to everything we say on this podcast. Yeah, they’re definitely going to hate what I have to say. So maybe we’ll invite all three of you together in a future podcast or something to talk about this. But we want to give Ivan a chance to give his point of view first. And I should emphasize that this is in no way a debate. First of all, I don’t think I’m knowledgeable enough to debate Ivan on this subject. Maybe in the future, I’ll be able to do that. But I mean, you have to actually know the subject to be able to have a debate. And I haven’t really learned it well enough yet. I haven’t been interested enough, but I’m starting to get interested based on stuff I’ve listened to recently and some of the things Ivan has pointed me towards. But really the goal here is to give Ivan a fair hearing to explain Bayesian epistemology in a way that he hopes is going to be acceptable to a critical rationalist or at least understandable to a critical rationalist. And that’s what I’m kind of hoping for. We’ll try to ask intelligent questions, but we’re not here to debate Ivan. We’re trying to give him a fair hearing at this time. Any debates, that’ll be a future podcast.
[00:04:11] Green: I don’t want to say that I understand critical rationalism. I have been exposed to it. I’ve been following it for a long time because I think that it’s interesting. But I’m still puzzled by some concepts and ideas.
[00:04:28] Red: And
[00:04:28] Green: so I’m here as much as anything else to learn from the feedback that I get today. There are, of course, parallels between the two. So when I’m understanding critical rationalist ideas, I’m looking at them in Bayesian terms. And of course, they have to line up in some areas because they’re both trying to explain the same thing, namely the success of science.
[00:04:54] Red: Makes perfect sense to me. I do think that there are some definite parallels between the two epistemologies, probably even in areas that both sides try to claim there isn’t. It’s a little bit of a religious war at times where we want to be more different than maybe we really are. And that’s not to say there aren’t legitimate differences because there undoubtedly are legitimate differences. But I would like to get down to what are those actually, not the ones where we kind of fake differences. So also, I just wanted to say, so I can accept what you’re saying that you don’t feel like you maybe fully understand critical rationalism, but I wonder how many crit rats have actually read Logic of Scientific Discovery, right? So you’re probably as knowledgeable as most of us is my guess, at least us laymen. I mean, I don’t claim to be an expert in critical rationalism either, right? So you’re probably relatively knowledgeable, and I would guess that probably a lot of crit rats have read Logic of Scientific Discovery, but it’s not the most popular book to start into. And there’s definitely an opinion amongst a lot of crit rats I know that there’s really not that much reason to read that one, which I really disagree with because I feel like that is by far the most important of Popper’s books to read, like by far, like not even close. So the fact that you’ve read it, that impresses me and that’s one of the reasons why I wanted to bring you on the show and have you talk with us. So, all right.
[00:06:27] Red: Do you want to go ahead and share your screen and we will get into this and we’ll turn off our video beats while we’re letting him share here. Bayesianism for crit rats, right? 32 slides, by the way, guys.
[00:06:42] Green: There’s so much to say. Yes. Most of the presentation is stuff that’s non -controversial. It’s about what Bayes’ theorem has to say and what the Bayesian updating looks like. There’s plenty of conflict along the way for us to talk about. So, I wanted to say a little bit about myself just to manage expectations a bit. I am a fan of the theory of anything podcast. It’s my favorite podcast to listen to because it’s exactly epistemology. We should all love epistemology, right?
[00:07:21] Red: Yes, I think so.
[00:07:24] Green: We should teach it in school. I’m not a mathematician or academic. I do have a PhD in theoretical physics. I work in the software industry. But I am involved in science and critical thinking outreach. I did write a book in 2021 called Textbook Rationality. Rationality and why we should teach it in schools. Based on Bayesian epistemology, correct? Based on Bayesian epistemology, yes. And I’m the former organizer of the Chicago Philosophy Meetup Group. So, I’m quite interested in philosophy and how to apply Bayes and some philosophical questions. And the outline of my presentation is, the first thing I’m going to do is talk about conceptually what is the difference between the popular idea of the scientific method, the critical rationalist idea and the Bayesian idea. What is the emphasis of the different pictures? Then I’ll talk about Bayes’ theorem, the non -controversial theorem, right? So, Bayes’ theorem, subject to certain assumptions, is not controversial. And in fact, in the logic of scientific discovery, one of the things that Karl Popper does is he wants to verify that his version of probability theory satisfies Bayes’ theorem. So, you have to make a distinction between Bayes’ theorem and Bayesianism. Bayesianism, yeah, go ahead.
[00:09:01] Red: I was just going to say, if there’s any critical rationalist out there listening that aren’t sure if what he’s saying is correct, that Bayes’ theorem is non -controversial, that is absolutely, absolutely true. There is zero controversy over Bayes’ theorem. I’ve heard Deutsch say that as Ivan just pointed out, Popper tries to satisfy it in his books. There’s like really, really no controversy over Bayes’ theorem at all. Or really, a lot of the reasoning that comes out of the math I should probably say, I should probably be careful with the word reasoning, that comes out of Bayes’ theorem. It is what is used in machine learning today. I have a degree in machine learning. And typically, they start with a textbook like Christopher Bishop’s pattern, what is it called? It’s pattern recognition in machine learning. And it’s actually the Bayesian viewpoint. It is just absolutely the basis for modern machine learning and things like that. And we’re Bayesian reasoning in machine learning by David Barber or machine learning by Kevin Murphy are all introductory textbooks for machine learning and they are all the Bayesian viewpoint based on Bayes’ theorem. So just wanted to comment on that, that he is right, it is non -controversial.
[00:10:23] Green: Right. And after I’ve talked about Bayes’ theorem in the non -controversial sense, then I’m going to introduce Bayesianism. Bayesianism is really an extension of using Bayes’ theorem beyond where you might prove the theorem true in the non -controversial way. And then I will show how I, as a Bayesian, look at Popper’s Ratchet, which Bruce introduced in a prior podcast, which is a way of deciding how should you support theories? What do you do with ad hoc additions to your theory? What is allowable and what is not? Also, refutation and Occam’s razor, how I think of those things in Bayesian terms. And then we’ll at the end get into what I think are the critical rationalist objections to Bayesianism and why I am as yet unconvinced.
[00:11:31] Red: Okay, sounds good. So just one thing to clarify. Bayesianism is that equivalent to Bayesian epistemology, which is distinct from Bayes’ theorem?
[00:11:44] Green: This is a good question. I think that Bayesianism, in the sense that I’m using it, is perhaps a superset of Bayesian epistemology. And the only reason I say that is that I think that most people, when they talk Bayesian epistemology, probably have a narrower domain in which they want to use it. But my view is that Bayesian epistemology should be applied to everything. So it should be applied to epistemology itself. It should be applied to things like the limits of meaning and language.
[00:12:24] Red: And how much are you involved with effective altruism since they consider themselves Bayesians, and particularly long -termism? And do you have any associations with that
[00:12:38] Green: epistemology? I don’t really have associations with it because I’m not utilitarian. When I say I’m not a utilitarian, I’m a moral subjectivist. So I don’t think that any one moral system is true. I think that if a utilitarianism says something is wrong, you should treat that like as a warning light on your moral dashboard. It’s something you should pay attention to. But I don’t think that utilitarianism is strictly speaking true. It’s not something that is high on my interest. Long -termism, I think, is somewhat problematic. It’s so difficult to predict the future that I think it’s difficult to justify allocating resources away from people who need it today for the sake of people who might exist tomorrow. I think that it’s certainly possible to abuse Bayesian inference by setting up a Pascal’s wager where you look for some world where there’s going to be some vast number of people in the future. Let’s say trillions of people in the future. So now this is going to ask you to weight your priorities in favor of those trillions of future people instead of the millions of people today who might need something. That strikes me as questionable.
[00:14:25] Red: I’m actually glad to hear you say that because I think that’s one of the biggest things that I have struggled with with supposed Bayesian epistemology as the long -termists. Vaden and Ben have written some great pieces criticizing that viewpoint. Certainly the long -termists. I don’t have a ton of association with them, so I may be putting words in their mouth that is inappropriate. But I certainly have come across with the idea that they believe that this follows naturally from Bayesian epistemology. You’re saying that you’re not sure you agree with that. Is that correct?
[00:14:58] Green: Well, I think that it may follow from Bayesian epistemology plus utilitarianism.
[00:15:05] Red: I see. So if you think that utilitarianism is true, just full stop.
[00:15:11] Green: Then you might be able to infer something about what you should do today. Like if you say, I really think that it’s very likely there’ll be trillions of people in the future if we do this and we should take away resources from helping people who are suffering today in order to guarantee it’s more likely that these trillions of people will live in the future. Then you might be able to construct an argument in that way. But I’m not a utilitarian, meaning I don’t take utilitarian claims. I don’t ignore them. But I also think that some things are morally… like our moral virtues or maybe are deontologically true. And so the idea that I should allow somebody to suffer for people who don’t exist yet, for trillions of people who may exist in the future, if morally I don’t like that, then utilitarianism, I think, does not have the power to change that decision. At least that’s my view. I think if you are locked into utilitarianism is the absolute truth, then you have fewer options. Then it seems like it’s compelling you to do something. But the way I think of utilitarianism is like it’s an inference from our moral intuitions. We have these data points. This is how I feel about these moral situations. So then you draw a line through it. That line, that extrapolation is utilitarianism. But then later when that line disagrees with your moral intuition, now you have to throw away the data point. I don’t think that’s right.
[00:17:10] Red: Okay, I’m
[00:17:10] Blue: with you. Do long termists deny being utilitarians or do they embrace that?
[00:17:16] Green: They embrace utilitarianism.
[00:17:18] Blue: They do embrace that openly.
[00:17:20] Green: I think so. I’m certainly not an expert on this. Were you asked whether I was connected with it at all? I’m not really connected. I just watched it a little bit from afar.
[00:17:35] Blue: Well, the argument about knowledge being fundamentally unpredictable that critical rationalists bring up a lot. It sounds like you agree with that. To me, that just decimates the whole assertion that we should be completely worried about what people 100 or 1,000 years from now are what their lives are like. I think that this knowledge being unpredictable is actually not the driving force for me.
[00:18:08] Green: It’s more like… If you think about the trolley problem where there’s a variation… Do you throw the switch so that the trolley kills one person instead of five people? That’s a relatively… For most people, I think that’s a relatively easy choice. But then there’s the other variant where you can push somebody off the bridge, basically murder someone in order to prevent the trolley from hitting five people. And some people misinterpret this argument as a proof that you should push the person off the bridge. That’s not what the argument is. It’s really a demonstration that moral intuitions are not utilitarian. That most people have the intuition that it’s wrong to murder someone to save five people. And so this is a case where you… It’s almost the disproof of utilitarianism. Maybe not a disproof, but it’s something that is an intuition pump, maybe, that utilitarianism isn’t quite right. So in that situation, if you knew for certain that you could save a million people by committing a murder or something, then you might do it. I’m not saying that it would even necessarily be justified. I don’t think that utilitarianism is true, but you would be in a situation where… It would be challenging your intuitions.
[00:19:46] Red: But
[00:19:46] Green: if you’re not certain, if there’s an 80 % chance that a million people will die if you don’t murder someone, then it seems like you can no longer do it. How certain do you have to be? So I don’t have to think that knowledge is completely unpredictable in order to say, I just don’t think that we’re certain enough about the existence of these future people or that our choices are critical to their existence, that it’s worth harming people today to achieve that goal.
[00:20:21] Red: So I was going to say that I suspect many crit -rats listening to this show are probably shocked that long -termism isn’t exactly equal to Bayesian epistemology.
[00:20:33] Green: In fact, I think I thought that
[00:20:35] Red: at one point, right? So I actually think that’s very good that we’re showing that Bayesian epistemology is not the same necessarily as long -termism. It’s not something that just follows naturally from Bayesian epistemology.
[00:20:52] Green: Right. I mean, in long -termism, you have to have the value, you have to have a value system and a picture of what guides your morality in order to know, because what long -termism is, is a recipe for action. And in order to have a recipe for action, you must have some value that you think is going to be satisfied. So the epistemology side of things is going to be what will happen if we do this or what will happen if we do that? That is what the Bayesian epistemology tells you. But the question is whether something is right or valuable, whether you actually should do that, whether this action maximizes your values is a different question. Right. Okay.
[00:21:44] Red: That makes perfect sense to me. All right. I’m sorry for that aside, but I actually am glad that we got that out of the way.
[00:21:50] Green: No, it’s a good question. I mean, especially, you know, it’s very relevant to what we’re talking about, like what Bayesian epistemology is about. The thing about Bayesian epistemology is that it is a, I think the danger that most people see in Bayesian epistemology, the people who don’t like Bayesian epistemology, is that it gives you the illusion of rigor sometimes, that because we have an equation that tells us how we ought to update our confidence, you’re just gonna put in some numbers into this equation and get some numbers out. And if you’re not careful, you might think that you’re getting some rigorous result from that. Whereas really, it’s just like as critical rationalists want to sort of rank theories, Bayesians are really using this to rank theories. They’re just ranking them with a bit more where it’s like, no, this is like at least 10 times better than the other theory. That’s kind of what Bayesianism is doing, I think.
