2024-10-01 Increments #74 - Disagreeing about Belief, Probability, and Truth
Duration: 01:32:02
Transcript
David Deutsch
Even in the examples that the two of you just gave me, the reason why I was shaking my head is that you, you, what you actually said was wrong.
Ben Chugg
We’re absolutely thrilled to be joined by David Deutsch on Increments today. David, thanks so much for coming on the podcast.
David Deutsch
Thanks for inviting me.
Ben Chugg
So as our listeners will know, your work has been hugely influential on both of us. And hopefully an exploration of your ideas will be pretty well known to our audience because of that. Many of your ideas surface in many of our episodes. So in the spirit of critical rationalism, we thought we’d actually take the time with you today to explore some potential areas of disagreement between us. And potentially some areas where we think you might disagree with Popper. And so we’ll just kind of dive in and see, yeah, see where we go, see where we land. So the first area comes from a couple tweets you’ve made, actually. And it’s the subject of belief. So I believe you’ve mentioned a few times that you don’t think belief is a useful category for thinking about human thought. So maybe I’ll just let you expand on that and then we can go from there. Yeah.
David Deutsch
I don’t think it’s a useful category for most kinds of thought. It can be useful when speaking about, for example, religious faith. And you say, you know, you can ask a religious person, do you believe in this tenet or that tenet of your faith, of your denomination and so on. And that person is likely to go to their spiritual advisor sometimes when they’re perplexed and they might ask questions like, what do we believe about so and so? And then the spiritual advisor may say, well, we think that this is wrong, but that is right. And then they will go, they will say thank you. And then they’ll go away and then they will believe it in some sense. Now, I don’t deny that that sense of belief exists. On the other, at the other end of the scale, you can ask somebody, you know, does the number eight bus still stop at this bus stop? And they might say, well, I believe it does. But you know, and then their tone of voice will tell you that that if it doesn’t, it’s not their fault, you know, they so their belief means the opposite of what it did in the first example. And then in between, when we’re talking about how we use theories, how we use ideas, I don’t think I think belief is nothing but a misleading category. For example, and you know, Bayesian Bayesians may may know about this example. In everyday parlance, beliefs have strengths. So you can say, I believe that but not very strongly. But if you give me this evidence, I’ll believe it more strongly, or I’ll believe it less strongly, and so on. And that sort of says that that somehow I ideas are we know that ideas are somehow encoded in our brains. And the idea there is that with every with every idea, there is there is well for Bayesians, there is a number between zero and one, which tells them the strength of that idea. And when they consult the idea, like, is the number eight bus coming, they also consult that number. And if that number is 0.99, then they will say, yes, it does stop at this stop, and so on and so on. Now, I don’t think those numbers exist. And in the so you might say, well, they don’t exist in the sense of being recorded in a memory location next to where the idea is recorded. But it’s just a convenient way of speaking about the whole gestalt or whatever you call it of the mind in regard to that idea. But that’s not true either. I don’t think we consult this gestalt at all. And what’s more, in the case of the bus, the person you’re asking may not even have a location in their brain where the number eight bus timetable is stored. They may create it on the fly after being asked. And they take into account all sorts of other things that they consult more often or where they have where they have no criticism. If they can link the bus question to one where they have no criticism, where they can think of no criticism, then they will just say yes or no to the bus question. And the and note that they are then talking about the bus entirely talking about the bus and its timetable, not at all about their own brain, which is what I believe or what Bayesians think that not just Bayesians, I mean, it is the prevailing theory of knowledge and of how the mind works that beliefs come in strengths.
Ben Chugg
Okay, so maybe let me try and make the case for not like a quantitative version of degrees of belief, which I think we all want to disavow, where you actually attach numbers to these things and then do arithmetic and calculus with these numbers, but maybe a softer form of degrees of belief. So on a different podcast you were on, Dwarkesh Patel asked you, he wanted to advance some theory based on our current theories of cosmology. And you weren’t prepared to adopt the conclusion of the theories because you said something like our fear at this point, our theories of cosmology are changing quite rapidly on the something like once per decade almost they’re being revolutionized. Could you not frame that in terms of you’re not prepared to adopt a conclusion because your degree of belief, you know, you don’t have to attach a number to it. But like you just have less confidence in our theories of cosmology, our current theory of cosmology, even though it might be our best explanation of cosmology at the moment. You’re just less confident.
David Deutsch
Yeah. So if you if you strip the idea of belief of all its common sense implications about how one makes decisions, then you can retrospectively frame any decision in terms of belief, you know, you can you can, you can say, I made this or that bet on the roulette wheel, because I believed so and so about the roulette wheel. But and that that, in one sense, it’s harmless, because you’re simply because it can be attached to any kind of thinking. It doesn’t add or subtract anything from the thinking. But the trouble is that the theory of belief is a substantive one. It’s a claim about how the mind works. And it’s a false claim about how the mind works. Therefore, sometimes it will lead you into error. And there are well known paradoxes to do with belief like the paradox of the intransitivity of support, Hempel, Hempel’s paradox. So Hempel’s paradox is is that if you if a theory is true, then you can deduce from that that that all its implications are true. If a theory is false, there’s nothing you can deduce about the implications. So in inductivism, or Bayesianism, or various theories of quantified belief, say, okay, well, that’s a bit of an awkward problem. What happens if because in real life, you don’t ever know for sure that the theory is true. So suppose you only believe that it’s true, suppose you believe that it’s true very strongly, can you then rely on its implications being true? Like its predictions, for example, okay, if you believe the theory is true, can you rely on its predictions? Well, it turns out as a matter of logic that there are if the theory is in so given a quantification of belief, if a theory has less than 100% belief in your mind, then there are always implications of it, which will be rendered less believable by more evidence for the theory. And that’s Popper and Miller’s theorem, one way of putting Popper and Miller’s theorem. By the way, I and my colleague Matjaž Leonardis have been working on a paper about this for years, I think it’s four years now. And we always think that we’re about to we’re about to finish it. And the paper is basically just Popper and Miller’s theorem. But we’re trying to explain it so that people get it. I it’s a tough theorem to understand. I struggled with it. It’s very tough, because it’s so counterintuitive. And he uses arcane notation as well, which I had a difficult time. Unfortunately, yes, yes, our notation is much better. That’s one of many things that we improve. But you so I first encountered this theorem, I don’t know, 20 years ago, and I thought, Whoa, that, that’s so powerful, you know, it destroys Bayesianism, and it destroys belief, and so on. And, but I don’t quite get it. So I didn’t quite get it. So I went through it line by line, making sure that I understand, I understood the logic of every line. And I got through to the end, I was like, right, it’s correct.
