Episode 126: The Concept of Concepts

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Unofficial, reviewed transcript. It may still contain mistakes; check the podcast when wording matters.

Speakers are labeled by first name where identified. Unidentified-speaker labels may refer to different people. Bracketed question marks indicate uncertain wording.

Transcript

[00:00:00]  Peter: Hello out there. This week on The Theory of Anything Podcast, we discuss, what is a concept? What is a theory? And was Karl Popper wrong when he said theories are a hundred times more valuable than concepts? But where then do conjectures come from? Bruce explores these ideas and more in this week's shorter episode.

[00:00:33]  Bruce: Welcome to The Theory of Anything podcast.

[00:00:35]  Unidentified speaker: Hey, Peter.

[00:00:36]  Unidentified speaker: Hey, Bruce, how are you doing today?

[00:00:38]  Bruce: Good, I'm excited for today's episode today.

[00:00:42]  Peter: I hope you're sleeping at night.

[00:00:44]  Unidentified speaker: You're in a real creative streak here.

[00:00:48]  Bruce: Yeah, you know, I am not sleeping at night, though it's got nothing to do with the podcast. But I don't know if everybody, I'm really excited about today's episode. We're going to talk about The Concept of Concepts. And the reason why is because we're really getting to the heart of my AGI nerdness now, right? But I kind of wonder if anybody else but me is going to find it as interesting as I do. Probably not.

[00:01:17]  Peter: Yeah, someone will.

[00:01:19]  Unidentified speaker: Yeah.

[00:01:20]  Peter: I mean, we might lose a Patreon or two, but the Concept of Concepts, but not the Concept of Concepts of Concepts.

[00:01:32]  Unidentified speaker: No.

[00:01:33]  Unidentified speaker: Okay.

[00:01:35]  Bruce: So think back to like Episode 112, Words versus Concepts. We did a little video on that. And I talked about how concepts were more important than words.

[00:01:43]  Unidentified speaker: Okay.

[00:01:44]  Bruce: That was kind of my first dipping my toe into the Concept of Concepts.

[00:01:49]  Unidentified speaker: Okay.

[00:01:50]  Bruce: And now if you're a big Popper fan, you're probably already aware of the fact that Popper did not think much of the Concept of Concepts, and in particular, considered them to be vastly inferior to theories. As Popper put it in, interestingly, one of his talks on evolutionary epistemology that we just covered in the previous episode, he says, theories are a hundred times more important than concepts. Theories may be true or false. Concepts can at best be adequate or at worst be misleading. Concepts are unimportant in comparison to theories. That's from All of Life is Problem Solving, page 45 under the...

[00:02:28]  Peter: Is a concept, is that a related idea to a Platonic ideal? Is that how I should get my mind around what...

[00:02:36]  Unidentified speaker: That's a good question.

[00:02:39]  Bruce: So, here's the thing. I'm going to quote what he says about it. And yes, he does liken it to a Platonic ideal. So Popper is seeing a connection between the problems of Platonism and the idea of a concept.

[00:02:57]  Unidentified speaker: Okay.

[00:02:58]  Bruce: I don't think I agree, right? Like I kind of agree, like I'm gonna explain it. Like I'll explain in what sense I agree with him and in what sense I don't agree with him, okay?

[00:03:08]  Unidentified speaker: Okay.

[00:03:09]  Peter: But maybe for our 100th episode, we got David Deutsch.

[00:03:15]  Unidentified speaker: Here's what I'm thinking.

[00:03:16]  Peter: 1000th episode, we can have the AI version of Karl Popper on here to argue with you. I'm seeing the future.

[00:03:25]  Unidentified speaker: You know, that's not an entirely bad idea.

[00:03:27]  Bruce: You know, I have an AI Karl Popper, right?

[00:03:30]  Unidentified speaker: Oh yeah.

[00:03:33]  Bruce: I could program to be really argumentative with me, and then we could have him on the show to argue with me.

[00:03:40]  Unidentified speaker: Yeah, yeah.

