Episode 91: The Critical Rationalist Case For Induction!?

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Transcript

[00:00:07]  Blue: Hello out there. This week Bruce takes a deep dive into induction. Is it really so bad? Does induction make sense from a critical rationalist perspective? Are there perhaps different kinds of induction? I found it pretty interesting and I hope someone out there agrees. Welcome to Thuram Anything Podcast! Hey Peter! Hello Bruce, how are you doing?

[00:00:31]  Red: Good! We are going to today talk about the problem of induction or maybe the lack of problem of induction would be a better term for it. But we’re taking this from Hopper’s essay on how to… what was actually… I can’t remember the name of the essay now, it’s in my notes here somewhere.

[00:00:54]  Blue: The status of science and of metaphysics.

[00:00:58]  Red: Excellent! And the

[00:00:59]  Blue: first part was called Kant and the logic of experience. They are two, I guess, radio addresses. I mean it seems like he was basically just reading an essay on the radio, but that’s what it said.

[00:01:14]  Red: So on this podcast I have multiple times posed the question several times now, what is the difference between a good metaphysical explanation and a bad explanation? And while I’ve hinted at an answer to that question, I’ve never actually come out and answered the question. And the typical answer from Deutschians that I get is a bad explanation is easy to vary and a good explanation, even if it’s metaphysical, is hard to vary. But in episode 81 of this podcast, Easy to Varyness versus Ad Hocness, I pointed out a problem with this answer, namely that no one ever seems to agree what counts as easy to vary versus hard to vary. It seems to mostly just mean I personally like this theory, that equals therefore it is hard to vary, and or I personally dislike this theory and that’s equal to easy to vary. I’ve received some feedback on this problem and the typical answer seems to be, well, I’d not expect everyone to agree on everything. Or, well, some criticisms will land for you and others won’t and may differ by person. But these answers are themselves easy to vary. I literally could give this answer no matter what the theory is involved, and it would always somehow be true. So I’ve hinted at a possibly better answer to this based on Popper’s Ratchet. And basically, I haven’t said this previously in the podcast, but basically when it comes to Popper’s epistemology, it’s not the speed, it’s the acceleration that matters. What do I mean by that?

[00:02:47]  Red: What I mean by that is that how empirical, explanatory, or testable theory is doesn’t matter so much as that you follow the no ad hoc rule and choose to formulate all your theories, including auxiliary theories meant to save a theory from a potential refutation, as having independently testable consequences. I called this idea Popper’s Ratchet, i.e. only solve your problems by increasing the empirical content of your theories. So now Brett Hall’s theory of intelligence is highly explanatory. It explains a lot. It explains everything in intelligence in terms of that we value some knowledge more than others. But the defenders deny it is testable and claim that it’s just a metaphysical theory. Now, by comparison, what they see as their competitor IQ theory is not very explanatory, but it is testable and in fact has survived sincere attempts to refute it. So IQ theory will, according to Popper’s Ratchet, over time grow into something increasingly correct as Popper’s Ratchet gets applied to it because it allows itself to make risky and bold predictions that help us find the errors within it. The end result, over time, could end up looking nothing like the original theory. A great example of this is atomic theory that started way back in time, Aristotle’s era, and the theory today looks zero like the original theory. And this is the beauty of Popper’s Ratchet, is that you keep reformulating the theory in such a way that it can be error corrected and you’re not so worried about whether the original theory was correct or not.

[00:04:31]  Red: Now, Brett’s theory of intelligence could do the same, and this is what I’ve argued, but currently the proponents of the theory aren’t interested in error correcting the theory, so it will stagnate until someone comes along and starts to apply Popper’s Ratchet to it. Basically, you have to figure out how to make it an empirical theory. I’ve pointed out examples of how you could do that. It’s not even that hard, okay? But this is what I mean by it’s not the speed, it’s the acceleration. So long as you keep intentionally reformulating your theories to be empirically testable and never ad hoc save your theories, your theories will keep improving their explanatory content and their predictive power. Now, Popper’s Ratchet explains why a low explanatory theory, such as oranges stop scurvy, or if you prefer smoking causes cancer, are valid scientific theories, while highly explanatory theories like communism, Brett’s theory of intelligence, and some forms of Austrian economics are not valid scientific theories, are instead maybe arguably metaphysical theories. But what we really want to know is not, are they scientific theories or metaphysical theories, but are they good explanations or bad explanations? So how do we tell a good metaphysical theory from a bad explanation? Now, before I try to go on to give my not very good answer to that question, which won’t be in this podcast, I wanted to go over Popper’s own attempt to answer that question from conjectures and refutations chapter eight on the status of scientific of science and metaphysics.

[00:06:06]  Blue: Just to clarify, when I read this essay a couple times, I felt like the main topic was refuting empiricism. Is that a fair, I mean, I felt like it was just checkmate against this idea that our theories come from nature rather than other theories.

[00:06:31]  Red: So that’s interesting because when I read it, I saw it more as refuting induction. Now, of course, there’s a tight tie between those theories to the point where I’m not even sure you can totally tease them apart amongst certain philosophical schools. But I’m actually going to take the stance that he was checkmating against induction.

[00:06:54]  Blue: Just thought I’d throw that out there.

[00:06:56]  Red: Now, this is a big subject. We’re not actually going to in this podcast, even though this is a setup for trying to answer the question, how do you tell a good metaphysical explanation from a bad explanation? We’re going to cover the first half of this essay, which is really this checkmate against induction and what Popper’s argument was.

[00:07:23]  Blue: It’s reasonable to see empiricism and induction as intertwined ideas.

[00:07:30]  Red: And justificationism. Those three are so deeply intertwined that people will often talk about them as if they’re all one thing. And a lot of confusion comes out of that. In fact, that’s one of the things I’m going to talk about is the confusion that comes of trying to intermix ideas together as if they’re all one in this kind of vague model and how it’s actually quite useful to tease them apart and look at them separately. And you can usually make much quicker work of these theories by doing that. So we’re going to be covering the problem of induction today or rather the lack of problem of induction.

[00:08:09]  Blue: Okay.

[00:08:10]  Red: So let’s talk about Popper’s proof that induction is impossible. So Popper questions if science is based on induction. Popper asks if Newton came up with his theory via induction and from page 251 of conjectures and refutations, he says Newton himself asserted that he had rest its functional principles from experience with induction. Newton asserted that the truth of his theory could be logically derived from the truth of certain observation statements. So Popper argues, the assertion is not intuitively credible, not intuitively credible, especially when we compare the character of Newton’s theory with the character of observation statements. He also says it’s historically false and that it’s logically false. That’s on page 251. More specifically, Popper says on page 18 of logic of scientific discovery, in my view, there is no such thing as induction. Now, Deutsch doubles down on this quite a bit. And so I got some great quotes from Deutsch. So in fabric of reality, page 70, he defines induction. So induction, a fictitious process by which general theories are supposed to be obtained from or justified by accumulated observations. And then from fabric of reality, page 61. But if we want to understand the true nature of knowledge and its place in the fabric of reality, we must face up to the fact that inductivism is false, root and branch, no scientific reasoning and indeed no successful reasoning of any kind has ever fitted the inductivist description. That’s on page 61. On page 59, he gives a picture of what he means by the inductivist scheme. And basically it’s four boxes. I’ll just describe it to you. Box one, observations that has an arrow to box two are generalized to form a theory.

[00:10:04]  Red: Box three, then more observations goes to box four, justifies the theory. So inductivism is just basically induction. So in episode 13.5 of this podcast, special edition theory of anything host David Deutsch, David Deutsch doubles down on this idea. And he says somewhere around 42 to 43 minutes, he says the Bayesian picture of science, which is basically inductivism, is just wrong, root and branch, false, root and branch. This idea that induction does not exist. And is written branch wrong is going to become important later. But this is why crit rats have an allergic reaction to any theory that feels even slightly inductive. So I argued in episodes 85 and 86 that crit rats actually got this backwards real phenomenon, such as Hofstadter’s theory from episodes 85 and 86, or for that matter, machine learning can’t be dismissed on the grounds that it is inductive since induction is root and branch wrong and doesn’t exist. Rather, the existence of something that is inductive must either be subsumed into Popper’s epistemology by being able to explain it in terms of his epistemology, or Popper’s epistemology is refuted. So let’s actually now take a look at Popper’s proof that induction does not exist first. So this is discussing the character of Newton’s theory. So he says on page 251, to see this we must merely have to that Newton’s theory doesn’t, that it doesn’t match induction. He says to see this we must merely remember how utterly Newtonian theory differs from any observation statement. Observation statements are always inexact, while the theory makes absolute exact assertions. It was one of the triumphs of Newtonian theory that it stood up to subsequent observations with precision that went far beyond what could be obtained in Newton’s own time.

[00:12:08]  Red: This is from page 251. In other words, this is the theory that has reach. Now on page 252 he says, how could the absolutely precise statements of the theory be logically derived from less exact or inexact ones? Then he goes on to say, each observed situation is always a highly specific situation. By comparison Newton’s theory claims to apply in all possible circumstances. Remarkably, the theory makes assertions about gravitational pressures inside of stars, which obviously we’ve never observed. Observations are always concrete, while theory is abstract. We never, I repeat, never observe anything like Newtonian forces. Admittedly, since forces are so defined, they may be measured by measuring acceleration. We can indeed measure forces. Yet in all of the measurements, without exception, we always presuppose the truth of Newtonian dynamics. Without the prior assumption of a dynamical theory, it is simply impossible to measure forces. Thus, some of the objects of which the theory treats are abstract and unobservable objects. For all these reasons, it is intuitively not credible that the theory could be logically derived from observation, page 252. Then proper shows that the precursor to Newtonian physics was the theory of Copernicus, and that without Copernicus would not have had Newton. So was Copernicus’s theory derived from observations? No, it wasn’t. On the contrary, proper shows that theory was actually derived from false Platonic theories. So on page 253 now, the Sun plays the same role in the realm of visible things in Platonic theories, as does the idea of the good in the realm of ideas. Accordingly, the Sun, which endows visible things with their visibility, vitality, growth, and progress, is the highest in the hierarchy of visible things in nature.