David Deutsch
It’s true. It’s proved. I still don’t get it. So I, from then on, I would, I would ask friendly seeming mathematicians, you know, to explain it to me. And typically, they would say, it’s obvious, it’s a completely trivial theorem, as it is, it’s a trivial theorem, it takes about, I don’t know, eight lines to prove it. Finally, I asked Matjaž, and he said, Well, it’s a trivial theorem, but that’s bloody hard to explain. And I thought, right. You know, that was several years ago, and we’re nearly finished explaining it.
Ben Chugg
So I just want to comment on one thing you said, and then perhaps we should move to two other subjects. But going back to this idea that talking about belief or appending the dimension of belief onto any thought doesn’t add or subtract anything. So just a tiny bit of background, you are pushing on an open door with us when you’re critical of Bayesianism, we have probably spent upwards of 20 or 30 hours criticizing Bayesianism. So 100% on the same side. But I do want to defend one tiny aspect of belief. And this is belief not as applied to theories, but just as applied to a single fact. And so here’s here would be my simple example. You’re driving home from a party and your wife asks, what was the name of that person we were just chatting to? In one scenario, you say it was John. In another scenario, you say, I think I think his name was John. So we’re not talking about explanations. We’re not talking about theories. We’re talking about a single fact. And the only difference between these two scenarios is the qualitative degree of certainty you have around that fact. I claim that that’s valuable information. So if my partner says confidently that is John, I’m going to act in one way that if my partner says, unconfidently that it was John, then I’m going to act slightly differently. Perhaps I’ll text John’s friend and get that information. And so I am 100% on board with you when we are talking about expunging belief from epistemology, separating it from theories and from explanations. But it seems like it’s possible to go maybe a bit too far and say that belief is utterly worthless, and we should never talk about it. And I’m just curious what your comments are on that more mundane use case of belief when it’s just added to a single fact a single piece of information.
David Deutsch
Again, that’s probably not the most harmful case of using the concept of belief, but I still think it’s at the very least unnecessary in that case, because somebody asks you, you know, what’s the name of that person? And you think it’s John, but you also think it might not be John. Now, this just that doesn’t tell you anything, because that is always true. It’s given meaning in the light of your explanatory theory. Your theory is that you have a memory. And this memory is reliable in some cases and not reliable in other cases. And so first, you think, well, is this a case where my memory is reliable? Now, even when your memory is reliable, of course, you don’t know that the cosmic ray hasn’t just hit you. You don’t know that your theory of your own brain is true. You know, that there’s a lot of things you don’t know, which could be false with you just that since that’s always true of everything you say, and you can’t prefix every statement with a statement of unreliability, you don’t have to say that. So you’re doing some introspection to determine what sort of a memory your memory of its being john is. For example, if you’ve known john for 25 years, and he happens to have turned up at this party, then you know, he’s john in a different way from if they introduced you to at the party to 13 people, and one of them was john. And you’re not very good at remembering names. If you say, I think it’s john, that means that you haven’t got any decisive criticism of its being john. For example, looking back, you can remember all the names of the people you were introduced, or you think you can remember. Or if you if you think you can remember none of them, and john was new to you, but you happen to remember that that one was john, then you would have a weaker criticism, or a less good criticism, shall we say. So that’s one scenario. If that’s a good explanation, then you’ll just say I can’t remember. If it’s a bad explanation, well, you need to look around for a good explanation before opining, you know, you might say, I have no idea. You know, I was I was introduced to so many people, I can’t remember what his name was. That’s, that’s, that’s another thing you could say. And that that doesn’t refer to your belief, it refers to your memory. So I mean, does that answer your question?
Ben Chugg
No, it totally does. It’s kind of like everything you said, the way that I shorthand that is to just talk about belief, I guess. But it’s good to know that you can bottom out a comment about belief on something more epistemologically rigorous. And so I see kind of your statements as is providing that mapping. So if someone really wants to interrogate what I mean, when I say I believe something, then I would map back to the comments about explanations and presupposing various theories. And that’s really, really important. But my partner, Helena doesn’t have an hour and a half in the car for me to explain that. And so I’ll often just shorthand it and say, my belief is that I won’t even say the word belief, I’ll just use my tone of voice. But that tone of voice will indicate certainty and the degrees of certainty that I have with enough fidelity that I think will give her decision relevant information.
David Deutsch
Well, maybe just your tone of voice indicates your opinion about the problem situation and your best explanation.
Ben Chugg
Okay, so discussing Bayesianism brings us closer to the topic of probability, which is another thing we wanted to talk with you about. So you gave a talk a while ago now, perhaps, perhaps a decade or so, where you wanted to you were criticizing various theories of physics for their reliance at bottom on the use of probability. And I believe the takeaway of that talk was that we should sort of withdraw, we should expunge probability from our theories of both our theories of physics, and our epistemology. So I think you were attacking both Bayesian epistemology, and then an actual and then actual physical theories that rely on probability. And so I think this has caused some split among people who really follow your work. There are those of us who think there’s still use for probability and statistics in various realms of endeavor, so not necessarily in physics and epistemology, but just as a tool to use to tackle other problems. And there are those who are just sort of critical of the use of probability and statistics across all fields of human endeavor. And so I just like to ask sort of Yeah, where do you come down on that? Like if probability and statistics aren’t useful in physics, are they useful anywhere? Or is this a use? I ask it somewhat self consciously as doing a PhD in mathematical statistics. So I
David Deutsch
Yes, well, of course, in mathematics, probability has a different meaning. It’s just a set of numbers that obey certain axioms. And certainly one can imagine numbers that obey axioms. And one can formulate theories about a theorem about them. And that there’s nothing wrong with that. So that’s one place where probe but that’s not really probability that’s in everyday language probability means a stochastic process where the physical system can be one thing or another thing. And does randomly. So that randomly is the thing that I deny. Sure. Yeah. Now there is a use within quantum theory, which I’ve done quite a lot of work on, which is that in some cases, the where the where different outcomes happen in different universes, it is one can prove that one should that it’s rational to bet on these outcomes exactly as if they were controlled by probabilities. So that’s that. So it’s in those situations, like when one is interpreting the results of a quantum mechanical experiment, one can refer to those numbers, the modulus squared of the amplitudes of various parts of the wave function as probabilities. And one won’t go wrong, because we know that those numbers in certain circumstances, obey the laws of probability calculus. So you won’t go wrong, but not in all circumstances. And if you if you try and analyze what goes on inside an interference experiment, the part that you can’t see, if you analyze that using probabilities, you will get systematically the wrong answer. Probability. Quantum theory just doesn’t obey the probability calculus. In general, it only does in special cases where there’s certain kinds of measurement being performed and so on. Interesting. So the other place where probability is useful and legitimate, but again, only only in a narrow range of circumstances is the area where probability the theory of probability was invented, namely game theory, theory of games of chance. So there are no games of chance in real life, because game of chances is defined by having stochastic processes dealing with the shuffling of cards or the rolling of a die. But luckily, we don’t need a theory that that predicts the outcome of the rolling of a die. Even though in deterministic physics, it is determined, but you just don’t know. And anyway, the reason it can be used in games of chance, the reason probability can be used in games of chance is that what you really want of a shuffling of card process that shuffles cards or rolls rolls a die is not that it be random. It’s that it be fair. Fair to all the players in that there is no algorithm that will enable one of them to unfairly win the game. So everyone’s on equal footing. And it’s, it’s, it’s, as long as it’s unpredictable, it doesn’t matter whether you use the digits of pi or the rolling of a die. So both of them have the right properties. And the right properties are that they produce the numbers one to six, roughly equally often, for large number of rolls. And people sometimes say an infinite number of rolls, because there never is an infinite number of rolls.
