# 2021-03-01 - Oxford Karl Popper Society - Musings about Statements, Propositions and Truths [YouTube](https://www.youtube.com/watch?v=DZ-opI-jghs) Duration: 01:30:02 ## Transcript ### Sam Kuypers 00:00:00 - 00:00:59 Good afternoon, everyone. Thanks very much for joining us. Today we have David Deutsch, author of The Beginning of Infinity and Fabric of Reality and physicist at Oxford. And David will talk about truth and propositions. And we have a slightly different format today, because David will be giving a kind of, this will be a conversation. So David will give a brief couple of remarks on the topic, and then we will have a discussion with David. And I think first Liberty and I will join into the discussion and later on we'll open it up for everyone. And with that being said, I give the floor to David. David, thanks for joining us at ... ### David Deutsch 00:00:59 - 00:05:58 The Popper Society. Hi, well, thanks for having me. It's statements, propositions and truth that I'm going to muse about. And the context in which I was musing is, first of all, Tarski's theory of truth as adopted by Popper, which is called correspondence theory of truth. And the idea is that a statement is true if it corresponds to the facts. So if I can, yes. Right. Now, there's a statement, and there is a fact. And that statement is true if and only if that really is a dog. And that's the correspondence theory of truth. And I thought it was satisfactory, and I believed Popper's treatment of it. But I started musing further about this in conversations with Lulie Tanett and other people, and also because of the talk that was given here by Danny Frederick about a slightly different issue, whether truth can be our epistemic aim. Not quite sure what he meant, but in any case, I realized that my own conception of truth was somewhat flawed. And I came up with some ideas to fix it, which I could have called it a simple theory that resolves all your misgivings about truth. Of course, it might not resolve all your misgivings. It might not be true, or it might be true but not original to me, in which case it's most likely to be found somewhere in Popper. Anyway, so there's a problem. What is the problem? Well, for a start, that's not a dog. That differs from a dog in a number of really vital ways. For a start, it's a cartoon. No dog actually looks like that. And secondly, when I say this is a dog, how do you know that I'm referring to that dog and not to some elephant that's in the room? So it might be referring to the elephant in the room, and then it would be false. And so I could make it more precise by saying on this page, this is a dog. That's more precise. But you see the point. I could go on adding qualifiers and explanations and so on, ad infinitum, and it still wouldn't be completely unambiguous. Yet reality is completely unambiguous. So how can an ambiguous thing correspond to an unambiguous thing? So that's one thing that's the problem. Something that's perfect and objective but not directly perceptible, that's the dog. How can that correspond to something that's imperfect, parochial, and perceptible, which is any kind of statement about a dog? Anything physical is like an idea in our brain or a statement in words, which can never be perfect, so it can never be perfectly true, nor can it be perfectly precise and perfectly unambiguous. So by the way, there's also a meta-language involved in this theory of truth, which says something like that, and this is true if this is a dog. So that's a statement in the meta-language. So there's a sort of triangle here of a statement and some reality and a meta-statement. ### David Deutsch 00:05:58 - 00:10:31 That's Tarski's theory. Another reason why, apart from being ambiguous and so on, we are fallibilists. We expect to improve our ideas, and so the ideas in our brains and our statements of them can't be perfect if they can be improved. So here's what I thought might resolve this. So in addition to statements and some reality, by the way, the reality could be mathematical reality and so on, but I'm using physical reality to simplify things. We could be talking about prime numbers and exactly the same issue would arise. So there are some things here which are perfect and pristine and beyond our reach, which we can nevertheless talk about and form theories about, and that is the class of abstractions. Something like what Popper called World 3, but I just prefer to say the class of all abstractions, which include things like numbers. So it's up here. There's number five. That's an abstraction. And again, I can't draw the number five. I can only draw some marks on my iPad screen. That thing there is just the marks on a screen, and it's not a five because, for example, that is not a five. It's a 50, even though it looks exactly like this five. So again, anything I might draw or say is ambiguous and partly wrong and all that stuff, but the thing I'm referring to here, the actual number five, that's a perfectly definite thing. And there are also up here propositions. So propositions like five is a prime is a proposition, except what I just said is a statement. I can't say propositions. It's impossible. So there are propositions up here which I'm representing. So there's a P and a not P and not P and not P. These are all propositions. And propositions have the property that they can be true or false and nothing else, absolutely nothing else. There's no, that it's the excluded middle and they're perfectly precise. They're perfectly unambiguous. Here are some propositions. And this one is actually true. I mean, the proposition, this one proposition I'm referring to is actually true, but unfortunately that's because it doesn't assert anything about anything. And also this P and not P, strictly speaking, those aren't propositions either. They stand for propositions. They are propositional variables. So this thing is true because it's true regardless of what P stands for. But just this one is a propositional variable and it stands for something that's either true or false, but it itself just represents that. It's a variable. By the way, it's quite usual in talking about the world and about ideas that we're super used to things that stand for other things and calling the things that stand for other things the things. And sometimes we have to be careful and make sure that the map isn't confused with the territory, as they say. But usually one can disambiguate sufficiently well, but that's just another level of ambiguity that cannot be perfectly resolved. So if I try to write down here an actual proposition, the traditional ones are things like, maybe I can change color. ### David Deutsch 00:10:31 - 00:14:54 I hope this works. Yes. Okay, so there's a traditional proposition, all men are mortal, and it suffers from the usual ambiguity, like whether this refers to people who were alive at the time of Aristotle or something's not clear whether men includes women or whether men includes men who've already died or men who have yet to be born and so on. But nevertheless, there is an idealization we can think of, which is that qualified by an infinite number of qualifiers, as it were, enough to make it which we could never actually do in real life. But this kind of represents a real proposition somewhere in there. And this proposition could be true of the world with people in it, and so on. And they're either all mortal or not all mortal. And then that's true if they are all mortal. So the more you try to define this, the more vague it gets. But like with the five and so on, there is a real thing there, a real abstract thing, and here's another real thing, the world, and they could correspond with each other. And my idea is that the correspondence theory of truth refers to this correspondence, the correspondence between an abstract thing and a real thing, both completely unambiguous and completely objective. And our statements about them are always attempts to express them well enough to solve whatever problem we're addressing. So I can draw a dividing line. Anyway, if I can move this aside, I can say that there are the abstractions, and then there's the reality, then there's a correspondence, and then there's meta theories saying true if they correspond. There's the meta theory, and it