¶1John Norton, welcome to the podcast. >> Happy to be here. >> Why don't you start by laying out the distinction, which is fairly abstract to begin with, between a formal theory of induction and a material theory of induction. I think that's probably the most important like distinction to make and then we can talk about further interesting things related to fine-tuning and how it all fits together. But I think that's that's a good place to begin.
¶2>> Sure, happy to start there. um a formal theory of induction gives a particular sort of answer to the question of is this a good inductive inference is it not a good inductive inference. The way a formal theory works is that there's some set of templates a a book of good inductive inference forms if you like and if you present it with an inductive inference it will then go and check to see whether the form of that inductive inference fits with what's in the book. uh the absolutely simplest example is induction by simple enumeration. If I say this sample of radium chloride is monoc clinic, therefore all samples of radium chloride are monocinic.
¶3You flip through the book and find uh the uh um argument for enumerative induction. Some A is a B or this A is B. Therefore, all A is a B and you say bingo, got it. Very very simple. Um clearly that's a very poor argument form.
¶4well known for having more exceptions than than cases when it works. But then we can wind through that all all the way through to um um um more sophisticated cases like um hang on, let me just I'm just going to move my screen over. Okay, so I get distracted. Um uh more sophisticated cases like the probability calculus, I can give some sort of analysis. you you look at the probabilistic uh the rules of probabilistic inference and just check that your combination of probabilities is is matching what's in the axiom system.
¶5Uh now I'd compare that with the material theory of induction that says that it's background facts that are doing the warranting to determine whether particular inductive inference is a good one. You you look to the specific context in which the inductive inference is being carried out. uh and then you check whether there's a background fact that will authorize it. Uh so in the case of Marie Curi's inductive inference on samples of radium chloride, you wouldn't look to some AB therefore all ASAB B. You would look to factual work the factual discoveries that were made in the course of the 19th century that crystalline substances fall into a small number of very definite families.
¶6Very difficult result to arrive at by the way. It took a tremendous amount of work, a lot of work in atomic theory, a lot of work in group theory, a lot of work in chemistry, even just figuring out what the elements were. All of this had to be done. And once you have that, it's a factual property of crystalline substances that they tend to fall into just a small number of different um characteristic groups. And so if you found a sample that's in one of them, you've got good reason to think that all the others will be in that unless there are some extenduating circumstances.
¶7Dorphism. Same applies to probabilities. If you want to give uh if you want to um infer probabilistically, you there's a positive obligation on you to demonstrate that the background facts in the particular domain are authorizing the use of probabilities. The simplest and clearest example of that is when we're working in quantum mechanics and we want to talk about the probability of a spin up or a spin down measurement or the probability of some particular uh transition. uh then the quantum mechanics through the bourne rule is authorizing as a matter of fundamental uh principle uh that there are pro the probabilities are applicable.
¶8I know the born rule is subject of tremendous discussion in foundations of uh quantum mechanics but let's set that aside or if you're doing something in population genetics and you want to know if this uh if if this um uh sample taken from a suspect the sample of DNA um um uh matches um uh the one at the uh taken at at the crime scene and you want to use probabilistic reasoning to justify that. What justifies it um is the the assumption that you're treating the samples as if they've been uh randomly chosen from the population. Right? In other words, each um DNA type has a equal probability of being chosen and then the arguments go through. In so far as that sampling assumption is is correct, uh then the inference works.
¶9Um if you if you don't assume that then of course you you could just be a crooked policeman cooking the books right to um um you know to so that's the difference. >> Okay. My initial impression when I heard about the material theory of induction is that it seemed to make the inductive inference itself kind of redundant where as I hear you the idea is like you you need to have material facts in the background which license this inference from essentially your sample being representative of the whole. But it's kind of like if you require antecedently to know that the sample is representative of the whole, you would already need to know the properties of the hole to then make sure they're represented properly in the sample. So I don't know.
¶10What do you think of this vague concern? >> Well, I don't accept your formulation. >> Um it's it's not a kind of a uniformity assumption at all. It's very particular facts. Uh I mean there you know I've got two books written on this and they're full of examples and none of them have that kind of uniformity uh uh assumption.
¶11Look at the two examples I just gave you the example of Marie Hury and radium chloride. It was quite specific assumptions about you know about the about the about the nature of matter. And you can investigate uh um whether matter is truly atomic or not. That's another inductive inference. In the case of um um you know the the quantum mechanical probabilities again this is just this is just a matter of um of looking at the at the particular quantum systems that you're concerned about that initially it all comes out of um um um work in in spectroscopy in the 19th century you know and the intensity of various emission lines.
¶12That's the beginning of it all. >> Yeah. Yeah. Yeah, I guess I just kind of meant like in the case of investigating the atomic properties of elements like if we already need to know that the element that we are viewing is pretty much the same as every other instance of that element, then the kind of inductive inference you're giving is just relatively weak compared to what I guess a lot of people think of induction as doing. It's like we need a background theory that tells us that this element is the same as all the unobserved ones.
¶13So then yeah, we crack open the box and we see what the element is. Then it'll tell us what the other ones are. >> This can go on for a long time, but you've given me a very vague example and it's not really easy for me to respond to a to a vague example. Um I um the difficulty is that once once you start characterizing the examples vaguely then the sort of facts that you need are vague and we start and we just wander off. Um um can we be specific?
¶14Is there a specific inference that you'd like to talk about? I'm happy to do that and we can try and figure out what the background facts are. It can be quite difficult to uh to isolate them but you know um it it it can be done. Um uh why would we think that all the all the elements are the same? Maybe maybe that's something uh we can ask.
¶15Um well, they aren't. Uh that's pretty straightforward. Uh there are isotopes. So you might start out thinking that all samples of of carbon are the same, but it turns out um no, there's carbon 12, carbon 13, and carbon 14. Uh why would you think that all the elements are the same?
