Problems of micro-chance reductionism (contd.)

0:00 Okay, Q's going to be true or false later today. I think we all know whether it's going to be true or false. Let's suppose it had a non-trivial probability X. And this is, MD stands for micro-derived probability. So the Laplacian demon just takes a snapshot of the state of the world now and comes up with the number X. How does he do that? Well, you look at the state of the world now and you just use the quantum probabilities to calculate the probabilities of all future, possible states, and then in the right region of space-time, and then being a Laplacian demon, you look at each one of these and check whether it's a future evolution in which Q is true or not, and then you just add up the probabilities. So what is this micro-derived probability? I say it's a huge, it's the probability of of a huge disjunction, of a huge conjunctions of quantum-level events. It's a big mess. In terms of quantum particle transitions, what does proposition Q amount to? What's an incredibly huge mixed heterogeneous bunch of disjuncts, each disjunct of which is a huge conjunction of statements about quantum-level particles. so it's what I'm calling a monstrous Boolean combination of sorts of events that have direct quantum probabilities now generic macroscopic chances like probability of getting lung cancer given you're non-smoking female age 60 etc etc those kind of chances would be even bigger disjunctions of even bigger conjunctions if we don't think they're even impossible conceptually they require even more god-like powers to derive. So now think about the single case like Q. If the Laplacian demon tells you what X is, should you guide your credence by that? Well, the best system is not going to have a macro-level chance like Q. It's just an event that happens once in the history of the world, and there's no reason for it to be there in the best system. So there's not going to be a macro-micro conflict. So you might as well, I suppose, believe the Laplacian demon. But on the other hand, of course, there can't be a possible consequentialist justification for believing, setting your credence by the Laplacian demon,

2:30 because there's just one test case, and it's, I'm either going to drink more than a pint, or I'm not, and that's it. So consequentialist justification, there is none. So I think neither, when it comes to single case, items like this, neither microderived nor macrolevel chances can claim any a priori better status in terms of value and credence. The really interesting question revolves around probabilities for generic events, oft-repeated setups, and whether we should use the macrolevel chances, say that medicine gives us, or the Laplacian demons advice. So suppose we have a macro probability for lung cancer given these factors. It exists and it supervenes pattern of events. And it's non-trivially different from what the Laplace demon tells us is the micro-derived objective chance. Which do we set our credences And I'm going to discuss the argument that you should trust the macro chances and not the micro chances using as we always do a point model built out of coin clubs. So here's our microscopic theory. The obvious one. analog of quantum events, right? So the world has many, many trillions of these events in it, and those are the fundamental things, but it's still a finite number. Now, the generic macro event like a person gets lung cancer when they're aged 60, female, et cetera, what does that equate to in terms of coin flips? Well, it's going to be a huge disjunction of a huge conjunction of specified patterns of outcomes of flips. And these disjuncts are going to be extremely heterogeneous in appearance. When you just look at them at the micro level, as a pattern of heads and tails, they won't look like they have anything in common. Just like if somebody sort of write out the quantum wave function for all the people who get lung cancer, as a physical thing, in common amongst all these different things. Only the Laplacian demon can see what they have in common. Now, so we'll suppose that the coin flip probability for this huge monstrous bullion disjunction is 0.1.

5:00 And on the other hand, our toy medical doctors looking at the actual rates of lung cancer Plus, no, the probability is 0.03. And let's suppose they've looked at enough of the pattern to be sure of what they're saying. So what should our credences conform to? The macro or the micro? Well, it's obvious, isn't it? If you bought my justification of the principal principle at all, it's obvious that the macro probability is guaranteed to be close to the actual frequencies. that's by the definition or the nature of human chance as I sketched it if there is a human chance at the macro level like that it's got to be pretty close to the actual frequency but the toy micro the micro level probability that the Laplacian demon calculated doesn't have to be close to the actual frequency and indeed it's not if it's 0.1 instead of 0.03 it's not close to the actual frequency So, when you build up these huge disjunctions of conjunctions based on the micro level, well, I say the frequencies can diverge, in principle, there's no reason why they can't diverge greatly from the actual frequencies, but the macro level chance cannot. And so, based on the kind of, sorry, let me just go back. This divergence from the actual frequencies does not in any way disrupt the micro theory as a good theory for coin flips at the lowest level. The pattern of outcomes among flips of coins could still be as perfectly stochastic looking as you want, stable, 50%, etc. It can even be true that the frequencies in most n trial subsequences, or is very close to n, to 0.5 as well, for every reasonable n. The point is that this microderived probability is what you might call a gerrymandered huge Boolean construct. And it's just a mathematical fact, I think, that in a finite outcome set, it's always going to be the case that some such gerrymandered Boolean constructs