refers to those three things. And then there's statements. These are the nasty, dirty things that we can actually say, and above this line is pristine truth and the exactness. And the miracle is that we can actually gain knowledge about these things. We can say things about them never perfectly. So we have here, instead of just this abstract statements corresponding to reality, which is what I thought Tarski's theory of truth ought to say, it's a triangle. It's this, this, and this is a triangle. And if you like, this meta statement, I have to somehow bring it out of the page to form a tetrahedron. So it's either a straight line converted to a triangle or a triangle converted to a tetrahedron. And that is my theory of truth, which it is. And now you can shoot it down. ### Sam Kuypers 00:14:55 - 00:15:14 Great. Thanks so much for the introductory statement. So the first question I have is how can it be that these infinitely long propositions can be approximated by finite statements? ### David Deutsch 00:15:17 - 00:17:44 Yes, I don't think there's any guarantee that they can. Yes, well, so I think the situation is worse than what you say, because saying that the abstract perfect thing is like the imperfect thing with an infinite number of qualifiers, I don't think there's any guarantee that even an infinite number of qualifiers would, even if that were possible, even if that were possible, which it isn't, that even that would do. So how can we expect our statements to correspond to this pristine truth? Well, one thing is, there is no guarantee they might not be able to. I argue in my book that there shouldn't be any limit to how well we can do this, but even though we can never do it perfectly. And the thing to remember, as always with Popper, is when Popper says, at least I think, when Popper says we're striving for the truth, he always means we're striving to eliminate error. Of course, we can't be sure of that either, but when we use truth as a value that we are aspiring to, we're not aspiring to be able to utter true statements. We are aspiring to eliminate false statements from the things that we say, which always leaves more false statements, and we can't be sure that we haven't eliminated a true statement. So there is no guarantee, and there's no reason, not just no guarantee, there's no reason in the structure of all this, if I'm right, that implies that there should be statements that represent an abstraction perfectly, even infinitely long statements. So I don't know if that's good enough, maybe it isn't. ### Sam Kuypers 00:17:45 - 00:17:55 But so you think that we can guess at the correspondence between the statements and the abstractions, and that is how we kind of aim to find out about reality? ### David Deutsch 00:17:56 - 00:18:52 Yes, yes, we guess that our statement is some kind of indicator of the abstraction. If I say two plus two is four, that is in the light of a whole slew of theories that connect statements in the English language to integers, and then there's a theory of integers, which we can't prove true either, it might be inconsistent for all we know, but somewhere in the set of all abstractions there are consistent things, and we have a theory that the set of all integers is a consistent thing, and that what we say about it correspond to true propositions about that thing, and in all those ways we're bound to be inaccurate and ambiguous, but nevertheless we might have some genuine knowledge about it. ### Sam Kuypers 00:18:55 - 00:19:05 Right, and I see people are raising their hand in the chat, I also think that Liberty has a question, so Liberty go ahead. ### Liberty Fitz-Claridge 00:19:05 - 00:19:18 This might be the same as Sam's question, but do you, is there anything specific in Danny Frederick's kind of sceptical view that you think this resolves? ### David Deutsch 00:19:22 - 00:21:52 Well I must say I didn't entirely understand his sceptical view, it was directed against something slightly different from what I'm talking about, namely the question of whether we can regard science or just thinking in general as a quest for truth, and he was saying we can't, now I don't see that's a very important question, I mean I'd rather say what we are doing rather than say whether it's legitimate to call that a quest for the truth, but I think in the, you know his was a much longer statement than my musing here, I think he also touched on the problem that I'm talking about here, namely that we can never capture a proposition, and true or false, and that therefore we can never capture a truth, but I don't think that's important, as long as we know that we're not trying to capture a truth, so we're trying to eliminate errors, and I think someone asked him that and he answered, and again I didn't quite understand the answer, but anyway I think this is a simpler issue, it's, my problem is if truth is correspondence with the facts, how can a statement which is incapable of being true or false correspond to a fact which either is there or not, and you know that thing, in real life there is an attribute being a dog which any given thing has or doesn't have, we can't specify that unambiguously, but we can specify it unambiguously enough to meet whatever problem we're trying to solve, and this sort of a higher level thing of whether that counts as pursuing truth, well I don't really mind, I don't really mind either way. ### Sam Kuypers 00:21:54 - 00:22:01 Right, so this is not trying to address the kind of skepticism that Danny was advocating? I don't think so. ### David Deutsch 00:22:01 - 00:22:02 I don't think so. ### Sam Kuypers 00:22:07 - 00:22:43 Then, I mean you really explained it quite well, but then I still, so I understood your construction from that conversation with Danny, and I kind of saw it as a defense of realism and of the aim of science being the search for truth, but so I think I had a misconception about what your construction was trying to address, and I see, so I think your problem, and I think because of that misconception I also misunderstood the problem you were trying to solve, so could you re-explain very briefly what the problem is that you're trying to address with your construction? ### David Deutsch 00:22:43 - 00:24:23 Yes, so given the, so here we have some reality that's pristine, that's sort of perfect, and we have some abstractions which are pristine, and that's perfect, and therefore it's meaningful to say that there is a perfect, is or isn't a perfect correspondence between them, and we can, when the correspondence is perfect, we can say that this abstract proposition is true, and then there are these statements which are riddled with error and ambiguity and so on, and the problem was how can one of these possibly correspond to any of that? Right, so the answer is it can't, and it doesn't, it's this which corresponds to that, and we are merely guessing that this is what this is, and what this is, and what the correspondence is, and we're just hoping that our guesses are better than our previous guesses. Right, and this doesn't, our statements don't actually have to correspond to that, right, and this doesn't, our statements don't actually have to correspond to anything in the sense, in an exact sense, which would be required if we're defining truth that way. ### Sam Kuypers 00:24:24 - 00:24:28 Right, would it be fair to say that you are defending realism? ### David Deutsch 00:24:28 - 00:24:33 Oh yes, but I think Danny would say that he's also defending realism. Yes. ### Sam Kuypers 00:24:34 - 00:24:36 But we might think he isn't. Yes. ### David Deutsch 00:24:36 - 00:24:39 But I really am. ### Sam Kuypers 00:24:40 - 00:24:51 We fallibly guess that you really are. Cool. I see there's some more people who have questions, specifically Luli, as her hand raised. Luli, go ahead. ### Lulie Tanett 00:24:53 - 00:25:22 Yeah, so usually we talk about abstract things which are like philosophy and maths, and then practical like down-to-earth things like, you know, this water bottle or whatever, and you're saying that all statements correspond to abstractions. Is this like, is this like a technical sense, or is there a meaningful difference between abstract statements and these kind of like practical statements? ### David Deutsch 00:25:22 - 00:26:26 I