[00:23:03] Red: So I have to tell a story here because it’s relevant to what you just said. Back in the battle days, there was a teacher that I knew. She was the mother of a friend of mine. And she would write down grades for kids and then turn them in and the parents would come in and argue with her about whether their kid deserved that grade or not. So this would be elementary school or something. And they switched to using computers and all the parents stopped coming in to argue because now it was being printed out by a computer. And what they didn’t know is that it was really easy to just manipulate the computer any way you want to give any grade you want that you feel is appropriate for that childhood. But just the very fact that it was on a printout, it was coming out of a computer, was causing parents to think, oh, well, that’s got a lot of rigor behind it. I can’t argue with that.
[00:24:04] Green: Wow. For those who are audio only, I’ll do my best to convey what the diagrams I’m displaying are saying. But what I’m contrasting here are the steps in the scientific method or features, concepts in the scientific method as seen, first of all, in the popular conception, then in critical rationalism and then in the Bayesian conception. So the standard conception of the scientific method is that flow chart that you learned in school where you make some observations, you come up with a hypothesis, you then test the hypothesis with further observation and then decide was this hypothesis refuted or was it confirmed or verified. And I’m rather critical of this flow chart as a Bayesian knot, mainly because of this step where you say, did it pass the test or not? And the most frequently taught science experiments have obvious and decisive interpretations. So when Galileo sees a phase of Venus that’s impossible in the geocentric model, he’s done because that’s an impossible result in geocentrism. And that’s a famous experiment or the Millikan oil drop experiment where it’s like a qualitative result or Galileo dropping testing the rate at which masses fall, it’s either Aristotle said that the heavier mass will hit the ground first because it wants to get there more, because it’s heavy. So you get these results that the thing that you pick up is that you’re going to do the experiment and you’re just going to know, your intuition is going to tell you whether the theory is refuted or confirmed. So in critical rationalism, the model is not too much different except that the creation of the hypothesis, a lot of emphasis goes into this. So you have an observation. Your observations are theory laden, right? So
[00:26:32] Green: the kinds of observations we make depend on the theories that we already had. And then you have a problem, you find that your observation doesn’t meet your expectations and then you creatively conjecture a new hypothesis that will explain your observations. You then, this theory makes predictions, you make more observations and then something happens and you either refute your theory or it survives the test. So instead of saying that the theory has been confirmed or verified, you say that it survived that test. It has not been refuted by this. So it’s trying to eliminate this notion of conformational verification and a lot of the emphasis goes into that creativity aspect. And I think that my own impression is that perhaps because Carl Popper had a lot to say about ideology as well as epistemology, that I think that creativity in conjecture means a lot to people in a sort of non -epistemic way, right? That it says that maybe humans are very special and there’s some sort of magic that we’re doing when we do creativity. There’s also a techno -optimism involved here where technology creates problems but the solution to this is more technology and more problem -solving. And I can vibe with some of that but I also think that when I’ve been in discussions about critical rationalism versus Bayesianism that there’s a lot of emphasis on things that I don’t think are maybe as epistemically relevant.
[00:28:37] Red: So I’m trying to decide… I don’t think there’s anything inaccurate on this diagram and I actually have heavy, heavy suspicions that many crit -rats would say, yes, this is an accurate picture of critical rationalism. I would like to hear from people in the audience like before you go on to listen to the rest of the episode, look at this diagram up on the screen and decide for yourself if this is a correct understanding of critical rationalism. Now, I think one thing that is critical rationalism is such a big subject, one obvious thing you could criticize about any diagram that you came up with is, well, you’re only capturing part of it. And I think most people would probably see that, that Hopper has all sorts of ideas that take up books and books and books and obviously we can’t put that into a diagram. Okay, so maybe that’s a fair criticism but maybe it’s also an unfair criticism because the whole point is to try to say in a nutshell what is critical rationalism compared to the original scientific method. And this captures the idea that we start with a problem instead of just generic observations. This does emphasize the conjecture and creativity aspect which I hear all the time from critical rationalists, from crit rats. It emphasizes the idea of prediction which is very key to at least on the, there’s this whole idea of the demarcation of science or empirical science and non -empirical theories. This is obviously talking about one side of that demarcation so it’s talking about where you can actually can make empirical predictions and that is where Hopper spends almost all his time. So I think that’s an appropriate way to describe Hopper’s epistemology.
[00:30:29] Red: So it has these predictions, you then go on, you do the experiment. We maybe are missing a box that says do the experiment but I’m assuming that’s part of quote observation, right, that we’ve done an experiment and that experiment has a result and that’s what the observation box means. And then I think that crit rats would say, yes, and then you never actually accept the theory because they’re huge, huge, huge into justification isn’t rightly so because Popper was. And so you either refuted the theory and you’re gonna have to go back with a different conjecture or you’re going to, it’s gonna survive and he has the box acceptance. Maybe a crit rat would take exception to the word acceptance right, they would just say, well, it’s just a theory that has survived. There may be more than one, maybe there’s only one, maybe we accepted in the sense that it’s now the best theory. Maybe we wouldn’t even say the word acceptance in that case because maybe that carries too much justificationism, some might say, but I think basically the flow matches the way I’ve typically heard crit rats describe Popper’s epistemology. Now, would I accept this as an accurate conception? I think Popper’s epistemology has way more to do with the methodology, right? I think that Popper’s epistemology is a set of rules that you’re either normatively following because you believe they’re the correct rules or maybe they’re just kind of not, you’ve given it no thought, but it’s part of the institutions of how science works and in that sense it’s non -normative, it’s just a description of what science does.
[00:32:08] Red: But I think that a huge part of logic of scientific discovery is trying to work out what are these rules that allow us to make progress. And I don’t think that any of that is captured in this slide and I’m not even sure how you would quite put that into a slide, to be honest. And I know that I’ve emphasized that more on my podcast and what’s on this slide, even though I’m not disagreeing with it, I’ve emphasized it less. And partially because of exactly what Ivan just showed that it’s actually just the original concept of the scientific method but with a relabel scheme. And so it doesn’t seem as important to me, not that I’m again denying it in any way, but it doesn’t seem like if this is all Popper did was do a relabel scheme to the old version of science, that wouldn’t be a particularly meaningful thing to do. And so I tried to look for what is it that Popper really did that to me makes him different and is saying something that has been missed elsewhere. Anyhow, I just wanted to make that comment about that.
[00:33:16] Unknown: I think
[00:33:16] Green: that’s a fair critique. I think that this is partly the way critical rationalism appears in my consciousness because the box where I have the reasoning and quotes and deciding, the decision as to whether a theory is refuted or survives, that this is relatively under -emphasized, shall we say.
[00:33:47] Unknown: It
[00:33:47] Green: depends on method, shall we say. In logic of scientific discovery, he talks about a decision that is made by the scientists to say this is what my basic statement is, this is what my result is. And instead of introducing additional axioms into his system, he speaks of method, like the scientific method, methodological choices. And for me, that was a bit of a red flag because to what extent is that methodological choice different from an axiom? Now, again, I want to say that I think that his work, logic of scientific discovery is a good read for anyone and it’s very sophisticated and it’s one of those things where you read it and then you go, oh, wow, I am not as smart as I thought I was. Oh, I had the same experience,
[00:34:57] Red: yes. You’re reading through it and you’re going, holy crap, I could never do something like this.
[00:35:03] Green: Yeah, so it’s very sophisticated work. I really admire it. But I also think that when he is, he’s actually somewhat complementary, I think, to the subjective or to my perspective on science, but he wants to reject it for certain reasons. And when I looked into those reasons, that’s what I was kind of homing in on, I did not find his counterarguments very compelling. But I’ll get into that later. So as a contrast to this diagram describing the critical rationalist conception, the Bayesian conception of science is quite different. And this is, again, is just partly a matter of emphasis. So a Bayesian is not going to say that observations are not theory -laden, is not going to say that we don’t need conjectures. But it’s really more that that’s not what the emphasis of Bayesianism is about. So what a Bayesian is doing, a Bayesian is looking at multiple theories at once. And a Bayesian is talking about acceptance all the time. So you go into a situation with a degree of belief or a degree of credence in a set of theories. And you always have more than one theory, because if you have one theory, you have another theory which says it’s not that one theory. So if you have theory A, then you have at least one more theory which is not theory A. And what you’re doing is you are using the predictions of these theories and your observations to continuously update in an iterative fashion your degree of belief in a theory. So I think this is a very intuitive idea. Let’s suppose we have two theories to explain dark matter. So the rotation curves of galaxies. One of them is that there are heavy, invisible, weakly interacting stuff out there.
[00:37:27] Green: So there is literally dark matter, something like weakly interacting massive particles. And another explanation is that our theory of gravity is wrong on some large scale or at small curvature or something like that. And when the two theories are introduced, you may have some intuitive idea of which theory you prefer more. Maybe you don’t know which theory is better. And so you say, well, it’s 50 -50. It could be theory one or it could be theory two. Or maybe it’s something else. And then as data rolls in, you get information from the James Webb Space Telescope or observations of rotation curves of galaxies and so on. You’re going to shuffle your acceptance in these theories. So a study may come out showing that the leading theory of alternative gravity does not explain the rotation curve. And that means that then you’re going to decrease your confidence that an alternative version of gravity is the explanation. And so you get this loop. So you start out with a prior confidence in your theory. You then take your theories, make predictions for what you should observe, compare it with observation, and then Bayes’ theorem tells you what your new confidence levels should be in these theories. So whereas the popular conception of science doesn’t really talk about what constitutes a test and whereas critical rationalism, I want to say, sort of shunts that work into methodology. Bayesianism is all about doing this probabilistic reasoning.
[00:39:25] Blue: Would you say that this is completely compatible with fallibilism? I mean, I think that some people are going to jump on this word acceptance. But really what you’re saying is just you accept it as the best theory right now. It doesn’t mean that it’s an infallible truth that you have to not question or something like that. But maybe the difference is that it just comes down to Bayes’ theorem in a way is that, I mean, whether or not that has any validity in this whole puzzle.
[00:40:06] Green: Yeah. I mean, theory N, the last theory there is that it’s something else.
[00:40:12] Blue: Yeah.
[00:40:13] Green: Right? And no matter how good your experiments are, your theories are, there’s always the possibility that something went wrong with your measuring equipment. So your subjective probability, your degree of acceptance of the theory never goes to 100 % or to 0%. Just like in the movie The Truman Show, right? He’s got this entire marvel of how the world works, which is wrong because the deck has been stacked against him. Sorry if I’m spoiling the movie for anyone. But it happens very frequently, right? Like the matrix. You take the pill and all of a sudden reality isn’t what you thought it was. And so there’s always some possibility, however improbable, that the theory that has proven so well to work out so well is actually not true in some respect. Being rational is no guarantee of being correct. Being rational is about accepting what is most likely to be correct given the evidence that you have. And sometimes you get unlucky. The evidence you have is misleading.
[00:41:43] Red: Could I raise an objection here that comes from David Deutsch? Sure. So I sent you a link to this. It’s David Deutsch’s simple refutation of the Bayesian philosophy of science. It’s quite short. And it’s relevant to something that you just said. You talked about how there’s always at least two theories. There’s the theory and then there’s the not the theories not right as a possible theory. So Deutsch is actually attacking that. And he says, if it’s okay, I’m going to read the whole thing. It’s pretty short. He says, but by Bayesian philosophy of science, I mean the position that one, the objective of science is or should be to increase our credence for true theories and that to the credences held by rational thinker obey the probability calculus. However, if T is an explanatory theory, example, the sun is powered by nuclear fusion, then it’s negation, not T. The sun is not powered by nuclear fusion is not an explanation at all. Therefore, suppose implausibly for the sake of argument that one could quantify the property that science strives to maximize. If T had an amount Q of that, then not T would have none at all, not one minus Q as the probability calculus would require if Q were a probability. Also, the conjectured T, T one and T two of two mutually inconsistent explanatory theories, T one and T two, such as quantum theory and relativity is probably false. Therefore has zero probability. What in plain English, what he means there is quantum theory and relativity are known to be at odds with each other and it’s believed that they are both false. So their probability is zero.
[00:43:28] Red: Yet it is it embodies some understanding of the world and is definitely better than nothing. Furthermore, if we expect with Popper that all our best theories of fundamental physics are going to be superseded eventually and we therefore believe their negations, it is still those false theories, not their true negations that constitute all our deepest knowledge of physics. What science seeks to maximize or rather create is explanatory power. That’s the end of his explanation. So just in plain English to use your chart theory and you specified as something else. What he’s saying is is that theory and is always 100 % probably true. Always always always that there’s nothing that will ever make it anything but 100 % and all the other theories are always zero probability. Because of this whole idea that theory and is not an explanatory theory. It’s just the negation of all the other theories that something else is true. So what do you think of that? How does that maybe fit? How would you respond to Deutsche’s criticism there?
[00:44:35] Green: Do you mind if I ask a counter question first? Yes. Do you have an answer to that yourself? Like you don’t have to go into what your answer is but do you think that it’s a good critique?
[00:44:51] Red: Yes, I do. I think it’s a good critique.
[00:44:54] Green: So I think the way I answer that.
[00:44:57] Red: Let me say something. So I do think it’s a good critique. I think it’s a good critique up to what you’ve explained so far. But based even on my minimal understanding of Bayesian reasoning, I do think that there are baked into his answer some assumptions that don’t necessarily need to be true. And I do think it would be possible to adapt Bayesian reasoning. And in fact, we do that in real life in machine learning. Machine learning handles Bayesian reasoning in such a way that I’m not sure that this critique would be accurate anymore. And another thing I would point out is that I have seen this response from Deutsche used in some pretty bad ways that really are problematic. And one of them is that I’ve seen crit rats on a regular basis claim that anytime you have an explanatory theory of any sort, the negation of it isn’t an explanatory theory. That is not true. It is absolutely possible to have two competing theories where one simply the negation of the other. However, when we come to a complex explanatory science like general relativity or quantum mechanics, I do think Deutsche is spot on that the negation of it is not an explanation. And I do think that that does cause a problem for the way you just explained Theory N on your slide here.