¶16Well, in the course of the history of chemistry, um um the stability of the elements was uh was was slowly established. Our present argument is essentially quantum mechanical. Uh we understand that elements are distinguished by their um uh quantum mechanical structure. Um hydrogen consists of a proton with a single electron orbiting. Helium is two protons with two electrons orbiting and so on all the way up.
¶17All right. Um once you've made that identification, it then follows from quantum mechanics that all of them are going to be the same. All right. Well, you have to be a bit careful because all of them aren't the same. So what distinguishes carbon 12 from carbon 14?
¶18Well, it's going to be the atomic um uh weight of the nucleus. So there'll be certain number of protons and a certain number of and a certain number of neutrons. So the uniformity of of the um um uh of all carbon is not coming from some general idea that things are uniform in nature. Um if you ask specifically about that you get a response that looks like the one that I just gave you. We know from quantum mechanics that the this is the arrange range of possible elements that there are.
¶19There are none others that are going to be allowed by quantum mechanics. Right? And um what sort of uniformity will there be? Well, at first if you didn't recognize the existence of of um of isotopes of neutra the different numbering of neutrons in the nucleus, you wouldn't recognize that carbon comes with with different isotopes. And that's going to be the sort of answer that a scientist uh would give you, right?
¶20If they're if they're really thinking about the quantum mechanics doesn't know, okay, but now but now you see what happens next. What happens next? And I'm hope you're thinking this because it's what you should be thinking. But how do we know quantum mechanics? We just repeat the operation again, right?
¶21What is it? You know, what are the basic principles of quantum mechanics? How do we know them? There'll be further things that we know. So the net effect of all of this is going to be that what starts out as a fairly simple question.
¶22Why are we justified in thinking that um you know um all samples of carbon setting aside the isotope issue are the same? We get thrown into another branch of science. We get thrown into quantum mechanics. We start asking why should we think all matter is quantum mechanical and it just keeps going round and round and and and round like this. Um I've written two books on the material theory of induction.
¶23Uh this [clears throat] question is not addressed in the first book. It's addressed in the the second book. >> And that's the answer. That's the answer that I give. That's look that's going to trigger more questions.
¶24I don't know if you want to go there, but you know, there's a whole book you can read about them. I can't um I can't anticipate what your next thought's going to be, but I look forward to it. >> Yes. Well, I I want to shift a bit and ask about the relationship between basianism and a material theory of induction. It are these competitors because you might think and perhaps naively but you might think that like the the material postulate so to speak provides the grounding for the various probabilities that you then plug into B theorem to relate evidence and prior and posterior probability of the hypothesis.
¶25So how do the two how do the two approaches to inductive logic relate? >> Well, I've already described it. Uh first I should make very clear I am I'm not opposed to probabilistic reasoning. In fact I think probabilistic reasoning used in the right context is extremely powerful uh almost veering on appearance of being magical in its powers. I mean I I you know I like probabilistic reasoning.
¶26If you look at other work that I do I've written very extensively on questions in foundations of statistical physics. That's probabilistic all the all the way through. And I'm I'm very happy to use um you know probabilistic methods uh all all the way all the way all the way through there. Now the key thing for conformity with the material theory of induction is that if you are using probabilities for some sort of analysis, you must be able to demonstrate that they are used appropriately by tracing the probabilities back to some sort of background fact. There has to be some sort of background fact that's saying yes, this is the right thing to do.
¶27uh in the case of uh statistical physics, there are assumptions that look something like erodicity. It's a kind of a an open foundational puzzle in statistical uh physics as to exactly how we're going to get the probabilities in there. But I think that's a I think that's a soluble problem. I think it's you know I I think we've made great advances. So I'm not really worried about that.
¶28Where I part company with the basians is when it becomes a universal doctrine. So where I part company is with the attitude that whenever we see something chancy, something uncertain, some ignorance maybe and you know this goes across mental states all the way through to um you know to to to physically chancy situations where we then have the assumption that probabilities will always apply by default. And that's what gets us into trouble, right? Because once you once you assume that sometimes you'll be lucky. You'll be using probabilities in a case where if you'd look more carefully you could indeed find that the probabilities were warranted by some background fact.
¶29But there'll be other cases where they're not warranted and then you start to produce results that are simply artifacts of a misapplied logic. Right? And you start, you know, you start committing um induct inductive fallacies. Uh this tends to happen in areas where we know less right we have less control of of what's happening. Um normally the characterized as cases of you know great ignorance.
¶30We often artificially put ourselves in that position and we assume we know we know very little anticedently knowing nothing. What would you think is the case there? And then you use some sort of probabilistic reasoning and you start committing um um fallacies. So um my concern with basianism and philosophy of science is if you then look at the entire enterprise of science and try to start to fit um probabilistic reasoning to it at an extremely general level that's going to cover everything. Uh then then you start um getting into trouble.
¶31I mean I've done a lot of work on this. I I I should mention that I've worried about this idea of applying basian analysis from you know to the totality of science for a long time because it's always been troubled by you know the problem of the prior you always need to inject something external to get the probabilities going and inevitably you end up injecting something that's completely arbitrary and so I tried for the longest time to um to find an alternative calculus that didn't have that problem. Nothing I tried worked until I finally realized that there was a very good reason why nothing I tried worked. I don't know if you've ever had that experience of trying to prove something and it fails and fails and fails and then you realize I'm trying to prove a falsehood and and so oh must have been six or seven years ago I published a a negative result. The result says this.
¶32Think of any general calculus you might want to use. All right. Uh that would uh that would deal with chancy situations. All right. Uh and any such calculus if it is to have non-trivial results must inject external inductive content that's outside the calculation.
