Problems of micro-chance reductionism

0:00 Thanks, Stephan. It's really nice to be back here. I'm not sure whether I'll do this talk sitting down or standing up. Sitting down is easier for the computer. pace back and forth when I talk, so we'll see what happens. I've left this up here long enough that you might have read it. If not, it doesn't matter, because I should get there in the end. And I also don't care very much whether the thesis is true or not. I've got this rather large new paper about a human view of objective chances, and I think it has this interesting consequence about reductionism. But if it's not correct, in the end, I still think the human view of chance stands on its end perfectly fine. So the background to this talk then is this thing that I've been working on for a number of years, which is to answer my metaphysical questions about the nature of objective probabilities or objective chances that I think are out there in the world and which philosophers sometimes talk about that certainly scientists use all the time in lots of different contexts. And I don't think we have yet a very good philosophical story of theory of objective chance that does very well at all. And I can appeal to Colin Housen's nice BJPS paper for a review of all these different classical positions, which are, I think, all of them very problematic. telling you about that. I got interested in objective chance by hearing David Lewis give a talk in 1993 in California, laying out his view about what objective probabilities really are and I thought it was really fascinating and deeply problematic in a lot of ways and that set me off working on something that was quite related to Lewis's ideas but different in many ways of detail. One thing I think that Lewis got exactly right is his playing, which he started making in the 1980s, that what he calls the Principal Principle is the

2:30 core or the key of everything we can say we think we know about objective probabilities. In other words, I think it's sort of the essence of the whole notion of objective chance. So here's a very simple version of the Principal Principle. Of course, he calls it on the most important principle that you might want to talk about related to change. And what this says is basically CR is a rational person's credence function, subjective probabilities, and A is any old proposition that's in the domain of objective probability function, So written P-R here. And X is the statement that tells you that the objective chance or objective probability of A obtaining is little x, and E is just your other background knowledge or your other background information. And so what the principal principle says is something very, very simple and intuitive. It says, well, if you don't have any idea of whether A is true or is going to be true or not, but you do happen to know what A's objective probability is, then you should set your degree of belief exactly equal to that objective probability. It's so obvious that it doesn't get articulated very often. One simply moves very quickly from talking about what the objective priorities are to what one should do without even bothering to make this sort of connection. I should say the word admissible there is kind of crucial. It's important that your background knowledge or the rest of the things that you know over and above X, shouldn't include anything that sort of tells you whether A is true or not. So, for example, if A is a proposition about the next coin flip I do will land heads, so that's for A, and you have a crystal ball, and you happen to have looked in the crystal ball earlier, foreseen the future, and you know that it's going to land heads, well, if that's part of your E, that's part of your background knowledge, that's inadmissible stuff, because you'd be crazy to set your subjective degree of belief in heads equal to 50% if you actually know what the outcome is going to be. But usually the rest of our background knowledge

5:00 is perfectly admissible and doesn't tell us anything about what's going to happen with chance events. Okay. Now, Lewis raised the principle to the essence of what objective chance is all about. It's about guiding our behavior and our expectations in the face of ignorance. And he said, well, you know, if we're going to have a good philosophical account of what objective chances are, objective probabilities are, the nature of that account, the nature of that philosophical analysis, ought to show us that PP is a rational principle. And, well, for example, just to take a different view of objective chance that's kind of standard we'll have a hypothetical frequency that, in sort of the first naive approximation, says, well, the objective probability of A is just the long-run limiting frequency of A in all the cases where it's run, where that goes to infinity. Lewis would say, and I would agree, that hyperplacal frequentism fails this test spectacularly. It doesn't. The fact that if you did something an infinite number of times, such and such would be the ultimate limiting frequency. What does that tell you about what your credences should be about in the next clip of this point? I think it's called ease of grammar. After I've said more about my humanism, you might say, you're just saying, Um, and I think that, um, so does another popular account among philosophers of objective problematies, which is to talk about them as physical propensities or tendencies. But in any case, here's a nice quote from Lewis, who has become widely known. In his 94 presentation of his views, he says, Be my best, posit all the primitive, unhuman whatnots you like, but play fair in naming these things. Don't call any alleged feature of reality chance unless you've already shown that you have something, knowledge of which could constrain rational credence, in the way that Keith B. tells you. I think I see dimly but well enough how knowledge of frequencies and symmetries and best systems could constrain rational credence. I don't begin to see, for for instance, how knowledge that two universals stand in a certain special relation, n star,