David Deutsch
It’s just got to be a number that’s large enough, so that you so that there’s no way for you to predict it. There’s no way for you to predict how many of them there will be after let’s say 300 rolls, how many sixes there will be, just that it will be roughly one sixth.
Ben Chugg
You just to build off that a bit. So I like that you talked about the proper uses of the probability calculus, and sharply distinguish the probability calculus as a set of algebraic manipulation rules from probability from as a metaphysical thing almost, is what chance actually is. And so talking about valid applications or invalid applications of the probability calculus. One thing I’d like to hear your comments on is just data science. And so let me give just a simple example. You are a hospital, and you look over the last 30 years of data, and you see that in December, you get this number of car crashes because of peak holiday season. So then next year, you kind of do some very simple math and you come up with a probability of how many crashes you’re going to get. Now is this metaphysical probability? No, this is just some rough, heuristic, some approximation given a bunch of assumptions. But importantly, it’s assumptions about human behavior and human creativity. However, you have to choose some number of doctors and nurses to staff because you can’t go totally blind. So you use that previous data. And that’s how you determine how many nurses and doctors to staff in December. So I’m curious, would you accept that as a valid application of the probability calculus or no?
David Deutsch
No, I think something you may you may say that something similar to that is valid. But I think that taken literally what you’ve just said, that is a good way of killing people. And okay, and it’s often it’s often used in that way. The point is, when you take last year’s statistics for the increase in accidents over Christmas, and purport to use them this year, you’re using substantive theories about the population of car drivers and pedestrians and you know, whatever. If those theories are false, even a bit false, you will make the wrong decision. So if you’re planning for coming Christmas, and there’s been a COVID lockdown, it’s going to run a coach and horses through your implicit assumptions about the behavior of drivers and pedestrians over over Christmas. It might be that there are no accidents over Christmas. Or suppose there has been a rush of immigrants into your into your catchment area of the hospital, and they don’t celebrate Christmas. Or suppose it’s there’s been a rush of immigrants who do celebrate Christmas more vehemently than the original population.
Ben Chugg
But that’s all baked into the idea of using probability in the first place, right? So nothing about looking at previous data and saying, Okay, I think the probability is X, and therefore we’re going to staff this amount of doctors and nurses. And I know that this is infallible. And I know that this is imperfect. And I know that as soon as I get more information, I need to change what I’m going to do. But one has to do something. And I don’t see the probability calculus as doing away with theories and explanations. That’s all baked in. It’s just baked into the kinds of assumptions you’re willing to put into the system. And also baked in where you’re going to be looking for information about when your assumptions are wrong in order to change, change what you’re going to do. And so I guess my question is something like, if you don’t think we should be looking at previous data, in conjunction with our theories and our explanations, then what would you tell a hospital to do?
David Deutsch
I would be telling well, I wouldn’t be telling them because …
Ben Chugg
They would suggest what would you suggest?
David Deutsch
I would say, look at your explanations, rely on good explanations, the best explanations you can find. If there was a rush of patients last year, and you’re able to check whether there was one the previous year as well, that’s good. Because that will allow you to test the theory that the propensity of having accidents is constant over time. If you have a good explanation that the factors which have changed in the past don’t apply this year, then again, then again, but by the way, it’s not really probability or really predicting the number of accidents that will come into the hospital. You don’t need to have the number divided by the total number. You’re really saying that the factors that your explanation says affect that number haven’t changed since last year. Now, of course, it might have changed. But if you don’t have a good explanation for how it’s changed, then I think it’s rational to ignore that possibility. And again, that’s what I would tell the hospital administrator. It’s you shouldn’t be preparing for things that have a bad explanation. Like, it could be that aliens will land next year, and interfere with those numbers in arbitrary ways. And there’s an infinite number of possibilities of that kind, which are logical possibilities, which it is irrational to take into account, even though they are possible. And if they happen, you will be wrong, and so on. But as a methodological rule, we should rely on our best explanations, not on extrapolating numbers.
Ben Chugg
But it seems like extrapolation can be part of explanation, in some sense, right? So if you look at, say, you look at the last 20 years of hospital data, and you see that some fraction of the population, plus or minus a few percentage points tend to come into the hospital, there tends to be a flux of people in the hospital in December. And let’s say you have no good reason for thinking that that trend is going to change this year, right? People haven’t stopped celebrating Christmas. They people seem equally as excited about Christmas this year. There’s no reason alcohol sales have been abolished or something like that, right? That’s all an explanation of why this year, you should expect to see something similar as last year, in which case it seems reasonable to use the statistics from previous years to inform your decision about precisely how many members of staff
David Deutsch
You have, then a good explanation of what the number will be. Right? You haven’t ever heard of probability, you would still have the same explanation and you’d use it in the same way.
Ben Chugg
But I would just want to add that the explanation would then perhaps suggest that the probability calculus can be a useful tool to aggregate your data. So you’re not saying I have an explanation that says that hospital crashes are going to be normally distributed. Of course, that’s, that’s an assumption. But the explanation would justify why that assumption may be useful, not true, but just useful. And so to return to the distinction between like metaphysical probability, and just the probability calculus, the calculus is just manipulation rules. And your explanation would suggest something like, yeah, we can actually use these manipulation rules under certain assumptions, which will change as soon as our explanations change, etc, etc.
David Deutsch
Well, yeah, but it’s, I told you, you’d say the difference is only very small. But the thing is, the difference in methodology is quite big. And when people are saying they are using when people say they’re using statistics gathered from past instances or whatever, they aren’t, at least, if they’re if they’re behaving reasonably, they aren’t what they’re using is their explanation of those past numbers. And, you know, I can invent lots and lots of ways in which your thing could be wrong. For example, you know, if you go back 30 years, it may be that 15 years ago, the hospital was rebuilt with twice the number of beds. And that would make your long term statistics unusable or usable with any different, different assumptions. But, you know, if something goes wrong, let’s say, let’s say there’s a pandemic, and the supermarkets run out of stuff. And somebody says, to the boss of supermarket, you have caused this disaster of your shelves running dry. And the number of extra deliveries you would have had to have is only about the same as you have every year at Christmas. And he might say in his defense, Yes, but that’s a Christmas. This was in the spring. And we look back, and there’s never been a rush on shelves in the spring. So we were right. And he was wrong, because the accusation is that he didn’t use a good explanation. And his defense is that he did use the right statistics, the right source of data. And he is wrong. He’s being accused of not thinking carefully about the reasons for the numbers. And once the once it was known that there was a pandemic on the cards, you know, in January 2020, or whatever, then what is reasonable to assume about demand for toilet paper in the spring changes drastically?