[00:03:42]  Unidentified speaker: That would be epic.

[00:03:43]  Unidentified speaker: Wow.

[00:03:44]  Unidentified speaker: I look forward to that.

[00:03:46]  Unidentified speaker: Okay.

[00:03:46]  Bruce: Do I agree with Popper on this, or am I dissenting with him? It turns out to not be a simple yes or no question. However, let me frame it this way so you can kind of see where I'm coming from. The term concept, so the word we're talking about, is, at least to me, a term that we use to refer to human ideas. As such, if you are an AGI nerd like me, you recognize that the study of AGI is the study of concepts, whatever those turn out to be. This means programming AGI is a matter of understanding human concepts well enough to be able to implement them. Today, we're not entirely sure what a concept is, and it's an open area of research. Certainly, we don't understand it well enough that we could implement it into an algorithm. There have been various attempts, and obviously they haven't really gone anywhere with it yet. Now, in episodes 85 and 86, we looked at Douglas Hofstadter's Theory of Concepts, and he treats them as fuzzy categories, which I find a useful starting point for the discussion, but I've honestly got no idea how accurate his theory is. It's surely not yet an implementable theory, or at least insofar as he was able to implement it, it was really kind of primitive stuff, his copycat program, for example. Certainly not some giant breakthrough in AGI at this point. So given the importance of concepts to AGI, why was Popper so negative on them? Is he correct that theories are 100 times more valuable than concepts?

[00:05:19]  Bruce: To answer this question, note that Popper was focused in his research in his life almost entirely on formulating a critical method by working out how we criticize scientific theories via his falsification, okay? Through use of empirical experiments and the associated logic that that process utilized. If we're talking specifically about the critical method, as applies to science, and therefore falsification in its purest form, then I actually feel like I wholly agree with that quote from Popper. When it comes to the critical method, I have no doubt that theories are a hundred times more valuable than concepts. But as I'll cover in a separate podcast, the next one, if we are not talking specifically about Popper's critical method, then I do not agree with Popper's statement that theories are a hundred times more valuable than concepts. But before I get into in the next episode why I say that, let me first as much as I can agree with Popper in this episode before I disagree with him in the next episode. So a separate question that we'll only touch upon in this episode, but that I want to dig into in some future episode is the question, what even is a concept and how does it differ from a theory? Now, as we see in today's episode, Popper does briefly attempt to answer this question, and I'll go over his brief answer. Let's actually dig into it a little to understand Popper's view. Popper said, this is quoting him again, theories are a hundred times more important than concepts.

[00:06:50]  Bruce: Note that Popper is not claiming concepts are unimportant, merely that theories are more important, a hundred times more important. I would note here a possible disagreement between me and Popper on something, though I doubt it's yet of much importance. Popper effectively treats concepts as the same as words. So consider a quote from Popper where he treats concepts and words as interchangeable. So here's the quote. This is from Quantum Theory and the Schism in Physics. Theories are also described quite wrongly as conceptual systems or conceptual frameworks. It's true that we cannot construct theories without using words or if the term is preferred, concepts. Okay, so note that Popper is equating concepts and words there as if they're one and the same, okay? Now, if we read Popper here very literally as meaning that words and concepts are the same, then I for sure disagree with what Popper is saying here, okay? As we saw back at episodes 85 and 86 on Douglas Hofstadter's theories, there is no one-to-one correspondence between words and concepts. There are far, far, far more concepts than we have words. And there's like an economy of words where we have to reuse words for multiple concepts because that's just the way reality is, okay? There are even concepts, as Hofstadter points out, for which we have no words, that there's simply no word for the concept, and yet we can still conceptualize it. However, I don't think there is any need to read Popper in such a radically literal manner.