¶33In other words, something like the difficulty with the prize is inevitable in any calculus that has um minimal minimal properties. So um so the general result is that trying to think too formally and too generally about inductive inference is going to get you into trouble. Uh the material uh approach gets you around that. It says you have to always think locally and trace things back to particular facts in the background. >> So >> are these answers too long?
¶34I should ask you. >> No no not at all. Not at all. >> Okay. Okay.
¶35>> No no. So how how does this approach to inductive reasoning and probabilities make sense of claims we might otherwise want to make that we find quite reasonable? So for example suppose I say the probability that the theory of evolution is true is very high. You know I mean technically what I mean here is like the epistemic probability for me given all of the evidence I'm aware of. You could make it more general given all of the empirical evidence we have the epistemic probability of a theory of evolution being true in the actual world that that's very high.
¶36>> Yeah. >> And is that a claim? >> Can I can I reframe the question? Can I reframe the question for you? >> Well, my question about beliefs >> you what >> I don't want to talk about beliefs.
¶37Can we talk about evidence? Evidential relations. Oh, yeah. Sorry. Go and ask the question and then I'll I'll I'll make my speech.
¶38>> Yeah. >> What was I talking about beliefs? I said the epistemic probability of the theory of evolution is high. >> What is Yes. And what is epistemic probability?
¶39>> I mean you could understand that as a credencebased notion of a degree of support but I mean degree of belief but you could also understand it as degree of support which isn't like evidential probability. I'm fine with that interpretation. >> That's what I want. >> Yeah. Good.
¶40So but my question for you is do you accept that sort of probability statement? Because anyway, does that on your view does it make sense to say like the probability of the theory itself given our evidence is very high. >> Well, you're making the assertion and my question to you is what's what's authorizing your probabilities? If you can show me what's authorizing your probabilities, I'm perfectly happy. Um, can you >> Well, I mean, but you would agree that the theory of evolution is almost certainly true, right?
¶41>> Yes. >> Right. But that that sounds like a probabilistic claim. It's almost certainly true. It's probability is very high of being true.
¶42>> Um in an informal sense, yes. But you've turned it you're committing exactly the fallacy that I'm urging you not to commit. You're going from very strong evidential support. And then you're saying, "Oh, it's a case of uncertainty. So therefore, there got to be probabilities." And I'm saying, "Don't do that.
¶43Please don't do that." >> That's what I want to know. What does it mean to say that the degree of evidential support is high? If not, the posterior probability of the hypothesis is high like what what does the notion mean if not a probability? That's what I am asking. >> Um well, this is one of the cases I've looked at.
¶44Um the normal argument for um uh for evolutionary theory is an inference to the best explanation, right? Inference to the best explanation argues that evolutionary theory is the best explanation of a huge range of evidence that we have. Uh fossil evidence, diversity of species, the fact that many of the um particular properties of organisms seem artifactual. Um one of Darwin's examples was there are terrestrial geese that have web feet. Why why would why would we think that they have um uh uh web feet?
¶45Um um well if you have an evolutionary story you can understand um um uh where this comes from. Um if you have a theistic story you can't um other than to say well God willed it. So so um I spent a fair bit of time trying to reconstruct I mean this was Darwin. Darwin he doesn't talk about probabilities. There are no basing calculations in Darwin.
¶46And and I take it you you're comfortable that Darwin had good reason to believe evolutionary theory. It is possible to have an understanding of the strength of evidential support for something uh without being a probabilist right um that it has to be translated into probabilistic terms. If if I can look at you and say that's your problem, right? you now have a big burden on your hands to explain to me how on earth we're going to adapt probabilities to the sorts of arguments that um um that Darwin gave. Now, this kind of argument continues up to the to the present time.
¶47I I'll just mention I've got two chapters on on inference is the best explanation uh in the in the first book on on inductive inference. Uh one of the things that comes out of it is that uh I could find no inductively potent concept of explanation that would do the work. Um I was very puzzled by it. So I looked at a lot of historical examples of inference the best explanation. And I found that the argument form that's being used is is is rather different.
¶48Um the argument form proceeds as follows. The key thing is to first have the theory that you like and then have a foil and a very serious foil and you would show that the theory that you prefer is adequate to the phenomenon. Sometimes just entails it or or or in some sense does a good job with it versus the foil which does very badly. Right? And I just ran through how that works for for for Dwian evolution.
¶49Um um if you really really have to think of things in terms of of of probabilities, be careful because you're going to you're going to start running into all sorts of inductive fallacies. Um make sure you're using them responsibly is the advice I have for you. Um I didn't see that you were when you just said Darwin has good ev has has has strong evidential support for um evolutionary theory. Therefore, he must think it has a high probability. Well, if you just mean loosely, he thinks that yeah, very likely.
¶50Yeah, sure. Fine. That's that's just a a loose way of talking about it. But if you now have some formal theory of probability in mind, what's your outcome space? Where are your pri probabilities coming from?
¶51What justifies them? You've taken on a big burden um completely unnecessarily because I think Darwin did a perfectly good job without them. >> Okay. So, there's a lot to say there. I mean I think you can represent what Darwin is doing and what any inference to the best explanation is doing probabilistically.
¶52So the mere fact that Darwin himself wasn't thinking in terms of probabilities doesn't doesn't bother me as a basian because I think you can capture an inference to the best explanation through B theorem and in fact in my view IBE inference to the best explanation is a useful heruristic it's like reasoning in a coarse grained way uh for it's a useful heristic for more precise basian reasoning and so I often find that cashing things out in terms of inference to the best explanation keeps things more vague. than when we make it like probabistically precise because I I guess my fundamental point is that I don't even know what it means to say that the evidence highly supports this theory or this theory is very likely to be true if that's not an expression of probability. I don't even know what it means then. >> Yeah. Okay.