think it, whenever we say anything, we're about the world, let's say, we're doing it via an abstraction. We don't usually say so or even think of it in that sense, but that's because of our just being totally accustomed to having things which stand for things which stand for things which stand for things, and just speaking as if the first one was equal to the last, was the same as the last one. But in reality, if you want to make sense of what theorizing means and what truth means and what having a theory about the physical world or about the abstract world means, then I think you've got to say, well according to my theory, you've got to say that all our statements are referring to abstractions which refer to the thing that we're talking about, rather than just referring to the thing we're talking about. ### Lulie Tanett 00:26:27 - 00:26:37 So there's no such thing as a purely abstract statement? Sorry? So there's no such thing as a purely abstract statement or a purely non-abstract statement? ### David Deutsch 00:26:37 - 00:27:58 Well, there is no such thing as, yeah, I see what you mean. Yes, well we can't utter an abstraction, we can only utter physical objects like sound waves and so on. So we are purely physical and our theories are always expressed purely physically, but we can theorize about, let's say, the world and about abstractions. And when we say this is a dog, and we say that in the context of some problem we have, then because there is no such thing as a correspondence between these statements and real objects like physical objects like dogs, but there is such a thing as a correspondence between an abstract proposition and a physical object like a dog. Therefore, we must always be talking about that abstract proposition whenever we say things that we're hoping are true or truer or whatever. If the concept of truth applies, we must be talking about propositions because it's only propositions that can be true or false. ### Sam Kuypers 00:28:02 - 00:28:13 Right, then I think I have another question, which is that, unless Luli wants to expand on her question, I hope I'm not interrupting. If not then... ### Lulie Tanett 00:28:13 - 00:28:15 No, go ahead. ### Sam Kuypers 00:28:15 - 00:28:50 Your idea of a statement is that purely linguistic? Because, for example, you were talking about the cartoon dog at the beginning of the presentation and it's basically... That also seems to be, in some sense, a statement, so it seems to be about not just sentences that we can construct, but also the cartoon dog is a statement that corresponds to some abstraction. Yes, I don't know... Okay, I hadn't thought of that. ### David Deutsch 00:28:52 - 00:30:08 You could call this dog... You could call this mark that I made here... You could call that a statement, because... But it would normally be called more like something like a model or a representation. Statements, models, representations, and utterances, and sentences written down, all those things... The important thing from my point of view here is that those are all physical objects, and so they can't have the property of being true or false. But yes, this cartoon is, for present purposes, it's a statement about a dog, but I want, in this context, I want you to take that as if it was a real dog, so that I can talk about whether that other statement there on the left refers to it or not, or corresponds to it or not. But I can't, no matter how I try to talk about abstractions or reality, I can't directly represent them. I can only represent them as physical objects that aren't them. I see. Okay, thanks. Then Charles, I see ### Sam Kuypers 00:30:08 - 00:30:23 Charles has his hand raised. Go ahead. Yes, I'm going to go to Charles. His hand raised. Go ahead. Yes, okay. Thank you. Hi. Thank you, David. ### Charles Bédard 00:30:26 - 00:31:57 Well, it's not a question. It's many ideas that I think would be quite cute to relate with other ideas of yours. I recently came about the chapter five of the fabric of reality, in which you speak about the Turing principle in a very grandiose way. Namely, I was kind of aware of the idea that computer programs can be put into correspondence with simulations of physical systems, but the chapter ends with the idea that not only physical systems can be, or virtual reality rendering of physical system can be given by computer programs, but also virtual reality renderings of abstract entities. So all that what mathematicians think and all men are mortal, can be also in a sense thought of abstract renderings. Well, no, virtual reality renderings of abstract entities. So the quest of science as search for truth in this context of trying to get a map between our virtual reality renderings of the reality out there can actually make sense, no? Because this is what we're kind of trying to do to get our ideas to correspond to the physical world. ### David Deutsch 00:31:57 - 00:32:02 Well, yeah, okay. I was agreeing all the way out. ### Charles Bédard 00:32:02 - 00:32:19 Sorry, I don't have any precise questions, but I just think that maybe it can give you the idea of commenting on this link between the Turing principle and this theory right here. ### David Deutsch 00:32:19 - 00:33:32 Well, there's no direct link in that sense, I think, because the set of all things that we can represent in virtual reality is basically the set of Turing computable functions. And the abstractions that we can speak of are a much larger set than that. We can talk about, say, the real numbers without making a virtual reality rendering of all real numbers. So I thought you were going to say, therefore, our quest to understand the abstract world is exactly the same quest as our quest to understand the physical world. And they are both done by making guesses about these abstractions, which are propositions. And that I would have agreed with entirely. But I don't think it's the case that we are just investigating the computable. We can perfectly well investigate the non-computable. ### Charles Bédard 00:33:32 - 00:33:38 But don't we investigate the non-computable through models of real numbers? ### David Deutsch 00:33:38 - 00:34:40 Yeah, but that's it. Yeah. I mean, we're poor, imperfect creatures. We also investigate it through much more crude things than just models. We investigate it through things like neurons and moving lips and so on. It's kind of a miracle if this is maybe an answer to Sam's question at the beginning. It's maybe a kind of miracle that something so crude and error prone as the part of the physical world that we control can have such tremendous reach, not only in the physical world, but into abstractions. I don't think it's the case that we're limited in what we can model. But to think of knowledge as just a model is not true. Where we can talk about things that we can't model. We can understand things that we can't model. ### Charles Bédard 00:34:40 - 00:34:56 But how do we understand them if we don't give ourselves some theory in some virtual reality rendering of the real numbers? ### David Deutsch 00:34:56 - 00:35:30 For example, most mathematicians think that p doesn't equal np. And it could be true that p doesn't equal np. Suppose it's true and suppose it's not decidable. Well, we can still perfectly well have a theory that p doesn't equal np. It doesn't stop us at all. The fact is undecidable. We can even argue for and against that proposition. Because argument isn't proof. And by the way, proof is useless without explanatory argument. ### Sam Kuypers 00:35:33 - 00:35:56 Yeah, I think that's a very nice point because obviously mathematicians do research into which functions aren't computable. So they have to be able to tell something. They have to be able to describe those kinds of abstractions in some way. Otherwise, they couldn't do their research. We couldn't be having this conversation about them right now. ### David Deutsch 00:35:56 - 00:36:39 Yes. And before they can prove anything, they will have had a conjecture. A mathematician could spend 10 years proving that such and such as such a proposition is undecidable. But that's because the mathematician will have had arguments in mind that not only that it is undecidable, but that there's a way of proving it and so on. And if he fails to prove it, he may still think