Ben Chugg
Yeah, I can’t tell to what extent we’re disagreeing exactly. I mean, I so I think we’re all on the same page that the use of statistics has to be informed by explanations. You can’t just you can’t start with numbers, and then assume the future will look like the past and then all will be well and good. That’s obviously an irresponsible technique for trying to solve any sort of problem. But I want to say something like, you know, probability and statistics are useful in what Savage who was a Bayesian, ironically enough called like these small worlds where all every there are no unknown unknowns, there’s just there’s just known unknowns, right. And so these are this perfectly describes game of games of chance. And then we apply these models to messy complex real life scenarios, when we have a good explanation of precisely when they apply. So when, for example, we’re doing a clinical trial and want to see if there’s a difference between the treatment effect, and the null effect, right, we want to see if a drug is actually helped people on average or something. There, we’re not saying statistics is getting us infallibly to the truth. There, it’s not even positing a mechanism necessarily by which the medication is working. But we’re using it instrumentally to help us achieve certain goals, and to like take actions in the world. And I, you look suspicious of my description there. And so maybe
David Deutsch
Misleading. You do have an explanation when you do a clinical trial, to see whether a drug has an effect on the disease or not. You’re bringing to the trial a mass of explanatory theories, which tell you, for example, what is not going to affect the outcome. So that you don’t have to control for it, you can’t control for more than like half a dozen factors in a real trial, because for every factor that you control for, it multiplies the number of patients you need to for the trial. So you can’t you can’t control for a million factors, you can’t even control for 10 factors, you can control for the factors that you have a theory could affect the outcome. And sometimes you’re wrong. That doesn’t mean it’s not the right methodology that the methodology I am advocating isn’t infallible, it can produce disasters. But it’s not true that that the model of what we’re doing as sampling from a distribution, and then drawing conclusions from the outcomes of that sample. It’s not true that that is a good model. You it’s only a good model to the extent that your explanation of what links the real thing to the statistics is true, and it might not be true, it often isn’t true. And I was just reading the other day about discovery of pulsars. And it turns out at least according to this article that I read, I can’t remember where I read it. But nevermind, even if it isn’t true, it’s a good example. There was an open day at an at an observatory. And members of the public were coming in and looking at stars through the through the thing through the through the telescope. And one of the ladies who was looking through it said to the demonstrator, that star is flashing. And the and the demonstrators, I don’t know, that’s just twinkling, you know, that that’s the old stars do that. And she said, No, no, it’s not twinkling. It’s flashing regularly. I think 10 times per second or something. So he said, Okay, I’ll look and he couldn’t see it because very few people can see flashing in the dark. With that acuity. So the data point was completely missed. And pulsars were officially only discovered later. And there’s nothing wrong. I mean, this is no indictment of the demonstrator or of the scientists that set up this demonstration. Because they had a theory in which stars flashing regularly doesn’t happen. But it’s not because it had never been observed that that that’s that’s a completely you know, that that’s like saying you’ve seen 1000 buses. But that’s not the reason why it’s because we have a theory of how stars work.
Vaden Masrani
Perhaps one distinction between Ben and myself and yourself is that Ben and I are saying it’s explanations and some statistics on top. But I think in your world, you’re used to battling with Copenhagenites for whom explanations are replaced by statistics. So it’s a statistics versus explanations because of the battles that you’ve been waging. But I guess I’m curious if you would agree that that can potentially characterize the difference of views here because neither Ben nor myself are denying the importance of explanations. We agree that it’s at the that’s the most fundamental thing. And that any statistics we decide to use on top of that are always going to be conditional upon and informed by our various explanations and theories. And to the whenever statistics starts to actively corrode the explanations, then both Ben and I would agree. Red alert here people explanations are always primary. But I think in the examples of the hospital, or Netflix recommendations, for example, this is this is explanations, plus some statistics on top to do something, I guess. Would you accept that characterization of our slight difference in emphasis here? Or perhaps not?
David Deutsch
Well, statistics aren’t probability. So in many cases, talking about statistics is just a sort of ideological rephrasing of counting. We know the number we know the number of patients we know we know the number of trials that have been done on the roulette wheel.
Ben Chugg
But it’s also the discipline of formalizing what you can do with different kinds of counts. Right. So it’s not purely an ideological thing. It’s a it’s a discipline.
David Deutsch
No, yeah, well, there’s such a thing as the field of statistics. And part of the field of statistics is isomorphic to the field of probability. And it is customary in the field of statistics, to refer to frequencies as probabilities, that is frequencies within a sample or something as probabilities. Now, as you know, the frequencies are never equal to probabilities, what can happen is that there is a good explanation that it’s a good approximation to regard the frequencies as probabilities or as approximations to probabilities. Okay, they don’t add up exactly to one, then, okay, that does happen. But it’ll be near enough to one, it might be near enough to one to not make a difference in what you’re doing. So if you if you test the roulette wheel at the casino, 1000 times, and you see that the numbers come up with the predicted frequency, then you can infer something about the mechanism, namely that it’s a pseudo random number generator with certain accuracy. And then you can talk about the probabilities as a as a an approximation to the frequencies as predicted by your best explanation. But even in the examples that the two of you just gave me, the reason why I was shaking my head is that you what you actually said was wrong. So you actually said that we look at the statistics of previous Christmases or and we don’t we look at our explanation of Christmases. And it’s the same with the drug trials, we don’t just give the drugs to the patients and then analyze the statistics, we first form explanatory theories about what the effect of the drug should be, and what might confound that, that effect in our example. Sometimes a drug works, it doesn’t seem to work. Because we’ve we haven’t chosen a sample, for example, if we don’t choose a sample that includes the sick people, then it might be that the drug’s effect on the healthy people has nothing to do with its effect on the sick people and so on. There are notorious cases where people have used a drug on themselves, in order to test a theory, which is difficult to test otherwise.