[00:14:00]  Red: Based on this, Plato believed that, if the Sun was to be given right of place, then it was hardly possible for it to revolve around the Earth. We talked about this in a past podcast, the fact that the way we typically try to put Galileo as at odds with science is really a complete misunderstanding of the nature of science as it was understood back then. And then in fact, Galileo’s theories were derived from Copernicus’s theories. They were the same as Copernicus’s theories. He was advancing Copernicus’s theory, which was itself based on Plato’s theories, just a different interpretation of it. So Newtonian physics grew out of Copernicus’s theories, which grew out of not observation, but mythology. Kepler’s laws similarly came out of, this is from page 254, Kepler’s law similarly came out of trying to force fit observation theory to Tycho’s theory that planets followed a circle. So Hopper then argues to page 255, Kant argued that physical experiments are not prior to theories. And then he goes on to say, our reason can understand, sorry, our reason can understand only what it creates according to its own design, that we must compel nature to answer our questions for purely accidental observations made without any plan having been thought out in advance cannot be connected by law, which is what reason is searching for. Now I’m going to repeat part of that again, because it’s going to become very important in a second. For purely accidental observations made without any plan having been thought out in advance cannot be connected by a law. Okay, want to make sure that was emphasized.

[00:15:46]  Red: Hopper then summarizes, Kant shows how well he understood that we must confront nature with hypotheses and demand a reply to our questions, and that lacking such hypotheses, we can only make haphazard observations, which follow no plan and which can therefore never lead to a natural law. I’m going to again repeat that, which follow no plan, the haphazard observations, follow no plan which can therefore never lead to a natural law. Hopper then claims, Kant saw with perfect clarity that the history of science had refuted the Baconian myth that we must begin with observations, begin with observations, in order to derive our theories from them. Hopper then shows that it is all logically impossible anyhow to ever derive generalizations from specific observations. Popper’s proof of this is startlingly simple. Imagine a set of past observations based on some law, maybe observations of an eclipse, that’s the example he uses. Clearly, this set of true past observations must be logically consistent, since they actually happened. Now, say we conjoin to this set of past observations, a future observation, that an eclipse will happen tomorrow. This clearly doesn’t create any sort of logical contradiction, because those were all observations in the past. Suppose we then conjoin an additional future observation that an eclipse will also happen the day after that. This also clearly doesn’t create any sort of logical contradiction for the very same reason. Yet clearly you can’t really have two eclipses two days in a row. But you really only know that because you have a general theory or explanation of what causes an eclipse. The observations themselves are in no way a logical contradiction. In fact, this is now quote page 257. No logically possible future observation can ever contradict the class of past observations.

[00:17:51]  Red: Popper now clinches his argument that if any future statement B can be conjoined to past observations, then they must be true of any theory that can be derived from those past observations. Thus no future quote, no future observation could possibly contradict Newton’s theory and the past observations if Newton’s theory is in fact derivable from those past observations. Yet clearly when we combine Newton’s theory with those past observations, we can come up with future observations that are logically impossible, such as two eclipse two days in a row. Okay, let me restate that in plain English in case it wasn’t obvious. If what you’re saying is is that the past observations implied or entailed Newton’s theory, then you don’t need Newton’s theory, you should be able to show that those past observations plus the observation statement that will be in eclipse tomorrow and that there will be an eclipse the day after tomorrow, you should be able to just from those observations show that there’s some sort of contradiction. But in fact, there is no contradiction between those observations, nor could there ever be a contradiction between those observations. So clearly when we say that the observation state, the prediction, that there’ll be an eclipse tomorrow and the day after that, those clearly are in contradiction in some way, but only because we know Newton’s theory. If Newton’s theory was really derivable just from those contradict the original observation statements from the past, then you shouldn’t need Newton’s theory to be able to tell that the prediction there will be an eclipse tomorrow and that there will also be an eclipse the day after that.

[00:19:34]  Red: You shouldn’t need Newton’s theory to be able to tell that that those are false statement, one of those must be a false statement. So clearly we are going past well beyond the observation statements, which means, and this is the main argument, that Newton’s theory was never derived from the observation statements to begin with. So popper’s conclusion then, page 257, Newton’s dynamics goes essentially beyond all observations. It is universal, exact and abstract. It arose historically out of myths and we can show by purely logical means that it is not derivable from observation statements. Page 259, Kant’s solution to the problem is well known. He assumed correctly, I think, that the world as we know it is our interpretation of observable facts in the light of theories that we ourselves invent. As Kant puts it, our intellect does not draw its laws from nature but imposes them upon nature. While I regard this formulation of Kant’s as essentially correct, I feel that it is a little too radical and I should therefore like to put it in the following modified form. Our intellect does not draw its laws from nature but tries with varying degrees of success to impose upon nature laws which it freely invents. The difference is this, Kant’s formulation not only implies that our reason attempts to impose laws upon nature but also that it invariably is successful in this. For Kant believed that Newton’s laws were successfully imposed upon nature by us, that we were bound to interpret nature by means of these laws, from which he concluded they must be true a priori. This is how Kant saw these matters and Poincaré saw them in a similar way. Okay, so induction is wrong. All right, Popper has shown induction is wrong.

[00:21:22]  Red: Okay, so what is the problem? Why do people even perceive there to be a problem of induction? So the question whether induction inferences are justified or under what conditions is known as the problem of induction, so that is from logic of scientific discovery page four. Or on objective knowledge page 90, Hume’s problem of induction, it is a problem. It is the problem. How can it be shown that inductive inferences despite being shown to be problematic by Hume are nevertheless valid or can be valid? Note that these quotes from Popper that the main issue with the problem of induction is put in terms of that of justification. But his proof that we just went over is actually about how it’s impossible to induce or generalize solely from observations. Now here’s Deutsch on the problem of induction. For some reason conventional wisdom adheres to a trope called the problem of induction, which asks how and why can induction nevertheless somehow be done yielding justified true beliefs after all, despite being impossible and invalid respectively. That’s from, by the way, the podcast, Why Has AGI Not Been Created Yet, around minute 23. And then he goes on to say, thanks to this trope, every disproof such as that by Popper and David Miller back in 1988, rather than ending inductivism simply causes the mainstream to marvel in even greater awe at the depths of the great problem of induction. That’s around minute 23 also.

[00:22:56]  Blue: Sorry. What podcast is this? Our podcast?

[00:22:59]  Red: No, no. It’s like if you go Google, Why Has AGI Not Been Created Yet, that’s a famous essay that David Deutsch himself put out on YouTube and read it. Okay. So it’s

[00:23:10]  Blue: not actually podcast. It’s just him reading his essay.

[00:23:13]  Red: Yes.

[00:23:13]  Blue: Okay. Just to clarify. Okay.

[00:23:15]  Red: Okay. In fact, you can probably just look this up inside of Why Has AGI Not Been Created Yet and I’m pretty sure there’s a written version of it too out on the internet.

[00:23:23]  Blue: Yeah.

[00:23:25]  Red: Okay. And then in the Popperian podcast, where he was interviewed, Deutsch goes on around minute 24. Deutsch goes on to say, induction just isn’t true. It’s not just that induction is invalid, which is something that has been known since antiquity. But Popper added to this that induction just doesn’t happen. It’s not that we do it, but it’s invalid, but it somehow works. We don’t do it. What we do is we have a theory first and in the case where we’re creating new knowledge, this theory is a conjecture, which is not based on anything. It’s a hoped for solution. Then he goes on in the podcast with where Elyteer interviews David Deutsch around minute 55, which is called Popper’s Problem -Oriented Epistemology. Deutsch says somebody down the street might say that he doesn’t like Black people because Black people commit crimes. And then I could say that that’s wrong, the wrong way of thinking of it. It’s actually poor people who commit crimes. Then he goes on to say, I mean, I don’t believe either of those theories, but I’m just using it as a very simple example. Then he goes on to say, now he thought, his neighbor thought he was inducing this theory because to him, he saw Black people commit crimes. Now, the Black person commits a crime and so on. And to him, he was thinking that he had induced this theory, whereas a different person sees the same data and he sees poor people committing crimes and so on. Both of them have actually just been interpreting the data in light of their preexisting theory and have pretended to themselves.

[00:25:00]  Red: I mean, they don’t know that they’re doing this, but they have reinterpreted the thought process in their own minds as one of extrapolating a theory from data. Actually what they have been doing is interpreting the data in light of a theory and the theory came first. So let’s test what we just read. Here’s the deal. I’m going to test Popper and especially Deutsch’s view. I have a function in mind. Our function is in a stand -in for a law or a theory because it constrains things. I’m going to pick random points on this function. That is to say, I’m going to pick random points but constrained by a law, the function, that can be represented in a straightforward, be represented as this function. So this is analogous to how science works, kind of. I’m going to pick random points from this function, then I’m going to show them to you, Peter. And I want you to do your best to induce or generalize to a function that explained these points. No, this is not a trick question at all. Okay, I did pick the points at random and not in a way to trick you. And to be frank, if you don’t second guess yourself and just go with your gut, you’ll get the right answer because this was never intended as a trick question. But let’s go ahead and see how you do it inducing a general law from observations. Here are the observation points. Can you induce a general law?