¶53Um two things. Yes, inductive inference has that kind of vagueness to it. I agree. Um but that's the way it is in science. What you're doing, however, is no remedy.
¶54Um, you're introducing an illusion of precision where there in fact is none there. You're taking something that has a level of vagueness that you've described, right? Um, in the case of of Marie Curi, there was always some danger, you know, that there were that there were that was um um I think dimorphism, the possibility that the that the radian fluoride might might have uh variance in other in other families. um um carbon diamond graphite is an example of that one that one that's very familiar. Um you're better off recognizing the vagueness there than pretending that you have a precise account when you don't.
¶55If you do have a precise account of Darwin's argument um in support of evolutionary theory, let's start asking the questions. What's the outcome space? Probability is not well defined unless you have an outcome space. What is your outcome space? >> You mean the space of possible theories?
¶56>> I'm asking what is the outcome space? >> I'm asking what you mean by that. I'm asking what is the >> probability measure is defined over an outcome space. If you've seen the Kaggorov axioms >> that's that's what you're the guy introducing the probability. So I'm asking you >> I know okay I'm asking you to help guide me through this.
¶57So, >> no, I'm telling you >> this isn't a gotcha moment. I'm not trying to put you in a gotcha moment and I don't want to be put in a moment. >> You are putting me No, no, no. We're having a debate here. You're defending Basianism against a critique of Basianism.
¶58So, let's just be clear on >> But in good faith, I'm not trying to embarrass you. I'm really trying to understand the theory. >> I'm genuinely trying to understand the theory. >> What do you think I'm doing? I'm trying to explain to you what why I think there's a problem.
¶59>> Okay. So what is the outcome space that you mean in this case? Like what what does it even mean is what I'm what I'm asking. >> Yes, I know. And I'm saying to you, I don't think you know.
¶60>> I don't know in general what the term even means. That's that's what I'm asking for help with. >> I'm asking you. No, no, we had a particular case. We you you you were suggesting that the correct way to understand um uh Darwin's claims of having strong evidential support for evolutionary theory is probabilistically.
¶61You introduce the term probability. And so I'm asking, you know, I'm saying if you want to use that term, you have to provide um factual background for the appropriateness of the use of the term. That's that's my claim. If you don't do that, you're going to be committing um uh you're going to be at grave risk of of committing inductive fallacies. >> Okay, good.
¶62And I'm asking you to condescend to my level, if you will, of ignorance about these terms of probability and to help me understand like you asked me a question. What is the outcome space? And I'm saying, well, hold on. What does outcome space mean here? Are we talking about the space of possible theories like evolutionary theory, intelligent design, blah blah blah, or or what exactly is is the outcome?
¶63>> But I'm asking, but you're the guy I I'm sorry, this is going to go nowhere. Um, you introduced the term probability. I don't know what you mean by it. And you're asking me to tell you what you mean by it. I can't do that.
¶64I can tell you that that to define a probability, the first step is to define a probability space. You know, the Kaggorov axioms. Sure. Right. There's a there's a space.
¶65A probability is an additive measure over the space. So you've talked about probability. What what's the space? >> It's it's the most elementary question you ask whenever probabilities are introduced. >> Okay.
¶66Good. So what I'm hearing is that the space is like the space of possible theories to begin with for one thing. So that then what I'm I'm sensing the problem is like how do you come up with a prior probability for evolutionary theory if the space is infinite uh that would create problems of normalizability like next to evolutionary theory how many other theories are there well I don't know um but I would think that the problem of the priors and all of that uh doesn't show that probability talk is incorrect here Because it seems to me what we should think in a case like that is okay, I'm not quite sure how to solve the problem of the priors. But I have no other account of what it even means to say that the evidence strongly supports some theory X and is highly likely. I don't even I don't even know what those words would mean if not cashed out in terms of a probability.
¶67And I think that people can talk all of the time about probability and know basically what they mean even when we can't specify the outcome space or make it like technically rigorous in that respect. Like we we have a concept of probability and so I'm saying okay if that doesn't apply the concept we all understand what I'm talking about. If that's not it, what is it when we say there's a relation of strong support between the evidence and the theory? >> I'm not that's a statement of your your attitudes and belief. You told me you don't understand relations of inductive support.
¶68You've told me you don't understand relations of inductive support other than through probabilities. I've told you my view. Um I don't think you have improved matters by taking something that has some looseness to it. I I agree it does that that's that's just the way relations of inductive support are in science. I I I gave you the cury example.
¶69It's like that. Um, you don't do you anybody favors by taking something that's, you know, that has some looseness to it, as this one does, and by embedding it in a formal context where it looks like you have precise results, but you don't, right? So, you kid yourself into thinking you now have some kind of precise analysis when you don't. Um, honestly, the fact that you can't, you know, nail down what the outcome space is is telling me that your use of probabilities is rather figurative. So, it's just as vague as as as anybody else.
¶70If you have can't specify, I mean, asking you to specify the probability space is just the first step. We're then going to have to go through the the prize and the likelihoods and where you're getting all of this from, you know, it's it's going to be, you know, um it's it's going to be messy. Now, if everything always worked out when someone does that, I'd be a little more tolerant. But what I see time and again, especially in matters of philosophy, is when people just launch off and start using probabilistic analysis, when they can't identify what in the background is justifying it, they start committing uh inductive fallacies left, right, and center. And they get and they get results that um that are on their face implausible if you just looked at them and said, "No, this is nonsense.
¶71is copyright. I mean examples the computer simulation argument right um somehow you argue by means I you know that that I think are dubious that um there are some ways the world could be real and many many more ways that the uh uh that um that the world could be uh a computer simulation and we have no idea which you can't you put yourself into a circumstance of of ignorance um fine And okay, you've imposed an ignorance on yourself and and that's all you have. Stop there. And and nothing bad has happened other than that you are imposing an ignorance on yourself. But then what you say is I can represent that ignorance by a roughly uniform probability measure over all of the outcomes.