7:30 are going to have frequencies significantly different from their chances. It's guaranteed by the finite nature of the outcome space. It may be that you have a nice random-looking pattern of finite outcomes, meaning that whenever you take a nice-looking little chunk of it, 100 consecutive flips, thing that looks nicely random. But if I'm allowed to sort of pick and choose my outcomes any way I want, then I can construct some strange Boolean proposition about heads and tail outcomes, which is going to have a frequency quite different from its objective probability calculated using the micro theory. This is why it's hard to give a definition for randomness for finite outcome. If you have a finite sequence of outcomes, it is difficult to give a kind of a nice intuitive characterization of what it is for them to be random, at least along the lines that von Mises wanted to give. Okay, but our deduction of the principal principle showed why it's reasonable to set your credences at or close to the frequencies. And so the macro chances deserve to guide credence, and the microchances don't in this hypothetical case. So you should ignore those Laplace demons whispering in your ear. Now, this conclusion I'm not claiming is completely generic. I'm not claiming that no matter what the micro theory is and no matter what the macro probability is, you should always trust the macro probability. But I'm just trying to show that there can be cases, and indeed there's no reason why there shouldn't be lots of cases, where you'd do much better to guide your credence derived chances. Near the end, promise. Haven't I just given a nice reductio of the human view of chance, right? Because haven't I just said that the whole best system in this kind of world will be inconsistent? After all, we've got chances that we can derive or a Laplacian demon could derive from the micro chances, and then we've got the macro-level chances, and they say something different. Sort of a contradiction, isn't it? Yes, there's a sense in which that's true. The deductive closure of the BESS system, plus whatever the world-classian demon needs to do his or her work, will contain these micro-derived probabilities that conflict with the macro-level probabilities, and that's

10:00 kind of contradiction. Is that meant to be a joke? Yeah, that's the answer I've ever seen. But all I say is that it doesn't show that it's a bad theory. It shows that to the previous restriction we had that we shouldn't use human chance when we're looking at patterns, future outcomes big enough to undermine, like that, we have to now add a further restriction. Don't apply the human chances to monstrous Boolean constructs out of your basic chances that the pattern gives you. So, the human account of chance doesn't give you contradictory advice. Whether it is in some sense the logical closure of it is a contradictory thing or I don't care. I just don't care. But surely, nevertheless, even if that's okay, this must be wrong. So the challenge that might occur to you is that granted that some big gerrymandered disjunctions are bound to have frequencies different from their effective chances and that's guaranteed by finitude, still in any given case, like your lung cancer case, isn't it extremely unlikely to turn out to be the case? And I reply, what do you mean by unlikely? If you mean, if you're talking objective probability and what you're telling me is that, well, this kind of divergence is something that I can also ask the Laplacian demon to calculate The Laplacian demon will tell me it's low. Yes, that's right. So what? Because the point was, we were asking the question, should you guide your credences by what the Laplacian demon tells you after making these huge calculations? And the answer, the argument was meant to say no. So this objection, if it works at all, it works by begging the question and assuming that you can go from that unlikelihood as an objective probability derived from the micro level Subjectively, you should give it low credence. So, as I said, we're just begging the question against the argument that we have at hand. A second challenge. What was wrong with Sober's argument that I gave before that you should always use the micro probability because the principle of total evidence tells you to use as much evidence as you can?