[00:26:25]  Blue: Creating a function based on these points and drawing a line through them?

[00:26:30]  Red: So you would draw a line through them?

[00:26:33]  Unknown: Okay,

[00:26:34]  Red: sure. Okay, you just came up with a general law based on only observation statements.

[00:26:41]  Blue: Okay,

[00:26:42]  Red: now here was the actual correct function.

[00:26:45]  Unknown: Okay,

[00:26:45]  Red: okay. You induced the correct law based only on random observation statements. Okay. Because the law was, in fact, just a line. Now, you could have induced this because that would have also covered the same points or you could have induced this. Okay, but you didn’t. You out of an infinity of possible functions that it could have been, you induced the correct one in one try. Okay. And for those at home that couldn’t see the points, I will actually include a link in this podcast so that you can see what it is. But all it really was was points that very clearly formed a line. And then he correctly induced that they formed a line. And the alternatives were big wavy things that went through the points but weren’t a line. He could have induced those but he didn’t. Okay, so here’s the problem. The problem is that no one believes humans don’t induce things or more to the point we do induce things from observations. That’s a fact. You just did. You were easily able to induce a function, a generalization from a set of points. So from an excellent paper by, I cannot pronounce this name, artificial intelligence and popper solution to the problem of induction, he says, hopper maintained that induction plays no role in scientific inquiry, practical action or belief formation processes. Development in artificial intelligence, AI and closely the related fields of investigations such as machine learning have been claimed to undermine this view. So according to Tim Burrini, many machine learning researchers have traditionally seen machine learning as refuting popper’s solution to the problem of induction and thus refuting popper’s epistemology, his theory of knowledge.

[00:28:51]  Red: This is the opposite of the critratch that strangely see popper as refuting machine learning even though it actually works in real life and really can induce things. So who is correct here? I’m going to argue that they both have it wrong. Not Tim Burrini, he’s actually got this right. The people he’s quoting is what I mean. So does the fact that we can induce from observations refute Karl Popper? This ties back to our discussion in episodes 85 and 86 of how Hofstadter’s theories are supposedly inductive. Hofstadter’s theories are called inductive because they are about generalizing from specific observations. But this version of induction, quote induction, lacks any of the problems Popper claimed the theory of induction had. It is not about learning from repetition. It’s not claiming any sort of justification. Hofstadter’s very specific that it’s neither about repetition or justification. It’s often wrong. And it doesn’t even claim to generalize solely from observations, but instead relies on preexisting theories as well as observations. So Hofstadter’s form of induction seems to merely be a word to refer to a general human ability to generalize. Now, nobody doubts that humans can generalize. So this sort of quote induction actually exists.

[00:30:15]  Blue: So as I’m hearing you, it’s kind of almost like a secondary problem of induction. So even though Popper makes a very, at least in my mind, a very strong case against induction, the problem is that a, humans use it every single day in our lives all the time. And it seems to work pretty well for most things. And B, it works in machine learning.

[00:30:44]  Red: Is that fair how I put that? You’re understanding what I’m implying, but I’m about to show that’s all wrong.

[00:30:53]  Blue: Okay. So

[00:30:54]  Red: but I think this is what it’s going on here is I’m trying to help you help everybody understand why people believe induction exists. It’s because it does exist if by induction, you just mean the ability to generalize. What Popper refuted was something different than that. He refuted Baconian induction or logical induction, which is this idea that you can get a general law out of solely observations. And those two are just not the same. Now, here’s the problem. And this is where Popper’s theory is actually quite useful. You can see how the word induction would point to a fuzzy category, which is this vague idea that human beings somehow generalize from observations. That’s not very specific about how. Okay. And that back in antiquity, people noticed human beings generalize from observations, which is true. So they started coming up with ideas that became part of philosophical schools. And these particularly bacon, but I don’t think bacon actually invented any of his ideas. So I think they predate him, but he certainly popularized them, but it included all sorts of additional ideas started getting attached to it, such as that we generalize solely from observations. Okay. That isn’t necessarily part of the fuzzy category, but it is part of Bacon’s theory of induction or that it justifies things that if you have enough repetitions, then you can become relatively certain that you’re correct or something along those lines. Okay. That isn’t necessarily part of the original fuzzy category either, but that did become part of the school of thought around induction. It got tied up to obviously that was how it got tied to justification is even though the original busy concept doesn’t say anything about it justificationism. Likewise, it got tied into empiricism because

[00:32:56]  Red: they started to try to work out, well, how does induction work and how does it justify things? Because now that’s part of what they’re thinking of when they’re thinking of induction, because that’s become part of how they think of it. And they started to work out this theory of, oh, you see, you can trust sense inputs. And that’s how induction actually works. And that’s how it justifies things. And they tried to work out a theory of justification that was part to explain why induction worked. And that became part of this philosophical theory of induction. And yet none of this is part of the original more fuzzy category of the ability generalized. Okay. And in people’s minds, the fuzzy category and the more specific theories are all entangled because of that’s just the way human beings happen to think is in terms of fuzzy categories like this, where we get all these ideas attached. This is where Hofstadter’s theories become very helpful in trying to understand why there’s so much confusion around induction. Okay. So one strategy here is that we could become essentialists and we could insist that the ability to generalize is not induction at all. Okay, this general ability that Hofstadter’s talking about. And thus Hofstadter is simply wrong when he called his theory inductive because he did call it inductive. We could do the same thing for machine learning. We could say machine learning is not inductive. Okay. Where inductive in this case means Bacon’s theory of induction. All right. In fact, Deutsch does say this in some tweets. I’ve got some cool tweets from him. One was induction doesn’t exist. Machine machine learning does exist and is useful, though misleadingly named, misleadingly named.

[00:34:42]  Red: And then in a different quote, different tweet, induction never happens. So what’s called machine learning isn’t induction. Okay. So this is kind of the essentialist approach where we insist on the word induction means the Baconian kind of induction and that’s it. And it doesn’t mean anything else. And if that’s what we mean, then I actually believe Deutsch is correct. Induction does not exist because now we only mean the Baconian kind and machine learning is not inductive as we’re going to see in machine learning is not inductive. Okay. So that is one approach. I think the more correct way is to not be an essentialist and to admit that the word induction has multiple meanings. So the first kind of induction, the kind that Papa refuted, that’s the Baconian induction or probably better named logical induction, or maybe we could call it philosophical induction. Okay. I’m probably going to call it Baconian induction, but it probably the best name, the most accurate name is probably logical induction because it was based on this idea that induction forms some sort of logic that’s extends deductive logic. Okay. And that’s the thing that doesn’t exist. It is the kind of idea that you can generalize from only observations and that the result is justified. That’s what we mean now by Baconian induction. The second kind of induction is just a general term for the act of generalizing with no specifics on how and no claim of justified results. We will call this just for the sake of separating it general induction. Maybe I could have caused it the fuzzy category of induction could have called it that instead.

[00:36:22]  Red: Or if poppers correct, we might just call this kind of induction poppers epistemology, that might be the actual correct thing to call it. Okay. So poppers own epistemology is about how we create generalizations. So technically it is a kind of induction in this fuzzier more general sense. Hopper agrees, he says in objective knowledge page 94, one can of course call induction whatever one likes. One could call my theory of criticism and growth of knowledge, my theory of induction. He then promptly goes on to say, but this is misleading. Don’t do that. So in that paper by Tim Burian or Burini, artificial intelligence and popper solution to the problem of induction, he points out that this very problem, he says, Craig, who is a researcher in in machine learning who’s looking into these same things. He says, was careful to observe that the AI and philosophical communities use the term induction in rather different ways. In fact, Tom Mitchell from the field of machine learning explains this connection between poppers epistemology and induction with a very convincing argument. So let me explain who Tom Mitchell is. There was a textbook called machine learning that was the top textbook of machine learning for a generation ago. In fact, it’s still around when I took machine learning in my graduate program, which was only two or three years ago now. Remember, I went back to school for fun and got a graduate degree in machine learning. Tom Mitchell’s book was the text for two of my classes. So it’s still a popular book. I have been told by Vaden that it’s kind of receding to the background and that Chris Bishop’s book on machine learning is now kind of the standard introductory textbook.

[00:38:09]  Red: I didn’t go that one over that one in school. And you know what? I’m really glad. I Bishop’s book is excellent and it’s probably better than Tom Mitchell’s in terms of actually teaching you modern machine learning techniques probably by far because Mitchell’s book is so old. But Mitchell’s book is deep rooted in epistemology, although he doesn’t call it that because he’s got no study or training in epistemology. He’s trying to work out what machine learning can and can’t do, why it works. And he uses toy examples of machine learning algorithms so that he can work out principles around machine learning. And the book’s very heavy into hack learning, probably approximately correct, which we’ve covered elsewhere in this podcast. So I want to go over Tom Mitchell’s theory of the futility of unbiased learning, aka why Popper is correct, although he doesn’t call that because he doesn’t know who Popper is, aka an explanation of when you can and can’t induce things, aka the kinds of induction that do and don’t exist. Now I’m going to do my best. I’m going over something that’s in a fairly technical machine learning textbook and I don’t have any visuals, but I think I can explain this so that even someone listening can understand the gist of what I’m talking about. I would love to in the future do a podcast where I do a video podcast and I spend a little more time on this and we actually go over the algorithms that he is discussing in detail, program them maybe and really try to understand the argument he’s making. I feel like the argument he’s making here should be of uber interest to critical rationalists. I’m really surprised critical rationalists aren’t trumpeting this all over the place.