[00:46:29] Green: Yes. I think that that’s true when you say that something like Theory N may not be an explanation. But that’s because Theory N is in some sense like the null hypothesis.
[00:46:46] Red: Yes.
[00:46:48] Green: But it doesn’t really affect the result. And I’ll try to explain that later. But to answer the question briefly, I think the idea that Deutsche is relying on here is the idea that let’s say Theory 1 is Einstein’s field equations. And so if you take Theory 1 to be literally its Einstein’s field equations at every scale, at every distance scale, every energy scale, then I would agree that’s almost certainly false. And I think if you ask any physicist, they would say that’s almost certainly false. So the probability of that being true is virtually zero. And then we would really be in trouble. But that’s not exactly what the theory is. So Theory 1 says that Einstein’s approximation to the world is very likely correct over this domain. And so to that extent, it’s perfectly compatible with quantum theory that says that quantum theory is very likely to give you the correct result over the domain between low energy and let’s say 20 TeV that the standard model is going to work. But it doesn’t mean that the standard model is true at every scale and is like a universal truth. And no physicist thinks, well, I should be careful when I say that. But maybe
[00:48:45] Red: I’m not going out.
[00:48:46] Green: There’s always somebody, Ivan. Yeah, there’s always someone. I don’t think physicists think that the standard model is literally true at all scales, period. Because it’s formulated in quantum field theory in flat space. It’s not going to work inside a black hole. So we know the standard model is going to break down at some point. But we still have confidence in it. What do we mean when we say that? We mean that up to this energy scale where it’s been tested, in this region, we think it’s very unlikely to give us a false result. So within Theory 1, so let’s say Theory 1 is Einstein’s field equations, there are actually numerous sub -theories. The Theory 1 that says Einstein’s field equations will give you a good result actually means that whatever theory explains the world is going to be one of these theories that in its small curvature approximation matches Einstein’s field equations. And I have a slide later on where I talk about Newton versus Einstein, which I think I hope will clear up what I mean by this.
[00:50:16] Red: Okay. So can I maybe clarify this then? So what I think I’m hearing you say, so my apologies if I am straw -manning you, is that the right way to look at this slide where I have Theory 1, Theory 2, et cetera, down to Theory N, from the Bayesian viewpoint is not that we’re trying to treat the theory as universally true. But instead we have some sort of domain that we’re dealing with and we’re only trying to say it’s true for that domain and it’s going to be a much more limited look at the theory. And so you really only can, because of that you feel that that is a proper, that could show how Dwight’s criticism may not work because you’re really only applying it to some sort of domain anyhow. You’re just trying to say, well, within flat space we believe that Einstein’s equations hold. We’re not making any sort of claim that it is a universal truth. Obviously if we try to treat it as a universal truth, then it’s definitely false. And so for our purposes, we’re trying to say it’s true enough for this domain out of the theories that we have available. And that’s really what you’re trying to measure in this case. Is that correct or am I misunderstanding?
[00:51:44] Green: I think that’s correct. That’s my take on it. But there is a sense in which we are saying something universal. We’re saying that it is within this theory. This theory contains sub -theories. It contains more detailed theories, better explanations that have this theory that fit into this approximation. And that the reason that we think that the true explanation is going to be within this is that whatever new explanation comes along has to explain why this theory was successful.
[00:52:30] Red: Right. That’s a big part of Popper. Okay, I’m with you. And thank you for responding to Dwight’s short article there.
[00:52:44] Green: Yeah. I have a text here on my diagram that says, Iterative subjective probability updating. I used the S word there, subjective. And I know that’s a trigger. I find words.
[00:52:58] Red: I see red the moment you say it. Like I just go, I just get mad. Right.
[00:53:04] Green: But I want to make a distinction that I’ll talk about more later between subjective and intuitive. Right. So I think when people say subjective, they think, oh, you know, you believe this because, you know, you grew up in a small town where this happened to you when you were a child. And now you think this is more probable or you have this bias. But what I mean by subjective is that it’s subjective to you based on the information that you have. So we’re talking about here about maybe instead of subjective probability, I should say epistemic probability. So if I flip a coin, right, flip the coin up, lands on my hand, cover it with my hand, and I say, what is the probability that this is heads? Well, you could say it’s either 0 % or 100%, which is true. It’s going to be one of those. But that’s a sort of God’s eye view of what happened. But we’re talking about what is your eye view of what happened? What is your epistemic probability? And so for you, because you lack information, it’s 50 -50. That’s what I mean by subjective here. So a lot of what Bayes is doing is algorithmic. It’s not something that is necessarily biased. If you look at the Stanford Encyclopedia of Philosophy article on Bayesian epistemology, you’ll see that there is a group of Bayesians called objective Bayesians who want to set all of their priors in some objective way. They’re not doing something where it’s just based on intuition.
[00:54:58] Green: But most Bayesians, I would say, will accept that if you are a doctor and you see a lot of patients and somebody comes in with a respiratory ailment, that your intuition is going to tell you something somewhat reliable about what ailment they have. So even though you haven’t been statistically rigorous and gone to your patient list and done some statistical analysis, that you have some intuition based on your experience, which is valid. Now, obviously, frequently, that is not the case, right? People can be mistaken about their beliefs, or if you’re not engaged constantly in making predictions about the world and then getting feedback, then your predictions are probably going to be bad. Okay, I better hurry up along, because we’ve been at this for a while. And we’re on page six. And we’re on slide six.
[00:56:02] Red: Yeah. Yeah.
[00:56:02] Green: So buckle up, everyone. So what I’m going to talk about now is to give you some intuition for what Bayes theorem says. And the following is in the non -controversial sense. So this is true subject to the assumptions that are made in the problem. And so I’m going to show you what Bayesian updating is about and introduce a visual representation, which I’ll try to explain for those who are on audio only. The picture here is the famous picture of the Reverend Thomas Bayes, after whom the theorem is named. He died in 1761. This picture appeared while I was preparing this presentation. I was like, wait, where did this picture come from? It came from some book published in the 1930s. I want to say about insurance. But historians have looked at the way he’s depicted. It’s not consistent with how somebody would have dressed at the time. So this could be a picture of somebody completely random. But it’s the one that’s associated with Bayes.
[00:57:09] Red: All right.
[00:57:12] Green: There’s a standard notation that’s used in probability theory, where you just say instead of saying writing out the text of probability of, you say P in parentheses. So the probability of a theory being true, you say P of theory, or the probability that you’ll see some evidence being P of evidence. But there’s also this notation for conditional probabilities. And this just means, for example, the probability of seeing evidence if a theory is true, conditional on the theory being true, or given that the theory is true. And that’s what the vertical bar means. And then you’ll see here there’s something we call the posterior probability, which is the probability that the theory is true given the evidence. And of course that is what Bayesians are after. We want to know how much confidence should I have in this theory given the evidence.
[00:58:10] Blue: If I may interject just one quick thing. I was just looking at dates about when Bayes lived. It’s kind of cool to think about that his life actually overlapped with Newtons quite a bit. They might have even known each other. They were both English. And I mean, Newton died in 1727. And Bayes was born in 1701 and lived to 1761. So I thought he would be much later than that.
[00:58:42] Green: Yeah. So his work was published posthumously. And did not create much of a splash. But his theorem was rediscovered by Pierre Simon Laplace in the next century. And then when that was brought to light, then it was pointed out that Bayes had come up with the theorem first.
[00:59:04] Blue: Oh, that’s interesting.
[00:59:05] Green: Okay. So first I’m going to talk about what I think of as forward probability reasoning. Once you know probabilities, you can make predictions about what to expect. So suppose that either Alice or Bob has made your coffee and you have no reason to think that it’s either one or the other, more likely one or the other. So it’s 50 -50. I suppose that Alice adds sugar 60 % of the time and Bob adds sugar 20 % of the time. What is the probability that your coffee will have sugar in it? And the answer is to multiply out the probabilities. One thing to note about probability theory is that it’s not intuitive to human beings. So usually if you’re trying to work something a problem like this out, it helps to speak in terms of frequencies. So if you imagine that you had this scenario repeated 200 times, then because the probability of Alice and Bob starts at 50 -50, it means that Alice would make 100 of your coffees and Bob would make the other 100. Alice would add sugar 60 % of the time, so that means 60 coffees from it. Alice would be sugared and 20 coffees from Bob would have sugar. So it’s a total of 80 coffees would have sugar in them out of 200 and it repeats. So that explains why there’s a 40 % chance that your coffee would have sugar in it based on the assumptions that I’ve listed here.
[01:00:52] Green: The formula that I’m displaying here says that the probability that you have sugar in your coffee is equal to the prior probability that Alice made your coffee times the likelihood that Alice put sugar in your coffee plus the prior probability that Bob made your coffee times the likelihood that Bob put sugar in your coffee. And you’ll see this pattern in all of the formulas that follow that the interesting quantity is a product of prior probability times likelihood. So it’s prior probability of Alice times likelihood Alice puts sugar. Prior probability of Bob times likelihood that Bob puts sugar.
[01:01:41] Blue: Are we to understand this is something that’s really an amazing assertion or is this… I mean, this to me just looks like basic algebra so far. This is basic algebra. I just want to make sure.
[01:01:56] Red: Peter, not everybody’s a math teacher, so you can’t assume that.
[01:02:04] Green: So again, suppose that either Alice or Bob has made your coffee and you initially assess that the prior probability of Alice equals the prior probability of Bob equals 50%. So it’s 50 -50. Those are your priors. And then suppose that Alice, again, that Alice adds sugar 60 % of the time and Bob adds sugar 20 % of the time. These are your likelihoods. These are essentially the deductions or predictions of your theory, your Alice theory and your Bob theory. But now we add an extra step. You taste your coffee and you find that it’s sweetened. So now you ask, what is the probability that Alice made your coffee? Or in other words, what is the posterior probably epistemic probability that Alice, the Alice theory is true, given the evidence that the coffee was sweetened. And I used the term posterior probability. It means posterior to receiving this piece of evidence. So it was 50 -50 prior to the evidence. And then we want to know, now that you have this evidence that your coffee was sweetened, you can update your confidence in who it was that made your coffee. This is where Bayes theorem comes in. And Bayes theorem, which is a formula that tells you this posterior probability, says that the probability that the theory is true given the evidence is equal to the prior probability that the theory was true times the likelihood of seeing the evidence in that theory divided by the probability of seeing that evidence in any theory. And we can put in the specifics here for Alice and Bob. So the probability that Alice made your coffee, given that it was your coffee is sweetened, is the probability,
[01:04:03] Green: the prior probability that Alice made your coffee times the likelihood of Alice putting sugar in your coffee divided by the number that we came up with on the last slide, which is the total probability of having sugar in your coffee. And again, I’ve sort of color -coded this on my diagram here, so the priors are in green and the likelihoods are in purple. And you can see that it’s a prior times a likelihood divided by the sum of the priors times the likelihoods. And that’s the pattern that you can see in Bayes theorem. And we can work this out. You can put in the percentages and you’ll come up with 75%. Another way of seeing it is as we said earlier when we were doing forward probability that if you went through this experiment 200 times, that you’d have 80 sugared coffees. And of those 80 coffees, 60 would be from Alice and 20 would be from Bob. So that means 75 % of your sugared coffees come from Alice. And that’s why the posterior probability looks as it does here, 75%. So you can work this out. I’m not doing a proof here of Bayes theorem. I’m just showing you that if you work it out in terms of frequencies, you can see where this is coming from.
[01:05:33] Blue: But still nothing you’ve said is remotely controversial.
[01:05:36] Green: This is not controversial. One of the reasons it’s not controversial is that I laid down that there are just two theories. There’s Alice and there’s Bob. And these are the percentages by which they sweeten their coffee.
[01:05:49] Blue: It’s more like when we apply this to real life, we’re going to get into some controversies. Yes. I guess. Okay.
[01:05:55] Red: By the way, I do cover Bayes theorem in episode, way back in episode seven of this podcast and actually go through a little bit why it’s true and give an example where I actually lay out why it turns out to be true just in terms of if you were to actually show the instances of it. So if anybody’s interested, you can check out episode seven.
[01:06:18] Green: So one more example, this one involves dice and I have on my desk here in my hand, I have a six -sided die and a 20 -sided die and everybody is sick of me talking about them.
[01:06:32] Blue: I think you’re a fellow nerd. I’ve got a bag full of dice myself.
[01:06:38] Green: So in this, this is a sort of a, I call it a game. It’s not really a game. It’s a bit of a puzzle, but it’s interesting to ask people these questions. So I have a six -sided die and a 20 -sided die in a bag and I take out one of the dice at random. What is the probability that the die in my hand is the six -sided die?