12:30 Well, I have to work on this and think about it more. I haven't gone and looked up the history of the principle of total evidence to see how it's been justified. My understanding is that it's a principle about subjective probabilities. And Sober says in a footnote that he just assumes that it goes for objective probabilities as well. And that would mean that, well, take the objective probabilities and plug them into PP. and then your subjective credences then should also be based on the objective probability based on conditionalized on more information. But that's again begging the question here, because to use Sober's argument here, you have to assume that PP should be applied to the microderived chance. Why does it feel like this argument that we should trust the macro chance instead of the micro chance, the micro-derived chances, seems wrong, if it does feel wrong to you? I have an intuition diagnosis. That's that we feel there's got to be something right about using the micro probabilities because we really think that these are the probabilities that guide the unfolding of events. At least I know a lot of philosophers who like to talk that way. The quantum probabilities are really making everything happen with just the right sort of frequencies that quantum mechanics gives us. And that's why we should trust them for everything, because they do all the real work. But if you're human about chance, that's just a mistaken way of thinking about it. Probabilities don't guide the unfolding of events. The events are there. They have patterns to be discerned in them, but the chances don't explain the patterns. The chances supervene on the patterns. if that was your intuitive reason for thinking the argument is wrong then you're just not being human which is okay if you want alright so my conclusions microderived chances are in general impossible to know if they in fact even exist in a human view of chance they don't have any automatic claim to guide our expectations and in a non-human view suppose you like a propensity account of chance and you really like to think of some underlying metaphysical what-nots that guide the unfolding of things. Well, the problem is that those kind of metaphysical what-nots,

15:00 I say, and David Lewis says, they have no claim to guiding expectation ever at any level. At least not until somebody gives us an argument for why they should. the special sciences that aim to discover and use macro-objective chances need not fear the hegemony of micro-physics. That's it. Yeah, we have some kind of discussion. Hold on. You promised me that we'd go back some on visas. You promised me that we'd go back some on visas. Well, I can rephrase the question. Suppose you said that you can't think of a just, if you're a frequentist, you can't think of a justification. chances as frequencies. Virtually these long-run frequencies should guide expectations. Oh, wait, wait, wait. So we're Von Mises now? Yeah. So Von Mises you know, if you think of the classic sort of frequency theory it's probably Von Mises. So I was thinking that a Von Mises collective can have any finite initial segment you care to name and in that finite initial segment can look as arbitrarily different from the finite frequency, the limiting frequency as you like, but we're never, I mean, it's the usual. Way before we get to the long run, we're all dead. And I want something that justifies the use of chance in my lifetime. Yeah, but the, um, if you say, well, um, suppose I'm, my pre-links function, or whatever you want to call it, is, you know, it's based on my sort of fair bet, views on what a fair bet would be. and I set odds differently to what I know the long-run frequency is going to be, then I'm going to lose money. I'm guaranteed to lose money if I keep doing that. Therefore, I'm betting on unfair rate. Therefore, it doesn't reflect, unless I set my fair betting rate to the actor at long-run frequency, be a fair betting rate, because I'd be guaranteed to lose money. Under what circumstances are you guaranteed to lose money? Because, in the long run, the average gain is certain to diverge. Oh, yeah, but I just don't care about the infinite long run. No, that's not the point, though. The point is fairness. I mean, you know, assuming that's all I know at a given stage, there's nothing to stop,

17:30 and then it's a fair bet at all those stages. So what you've got is basically a sum of fair bets leads to a certain loss, which sounds as if it's contradictory. I don't know what to say over what I've said. This idea of a fair betting quotient having to be based on the infinite. It's not that it has to be based on the long run. It's just that what you get, if I believe that if I'm told that the limiting frequency is a certain set and I set my odds differently and at each stage all I know is what that long run frequency is and so somebody keeps asking me to guess over and over and over and my odds are different from that, then after enough of those bets, I will suffer a guaranteed loss. Because... Not for any finite, I think. Oh, yeah, no, yes you will. Because at some point, the finite, at some point, the frequency will diverge by a small amount you like from the limit. Basically, I think that. Okay. So I guess the answer that I would want to give, if it works at all, is to remind you that the way a human wants to think about the best system is the best system for us, right? It's meant to be user-friendly. So while we sort of care about the entire universe in an abstract sense. Really, all we care about is human history. So, if you can show me, I mean, if you can define long-run frequency in a way that you're guaranteed to get those results of loss within the space of human history, then I would agree that that can't be the right, but I don't think that you can. I mean, all right, I'll take you quite a bit. I'll just say one thing that you can go to somebody else. I mean, you seem to be, there's something about human, you know, there's this guy who can buy metaphysics and all the rest of it. But what seems to be happening here is quite the reverse. A sort of strong metaphysical view is being imposed. So, you know, you've got to restrict yourself to human history, this, that, and the other. And I'm not sure that's very reasonable. That's just convenient. In other words, I don't see why you have to take this human view in the first place.