it's undecidable. And I think p doesn't equal np is a good example of how easily that can be true. Everybody believes that. And it could be that nobody will ever prove it. ### Sam Kuypers 00:36:39 - 00:36:45 Yes, that's an excellent point. Yeah, Charles, I'm not sure if I'm ### Charles Bédard 00:36:45 - 00:36:50 Interrupting your conversation. Yeah, no, it's good. It's good. I'll think about it. Thank you. ### David Deutsch 00:36:52 - 00:37:00 By the way, another thing is just that the arithmetic of the integers is consistent. Again, everybody believes that too. ### Charles Bédard 00:37:00 - 00:37:01 But it's unprovable. ### David Deutsch 00:37:01 - 00:37:02 Yes. Yeah. ### Sam Kuypers 00:37:02 - 00:37:22 Yes, I think there's various paradoxes that pop up here. Anyway, I see there's another question in the chat by Jake. I'm going to mispronounce your name. Sorry, Jake Orthwein. I hope I said that right. Go ahead. ### Jake Orthwein 00:37:22 - 00:38:04 Yeah, thanks. So I have a question about this relationship between, I guess, I guess it could apply both to the relationship between our statements and the abstractions and to the relationship between the abstractions and the world. I'm sort of more concerned about the relationship between the abstractions and the world. But I guess I'm wondering about what it would mean to say that the abstraction corresponds to the world or even refers to the world, that certain pieces of the abstraction pick out certain things in the world and not others to refer to them and what the nature of that relationship is. Independent of whether it's true. What does it mean to even refer? Yes. Well, you're quite right that there ... ### David Deutsch 00:38:04 - 00:39:22 Could be an abstraction. There are abstractions out there that don't claim anything. Let's say you could have the mathematical model of the standard model of particle physics. And let's suppose that that was true. It still wouldn't be an assertion. So it couldn't, whether it corresponds to anything depends on what it's claimed to correspond to. Because if somebody said that that mathematical model is a mathematical model of the weather on the planet Earth, then that would be false. So the claim is another abstraction. So the proposition would be something like the real world, the real physical world, consists of fields and particles that obey these equations and then some equations. And then that abstraction would have made a claim about the real world. ### Jake Orthwein 00:39:22 - 00:40:04 But doesn't that like threaten a kind of infinite recursion there where it's never actually getting explained how it is that say the referent of particles picks out certain things in the world and not others? I just lost David's face on the screen there. I'm still here. Yeah. So the question is like, so it's not so much whether this description of particles is true of the world. It's what does it mean to pick out some subset of the world and designate particles and therefore have this reference relationship between- ### David Deutsch 00:40:04 - 00:41:45 Part of the implication of this proposition that I'm imagining is that there is a physically real world. So that's one thing it would have to imply. And then it would say that in this physical real world, there are things like electrons and then so on. And they obey these equations. Now it could be that that still doesn't say what distinguishes the physically real world from anything else. And it doesn't explain why there is one and only one of those. And there could be none of those, or there could be three of those or whatever. But that's just a consequence of the fact that I can't imagine this perfectly exact proposition. It doesn't say that in the world of abstractions, there isn't a proposition about the world which is capable of being true or false. And if you think of the true one, then there is also just not that which is definitely a false one, though it's not an explanation. Because as I'm always saying, the negation of an explanation is never an explanation. But the proposition which is an explanation could be true. It might not be the whole truth about the world. It is just talking about the standard model in the world. But that could be true. And if it claims that it is true, then it's a claim about the world, including a claim that there is one and only one world and physical world. ### Jake Orthwein 00:41:45 - 00:42:54 I mean, so I just had sort of one more one more related question. So I guess it's not that there is a world that seems problematic to me, but the division of that into an ontology and kind of how you carve the joints of that ontology. And if you think about like a natural language statement like this is a dog, the reference relationship there could be accomplished just by appealing to the context. So if I communicate this is a dog and you and I are in the same room and we're having the same kind of percept of there being a dog there, then the reference of this is just going to get worked out automatically by the context that we share. But when we're talking about the way reference relationships get determined between abstractions and the world, I have no idea how that would be accomplished. And then I also wonder if we stay in the same relationship to the abstractions as we stand to the world, which is to say we don't have access to them, why introduce the idea of the abstractions and not just talk about an error prone contextual problem solving relationship to the world. ### David Deutsch 00:42:54 - 00:44:20 So in the sentence this is a dog, the word this is indexical, it gets its meaning from the context. The proposition that refers to doesn't have a physical context. So it would have to explain what this is. It would have to say in the physical world there is a planet with such and such characteristics and at such and such a time defined by these physical characteristics there's a person sitting in a room with an animal which is in fact a dog and so on. But it would say all that with perfect precision. So it couldn't say anything indexical, that's quite right. But I think the other part of your hesitation I think I disagree with. You seem to be assuming that abstractions inherently must refer to other abstractions. They can't get out of the world of abstractions. But I think that is not so. I've just given an example of something. If it says there is in physical reality, there is such a thing as physical reality, then it is saying, I mean it might be false, but it's saying something that isn't referring to just abstractions. ### Jake Orthwein 00:44:21 - 00:44:49 Yeah, no, it's not that I think that the abstractions can't get outside of abstractions. I guess when you say there is a dog, my question is what does it mean for that piece of the abstraction to correspond to some particular thing in physical reality? So it's not whether there's physical reality at all. Whether physical reality comes divided into things like dogs or cups or whatever other kind of everyday scale. ### David Deutsch 00:44:49 - 00:44:54 Well, if it doesn't, then the proposition would be false. ### Jake Orthwein 00:44:56 - 00:45:12 But then you seem to be taking this reference relationship and bringing it back into this truth relationship. So is everything about whether a proposition refers to the world subsumed by whether it finally is true? ### David Deutsch 00:45:12 - 00:45:17 No, because it could be asserting something false about the world. ### Jake Orthwein 00:45:18 - 00:45:31 But okay, but so then I guess, but if to say that if dog doesn't pick out anything in the world, it's not true and that's why it doesn't refer to the world. ### David Deutsch 00:45:31 - 00:46:42 It's not dog that doesn't. So in my story, it started off by saying there is a real physical world in that world. There was a big bang in the big bang. There was a star, which we shall call the sun, which and so on. And in each case, it gives enough context within the thing is referring to define it uniquely and perfectly. Now, if at any point that doesn't correspond to reality, then the proposition is false. It's still asserting something. It could say that there is this planet that's loose without a star. And in that there's a person called David Deutsch who's referring to a now as soon