[00:08:21]  Bruce: So even Hofstadter openly admits that there's a very close relationship between words and concepts, and how there's even, they are even in many common circumstances, words and concepts are one and the same. He talks about how you're walking along and you think, you know, oh, cute girl or something like that, right? That's an example of where you're invoking a concept using a word, because words and concepts are sometimes the same thing, when they're treated as a kind of a giant fuzzy category. Moreover, Popper was, of course, well aware that words can point to multiple concepts, okay? So you often find Popper making the very sorts of clarifications between words and concepts that I've advocated all throughout this podcast.

[00:09:06]  Unidentified speaker: Let me just give you just a sampling.

[00:09:08]  Bruce: He does this all the time. Here's a sampling of Popper making it very clear that he understands the difference between words and concepts, okay? Quote, I want to make it clear that I'm using the word thought only in Frege's objective sense, and I'm speaking only about the objective content or the logical content of theories.

[00:09:28]  Unidentified speaker: That's from objective knowledge.

[00:09:31]  Bruce: Quote, these very trite examples have only the function of helping to clarify what I mean when I speak of knowledge in the objective sense, also from objective knowledge. Quote, in several of many customary senses of the term metaphysical, and in a sense in which it can be used in contradistinction to logical, methodological, or epistemological. That's from Realism and the Aim of Science. Quote, the term anticipation is used by Bacon in a deprecating sense as a synonym for prejudice. I use it in a positive sense as a synonym for expectation or assumption from two fundamentals. So this next one is important. This next one is a great quote. It's also important to the debate between modern crit rats and Bayesians. Quote, I am ready to admit that the word probable and probability are often used in a sense similar to the one in which I propose to use the somewhat awkward expression degrees of corroboration.

[00:10:30]  Unidentified speaker: Think about that.

[00:10:30]  Bruce: That's from the Realism and Aim of Science. He's literally saying that in many, most cases, the words probable and probability are exactly the same as what he calls degrees of corroboration.

[00:10:42]  Unidentified speaker: Think about that for a second.

[00:10:43]  Unidentified speaker: Okay?

[00:10:44]  Bruce: In each of these things, I could go on.

[00:10:46]  Unidentified speaker: There's like tons of these.

[00:10:47]  Bruce: So Popper clearly was aware that words sometimes have to be clarified as to how one is using them to point to different underlying concepts because words can point to many different concepts due to concepts outnumbering words by a wide margin.

[00:11:05]  Unidentified speaker: Okay?

[00:11:05]  Bruce: So because of this, I'm not sure I actually disagree with Popper on this. I think if you read him literally, I do, but I don't think you should read him literally here. Given all this, I prefer to read Popper as more or less agreeing with Hofstadter, that there's a close relationship between words and concepts, but they aren't quite the same thing. Specifically, words have meanings, those underlying meanings, those are the concepts. I doubt either Popper or Hofstadter would disagree on this point, at least from my read of them. It is specifically meaning, though, that Popper takes issue with. Popper feels meaning is only important insofar as it's instrumentally necessary to communicate a theory. In fact, Popper's criticism of meaning helps us understand how Popper differentiates between a concept and a theory. So, let's consider some quotes from Popper that show this. From Unended Quest, page 18 to 20, Meaning philosophies and language philosophies, so far as they concern with words, are on the wrong track. In matters of the intellect, the only thing worth striving for are true theories, or theories which come near to the truth. This, I suppose, most people will admit, but they will be inclined to argue as follows. Whether a theory is true, or new, or intellectually significant, depends on its meaning. And the meanings of a theory, provided it is grammatically unambiguously formulated, is a function of the meaning of the words to which the theory is formulated.