20:00 very restrictive, and sort of, you know, sort of, I mean, sort of restricted, I suppose. Why be a human? Why be anything? I mean... Why be a human? Because that way you can offer at least some kind of argument that the principle principle makes sense. I mean, you have, you think there's an objective feature of the world, it's called the objective chances of certain kind of outcomes in certain settings. Right. Now comes along David Lewis and says, and why should my degrees of belief be anything features of reality that you call the objective chance. And now, he wants an answer to that question. He says, I think if I go Humean in the way that he wants to, in the way I want to, you can give an answer to that, actually. Probably only my way, not his way. But anyway, some sort of answer, however fragile it is, can be given to why it's rational to use it to guide expectations under uncertainty. But I think, literally, the hypothetical frequencies that bases it on on non-actual, hypothetical, infinite... Non-actual, definite, predictable loss, if you better do not. All right, it may not happen in human history. It might happen, you know, when everything's gone sort of into a sort of thermal depth. You can give a different kind of consequentialist, you can give a hypothetical consequentialist derivation, where I can give a real consequentialist reason for being. Well, on the assumption, Carl, that you're, with probability one, you're going to have a pints of lava later on. Maybe we could presume this is back to them being somebody else. I want to talk about your 43 spot, you left it a little bit more. Yeah. On this example you say, in actual history, it was only to say a thousand times, and the frequency of getting zero, zero was 25. But if we were to have with that, I want to say, any sequence of one of the outcomes that actually could, It might. It depends on how the outcomes are distributed over that thousand spins. Yeah, but surely then. Suppose you and I don't have that, and we don't know how this would be difficult. Someone else just takes a hundred of them, say, just about half. They just don't have what they want, and they've got that between you and I. Are we thinking that these are going to be randomly selected from the entire, or are there going to be 100 consecutives?

22:30 I think that's, if the pattern is pretty stochastic looking, that's true for most of them. But it might be, for example, that suppose that the way it breaks down, if we just were going to bet on the first hundred and then bet on the second hundred and so on, that's up to a thousand. It might be that most of the divergence from one over 43 happens in the last 200 spins, in which case I win the first eight bets and you win the last two and I do better. Now, that's not going to happen most of the time. I agree. I agree but I was just trying to say that... Well, I'm sure that your original I was going to do it when I was going to go to a school learning most of the time, anyway. But I wanted to consider if you take a sequence of 100, and take a net deck of 100, anyway, and so on. And all the possible combinations you can do, you're going to do that. That's right. That's right. I'd probably have to say more over time, yeah. Right, I'm just going to go back and explain to me a chance to say that the only, the only relying on movement of language points at most and are most, but you're not actually I might excuse the question, but it isn't most, more than a half. We have two different outcomes. Right now, if you have a view of this final chance, then that seems to me to be preconceived. If you have preconceived and final outcome is a chance, then it seems afterwards based on what it is called. I agree that most entails more than half. I don't think it usually means more than half because it's a little weak, actually. Most is something bigger than more than half. But I don't... Let me... I guess I'm trying to make a contrast between the kind of argument that you might wish initially that you could make to justify human chance, which would be an argument that if you set your credences