[00:39:55]  Red: So let me take you through just at a high level though what his argument is. He says, imagine we’re trying to solve a toy problem. We want to induce under what conditions an unnamed person enjoys sports. So we’re going to be given several observations of conditions under which they do and don’t enjoy sports. Just for your sake, Peter, I’m going to show you my screen here for a second. What I have here is a list of observations. There’s a number of attributes like what’s the sky, what’s the air temperature, what’s the humidity, wind, water, forecast, etc. And we have different conditions that existed. And then we have an observation that the person that we’re trying to figure this out for either did enjoy sports or didn’t enjoy sports on that day. So we’ve got negative and positive examples by which to train from. So there’s not much to it. This is really just a tiny toy example to try to teach us some general principles. Okay. Now, what are the possible values for sky? It can be either sunny, cloudy or rainy. That’s all we’re going to care about in terms of that attribute for air temperature, either warm or cold for humidity, either normal or high for wind, either strong or weak for water, either warm or cold. And for forecast, either forecast of the same or a change of forecast. So we’re also going to format a hypothesis. The format of any hypothesis that we’re going to consider valid is always going to be a conjunction of these values. Now in logic, a conjunction means and. So that means you can end them together but not or them together.

[00:41:35]  Red: So for example, sunny and warm is a legitimate hypothesis, but sunny or warm is not. This is the format that we’re specifying for the sake of this algorithm. Okay. Obviously, that’s going to turn out to be a limitation of the algorithm, but we’re going to come back to that. Now, given these observations determine the ideas or determine the correct generalization or theory or explanation, in other words, of when this person does or doesn’t enjoy sports. Now, note that there is a finite set of possible explanations that we’ve by definition, we’ve defined the algorithm in such a way that there is a finite set of possible explanations that given our rules. Namely, you take the number of attributes and you multiply them together. So there was three times two times two times two times two times two, which is 96. So we are searching through 96 hypotheses for the correct ones. Now that’s obviously very tractable because 96 isn’t very much and a computer could run through it. But suppose we keep adding new criteria, which in machine learning, we throw tons of hundreds, thousands of attributes at the machine learning algorithm. This algorithm would quickly grow exponentially and start to become intractable. So that’s one problem. Plus, the way I’m currently describing it, the algorithm would end up outputting a list of compatible explanations rather than a correct generalized explanation. This is actually very confusing. It’s something we need to resolve. Let me explain what I mean though. Suppose the correct explanation for this person of when they do and don’t enjoy sports is that they enjoy it on days that are sunny. So really, only one attribute is going to matter. The other attributes can be ignored.

[00:43:17]  Red: That’s the correct explanation, but we don’t know that’s the correct explanation. We’re trying to figure it out from observations. So we would represent this explanation right now, the way I’m currently describing the algorithm. It would have to come back with 32 hypotheses and it would be sunny plus every combination of every single other attribute. And you wouldn’t be able to look, you’d have this, that would turn out to be 32 hypotheses. You’d have to notice that the only thing that’s consistent is sunny and that everything else is just multiple different combinations that don’t matter. And it wouldn’t be obvious by looking at this list of 32 hypotheses that the correct explanation is they like it sports when it’s sunny. It’s also very wasteful to do it that way, because then you have to look through 32 hypotheses. What we really want is a single final hypothesis that is logically equivalent to that list of 32 hypotheses. What we really want is we want it to come back and say that the correct explanation is sunny and you can ignore the rest of the attributes. As an added bonus, if we do come up with a way to do that, our search space shrinks and it makes the algorithm more tractable, which was the other problem we’re trying to deal with. So to handle this, let’s allow two new conditions or two new possible attributes, values for the attributes that allow us to represent a more generalized hypothesis. So one of them will be a question mark. If we come back with a question mark, that means any value is acceptable. This attribute is irrelevant. Or we can put a null sign or let’s say a zero, but a null symbol.

[00:44:57]  Red: That means no value is acceptable. So if the correct hypothesis is that the person enjoys sports on a sunny day and all other attributes are irrelevant, which is what we want to have the algorithm come back with is sunny for the first attribute and then question mark, question mark, question mark, question mark for the other attributes. That’s a single row that comes back and it’s immediately obvious that what this means is that the explanation is that they enjoy sports on a sunny day. So if the correct hypothesis is the person never enjoys sports and all other attributes are irrelevant, then we want to output no, no, no, no, no. Basically something that shows that they just never enjoy sports. These two new additional values now allow us to represent a general rule or set of rules in a compact form and it’s more human readable also. But this expands the possible hypothesis, number of hypotheses. So before it was three times two times two times two times

[00:46:00]  Unknown: two.

[00:46:01]  Red: Now it’s going to be five times four times four times four times four times four. That’s 500, 5,120 possible hypotheses. Realistically, if you have even a single null, that’s equivalent to having all of them be null because if there’s even one attribute that says never, then that’s the same as having all of them be never, never. So really this reduces us to 973 possible hypotheses. This is called the hypothesis space in machine learning. It’s the hypothesis space of an algorithm, often abbreviated H.

[00:46:36]  Unknown: In

[00:46:36]  Red: the set of hypotheses, it’s the set of hypotheses we’re going to search across. Our goal is to search across the entire set of hypotheses using the observations available to us to induce the correct explanation. So on page 23 of Tom Mitchell’s machine learning, he says, concept learning can be viewed as the task of searching through a large space of hypotheses implicitly defined by the hypothesis representation. So hint, the word search is very important here. If you’re a regular listener of this podcast, you realize that search is a kind of variation in selection algorithm and thus consistent with Campbell’s and Popper’s evolutionary epistemology. So we’re going to use an algorithm called the candidate elimination algorithm to be able to do this. It’s pretty much exactly what it sounds like. It takes every possible hypothesis and eliminates or refutes the ones that don’t match an observation. However, it does this across the entire set of hypotheses, which as you recall now includes the generalized hypotheses. So like one of the answers in the set is sunny, question mark, question mark, question mark, question mark. So it’s going to be able to find that one is the correct answer now as it uses the observations to refute other hypotheses within the hypothesis space of the 973 that are possible. How do we search across this set, including the generalized hypotheses efficiently though? So the candidate elimination algorithm doesn’t want to run through every single one and just eliminate them because that’s not the most tractable way to do it. Instead, it wants to be able to search in a much smaller space. So the algorithm deals with this problem by starting with the most general and most specific possible explanations.

[00:48:28]  Red: So in other words, this person always enjoys sports would be the most general and this person never enjoys sports is the most specific. And then simultaneously, an error corrects the upper most general and lower most specific bound using the observations available to it. Now at any given moment, there is a set defined by this upper and lower bound of hypotheses that are consistent with the observations we’ve seen so far. This set of the hypotheses, which would be a subset of the hypothesis space, but it’s the subset that is consistent with the observations. In other words, they are the ones that have not yet been refuted. It is called this is called the version space in machine learning. But in the language of popper, the version space is really just the set of theories not yet refuted. That’s it. This forces the algorithm to attempt to search for the most specific and most general hypotheses that are consistent with all the observations, i.e. not yet refuted by observations. If those two at some point match, we found the correct hypothesis. If the most general and the most specific are the same, then the algorithm can quit and say, I have found the correct explanation. Okay. And we avoid getting a giant list of hypotheses by doing this. So literally, if we run this algorithm and we have enough observations that it can actually induce the correct explanation, it’s going to find that the most general and the most specific are both sunny, question mark, question mark, question mark, question mark, question mark, and it’s going to output that. And you’ll be able to look at it and go, oh, this person enjoys sports when it’s sunny.

[00:50:01]  Red: And you’ll know that that is exactly the correct explanation. By doing this, we’ve avoided getting a giant list of hypotheses back. And we also increased the tractability of the algorithm because we’re searching across a much smaller space now than if we’re searching across every single one, trying to feud every single one. Know that the candidate elimination algorithm is really a very naive version of Popper’s falsification to falsify false explanations until we’re left with whatever’s left. And then we accept that one, at least tentatively, as the true explanation. To keep it simple, we’re making some assumptions that would not likely hold in real life, namely, we’re assuming that the correct hypothesis is found within the scent of conjunctions of these particular attributes. That was one of our starting assumptions, but it could be false. We’re also assuming that there are no errors in the training data. Think about what would happen if there was even one error in the training data, and it happened to be, let’s say that it refuted sunny, which is the correct answer. It’s just because we wrote the data down wrong. If these assumptions don’t hold, the results will obviously be incorrect. So obviously, if there’s even a single error in the training data that happens to refute the correct explanation, that one’s going to get removed and refuted and the algorithm will not output the correct explanation. This is in a nutshell the inverse of the do and claim problem, since the problem might be that our observations were wrong, not the set of theories that we were searching across. So you can’t really be sure that you can falsify theories based on observations, because the observation might be in error.