as it has said that it is false, but it's still it's still an assertion. It's still a in my imagination, a perfectly precise meaningful assertion. It's an assertion about something which logically could be like that, but in fact isn't. ### Jake Orthwein 00:46:46 - 00:47:00 So if I talk about the sun revolves around the earth, the sun has a reference in physical reality, but that statement about the sun would be false. Yes. But I guess ### David Deutsch 00:47:02 - 00:47:32 Independent of whether that statement is true or false, what does it mean for the sun in that statement to refer to the thing in physical reality? So like what does it mean to pick out a thing in physical reality for the abstraction to refer to? The trick I thought of and there are probably many other tricks is to first refer to the whole of physical reality, and then define unambiguously various bits of it until you zoom in on the one you want to talk about. ### Jake Orthwein 00:47:33 - 00:47:41 So in this world of abstractions, something like a cup gets built up from the whole of physical reality all the way up? ### David Deutsch 00:47:41 - 00:47:44 Yeah, that's one way to do it. ### Jake Orthwein 00:47:44 - 00:47:45 Okay. Okay, interesting. Thank you. ### Sam Kuypers 00:47:45 - 00:47:55 Might be a more efficient way. Okay, then I think Toby is next. Toby, go ahead. ### Toby 00:47:58 - 00:48:43 Yes, in your book, I think you wrote that there's only a finite number of abstractions that could apply to the physical world, namely the computable abstractions. The countable number, yeah. The countable, yeah. So is it possible if there is a finite number of abstractions that could apply to physical theories or unique physical theories that we could rescue Popper's theory of truth-likeness so that we can get close to the truth because there's only a finite number of different physical theories we could discover? Yeah, well actually I think there's an infinite ### David Deutsch 00:48:43 - 00:50:44 Number of physical theories. It's just countably infinite rather than finite unless you are thinking that a finite regional universe can only contain finitely many distinct states, which might be the case, you know, from the Bekenstein bound and so on. So yes, but I think even then it would be pointless to resurrect Popper's notion of truth-likeness because the fact that, so this would allow you to sort of say whether two theories are lexicographically close to each other in the dictionary of all possible statements, but that's not what Popper meant by being close. He meant the set of all implications of the one is somehow close to the set of all implications of the other. I forget how it goes. It's the true implications of one other than tautologies, you know, he was making it up in that kind of way. That would still be an infinite number, and I think it would still be infinitely ambiguous. It would depend on what your purpose was in comparing these two theories. One of them might be closer to the kind of truth you want to talk about, and the other one might be close to the kind of truth that someone else wants to talk about. So, you know, for example, there's the kind of truth that leads to accurate predictions, and then there's the kind of truth that leads to better future theories. So why bother? I think that Popper in the end basically said why bother as well. ### Toby 00:50:45 - 00:51:35 What I had in mind was, I've noticed with theories as they've gone through time, they changed the kind of invariant symmetry. So we had Galilean invariance, and then we had Lorentz invariance. I was wondering if in that case, if we were seeking hard-to-vary-ness in theories, whether that process, whether there, you know, if there's a finite, perhaps there is a finite number of those different unique variant mathematical structures, which could apply to our universe. But that was where I was kind of basing that idea from. Well, so first of all, if there was just a finite number, but it was 10 to the 500, ... ### David Deutsch 00:51:36 - 00:52:31 We wouldn't be much better off. So if there was a finite number, and some people think that there's, eventually there will be a single mathematical object, which is the only reasonable one to theorize corresponds with the physical world. And I don't think that would be the end of the story either, because there'd always be the problem of why is that physical object, why is that, sorry, abstract object physically instantiated and not some other one? It couldn't itself contain the explanation of that. Yeah, I see what you mean there. Yeah. Well, thank you. Then I kind of have a, ... ### Sam Kuypers 00:52:31 - 00:53:04 Because Toby mentioned Popper's theory of truth likeness, do you think that with this theory of correspondence to truth, that we can still talk about theories containing more truth over time? So I know that this is slightly different from the problem you're trying to address, and I'm kind of drawing it back to this conversation we had with Danny Frederick on the same topic, or on a related topic. And yeah, do you think that this calls ### David Deutsch 00:53:04 - 00:55:44 Anything about it? So first of all, my view is that it's, in some cases, you can say that one theory is unambiguously better than another theory, because the set of true implications of one of them includes the set of true implications of the other, and vice versa, the set of false implications is contained in the set of false implications. But that's not always the case, and in that case, the set of true and false propositions just overlap. But if you think of it not in terms of truth, but in terms of knowledge, then when we have eliminated some errors, and we hope not introduced other errors, then we have unambiguously made progress, regardless of what the true implications are of the relevant theories. When we have successfully made a vaccine that cures the disease better than all previous medicines, then we have made progress. And the question of truth doesn't really, we don't really need to measure how much truth it has. It might have been built on a thin theory of RNA, which is overturned next week, but where the overturning doesn't actually invalidate the explanations that led to the vaccine. So in that case, inventing the vaccine was genuine progress, genuine growth of knowledge, even though it used a theory that was worse than the previous theory. I mean, maybe that's a bad example, because these things have lots of different theories associated with them. But you see what I mean? I mean, science is about problem solving, so is life. And with problems, what we want to do is eliminate errors. If we can eliminate some errors, it doesn't matter how true the theory is. ### Sam Kuypers 00:55:44 - 00:57:29 Yes. Yeah, I think that's a very nice reply. And I also have what is kind of a devil's advocate criticism of your theory about truth. We say that we fallibly guess that there is this correspondence that we, for example, this is a dog corresponds to there being a dog on the page. And I think this is what Charles was alluding to. There are many cases where there is a lot of ambiguity and sometimes paradoxes that arise when we try to write down a statement. There's Berry's paradox, where you say something like, let me look it up here, it's something like the smallest positive integer not definable in under six letters, which is itself a description of that integer. And so you have this kind of self-referential paradox where the integer isn't well defined. And initially, that seems to be a perfectly well-defined integer. I think when I first read that sentence, it goes, oh yeah, that must be an integer that exists. But in fact, it doesn't. And there is a paradox that arises. How do we know that this isn't always the case, that there aren't many of these things plaguing our statements, that our statements are much too vague to ever reach out into the abstractions? ### David Deutsch 00:57:29 - 00:58:21 Well, again, we can't be sure. And if the arithmetic of the integers really is inconsistent, then we're talking nonsense most of the time. At least we're talking nonsense in the sense of logical implications of what we say, but not in the sense of problem solving. All our theories are false. That doesn't mean they don't