25:00 equal to the chances, then you're very likely to do well. And if I expressed it that way, then the legitimate question to ask would be, likely means probable, so you're talking about there's an objective probability that you'll do well, fine, how does that guide my credence? Why does that make me believe that, why should I then believe that you'll do well? So it ends up running in a circle. Now, I didn't get the part of your question that went from most to me relying on a tacitly probabilistic notion, I hope you can see that sort of thing. an objective chance is something that it's the actual pattern of things in the finite. Given that the inverse of finite is what actually happens, then you're saying more than half. Why is the certain set of probability? No, no, no, no. That's not true at all because there are lots of things where I can say more than half of A's are B's and it doesn't give rise to any objective probability at all. It depends on what's the pattern of co-occurrences of A's and B's, and is there a well-defined setup in which we can say that there's something that looks like a chancy pattern that grounds a conditional probability of B getting an A and so on. So most, not every sort of statement about most of these or those can be translated into objective chance. I agree, but it seems that in the case where you want to use it, like you do want to talk about it, that's exactly what you want to apply it. we want to avoid from a sorting machine exactly and sort of the point of light if it was, and if your response to this is moving to the most, and now if your response to the most that arise, that's not a chance of any more. Then you can as well start with the light if it was. No, no, no. See, I don't think that most is analytically connected to probability in any way.

27:30 That's what I meant when I said that there are lots of cases where you can say most A's or B's and it has nothing to do with an objective chance. Now, the specific case that I'm talking about, you could say, okay, but that kind of most is going to be nicely stochastically distributed and so on, so actually, given your pattern-based view of chance, it does have a corresponding probability to it. Yes, yes, but I didn't rely on that as a step in my deduction. It does then turn out that I could go ahead, after having done the justification, then I can go ahead and make the statement about, you're likely to do well. But I first had to simply express it as an ordinary language quantifier so that I wouldn't be begging the question. I think that's what I want to say. I'm thinking about Lewis and Stephen Newton and how it's related to this. Can you remind me of the paradox? So Stephen Newton is in a different point in some way. And so what's happening is following you, she's put to sleep, and then she's awoken on Monday, right? Then she's put back to sleep, and then she's asleep, and then she wakes up and looks up. In case it stales, she's awoken on Monday, she's put back to sleep, she's awoken on Tuesday again, that she would have forgotten that she was working a lot better, so I mean she had to do something, right? She went back to sleep and she slates it off and that's it. My question is when you wake up sleep in beauty and you say, what do you think that the cornflip was all about? What's the chance that it gets, right? that if I remember well Lewis says she should say a half right and I think he said it on his own saying that because I mean think about the following so I'm sorry I said a complicated case does Sleeping Beauty knows about the amnesia possibility yeah yeah she knows everything so I mean I like to think about in terms of the following analogy sorry I'm a complicated case Suppose there's a computer game, right? Clips a coin, heads or tails, right?

30:00 If it's heads, a minute later, there's a ring, and the computer game starts over. If it's tails, a minute later, there's a ring, and a minute later, there's a ring. So, two rings, right? Computer game starts over, there's a coin, and so on. Now, if you opted to prove, and you hear, hey, the ring, what do you think that came from? Heads or tails, right? when you should say, you're stales. If there's two times in three, you win, you say that, all right? And I think in the same way, Stephen Newton should say, you're stales. If there's two times in three, if you think your frequency turns, she's right, right? I'm wondering whether Lewis is excited about his objective chance, because of his principle principle, and that that's what's driving you to say a cat in the sleeping beauty case. And it seems to me that the mistake that's being made is that you've got to know more than just the objective chance of this point, you have to know how it is that the question came to you. Right. There's information that's contained in that. and that's being captured by the frequency account. So it seems to me that when the frequency account diverges from the objective chance account precisely in that sort of issue. It seems to me that the frequent, there are two different questions being asked. What is the chance that the coin, when it was flipped, landed heads and what's the chance that it landed tails? if it's a normal coin, it's going to be 50-50. A different question is, you've got a bunch of Sleeping Beauties that are presented with just being woken up, and then they have to decide whether it was heads or tails. Now, should Sleeping Beauty make her credence about tails conform to the objective chance that I just mentioned? And the answer is no. I think you're right about that. And I guess I want to say that she has inadmissible information whether it was heads or tails that doesn't consist only of knowing that it's a coin flip because she knows the structure of her own setup. She knows that she might have been woken up once before that she can't remember. Indeed, she knows that two-thirds of the time when she does this