[00:51:45]  Red: We perhaps wrongly are assuming here that there’s no error in the observations. But if these assumptions do hold, if in fact there is no error in the observations, and if we actually can represent the correct theory using a conjunction of these attributes, then we will induce the correct explanation as per Popper’s epistemology. For exactly the reasons Popper explains, because the incorrect explanations will get eliminated and refuted and the correct one will remain. So here are the key points you should take away so far. This induction algorithm does not require you to already know which explanation is the correct one to then extrapolate from. It literally finds the correct generalized explanation from, it does literally find the correct generalized explanations from specific observations. This is not the mere case of interpreting data in the light of already existing final explanations. And this induction algorithm is already utilizing Popper’s epistemology of conjection refutation. Note how this induction that it does comes from a variation selection algorithm, just like Donald Campbell claimed to be the case in his theory of evolutionary epistemology. So this is an example of how Donald Campbell’s evolutionary epistemology is usually correct. Though as I explained in episodes 25 and 26, especially 26 of this podcast, Donald Campbell’s theory is actually incorrect, and there are some counter examples to his theory. But Campbell is correct so often, so overwhelmingly often, that there is clearly a large amount of verisimilitude to his theory. This is just one positive example corroborating his otherwise refuted theory. So now, with this all in mind, I’m going to now explain Mitchell’s argument of the futility of bias free learning and the significance that this has to Paparians.

[00:53:38]  Red: So if induction doesn’t exist, as Popper and Deutsch claim, why does this induction algorithm work? Recall the two kinds of induction, general versus Baconian. I claim that the induction of Hofstetter was unproblematic for Popper and vice versa, because Popper refuted only Baconian or logical induction, whereas Hofstetter was talking about general induction. The same answer applies here. This machine learning algorithm does induce from observations, but does so with the following criteria. Number one, it uses a set of observations plus a collection of assumptions, which are really just the same as saying starting theories. It may at first seem like it justifies the outcome because it does give you certain guarantees, but it actually only does that if your assumptions are correct. It’s guaranteed to give the right outcome if there’s no error in the observations and that the correct explanation is contained within the hypothesis set space H. But in reality, those are assumptions that you can’t guarantee will be true. So this algorithm does not justify its outcomes. So this induction quote induction algorithm clearly falls into the second category of merely generalizing from observations without the additional Baconian assumptions that Popper refuted. In fact, it is particularly satisfying to me as a Paparian to note that this induction algorithm is actually just a straightforward example of Popper’s falsification as to epistemology and that that is how it really works by refuting explanations. Now, is this only true? Are these realizations that I’ve just gone over? Is this only true for this particular induction algorithm? Or can we generalize? Can we safely draw the following conclusions? For example, number one, all machine learning induction algorithms are the kind of induction that poses no problem for Popper’s refutation. Is that a safe conclusion or not? Number

[00:55:37]  Red: two, all machine learning induction algorithms are really just cases of deductive logic. Okay, is that true? Well, we’re going to take a look at that. Or could we even go further? This one maybe might seem a little bit sheer, but are all machine learning induction algorithms really secretly just Popper’s evolutionary epistemology in disguise just like the candidate elimination algorithm is? So surprisingly, Tom Mitchell, one of the world’s most venerable experts in induction algorithms, produces a theory that is that it is completely impossible to create a Baconian style induction algorithm of the kind Popper says doesn’t exist. So I’d like to go over his explanation, his conclusions, because I think it’ll be a very strong interest to critical rationalists. So our assumption that the hypothesis will be one of our assumptions so far is that the hypothesis will be found within the set of conjunctions and not disjunctions of the attributes, disjunctions or ores, conjunctions or ands. This seems really questionable. What if somebody enjoyed sports on both cloudy and sunny days? This hypothesis is not even contained in the hypothesis space. So Mitchell suggests we try to rectify this problem and see what happens and see what we can learn from trying to rectify that problem. So he says on page 40 of his textbook machine learning, he says, suppose we wish to assure that the hypothesis space contains the unknown target concept. The obvious solution is to enrich the hypothesis space to include every possible hypothesis. Then on page 40, he continues, he says, the obvious solution to the problem of assuring the target concept is in the hypothesis space, H is to provide a hypothesis space capable of representing every teachable concept.

[00:57:28]  Red: That is, it is capable of representing every possible subset of possible hypotheses. Recall that we previously had 96 possible observations and 5,120 hypotheses if you include the generalizations, although that dropped to 973 if you dropped out the duplicates. To be able to represent any combination of attributes, we need to allow every possible subset of the set of X. So on page 40, he says in general, the set of all subsets of a set X is called the power set of X. Now, we know from mathematics how to calculate how large the power set is. So the power set of 96 elements is 2 to the 96th, which is equal to 10 to the 28th distinct target concepts. Now, 10 to the 28th, 10 with 28 zeros after it. And we’re only dealing with this same small set of attributes. So our original learner is biased in that it’s only searching across 973 of the 10 to the 28 possible targets. So he says it is, quote, a very biased hypothesis space indeed, page 41. This is called an inductive bias in the machine learning community. It’s a very important concept with machine learning because every machine learning algorithm has an inductive bias. Mitchell, about to explain why that is. On page 41, he says, let us reformulate the enjoy sports learning task in an unbiased way by defining a new hypothesis space H, which can represent every subset of instances. One way to define such a hypothesis space is to allow arbitrary distinctions, distinctions, conjunctions, and negations, page 41. So if the correct hypothesis was enjoying sports on sunny or cloudy days, we want the algorithm to output something like sunny, question mark, question mark, question mark, or cloudy, question

[00:59:31]  Red: mark, question mark, question mark, question mark. Okay. The current algorithm can’t do that. But that if let’s say that’s the correct answer, this new algorithm we’re trying to write needs to output that. Since you can’t see the actual notation, don’t worry too much about it. The point is that it’s now a very complicated hypothesis space that allows for any possible combination. Okay. So on page 41, Mitchell says, however, while this hypothesis space eliminates any problem of expressibility, it unfortunately raises a new equally difficult problem. Our concept learning algorithm is now completely unable to generalize beyond the observed examples. The problem here is that with this very expressive hypothesis representation, this is all on page 41, the lower boundary will always be simply the disjunction of the observed positive examples, while the upper boundary will always be the negated disjunction of the observed negative examples. Therefore, the only examples that will be unambiguously classified by the two bounds are the observed training examples themselves. In order to converge to a single final target concept, we will have to present every single instance in X as a training example, all end of the 28th of them, page 41. Does this sound familiar? It is precisely Hopper’s proof that induction is impossible that we just barely went over earlier in this podcast. This is why all machine learning algorithms must have what Mitchell calls an inductive bias. The above discussion, this is page 42. The above discussion illustrates a fundamental property of inductive inference. A learner that makes no a priori assumptions regarding the identity of the target concept has no rational basis for classifying any unseen instances.

[01:01:28]  Red: In fact, the only reason that the candidate elimination algorithm was able to generalize beyond the observed training examples in our original formulation of the enjoy sports task is that it was biased by the implicit assumption that the target concept could be represented by a conjunction of attribute values. Or to put this in another way, the only time you can induce anything ever is if you have some sort of starting theory that allows you to do so. That’s what Mitchell is saying. Okay, on page 42, because inductive learning requires some form of prior assumptions or inductive bias, we will find it useful to characterize different learning approaches by the inductive bias they employ. Let us define this notion of inductive bias more precisely. So let me be clear what he’s saying here because this is such a big deal to a critical rationalist. Every single inductive algorithm in machine learning can be defined in terms of its inductive bias, or in other words, in terms of its starting assumptions or starting theories or starting explanations. And that’s actually how they classify different machine learning algorithms into different classes and how they study what they’re capable of. Okay, so he says on page 42, because L is an inductive learning algorithm, the result that it infers will not in general be provably correct because that’s an aspect of induction. That means there’s no justification. That is the classification of a new instance need not follow deductively from the training data. However, it is interesting to ask, this is Mitchell still, what additional assumptions could be added such as the resulting classification would follow deductively. Let’s define the inductive bias of a learner as this set of additional assumptions required to make the results follow deductively.

[01:03:25]  Red: Page 42, plain English, a so -called inductive bias is really the starting theories required to allow a learner to generalize from observations. And if you include that set of additional assumptions, it’s actually just deductive logic from that point forward. An inductive bias, page 43, inductive bias of candidate elimination algorithm, the target concept C is contained in the given hypothesis space H. That is the inductive bias of the candidate elimination algorithm that we’ve been discussing according to Mitchell. The inductive candidate elimination algorithm takes two inputs, the training examples and a new instance to be classified. Okay, that makes sense, right? So you have a bunch of training examples, and then you have the new instance you want to see classified and the candidate elimination algorithm is going to output the correct answer, whether this person is going to enjoy sports or not on this day, because it’s found the correct explanation that they enjoyed on sunny days. So it just uses that to figure out what the correct classification should be. So he says, suppose instead a deductive theorem prover is given the same two inputs plus the assertion that one of the 971 explanations contained in the hypothesis space is the correct explanation. Okay, you would have to write that out in terms of deductive logic. This is Mitchell. These two systems will in principle produce identical outputs for every possible input set of training examples and every possible new instance. This is from page 43 to 44 of Tom Mitchell’s machine learning.

[01:05:04]  Red: In plain English, the so -called inductive bias is not only a set of starting theories to allow induction to work, but they are exactly the set of theories required to make an inductive, a quote, inductive learner into essentially a deductive theorem prover. That is to say Mitchell has just proven that machine learning induction is actually 100 % inductive and completely consistent with Popper’s reputation of induction. Mitchell refers to this as the futility of bias free learning. Let’s be clear what Mitchell is claiming. He’s claiming that all inductive learning algorithms are, in fact, one, not inductive at all without some sort of theory by which to interpret the observations, exactly like Popper and Deutch claim. He is also claiming, too, that the theory required to make the induction work is exactly equivalent to the theory necessary to turn the inductive learner into a simple deductive theorem prover. I’m startled that this theory of Mitchell’s and his accompanying argument isn’t being trumpeted all over the community. Once you realize that this is the case, it is strange that the CritRat community tries to dismiss at times, not Deutch, but other members of the CritRat community tries to dismiss machine learning and inductive learning as quote, bad philosophy. In this podcast, I have claimed that critical rationalism is really about subsuming your opposing theories such that they can do nothing that you can’t do better. Mitchell’s argument to convert machine learning from inductive learning into deductive logic is precisely an example of what I had in mind. It’s precisely an example of how critical rationalism can entirely subsume machine learning and inductive learning as being part of critical rationalism.