[00:12:32]  Bruce: So Popper here is talking about words, but we see he really means meaning of words, or in other words, he's talking about the underlying concepts. And this, the idea of meaning, is specifically what Popper is now going to criticize. Quote, this view of the meaning of a theory seems almost obvious. The argument that he just made on their behalf, steel manning it. It is widely held and often unconsciously taken for granted. Nevertheless, there is hardly any truth in it. I would counter it with the following rough formulation. The relationship between a theory or a statement and the words used in that formulation is in several ways analogous to that between written words and the letters used in writing them down. Letters play a merely technical or pragmatic role in the formulation of a word. In my opinion, words also play a merely technical or pragmatic role in the formulation of theories. Thus both letters and words are mere means to an end, different ends. So Popper is arguing that words and their concepts are pure instruments. They are really only meaningful insofar as they help us make sense of a theory. Thus Popper goes on to say, And the only intellectually important ends are the formulation of problems and the tentative proposing of theories to solve them, and the critical discussion of the competing theories. The critical discussion assesses the submitted theories, the terms in terms of their rational intellectual value as solutions to the problem under consideration, and as regards their truth or nearness to truth.

[00:14:09]  Bruce: So to Popper, a theory is an assertion about reality that could be tested and potentially falsified. Popper goes on to say, truth is the main regulative principle in the criticism of theories. Their power to raise new problems and to solve them is another. By comparison, a concept isn't really making an assertion that can be either true or false. Now, think back to the quote from Popper we started with at the beginning of this episode, and its full import will now be understood.

[00:14:38]  Unidentified speaker: Let me quote it again, okay?

[00:14:40]  Bruce: Theories may be true or false. By comparison, concepts can at best be adequate and at worst be misleading. So there is Popper's answer to the question, how do theories and concepts differ? A theory is falsifiable.

[00:14:56]  Unidentified speaker: A concept is not.

[00:14:58]  Bruce: Popper's answer is, surprise, his falsificationism! Gosh, I didn't see that coming. Popper goes on to develop a pretty strong argument against the idea that the meaning of a theory is what matters. Now, I really agree with his argument, and I feel it's important, so we're going to dwell on it a bit before I then later take some issue with it. Popper's argument is this, it is entirely possible to word a theory and explain its meaning differently in entirely different words, such that it feels like two entirely different theories. Yet, if those two theories make identical truth claims, about the world, they ultimately, Popper is arguing, must be considered the same theory. Quote from Popper, theories are also described quite wrongly as conceptual systems or conceptual framework. It is true that we cannot construct theories without using words, or if the term is preferred, concepts.

[00:15:51]  Unidentified speaker: Now here's the rest of the quote.

[00:15:52]  Bruce: But it is most important to distinguish between statements and words and between theories and concepts. And it's important to realize that it is a mistake to think that a theory T is bound to use a certain conceptual system C. One theory T1 may be formulated in many ways, and may use many different conceptual systems, say C1 and C2. Or to put it another way, two theories T1 and T2 should be regarded as one, if they are logically equivalent, even though they may use two totally different conceptual systems, C1 and C2, or are conceived in totally different conceptual frameworks.

[00:16:32]  Unidentified speaker: This is from Quantum Theory and the Schism of Physics.

[00:16:34]  Bruce: Popper's argument here is simple. If you can put a single theory in terms of entirely different words and conceptual frameworks, then clearly, and you can, then clearly the theory cannot have been dependent on the conceptual framework. From this, Popper concludes that theories are ultimately what scientists must care about, and concepts must be purely instrumental in communicating theories. Let's now take a closer look at Popper's criticism of concepts and how it relates to his criticism of words. From Objective Knowledge, page 123 to 125, and this is where we are going to talk about Plato now. Plato believed that the third world of forms or ideas would provide us with the ultimate explanations, that is, explanation by essences. Thus he writes, for example, I think that if anything else apart from the idea of absolute beauty is beautiful, then it is beautiful for the sole reason that it has some share in the idea of absolute beauty. And this kind of explanation applies to everything. That's from Plato 1000 BC or whatever. Now, back in episode 85 and 86, we talked about Plato's error here. Words point to what I've called either fuzzy categories or fuzzy concepts. These concepts typically, though not always, have no essence to them that defines them.

[00:17:51]  Unidentified speaker: That's the norm.

[00:17:53]  Bruce: Such fuzzy categories exist as a series of analogies with some connecting idea at the time but no central essence that defines everything in the category. Again, think here of mother. This is Hofstadter's example. There is no essence of what it means to be a mother. It's just a series of different analogies. Thus, Plato's whole theory of explanations by essences was doomed from the outset because he has, he was fundamentally misunderstanding the nature of human concepts.