¶72And since I've figured out that there are vastly more cases of computer simulation, I now have the result that very probably we are in a computer simulation. All right. Now you can see that the result is actually an artifact of a misapplied uh probability. There's no there's no basis for introducing the probability there. It gives you a sense of oh now I'm reasoning now I'm reasoning um um um precisely and cogently.
¶73But no, you've uh you have an aura of false precision to to what you're doing and it produces a spurious result. I take it I mean is it is it just me? I I find it rather astonishing that people take seriously the idea that we really are very probably in a computer simulation. I mean this is you know >> or maybe your sensibilities are different. I don't know.
¶74I I I it it kind of depends on how you think about the import of self-locating evidence and philosophers have a variety of different principles that give you different results and >> it's not clear how to think about that. I I don't think the basian as such is committed to a particular principle. I think you could integrate basianism with a variety of different proposals like the self-indication assumption, the self-sampling assumption, compartmentalized traditionalization and so on and so forth. Yeah. No, I'll disagree there.
¶75First first I want to repeat again in the right circumstance Beijing inference is very powerful and works really really well. Um the the self-sampling assumption I think that that's what it's called. Uh that's that's that's an example of a probability without any proper basis and it immediately produces spirious results. Um so this is where the the high probability of doom comes from right you know the idea is that if you apply basian analysis to the fact that the world has existed for that or that some process it doesn't have to be the world but but something has lasted t years right um therefore very probably it will it will cease cease to be now the um the key the key step in that argument is to say um We we don't know where in this we are. So we apply uniform probability over that interval from from zero to t.
¶76Why should we be here right? Well, you want the likelihood to be as big as possible and the likelihood turns out to be as big as possible if you make big t as small as possible, right? And then you use likelihood type reasoning. you know the way it works um you do a ratio form of the bay bay principle and uh to to infer that therefore um the the value of big t is is as small as possible. Now, if if your um uh warning flags aren't going up when someone tells you, all I know is that a process that something has happened for two years and I now can tell you that very probably is going to stop, right?
¶77If you aren't thinking, wait a minute, you can't get such a strong result from nothing. How does that where does that where does that come from? Right. Surely, you know, I mean, I'm just hoping that you get that reaction. Um, because then it it then becomes obvious it is an artifact of a misapplied logic.
¶78>> You have no good basis for thinking that that this thing, we don't know what it is, is is going to um >> um is going to terminate very soon. >> Yeah. But the doomsday argument is a famous reason for rejecting self-sampling, not for rejecting probabilistic reasoning per se. Because I think one of one of the main arguments that proponents of self-inducation give is that you can provide an analysis that avoids the doomsday implication, the doomsday argument. >> I haven't followed that literature.
¶79So I'll I'll defer to you there. What I have noticed is that there are is that the simple likelihood calculation that I' that I've showed actually if you ask about normalization issues, you get into huge trouble. Good. So I'm so I'm glad because I hope no one's taking this sampling assumption seriously. Um, I'll still offer it as an example of the claim that I'm making.
¶80When you do take it seriously and arrive at the result of the doomsday argument, flat out, it's immediate. You have an artifact of a misapplied logic. And I think whatever else people have said, that stands, >> right? I I mean, I think I agree with you that if your argument gives you the implication that humanity is about to die very soon out of thin air, that that's that's a problem. But what I would want to say is the proper lesson there, the more economical conclusion to draw is that our >> principle for updating on self-locating evidence is wrong rather than rejecting a probabilistic framework in and of itself.
¶81If there are alternative principles compatible with the probabilistic framework that give you the intuitive results, then the doomsday argument as such can't tell against the probabilistic framework. That would be my preferred way to frame it. >> Oh, that's interesting. Um um so the idea is that once you've adopted the probabilistic framework, you're not going to use B theorem to update. Is that what you're telling me?
¶82Because you know the doomsday argument just works with a ratio form of B theorem. You're going to use a different Is that is that the idea? >> Um no. So you can combine self-indication with uh B theorem. What self-indication allows you to do is weight worlds with more observers more heavily.
¶83And in fact, when you do the numerical calculation, the support that the more observer worlds get exactly counterbalances the fact that we are born early in world history. And so that there's no confirmation either way is the rough and ready way to do it. But but it is basic. >> Okay. All right.
¶84Okay. Um yet again, this is this is another um another thing that I noticed with with basium. It's a kind of I I call it a folk theorem. It's not really theorem because I've not proved anything. Um but it looks like this.
¶85For any result that you anticcedently would like to get out of basian analysis, you can always find an outcome space a set of prize, right? Um and a collection of likelihoods such that you'll get it. And that's exactly exactly what you've done. >> I don't I don't think I think that's exactly what you've done. I don't think that's what I've done.
¶86>> Oh, yeah. You did it. You did it. >> Okay. I don't think that's what I've done.
¶87I think this is probably why I'm not Well, it's one of the main reasons I'm not a subjective basian. Those are the people I've got real beef with who would say that any probability distribution or credence distribution um so long as it's probabilistically coherent is rationally permissible. which means that you can get any posterior probability you like just by adopting the right prior probability and that you can even extend that to I believe >> so but that's why I'm an objective basian I think there are rational constraints upon the probabilities involved that are in addition to mere um probabilistic consistency or coherence >> if I were a basian yeah if I were a basian I would absolutely want to be an objective basian uh for for all those reasons I agree Um um now we've opened another rather big question whether there are indeed objective ways of choosing a prior probability. Um I I'm suspicious that there's any general way of of doing that. Um you know one of the one of the cases that I looked at in in some detail is the infinite lottery.