[01:06:50]  Red: If you couldn’t do that, then critical rationalism has failed in its task and it has an error that is in need of correction.

[01:06:59]  Blue: I’m curious, are there a lot of critical rationalists that you’ve spoken to that are aware of these issues in machine learning and are actively against them?

[01:07:11]  Red: No, there’s very, very few critical rationalists working in machine learning. I’m going to give you some articles from those that are and they’ve come to the same conclusions that I’m explaining in this podcast. So there is a few, but I can only find like three or four out of the literature. So there’s probably more because I haven’t done an extensive search. All I did was go to Google Scholar and try to find them and I came across the same few over and over again. So they’re probably the famous ones, if that makes any sense. And there’s probably plenty more that are less famous. So we’re

[01:07:44]  Blue: going for a niche audience here?

[01:07:47]  Red: Yeah, well,

[01:07:47]  Blue: but that’s just how we roll. So let’s

[01:07:51]  Red: look at this in a different way. Critical rationalists, there’s a ton more of those. They don’t tend to have any interest in machine learning because they see it as very inductive. And that’s exactly the wrong way to look at it. Machine learning is not inductive, it’s critical rationalist. It’s an example of poppers’ epistemology in action. So this is something that should be getting a bigger audience. It just isn’t. And recall from the previous article I quoted that most machine learning people just see machine learning as refuting poppers’ epistemology. They don’t realize that it doesn’t. And that in fact, poppers’ epistemology is a better way to look at machine learning. So we’ve gone a long way. At least in these examples, we could argue whether Mitchell’s argument is correct or not. But I’m throwing the argument out there. I’m explaining how I came up with it. It seems like a very good argument to me. And I think the implication is that there is no contradiction at all between machine learning, inductive learning is what we call it, inductive learning and critical rationalism, that there actually, critical rationalism has subsumed inductive learning into it. So I want to point out also this idea of subsumption, that’s actually the correct answer to the whole IQ theory versus Brett’s theory of intelligence. Neither really subsumes the either, either at this point. And they’re treated like they’re these two theories and I’m going to refute IQ theory and show problems with it. And then I’ll know that Brett’s theory of intelligence is correct or vice versa. It’s just the wrong way to look at it, right? It’s true that there is this contest of ideas that goes on in poppers’ epistemology. But the real goal is to subsume. Like,

[01:09:48]  Red: how does Brett’s theory of intelligence, how does it explain people who are mentally challenged or even just someone who becomes mentally challenged because they’re going senile, right? Clearly, you can’t explain that in terms of time and interest, like Brett’s theory wants you to be able to do. That’s an example of a problem that IQ theory can explain and Brett’s theory can’t. Okay, but on the other hand, IQ theory explains very, very little. And it’s basically just saying there’s, for reasons we don’t fully understand, there’s this g -factor that exists. And IQ theory kind of sort of measures it. Brett’s theory is a much better example of how you should have really gone about this. And you should have been digging into trying to come up with the mechanisms of what counts as g -factor. G -factor is an attempt to remove the aspect of that IQ is probably mostly just based on what types of knowledge we value. I mean, I think that’s a everybody knows that’s a problem with IQ theory. G -factor was an attempt to get around that. The two theories aren’t incompatible. They should really be combined together and they shouldn’t see themselves as, I’m going to refute you and then I’m the last standing theory. They should be trying to subsume each other is what they need to be doing. So now let’s actually take a look at some of the work done by some of these people in the machine learning space that are that are preparians that are looking at machine learning. Okay, so this is from artificial intelligence and popper solution to the problem of induction by Tim Bernini. He says, this is his conclusion,

[01:11:27]  Red: the difficulty surrounding inductive as construals of computational learning from examples revealed the conjectural character of the background hypotheses embedded in learning algorithms and suggest the opportunity of changing perspective. Learning procedures that are usually called inductive are appropriately viewed as hypothesis and test procedures framed into more comprehensive trial and error correction processes. Compare this to popper himself that in conjecture refutations page 259 says, reason works by trial and error. We invent our mythos and our theories and we try them out. We try to see how far they take us and we improve our theories if we can. Sounds very similar to me. In machine learning from examples, a non -inductivist analysis, Dotturi, Hosni and Tim Bernini. This is by the way, the other papers aren’t necessarily available, but this one’s available. You can get the PDF on the internet. I’ll try to include a link to it. This is an excellent paper. Okay, it goes through and it shows it takes representative examples of machine learning since machine learning algorithms fall into different families. It takes examples from each of the families and it shows that all of them are actually secretly poppers of epistemology. Okay, and it says in this paper, it has been suggested that AI investigations of machine learning undermine sweeping anti -inductivist views in the theory of knowledge and the philosophy of science. In particular, it is claimed that some mechanical learning systems perform epistemologically justified inductive generalization and prediction. Long story to this view, it is argued in this paper that no trace of such epistemic justification is to be found within a rather representative class of learning agents drawn from machine learning and robotics. Moreover, an alternative deductive account of these procedures is outlined.

[01:13:25]  Red: Okay, based on this, I want to now go back and look at Poppers and Deutsch’s statements about induction and I want to see if anywhere we can error correct their statements. So in terms of the statements I pulled from Popper, what Mitchell just came up with, there is absolutely 100 % agreement between them. So Popper and Mitchell are completely compatible. This doesn’t seem to quite be the case with some of the things that Deutsch has said, although it’s close. So I want to go through and I want to actually go through his statements and kind of take a look at them in terms of this explanation that we just went through with Mitchell. Okay, so the following statements from Deutsch can be understood as correct if we simply assume that Deutsch is explicitly talking about Baconian induction or logical induction. So for example, from fabric of reality induction, a fictitious process by which general theories are supposed to be obtained from or justified by accumulated observations, if by that we are using the word induction to mean Baconian or logical induction, this statement is a true statement. Furthermore, he says, but if we want to understand the true nature of knowledge and its place in the fabric of reality, we must face up to the fact that inductivism is false, rude and branch, no scientific reasoning and indeed no successful reasoning of any kind has ever fitted the inductivist description. This is all true as long as we’re assuming he means Baconian induction for exactly the reasons that Mitchell has explained. From, he says something similar in our podcast where he says that it’s basically empiricism, inductivism, it’s just wrong, rude and branch, false, rude and branch, again, if we’re assuming Baconian induction, it’s correct.

[01:15:17]  Red: And then he says in the Paparian podcast, induction just isn’t true, it’s not that induction is invalid, which is something that has been known since antiquity, but Popper added to it that induction just doesn’t happen. It’s not that we don’t do it, that we do it, but it’s invalid, but it somehow works, we don’t do it. What we do is we have a theory first, and the case where we’re creating new knowledge, this theory is conjecture, a conjecture that’s not based on anything, it’s a hope for solution. This last one in particular, if you read it as saying there’s no kind of induction of any sort whatsoever, clearly that’s wrong because inductive learning actually works. But if you understand induction, the word induction here to mean the Baconian kind, the idea of a biased free learner, then what he just said is completely correct. You absolutely must have an inductive bias that is a starting assumption or the inductive learner will work according to Mitchell. It’s possible to read what Deutsch is saying here as correct. Let me just point something out here. It’s important that we do read people charitably like this. We could read Deutsch is wrong. We could assume he’s talking about induction in the sense of general induction, and all these statements would be false because obviously Peter could induce from observations and machine learning does induce from observations, but it needs a starting set of assumptions to be able to do so. It has starting theory. Do you see where I’m going with this? It’s root and branch wrong because you can never induce from observations alone. If I understand it that way, the Deutsch’s comments are correct. Now, here’s the thing.

[01:17:03]  Red: Even when we read Deutsch charitably, he makes some comments that are actually a little bit problematic. Okay, so he says saying of his neighbor, now he thought he was inducing this theory because to him he saw black people commit crimes, another black person committed a crime and so on. And to him, he was thinking that he had induced this theory whereas a different person sees the same data and he sees poor people committing crimes and so on. Both of them, these are just examples, I want to make sure it’s clear that Deutsch is not advocating either of these theories. He was just picking an example off top of his head. Both of them have actually just been interpreting the data in the light of their pre -existing theory and have pretended to themselves. I mean, they don’t know that they’re doing this, but they have reinterpreted the thought process in their mind as one of extrapolating a theory from data. Actually, what they have been doing is interpreting the data in the theory and theory came first. Here’s the thing. Note that an inductive algorithm is not merely interpreting data in terms of the very theory that they think they’re inducing. That is not what Mitchell is saying and it is entirely possible to interpret data through a learning algorithm and come up with an entirely new theory like this person enjoys sports on sunny days. That wasn’t the starting theory, that was the theory that was output. There actually are using learning algorithms inducing a new generalization that they didn’t have before. So let’s formalize this. Deutsch is claiming in this quote that you need Theory A to be able to induce Theory A from observations.