contain knowledge. And a theory such as... oops, why does it keep doing that? Can you see the dog again? Yeah, we can see the dog again. Weird. Yes, sorry, lost my train of thought. ### Sam Kuypers 00:58:21 - 00:58:30 Yes, I think in a way, I was just re-asking the question I asked initially. And I just liked the example of Berry's paradox. ### David Deutsch 00:58:31 - 00:59:50 Oh, yes. So that's one of many ambiguities that you can accidentally slip in a sentence from the meta-language and mistake it for a sentence from the language, because we use English for both. So it's an understandable mistake to make. So when you say the least integer not definable, you should be saying definable within what language and what axioms, rather than just definable. Definable is a meaningless concept without saying what axioms you're defining it and what language in what you're defining it in. But that's, as you say, how do we know that there aren't infinitely many ambiguities like that, which render meaningless everything we say? Well, there could be. There could be. But we have a good explanation to the effect that we are in fact eliminating errors in our ideas, even if they're inconsistent. We're still eliminating errors from them. Yes. And also, as I said, it was kind of a devil's ### Sam Kuypers 00:59:50 - 01:00:02 Advocate criticism, because of course Berry's paradox is a very specific paradox. And we discovered it because other sentences aren't like Berry's paradox. Right. Yes. But I took you to ... ### David Deutsch 01:00:02 - 01:00:16 Mean that could arise and creep up on us. And there could be things that we don't know about that could also creep up on us. Yeah, exactly. We still like we have discovered a particular error ### Sam Kuypers 01:00:17 - 01:00:46 In various paradoxes. And whenever those errors arise, we tend to notice them and correct them and then go on to the next thing, which is why we learn about paradoxes like Berry's paradox. So yeah, there's more questions in the chat. I see Danny O'Regan. Go ahead. Ask your question if you want. Otherwise, Teknu. Hi. ### Teknu 01:00:46 - 01:01:31 I have a question about mathematical truth. I mean, some more technical question. You mentioned earlier the P equals NP problem, the possibility that this might be undecidable at some point. But leaving aside our abilities to settle those questions or not, consider the continuum hypothesis, which we know from the joint work of Gödel and Cohen that is undecidable from Zermelo-Fraenkel set theory with Axiom of Choice. I mean, that's a perfectly well-formed mathematical statement. Do you think that it expresses a proposition which is either true or false despite being undecidable because there are a lot of mathematical philosophers which think that this is just an indeterminate mathematical statement? ### David Deutsch 01:01:32 - 01:02:08 Yes. So I disagree with those philosophers of mathematics. I think that a perfectly well-formed mathematical proposition is either true or false independently of whether it is decidable or not. And decidable is in any case a matter of physics. So it seems to me ridiculous to base a theory of mathematical abstractions on what physics does or does not happen to be able to model. Well, I mean, I'm not sure whether set theory is really about physics because it ... ### Teknu 01:02:08 - 01:02:13 Postulates a lot of infinities that go beyond anything that physics might study. Oh, that ... ### David Deutsch 01:02:13 - 01:03:45 Doesn't matter. It's not the sets that have to be finite. It's the method of proof. So it is that mathematics assumes that a proof is a finite sequence of propositions, each of which follows from the previous ones by rules of inference, which are also finite. They're finitely many of them. They're finitely long and so on. And the proof is a finite one of those. And finite here just means can be instantiated in a physical object. It's perfectly possible, logically possible, that physics is different from the way we think it is and that the rules of inference are really either more extensive than we think or less extensive. And it could be that the continuum hypothesis could be added as an axiom and actually be true of something such as the infinite things that we want to talk about. P equals NP is maybe a better example because doesn't the continuum hypothesis thing rest on the fact that there could be models in which it's true and models in which it isn't true. ### Teknu 01:03:46 - 01:03:49 Yeah, I mean, Gödel proved one side and Cohen proved another side. ### David Deutsch 01:03:50 - 01:04:15 Right. But of course, those proofs are not final. There could be mistakes found in them. They are definitely ambiguous. So the ambiguity could be resolved one way or another. And it could be that our notion of proof, our notion of infinite, our notion of sets will be changed again, just as they have been changed in the past. ### Teknu 01:04:18 - 01:04:28 Well, I'm not sure how this I mean, assuming they didn't do mistakes in the proof, they are mathematical theorems. So I would that deal with perfectly precise notions. So I don't ### David Deutsch 01:04:28 - 01:04:47 Think that they are mathematical theorems given a certain set of rules of inference. But those rules of inference cannot be proved to be true. They might be false. They are just conjectures. And there might come a time when we conjecture different rules of inference are valid. ### Teknu 01:04:47 - 01:05:28 Right. And the second thing I wanted to ask that is similar to this one is how do you think about paradoxical sentences like the liar sentence, which asserts its own falsity? I mean, perhaps you might say that this is the object language, meta language error. But what would you say if, you know, you have what's known as liar cycles, and I say that whatever Professor Deutsch says is false, and you say that whatever I say is true. So you don't have this hierarchy, sorry, hierarchy levels, but it's just a cyclic clash, which cannot be so easily solved by an object language. ### David Deutsch 01:05:29 - 01:05:47 Yes. So if we jointly say things, which refer to each other, and which lead to a contradiction, then there is no proposition corresponding to those. Right. Proposition has to be either true or false. ### Teknu 01:05:50 - 01:06:15 Yeah, I'm thinking that if you'd say that about the liar sentence, which doesn't have the cycle, then perhaps you would get this sort of revenge paradox. And you say, well, this is kind of actually what it says, consider the sentence, the sentence does not express a true proposition. And if you say that this does not express a proposition that is either true or false, then in particular is not true. So you basically get it back. ### David Deutsch 01:06:16 - 01:06:39 Yes. So proposition also has to be perfectly precise and unambiguous. So I think those, by the way, I think that particular one is a language meta language error. Yeah, I know. I guess you can have it for the cycles back, but it's more explicit if you Okay, yeah. Well, if something doesn't make sense, it's not a proposition. ### Sam Kuypers 01:06:42 - 01:06:46 Okay. But propositions can be true or false. ### David Deutsch 01:06:47 - 01:06:48 Yes, must be. Yeah. ### Sam Kuypers 01:06:53 - 01:06:56 Okay, then we have another question by Podge. ### Podge 01:06:58 - 01:08:16 Thanks a lot for the talk, David. It's very, very interesting. I'm not sure if this will be a question, but I'm trying to wrap my head around the kind of three kind of levels, let's say of that you have a statement, which corresponds to abstract propositions as a kind of intermediary, you could say. So let's say if the statement refers to the physical world, then there will be an abstract proposition, which will correspond to the physical world in some way. And I guess my question is, previously, I would have thought of all. So I guess I'm thinking about like, whether all abstract propositions are absolutely necessarily true. And because statements or are so like some, some of the propositions about the physical world say will be contingent. Their truths will be contingent on the physical world. And I'm not sure if there's a solid question here, but I thought maybe you could just comment on that. Well, the, so the statements are ... ### David