Ben Chugg
Okay, so maybe this brings us closer to another area of possible disagreement, which is the possibility of sort of prediction and predicting human behavior in particular. And so there seems to be somewhat of a conflict between, you know, the notion of creativity and unpredictability. You’ve obviously talked a lot about the unpredictability of creative processes, and that humans are sort of fundamentally unpredictable entities. And in particular, the content of our future knowledge is unpredictable. Otherwise, and this is Popper’s big insight, otherwise, we would know it now. Right. So it’s sort of a logical proof that the future knowledge is inherently unpredictable. But it does seem like there are some areas in which predicting human behavior is possible. And so I’m thinking of certain things like in economics, right. So for the law of supply and demand to hold, in some sense, that’s a predictive theory of what people will do when prices are raised or lowered. And so do you think that’s a counter example? Or what do you think is going on there?
David Deutsch
No, well, the phrase in some sense is doing a very large amount of work in what you just said. Okay. When we when we take out an insurance policy, the there are actuaries in the in the insurance company that are using the theory of probability and based on past statistics, to work out what premiums to charge in such a way that the insurance company will make a profit. And if they get that wrong, or if they get it wrong several years in a row, then the company will go bust. And if they get it right, then they will they will be better. Their shareholders will be pleased with them. Right. Now, what are they doing? They’re assuming that humans are alike in certain ways. And under certain circumstances, under Yes, which they don’t know exactly. And that that’s why they are not always right. I’m Lloyds of London went bust couple of decades ago. I remember it as it can’t be that long ago. They were and they had a rule that their backers had to have unlimited liability. So a number of rich people became poor through having invested their savings in Lloyds and it had been very profitable before. And no doubt they looked at past years and they you know, they saw their you know, 50% return and 30% return and 35% return and they thought, yeah, statistically speaking, this is a good bet. Right. And how wrong they were.
Ben Chugg
But I guess but I guess the existence of a mistaken prediction doesn’t. No one is claiming that predictions are infallible or that all predictions will necessarily hold, right? Most of the time, the claim is just that using this information, we will be able to predict with a lot of assumptions and all an iceberg of explanatory theories underlying it with slightly better odds than if we just randomly guess. And when the baseline is random guessing, then the success mark doesn’t have to be perfect predictions. All circumstances just slightly better than that.
David Deutsch
No one no one ever says predictions are going to be perfect. So everyone concedes that there’s a possibility of error. But what they do often say and which is absolutely false is predictions can never be certain, but they can be probable. So they would say I believe let me just add icing to the cake. I believe that that Lloyd’s of London is a safe investment. And I agree that it could go bust, but I think it probably won’t. And I believe that it probably won’t.
Ben Chugg
But now we’re virtually on the territory of like terminology, right? Because it doesn’t really matter how they talk about it as long as we know that the actual methodology that …
David Deutsch
They’re conforming to is suspect that they were not that they were misled into making a bad decision by a theory that looking at the statistics will tell you what will probably happen. I suspect that most people who invest in Lloyd’s of London or in the stock market or in anything, do not use explanatory theories. And they lose money to people who do. Hmm. So when you when you if you’re a successful speculator on the stock market, it’s because you know something that most of the other investors do not know. And that’s because you have either you’ve done more research or you have a better understanding of the subject matter of the market. There’s a subject matter in every market, you know, that in Lloyd’s of London, there were hurricanes and buildings, and ships and so on. And people who didn’t know about hurricanes and buildings and ships gave them money on the basis of a false theory of belief and probability. You know, you shouldn’t you shouldn’t invest in a company that you don’t know something about the subject matter.
Ben Chugg
Yeah, okay. So is your answer to supply and demand something like it’s only a feature of current culture that people respond in that way to prices rising and this might change in the future? Or this is or we just have a theory of human like how humans behave under scarcity or something like that?
David Deutsch
More that I think that the model of prices, these two graphs and where they supply and demand that the I think the model, the way you find you find out what would happen is we’re seeing where the where that point of intersection moves under certain changes in circumstances, I think that model is typically wrong. So because it’s going to it’s going to depend on in the market, for example, it will depend on creativity, it’s not true that the supply and demand curves are constant or that you can infer what they were from last year’s values. Like as I was saying, like if there’s a if there’s a pandemic, but there could be there could be things making changes that that you don’t know about and only historians will work out actually what it was that no one knows what they were even at the time, the demand for something or other will drop off or skyrocket for no apparent reason. And if you do know something about the market, you may still lose your shirt. But you will you will try not to use probabilistic language. So I’m trying not to say you will tend to win at the expense of people who do not know when people who do not know win over people who do know there’s something unusual going on. And again, I’m not going to say something improbable going on.
Ben Chugg
Sure. Yeah. Nice. Okay, so I am wary of time and potentially your voice. And I know Vaden has some comments on truth and particular Popper’s take on truth and how it possibly diverges from yours. So Vaden, I’m wondering if we want to do that now.
David Deutsch
Yeah, we would do that now. I’m not actually an expert on Popper. Everything I say is informed by his theories. But I don’t know which of my opinions comes from which theory of his. And I also know that some of the things that he said, I think are false. And some are some are very roundabout ways of saying something true, which is not necessary now. And in regard to truth, there’s, there’s verisimilitude, and there’s world one, two, and three. And I, that is not part of my worldview. So I may well disagree with Popper on that. So if you want to ask, I mean, ask me about my opinions, and then you can judge whether Popper would have agreed.
Vaden Masrani
Yeah, I am. So I’m really curious to talk about the talk you gave, I guess it’d be three years ago now, where you were trying to substantiate, or let’s say, solve some of the problems with Alfred Tarski’s correspondence theory of truth. And I know in that talk, you had kind of prefaced it by saying, a lot of these ideas are preliminary. This is a tentative theory, and you’re just starting to get some feedback. So I don’t want to necessarily assume that your views today are the same as they were three years ago. And secondly, we should assume our audience doesn’t know exactly what we’re talking about. So maybe it would just be fun to have a discussion about your thoughts on the correspondence theory of truth. And I think and to the best of your ability, recount the high-level thesis of that talk, or even just how your thoughts have evolved since then. But just to add a little bit to that. So part of the reason I’m asking that question is some friends of mine had done a close study of that talk, and then tried to find some stuff in Popper that would address some of the issues. So to show my cards at the onset, I think this is an interesting spot where your views and Popper’s may disagree. And that’s part of the reason why I think it’d be fun to explore.
David Deutsch
Yeah, so as I remember the… well, first of all, my views then were rather fuzzy. And my views now are rather fuzzy. And I’m not sure it’s meaningful to ask whether they’ve substantially changed since then. But I think that there is a problem, which I was trying to address using the theories of Popper and Tarski. And the problem was roughly, I can state it in a plausible way, that is it really meaningful? Somebody asked, and I think somebody did ask in the talk prior to mine, which was one reason I gave that talk. Is it really meaningful to say that science pursues truth? Since we’re fallible, and we will never arrive at a true theory. Okay, that’s an interesting problem. I think it is meaningful. So I would like to defend the idea that we’re pursuing truth, even though we know that we will never reach the final truth of anything. So that’s one thing. I think that Popper’s take via Tarski on what truth is, is basically right. But once I’ve conceded that we will never find ourselves in possession of a true theory, or utter a true statement, what can it mean to say that we’re pursuing truth, because we know that we’ll never reach it.