[01:18:40]  Red: That is to say that you didn’t really induce anything at all. But the actual truth is that you need Theory X, the inductive bias, plus some observations to induce Theory A. That is to say the inductive bias, the starting theory, is not the same theory as the one output by the learning algorithm. You are not inducing the same theory you started with. You end up with a new theory when you’re using an inductive learning algorithm. Specifically, for Mitchell’s example, Theory X is the theory that the explanation took the form of a set of conjunctions between attributes out of the 971 possibilities. Well, the final output was a specific explanation made up of those attributes, one of the 971 possibilities. So there was a gain in knowledge after the algorithm was run. We did learn something. This is the difference between what Deutsch is saying in this quote where he’s implying you can only induce from the very same theory that you actually already had where induction, the general kind that actually exists, actually does allow you to create new theories that didn’t exist before, but just based on certain starting theories. This is a big difference and it’s something that is clearly missing in the way Deutsch is looking at induction, that he’s missing that’s important. So now in regard to how the AGI problem is perceived, this is now Deutsch talking about AGI, this has the catastrophic effect, the problem of induction has the catastrophic effect of simultaneously framing it as the problem of induction and making that problem look easy because it casts thinking as a process of predicting that future pattern of sensory experience will be like the past ones.

[01:20:30]  Red: Then he says that looks like extrapolation, which computers already do all the time. Once they are given a theory that causes the data, but in reality, only a tiny piece of only tiny component of thinking is about prediction at all, let alone prediction of our sensory experiences. Now the truth is, is that knowledge consists of conjectured explanations, guesses about what really is or should be or might be out there in the world. This is from why has AGI not been created around minute 25. The thing I want to point out here is he says computers already do this all the time. Once they are given a theory of what causes the data, that is false, that is not a correct understanding of machine learning. Inductive algorithms are not given a theory of what causes the data and then they extrapolate from it. They’re given a starting theory of the hypothesis space that it should be searching through, which is not the same as being given what causes the data. The cause of the data is the actual output. If the algorithm actually works correctly like we’re hoping and it gives us the explanation that this person enjoys sports on sunny days, that is the cause of the data. That’s the correct explanation that causes the data. And that is what we’re searching for using the induction algorithm. We’re not given that as a starting assumption. So one of the main things Deutsch has missed is that machine learning, while not inductive in the Baconian sense of inducing solely from observations, since that doesn’t exist, it is more often than not a form of evolutionary epistemology. This is a quote from Deutsch. What we need is first philosophical progress in understanding how creativity is implemented.

[01:22:15]  Red: We know a few things about creativity. It has to be, in the broadest sense, an evolutionary process. It has to work by variation and selection. This is typically what you hear is we know that human creativity has to work through some sort of evolutionary process. But this is a correct description of the candidate elimination algorithm that I just went over with you. That we’ve been discussing as well as most machine learning algorithms. On page 46 of Mitchell, Simon and Leigh, 1973, given early account of learning as search through a hypothesis base. So the vast majority of machine learning algorithms are, in the broadest sense, an evolutionary process and work by variation and selection. So most of our existing AI and ML algorithms already fit what we know about creativity. This is going to be a disappointing realization because instead of being something that’s a hint about how to do AGI, it turns out it does not differentiate AGI from the type of AI and machine learning that we already do. Deutsch goes on to say, but we need to know the details and the devil will be in the details. Bingo, that’s exactly right. There’s something else that we don’t know about creativity, human creativity. And it isn’t merely that it is in the broadest sense an evolutionary process or that works by variation and selection because almost all AI and ML work via that process. So, okay, that is actually my presentation. Let me just summarize with a few thoughts here. First of all, I want to kind of go back just for a second. And I want to look at that, again, that set of observations that I showed Peter.

[01:24:08]  Red: So the first one was the random points and it’s really obvious looking at it that it’s a line, that I’ve just selected random points on a line. What did Peter actually do? Now we don’t understand exactly how human creativity works and there’s still a bunch of mystery around it. And because of that, there’s going to continue to be mystery around, quote, how humans induce things. Understand the word induce here in the more general sense, not the Baconian sense, okay? But Peter absolutely did have a set of starting assumptions. In fact, I gave them to him. I said, this is a function. I’m selecting a set of random points and I’m not trying to fool you. Now, even if I had not given that set of starting assumptions, starting theories, Peter probably could have still induced the line from these points. If for no other reason than because human beings have starting assumptions, if I show you a bunch of points like this, the first thing that you kind of just know to do as a starting assumption is to try to figure out the simplest function that connect the points together, which is obviously a line. Now, that assumption may have been wrong. If I had just given you these points and I was trying to fool you, for example, Peter may have still tried to draw a line between them and he would have been wrong because I was trying to fool him. But let’s look a little bit at Mitchell’s explanation. Let’s understand what’s going on here.

[01:25:37]  Red: If the theory, if the correct function had been one of these funky lines, funky curves that connected the points together that were in the later slides, it would have been really weird that they happen to by random form a line. Okay, if I was really picking points at random on this complicated curve, they wouldn’t have formed a line except by some really, really improbable set of chances. So Peter, knowing that it’s random points on a function, knowing that I’m not trying to fool him, he basically can eliminate the infinity of other functions that are running through these points because I told him I selected them at random. So in fact, from a certain point of view, Peter was actually not inducing at all. He was actually just deductively coming up with the only answer that was possible given the starting assumptions I had given him. Now, granted, deductive is maybe too strong a statement. There was at least probabilistic chance that it was one of these curves and that just by chance that happened to form a line. But for all intents and purposes, we can rule those possibilities out on the grounds that they’re very improbable. And that’s how Popper, using his epistemology handles that, that he would say, well, give me another set of random ones. And he basically knows that the chance that it’s going to keep being a line is basically none, like it’s just advantageingly small. And so based on that, you can discount the other possibilities. So from a certain point of view, even though I use that as an example of how humans induce things, there was no actual induction going on at all because there were starting assumptions. However, I wasn’t giving Peter the line itself.

[01:27:32]  Red: He was able to induce or generalize from those observations. He was able to, based on these starting assumptions, come up with the one correct function that I had in mind, okay, just based on these observations. This is exactly what I’m trying to get at with Mitchell, okay, that there is no such thing as Baconi induction. You never, ever, ever induce from observations alone. But if you are talking about observations and some starting theories, not necessarily the theory you’re going to induce, you can induce from that. Now, is it justified? No, it never is. So first of all, there’s always the chance that I am lying. There’s, there’s all sorts of things that could go wrong with this. And even if I, even if I had not given Peter anything to start with, he almost assuredly would have just gone with it’s a line because he kind of just knows, go with the simplest explanation. We just know that as a rule of thumb that tends to work, but Occam’s razor, as it’s called. And this combination of things, including Occam’s razor, allows us to induce theories from a combination of our observations and our starting theories. And human beings are full of starting theories. We have all sorts of starting theories that we’re starting with. And from this point of view, of course, this means human beings do, do induction all the time, but it’s not the Baconian kind. Okay, have I made my case? Do you understand what I’m trying to get at here?

[01:29:09]  Blue: I think I do, Bruce, and you are a unique person with a unique perspective. And I think you’re doing something important here. And I hope other people recognize that.

[01:29:22]  Red: And I thank you for

[01:29:23]  Blue: this.

[01:29:24]  Red: Thank you. Because you, you made a question about it. Doesn’t, isn’t the issue here that human beings do, in fact, induce things? And the answer is yes, they do, right? In the more general sense, human beings absolutely induce things.

[01:29:37]  Blue: So yeah, well, it might be, let’s see, I can cut this part if it doesn’t work, but let’s, let’s maybe explore that a little bit from the perspective of explain it to me like I’m a five -year -old. So we, humans make observations and we have, we have theories. Our theories come more from other theories. But I mean, basically, okay, big picture, what we’re trying to do is work out the relationship between theories and observations.

[01:30:14]  Red: Yes.

[01:30:15]  Blue: And that’s induction is sort of one answer to this question. Yes. Right. And what you’ve, what you are asserting is that there’s really, the word induction is more complicated than maybe other people have are thinking about it.

[01:30:37]  Unknown: Yes.

[01:30:38]  Blue: And there’s really more than one kind of induction.

[01:30:41]  Red: That’s right.

[01:30:42]  Blue: Some of it is not valid. Like the Baconian induction is just false, right? Yes. But then the true kind of induction, what are we calling that more the machine learning induction?

[01:30:57]  Red: You know, I’ve traditionally called it statistical induction, but that ignores the fact that humans do this too. So let’s call it general induction for now. Just the idea that we generalize from observations.

[01:31:11]  Blue: Okay. General induction. Maybe we need a better word for that. We do need

[01:31:15]  Red: a better word for that.

[01:31:19]  Blue: So

[01:31:20]  Red: let me actually throw something out. I wasn’t planning to bring this up,

[01:31:23]  Blue: but

[01:31:25]  Red: critical rationalists will say you always start with a problem and that you cannot induce without a theory.

[01:31:31]  Blue: Now,

[01:31:32]  Red: they’re kind of right because you always have to have some starting theories. The idea that you always start with a problem is also kind of true. When I give you a set of points to look at, I mean, what’s the problem here? You were able to induce without a problem, right? Unless you want to stretch the word problem to say, well, Bruce is asking me to induce. That’s the problem, right? And unfortunately, that’s the problem with the word problem is that it’s easy to vary. It can basically mean anything, right? So one of the things that I think might be helpful here is to realize that we do induce from observations, but in general, we don’t induce from just any kind of observations. We induce from observations that surprised us in some way and that therefore could count vaguely as a problem, right? And so I give you this set of things and I’m asking you, hey, show me what the function is. Yeah, that’s a problem for you now. And so now you are going to try to induce from these observations, you’re going to hypothesize it’s a line and you’re going to turn out to be right. And the reason why you’re going to turn out to be right is because you got a bunch of starting theories that help you figure out what the correct theory probably would be in a case like this, right? Even though you know for sure, you don’t know for sure. And again, I worry that in the critical ashless community, we focus so much on this idea that it has to be a certain kind of problem.