[01:06:59] Unknown: Well,
[01:07:00] Green: by the principle of indifference, you have no reason, more reason to think it’s the six -sided die than the 20 -sided die. So it must be 50 -50. That’s your prior confidence in the six -sided die theory is that it’s 50%. So I have, you know, p of d6 equals 50%. So next, I roll this die that I took out of the bag and inform you that I rolled a three. And I’m reporting my results in good faith, so you don’t have to worry about me lying about what my rolls of the die were. So now what is the probability that the die is six -sided? Well, when I ask this question of most people, they actually say you still don’t know. It’s their first response. They want to say that because you could roll a three on both the six -sided die and the 20 -sided die, that there’s no difference. But essentially, they’re answering sort of a different question. They’re substituting the answer to a different question, which is, is it possible to roll a three on both dice? And it is. But you do have a new piece of information because the two theories, the six -sided die theory and the 20 -sided die theory, make different predictions for the frequency of rolling threes. You’ll roll a three one in six times on the six -sided die and one in 20 times on the 20 -sided die. And as a result, you can actually update your confidence in the theory. And the way to see that is to play this game 120 times.
[01:08:39] Green: So if we played this game 120 times and I randomly selecting a die each time, it means that I would be expected to pick the six -sided die 60 times and the 20 -sided die 60 times. And out of those 60 rolls of the six -sided die, I expect to get 10 threes. And on the 20 -sided die, if I roll a 20 -sided die 60 times, I expect to get three threes. And so that’s a total of 13 threes in my 120 games of which 10 of them are on the six -sided die. And so if you find yourself in this scenario where a random choice has been made and a three has been rolled, you should estimate that the probability that you’re working with a six -sided die is 10 out of 13 or 77%. So your prior probability that it was 50 -50 has been updated. Now your posterior, posterior to this evidence of seeing the three is now 77%. And because we’re in this narrow domain here where there are just two theories, that all the probabilities have to add up to 100%. So the probability that it’s the 20 -sided die has fallen from 50 % to 23%. So now you can ask, well, what happens when I take that same die and I keep rolling it? So I take the same die and I keep rolling it. I roll it another 13 times. And each time the result is in the range one through six. So you can ask, well, after 14 rolls of the die in the range one through six, what is the epistemic probability that I’m rolling a 20 -sided die?
[01:10:39] Green: Well, the probability of rolling a one through six on a 20 -sided die 14 times in a row is one in 21 million, roughly. So you are actually really confident that the selected die is a six -sided die now. You ought to be, right? Because otherwise you would have been really unlucky. You would have to be really unlucky to bet on the six -sided die and get it wrong if a one through six has been rolled 14 times in a row.
[01:11:15] Red: By the way, just as a side note, the existence of the multiverse in no way changes any of this. So I know some crit rats think it does, but it doesn’t. It simply works out to be the percentage of worlds and what the percentage of the different worlds are. And so there would be some set of worlds out there where you were unlucky that would be a very, very, very small slice of the multiverse by comparison to the rest of the multiverse. So it really does not change a thing to add the multiverse into this.
[01:11:49] Green: Right. And if you bet on the six -sided die, no one’s going to be laughing at you if you get it wrong, right? You made the right choice. You just got unlucky. But now suppose that I rolled the die a 15th time, and I inform you that the result is at 13. What now is the posterior probability that the die is six -sided? Well, then naively, the answer is zero, right? Because I can’t roll a 13 on the six -sided die. But this is an extraordinary claim because I was really confident that it was the six -sided die. So isn’t it more likely that I misread the die or misspoke or you misheard me? Even if we’re playing this game in good faith, but those kind of errors might be one in a million errors, right? One in a million times, if we play this all week 24 -7, I’m probably going to make a mistake at some point. A one in a million error. But a one in a million error is much bigger than a one in 21 million confidence. So the one in a million error rate, it doesn’t affect the game in the first round or two. But by the time you’re this confident in a theory, you no longer care about… Now you have to be exceptionally careful about uncertainty in your experimental results. So this is a sort of Bayesian way of looking at the Carl Sagan’s claim that extraordinary claims require extraordinary evidence.
[01:13:31] Red: By the way, we have now stepped into a more controversial realm just for the listeners on this. But this… I don’t think that I would feel comfortable saying that this is no longer controversial. You would probably get pushed back on some of this.
[01:13:47] Green: Yeah, quite possibly. Bring it on.
[01:13:50] Blue: Are we going to get into the Boltzmann brain thought experiment? This seems like a very simplified version of that in a sense where you think, well, it’s way more probable that your consciousness would just spontaneously form somewhere than there’s a million years of evolution and all that. So this kind of seems maybe related, but…
[01:14:20] Green: Maybe we’ll… If we have time at the end, we can talk about it.
[01:14:23] Blue: Maybe it doesn’t look too far out.
[01:14:25] Red: We’ll invite Sadia for that part because she loves that thought experiment.
[01:14:35] Green: So the scenarios that I just described, I hope give you some intuition for what Bayesian inference is doing. The general formula for Bayes looks like what I’m displaying here. So the posterior probability that theory one is true, given the evidence, is the prior probability that it was true times the likelihood of seeing that evidence in theory one divided by the sum of prior times likelihood for all of the theories. And there’s also, of course, the sum of all these probabilities, the sum of all the priors adds up to one. So that means that the last theory has to account for everything that you haven’t already incorporated. In general, it doesn’t matter, and I’ll get into that later. But the reason that it doesn’t matter is that a theory that is everything else doesn’t make any specific prediction. It spreads its probability across every possible outcome. And so the likelihood of seeing a certain piece of evidence is very small. Even if you gave it a larger prior, the likelihood is very small of generating any particular piece of evidence. So Bayes’ theorem, in problems like the one -on -five outline, it’s uncontroversial just because we’ve been very clear about the assumptions laid down, namely that there are just two theories, that we know what the likelihoods are, and we’ve got the principle of indifference. That’s why it’s not controversial. So before I go on to Bayesianism, I just want to give this visual representation of what I just did because I think it helps explain, it will help explain later when I’m talking about refutation and Occam’s razor. So the idea is that I have a bar representing everything that can happen. It adds up to 100%.
[01:16:50] Green: And that in the first scenario where I randomly draw a die from the bag, I’m splitting that bar into two sides. 50 % goes to the six -sided die, and 50 % of the prior goes to the 20 -sided die. When I roll the die, I further split this bar into the possible outcomes. So I’m taking the six -sided die, half of the bar, and splitting it into six parts. And I’m taking the 20 -sided die, half of the bar, and splitting it into 20 parts. And the likelihood of rolling a three on the six -sided die is the ratio of these line segments. When I make an observation, like I roll a three, I can imagine that I have this observation filter here. And what survives this filter is this chunk of the prior from the D6 theory and this chunk of the prior from the D23. And so then the probability that the D6 theory is true, given a roll of a three, is the ratio of these two sizes. And it’s exactly the same number. It’s doing exactly the same. It’s just a visual representation of the mathematics that I did earlier.
[01:18:16] Red: That’s excellent. You can immediately see what it is.
[01:18:21] Green: We can then move on to what happened in round two. Let’s suppose that after I rolled a three, I then roll a two. It’s the same thing. The difference is that the size of the initial bar for the D6 is now 77 % of the whole. And the bar for the D20 has shrunk to 23%. Because I initially rolled a three, I updated my posterior probability changed. In this round, the prior probability is the posterior from the last round. And so the segment representing the two is correspondingly larger. The segment representing the two in the D6 theory is correspondingly larger. And the segment representing the two from the D20 theory is correspondingly smaller. So you’re just applying Bayes theorem again, based on now taking the prior probabilities are no longer 50 -50 at 77 -23, you come up with 92%. And you can visually see what is happening with each round of this game. And just for a sanity check here, this is what happens if on round one we had rolled a 14. None of the parts of the D6 theory survive. The only part that survives is the 14 from the D20 theory. And so you get 100 % is the probability that the D20 theory is true if a 14 was rolled. Of course, this is making the assumption that there’s no error in the observation. So now let’s move on to Bayesianism, which is a philosophy. It’s an extrapolation, if you like, from Bayes theorem. The extrapolation is that it applies more broadly, that it applies across time as new theories are introduced and so on. And that epistemically, you don’t need to know every theory, so that it’s okay to say that one of your theories is none of the above.
[01:20:49] Green: So the reasoning behind that, like I say, is that the theory none of the above is in some sense not a theory. It’s not an explanation because it puts an equal amount of its prior into every possible outcome. But as long as you have some observations, some outcomes, it means that the theory none of the above is going to lose. So one of the things to note about the dice game that we just looked at, why was D6 favored? As long as the evidence was consistent with D6, why did it win? The reason that it won is that it focused its probability, it focused its predictions into a narrower range. So the prior probability of those predictions was higher compared to its competitor. So the competitor that spreads its predictions across a wider range, a theory which is compatible with any measurement you make, actually has an infinitesimal prior for any given outcome. And so it’s going to lose to anything that’s more specific. So the lesson from Bayes’ theorem is that a more specific theory wins as long as the evidence is consistent with that theory. So if you have a theory which is none of the above, well, that spreads its prior across every possible outcome. That’s like a trillion sided die or an infinitely sided die. And as long as the number you roll is finite or small, it means that the infinite sided die is going to lose.
[01:22:50] Red: Yeah, it makes sense. And I can see how you’re going to now tie this into Popper’s ratchet.
[01:22:55] Green: Yeah. So a Bayesian like myself, you asked previously whether Bayesianism is the same as Bayesian epistemology. I’m not even sure if there’s a formal definition of these terms. But like I say, I would argue that this is true of every kind of inference. And in fact, one of the things that’s attractive about Bayesianism is that it’s like a unified theory of inference. It says that Bayesian inference is rationality. We’re saying that one of the things that Popper talks about in the logic of scientific discovery is how you end up… If you take… I’m probably going to mangle this somewhat. But he talks about how the opposing view, the inductivist view, is you get this circularity, this problem of induction that leads to circularity. Well, my counter argument would be, what is your justification for the rules of deduction? The rules of deduction cannot be justified except circularly, right? If there are axioms of rational thinking, you won’t be able to justify them rationally without circularity. It’s just that within my axioms of rationality are induction. And in fact, I think that induction gets treated like a second -class citizen compared to deduction. And I don’t think that’s reasonable. I think that induction is arguably as fundamental as deduction is.
[01:24:59] Blue: Maybe this is a dumb question, but was Popper really arguing for deduction or more that it’s sort of a false dichotomy or something?
[01:25:13] Green: I think that he was using deduction. He wants to use deduction to say… He’s using deduction in his proofs to show that there are certain things that you cannot justify like all ravens are black. And I’ll be deductively proven by any finite sample of ravens, something like that.
[01:25:39] Red: So Ivan hasn’t had the advantage of hearing the podcast we recorded two weeks ago that isn’t released yet, where I actually talk about this, look at what Popper said and also compare it to Tom Mitchell’s machine learning. And I actually am curious what you will say after you have a chance to hear that podcast. I don’t want to give away too much because of course this one will probably come out before that one because you’re a guest, so we’re going to release it sooner. But I’m actually curious to talk with you after that one comes out. What I will say is that I made the argument that the word induction has multiple meanings and that Popper refuted a specific form of induction that was in fact false, but that the word induction can refer to things that Popper would have a little trouble with. Particularly if you’re using it to simply refer to something like what statistics does, which is a completely valid use of the word induction and in fact follows deductively from just the way things work as you’ve shown here. And I spent like two hours or something trying to go over this, so I don’t think I can really summarize it very well. So I actually would be interested in getting your feedback once you had a chance to hear that podcast when it comes out.
[01:27:06] Green: Yeah, I’m looking forward to hearing that. I do agree that there are multiple meanings and one of the things that looms sort of prominently in logic of scientific discovery is his conflict with the logical positivists with the Vienna circle. The logical positivists had a very… They had a beautifully rigorous system that they had tried to construct and it was so beautifully rigorous that there are now no logical positivists left. What other philosophy can you say was that so successful that there are none of them left? You meet people who are like, oh, they’re followers of Aristotle or Kant or whatever, but the fact that they survived I think is actually maybe not to their credit. The logical positivists, they were so specific that they’ve been refuted and so now they’re gone. And so the logical positivists had this idea, at least my interpretation of their idea is that just by looking at sense data that you would be able to infer a theory and that your theory just is sort of justified by the data in some direct fashion.
[01:28:35] Red: That is the kind of induction that I believe Popper was actually refuting and I believe he did a beautiful refutation of that, that it’s just simply impossible to do that. I call that Baconian induction rather than induction to make it more specific. I think the word just simply has other meanings that are some of which are legitimate. So my opinion is that Popper was specifically refuting Baconian induction. Maybe Baconian is not even the right term because it’s not even clear Bacon believed that. It was really the logical positivists he was responding to. But he certainly took it as this is what Bacon had in mind. You could argue that that’s not correct, I suppose. But I think Baconian induction is maybe not a terrible term for it. It was really that there’s an inductive logic that exists that’s separate from deductive logic that somehow justifies the outcome the same way we think of deductive logic as justifying the outcome. And I think he does do a very good job of showing that that just can’t exist.
[01:29:48] Green: It’s already been like a couple of weeks since I read Logic of Scientific Discovery, so I’m not going to recall specifically that piece. But going back to the concept diagrams that I drew earlier, Bayesians in general are not focused on where theories come from necessarily. So the logical positivists, it was very important that there be this sort of robust connection between making the observation and cooking up the theory. And the Bayesians, they’re like, I don’t care where this theory came from. What I’m doing, what I have is a formula for updating my confidence in the theory.
