Episode 127: Hofstadter vs Popper on Concepts
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Transcript
[00:00:00] Blue: Hello out there! This week, on the Theory of Anything podcast, Bruce starts with Popper’s assertion that theories are a hundred times more valuable than concepts. He then compares this to Douglas Hofstadter’s ideas on creativity and consciousness. If concepts are so unimportant, where do conjectures come from? Popper apparently does not have much to say about this. To Hofstadter, creativity comes from our ability to create analogies. We use our pattern -seeking self -referential brains, feedback loops, to overcome gaps logic can’t yet fill. If it seems like I don’t quite understand this perspective, even after reading at least one of his books, it’s because I actually don’t. But anyway, Bruce explains it much better here. I also want to say that sometimes I edit this podcast and realize that my questions or comments have little to do with what Bruce is talking about. And then I listen again and realize there are meaningful connections that I must have been making on some level that aren’t even that obvious to myself. Maybe that’s the definition of a good conversation. Not sure if that’s what’s happening here, but I hope it is. And regardless, I got a lot out of listening to Bruce and asking my maybe tangential questions. And I hope someone out there enjoys this conversation too.
[00:01:37] Red: Welcome back to the Theory of Anything podcast. Hey, Peter. Hello, Bruce. How are you doing? Doing good. All right. I’m excited for today’s episode. Our last episode, which was on Popper’s criticism of concepts, was in some way a setup for today’s episode, which is the one I’ve been excited about. Okay. So we’re going to talk about Hofstetter’s theories, and we’re going to work them in with Popper’s epistemology in an interesting way.
[00:02:05] Blue: Okay.
[00:02:05] Red: And ultimately, I’m going to end up taking issue with Popper’s claim that theories are 100 times more valuable than concepts.
[00:02:13] Blue: Okay. Well, if Hofstetter, if you’re listening, wait, is
[00:02:16] Red: he still alive? I don’t even know.
[00:02:19] Blue: Okay. Well, if you’re listening, we want you on the podcast. I’ll reach out. We may have to
[00:02:25] Red: ask Melanie Mitchell because she might be Douglas Hofstetter today.
[00:02:29] Blue: That’s right. I think he’s still alive. I haven’t heard he’s died, so I think he’s right that he’s still alive.
[00:02:36] Red: He’s got to be pretty old. Yeah.
[00:02:37] Blue: Okay. 45 born in the same year as my dad, and he’s still alive. Okay.
[00:02:42] Red: I’ll
[00:02:43] Blue: reach out. I will.
[00:02:44] Red: All right. Sounds good. Okay. So in the previous podcast, I quoted Popper as saying, theories are 100 times more important than concepts. Theories may be true or false. Concepts can at best be adequate and at worst be misleading. Concepts are unimportant in comparison with theories. I then agreed with Popper on this, but only if we are talking about the method of criticism. But I claim that if we’re talking about creating conjectures, that Popper’s statement is wrong. In this podcast, I’ll explain why I feel this way, and I will give explicit examples of how he is incorrect. One of the big known problems with Popper’s epistemology, and Jane from the Bayesian side also acknowledges the same problem with Bayesian epistemology, is that we have no real idea where conjectures come from. So neither Popper’s nor Jane’s epistemology pay more than lip service to conjectures. We just accept that humans have them and that we test them using falsification if you’re a Popperian and Bayesian analysis if you’re a Bayesian, which are not as different as you might first think. Where do conjectures come from? Popper had no idea. He didn’t even speculate on it. I obviously don’t really know either. If I did, I would know how to credit an AGI. But I’ve advocated for one theory, not so much because I’m actually sold on it, as it is just the only theory I even know about that attempts to answer this question. And as a Popperian, we start with theories that are on the table, true or false. That is, of course, Douglas Hofstadter’s theories, as covered in Episodes 85 and 86, where he claims that human creativity is due to our ability to create analogies, what he calls analogies.