Vaden Masrani
And we may utter it, but not know it, right? So it could be that some of our truths we do have, it’s just that we’ll never be certain.
David Deutsch
Yeah, so Xenophanes said that, according to Popper, but if I may state this in a mischievous way, the probability of us hitting on an actual truth is zero. That doesn’t mean we won’t. Why is that? Well, because, because we can’t achieve infinite precision. So our statements are always ambiguous to some extent. And I want to say, yes, it does make sense. Nevertheless, even though I concede that we will never utter the final truth. pace Xenophanes. I still think it’s true to say that we are seeking it. And we’re seeking it by trying to eliminate errors in our existing theories. And so then somebody will say, Oh, that doesn’t solve it. Because when you eliminate errors, you might be wrong. And you can never be sure that the thing you’ve eliminated really is an error, might not be an error. And I want to concede that as well. And I still want to say that science pursues truth, and in general, rational thought pursues truth. And also that is important. It’s not just a technical point in logic. It is an important practical thing that at the moment it’s at the center of an attack on the enlightenment by the deniers of the existence of truth. So you know, everything hangs on it, it’s not the opposite of a technical point. So how do we do that? Well, Tarski said that a statement is true, if and only if it corresponds to the facts. Or we could weaken that by saying it’s true, to the extent that it corresponds to the facts. Or I’m not sure he used the term statement, he probably said proposition, which is a formal logic way of modeling statements. So I begin there and say, Okay, so when we make a statement, we’re not uttering a proposition. Because a proposition by definition can only be true or false, it can’t be approximately true. So there’s no, there’s the law of dichotomy, the law of the excluded middle. Any meaningful proposition is either true or false, and nothing else is possible.
Vaden Masrani
May I ask a question?
David Deutsch
Yes, please. Please continue.
Vaden Masrani
I’ll ask my question at the end. Sorry. Okay. Actually, I’ll ask one clarifying question about that. Just the law of the excluded middle. What do you do with examples like, you know, the color of Hamlet’s socks was red. People often use this as an example of something that might like a statement that might disobey.
David Deutsch
Yeah, that’s a statement with built in ambiguity.
Vaden Masrani
So are you defining propositions in terms of propositional logic? Or is there any statement in any language that has a clearly defined yes or no answer, true or false answer?
David Deutsch
No, it’s an idealization of what you just said about language. So in language, there are statements, propositions are abstract things that we approximate by statements, or we can approximate them by mathematical symbols. We can approximate but for any given way of approximating propositions, we can improve it and make it more precise, but we can never make it perfectly precise. So therefore, propositions are inherently abstract. We can’t say one, we can only say a statement, which, according to our best explanation, expresses that proposition as accurately as we shall need for the current problem.
Vaden Masrani
I just want to add something for the listeners that this distinction that you’re making David between statements and propositions is one of the contributions of your talk. And this is kind of the one of the ways that you’re trying to make progress on this problem by making the sharp distinction. But outside of this conversation in that talk, the distinction between propositions and statements isn’t exactly as you’ve described to most people. So I just wanted to add that for listeners just to make sure that they’re clear that this is part of kind of your innovation into this space.
David Deutsch
I don’t necessarily agree that it’s an innovation or that it’s my innovation, but it’s more interesting to say whether it’s a useful distinction to make and whether the things I say about it are true. Okay, excellent. Or how true they are. So the next step in this musing about perfection and truth, and statements and science and rationality and what we’re seeking. The next step is to say is to realize that although a statement can never be true of the world, in the sense that true is used in logic, it can never be perfect. A proposition can be. So trouble is we can never we can never get a proposition and put it in our brain and then let it exit through our mouth because that is a fallible process. However, in the world of abstractions, which may or may not be the same as Popper’s world three, I don’t argue about whether it is or not. I think that theory is itself rather vague. But in my conception of what abstractions are, there is a, in the set of all propositions, there is one that correctly says what a dog is or what shall we say what an electron is, or if dogs and electrons are also inherently vague, then they correctly say what there actually is in the world that we approximate as dogs and so on. So proposition can be true. A different proposition can be false. All of them are either true or false. When we utter a statement, I think we’re not uttering a statement about the world like about dogs and all dogs have four legs or something. We think of it as asserting a connection between some words in a grammatical sentence and the physical world. By the way, we can’t because of Plato, we know that we can’t grasp the physical world either. We can only grasp sense impressions and even those we never see as what they really are. So we have sense impressions which are theory laden. We have the theory first and then we interpret sense data. So we can never grasp the physical world perfectly. We can never grasp the world of abstractions perfectly. But the world of abstractions can grasp the physical world accurately, perfectly. So when we assert something, when sort of grammatically or when our intention is to assert something about the world, what that really should be expanded into is that we’re asserting that our statement, the thing we utter is a good approximation for the current problem. We’d have to add that good enough for the current problem of a good enough approximation of a certain proposition, namely, the proposition that truly describes reality. We can’t say that we can’t say that what we’re precisely doing is claiming that our proposition corresponds to reality, because it never does. We can say it corresponds to reality approximately, but then we don’t know what it is. So I think it’s useful to go via something which really can correspond to reality and say that in both cases, we don’t have access to the world of propositions, we don’t have access to the physical world, we can only form theories about them, which are always imperfect. And we’re asserting that this one abstract thing corresponds well to this physical thing.
David Deutsch
Just like I say about mathematics, that that we don’t and mathematicians think we that they have access to certainty and certain knowledge about the numbers and prime numbers and so on. And I would say that I have said that that what mathematicians what mathematicians do is they study necessary truth, necessary connections between abstractions. But necessary truth is not a property of their brain once they’ve done this. It’s once they’ve done it, their brain is as fallible as ever. Sure. Yeah. Okay. So that’s my best statement of what I think.
Vaden Masrani
Yeah, I’m overjoyed. This is the one, one of the very few areas that I think I do disagree with you on, only because I’m coming more from the Popper side. But I think it’d be interesting to spell out a little bit where your idea of abstractions differs from Popper’s conception of the three worlds. I mean, the so just for the listeners, Popper’s third world is the world of the product of the human mind, the world of manmade ideas. And the very strong distinction between I think how you think about abstract notions and Popper is that Popper would say that the concept of for example, an equilateral triangle did not exist up until the point that we invented the axioms of geometry. So in his conception, abstractions start at the point of the human mind. So before we invented the natural number system, there didn’t exist prime numbers, for instance. What he says prime numbers are in his book Knowledge and the Body-Mind Problem, he compares it to say the Queen’s Gambit in chess. So we invent the rules of chess. But then what we discover are the logical consequences contained therein. So once we posit the axioms, then what awaits us to be discovered are these necessary truths that the mathematicians work through. So how this relates to what you just said, and how I think your views differ from Popper’s is that he views statements and propositions as either a formal system or natural language system. And so he wouldn’t, he would view statements as language, a language that humans have invented. Meaning that when you talk about propositions as being abstract and perfectly precise, and corresponding perfectly unambiguously to a perfectly unambiguous world. His question would be, in what language are these propositions? Are they in English? Are they in Mandarin? Are they in Spanish? And does it make sense to talk about these timeless propositions? Before we’ve invented English or invented propositional calculus?