7:30 would constrain rational credence about the future co-instantiation of those universals. So here he's poking fun at David Armstrong, whose view of laws says that they're just primitive metaphysical relations between universals. If you extend that Armstrongian view of laws to chance, well then you have what David Lewis is making fun of him. And here, knowledge of symmetry, frequency, and best systems, that's the kind of stuff that David Lewis decided we should build an account of objective chance upon, and so. If you accept Lewis's challenge that a good view of objective probability ought to be able to justify PP, then you're going to be, I think, attracted to his line of thinking and think that a Humean approach is the right way to start thinking about it. chances are not some sort of mysterious metaphysical force, capacity or primitive what not out there. What chances are, are nothing over and above facts about what actually happens. That's a crude statement of what Lewis calls Humean supervenience. And the obvious way of being a Humean about chance might be to just say, Well, I think the chances are the actual frequencies of what happens in the world, finite actual frequencies, and that's all the chances are. But since that actual or finite frequentism has some well-known problems, we'll scratch that and look at a more sophisticated approach to being a human about objective chance. So what are the basics of this approach? Well, as I said, the core idea is that objective probabilities are to be understood as, basically, patterns in the events out there in the world. I should say, events overall of history and all of space in theory, in principle, although for our epistemic purposes, the patterns of events here on Earth are allowed to be denied for most purposes. But these patterns can can be of many different types and at a variety of ontological levels, from perhaps microscopic particle interactions all the way up to as high an ontological level as you like. And of course the standard human definition of chance is just well stable finite frequencies. That's one kind of pattern that you can discern, but there's other parts to the story. There's

10:00 The best system accounted chance is one that gives you a consistent collection of chance functions linked to a variety of well-defined chance setups that offers a kind of maximal combination of simplicity and script. That's what the word best does in the phrase best system. Simplicity, well, we could have a chance for every different event that happens in the world and minimize simplicity, and that would be completely useless for us. We could never find out about it, or we would have to assign everything with the trivial probability zero or one. Instead, it's better in terms of simplicity to have a number of well-defined but exportable objective chances that apply to a bunch of different situations, but not And strength, well, we want sort of as many things to fall into the scope of objective chance as can be fit there, consistent with the simplicity and the patterns really looking like chance patterns. Now, Lewis did this best system approach together with a best systems analysis of laws of nature. So he has a joint account of laws of nature together with objective probabilities. And I don't go that route. I say, well, we could go that route, or we don't have to. We can just think about best systems of chance on their own. So what differentiates a best system account from just simple finite frequentism? Well, for example, you're going to smooth out and fill in the sort of partial or skeletal patterns that are out there in simple frequency patterns of events. Examples. Well, there's actually a lot of data out there in the events of the world about how dice land when thrown. But suppose that in actual history of the universe, only one die was ever constructed, and it was only rolled a few times. Then the frequencies of how that die landed wouldn't be enough of a pattern to base things on. On the other hand, stepping back a bit, there's this higher level pattern that we can discern. When you have a regular N-sided polyhedron, and it's rolled a bunch of times, the frequencies tend to come out equal for all the sides.