[01:30:30] Red: That is something that I’ve, so when I’m talking to crit rats, so that would be the community that of people usually, not always, that has certain views of critical rationalism. So crit rats, in my opinion, don’t always agree with Hopper’s critical rationalism and sometimes even strike me as being strongly at odds with it. But the crit rat community in general, one of their big objections to Bayesian epistemology is that it does not explain where conjectures come from. And I confronted one and I said, look, I agree with you that it doesn’t do that. But can you as a critical rationalist explain where conjectures come from? And the immediate answer was, well, no, we don’t really know where they come from either. I’m like, okay, then I’m not sure I see why this is a valid criticism against Bayesian epistemology. Maybe they should be talking more about conjectures, but none of us know where they come from. I mean, if we knew, then we would be able to build an AGI, right? That means a theory that’s missing at the moment. Because of that, I mean, I could easily just trivially change Bayesian epistemology to be conjecture and Bayesian update. And I would resolve the criticism that you’re leveling against them. And it wouldn’t require any actual changes at all. So it doesn’t strike me as an actual valid criticism, even if I technically agree with you that they should be talking more about conjecture. It’s just so easy to defeat this criticism that I don’t feel it’s a criticism that should be used.
[01:32:19] Blue: Yeah, I agree. Okay,
[01:32:21] Red: so you agree with that. Can
[01:32:22] Blue: I see a quick question, Bruce? Sorry if I’m getting off track here. I’m just kind of hung up on this. Would you say it’s a fair statement to say that Carl Popper was as against deduction as induction?
[01:32:36] Red: No, no. He rooted his entire epistemology in deductive logic. He wanted to show that we did not need an inductive logic. We only needed deductive logic to be able to make progress. Okay, but he was mostly focused that he thought that deduction had its place in logic and mathematics. So the reason why it’s called the logic of scientific discovery is because he’s showing that scientific discovery is rooted in deductive logic, not inductive logic. That’s really the meaning of the title of the book.
[01:33:12] Blue: But you would not establish falsifiability through deduction. So
[01:33:18] Red: falsifiability fits the logic. So we did an episode on this and I don’t remember which one it was or I would give an episode number. So it’s when I have a theory and it makes a prediction and it says your reality should be constrained such that you can’t get anything but a one through six and you suddenly get a 13. Then under the logic of scientific discovery that he’s setting up, we can deductively say a 13 means that theory is wrong. It’s falsified. Okay, we can deductively do that because while you can’t go from observation to theory, you can’t positively go from observation to theory. If I get the observation, I can’t deduce the theory. I can if I get an observation counter to the theory deduce that something’s wrong with the theory. Now it’s more complicated than that and he admits that because what you’re really doing is you’re refuting the entire combination of theoretical systems, which might to Ivan’s point include the theory that I’m reading the die correctly. And so it’s you’re really refuting that combination, not the specific theory that you’re interested in. And then Popper doesn’t talk very much. He does like in some of his books. He explains how he thinks we then use and I need to do a separate podcast on this and I don’t think I can do it off top of my head without actually having the quotes handy, but he actually works out how you would then go about trying to figure out which of the theories is wrong in the system of theories. And how you try to narrow that down. And this is one of the things that I actually feel like is missing from even most critical rationalists.
[01:35:13] Red: They just never even seem to notice that he did this. And this is what led to David Deutsch in his excellent paper, The Logic of Experimental Tests, landmark paper in my opinion, but he tries to set up this idea that you can’t refute a theory without a second theory, which really is at odds with Popper’s epistemology. In an important way. And I’ve always suggested that they’re both right, but under different senses of the word refutation. And that’s the way I’ve kind of put it out there. But it’s really it’s worse than that. It’s that Deutsch has misunderstood what Popper meant by the word refutation because he understood it in a more natural way where Popper was using it in a more formal way. And by doing this, he has created there is this confusion that exists within critical rational circles where it’s not at all clear what refutation even means. And I even have a wonderful thread that I’ll sometime bring up in a podcast where there’s crit rats arguing over whether falsification is even an important part of Popper’s epistemology or not. Because of this confusion that’s entered into the critical nationalist community, the crit rat community over what even falsification just means in the first place in Popper’s mind. So anyhow, that was my long answer. And I feel like I cannot give you a more detailed answer without actually doing my research and having the quotes handy and giving you the example. No,
[01:36:42] Blue: that’s good.
[01:36:43] Red: Sometimes you
[01:36:44] Blue: ask a dumb question and you get a great answer. So I appreciate that.
[01:36:53] Green: So just to continue a little bit with this idea of like a unified theory of inference, to a Bayesian, a hypothesis and a theory are essentially the same thing. Everything is a theory and whether something is a fact or whether something is a hypothesis is just what is your subjective probability that that theory is true. And it’s just a matter of looking at the predictions of the theory and so on. What we would say is that if a theory doesn’t make narrow predictions, it’s not a good theory. Just because you essentially practically can’t raise your confidence in the theory as a result of observation because it doesn’t make narrow enough predictions to do so.
[01:37:59] Red: Right. One of the
[01:38:01] Green: reasons
[01:38:02] Red: why I think you’re right, the fact that Aristotle’s theories have stuck around is a problem for Aristotle’s theories.
[01:38:10] Green: Right. And I think one of the things that has come up while I’ve been listening to your podcast is that there’s not a strong distinction being made between a good theory and a good theory candidate. So I think a Bayesian would say that a good theory candidate is one that makes narrow predictions. But it could still be a false theory, right? You do the experiment and you get the wrong… That’s right. But, you know, it doesn’t match. And so…
[01:38:44] Red: Yeah, Deutsch tried to make a distinction there, particularly in his logic of experimental tests. And I feel like the way he’s worded it has again caused a great deal of chaos amongst rat rats. So what he suggested was, and he also does this in beginning of infinity, where he talks about a good explanation is not necessarily a true explanation. So he tries to make this distinction between a good explanation. And I have talked to so many rat rats who will say just the idea that a false theory could be a good explanation. It just blows their mind, right? Even though you can quote David Deutsch to them and they claim they agree with David Deutsch, but they’ll say, no, that’s not a good explanation. It’s false. And I’ll say something like, look, is induction a good explanation? Like, oh, no, no, induction is a bad explanation. I say, wait, wait, wait, wait. Do you mean it’s a false explanation or do you mean it’s a bad explanation? Oh, it’s the same thing. You know, I mean, I’ve had so many conversations with people about that. And I think it’s because it’s this idea of good explanation. It’s so tied up into being true in people’s minds that it’s very difficult to make the distinction that actually needs to be made. Which is, as you put it, it’s a good candidate because it makes these really narrow predictions.
[01:40:07] Green: Right, right. So what emerges from Bayesianism in my mind is that every rational inference from evidence is analogous to the Dice game, right? So if there’s something that you believe is true about the world based on evidence, it’s because the theory that you believe in, if your inference was rational, it’s because the theory you believe in is the one that is analogous to the six -side idea. So for example, if you believe that the neo -Darwinian synthesis is correct if you think that evolution is true and you think this based on evidence, you ought to be able to put this into Bayesian form. And one of the interesting things that you’ll see if you look for explanations of why evolution is true, what you tend to see, like on YouTube, would be videos talking about the evidence. Well, evidence doesn’t speak for itself, right? Evidence features in a Bayesian explanation, but it doesn’t speak for itself. It has to be part of an argument. And so it has to be that evolutionary biology predicts something much narrower than the alternative. And that’s what it does. And that’s why evolution is true. So there’s a lot of implicit reasoning that’s going on in science and in people’s understanding of science or in people’s understanding of the world. And what I like about Bay is that it forces you to try to bring it out of the implicit and into the explicit so you can find mistakes. So why do we think Bayesianism is going to be true? Well, one line of argumentation comes from something called Dutch book arguments. And I’m not going to go into any depth on it here. Again, you can read about it in the Stanford Encyclopedia of Philosophy, for example.
[01:42:19] Green: But the idea is that if you do not update in a Bayesian fashion, then you’ll take wages that will always lose. One of the things that’s confused me about critical rationalism is the attempt to escape this notion of belief. I do not understand it. And part of the reason I don’t understand it is that I think that Bayesianism is solving in some sense solving a different problem than Popper was trying to solve. What Popper wanted to do is he wanted to have a model for the scientific process. What Bayesians are about is they want to know what should I believe based on the evidence, which is a slightly different question. And the idea is how should I bet? So I’ve been in debates where critical rationalists tell me that you just simply accept the theory which has survived and there’s no question of belief. And then I feel like, well, who decides whether there’s one theory left? Who decides whether this theory has survived critique? And who decides whether? No, there are still other theories on the table that haven’t been refuted. My criticism hasn’t been answered. So now there are two theories. So it’s a tie. That doesn’t seem right. And so I guess my question for critical rationalists would be, how do you make wages based on your theories? If you can’t assign a probability or a degree of belief in your theories, how do you bet on which theory is true? Is it just you haven’t had a problem with your theory? So you have total confidence in it or is something else going on? That’s the thing I don’t really understand about critical rationalism. And maybe we’ll get into that at the end and you can help me see the light.
[01:44:44] Red: Would you like me to read that statement I got had from David Deutsch on?
[01:44:49] Green: Yeah. Yeah, go ahead.
[01:44:51] Red: Okay. So I think like yesterday or a day before or something, I came across somebody on Twitter that put up a quote from David Deutsch about, so science is a way of dealing with theories regardless of whether one believes them. And then here’s the broader quote. There is no such thing as a good reason for a belief. A scientific theory is an impersonal thing. It can be written in a book. One can conduct science without ever believing the theory just as a good policeman or judge can implement the law without ever believing either of the cases for the prosecution or defense. Just because they know that a particular system is better than any individual human opinion. And the same is true of science. Science is a way of dealing with theories regardless of whether one believes them. Now, let me say that I agree with everything David Deutsch just said there. And I also feel like these quotes are massively abused by the community and sometimes by David Deutsch himself. So you may find me somewhat more sympathetic to the idea that humans have beliefs. Humans absolutely do have beliefs and the idea that I’ve seen crit rats say, oh, I don’t believe anything. It’s like, okay, that’s like ridiculous. Right. Like if you were saying we shouldn’t like morally we shouldn’t and instead we should treat it that way about almost by that. But this idea that that crit rats don’t have beliefs is just not true. And in fact, a great deal of this podcast has been pointing out a lot of the different really pretty questionable beliefs that crit rats often do have. Based on as far as I can tell not really a good critical analysis at all.
[01:46:36] Red: So I think beliefs are a huge part of what humans do. However, I do take this quote from Deutsch as being more about the institution of science than individuals. And I think when taken that way, it is absolutely a true statement in my opinion. Maybe you would disagree with me still because of that, you may find me somewhat more sympathetic to your viewpoint that yes, we do have beliefs. Also, because I’ve studied machine learning, the concept of belief in machine learning isn’t really human beliefs. It’s not this subjective opinion of what I think is true. It’s whatever your model currently says, that’s called a belief, right? So it might be like a single celled animal, which clearly has no beliefs in the human sense. But it has a belief about its environment based on its updates, which might be Bayesian updates. That’s one of the theories about how these things work. And it has some sort of model and that model is its belief about what’s going on in the real world since it has no real access. Nobody ever has access to the real world, right? And so because of that, I understand that the word belief really could mean something as simple as which theory do you currently hold, right? Even if it doesn’t have to have any religious faith based content to it at all from the way out. It seems to me a little bit…
[01:48:02] Green: Go ahead, Peter.
[01:48:03] Blue: Seems to me a little bit different way to look at it is just that beliefs are great. We can’t escape having beliefs on all kinds of things, but when we are reasoning, we’re arguing for our beliefs and questioning our beliefs and putting our beliefs out there and not trying to shut other people down for expressing their beliefs. That’s really where reason comes is within the arguments more than anything. At least that’s kind of what the kind of political rationalism that makes sense to me.
[01:48:41] Green: Okay. So I think I have an idea what’s going on then. I think there’s an equivocation on the word belief. So when I’m using the word belief or epistemic belief, I want my epistemic beliefs to be the result of inference. And I wonder if I interpret Deutsch as saying that no, like the conclusions should just follow from inference, not belief. In other words, he’s sort of taking the parts of belief that we think are irregular or irrational and casting them aside and saying, we don’t need any of that. We don’t need this intuition. We just need inference. Although they don’t usually like… Priests don’t usually like inference either. But I feel like there’s something going on there. Okay. So I have multiple theories. Let’s say I have Newtonian gravity and I have Einsteinian gravity. Science, I can just follow the equations. They make predictions and the predictions of Einsteinian gravity are better. What is David Deutsch referring to when he says I don’t need beliefs? So let’s say I want to create a very high -speed space probe that’s going to go at relativistic speed. Which theory should I use? Both of them are objectively going to make certain predictions. And in the past, Einstein’s field equations have been more accurate. But it seems like there’s something normative or some sort of inference going on that says that, hey, I should discard Newton’s gravity.
[01:50:45] Red: Yeah. So okay, obviously the way I think Deutsch or a crit -rat would respond to this is they would say, well, it’s because we’ve refuted Newton’s theory by observation and we haven’t refuted Einstein’s theory by observation. So there is actually a reason to discard Newton’s theory. And there’s really only one theory left that talks about what’s going to happen in the domain that you’re referring to, relativistic speeds. And so that is, it’s just rational to go with the theory that hasn’t been discarded yet. There are various things that could be a problem here. For one thing, we could argue that it has been discarded because it’s at odds with quantum mechanics. But I still think the basic idea is exactly what I just said is that they would say it’s not that we believe the theory. Like we may believe it to be false even, but it simply is the best surviving theory. And so of course it makes sense to go with that one and not to go with Newton on some sort of lack of explanation where we say, well, maybe Newton’s right this time. Right. And that’s not an explanation. Right. We would expect there to be an actual explanation. If we’re going to go with Newton’s, we need an actual testable non -ad hoc explanation as to why Newton’s actually is the better theory in this case. And we know that can never be because it’s already got observations that are at odds with it, whereas general relativity does not.