[01:33:05]  Red: I mean, you’ll hear crit rats in particular, Deutschians say, well, it has to be a clash of ideas by which that means a clash of theories. And it’s like, well, and then they’ll turn around and they’ll say, oh, but you’re solving problems all the time. You have to go like, go figure out how to feed yourself. You know, that’s not really a clash of ideas. And they’ll try to come up with some way to vaguely make that a clash of ideas. And because the idea of a clash of ideas is itself easy to vary, you can always find some way to force fit it, right? I don’t think these are, they’re not wrong, they’re just vague. And I don’t think these are the most clear, bold ways to try to understand critical rationalism. Again, it’s not that it’s wrong. You do always start with a problem in some sense, right? And you do always start with a clash of ideas in some sense. But it’s such a vague idea. And I really think what we’re really typically starting with is you see something that your previous theories didn’t explain well. And so you’re trying to make sense of it. And it could be something like very scientific, like the, you know, perihelion of Mercury that can’t be explained well by Newtonian physics. Or it might even just be that you see something, you know, happen and you’re trying to figure out how to live your life. You don’t have any specific ideas in mind, but you’ve got this problem, you know, where maybe I need to avoid this tribe over here because they’re the ones that want to kill me, you know, thinking about maybe an ancestral environment.

[01:34:48]  Red: And you would, in such a case, you would have enough starting theories that you could induce something like I should stay away from the something tribe because they want to eat me, you know, or something along those lines. And you wouldn’t need to have the theory stay away from that tribe to be able to then interpret the fact that they’re trying to kill you. You actually would see them try to kill you and you wouldn’t induce a theory. Maybe I should stay away from these people. And you aren’t inducing solely from observations. You also have a set of theories that helped you do that. But yeah, I mean, like human beings absolutely induce from observation all the time. That is to say there are observations that we see that cause us to want to create an explanation and we then use our starting assumptions and we come up with explanations. And that process of coming up with the explanation, however it works. Now, this is something that I kind of brought up in the Hofstetter thing and why I feel like Hofstetter’s theories shouldn’t be dismissed out of hand. I don’t know how far I want to endorse them, but why I don’t think they should be dismissed out of hand. His theory in essence is that the human mind does a search process across a space of analogies. So when a human being has this idea, and this is one of Hofstetter’s real life examples where the guy has had a bad experience with a translation to his book that was in a European language that he understood somewhat. So he could see it was a bad translation.

[01:36:31]  Red: So now he’s induced this theory that maybe he should be wary of translations, so he won’t agree to a Korean translation, even though it’s a totally different language with totally different translators. He’s got no logical reason whatsoever to believe that just because the European translation was disappointing that the Korean translation is going to be disappointing. The idea that he didn’t induce this from observations is just false. He absolutely did. Now, how did he do that? No, we don’t really know that in detail. That would be the AGI algorithm. But if we accept Popper’s epistemology, which says that there’s just no such thing as Baconi induction, for that matter, if we accept how Mitchell’s theory of induction, which says there’s no such thing as Baconi induction, then we know he didn’t induce that solely from observations. Instead, Hofstetter is suggesting that there’s this space of analogies in his head that a generalization has taken place, that in his subconscious, not his conscious mind, that a Popperian process of evolution searched across this space of analogies and found this analogy and then it latched onto it and then it sort of controlled his thinking. He couldn’t help but think this is going to be another case of translations being disappointing. Now, is that true? I don’t know. I’m not trying to advocate for specific theory. What I’m trying to point out is that Hofstetter’s theory is in no way in contradiction to the idea of Popper’s epistemology, which simply says that there would have to be some sort of trial and error algorithm in the subconscious that somehow has this quality of open -endedness and allows us to create these fuzzy categories and that allows us to think more fluidly.

[01:38:22]  Red: I mean, there’s lots of interesting ideas that could be explored if you were to combine Hofstetter’s theories and critical rationalism. They’re not yet in contradiction and Hofstetter’s theories are in some sense saying, yes, we induce things but we do it through something that is a variation selection algorithm. It’s not at odds with Popper’s epistemology. That’s why I find it at least interesting. Now, is this the right thing to do to discover AGI? I really have no idea. If nothing else, Hofstetter’s theories, even though I do find them interesting, they’re vague. They aren’t to the point where I can really turn this into an actionable algorithm and try out what intelligence is through some sort of algorithm. That’s really what’s missing. He tried to do that and that was a big part of his career, but I really feel like that the Copycat program that he came up with just doesn’t, it’s just too specific. It’s to basically finding analogies between letters. It’s nothing that’s an actual learning algorithm that would be useful in any way and it doesn’t really do much to enlighten how human beings create analogies. On the other hand, that means that there’s fertile space here. It’s probably worth somebody who’s a critical rationalist and that is into AGI to go try to explore Hofstetter’s theories in a more direct way than he was able to. There might be a good starting point for giving this some deeper thought. I guess this is what I’m trying to say is let’s not throw these theories out. Let’s talk about them more. Let’s think about them more. Let’s criticize them more. Let’s understand the term induction in a way that we don’t just have an allergy to the term.

[01:40:05]  Red: It’s totally fine if some things seem very inductive because they probably are, in the general sense, inductive.

[01:40:13]  Blue: How about if we call this podcast the critical rationalist case for induction? I think that will be provocative enough.

[01:40:23]  Red: You know, that’s not a bad title. I was thinking I was going to call it the lack of problem of induction, but I actually like yours better, the critical rationalist case for induction, which basically boils down to when you see something that’s inductive, it is, in fact, really just critical rationalism, or should be, or should be. I mean, maybe we can’t explain everything in terms of critical rationalism. For example, we can’t really yet explain how human beings induce things because we don’t know what the AGI algorithm is, but we have every reason to believe that it should turn out to be some form of epistemology that is at least similar to Popper’s epistemology. It won’t be exactly the same for the obvious reason that if it was, then we would already know what the AGI algorithm is. This is why Deutch said we need to break through in epistemology, in philosophy, to be able to discover the AGI algorithm. I totally agree, but that’s exactly why the final epistemology that AGI is going to be built on, it’ll have the flavor of Popper’s epistemology, but it won’t be Popper’s epistemology. It’ll be a generalization of Popper’s epistemology to cover everything. And that’s really what we’re looking for. In this episode, we talked about an intriguing overlap between Ethereum machine learning and Karl Popper’s epistemology. Specifically, we talked about how Tom Mitchell’s theory of the futility of bias -free learning was identical to Popper’s disproof of Baconian induction, except more detailed.

[01:42:02]  Red: By putting one of Karl Popper’s disproofs of Baconian induction into the form of algorithms, this shown a bright light on the subject, what we found was that sometimes critical rationalists misunderstand some aspects of epistemology due to mistakenly thinking they are inductive when really they are completely compatible with Popper’s epistemology. I have in mind here Deutch’s claim that it is impossible to induce a theory from observations and that, therefore, anytime a person thinks they’ve done that, what they’ve really done is that they’ve already held that theory, let’s call it theory A, and they interpreted the data in terms of that pre -held theory A. But we saw in Mitchell’s theory of the futility of bias -free learning that that isn’t quite right. You do need some existing theory X that when combined with observations results in a generalization, that is theory A. But theory A itself doesn’t have to be identical to theory X, as Deutch thought, to allow for generalization to happen. And all this was put into a very formal form so that anyone can go check it for themselves. It doesn’t have to be expressed merely as some matter of opinion. You can actually go work out the math for yourself. This is just one example of a myriad of interesting things that come out of combining artificial intelligence and machine learning with critical rationalism. There are so many more. It’s an exciting subject that really no one ever seems to talk about, and I find that a little frustrating. I’ve considered holding a class who discussed this topic more. What I have in mind would be to go over the Stuart and Russell curriculum, which is the curriculum used in nearly every AI 101 class in existence, plus some of Mitchell’s textbook.

[01:43:42]  Red: So this would be a regular class on artificial intelligence, except through the lens of critical rationalism. Now, if I’m being realistic, this is a subject that maybe I’m the only person in the world interested in it. Most people that I know think AI and ML are wholly unrelated to Popper’s epistemology. So they just see no value in combining the two subjects. I think I can show that there’s actually a lot of interesting ideas that are being overlooked because of this. Moreover, I think looking at AI through the lens of critical rationalism in some sense turns AI from being merely a set of interesting algorithms that are useful back into what they were originally intended to be, sincere but failed attempts to create AGI. So a big part of the class, if I were to ever hold one, would be discussing why did they think this would lead to AGI and why did it fail to do so, and what can we learn about epistemology from this failure? So I think that such a class, if I were to ever hold one, would be of interest to those interested in AGI, if only to try to learn from past failures. So I’d be curious if I’m the only person interested in this idea, or if there are others out there that might be interested in joining such a class if we decided to hold one. I have no idea if I’m ever going to follow through with this idea or not. I am just curious. It’s not like we’ve got some huge audience, and so it’s not like there’s thousands of people listening to this, and there’s bound to be lots of people out there interested in this subject.

[01:45:13]  Red: Most likely we’ll find that I am the only person interested in trying to combine artificial intelligence and Karl Popper’s epistemology. If you would be interested in such a class, consider emailing me, BruceNielson1 at gmail.com, although I’m going to have to spell my last name. It’s B -R -U -C -E -N -I -E -L -S -O -N1 at gmail.com. Alternatively, you could leave a message on Facebook or on Twitter, or you could private message me on Twitter.

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