12:30 Okay? Understand? And that's a higher-level pattern, which then we can say is enough to let us fill in and get us a probability for the rolls of a die, even though the actual frequencies out there are not sufficient to give that kind of pattern. Okay, another feature of the basic view that I talk about in my paper, something I call the stochasticity postulate. And Roman pointed out to me this morning that probably I should change its name because it's not so much a postulate, but something which I'm claiming is just a fact about the events that we see out there in the actual mosaic of Humean events. and the stochasticity postulate says it's a fact about actual events in our world that at many different levels of scale but especially, this is true at the micro scale events just sort of look stochastic or random with certain stable distributions over time and physicists and doctors and all sorts of scientists rely on this sort of stability in many physics experiments you design them with the assumption can count on a very stable pattern of interference from noise outside your experimental situation. And that's an example of what I mean by the stochasticity posture. You count on a lot of stuff out there in the messy world looking random and stable. Okay, another thing I want to briefly comment on is something I want to call stochastic nomological machines. Those of you who've read Nancy Cartwright's most recent book know. She talks about nomological machines, a concept that it's fair to say has not caught on like wildfire amongst the philosophical community. Nancy's view is a nomological machine is what explains the extent to which it's proper to talk about there being laws of nature. She thinks it's a very limited extent, but she says when we do have laws that work, it's because we have nomological machines. And that's, in her terms, a fixed with stable enough capacities that in the right sort of stable enough environment will, with repeated operation, give rise to the kind of regular behavior that we represent in our scientific laws. So notice what she's giving an explanation for why there is the appearance of law-likeness out there. And she does it in terms of these things which I think are metaphysical whatnots, which are causal capacities.

15:00 My idea is quite different. my interest is not in undercutting the idea of laws, but just in recognizing that some chances, objective chances, are not primitive but rather explicable and often you in fact have to invoke laws of nature to get the explanation going so here's my definition of a stochastic nomological machine some stable macroscopic chances that supervene on the overall pattern can be regularity is guaranteed by the structure of the assumed chance set up, and usually with the help of the stochasticity postulate. And those should be called stochastic nominal machines. Examples that do use the stochasticity postulate would be almost every kind of well-made classical gambling device. Point flips, Kraft stables, and so on. But I think also I want to say that simple quantum systems, like a radium atom that has a set probability for decaying in a given half-life, is another example of a stochastic nomological machine, although not one that's explicable on the basis of an underlying structure. Here's something I've mined from a recent paper by Elliot Sober that illustrates the idea of a stochastic nomological machine pretty well. This is a model made by Percy Diaconis of a coin flip. And the initial conditions, on one axis we have the rate of spin of the coin, along the other it's vertical velocity, I think. And this is purely a very simplistic Newtonian model of what happens when a coin is flipped with a certain initial spin and a certain initial upward velocity. and you assume it lands without bouncing, and then this model tells you whether it lands heads or tails. I forget whether black is heads and white tails or what, but the idea is simple enough to see. This is a good stochastic nomological machine because if you put in a nice random-looking bunch of initial conditions, in other words, if you have a bunch of random points just sort of tossed onto the upper right-hand corner of this model. Well, the model will tell you about whether the point falls in the white area or the black area, whether it's going to land heads or tails, but the overall

17:30 frequency is going to be about 50% each. And, you know, if these things are done in series, it's going to be a nice random-looking distribution, just like we think points will talk. So let me summarize what I call a Humean objective chance. Chances are constituted by the existence of patterns in the Humean mosaic of events, which is just everything that happens. And these patterns are such as to make the adoption of credences identical to the chances, rational in the absence of better information if one is obliged to make guesses or bets concerning the outcomes and future chance setups. I should point out that this, what I say here, that these patterns are such as to make setting your credences equal to the chance rational is something I'll try to justify later if that's not yet been shown. One aspect of the mosaic of events in our world is what I've called the sarcasticity postulate, All genuine objective chances have to be derivable from that. If you have the right sort of stability and random enough lookingness of the outcome distribution, overall history, that's enough right there to constitute an objective chance. Moreover, there are certain kinds of setups that have few actual instances in the world's history, but they have the right sort of similarities to other chance setups that do have a number of cases in world history, and that may be enough to ground an objective chance for them based on symmetries, similar dynamics, and so on. And I say in the end here that the full set of all the objective chances that there are in our world supervening on the pattern of human events is you might call a sort of best system, and Roman was saying I should stop saying that as well this morning. There's nothing terribly systematic about it. I might or might not give that up. Certainly, I'm not interested in all these probabilities fitting together derived from one underlying theory. Lewis really is interested in that. I don't care about that. I think that there are two extremes one could have, that everything falls under the