[01:52:21] Green: I just feel like because it’s going to effectively generate the same action, we hope, that maybe it’s hidden in the methodology or in something normative. But I feel like it has to kind of work out in the same way, kind of result, give you the same Bayesian result. Like what does it mean? Do you believe that if you’re going to make a wager on launching this high -speed space probe, is there no wager? Or what about the use of hydroxychloroquine or something to treat COVID? You’re going to make some bet on whether you should use this compound or not. I guess the thing that confuses me is that if there’s no probability associated with these things, then is it 50 -50? Can I just not make bets? Is betting outlawed? But it can’t be outlawed. You have to try something. That’s the reason why the idea of excluding the probability of a hypothesis being true doesn’t really make… I just don’t know what to do with it. I’m kind of completely baffled by it.
[01:53:52] Red: Wait, say that last part again.
[01:53:55] Green: So Papa wants to say that the probability of a hypothesis being true is meaningless or does not work. But if I don’t have probabilities that hypotheses are true, then I can’t make bets. I can’t take actions where I have expectation values because there is no expectation value if there’s no probability.
[01:54:28] Unknown: So Ben
[01:54:30] Red: and Baden have a podcast where they actually talk about this. And what I recall them saying was you can always just not make a bet. And that’s actually one of the things that I’m a little unclear on. Obviously, you do not have to make a bet. I would agree with that statement.
[01:54:48] Unknown: But
[01:54:49] Red: you can always imagine some scenario where you had no choice. Aliens are holding guns on you. You can imagine some sort of scenario where you would have no choice. And I’m curious how they would respond to that. In fact, I’m planning to invite them on the show at some point and ask them some of these questions to try to dig deeper into how they look at this. Let me just say, though, that regardless of making a bet, I’m not even sure what if I need to build a probe and maybe let’s say my life is on the line. So we need to make a rocket that’s going to go relativistic speeds and I’m trying to go out to Alpha Centuri or something along those lines. It’s the movie
[01:55:31] Green: Interstellar.
[01:55:33] Red: Right, it’s the movie Interstellar. I’m not really making a bet. I mean, like I’m not. Yes, there’s a bet in the sense that it might not work. The theory may be wrong in some way or it could even just be one of the auxiliary theories is wrong. We make a mistake on how we build the rocket. The O -ring is broken or something and the rocket blows up. I mean, it’s all sorts of things. So in a certain sense, yes, I’m betting my life on it. OK, but I don’t I don’t even need to have a need to sit down and try to figure out. Should I use Newton’s theory or should I use relative general relativity? I’m absolutely going to use general relativity period end of story. There’s no reason to even think about in terms of a wager that maybe Newton was the theory I should have been using. Right, I mean, like I wouldn’t even go there. There wouldn’t even be a need to turn it into a bet in a case like this. Now, I can think of cases where I would need to take it, turn it into a bet. So I’m not necessarily denying that sometimes the wager thing makes some sense. OK, but in this particular case where I’m actually just trying to choose between Newton, a totally discredited theory and a known to be superior theory, general relativity. I’m not making any bets at all. I’m just going with with general relativity. And I do think that is the way a critical rationalist would generally look at it if they’re trying to look particularly if they’re trying to look at on the science side of the demarcation line.
[01:57:00] Red: Where this is a testable theory, we can actually refute it by observation. They would they would say, look, we’re not we’re not saying general relativity is true. In fact, it isn’t true, right? We’re not working out a probability that it’s true. We don’t even care. We’re just saying it’s the best theory. So of course we’re going with it. And I think that is the critical rationalist view in this particular scenario.
[01:57:29] Blue: Can I just throw up? Sorry. Go ahead. I hope this doesn’t take us down a tangent. But I was just going to say, I thought that the other week you said something really Bruce that I thought was interesting, where you were talking about Templars paper, the Obama tribe, curvature of constitutional space. Yes. Where you said that I mean, it sounded like he was kind of making a political point against sounds like a crazy paper, but political point against Obama and his use of his use of modern physics. But one of the things he said that it sounded like you to you agreed with, or you thought that it at least had some validity, was that this popular popular notion that I think Popper and Deutsch talk about a lot is that that general relativity refuted Newtonian mechanics is actually, according to Tipler, not true that both general relativity and quantum mechanics are extensions of Newtonian mechanics rather than replacements.
[01:58:40] Red: Does that have some validity? Yes, it does. Let me let me explain it slightly differently because the way you were. Okay. I don’t know. Tipler would quite agree with, although I think you’re close.
[01:58:49] Green: Okay.
[01:58:49] Red: So, Tipler in the paper, bear in mind, I’m not a physicist, so it’s not like I can actually follow his argument. Okay, but I’ve talked to physicists who said that he’s actually technically correct, but they think it’s kind of a dumb point. Well, we do have a physicist here, so. Yeah, so his argument is that that Newtonian physics actually did imply curvature just like Einstein’s theory. I don’t think he goes any further than that. Okay. And from talking to physicists, I’ve had them tell me, yes, that’s true, but only if you first understand Newtonian Einstein’s general theory relativity, you’d never realize that without having actually known about general relativity. So because of that, Tipler is not saying relativity is equivalent to Newtonian physics. He still, Tipler would very much tell you that Einstein’s theory of relativity is the best theory and not Newton’s, and that Newton’s is a refuted theory. Tipler is entirely a four -strander, so I’m almost certain that’s exactly what he would say. Right? Tipler invented the four strands, not Deutsch. On the other hand, I think what Tipler would say is that this whole idea that relativity is this theory that’s totally distinct from Newtonian physics is just not true. It’s actually a piecewise improvement on Newtonian physics. Typically, we say, well, under Newtonian physics, there was no curvature of space, and then we had to reimagine gravity being this curvature of space. And he would say, no, a lot of that was actually implied in Newtonian physics. We just didn’t realize it until we had Einstein’s physics, and therefore it was actually just a piecewise improvement. Now, why does this matter? As far as I can tell, it doesn’t, right?
[02:00:46] Red: I mean, in some sense, all theories are just piecewise improvements on previous theories, or you can think of them as new theories. There’s no real distinction between this theory is false and this theory is true because they all have so many ties between themselves as we build these additional theories. If we were to talk about Darwin’s theory of evolution, what do we mean? Do we mean the original theory that was in his book, Origin of the Species? Or do we mean modern synthesis, which we usually call Darwin’s theory of evolution still, which is a drastically improved theory at this point, right? And so I think he’s making a fair point that the distinction we make between Newtonian physics and Einstein’s theory is somewhat artificial. It’s almost an intuition, we’ve crossed a barrier where now we’re going to consider it not a refinement of a previous theory, but a separate theory. And he’s arguing we shouldn’t have done that. It’s actually refinement on a previous theory. And then he uses it for the stupidest of all purposes, right, to try to show that Obama doesn’t know what he’s talking about in this political paper. And it’s almost to the point of absurdity at this point, because of course Obama’s not trying to make any sort of point based on physics. He’s just he’s trying to say sometimes we need a new paradigm when we’re looking at things. And I think almost everybody would say Einstein’s theory was a new paradigm, whether you want to retroactively argue it’s just a piecewise improvement. It certainly felt like a paradigm switch and allowed us to rethink things in a new way, which would mean that Obama’s point was actually valid.
[02:02:27] Red: Regardless of whether we want to think of it as a true paradigm shift or a piecewise improvement, it certainly felt like a paradigm shift and caused us to think of the world in a new way. So that’s kind of my summary of that paper from Tipler. And from what I’ve been told, he’s technically correct. He’s kind of using it in a way that I don’t think makes a ton of sense.
[02:02:52] Blue: That sounds interesting. Thanks.
[02:02:57] Green: Okay. I’m going to move on to talk about Popper’s Ratchet and refutation. So I cooked up this example. It’s an example I’ve used before to talk about this principle. Popper’s Ratchet, or Nielsen’s Ratchet as I like to call it, is this… I’ll see if I can summarize it. I’m probably going to mangle it a little bit. But the general idea is that you’re not allowed to defend your theory against contrary evidence with an ad hoc addition to your theory unless that addition to your theory makes narrow predictions of its own.
[02:03:41] Red: That’s correct.
[02:03:44] Green: So the example that I used to illustrate this is a large emerald has been stolen from a museum safe. A defendant is brought into the dock, and all evidence points to his guilt. He was found at home with the emerald in hand, with safe -cracking tools and a book on how to crack safes. He was captured on CCTV and spotted by eyewitnesses at the scene. His fingerprints and DNA were found on the safe. So it looks like an open and shut case, right? But at his trial, his lawyer argues that his client is the victim of a conspiracy. And of course, the conspirators who want to frame him will be expected to have fabricated just this kind of evidence. Since both the defense theory and the prosecution theory make exactly the same predictions, neither theory has an advantage. So it’s a tie. What has gone wrong?
[02:04:42] Red: Whenever I give this example. Yeah. Because clearly that is wrong. So yes.
[02:04:46] Green: Right. But whenever I tell this story, I always think of that little clip at the end of Thor Ragnarok where the grandmaster says, it’s a tie.
[02:04:58] Red: Right.
[02:05:02] Green: So I’m representing the prior probabilities here in this example. And over on the left, I have guilt in red and on the right, I have innocence in green. And guilt has a smaller prior probability than innocence, right? Because we think that only a small subset of people in the city are guilty of this crime, all things being equal, guilt has to have a smaller prior. Most people are innocent of this crime. Even if they’re guilty of other crimes, they are innocent of this crime. So the prior for guilt is smaller. But within these priors, there are more detailed theories of what actually happened. So for example, there’s some subset of the innocent side of the prior that represents people who are innocent by way of being at the supermarket at the time of the crime. That was their story. They were not committing the crime because they were at the supermarket at the time. Well, another small segment of the innocence prior belongs to being innocent by way of being framed by some deep conspiracy. And another tiny sliver of the prior of innocence is they were innocent because they were just mind controlled by someone on Mars, right? So there are tiny slivers of the prior of being innocent that belong to strange theories. So what has the defense done? If we use the diagrammatic technique that we used earlier, if we find evidence of guilt, well, all of the prior for guilt flows down into step two. And just this tiny sliver representing the defendant being framed comes down to the final stage. We have this visual representation of Bayes’ theorem, and the guilt part of the prior is just larger than this tiny sliver.
[02:07:26] Green: So in other words, when you make an ad hoc change to a theory, to save the theory, you also reduce the prior correspondingly. So in other words, in the original theory of innocence, there was a sub -theory, a tiny sliver of that prior belong to the sub -theory that the person was framed. And by making this ad hoc addition to the theory, you’re selecting out just that tiny sliver of the prior. So even though you’ve been able to match the likelihood of seeing the evidence that you make the same predictions now, you have shrunk your prior dramatically. Now exactly how much you’ve shrunk it depends on things like, well, how many people that are found with evidence of wrongdoing turn out to have been framed? So there are other values here that have to be assessed in other ways. But in scientific theories, it’s usually… So if we were to use the same example here as an analogy for evolutionary biology,
[02:08:54] Unknown: right?
[02:08:55] Green: So guilt here corresponds to evolution did it, and the green bar is something else did it, let’s say design. And what is the evidence? Well, the evidence is descent, right? There’s common descent, common composition that it took millions of years that there’s no apparent purpose on this planet apart from survival. And there are millions of species. These are all predictions of evolutionary biology that didn’t have to be that way if life was designed. Now you can say, aha, but my theory is that life was designed, but it was designed in such a way that it looks like evolution. It’s precisely this. And in the same way that we can rule out the innocence of the suspect, we can rule out the innocence of evolution. At least that’s what a Bayesian would do. So now I want to talk about refutation. And what I was saying earlier is that these bars, when I say that I believe that the Newtonian approximation has like my entire prior, right? At the end of the 19th century, Newton reigned supreme, right? So everyone thought, yes, the Newtonian approximation is true. Well, within the Newtonian approximation, there are sub theories. One of the sub theories is pure Newtonian truth, like Newton’s laws are it. That’s the answer. In other words, Newtonian approximation isn’t an approximation, it’s actually true. The reason that the Newtonian approximation works is that Newton’s equations are literally exactly true. But also within the Newtonian approximation is the Einsteinian approximation. And within the Einsteinian approximation is pure Einsteinian truth. Well, when we did after the Eddington experiment, the Einsteinian approximation is what survived the test. Pure Newtonian truth did not. Pure Newtonian truth was refuted, but the Newtonian approximation was not.
[02:11:25] Green: Now, within the Einsteinian approximation that survived, there is a sub theory within that which is that Einstein’s equations are literally true and that’s the end. We don’t have high confidence in that, right? The prior on that is very small. We think that Einstein’s field equations are going to break down on at some point. But they’re not ruled out. The other thing that I think that we can get from diagrams like this is Occam’s razor. So if we take this view here where you have Newtonian approximation subdivided into different pieces, the prior probability that Einstein’s approximation is true is smaller than the total for all of Newtonian approximation. So when we were conjecturing about what the laws of physics were, it’s not unreasonable to go with the Newtonian approximation. It contains a lot of other theories. If we had leapt to Einstein, we would have been lucky, but there are other theories we can cook up which differ from pure Newtonian truth, but which also differ from the Einsteinian approximation. So Occam’s razor says that basically if you start adding things to your theory, what you’re doing is you’re selecting out subsets of your prior which must have a lower probability than the whole. So if now there’s nothing wrong, it could be that obviously we think that the small subset of the whole is going to be the truth. And that’s okay as long as it survives the experiment. It makes the narrow prediction. So any theory like design, design versus evolution. Evolution, I think that the design is, as far as anything in science can be ruled out, is ruled out. But it could recover, right? The probability is not zero, it’s just awfully small.