[00:18:24]  Unidentified speaker: Okay.

[00:18:25]  Bruce: Now, Popper explains further why Plato's Platonism was such a problem, epistemologically speaking. Quote, this is a theory of ultimate explanations. That is to say, if an explanation whose explicans is neither capable nor in need of further explanation, and is a theory of the explanation of essences, that is by [hypostasis?] words. If Plato was correct, then figuring out why both a woman and a piece of art are both beautiful, would simply be a matter of figuring out what they had in common. Then throw in there a beautiful sunset and a beautiful sword, and you just keep seeking the properties that all of these different types of beauties share, and that would be the explanation of beauty. This is exactly what Plato got wrong, and why Plato's Platonism is an incorrect idea.

[00:19:11]  Peter: That's a great distillation, wow.

[00:19:14]  Bruce: Popper goes on, something like non-material things, or perhaps like stars or constellations, to be gazed at and intuited, though not liable to be touched by our minds. This is why the inmates of the third world, the formers or ideas, become concepts of things or essences or natures of things rather than theories or arguments or problems. Continuing the quote from Popper, this had the most far-reaching consequences for the history of philosophy. From Plato until today, most philosophers have either been nominalists or else what I've called essentialists. The essentialists, they are most more interested in the essential meaning of words than in the truth and falsity of theories. Popper then offers a famous diagram that I'm sure most of my listeners have seen, because it's in more than one of his books. I'm going to read it. It can be read in multiple directions. That's part of what makes the diagram clever. I'm just going to read it straight, which loses a lot in the translation.

[00:20:10]  Unidentified speaker: But then I will continue with what he said here.

[00:20:13]  Bruce: It's ideas. There's a left side of the diagram and a right side of the diagram. And Popper is going to argue that the things on the left side of the diagram are not very valuable and the things on the right side of the diagram are very valuable, even though most people equate the two together. Ideas that is, designations or terms or concepts, left side, right side, statements or propositions or theories may be formulated in left side words, right side assertions, which may be left side meaningful, right side true. And their left side meaning, right side truth, may be reduced by way of left side definitions, right side derivations, to that of left side undefined concepts, right side primitive propositions. The attempt to establish or rather than reduce by these means, their meaning, left side truth, right side, leads to an infinite regress. He continues, My thesis is that the left side of this table is unimportant as compared to the right side, which should interest, what should interest us are theories, truth, argument. If so, many philosophers and scientists still think that concepts and conceptual systems and problems of their meaning and the meaning of words are comparable in importance to the two theories and theoretical systems and the problems of their truth or the truth of statements. Then they are still suffering from Plato's main error, which in his footnotes, he defines Plato's error as, The error which is traditional is known as the problem of universals.

[00:21:46]  Bruce: This should be replaced by the problem of theories or the problem of theoretical content of all human language. Okay, so let's try to now summarize Popper's criticism of concepts and how he feels they are less valuable than theories. Popper's argument is as follows. The falsifiable truth content of a theory is what matters, not how we conceptualize the theory. True, you have no choice but to conceptualize it somehow, to make sense of it. But a theory can always be conceptualized in multiple ways. That is to say, it can be explained in very different words that may sound different. But if a theory still has the same truth content, it is the same theory. Moreover, concepts can't be falsified, so their truth content is zero. This is why, so argues Popper, concepts don't ultimately matter where as theories do. Now, so far, I entirely agree with Popper. Other than a few aforementioned nits about how words and concepts shouldn't really be equated, but I feel like that nit has no real bearing on his overall argument.

[00:22:48]  Peter: Can I just ground this, thanks to our, to my BFF ChatGPT here, a chart that I think really distills this, that I think just reiterates what you're saying. So to nominalism, universals are just names, no independent reality. To realism, universals exist independently of particulars. And then how I'm seeing this, just as fallibilism or critical rationalism offers a third way outside of subjectivism and objectivism, in Popper's view, concepts are human-made tools to describe reality fallibly. So reality exists independently, but concepts are tools to understand it.