20:00 domain of chance functions. That's wrong. Not everything is a chance event. And the other is that there is no chance out in the world at all, like Definetti said. That's far too extreme. I think the right account is somewhere in the middle. And it all comes down to the patterns that you can discern among the outcomes of real events. And what unifies all chances is exactly their ability to play the role of guiding our degrees of belief, giving us at least good advice as codified by the principal principle. So that's two questions that I'm going to look at today which correspond to the last two sections of the paper. How can the principal principle be justified if this is the right story about objective chance? And answering that question to the extent that I get it right at all is going to lead me to say that there are indeed intrinsic limitations on how widely you can use the notion of objective probabilities. It's got its sort of restricted domain built in. And in particular, I'll say that you can't apply the notion of objective chance to set your credence when you're looking at huge chunks of the overall pattern of events on which the chances supervene. This is something which I argued already in 1997, going against pretty much the rest of the whole community interested in these objects, in these kind of chances. And today, what I think is a novel consequence that's come to my awareness recently, is that it's not justified either to take very microscopic-level chances, like, say, quantum mechanical chances, and let them bubble up somehow to determine all the macroscopic chances that there are. Okay, so the first task I want to do is try to discharge the Lewisian obligation, to show that if you have this view of objective chance, then you really can justify the principal principle. So Lewis didn't do any of that work, except he wrote in his paper that he thought he saw dimly but well enough how knowledge of frequencies and symmetries to constrain rational credence. And others have been giving him the raspberry lately, saying, oh, yeah? I don't think you saw anything, Lewis. So Michael Strebens says that there can't be any argument

22:30 for justifying PP. He has a nice paper where he tries to go through all the options and exclude every one of them. Ned Hall from MIT said, no, that's not right. Basically, everybody can justify PP except the Humeans. So I think they're both wrong, but I won't go into their arguments. Instead, I'll just try to do it. And what kind of rationalization or deduction of the PP are we looking at? We're looking at what you might call a consequentialist deduction, one that says, well, if you do guide your credences to the objective chances using PP, you're more successful than if you do something else. Okay. so it helps to get the argument going we can just think of human chances basically as being like actual frequencies with the following additions or amendments first the distribution of outcomes has to look chancy has to look stochastic if you have a very naive definition actual frequentism if this is the actual pattern of coin flip outcomes in the whole history of the world just keep going like that you would say the chance is 50-50 because there's half heads and half tails but of course no one would say that there's an objective chance about this if that pattern of strict alternation were the real story about coin flips now it has to look still kind of stick in the right way. As I said, the system aspect of it means that you can sort of extend patterns from a higher level down to give you chances at a lower level even when the frequencies are not sufficient to do it by themselves. This is important and probably another thing that the rest of the community wouldn't like. It seems clear to me, though, that you have to anchor the notion of chance to our epistemic needs. When we talk about the best system combining simplicity and strength, that notion of simplicity and the notion of strength is really deeply linked with our epistemic needs and limitations. I don't think that's a defect, nor do I think it particularly makes these

25:00 non-objective chances. It just makes them objective features of the world that are good for us, and that's feature of them. And finally, insist that the proper domain of application of chances is intrinsically limited for reasons we'll briefly look at. So the principal principle says, set your degrees of belief equal to the chances if you have no better information. And what do we need to show? That taking this advice is better than setting your credences to some other level. that have credences of some level or other. So why is setting your credences equal to the chances better than any other non-trivially different credence to have? I think we can suppose, without loss of generality, that we're just going to make the argument for a simple time-independent chance setup. S is the setup, and we're looking at the probability of the outcome, A. Like, just have in mind the coin flip, All right, so the first case to think about is when there's lots of occurrences of the S set up throughout history, and we have to bet on the proportion of A outcomes in a bunch of medium-short runs of N files of S. Say, for example, we're going to bet on the frequencies in hundreds of coin flips, groups of hundreds. So I say that the assumptions on the previous slide, a through d entail that first of all the frequency of a outcomes overall of history is near to x near to the objective chance because there's a lot of these things in the best system if you've got a lot of instances of the setup the frequencies can never get that far away from the objective chances because if they were different you would simply the best system would be to move the objective chance and set it to something closer to the frequency. So the frequencies have to be overall near to the objective chance. And because I said that the overall distribution can't be like that, it has to be stochastic looking, well, in every sort of medium, large sized chunk of S trials that you look at, the frequency is also going to be near to x. At least in most of these sets of n consecutive troughs. There will be some deviations. The