[00:04:24] Red: I feel like that’s that best eliciting term. Unfortunately, Hofstadter’s theory is posed as a form of induction, though in Episodes 85 to 86, I explain why you as a critical rationalist should not be put off by that term in this particular case. Now, Hofstadter argues that our creativity stems from our ability to create analogies. We have some knowledge in one area, and we attempt to reapply it into some other area. Critrats that I’ve talked to about this saw this as an inductive sort of infinite regress because the knowledge never gets created in the first place. But this isn’t correct. Hofstadter actually argues for the idea of fuzzy concepts that evolve over time via analogy. So we move from simpler analogies to more abstract analogies, thus avoiding the infinite regress that Critrats are concerned about, and kind of rolling the whole thing into a sort of evolutionary epistemology. If this is correct, that’s a big if, then Hofstadter’s theory is not inductive per se, but more like Popper’s evolutionary epistemology. This is maybe not so surprising, especially if you buy Campbell’s and Popper’s version of evolutionary epistemology, which we’ve talked about a lot on this podcast, where all induction turns out to be evolutionary epistemology. Right or wrong, that is what they argued. In this podcast, we’ll go over an extended example of that from Hofstadter himself, from his book, Services and Essences, and along the way I’m going to show what seems to me to be a very real problem with how Critrats today conceptualize a certain aspect of Popper’s epistemology. To make this problem as sharp as possible, let’s consider the following very popular Critrats saying, now suppose a non -Critrat says something like this, this observation suggests this theory.
[00:06:15] Red: For example, maybe somebody notices some weird anomaly, and to them it suggests some new novel theory that wasn’t previously on the table. Perhaps the interlocutor is quoting some stat, a study, or some other observation that they came across. Note that this is not the same as the essentialist problem that I’ve criticized in past episodes. I don’t hear mean that some experimental piece of new evidence was being used to corroborate a theory, and that the Critrats get confused over the fact that corroboration is an actual part of critical rationalism and that it’s a meaningful part of it. I mean literally some observation suggested a brand new theory not previously considered. Almost immediately, every Critrat I know will instantly respond to this interlocutor saying, no, proper prove that was incorrect. Observations can only be used to choose between existing theories and then only by falsifying one of them. I’ve seen this response so many times a lot count, even from the smartest of critical rationalists. Note that in context, this isn’t some merely pedantic use of words. Their response isn’t confused over the other, but that’s not what I’m arguing here. They are making a much different claim in this context. They are saying you can’t induce theories from observations, but for a specific reason, because observations are only used to select between theories, never to suggest new theories. This is so widely believed in the critical rationalist community today that believing this practically defines you as being a critical rationalist. It happens to be a technically false or at least very questionable statement, depending on how literally you choose to interpret it.
[00:08:10] Red: It simply isn’t the case that an observation can’t suggest to you a brand new theory and must only be used to select between theories via falsification. To anyone but a critical rationalist, this is just sort of obvious because we see observations and then suddenly an idea that we haven’t thought of before jumps into our mind. It’s a completely normal, super common human experience. This is such a common human experience, it just seems weird to non -critical rationalists that anyone would doubt that it’s real and it truly happens. Now to us critical rationalists, we’ve put so much faith in this idea that observations are only used to falsify theories that we sometimes can’t see the force for the trees anymore. Observations can and do suggest to us entirely new ideas and theories. To sharpen this point, let’s use a real life example. This is taken from Hofstadter’s book by the way, Surfaces and Essences. In 240 BC, Chrysopis, famous ancient philosopher, conjectured that sound was a wave just like water is a wave. Now how did Chrysopis come up with such a conjecture? Well, I don’t know the specifics, so let’s make up a believable hypothetical. Suppose Chrysopis noticed that echoes were bouncing off of his voice, were bouncing, and in his head, the idea suddenly popped. Whoa, that was like a water wave bouncing off a surface. Is this a believable and realistic story? It sure seems like it to me, like I can completely believe that the idea of Chrysopis deciding that sound was a wave like water was a wave, hypothesizing that, that that happened because he heard an echo, and suddenly he perceived sound as being like an invisible wave, and like water which is a visible wave.