[00:23:45]  Unidentified speaker: I think that's pretty good.

[00:23:46]  Unidentified speaker: Yeah.

[00:23:47]  Peter: Is that, is that, does that distill it?

[00:23:49]  Bruce: It's just, I think it distills pretty well what Popper is saying. I'm not necessarily saying I agree with that. I'm going to somewhat agree and somewhat disagree. But, but yeah, I think that does a pretty good job. ChatGPT did a fairly, I think, you know what, keep in mind, I'm no expert, right? Like I make this podcast and I look into this and I'm certainly a lay expert if that's such a thing. But like, I'm not overly concerned about philosophy.

[00:24:15]  Unidentified speaker: I'm not a philosopher.

[00:24:17]  Unidentified speaker: I get it.

[00:24:17]  Unidentified speaker: Okay.

[00:24:18]  Unidentified speaker: So let's, let's, so Bruce, Bruce Nielson's fourth way.

[00:24:21]  Unidentified speaker: Yeah.

[00:24:24]  Unidentified speaker: Okay.

[00:24:25]  Bruce: But what you just summarized seems to match what I think Popper just said.

[00:24:31]  Unidentified speaker: So I think it's a decent summary.

[00:24:33]  Unidentified speaker: Okay.

[00:24:35]  Unidentified speaker: Okay.

[00:24:37]  Bruce: So, so it's surely the case that concepts can't be falsified. So the truth content is zero. This is my main objection to people arguing over definitions, by the way. It never, never, never makes sense to argue over definitions. What you should do is just accept all definitions, numbering them if necessary, and move on and stop wasting people's time. Note that not that I've ever even once been able to convince anyone else to do that with me. Now, Popper goes on to argue that one of the main problems with concepts is that they can't be made exactly precise and trying to make them precise is a waste of time. So quote, in, in any case, concepts remain like every language, to some extent, vague and ambiguous. It cannot be made precise. The meaning of concepts cannot essentially be laid down by any definition, whether formal, operational or ostensive. Any attempt to make the meaning of the conceptual system precise, that's in quotes, scare quotes, by way of definitions must lead to an infinite regress and to merely, and to merely apparent precision, which is the worst form of imprecision because it's the most deceptive form. And then he says, this holds even for pure mathematics. That's from quantum theory and the schism of physics. Now in episodes 85 and 86, Hofstadter claimed there were some precise and [unambiguous?] words or concepts, within some context at least. And I agreed with Hofstadter at that point. And I even claimed that sometimes essences are real in, say, mathematics. It seems like Popper just disagreed with Hofstadter and me on this.

[00:26:11]  Bruce: So are I and Hofstadter disagreeing with Popper here? I'm not sure actually, but maybe. Okay, one of Hofstadter's examples was the term prime number, okay? That term has an unambiguous meaning in number theory, in mathematics. Did we just refute Popper's claim that even mathematics has no exactly precise terms? Okay, now I have a heavy suspicion that Popper would argue to me and Hofstadter that he did admit that there is such a thing as precision within a specific problem space. Don't we get the exact quote?

[00:26:49]  Unidentified speaker: So we can see what Popper says here.

[00:26:51]  Bruce: This is from Popper's critical remarks on meaning analysis. Exact or precise terms is a pseudo problem. It depends essentially upon the inexact and imprecise terms, exact and precise. These are most misleading, not only because they strongly suggest that there exists what does not exist, absolute exactness or precision, but also because they are emotionally highly charged under the guise of scientific character and of the character and of the scientific objectivity. They suggest that precision or exactness is something superior, a kind of ultimate value, and that it is wrong or unscientific or muddleheaded to use inexact terms. And then he puts in parentheses, as it is indeed wrong not to speak as lucidly and simply as possible. Continuing the quote, But there is no such thing as an exact term, or terms made precise by precise definitions. Also, a definition must always use undefined terms in its definition, since otherwise we would get involved in an infinite regress or in a circle. And if we have to operate with a number of undefined terms, it hardly matters whether we use a few more. Okay, so Popper so far is all criticism. But then he says this, and this is the thing that I wanted to emphasize here. Quote, of course, if a definition helps to solve a genuine problem, the situation is different. And some problems cannot be solved without an increase of precision. Indeed, this is the only way in which we can reasonably speak of precision.