27:30 smaller n is, the more deviations you'll get. That's what a stochastic pattern looks like. But also, the number of sets of n in which the frequency is greater than x will be about the same as the number of sets in which it's less than x. If you're just grabbing a bunch of sets of N outcomes randomly, so to speak, then this is going to be the case. So, therefore, at most places and times in world history, if you have to guess at the next N outcomes of an S set up, then if N is reasonably large but still short-run, compared to the entire set, the proportion of A outcomes in those N trials will be close to X most of the time. Did I say anything? It should be most of the time. And sometimes it'll be a bit greater than x, sometimes less. And there should be no discernible pattern to the distribution of when you get more than x and when you get fewer than x as a ratio. So the average error of the deviations of the proportion of a's in each set of n trials from x will almost always be close to 0. Now, you may be irritated and fidgety now, that I'm begging the question. But I think I'm not in any way because what I've used are ordinary language quantifiers most always. Almost always. Things like that. Instead, I haven't said anything about how you're likely to be successful. I haven't said anything probabilistic. I haven't said that you're guaranteed to win with certainty in the limit as n goes to infinity or as the number of trials goes to infinity. I don't care about that. All I care about is that in a The finite space of actual coin flips, if you guide your expectations by the human frequencies, most of the time you'll be successful. That can't be quantified any better than that. So we've shown, if you have to guess the proportion of A outcomes in a set of any S-trials, X is not a bad guess to make. But is there a better one? Now, notice that the wrong question to ask is this. Could you have even better accredences about the A frequency in the very next set of N trials that you're going to have to bet on? Because the answer to that is obviously yes.

30:00 If God whispered into your ear what the actual frequency of A was going to be in that very next N trials, you'd do better by guessing that, and it might not be the same as X. question. The right question is is there some other fixed level of variance that we imagine being applied all over history that would be better to have than x? And the answer to that is no. Because any x prime that would be non-trivially different from x is going to be such that it diverges from the actual proportion of a in a set of n profiles in a certain direction, plus or minus minus got the race there. More often, overall, than X does. And its average absolute error over a decent number of these sets of N trials is going to be greater. So you just do better with the objective chance. Now, almost always is not always, and I'm not pretending that it is. This justification of the PP is not meant to guarantee you that you win. There's no guarantees. But if everybody were betting all over the place, then most of the people who use PP win, and most of the people who use something significantly different lose. And that's, I think, enough to give a consequentialist justification. Loose ends, of course, that was just an argument. If it worked at all, it just worked for the kind of many guesses over many trials case that we were looking at. So can we move from end trial to reasonability for just a few trials? And you may want to press me on this in question period. I argue in the paper something rather weak. I just say, well, it doesn't seem to me that it's right to maintain that it's unreasonable in a given just in one coin flip to set your credence equal to one half. But it would be, of course, it is reasonable if you're going to have 100 such flicks. And unreasonables do not make a reasonable, I think. I recognize that's not a very good deductive argument. And I think, in any case, no information is going to be able to provide us with a better level of credence about the single trial without being information

32:30 that violates admissibility and hence gets us into a case where we wouldn't use PP anyway. What about a setup that has few but not really few actual instances in world history. So this is different. Here we were talking about, is it reasonable if you just have to make one bet? Here I'm talking about now, instead of coin flips, which there's trillions of them, what about that role of the N-sided die, of which there's very few in world history? Can you show that principal principle is reasonable also for that, on your human view of chance? Well, no consequentialist argument like what we just went through is going to work. There's not enough outcomes to get you any guarantee of winning or losing. But the point is, correspondingly, because there's few cases, there's not much harm that can be done by setting your credences equal to the objective chances. So there's no built-in punishment that can be shown either. And there's an interesting thing, which I try to argue in the paper. If there's few, but not really, really few instances of the total thing that we're looking at in world history, then, well, the actual frequency may be indeed significantly different from the Humean objective chance. Suppose we have a 43-slot roulette wheel. I'm supposing that nobody's ever made a 43-slot roulette wheel. It seems odd to have such a strange number. So let's suppose that one was made in Monte Carlo, It was spun a few hundred times, and then it was destroyed, because people didn't like it. Now, maybe the actual frequency of double zero for that roulette wheel was considerably different from 1 over 43. You might think, well, then, aren't you better off if you set your credences to the actual frequency and not the Humian chance? The Humian chance is definitely 1 over 43, because of the symmetry considerations, but the actual frequency is different. But no, you can't mount to the kind of consequentialist argument that I did just now to show that frequentism is going to do better than objective chance. It all depends on how these chances are distributed. So suppose that the ratio in an actual history is double zero. The actual frequency is 1 over 25 instead of 1 over 43.