Deutsch 01:08:16 - 01:10:21 Always going to be vague. And yes, they're contingent on the physical world, and their meaning is vague. And they might even be somewhat contradictory. But we are guessing that they correspond to sorry, no, I shouldn't use the word correspond in this context. We're guessing that there is a proposition that this statement is an approximation to, which is good enough in the context of the problem that we're solving. And what we're guessing there, and then we're guessing that the proposition is true as well. What we're guessing is that this exact thing, the proposition corresponds exactly to this other exact thing, the physical world. We wanted to say something about the physical world, but that's the only way we can do it via statements, which represent propositions, which are guesses about propositions, which then say something about the physical world. Usually, when we aren't interested in talking about truth, when we're only interested in talking about the world, we can do our usual thing of talking directly about the world and saying things like dogs have four legs. But it's only when somebody asks, what would it mean for that to be false? What does it mean for that to be true? What does it mean for it to be approximately true? What are you doing when you try and make it more precise by saying canis familiaris instead of dog? And so on. Then I think you're immediately forced to talk about the third side of that, third vertex of that triangle as well and say what we mean about it being true is not that the statement is true, it's that we're guessing that there's a proposition there that is true. ### Podge 01:10:22 - 01:11:38 Okay, okay. My previous kind of conception of this from reading your own work, I'm not sure if this is exactly your idea, but it's something I've gathered from reading Fabric of Reality, for example, and Beginning of Infinity was that. To say that a statement, a physical object of a statement contains truth means that the knowledge content, the information instantiated within the sound, let's say, that there's a physical, I think you referred to this as a self-similarity within the physical world or there's one part of the physical world that's analogous in some ways to another. So within this conception of, and that's previously what I thought the idea of truth was as well, but you're saying that it would actually be more that there's an abstract proposition which is in this platonic realm that's kind of required to stand between those or does that make sense? ### David Deutsch 01:11:38 - 01:12:23 I can't remember whether I said in either of my books that this sort of correspondence you refer to is truth, that's what it means for a statement to be true. I think I may have said it's what it means for it to contain knowledge. Okay, okay. And that I would stick to now. But I do think that I was a bit confused about truth in both of my books. So whatever I said about truth has to be upgraded with this new theory. That is assuming that there isn't some flaw in it. I'm hoping that you guys will find the flaw in time for me to not put it into my next book. ### Podge 01:12:23 - 01:12:30 Yeah, I certainly haven't found that. But thanks a lot for the talk and for answering the question. ### Sam Kuypers 01:12:30 - 01:12:38 Yeah, thanks for your question. Then I see Danny has a question. Danny O'Regan, go ahead. ### Danny O'Regan 01:12:39 - 01:13:59 Hi, can you hear me now? I seem to have very badly timed technical issues there the last time. I'm sorry to pause. This is less of a question and I'm just kind of hoping you can clear up some stuff for me to make sure that I'm following. So we have reality and reality is perfectly precise and it is the way it is. And then you have this world of abstractions which include propositions and they are perfectly precise as well. And that is what allows things like propositions to either be true or false. It's the fact that they have this perfect precision. Yes. And then we have the statements that we can make. So when we conjecture things, we can only ever conjecture statements and then there are propositions trying to be captured in those statements. And when you said near the start, you said we are fallibilists, so we want to make progress in our ideas. Is that about making progress in better capturing the propositions with our statements or is it making progress in the sense that you're ruling out false propositions? Let's say. Okay. ### David Deutsch 01:13:59 - 01:14:38 We make errors everywhere. So when we try and theorize about dogs, whether we write about dogs is one thing. Whether we write about the abstract proposition through which we're talking about dogs, like the canis familiaris sort of thing, whether we write that is a good way of being more precise about dogs. That's another thing that we can be wrong about. And in general, we are wrong and vague. ### Danny O'Regan 01:14:38 - 01:14:47 So we fallibly try to guess or try to represent fallible propositions about the world. ### David Deutsch 01:14:47 - 01:15:18 Yes, that I'm afraid. Putting it that way, that sounds a bit labored, doesn't it? It doesn't sound like God's truth. No, I can't see any way of avoiding it at the moment because of this fundamental thing that we can't say perfectly accurate things and but the world is perfectly accurate. So how can one correspond to the other? So I think this is the only possible way. ### Danny O'Regan 01:15:18 - 01:15:40 And very, very quickly. So are you saying that it's in principle impossible for a statement to ever perfectly capture a proposition? And that's because of the inherent vagueness and imprecision that's unavoidable in these statements? ### David Deutsch 01:15:40 - 01:15:53 Yes. I think it's in principle impossible. So Popper quotes Xenophanes saying, even if by chance he were to utter the final truth, he would himself not know it. I think that's actually, strictly speaking, false. ### Danny O'Regan 01:15:53 - 01:16:00 Yes, that was going to be my thing. Right. Okay, that's fine. That's fine. Thank you. ### Sam Kuypers 01:16:02 - 01:16:13 Does it also mean that there is more progress possible than Popper imagined? Because we can be even more wrong than Popper imagined we could be in some sense. Because Popper did think we could. ### David Deutsch 01:16:13 - 01:16:15 Good point. Yeah. ### Sam Kuypers 01:16:15 - 01:16:47 Yeah, I think that's true. Nice. Then just so people know, I think we have roughly another 10 minutes and then we will end the event. So we're approaching final questions, but not yet. We're not yet there. I see there are more people in the chat who have a raised hand. Ernst, would you like to ask a question? Yeah. Thank you. ### Ernst 01:16:49 - 01:17:36 So my question is only tangentially related to this theory. So it's about how to think about rational action in the face of ignorance. Now in this, during last year and so on, there was a lot of ignorance and a lot of actions and a lot of mistakes. And then Nassim Taleb, I don't know how much you know about him, but he is a sort of admirer of Popper. But he takes, in my understanding of him, he takes the Popper uncertainty to mean something mathematical. Whereas, and to translate it into some kind of probabilities. ### David Deutsch 01:17:36 - 01:17:40 Whereas that would be a mistake. ### Ernst 01:17:40 - 01:18:15 Yeah, that's a mistake. So, but his argument about, okay, when there is uncertainty, like, do I know if this pilot is a trained pilot or not? If that uncertainty exists, then you shouldn't get into the plane. But of course, we're always uncertain. So that can't be the explanation. But how do you think about this? How to think about actions when we don't know what is true? ### David Deutsch 01:18:17 - 01:19:57 I'm tempted to say, once you stop thinking in terms of probability, all the problems go away. Okay. You have a certain explanatory theory about how this person in the uniform that's getting into the cockpit of the plane got there. And the reason that you adopt that theory and act in exactly the same way that you would act if you were certain that it was true, which you can't be, but it is that all the other explanations, it's not that you can rule out all the other explanations, but all the other explanations