[00:09:57] Red: Note that this is not a case of Chrysopis having multiple theories he’s picking between, or something like that. It’s just an analogy that popped into his head, unbidden. Moreover, this is not inconsistent with Popper’s own view. For example, Popper argued that humans try to enforce regularity onto the world based on their observations. Quote from Popper, conjecture refutation page 60. Without waiting passively for repetitions to impress or impose regularity upon us, we actively try to impose regularities upon the world. We try to discover similarities in it. Want to emphasize, we try to discover similarities in it, and to interpret it in terms of laws invented by us without waiting for premises to jump to conclusions. These may have to be discarded later should observations show they are wrong. Note that Popper just explicitly put this in terms of similarities we discover, i.e. precisely what Hofstadter calls an analogy. This is one of the reasons why I was shocked when crit rats would dismiss Hofstadter’s theory out of hand as inductive and then refuse to discuss it further. Popper literally anticipated Hofstadter and said exactly the same thing Hofstadter said. This is the danger of being too dismissive of theories that don’t fit your intuitions right off the bat. The moment a theory seems inductive to a modern crit rat, they can’t help but throw Hofstadter’s theory into the inductive category and considering it ipso facto refuted, even though Popper argued exactly the same thing. In fact, Popper explains exactly why this is a problem due to the very same reason quote from conjecture refutation page 64, our propensity to look out for regularities and to impose laws upon nature leads to the psychological phenomena of dogmatic thinking or more generally dogmatic behavior.
[00:11:54] Red: We expect regularities everywhere and attempt to find them even where there are none. Events which do not yield to these attempts, which are inclined to treat to treat as a kind of background noise, we are inclined to treat as a kind of background noise and we stick to our expectations even when they are inadequate and we ought to accept defeat. Popper even claimed this was true for animals, not just humans, self in its brain page 137. Organisms do not wait passively for repetition or any event or two to impress or impose upon their memory the existence of a regularity or of a regular connection. Rather, organisms actively try to impose guest regularities and with them similarities upon the world. By the way, that is exactly our understanding of animal learning, this whole idea of operant conditioning and classical conditioning. That’s exactly what’s going on, right? So, okay, so we have something interesting to explain here with this hypothetical story of chrysalis. Chrysalis observed something namely in this hypothetical sound bounces. This observation caused him, just as Popper notes, to see a similarity in nature. Chrysalis, again, just like Popper claims, tries to impose this similarity upon nature via creation of a conjecture that sound is a wave in this case. And as Popper notes, this is just a conjecture at this point. It may have to be revised later in light of other observations. But wait, where did the conjecture itself come from? Well, it was suggested by the observation, of course it was. A similarity was noticed and that caused chrysalis to come up with a conjecture that sound is a wave. It wasn’t that chrysalis had some set of theories in mind. He was using this observation to select between.
[00:13:53] Red: The observation was the cause of the conjecture. Now to be sure, it surely is not true Baconian induction we’re talking about here. It’s not that chrysalis was some blank slate and his observation that sound bounces somehow was the sole cause of this conjecture coming into being. Clearly chrysalis had a lot of background knowledge that he was working with. Not the least of which was that he probably had a pretty solid set of knowledge about water waves that he can actually see, that we see and we observe and form ideas about. So there is no fear here of Baconian induction rearing its ugly head, which is why I reject the crit -rat rejection of Hofstadter’s theories on the ground that it’s quote inductive. By itself at least, this is clearly a bad argument. But there is I admit something odd or problematic about this example. First of all, it directly contradicts the crit -rat conventional wisdom that we only use observation to select between theories via falsification. In this case, the observation that his voice literally echoes literally suggests to chrysalis that sound might also be a wave, but just invisible. No falsification or selection between theories was involved, at least not consciously. But the problem is even deeper than that. Popper is often quoted as saying that even when we don’t think we’ve learned something from an observation, typically it’s because we had a tacit probably unconscious expectation that got violated. So for example, he says, Popper says, this is from Objective Knowledge page 344, we become conscious of many of our expectations only when they are disappointed, owing to their being unfulfilled. An example would be the encountering of an unexpected step in one’s path.