David Deutsch
I can certainly answer ghost Popper on that question. There are formal languages and there are real languages. And propositions are referred to by languages. I mean, try and be concrete about this. When I say there is an infinity of primes, that is a statement that arises within a formal system, which is one of the abstractions that I talk about. So there’s a formal system in which one could define sets and integers and numbers. And in that formal system, there are true statements. And I’m saying in English, that one of those is that there is an infinity of primes. There is also this statement corresponds to a certain abstraction. Now this abstraction is we can form propositions about it, but propositions aren’t the only abstractions. Numbers themselves, integers themselves, are abstractions which have certain properties. Primality is an attribute. That is, I assert, I won’t keep saying that. Primality is an attribute that some integers have and some don’t. And which of them have it and which of them don’t is not something that humans invented. In fact, there’s an infinity of that sort of statement as Gödel proved. There’s an infinity of that sort of statements that humans will never know of. And yet, some of those are still true, and some of them are still false, necessarily.
Vaden Masrani
In the same way that humans didn’t invent the Queen’s Gambit but discovered the Queen’s Gambit as a consequence of the rules that they did invent. I slash the ghost of Popper would claim actually, this is a verbatim quote from Popper in Knowledge and the Body-Mind Problem. Thank you. He would say the same about primes. So of course, we don’t invent primes, we discover them. But what we discover them in is our invented ideas about axioms of the formal system. So the formal system is what we invent. And then what we discover are the consequences therein. And so do you disagree with that take?
David Deutsch
We discover some of their properties.
Vaden Masrani
Yes, correct.
David Deutsch
With chess, it’s conceivable that we could discover all their properties because there’s only like two to the power of two to the power of 64 of them. You know, maybe if the universe lasts long enough, but we also we also theorize about infinite systems like the integers. And with those, we know, not only that there are propositions that we will never know, but that most propositions about them, we shall never know. We can also prove that all those some are true. In fact, half of them, I suppose, are true. And the and their negations are false, necessarily, even though we cannot ever know. So it’s not, you can’t get away with saying that they are true, because it follows from what we have set up from the system we have set up. Because that proof that it follows would be infinitely long.
Vaden Masrani
Are you saying there sort of needs to be a meta system on top of like when you’re reasoning about the integers, reasoning about properties of the integers, you need to speak in some meta language about the integers, because it’s not within the systems of just arithmetic plus the axioms of integer arithmetic that you’re saying things about statements about integers.
David Deutsch
Yes, but the same thing will be true when you add the meta language. So, for example, we can we can have a might be it might be undecidable whether every even number is a sum of two primes Goldbach’s conjecture. So it could be that let’s say for sake of argument that that’s an undecidable proposition, then we could add to the axioms of arithmetic, axioms of arithmetic, that statement Goldbach’s conjecture and the resulting thing would then be a consistent set of axioms. That consistent set of axioms would have within that set of axioms, there will be necessary truths that we still can’t know. And there will still be infinitely many of them. So it’s, it’s, it’s not just a matter of sort of self-referential questions. It’s, it’s an absolute necessary mathematical fact that formal systems that refer to an infinite number of objects have truths in them that are unknowable. So have we created those? You know, that to me, that is rather like saying, when you say there weren’t any prime numbers until we invented them. Well, when we first invented prime numbers, there might have been only 20 of them. Did the 21st one not exist? And if it only existed once somebody thought of it, then that process applied an infinite number of times until it gets to all primes still hasn’t scratched the surface of the truths about the integers.
Vaden Masrani
Well, I think the primes would have been discovered in the context of the natural number system, which is itself infinite, right? So if we posited a different number system that stopped at 11.
David Deutsch
So I think people were very skeptical in antiquity about whether an infinite number, whether infinity is makes sense or not. And as I say in my book, Archimedes seems to have not discovered a universal number system, precisely because he feared that it would be meaningless. And it’s only modern mathematics that has that has a sort of attached rigorous meanings to that, but not perfectly rigorous. But then what Archimedes knew about small numbers wasn’t perfectly rigorous either. And he didn’t know that.
Vaden Masrani
So I want to go back to something you said earlier, in your talk, I don’t know if you spell it out here, but I just want to add that to the listeners and then critique an aspect of it. So one of the reasons you propose this distinction between propositions and statements is because you say in your talk that reality is perfectly unambiguous. But statements can be ambiguous. That’s to have a correspondence, you need something else is perfectly unambiguous, such as propositions. And that’s how we can do the mapping between the two. But I claim that the attribute of ambiguous or not ambiguous doesn’t apply to reality that applies only to statements. So you would say, to my ear, that sounds like saying reality is perfectly grammatical, or something. Because when we talk about ambiguity, ambiguity is itself has this idea of correspondence baked into it. So if I have three sons, and I name them Bob, Bob and Bob, and then I say Bob’s gone to the store, that is ambiguous to the exact extent that that statement doesn’t correspond to one of my one of my sons. So it’s there’s ambiguity there. But you wouldn’t say that a rock is ambiguous. You wouldn’t say that an ocean is unambiguous. That just seems to me to be a category error. And so I’m curious how you respond to that. Because when I heard that reality is unambiguous, it was like, does that make sense?
David Deutsch
No, to say that reality is unambiguous is perhaps an unfortunate use of language. It’s you’re quite right, there is only statements that are ambiguous. And by the way, statements are just objects. They’re just physical objects as well. But I think I said that in the context that propositions are perfectly unambiguous, as opposed to you know, something else, like rocks are ambiguous. That the term ambiguous doesn’t quite mean the same. It’s not quite the opposite of unambiguous.
Vaden Masrani
But then the mapping doesn’t work if you mean ambiguous in a different sense with reality, as you do with propositions, then mapping between things that are out of it.
David Deutsch
If a proposition refers to rocks, then it won’t be true. Because the concept of a rock is vague. You know, is a pebble a rock? And so on. So there will be propositions that are true. But they will refer to things which don’t have this property of being vague. I shouldn’t say being ambiguous. Like the term rock can be ambiguous. A rock can be… It doesn’t have the property of… Yeah. So that may be just a matter of awkward my awkward turn.