[00:28:32]  Bruce: The demand for precision is empty unless it is raised relative to some requirements that arise from our attempts to solve a definitive problem. So it isn't—so it just isn't the case that Popper has an issue with precision in general. Even getting—even getting precise with definitions, he just said that that's okay within the scope of trying to solve a problem. Popper was okay with that if it was necessary to solve a specific problem. Now, I call this out because I've encountered a general misunderstanding of the CritRat community towards this point. The moment you ask them to make something more precise to try to work on a problem, they will say, no, Popper said getting precise is wrong, completely missing this kind of important caveat that he actually placed on that, that you do get more precise to solve problems, and then it's okay to get precise with your definitions.

[00:29:35]  Unidentified speaker: He just said that.

[00:29:36]  Bruce: There's no doubt he said that.

[00:29:37]  Unidentified speaker: Okay.

[00:29:38]  Bruce: It would be more correct to say that Popper had issues with sitting around defining things up front with precision, with no real problem in mind to be solved. Now a common problem, that is a common problem with philosophers today. So it's understandable that Popper had problems with that. This is a silly thing to do because it mistakes the true purpose of concepts, which was not meant to be a falsifiable truth assertion about reality. But in relationship to solving definitive problems, you'll often need to get more precise, to sharpen your theory and to make it more testable and criticizable. Compare what we're just talking about to a quote I love, that I've reused from Popper multiple times from Objective Knowledge page 25. A scientist tries to kill his theories. He is consciously critical of his theories, which for this reason, he tries to formulate sharply rather than vaguely. Here Popper is arguing for the importance of making your theories precise rather than vague, so that they can be easily criticized. Before we go too far down the road of concepts have no value, let's make sure we recognize that Popper never makes that claim. He is arguing for the value of concepts, but he believes in minimal instrumental value compared to theories. He does at times quickly mention ways in which concepts can be valuable, and I want to recognize that fact and quote him so that you can see that he does talk about the value of concepts at times. And this is also going to be useful for a future episode.

[00:31:09]  Bruce: Quote, for concepts are partly means of formulating theories, partly means of summing up theories. In any case, their significance is mainly instrumental, and they may always be replaced with other concepts, Objective Knowledge, page 123. Quote, although concepts may have great suggestive power, this is also, sorry, may have great suggestive power, and may thus influence the further development of the theory.

[00:31:37]  Unidentified speaker: It's kind of an important thing about concepts.

[00:31:39]  Bruce: It is not the conceptual system, but the theory that is of the real importance for the pure scientist. And the theory is not merely an instrument for him, it is more, he is interested in its truth, or in its approximation to the truth. Continuing the quote, the conceptual system, on the other hand, is exchangeable, and is one of among several possible instruments that may be used for formulating the theory. It merely provides a language for the theory, perhaps a better and simpler language than another, or perhaps not. That's quantum theory and the schism in physics.

[00:32:12]  Unidentified speaker: So that was all me quoting Popper.