32:30 horrible thing over and over it turns out to have been tails and so she has information which isn't admissible and so you don't apply the principal principle. Now Lewis might have thought it was admissible because it's all historical had the wrong definition of admissibility. He just got it wrong. He thought any factual proposition that applies only to the past is admissible. So he thought that Sleeping Beauty's evidence must all be admissible, so that might be why he thought the principal principle applied, and therefore she should have credence 50-50, but I think it's admissible. Yeah, sort of a question about this idea of best systems, if I understand correctly, that the right probability for, say, blood cancer if you're a smoker, might depend on, I don't know, patterns of banana, you know, deforestation of banana classes. Because, you know, but through some weird feature of the best system, there's some dependence that can lead to. That's it. So what you might get out is your probabilities for lung cancer, given that you're a smoker and if you ignored everything else, smokers and lung cancer might be different from your best system probabilities. It might, although I can't think of any reason why it would, but it's a possibility. Well, I don't know. It's just, it's a little bit of a sweep, but it's a discipline strength here. I don't know how those things, what those things yield. Let me just say, talking with Roman this morning, he was urging me to give up talk of that system because what you're, the kind of possibility you're raising is much more a possibility for David Lewis than it is for me, because he really does want it to be one big integrated system in the way, look, just to be blunt, Lewis thinks that quantum mechanics is probably the best system or something very close to it, and everything derives from that. And now, would he have the problem? I don't know, because he, of course, the patterns of events in banana

35:00 plantations are relevant for the truth of quantum mechanics. If they were vastly different, that would be different, but in another sense, they're not very relevant. There might be an ordinary way of consideration specifically. That's a fanciful example of it. Maybe that you think you're not called or something like that, but there's just a special kindness. You flip them, they don't behave like the same way as others. Anyway, so the reason why I ask that question is worries about your consequentialist argument. It seems to me that the consequentialist argument, it's clear to me that what a consequentialist argument is going to tell you is that your problem is going to track limited frequencies. So if your consequentialist argument is right, it's because there's something in what you're saying. There's something somewhere in there that you're claiming the best system is going to yield something that's going to track limiting frequency. why it should. I mean, if you really have, if you are trading off intellects and pristine strength, if you've got these sort of holistic considerations, it might be that they don't trade. And so that you're best, you know, when you're betting on repetitions of lung cancer, that you're best thinking Speaking purely in terms of betting probabilities, we should ignore what we're going to do. We should go with the limiting things. Yeah, there would have to be some really strong reason. Whenever the Humeian chances diverge seriously from frequencies, it's for one of two reasons, basically. the total number of outcomes in world history is pretty low and that the chance is determined by relevant patterns at other levels say at a higher level of generality and that's my case which you could give constrictions yeah that's what I think and then the other reason would be if considerations of simplicity just simply are strong enough to outweigh frequency and I think that happens

37:30 rarely and only to a small extent when you've got a high number of outcomes so I don't think it's a worry for me but it's a conceptual possibility the essential worry is that the justification is in the sense of the relative it's only in so far as you can attach your account to a frequency account that you're getting any justification that's right actual frequencies are not limiting that's right Some worries about reductionism, so let me try to get my pieces together. So you seem to have three options. One is reductionism is true, and the other is reductionism is not true, is you don't know. If reductionism is not true, you have nothing to worry about. There is no reason why you shouldn't do anything that the micro is described as if reduction is not true, so there is no problem. If you don't know what the reductionism is, it seems you don't have a problem either, because given the uncertainty of the situation, it's don't have a problem either. So now we're left with a case where we assume that reductionism is true. Then I'm not sure whether you're on a character versus you, because it seems that you are somehow in the case of the relationship. If reductionism is true, the only way that your objective chance can actually differ, when you look at the observable level, or the micro level is where you haven't observed enough. You only had one or two cases, they come out whatever, the frequencies are vast, the difference and what the real probabilities are, but then you're back to the real case and there you're will it divide into one of the four and three? You said, no, we should believe our principles rather than what we observed because of civic considerations and so on. So why, in the case of roulette wheel, we would have believed in the principles and not in the case of micro-critical reduction? So there seems to be a tension in the U.N. area