¶88If you if you're going to pick a uh a natural number at random such that each has equal chances um um you know what sort of prior are you going to use there? And I I know the mathematicians have worked on this. I I looked at this and they and and my feeling is they could just never really come up with anything that had a kind of antecedent um uh credibility to it. But but maybe we're getting I don't know if you want to go down this way. I I you know what >> I mean I I wanted I wanted objective basianism to work but >> now I guess so what what is the prime complaint with it that the the appealed to constraints feel arbitrary or lacking in justification like what's the what's the beef?
¶89>> Yeah. Um um I think one of the um uh one of the major places of this is James's book um what what's it called? probability, the logic of science and something like that. Um, and he tried very hard to uh to get objective prior for things like the um oh, who's the guy um uh who has all those uh probability um problems for principles of indifference. You know, if you if you um pick a point at random in in a circle, I think there are different ways of doing it.
¶90Um Oh my god, I'm blocking on the guy's name. Yeah, but but but you you know you know who I'm talking about. Um um my vague recollection is looking at James's earlier papers. Um he thought he had an objective prior that would settle it, but then when when I compared those papers with what's in the logic of science, um I thought he'd back I thought he'd backed away. Um in in any case, I mean I mean that's a that's a a perfect example of of how of how you would do it well, right?
¶91Um let's say we want to pick a point on the surface of the earth, right? We um uh we run in into exactly these geometrical problems by by how you're going to pick the you know how how you going to pick the point. Um do you do it by area? Do you do you do it linearly? Right.
¶92Um and and the answer is that there's no answer unless right unless you can specify a process that is introducing the probability. So what might such a process be? Well, the planet Earth is a sphere orbiting the sun, right? And there are asteroids um you know around things or meteors that will crash into us, right? And you can ask what is the probability of a meteor collision with this you know at this place in the earth and you would go back and you would look at the orbital mechanics to find out you know what is the distribution of of of meteors and how might they you know how might they they strike us.
¶93I'm assuming they're in a um they're in a belt belt around us. So maybe maybe it's it's more likely that we'll get something around the equator than we will at the uh at the North Pole. But that that would be an example where if you want to give a basian analysis of of the dis, you know, of the likelihood of meteor strikes, you would get a prior by looking at orbital mechanics. And that's all I'm arguing. You just you just got to do that.
¶94Um, and you know, so, so I I I I I know I know you're thinking this guy hates basianism and would never use it, but I've just given you an example where I think it it would be the best way to analyze analyze the problem. What it worries me is when you try and use it when you can't specify what you know what the pertinent background facts are that will give you the outcome space that will let you um um uh that you will let let you do the calculations. Yeah, I think at a at the highest level my worry about that analysis is that it seems to me like I what my worry would be is that if you can't have any a priori probabilities, so a justified probability distribution before the empirical evidence, then you can't have any a posteriori probability distributions. It's very hard for me to see how you get from one to the other, how you get from a place of indeterminacy because we don't have the empirical evidence to any sort of justified >> uh posterior probability conclusions or conclusions about what physical system and objective chance process is even operating in the first place. Presumably, we have to get there through a process of reasoning.
¶95And you can't then appeal to those objective chances in order to justify those probabilities. And so my worry is if we begin with indeterminacy where there's no empirical evidence, we have no probabilities, we could never get out of that. So I think you call this the bootstrapping worry or this might be related, but I wonder if you could comment explicitly on that. >> Sure. I've worried exactly about that as well.
¶96And uh I I really wanted to find a calc I've mentioned this before. I really wanted to find a calculus uh where um these problems would go away. And uh what I discovered was that they're insoluble. I mean, you know, it's a paper in BJPS. It's one of the chapters in uh one of the chapters in the book.
¶97If you want to have the sort of calculus that people like, in other words, something like the probability calculus or or any other calculus that satisfies, you know, those sorts of formal urges that uh that that we have. Um none of them are complete. they cannot be complete in the sense that they evade the need for some sort of e external inductive input. So if you're saying I'm really worried um you know um um you know that I'm always going to have to end up putting in something from the outside from outside the calculus from outside the the analysis that that's been given formal formally to give me something like a prior probability. Your worry is very well placed because it's demonstrabably provable that this is um an inescapable problem.
¶98It will always happen. Sorry about that. I was very disappointed by the way to discover this. I tried, you know, I I tried to get out of it and and and years and years of failure and I realized, oh gosh, I'm trying to prove it falsehood. Well, but in that moment, did that give you any pause or sense that maybe the right conclusion to draw then is that you can have a priori probabilities?
¶99>> No. >> Okay. Do you want to ask why not? I mean, I thought that's a >> sure follow. [laughter] Yeah.
¶100Um it's because by the time I had that final result I was als I was I'd also well developed the material theory of induction and I realized oh it fits perfectly with the material theory of induction. Remember the key thing is that all inducted inferences are local. Um whenever we start talking about huge generalities we get into trouble. Whereas um if you're doing a particular calcul calc calculation using some sort of calculus in a particular domain, it doesn't bother me at all that you'll go and look at very particular facts in the background that are outside of that calculation to direct you to what the uh to what the prize would be in the in the case of media strikes on the earth. Um you know then then the sorts of facts will will be facts about the motion of the earth, facts about the distribution of meteors.
¶101Um I I should mention by the way that I just thought up this example, you know, um you know, with I've not researched this, so I don't really know how it's going to go, but it it feels plausible that something will will work out in in in that way. correspondingly just you know um uh to go back to your evolution example um there I think the huge difficulty is and this is why I was pressing you on it the huge difficulty is we really don't know what the outcome space of alternative theories would be right um uh for Darwin it was a very very narrow space for Darwin it was evolutionary theory or um or special creation um uh this was a an artificial constraint, right? Because you know you know um um something like a Lamachian evolution, you know um um would be a natural thing that you might want to put in there as well, right? Um but he didn't. Uh but even that but there's a there's a sense that uh we now have three possibilities.