35:00 Can anyone mount an argument that, well, if you're only betting on some, not all, if you're betting on all the outcomes, you're going to win. But suppose you're just betting on 10 spins. Can anybody give me an argument to show that this is a better rational credence to have as opposed to one of the three? Answer is no. Because maybe the way that this turns out to be the case is that over the first 300 spins, the frequency is actually very much like this, but just in the last 100 spins, a huge number of fluke double zeros. That wouldn't matter. That would still be a Humian, a perfectly acceptable Humian pattern, because the numbers are low. So you can't mount an argument that the Humian objective chance does worse for you, at least something. OK, suppose for the moment that you thought this deduction was at least OK as far as it goes. does, what does it show? It seems to me that it shows that there's intrinsic limitations on what Humean chance is meant to be used for. So I think all objective chance, because that's what chance is, but if you're a Humean about chance, then chance is intrinsically something that's about guiding your expectations for relatively small bits of future events compared to the overall pattern. Humane chance is meant to be a good life when you've got to make predictions about a number of chance outcomes, or even just one, but the typical case is many. And you have no better information to be had, but you do somehow have the objective chance, and you're looking at a small part of the pattern. Why does it have to be a small chunk of the total pattern? There's this feature of being a humane about chance, and this is just as true if you're frequentist, as if you accept my account. There's this interesting feature about being a human about chance, which is that the whole story can be self undermining in a certain sense. How does that work? Undermining works like this. You suppose we've got a finite pattern

37:30 coin flip results in the overall mosaic of human history, but it's finite, right? So there's a finite future, and we're going to say that the problem depends on the path, as usual. Now, supposing somehow you knew that there was only going to be 100, or what other words, say 200 flips in the past history, and you know what they came out, and there's So the coin before the world is destroyed. This probability lets you calculate. What's the probability of all future flips come out heads? What is it? 1 over 2 to the 100. And that's not 0. It's darn close, but it's not 0. So plug this into the principal principle, and it says, well, you should have a very, very small degree of belief that that'll happen, but not zero. But on the other hand, you're a Humean. You think about what the whole history of the world would look like if that were, if there were 100 future heads here and there's 200 randomly distributed. And you think, I'm a Humean. If that's what the history of the world is like, then it sure isn't the case that the one-half. So to the extent that I know that the probability is one-half, I know that that can't be the future. So I have to give it credence zero. That's the problem of undermining, which perturbated Lewis quite a bit for a while. Human chances sort of undermine themselves. And the right answer to this problem, don't apply human chances so widely. Don't think that you can use them to set your credences about the entire future unfolding of events in the history of the world. That's not the right, that's not what human chances are meant to do. They're meant to guide your credences about little local sets of outcomes that are small compared to the big path. And that's what they do for you. Okay. And here's the, finally we get to reductionism. I think I've seen now a reason to say that It's also, you shouldn't apply humane chances extremely widely in a reductionist sense.