[02:13:43] Green: But it could recover if you come up with a theory of design that predicts things that even evolution does not, then it can recover.
[02:13:54] Red: So can I ask you some questions about this slide? Sure. So first of all, one of the things that Popper brings up is the way people thought of science prior to particularly Newton’s theory prior to Einstein. The fact is that they definitely weren’t thinking of it the way you were laying it out here. They thought for sure Newtonian, pure Newtonian physics, pure Newton’s theory was pure truth. Okay. And it was hard for them to even, like a lot of the philosophers he quotes, Kant and etc. He points out that they were struggling with this idea that how in the world did we derive a purely true theory? Now, obviously it wasn’t a purely true theory, which is what you’re saying here. And you and Popper would agree on that. So when you kind of lay this out, and I can make sense of what you’re saying, but surely this isn’t the way people have traditionally prior to Einstein. This is not traditionally how people looked at science. They actually did not think of it as a Newtonian approximation. They thought they were talking about the little box there, pure Newtonian truth. They sincerely thought that because they had never even once seen a counter example to it. And couldn’t even conceive the possibility that there could be. So could you comment on that maybe? So are you, and I guess what I’m trying to ask? I mean, they had
[02:15:26] Green: 200 years of glowing success. And I think that the intuition that physicists have when they’re doing their work is really quite naive. I mean, I know one of the reasons why I’m passionate about teaching Bayesian inference and teaching rationality is that I got a PhD in physics and I wasn’t taught any of these things. So when I years later discovered Bayesianism or Bayesian inference and cognitive bias, I was horrified. I mean, I’m interested in scientific reasoning and critical thinking. I was like, how did I slip through the cracks? What went wrong? And you realize that it’s just not taught in schools at all, right?
[02:16:21] Red: So this is definitely not how scientists actually look at it. This is what you think is really going on, but scientists have a naive view of it.
[02:16:34] Green: Yes, that’s what I think.
[02:16:36] Red: Okay. Sorry, next question or comment. One of the things that Popper makes a very big deal about is that we’re looking for improbable theories. And he uses this to argue against, I don’t think Popper, like Bayesian epistemology didn’t exist at the time of Popper, right? So he wouldn’t have been arguing against the specific theory that you’re laying out here because it got invented later. But one of the things he is trying to show is that we’re looking for improbable theories, not probable theories. And this slide shows that, right? The Newtonian approximation, as you call it, is clearly more probable than the Einsteinian approximation because it’s broader. At least that’s the way you’re portraying it. I would actually challenge that a little. But for the sake of argument, let’s stick with this for now. So Popper is correct, according to this slide, that we are in fact seeking a less probable theory. What you’re really saying, though, is that that’s in terms of the priors. But if you actually look at the evidence, because all the outcomes are constrained within the Einsteinian approximation, even though the Newtonian approximation under this way of thinking makes the same predictions, we would still start to favor the Einsteinian approximation because the Newtonian approximation, even though it could explain the same evidence, it’s just broader in terms of what’s possible. We would start to favor using the posterior probabilities. We would start to favor the Einsteinian approximation. Is that what I am seeing you say here, or am I misunderstanding?
[02:18:30] Green: No, that is what I’m saying. So you are understanding correctly. One thing that I would change is that the Newtonian approximation is seen more clearly to be an approximation because parts of it were refuted. So pure Newtonian truth has been refuted. It did not survive.
[02:18:56] Red: And that was actually what I was going to offer as a criticism, is that I don’t actually believe Newtonian approximation is a superset over the Einsteinian approximation. I think those are different theories that make different predictions, and one is not really an approximation of the other. It’s true that they get the same results under certain circumstances that Einstein’s theory tells you when that is, and Newtonian physics doesn’t. But, and I think that would be my main critical rationalist criticism of this slide, is that it isn’t really true in my mind that Einstein’s theory isn’t, sorry, that Newton’s theory approximates Einstein’s theory. Having said that, it’s true that post facto after the fact, and I guess that’s what you’re trying to say here. We can, once we have Einstein’s theory, we can say, oh, Newtonian physics approximated Einstein’s theory at least under certain circumstances that were very common. And that explains why we didn’t find these counter examples prior to this point, because we were never in a, never near a black hole and we were never moving near the speed of light. Or we did not have precise enough measurements.
[02:20:11] Green: Measurements to make it to see the difference.
[02:20:14] Red: Right, right. From that standpoint, I can see how this is at least partially a response to Popper’s, a response by agreeing with him, actually, that you can still differentiate between a more approximate theory and a less approximate theory using Bayes’ theorem.
[02:20:33] Green: Yes, I mean, so my last slide actually is a quote from McGee on just this point, that he says that the best theories have high information content, meaning that they make very narrow predictions, but then they have low probability. But the only interpretation of probability that seems to make any sense there is like prior probability, that if you didn’t have the theory, then seeing those kinds of correlations among your observables would have been tremendously improbable. And so that’s true, but it seems to be, it’s a very strange thing to say. I think that logic of scientific discovery was written in, was it 1934?
[02:21:24] Red: Yeah, I think that’s right.
[02:21:27] Green: And so the way we talk about Bayes today, we’re much more fluent with this idea of posterior probability, I think. At least the things that he said about subjective probability struck me as if he was not thinking like a Bayesian, like he had not been exposed to this way of thinking. And I think there’s a beautiful book, I’m going to forget the author’s name, but it’s about the history of Bayes. And that you would think that, oh, well, this has been known for many decades or more than a century, so surely everybody should know about it. But people really did not like the idea of subjective priors, and so it was sort of set aside. And one of the reasons that, I mean, Bayes made a comeback late in the 20th century, partly so late because its great successes in the 20th century were in military applications. So they were classified, things like breaking enigma. So Turing used Bayes to do that. So I think that it’s something that even though it has been known for a long time, having a comfortable formalism is relatively new. At least that’s my interpretation of why Papa said some of the things that he did that seemed peculiar to me.
[02:23:07] Red: So I agree that he had no notion of anything like Bayes’ epistemology. And it’s true that a lot of the ideas of Bayes predate Papa. You can only work with what culturally is available to you though, right? Yes. So Campbell references in an article that is itself famous, but that Papa strongly endorsed. He tries to work out an evolutionary epistemology. And he actually references the first AI program as an example of his case. But the term AI didn’t even exist yet, right? And linear regression existed, right? Logistical regression existed. Important machine learning techniques. But there’s just no way that these people, Papa and Campbell, would have any real notion of how we would think and act in terms of the existence of really successful machine learning that now exists, right? Even though theoretically they could have worked some of this stuff out because the theories were around, there’s just no way they would be able to. It would require it to really be part of our consciousness first. And to understand what the implications are in terms of how it gets practically used. So I agree with you that one could make a decent argument here. I need to probably think about this slide more before I could really intelligently respond to it. But I can see what you’re trying to do, that you’re trying to show that Papa’s argument that we’re seeking improbable theories only makes sense in thinking in terms of prior probabilities, not posterior probabilities. Yes. And based on that, you could make an argument that with posterior probabilities that you can actually end up favoring the less probable theory, such as Einstein’s theory in this case.
[02:25:12] Red: Just because it’s specifically because of Papa’s ratchet, because it’s a theory that is more specific.
[02:25:19] Green: Yes. Okay.
[02:25:21] Red: I’m with you on that. I’m not prepared to agree or disagree yet. I would definitely need more time to think about this. But I think that’s at least a good argument that I’m going to need to think about. Let me say that much.
[02:25:33] Green: And I appreciate your comment about saying the way I’ve drawn these overlapping in this way is not fully intuitive to you. And so I’m going to rethink this diagram and think about in what way I might be able to redraw it to support your claim rather than mine.
[02:25:56] Red: All right. Sounds good.
[02:26:00] Green: I created this table summarizing some of the themes in critical rationalism and Bayesianism. You can see there’s a number of checkmarks here where they both agree. So we were just talking about ad hoc conditions to theories being bad. They both agree on that. They both involve successive approximation. Fallibilism is the same in both. A Bayesian always is going to reserve some doubt in some theory because the data, it could have just been extremely unlucky. Creativity is a feature of critical rationalism. In Bayesianism, it’s implicit. It’s not a disagreement between the two. It’s just that Bayesianism doesn’t really talk about where theories come from. It’s really more about what you do once you have theories. Induction, critical rationalists say that induction is impossible. We talked about it earlier that maybe there are multiple definitions of induction. And that’s not to say, I think that even if I were to get into a room with Karl Popper and explain my point of view, he probably still wouldn’t like Bayesianism because it does have this additional axiom. He really was shooting for the most minimalist picture that he could, and so he might still not like Bayesianism even if he thought that it worked. He’s actually quite conciliatory to a lot of the ideas, but he’s also trying to reject them in places in the logic of scientific discovery. And I thought that was interesting that it wasn’t a war on induction precisely. It would be more an effort to construct something more minimal.
[02:27:58] Green: Justification, this is the area where I think I’m one of the areas where I’m most critical of justification, of critical rationalism, is that we talked earlier about ways people can be misled by the fact that Bayes’ theorem has an equation in it and you’re putting in numbers and getting an answer that you might be overestimating your confidence. You might see it as being more rigorous than it really is. But I think that I have a similar problem when it comes to critical rationalism and they talk about criticism that it seems extraordinarily hand -wavy. And that it’s very easy to support beliefs that are fringe. You could just say, well, the mainstream idea has not escaped my criticism. I’m not satisfied that my theory that this conspiracy is true. I’m not convinced that the world is roughly spherical. There are criticisms. My theory hasn’t been refuted for these reasons. That’s the thing perhaps that I like the least about critical rationalism.
[02:29:16] Red: You’ve listened to my podcast enough to know that I’m extremely, extremely critical of crit -rats on how they handle that.
[02:29:24] Green: Yes. I agree with
[02:29:28] Red: you that at least culturally crit -rats are incredibly hand -wavy with the term criticism. And I think could literally justify, and I think that’s the right word here, even though they would reject the word, I think they can literally justify any theory as best theory, the way they’re currently going about it.
[02:29:48] Green: Yeah. Just to be a little bit even -handed, there’s a website called lesswrong.com, which is in some sense the home of the Bayseans. And there is a lot of discussion over there where they take, there’ll be discussion about long -termism, where they’re applying Bayse theorem to these extreme cases. And some of it is great intellectual exercise and so on. But I also get the feeling that a vibe over there that people tend to become obsessed about these extreme scenarios. Right. Like we were talking about utilitarianism earlier, you get these extreme scenarios where maybe you look for some scenario, like the simulation argument. I think the simulation argument is not a terrible Bayesian argument, but I think that it doesn’t work, ultimately. It would work if we thought that there would be many simulations that are as deep and rich as life appears to be on Earth to us today. Then you probably would have a pretty good Bayesian argument. But I think that why would anybody do that? It seems quite peculiar. So in other words, in the Bayesian picture, you can get caught up with these sort of brain teasers or these puzzles where you look at extreme probabilities like Pascal’s wager sorts of arguments. And you can get trapped in those. When it comes to probability, Karl Poppo was emphasizing a form of frequentism. He’s even more specific than frequentism. So just to be clear, he actually invented his own philosophy of probability that was called the propensity theory of probability. And I can see how it might come across as somewhat frequentist, but he definitely did not see it as being the same as frequentism. Yes. He has very rigorous definitions and assumptions. He’s very clear about what assumptions he’s making.
[02:32:13] Green: What’s the most impressive about the work really is that attention to rigor and detail.
[02:32:21] Red: Yeah. I think that if you had to put him into the Bayesian or the frequentist bucket, I definitely think the propensity theory would come across far more like the frequentist philosophy. But like even in my A.I. textbook, they said there’s three theories of philosophies of probability and they listed frequentism, Bayesianism and the propensity theory. And even said that Karl Popper came up with the propensity theory. So it is generally thought of as its own separate philosophy distinct from either Bayesianism or frequentism.
[02:33:03] Green: This slide, I’m not terribly happy with this slide really, but I really invented it because I wanted to distinguish subjective probability from intuitive probability that I did earlier. So just because I’m using the S word doesn’t mean that it’s completely biased, that it’s some random thing from my brain. It’s relating to me the subject and the information that I the subject have, but it may well be algorithmic or even objective or deterministic in some sense, how I’m computing it. It’s just subjective in the sense that I don’t have all the information.
[02:33:45] Red: So since the people can’t see that slide, can we maybe read through it quickly? And because actually we don’t need to spend much time on it, but just so the top one was classical probability, mathematics of simple games, dice, cards, etc. I think even most Deutschians that have really strong problems with probability would agree with that aspect of probability for sure. Then you have logical probability, which you which you has the probability of favorable outcomes based on assumptions divided by the total outcomes based on assumptions. Then empirical probability, which is simply favorable favorable events divided by total events, paparian probability, which you see as similar to empirical probability with special rigor. Subjective probability, which you put as algorithmic slash deterministic probability based on information you have and on assumptions versus finally intuitive probability using intuitions and guess works and subject to bias. So really you’re trying to show a distinction of the last two that subjective probability is, you’re arguing it is more rigorous than just an intuitive probability.