40:00 and I wonder what you would say. Two things to say. One is that I already sort of said I have to think about that some more. Maybe that may change my mind about that. But the other thing is I don't see why you just claimed that it's obvious that if reductionism is true, then the only way that we can get this divergence between the microderived chance and the actual frequency, which we'll take to be the macroderived probability, is if the number of cases is small. And I don't see why you said that, because the example I was trying to use was the statistics about lung cancer versus what the Laplacian demon tells us about lung cancer. And there are lots of cases of that. It's not like the let me go at all. Yeah, but the whole point of talking about the demon rather than about the real scientist that made it is that the demon tells the truth by assumptions, human adoption is true. And the microphysical theory is true as well. So we have total science. I mean, that's a take, it is the set-up of the sort of experiment. So we have the true theory at the micro level. Reductionism is true, you have someone who tells you true relationships about the level. That's what the demon is supposed to do. They cannot do this because he wants to observe what is the truth on the fundamental level. No, no, no. The truth that the demon is telling me is what the objective probability, based on the quantum level, is for lung cancer, and the demon says it's 0.03, and in the actual world, the pattern looks much more like 0.1 or whatever it is, but there's this discrepancy. Well, see, now you're coming at me with a Colin-Housen counterfactual. You're saying if human history was much, much larger than it actually is, disappear. OK, if you believe that counterfactual, that's fine. I have no problem with that. But the point is, we've got actual human history. We've got the total pattern of finite frequencies is closer to one thing, and then the Kloss-Demann's given us a different. Which one should you bet with? That's all the question. Well, you don't address the relative anymore. I'm just setting it up in a way that there seemed to be conflict with the intuition about the roulette via this case, say, okay, I don't care about the acts of freedom,

42:30 so you go by what we have. But then if you find this, the roulette should go by what we have. The case is not really parallel, because it's one thing to say you've got 800 trials of a certain type of thing, S, in human history, or a thousand. It's a quite different thing to say that you have many billions. And the kind of justification that I was trying to mount is the kind that works in the case of much more than 1,000. Much, much more than 1,000. And so, again, I may have to change my mind about this, but what I was trying to say is that what you can say about who wins in a pattern that's constituted by just 1,000 chance events is going to be different from what you can say but then there seems to be something going on if they're just a smaller number and willing to throw the fundamental principles and suddenly if the numbers grow big you're in a way of willing to throw out fundamental principles throwing out fundamental principles it's that if you go the way of throwing out you're going to win you're just going to win most of the time the counterfactuals about what happens when history is larger than it is are fine I agree with you guys about that so if a god comes up and says to me here's the real microchance of lung cancer and by the way I'm also going to create a whole bunch of worlds that are physical copies of this world and I'm going to give them a longer history and let humankind live over and over, and then we're going to make bets about the frequency of lung cancer in that, in that new collection of different worlds, well then, I'll probably set my credence to what the Lacostean demon says, because nothing better to go by. But that seems to me irrelevant for what are good credences to have in this world. And how does this feel different from that? It's just a slice of the big repetition. Sorry to joke with you.

45:00 The difference between that world and this is simply, well, A, I was conceding that this world is atypical in the frequencies of lung cancer compared to what the microphysics entails, and it's the one that we really got to be successful at. But that's all, I mean, the difference is that. There's not an underlying micro-physical difference between the worlds. Sorry, my question is going to be too late. So on one side, you say, what is a part of the point that is this postway? out there. So, I want to be objective that, yes. Let's say, you say, well, as a human, we want objective chances to be constituted with certain patterns, but not every, but just certain patterns. For instance, not bullion monsters, would they? But, what's the objective difference between these patterns and the others. But, you can say, one of them cost you to make objective chances, the other don't. But from the starting point of view, all of them look random in a sense. So, intuitively speaking, you should have the same justification for going to they're looking random to their objective but what about the patterns that look random but because they are bullying monsters or whatever they are not or how are they objectives anyway