[00:32:14]  Bruce: To make things more confusing, Popper says sometimes a concept is actually hiding one or more theories. So quote, all universal concepts incorporate theories. Although some of these can be tested, they can never be exhaustively tested and can never be verified. The statement, here is a glass of water, is open to an indefinite and exhaustible number of tests, chemical tests, for example, because water, like anything else, is recognizable only by its law-like behavior. Quote, thus water is dispositional, like every other universal concept. Even red is dispositional, for this surface is red asserts that this surface has a disposition to reflect red light. That's all from Realism and the Aim of Science. Dispositional, if you don't know what dispositional means, it means having a disposition to behave in some way. So the concept of a disposition, dispositional, refers to the inherent potential capacity or tendency of an object to behave in a certain way under specific conditions or laws, rather than merely describing its current, immediate or observable properties. What Popper is saying here is that a concept may, what you're calling a concept may actually contain a theory, right? That was what he was trying to explain with his whole dispositional thing. And because of this, there is some confusion. We may call something a concept, but we're actually referring to a theory. So far, I've had little disagreement with Popper. I agree with him that concepts can't be falsified.

[00:33:43]  Bruce: Indeed, if Hofstadter's theory is at all accurate, concepts are meant to be slippery and totally unfalsifiable. You're supposed to keep extending concepts over time rather than falsifying them. Concepts or some concepts anyhow are in fact built on analogies. There is no true correct or incorrect analogy. Because of this, concepts are not open to falsification and thus can't truly be criticized, at least not in the scientific falsificationist sense. Further, you can always choose a different set of concepts to express the same theory. And nothing changes in terms of the truth concept of the associated theory. I agree with Popper on that. In fact, I completely agree with everything we just talked about from Popper here. However, is it therefore true that as Popper put it, quote, theories are a hundred times more important than concepts? My answer is a resounding no. Popper is completely wrong in this statement.

[00:34:41]  Unidentified speaker: Actually, let me walk that back just a bit.

[00:34:43]  Bruce: I'll even agree that he is right if we assume he was tacitly implying within the scope of the critical method, which was his main area of research interest. If he meant that, then I actually do agree with his statement that [theories?] are a hundred times more important than concepts. Popper's epistemology is often summarized as conjecture and refutation, or conjecture and criticism. But Popper said little to nothing about how we come up with conjectures, and he concentrated literally 99.9% of his effort, into understanding how scientific refutation works, and what institutions and conventions were necessary for it to function. And this focus made sense. Solving the problem of how we make conjectures is basically equivalent to solving the problem of AGI. It's one of the hardest problems imaginable. Since the critical method was Popper's main interest, I can see why he felt theories within the scope of what he was interested in, were a hundred times more valuable than concepts.

[00:35:42]  Unidentified speaker: On the criticism side, that's true.

[00:35:44]  Bruce: But if we're actually going to choose to pay attention to how conjectures are made, what then? I'm going to argue in the next podcast that if you look at the conjecture side of Popper's epistemology, that concepts are incredibly important to how humans make conjectures. Those theories, they don't come from nowhere, of course.

[00:36:05]  Unidentified speaker: That is the end of today's episode.

[00:36:09]  Bruce: Any questions there, Peter?

[00:36:12]  Peter: No, that was interesting and a lot, and there's no one else on your path, Bruce. You've left the rest of the world behind, as we should all strive to do, I think.

[00:36:28]  Bruce: I may well be the only person in the world working on both Popper's epistemology and Hofstadter's theories at the same time.

[00:36:37]  Unidentified speaker: Okay.

[00:36:37]  Peter: Well, thank you, Bruce.

[00:36:38]  Unidentified speaker: All right.

[00:36:40]  Unidentified speaker: Thanks, Peter.

[00:36:41]  Unidentified speaker: Bye-bye.

[00:36:48]  Unidentified speaker: Hello again.

[00:36:50]  Peter: If you've made it this far, please consider giving us a nice rating on whatever platform you use, or even making a financial contribution through the link provided in the show notes. As you probably know, we are a podcast loosely tied together by the Popper Deutsch Theory of Knowledge. We believe David Deutsch's Four Strands tie everything together. So we discuss science, knowledge, computation, politics, art, and especially the search for artificial general intelligence. Also, please consider connecting with Bruce on X at BNielson01. Also, please consider joining the Facebook group The Many Worlds of David Deutsch, where Bruce and I first started connecting.

[00:37:33]  Unidentified speaker: Thank you.