40:00 That is to say, you shouldn't think that macro-level chances are really legitimately to be derived from, say, underlying quantum probabilities, really microscopic chances. So what kind of reductionism are we talking about? Here we're talking about chance reductionism, which would be the view that if there are objective probabilities at the very lowest level that kind of cover all possible physical evolutions, like some people think is the case with quantum mechanics, then those micro chances being fundamental and ubiquitous, well, they must determine all higher level chances that there are. To the extent that there exists, say, a probability of my getting lung cancer, given the other factors about me, well, they must be determined by the quantum of all chance. And notice that the best system account that I just got through telling you about is not reductionist. I was assuming that the truth makers of chances about roulette wheels are not quantum probabilities, real spin outcomes actually come out in the history of the world. Yet at the same time, given this human understanding of chance that I sketched, we can already know pretty darn certainly that quantum probabilities are part of the human system. And notice, it doesn't matter whether quantum mechanics is the ultimate true theory or not. It gives us probabilities. We've discovered that those probabilities are reliable in the laboratory, and that's it. That's not going to change. unless you're an inductive skeptic I'll put that aside that's not going to change so for a Humean about chance we already know this wonderful bunch of chances that apply to microscopic events it doesn't matter even if the universe is ultimately given the true laws of nature deterministic this is something I didn't argue here but in the paper you can have a best system of Humean chances perfectly compatibly the universe. Who are these crazy reductionists? Always helps to have some names to hang on to these positions. So David Lewis was one. Barry Lower, Ned Hall, Jonathan Schaffer.

42:30 Seems to be confined to the east coast of the United States. Maybe there's even some people here today that would be tempted by this kind of reductionism. OK, a quick criticism of this kind of reductionism. Setting aside conceptual worries about whether this reductionism makes sense, which I think there ought to be. There probably are serious conceptual worries about that, but I'm not going to try to talk about that. Let's suppose that just as Laplace's famous demon in Newtonian physics could calculate the entire future from the state of the world at time t0, the demon could also calculate the chances of all future macroscopic events based on the fundamental quantum probabilities for any sort of macroevent we care to specify. Again, indeterminism is not necessary here. Also, I think it's important to bear in mind these calculations may be vastly harder than the deterministic case. Well, the point is simple and obvious. We're not Laplace's demons. of these micro-derived chances, except in the rare sort of case where we design, say, a physics experiment so that certain macroscopic outputs are determined by the microscopic happenings, you know, like in an EPR experiment. But typical things like people getting lung cancer or coins landing and so on, you're never going to derive the probability of those things literally from quantum mechanics. I don't even think, it may, it probably is even impossible conceptually for the classes demon, but we won't have to worry about that. So the first comment I want to make about micro chance reductionism is that since the best system means best for us, it's got to have macro level chances that are only supervening on the macro level events. Because we're never going to be able to discover this best system if we are reductionists. Okay, now something a bit worse, though, than the epistemic problem. Suppose that, just for a moment, suppose that there was a Laplace's demon and it was willing to whisper in your ears what the objective probabilities are for macroscopic type events that it has calculated on the basis of the underlying quantum probabilities. Then the question is, suppose also that you've got the medical doctors doing their studies

45:00 that tell you that the probability of lung cancer is X, and the Laplace's demon is telling you, no, no, the probability of lung cancer is Y, and they're quite different from each other, non-trivolent at least. Who do you believe? Who should you trust? So the reductionists say, well, in that case, the micro-derived chances are real chances, know. So listen to your Laplace's demon. For example, Silber, who was writing a paper in which he gave at the last PSA, defending the reality of macro-probabilities, even if there are micro-probabilities, Silber still thinks that if you can know both of them, you should set your credence by the micro-derived probability. So he says, suppose you know the system's macro-state at T1 and also the system's micro-state at T1, and you want to in state y at later times t2. If you know the values of both the macro probability, this might be given to you by medicine, and the micro probability that the Laplace's demon gives you, and their values are different, then the micro probability is the one you should use to make your prediction. And Sober derives this principle from two further principles, the principle of total evidence and the principle of synchronic meteorological supervenience. I'm just a mouthful. the microstate determines all the macro properties. I say, not so fast. I'm not at all clear that that's the right thing, that's the right advice to give. So remember, objective chances are patterns in the events of the world, such as to be apt for guiding credence under ignorance, i.e., they play the PP role. Now we saw, if my argument worked, we saw how to deduce the applicability of PP to best system human chances, And that deduction involved a very direct use of the kind of chances under restricted circumstances. Does that deduction further establish that microderived chances based on quantum mechanics would also be such apt to guide our ..