¶102That is that it right? um um you know the the probabilistic analysis at this point feels rather uh rather contrived to me. I'm I'm much more comfortable if we're doing a probabilistic analysis where we have you know a large body of masses bouncing around doing things because then we have some physics that's going to help us narrow down what the prize might be. >> Yeah. I mean, I think that when it and we might just be going back to a previous point and going in circles, but I think my issue with the language of highly likely and strong support versus weak support is that this seems probabilistic in so many words.
¶103This seems like vague probabilistic terms. And if we then deny no this isn't probabilistic. It's not just that what remains is vague and but we have a s it's that I don't see any content that's left. So whatever problems there are for a probabilistic analysis at least I know what's being said. Whereas if these terms aren't probabilistic at all.
¶104I have no sense of what they mean. It's not just that they're vague. It's that highly likely without being a probability. What is that? I I don't see there's a need for me to say anything.
¶105You've just made a profound confession of your ignorance. >> Do you have an answer to the question of what it means or is it just intuitive bedrock or or >> I've written two books on it. >> Okay. >> Um the meaning is going to vary from case to case and we can talk about each individual case if you like. uh in the case of Marie Kuri um the the sense is that it's very likely that a particular um u sample of radium chloride will fall within this particular monocinic um [clears throat] um family of crystalline substances.
¶106there's a chance although it seems rather unlikely that um these samples will fall in other cases and you know this is the way chemists uh do things and it looks like this across the board. I'm grinding to you that there's a looseness to it. There's a and there's a vagueness and there's a vagueness to it, but that's the reality of the way inductive inference is and to try and force it to be something more precise than what the scientists can give us is just going to get us into trouble. Okay, let me pivot here to a question about how this relates to the use of probabilities in science because I think you would agree having read your cosmic confusions paper that scientists sometimes make appeals to probability or improbability that you think are >> absolutely >> so one is genuinely a clarification. >> Wait, wait a minute.
¶107Wait a minute. You added a phrase there. I agree with you. scientists often make uh appeals to probability and then you said I think they're illicit. Did you have an example?
¶108>> Uh inferences in a multiverse >> so any sort of scientific publication about anthropic reasoning. >> Yeah. Good. Yeah, I I'll agree with that and I'm happy to defend that. Um um in the >> Well, do you want me to defend it or not?
¶109I don't mind. You can >> well but my specific question was and this is to help understand the material theory like on the material theory of induction are we licensed to say for example that like the initial low entropy condition of the universe is like in some sense improbable or is this like could could that be currently grounded in material facts and or no and therefore you would say no strictly speaking there's no probability claim we can make about initial low entropy. Yeah, I think that's I think um I think the probability claim is is difficult to make in this case, right? Um uh if you simply take a generic cosmology, right? Um and it is the fact that the initial state or the early states of the universe, there was no initial state, right?
¶110It was singular, right? But the but you know that the early state of the of the universe was was very low entropy. Um that's a fact that's a fact of observation and I'm I'm happy to to stop there. Right. Um now if if you want to be responsible about it and say oh it's extremely improbable uh that that it would be that right um then it is incumbent on you to present the facts that would authorize um that assignment of probability.
¶111Notice we we don't need that assignment of probability to do cosmology. It's an you know it's a you know if if you accept you know that the universe is is expanding and that we can wind back the expansion using um using um the Freriedman the maker of Robertson Walker stuff the the Einstein equation you know it's just a fact and and cosmology is doing perfectly fine okay if you want to argue that that is um uh improbable then you have to go through the exercise that I just described and the exercise that I just described is to figure out what is the outcome space and how are we going to have probability measures over that outcome space how's the whole thing going to work now the scientists are doing that right this is the multiverse assumption right there are various um um proposals for a multiverse such that our universe would be one among among very many right um okay good we we now have some sort of an outcome space now the next thing we need to get uh is a probability Where does the probability come from? Well, I've written about this because there's one rather striking example here. Uh in the case of eternal inflation where you have this um massively continuously expanding um um um huge multiverse uh in which um um you know the infotton field is doing all the work and expanding things very rapidly. What happens is that we are spinning off little pocket universes that would be like ours in in all sorts of you know different ways and our universe would be one of those.
¶112Okay, that's we now have we now have the outcome space. Next we have to get the probability. Where does the probability come from? Well, the cosmologists who have looked at this have found uh that there seems to be no unique way to assign a probability uh to this. There are multiple different ways that you would assign probabilities to the different universes that are being spawned off.
¶113And it's known as the measure problem. It's been there for, you know, I first heard about the measure problem over maybe 25 years ago. And I I don't think it's been solved because the assumptions that they're making about the dynamics here about the physics of the um of this um it's called eternal inflation are such as to give uh no unique specification of a probability measure but to allow multiple different specifications. Now I got interested in this because one of the things that um that I want to demonstrate is this uh in a precise environment it is in fact possible to have alternative calculi. You know when I say look for the background facts that justify probability well you could also have background facts that will justify something calculus that is highly nonprobabilistic.
¶114And um in order to to illustrate that what I'd already done uh um was to um um look at the case of the infinite lottery. And if you make the assumption that we have a you know a device that somehow picks a natural number such that each individual natural number has the same chance of being chosen. Right? It turns out that that background fact authorizes uh a weird kind of highly non-additive logic. it it can be very welldeveloped.
¶115I've got a whole chapter developing its formal principles and the consequences and the results. And I thought it was simply just an exercise in arbitrary um theorizing because you know I I know there are people I might even be talking to one who simply likes to take vague things, you know, and slap a calculus on them. So I thought here I'll I'll give you a calculus that is well >> justified. Not fair, John. >> No.