Vaden Masrani
Yeah, so to build on that. So I guess what Popper would say here is something like… So when we talk about correspondence, correspondence isn’t defined as a perfect mapping between two unambiguous things. Correspondence refers to the property of language to move an idea from my mind to your mind. And so an example that I gave in the Discord once is if you want to teach your toddler what a shoe is. So how does that work? You point to the shoe, you say shoe.
David Deutsch
That never happens. But yeah, okay.
Vaden Masrani
Well, so with Georgia, so you point to the shoe and they say shoe. And then what the toddler is doing is it conjectures in its little mind that by that sound, you mean to refer, and if they’re old enough, they can follow the point, you mean to refer that sound to that foot-like object. So the conjecture comes first, the explanation comes first about how that sound and then later those symbols map on to something in the world, approximately. And then every time they hear the word shoe, and as they’re going through their day, every utterance of that word, as used by other people serve as a potential falsifier of their initial conjecture about how that sound maps onto that object. And in this way, we can talk about the word shoe corresponding to shoe, not through this lens of it perfectly and unambiguously maps from this to that. But it is a way to communicate and move my ideas into your mind with enough approximation that it can solve the problem at hand. And if the fidelity isn’t high enough, then we increase the precision of our language. But you don’t need this perfect mapping to have correspondence in that sense, because the correspondence just is a property of language’s ability to move ideas from mind to mind to mind to mind. And so how do you respond to that? Or where do you disagree?
David Deutsch
I think what you said is true of the way that we use. It’s true about correspondence. But the trouble is that this concept of correspondence that you’ve just used is incompatible with its use by Tarski to define truth. Because, because when we define, because truth is something that is that is not vague or approximate. And that’s why I want to introduce propositions into the argument. A proposition can be true, a statement can’t. When you talk about shoes to toddlers. In what sense are you seeking truth? What you’re really seeking is to correct errors to solve problems that you have and that’s all fine. But you can’t get to the correspondence theory of truth that way.
Vaden Masrani
Sorry, absolutely excellent point. One thing that I didn’t add that I should have is that I think that this idea of correspondence is a higher order problem that applied once we solve the problem of how does language correspond to the world, then I think that is that strikes me as more the nub of your issue here is how does how do words correspond to reality. And once we have some sort of connection, then Tarski can just borrow that. So like when I was listening to your talk, it sounded much more like your critique was just about how does language describe anything more so than it was about the core definition of what truth is. Because once we have such a correspondence, then we can just use that and Tarski’s introduction of the meta language, let’s not forget the problem situation that he was in. He was trying to distinguish between other kinds of notions of truth.
David Deutsch
Not quite sure what you meant.
Vaden Masrani
Speaking of being ambiguous. Yeah. Let me let me try to rephrase that because if that was a poorly worded question, I’ll give it another shot. So it strikes me that your critique of Tarski is a more general critique of this idea that language can correspond to anything because of the ambiguity problem that you raised. So first, do you accept that? Or do you not accept that maybe that’s a good place to pause?
David Deutsch
I don’t see myself as criticizing Tarski. The thing I’m trying to solve a problem with or rather to defend science and reason against is the idea that science can’t possibly be about truth. Because we never have true propositions. And in terms of correspondence, the kind of correspondence that we get when we theorize about the world is not the kind that is that that logic uses. Logic uses a different kind of notion of truth and correspondence and mapping and so on. So if truth sort of belongs to the logicians, and the physicists use vaguer things, and I want to find a way of saying that these vaguer things are approximations to and heading towards those abstract, meaningful things which obey things like the law of the excluded middle.
Vaden Masrani
I would claim the truth also belongs to the judges too when they asked a witness to state the truth, the whole truth and nothing but the truth. And so maybe there’s an interesting distinction between your problems with regards to the logical notion of truth as handled by the logicians. But then there’s also the truth as people who haven’t studied philosophy know it, right? And in that sense, you don’t need to undergo a class on the history of 20th century logic to know what it means when someone says that Donald Trump isn’t telling the truth, for example. And so maybe I was thinking about truth more in the second camp, whereas you’re thinking about truth more in the first camp and that potentially can explain part of the reason that we’re thinking about it differently.
David Deutsch
I think I think that’s exactly right. Yes. So the in a courtroom and in everyday life, one uses one concept of truth. And in logic, one uses a different concept of truth. And Tarski. So Popper wasn’t interested in formal logic. He went into that field in order to solve problems in epistemology. So and I think that needs the connection between these informal ways of talking and formal logic, which he also used. But you know, what does that mean? And so on?
Vaden Masrani
Yeah, one final thing is so earlier when you were talking about properties of formal systems, or at least properties of formal systems that have an infinite number of consequences, and how we know many of those consequences will be unreachable in some sense, but we can still say things about them. Are you using that as an argument as to why abstractions existed before humans? Because there are these properties of any formal system that we can conjecture?
David Deutsch
Abstractions don’t exist in time. So it’s not meaningful to say that they that integers existed before the universe or not in integers just exist in a different sense to the sense in which physical objects exist. So there were no physical objects before the Big Bang. But it’s not meaningful to say that there were no prime numbers before the Big Bang, because prime numbers don’t exist in time. They exist in an abstract realm, where there is such a thing as truth and so on, where there are such things as integers, but which we can find out something about by our window on infinity, imperfectly. But it does not make sense to say that there’s only a finite number of integers, or a finite number of truths about integers, because the only ones that actually exist are the ones that we know about. That’s that’s, that’s kind of empiricism or solipsism or something of the kind that in another context, Popper would have had a fit.
Vaden Masrani
Oh, interesting. Nice. Well, yeah, I don’t think this exhausted the list of things that we could potentially disagree about. But I’m conscious of your time and your and your throat. So yeah, I think we can we can probably call it there. So yeah, thanks so much for coming on the podcast. Hopefully it was a bit of fun. And we resolved some disagreement. May I ask one very brief question before we conclude? How are your various book projects going? I know you’re working on a successor to The Beginning of Infinity and science fiction book and a textbook and just curious.
David Deutsch
There’s a very hard question to answer because finishing any kind of not just books, but papers, any kind of output that I produce, they suffer from the maxim that they’re 99% finished all the time. And as Artur Ekert told me once, I think he was quoting Michelangelo. Apparently Michelangelo said, the work of art is never finished. It’s only ever abandoned. You have to learn how to stop at 99%. Yeah, yeah. And actually that helped me to finish my first book. He said that to me when I was complaining about not being able to finish it. He told me that and I did. But I think I’ve backslid since then.
Vaden Masrani
So your first book was 99% complete. Amazing. Well, thank you so much for your time, David. I’ve been starstruck the entire conversation. So hopefully I didn’t let it show. Thank you, David.
David Deutsch
Thank you. Fun conversation. Okay, bye bye.
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