[00:15:42] Red: It is the unexpectedness of the step which may make us conscious of the fact that we expect to encounter an even surface. Such disappointments force us to correct our system of expectations. The process of learning consists largely in such corrections that is in the elimination of certain disappointed expectations. Now, Deutsch has taken this idea and gone down the path of insisting that humans don’t have beliefs at all, but instead they have expectations. An idea that actually literally comes from the Popper quote I just read. Popper’s utilizes this concept of expectations getting violated as a way to wrap this sort of thing into his falsificationism, that you don’t have a literal conscious theory, but you have an unconscious expectation which is like a theory that gets falsified. So quote, this is from Realism of the Aim of Science page 97, quote, the psychological or biological analog of a hypothesis may be described as an expectation or anticipation of an event. This expectation or anticipation may be conscious or unconscious. It consists of the readiness of an organism to act or react in response to a situation or a certain specific kind. It consists of the partial activation of certain dispositions. Classical examples of the way in which unconscious expectations may become conscious are stumbling down a step, I thought there was a step there, or hearing clock stop. I was not aware that I heard it ticking, but I heard it when it stopped. Our organism was anticipating unconsciously certain events and we became conscious of the fact only after expectations were disappointed or falsified. So this is how Popper tries to work falsification, wrap this into falsification, his theory of falsification.
[00:17:31] Red: Okay, but how do we fit this to the chrysalis story that we’re talking about into the idea of expectations getting falsified? Chrysalis likely heard a sound bounce an echo many times in his life before it occurred to him that sound might be a wave. So it’s not like it violated his expectations. So what got falsified here? For that matter, what’s the alternative competing theory that this observation that sound bounces like a wave supposedly falsifies? It can’t be that sound is not a wave because as Deutsch points out, the inverse of a theory isn’t a theory. Plus, does sound bouncing falsify the idea sound is not a wave? Not that I can see. So it seems like we’ve got a case of an observation suggesting a conjecture. Most would say a true conjecture no less because today we would say sound is a wave. That sound is a wave, even though there is no competing theories, no missed expectations and nothing got false falsified. Yes, go ahead.
[00:18:36] Blue: Sorry. You’ve just brought up something that I find really interesting about sound that may or may not relate to your point and that I might cut off, but I just want to get this cut out when I edit. But I just want to get this thought out here. So sound waves can be described by something called the Nyquist theorem perfectly accurately given to a basic dynamic range and frequency range. This is the basis of digital recording.
[00:19:15] Red: Yes.
[00:19:16] Blue: Right. Are you with me so far? Yes. So basically what this, I guess it’s a theory, but I don’t even think it’s that controversial amongst people who really know about it, is that digital waves are not stair steps. That’s a myth that basically these sound waves can be described as information, which to me kind of jives with this idea that reality is computational. Yes. That we get it from bit that reality is informational. Does that go anywhere for you when you’re talking about sound waves? I don’t know if it doesn’t. Okay. So
[00:20:04] Red: you’re actually making a good point here. I need to probably come back to it at the end of the episode though. Let me set you up though. One of the things that we might ask is the idea of a wave, is that a concept or a theory? It’s not even obvious, right? I’m treating it like a concept at the moment and certainly at the time we’re talking about it at the time of chrysalis. It was just a concept, but it has long since evolved into a very deep something that we would call a theory today. Can I? Okay. And one of the things I’m going to argue before we’re done with this episode is that there’s no clear distinction between concepts and theories. And I think this is a really good example of that, that we would talk about a wave and initially that would just be a concept, but over time we can and will turn it into the basis for not just a theory of waves, but for all sorts of different theories. Like waves show up everywhere, right? In all sorts of different theories. So let me come back to that because I’m actually going to give some examples of that. Actually, Hofstetter’s going to give some examples of that. I’m going to quote Hofstetter, giving some examples of this. Okay.
[00:21:22] Blue: Okay.