¶116Okay. Cheap shot. I thought [laughter] >> Yeah. It was I couldn't resist. I'm sorry.
¶117>> Um I I I'll give you a calculus that looks that that is radically different from the probability calculus. Then later on I was reading some of the literature on um on eternal inflation and the measure problem and they were using exactly the arguments that I was using for this infinite lottery case but they were using them as a way to say you know we can't have a probability measure here. They needed just to say oh wait a minute these facts can tell us which which calculus we can have and it's this one. So this is a published paper I think it's called um uh it's got internal inflation in the title so you can read it. >> Yeah if you want.
¶118It's in it's in one of the chapters of the of the book as well. >> Yeah. So what about the argument often given sometimes given for inflationary theory over the standard model without inflation an inflationary epoch where like roughly a way you could state it is that if we have a universe with an inflationary epoch our the flatness spatial flatness of our universe is rendered more likely or highly likely compared to in the standard model without inflation our observed flatness is in a sense highly highly improbable. And so on its face, you can give a basian interpretation of how that works. Do you think there's a a non-probabilistic interpretation of it or would you say no?
¶119There's really no sense in which observed flatness is improbable under the standard model. >> I can just talk about those arguments. There are a number of different arguments for inflationary cosmology. Uh the flatness argument is one. The uniformity homogeneity argument is is is another.
¶120without inflation um um matter didn't have enough time to interact with blah blah blah blah blah. Um here there's um for those two arguments um I don't I don't need to give you my view because there are a number of you know eminent um relativists I'm thinking of Bob Wald um and um I can't remember his collaborator's name now um they've argued uh quite correctly that that that doesn't work that doesn't work because you still need a further prior behind it and that prior is itself arbitrary so why so why bother. I'm I'm willing to say that there's a an emerging consensus in cosmology that the flatness argument and the homogeneity argument uh don't work. What does work very nicely is the structure formation argument. That's that's the one that I um uh that I that I think is is is doing well.
¶121And uh and the idea is that if there was an inflationary epoch um uh then we can tell a good story about uh how enough matter accreted so as to form galaxies and things. Um I didn't use the word probability there anyway. >> Okay. >> You can add it if you want but I did I didn't feel the need to just to state what I think is a good result. >> Well, as you may or may not know, the name of this podcast is the uncertainty podcast.
¶122So [laughter] often I end by >> you can use that. >> Yes. The question I like to end on is see if I can get it so I don't end on a preposition. Of which there we go. Of which of your philosophical commitments, your current philosophical views are you most uncertain?
¶123Tough question. It's not the sort of thing I want to answer off off the cuff. Um um when I'm writing a paper, I am uncertain about it all the time, right? Um I don't know if you've had that experience when you're when you're writing a paper and >> and you get about halfway through and then you have this, oh whoa, holy smoly, maybe it's wrong. Uh, and so yeah, I don't I don't I I can't answer it other than to say I have reservations and uncertainty scattered uh all the way through.
¶124Oh. Oh, yeah. I I'll give you one that's been that's been bothering me lately. Yeah, you'll get a you you'll get a sense of this. I've just written two more two new books now on empiricism.
¶125And one of the things that I um um that I found striking in writing on empiricism was that I could not find arguments for empiricism. I'm an empiricist. I I think we learn about the world. The only way we can learn about the world is uh is is uh is is through experience, right? Uh and I think um uh there's an urgent need for empiricists to argue for that.
¶126I've had to work, you know, from scratch to come up with arguments. And I think um I've got strong arguments for the um uh for the sufficiency of experience. Uh the harder one to make is the necessity of experience, right? And so that's that's one that at the moment is worrying me. I found that um I I I I don't think someone arguing positively that there are other ways um uh has much prospect.
¶127But I want to argue something a little stronger. >> Yeah. >> Uh that there can be no other ways. >> And I found that very difficult very difficult to uh uh to argue for. Um, if you go to the I've got a Metbook manuscript.
¶128Um, if you go and look at that, you'll see >> uh you'll see me struggling with it. I I I I do my best. >> Yeah. >> But um but you know, but that that is the that is the answer of the moment because it's the thing that I was most recently thinking about. >> Yeah, I agree with you about paper writing.
¶129I'm shot through with near total uncertainty until the very end when it feels like the pieces click together. That's when I get my thesis. Not always, but but more often than not. >> Yes, I agree. That's my experience as well.
¶130Um, this is a key thing to do philosophy. You have to write. >> Sitting and thinking about it and forming in in your head this idea. Oh, now I've got it. You sit down to write it out and boy, >> it all falls apart pretty fast.
¶131Yeah. >> Yeah. >> I agree. >> I agree. Well, uh, before we go, I want to thank Moy.
¶132He's a longtime viewer of this channel for pointing me to your work a couple years back and recommending I bring you on the channel. Uh so shout out to him. Um well, thank you for coming on, John Norton. I had no idea that uh debates about the philosophy of probability could be this heated, but I think it was fun. So I appreciate you coming on.
¶133>> I I I should mention I was completely unprepared to talk about this because I thought we're going to talk about fine-tuning arguments and we never did. Well, because I responded to the energy and I thought, okay, let's dive in here because these for me were like the ground setting questions to understand what's going on and that's how I usually do it. But then I just found a lot of fertile stuff right here. So, >> okay, >> that's organic conversation for you. >> Um, can I just mention one other thing?
¶134>> Yeah. Yeah. Yeah. >> This is the first interview that I've given on the material theory of induction uh after yesterday. I don't know if you know this, but uh the LSC announced that those two books have won the Lancash Award.
¶135So >> amazing. Congratulations. >> You got there. You got there first. >> I got there first.
¶136I got there first and I appreciate it. I think the YouTube algorithm will reward me for this. So, thank you for taking the time. >> Okay. See you.
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