[02:34:58] Green: Right. Now I think most Bayesians would say that intuitive probability is allowable for choosing priors when you have reason to believe that your experience is going to give you something, some valuable information. So if you have not been keeping copious notes or you don’t have access to, let’s say you’ve seen 30 patients a day for the last 25 years. If someone comes in with a cold or a flu or some common ailment, you can probably diagnose it really well. Even without putting all those medical records into a computer and doing an analysis to give you the exact number.
[02:35:47] Red: And certainly human beings do use that sort of intuition. I mean, wrongly in a lot of cases, maybe even often wrongly in a lot of cases, but we seem to put a great deal of stock in our intuitions based on our prior experiences.
[02:36:07] Green: Yes. And there have been psychological studies to look at how reliable are our judgments. And like the book Super Forecasting talks about this where people are asked to make predictions about the future. And if they’re getting feedback, they can actually be quite good. So if your day -to -day job is analyzing tax returns and you get feedback, you analyze somebody’s tax return, you want to let’s say minimize the probability that they get audited. You want to make sure they get the best tax refund and so on. And you’re getting feedback on your work, then you’re probably going to be quite rational in the way that you do it. It’s a good probabilistic model. But if you make predictions and you make judgments and you don’t get any feedback, then you’re probably not going to be making rational judgments there. So rationality, intuitive rationality, tends to be local to your field of expertise. So if you’re a doctor and you see patients every day, you might be very rational at judging what kind of ailment they have or what kind of treatment will work. But if that same doctor who may be very intelligent decides to go trading on the stock market, they probably won’t be rational. Intelligence and rationality are two different things. Intelligence IQ measures your ability to test for deductive coherence and for your creativity. But rationality is about figuring out which theory is more likely to be true given the evidence. And that’s something that, A, we do not teach and B, it’s only natural under certain narrow circumstances.
[02:38:30] Green: There are interesting experiments that show we can be very bad at doing this, but if we are given exactly the same problem in a social setting, in a social context, we can actually figure out the answer quite quickly. So the intuitive probability is something that’s been studied and if you are going to be receiving data, if you know that you’ve got access to a lot of data, you can start from an intuitive set of prior probabilities and then just update on the evidence and you’ll get straightened out. What’s more risky is taking your intuitive probabilities in a scenario where you probably won’t get any more data. So if you’re asking questions about, for example, what is the likelihood that there is intelligent life elsewhere in our galaxy? You don’t have a lot of data. We know about the history of life on Earth, but then how are you going to set your priors? You don’t have an intuitive grasp of the probability that life will be created elsewhere. Right, objections to Bayesianism. One objection is there’s the problem of induction, which is that you can’t say that induction has worked in the past, so it will work in the future because that is using the principle of induction to justify the principle of induction, so it’s circular. And my answer to that is that that’s true. I’m not going to justify a principle of induction without circularity because I think it’s one of the axioms of rational thinking, and so it’s inevitable that I can’t justify it with only half of the other axioms. A deductive proof of induction is not going to be there. Then there are the arguments we’ve talked about. Subjective probability is bad.
[02:40:43] Green: There’s the idea of psychologism that we don’t want to talk about the sociology of what scientists are doing. Like you say, when scientists in the 19th century thought that Newton was just literally true, pure Newtonian truth, but that’s not what we’re talking about today. We’re not talking about how do scientists think that’s a different question. Why do science work? What would ideal rationality look like? One of the things Popper says about subjective probability, his arguments against it, was that if you replace the probability of X in some experiment with degree of belief in X, it creates some nonsensical statement. But I don’t think that was a very fair critique. I could look up the quote, but I didn’t find that compelling. He did a trick of just because I hold that probability corresponds to a degree of belief, doesn’t mean that I can’t also have an idea of probability as favorable events divided by total events. One other objection is that the probability that a theory is true is zero because all theories are technically wrong and going to be superseded.
[02:42:04] Red: That was from Deutsche’s website.
[02:42:09] Green: Deutsche also says, the theory none of the above is not a theory. I talked about that earlier. I think that it contains many, many different theories and it’s true that it’s not an explanation because it spreads its predictions across all of the possible outcomes. The theory that it’s none of the above is in some sense like the worst theory, but from a Bayesian perspective, it’s still a theory. Deutsche has some cool things to say about explanation versus instrumentalism. I think it’s important that we try to find explanations, but I also want to say that I think that the way you interpret a mathematical theory is making the difference between those two things. If I have the field equations for this standard model, I can interpret some things as being fields or as being particles. It’s a layer that I’m putting on top of the mathematics, but I think that the predictive work is being done by the equations, not by the explanation. I think what the explanation helps us do is come up with more refinements to the theory. It’s involved in that creative process, that creative conjecture.
[02:43:40] Red: I don’t think he would argue that part. He might say it’s more than that, but I definitely think that’s kind of what he argues is that since scientific theories are explanations, not the equations, that would mean this, and you can start to work out what the implications are. A different theory that makes the exact same predictions may have different implications under a more in some sort of circumstance, and that would lead to a crucial test at some point.
[02:44:12] Green: Then finally, we discussed this also that good theories have high information content but low logical probability. I think if we interpret that as prior probability, then it makes total sense to me. It just doesn’t do anything. It’s not really an objection to Bayesianism because what the Bayesian is going to do is say that, well, I followed the evidence. Yes, it was highly improbable before I had the evidence, but now that I do have the evidence, the posterior probability is very high.
[02:44:49] Red: That’s something I had not heard before, so I’m really glad you brought that up so that I could have a chance to think about that.
[02:44:57] Green: My last slide is a quote from McGee on Popper that says essentially the same thing.
[02:45:03] Red: What we are interested in then are statements with a high information content. This can this consisting of all the non tautological propositions, which can be dused from them. But the higher the information content, the lower the probability according to the probability calculus for the more information a statement contains, the greater the number of ways in which it may turn out to be false. And then you say this seems to make sense only if probability is referring to prior probability of the evidence across all theories.
[02:45:34] Green: Yes.
[02:45:36] Red: All right, I got no comment on that today. I’m going to think about that one and I’m going to get back with you on it at some point.
[02:45:43] Green: Yeah. And the implication of that is that Popper was a kind of Bayesian.
[02:45:52] Blue: Is that is that? No,
[02:45:53] Green: no, no, no,
[02:45:54] Blue: I’m not kidding.
[02:45:56] Green: No, no, it’s really it’s more. I guess
[02:46:00] Red: you’re saying you’re saying what you’re really implying is that Popper’s not wrong, but it can be fit into the Bayesian framework.
[02:46:07] Green: Yes, yes, I would agree with that. Yes, I mean, I think that, you know, as a Bayesian, my view is that if your if your conclusion is rational, then there must be a good Bayesian argument for it. So I wouldn’t say that Popper was a Bayesian, but that I agree with his statement about our information content and the lower probability if I interpret it in this way. And it makes sense, right? Like a theory is picking out correlations of variables that without the theory would, you know, in the absence of theory would be highly improbable. If you look at all the possible measurements that could be made, this correlation is highly improbable. But given that the theory is true, that, you know, the expectation is that correlation is very likely to be true.
[02:47:08] Red: Right.
[02:47:09] Green: Subject to the theory, the conditional probability is high.
[02:47:12] Red: So Bobby Azarian had a book recently, The Romance of Reality, what’s it called? Peter, you’re the one who pointed. I think
[02:47:20] Blue: that’s exactly it. The Romance of Reality.
[02:47:23] Red: He claims in that book. Now, first of all, let me say that Bobby Azarian is a totally legitimate scientist in his own field. But in this book, he is definitely covering theories that are well outside of his expertise. And it’s a very Deutsch -like book, except that he’s not a physicist like Deutsch is. And so he backs up what he’s saying using other scientists. And I’m not sure he understands the theories as deeply as Deutsch understands his theories, which would make sense because Bobby Azarian is trying to pull together other people’s theories. In some ways, he almost feels more like me, like I don’t come up with any of my theories. I’m just trying to explore theories and I’m trying to interpret them. But I’m probably never going to understand the constructor, constructor theory as well as Deutsch does. But Azarian actually in the book, and I need to probably buy a text version to see if it’s got references so I can look it up. He makes the claim that Campbell’s evolutionary epistemology, which is really just a generalization of Popper’s epistemology. And by Campbell’s own admission, that was what he was doing. And it was strongly endorsed by, at least parts of it were strongly endorsed by Popper. And he claims that, so one of the terms that’s used for evolutionary epistemology is universal Darwinism. There’s a whole field called universal Darwinism, which was fathered by that paper that Donald Campbell wrote back in the 70s that Popper wrote this glowing endorsement of. And then there’s also this idea of universal Bayesianism, which is really what you’re talking about. Azarian claims the two are equivalent.
[02:49:07] Red: And I need to probably look into why he’s making that claim because he obviously doesn’t go into deep detail over his claim. And I would like to see if there’s like references or studies or, you know, papers that I could read that would try to work that out. But he is making the claim that there is, in fact, a Bayesian interpretation of Popper’s epistemology and vice versa, and that the two are actually equivalent. Not endorsing that view. I just wanted to point out that there’s someone out there that has made that claim. And I probably need to dig in deeper into what his references were to even find out if I would even agree with him or not. But that is interesting that I did come across that in and I do think highly of his book. So I think that he comes up with all sorts of interesting things. I would love to bring him on the show and interview him. But he’s probably not interested in coming on a very small show like this. He’s clearly trying to go hit all the really big podcasts. But the excellent book and I would recommend it, but I just in passing it’s interesting that he did claim that they were equivalent.
[02:50:24] Green: Yeah, I don’t think I know enough about the evolutionary approach to be able to say yay or nay on that. I did listen to Bobby Ozarian’s book, though. I just don’t recall. I know that I was quite critical of it, but I can’t recall exactly what it was that I said, so I’d have to try and…
[02:50:50] Red: I’ve got a collection of criticisms too, so I hear you on that. So there are certain theories that he references that to me seem pretty silly that he clearly thinks highly of. And I can’t remember which one it was. There’s like one in particular that I thought, oh, and it just sort of groaned when he brought it up.
[02:51:09] Green: I think the thing that I recall that he was talking about was ideas about the very deep future of humanity and being able to have maybe infinite computing power or things like this where he seemed to be taking something that was possible and turning it into something that was probable. And that seemed maybe unconvincing to me. So convincing or not, I think spiritually speaking, I’m totally in the Azarian camp, right?
[02:51:51] Red: I want to be an optimist and believe in the types of things that he is trying to argue for, but I think I agree with you that some of his arguments were kind of weak. Or
[02:52:04] Blue: you were referring to, what was his interpretation of quantum mechanics called? Or the one he favored? It was quantum Darwinism. Oh, that’s right.
[02:52:12] Red: It’s the only interpretation I haven’t looked into. So I’ll often say on this show that many worlds is the best and in fact only interpretation of quantum mechanics. I always have to kind of caveat that with except that I haven’t looked into quantum Darwinism. So I don’t actually know if that’s a legitimate interpretation of quantum mechanics or if it’s actually… I agree with Deutsch that the Bohem interpretation of quantum mechanics is really just many worlds in disguise. There are certain things that I would have to do a podcast separately on why I feel this way, but I really don’t know enough to even assess quantum Darwinism.
[02:53:00] Blue: Well, it sounds like a future podcast and we should probably wrap this up. It’s been epic and I have truly appreciated what you’ve done here, Ivan. It’s been eye -opening for me. I’ve learned so much and the great thing about being on this podcast is that I continue to learn when I edit it and listen again. I’ll get even more out of your insights here and who knows, maybe I’ll jump ship and become a Bayesian. I don’t know.
[02:53:37] Red: And I want to actually add that to my appreciation for what you’ve done. I came into this with a kind of vague understanding of Bayesian epistemology and what I thought I agreed and disagreed with it over. And I feel like I have a much clearer picture now thanks to your excellent presentation of this. And honestly, I don’t know if a regular Bayesian could have explained it the way you did, right? I really think that this was awesome how you, using your knowledge of critical rationalism, was able to put it in a way that would just make more sense to me so that I could think more clearly about the difference between the two. If, assuming there is difference, I’ll give a nod to Bobby Azarian on this one. Maybe there is no difference ultimately, I don’t know. So I’m going to need to give that more thought.
[02:54:25] Green: I wanted to thank you both for having on me on the podcast again. I really enjoy being here. It’s great to have these discussions with you and get the feedback. And I, like I said, I’m a big fan of the podcast.
[02:54:38] Red: Thank you. Thank you very much. We have a lot of fun with this podcast and it is definitely a labor of love.
[02:54:44] Blue: Well, we’re just following the fun here. We’re following the fun criterion. Absolutely. Okay. Thank you guys. Have a great day. Thank you.
[02:54:53] Red: Thanks. Bye -bye.
[02:55:01] Blue: Hello again. If you’ve made it this far, please consider giving us a nice rating on whatever platform you use or even making a financial contribution through the link provided in the show notes. As you probably know, we are a podcast loosely tied together by the Popper Deutsch theory of knowledge. We believe David Deutsch’s four strands tie everything together. So we discuss science, knowledge, computation, politics, art, and especially the search for artificial general intelligence. Also, please consider connecting with Bruce on X at B Nielsen 01. Also, please consider joining the Facebook group, the mini worlds of David Deutsch, where Bruce and I first started connecting. Thank you.
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