that you can't rule out are bad explanations. They are all of the form. Well, it could be that the real pilot was mugged on the way here. And this guy is actually a fantasist who thinks he's a pilot, but will actually crash the plane as soon as it takes off. Now, the thing is, I just made that up. I could make up lots of stories, some of which would mean that you were even safer than you thought. And some of which would be even more dangerous than that. And they'd all be bad explanations because they can all be just made up at will, any number of them. You have to reject all explanations like that, not because they're unlikely, but because the practice of adopting one of them in preference to the others is irrational. So it's good explanations all the way down. ### Ernst 01:19:57 - 01:20:00 So then when we don't have good explanations? ### David Deutsch 01:20:01 - 01:23:55 Well, if we don't have good explanations, then we have inadequate explanations. If we have only bad explanations, then we don't know anything. We're just in trouble. It's like saying, I'm either going to kill you or not, depending on whether you say A or B. Now say something. Well, if you don't know, you don't know. There isn't a right thing to do. But the cases you're talking about, like decisions about the pandemic, are cases where we have some explanations that aren't good enough in the sense that they are the only good explanation left, that the others can all be ruled out by one argument or another, or that the rival explanations are all bad. But we have two or three or a hundred fairly good explanations, but the others can't be ruled out. Well, in that case, there is more than one reasonable way to behave. Different people will see this spectrum of a hundred decent, but by no means good enough explanations. And their background knowledge and other theories will select between them. That is, we will differ as to how good the good explanations are. We might agree on what's the bad explanation, but we may not agree on how good the good explanation is. And then there are other considerations like we mustn't make choices that will prevent us from learning things. But of course, we don't want to use that as our only criterion, because if we learn something by wiping out half the human race, yes, okay, the other half will be well off then, but the half that are killed will still be killed. So that's just one of the considerations that come into the situation that there's more than one reasonable choice. And I've been tweeting a lot about choices in the pandemic situation. And quite often the point I'm trying to make is that people are getting very upset and enraged with each other, because they think that the other person's explanation isn't as good as theirs, but they don't have an actual scientific argument or scientific evidence or watertight argument that says that. They just think it's true for some reason or another. Sometimes people think that bad explanations are actually good, but that's not what I'm talking about. I'm talking about disputes about rival good explanations, like masks work. How well do masks work? Now, there's really no evidence about how well masks work. It stands to reason that masks work up to a point, but then there are issues like, well, yes, but if the government says that people should wear masks, then people will get correspondingly more lax in their other distancing behavior, and the net effect will be worse. And there is no way that science can't answer that question just yet, and it won't be able to answer it in time, but reasonable people can disagree, and that's what we have to do. We have to disagree. ### Ernst 01:23:58 - 01:24:00 All right. Thank you very much. ### Sam Kuypers 01:24:00 - 01:24:05 Thank you for your question. And then we have Mike Skiba. ### Mike Skiba 01:24:06 - 01:24:19 Go ahead. All right. Hi, David. Thank you, Sam. So yeah, early on the discussion, you mentioned P and NP, and you described P as like a propositional variable, which, ... ### Sam Kuypers 01:24:19 - 01:24:20 Yeah, I think ### Mike Skiba 01:24:20 - 01:24:32 Is an interesting concept. And I was wondering- Sorry, that was a different P. Oh, sorry, a different P in terms of the NP? Yeah, yeah. Or P and not P, were you saying? We still have it all. ### David Deutsch 01:24:33 - 01:24:39 That's here in this, that's not P and NP. That's just P, a propositional variable. ### Mike Skiba 01:24:40 - 01:24:41 Okay. ### David Deutsch 01:24:41 - 01:24:47 Yes. Yeah, my mistake. And yeah, I guess kind of seasoned on that propositional variable idea. ### Mike Skiba 01:24:48 - 01:25:07 I was wondering if, based on kind of the centrality of the laws of physics in your worldview, and assuming that there is not really a finality that we can speak to of the laws of physics, if you would describe them as a propositional variable, kind of in this sense of statements and abstractions. I was wondering if there was a link potentially there. So- ... ### David Deutsch 01:25:07 - 01:26:34 Yeah, so I tend to regard statements about the world and statements about abstractions uniformly. We're fallible in both cases. We can make mistakes. We are inherently imprecise and all that stuff, but there's no limit to how much knowledge we can know about. So P versus NP thing is an example of an actual proposition, which could- This P, the propositional variable, could be set equal to P, the actual proposition about computability. So yeah, I view them all as the same kind of thing. We can guess about mathematical objects. We can guess about sets. We can guess about the physical world. We can guess about morality. We can guess about beauty and all those things we can gain knowledge about. We gain it in the same way. Nothing is ever certain, including the most mathematical things and including propositions about necessary truths. Our knowledge of them is always fallible as well. ### Mike Skiba 01:26:36 - 01:26:47 No, that's helpful. Yeah, just because knowing the laws of physics and what they mean in your momentous dichotomy, just that that also qualifies in that range too. So thank you. ### Sam Kuypers 01:26:47 - 01:28:01 Great. Okay, then I have a final question before we end the talk. So in your construction, there's really two worlds. There's the world- Well, it seems like there's three worlds. There's the world of statements, propositions, and reality. Yeah, statements are part of physical reality. Yes, and we are guessing at both of them in a sense. We're guessing at the statements and we're guessing at reality through guessing at statements. And so part of what we do when we try to learn about something is being as precise as necessary. Do you think that this means that paradoxes are problems that can be resolved? They're problems with how we think about the abstraction. So if someone utters the liar's paradox, they're being imprecise, but they're meaning something real, and we can make progress in our thinking about the propositions as well. Yeah, I think it's very rare for people to intentionally talk nonsense. ### David Deutsch 01:28:02 - 01:28:08 No doubt it could be done and no doubt it is done in some circumstances, but basically ### Sam Kuypers 01:28:08 - 01:29:05 When people talk nonsense, it's because they really mean something. And that nonsense is actually an attempt to understand the world or to understand an abstraction or whatever. And at the other end of the scale, as I keep saying, we might all be talking nonsense if things like the arithmetical integers are inconsistent. So yeah, is that what you meant? I think I meant that there's a sense in which we can resolve a paradox. If we ever stumble upon a paradox in formulating physics or something, then there is a way of being more precise and ... ### David Deutsch 01:29:07 - 01:29:16 Resolving the issue of guessing at the abstractions. Accidentally hitting on a paradox is just one of the many ways we can be mistaken. ### Sam Kuypers 01:29:16 - 01:29:23 Right, great. Yeah, with that, thanks so much for joining us. This was great. Thanks everyone for the question. ### David Deutsch 01:29:23 - 01:29:25 Thanks for having me. ### Sam Kuypers 01:29:25 - 01:29:29 Yeah, okay. Thanks so much and see you at the next event. Bye-bye. ### David Deutsch 01:29:43 - 01:29:44 You ...