[00:21:23] Red: So, okay. So there’s, there’s a, I just, just to repeat here, I just said that this idea that sound is a wave, there is no competing theories, no mispect expectations, nothing got falsified. You simply heard sound bounce and echo and you had the thought it’s a wave. And it does not match the falsificationist approach that Popper is, is that crit rats normally ascribed to at all. Okay. There’s, there’s more of a problem here. There’s an even bigger problem. I’ve been treating this idea that sound is a wave like it’s a theory that could be falsified. But in fact, it is not a theory at all, at least not at this point in time. If by theory we need something that can be actually falsified, recall that to Popper, one of the main differences between theories and concepts was that theories could be falsified concepts can only be at best adequate and might even be misleading.
[00:22:19] Blue: Okay.
[00:22:21] Red: It’s actually just an analogy at the time of chrysalis. And as we’ll see, it’s not even an exact analogy or to put it more bluntly, sound is a wave is really not a theory, but a concept. And Popper told us in the previous episode, and I agreed with him on this point that concepts can’t be falsified. Why do I say that this is not a theory, but a concept? Well, let’s now read what Hofstadter actually wrote and he’ll explain it better than I can. Okay. So this is now from services and essences page starting with page 210 and then I don’t know how many pages I’m going to read through here, but just starting at page 210 already in roughly 240 BC, the Greek philosopher chrysalis had speculated that sound was a kind of wave. And some 200 years later, his ideas were developed more fully by the Roman architect Vitravis, I don’t know how to pronounce that, who explicitly likened the spreading of sound waves from a source to the circular spreading of ripples on water. What Vitravis did is in fact, extremely typical of the thinking style of all physicists taking a familiar visible every day phenomena and seeing it in one’s mind, in one’s mind’s eye as taking place in another medium. In this case, the familiar phenomena is ripples whose wavelength and frequency are extremely apparent. And in the new medium, and the new medium is of course air note that prior to chrysalis, there was no real reason to believe sound was a wave. And here is the critical point, sound is not a wave under what the term meant at that time. Whatever the Greek or Roman equivalent would be.
[00:24:12] Red: Not surprisingly, there were, this is now quoting Hofstadter again, not surprisingly, there were some significant discrepancies between sound waves in the air and waves on water. Among the most important is the fact that unlike water waves, sound waves are longitudinal, meaning that they involve motions of air molecules along the direction of propagation of the noise. This is sometimes called a compression wave, since the traffic is getting more and then less compressed. Compression waves always are longitudinal, in that the distance grows and shrinks along the direction which the wave itself is traveling in. Continuing the quote from Hofstadter, comparing sound waves with water waves seems easy, but there are hidden subtleties. Water waves are called a transverse wave. However, that’s a different kind of wave. However, it happens that ripples are not that simple. Hofstadter goes on to explain that water wave waves is partially longitudinal too. Today we’d say water waves are transverse waves or partially transverse, partially longitudinal waves, whereas sound waves are purely compression waves, which is considered a kind of longitudinal wave. So strictly speaking, based on the meaning of the term wave, at the time sound is not a wave. It was merely somewhat analogous to what was then called a wave. Quoting Hofstadter now, yet another major discrepancy between sound waves in the air and ripples on the water is that whereas water waves travel at different velocities, depending on their wavelength, for which they are said to be dispersive, sound waves are much simpler. No matter what their wavelength is, all sound wave propagates at the same velocity in a given medium, which entitles them to the label non -dispersive.
[00:26:04] Red: This is lucky for us, speaking creatures, since otherwise the different waves constituting our voices would all disperse and we couldn’t understand a thing anyone said. This is why I say, this is why, this is Bruce now talking, this is why I say that the idea that sound is a wave is really a concept, not a theory, and thus can’t be falsified. Surely if it had been conceived as a specific theory, meaning that sound is exactly like a water wave, it’s a false theory, then it could be falsified and it would be false. Put another way, Christopher’s idea that sound is a wave, like water is a wave, if treated as a strict theory is a false theory. There are easy experiments you can do to falsify this theory, but since it was actually just an analogy and a somewhat vague one at the time, there is no realistic way it could be falsified. That’s why I agree with Popper that concepts cannot be falsified. Recall that Popper’s quote we started with was, theories are 100 times more important than concepts. Because he explains, theories may be true or false, whereas concepts cannot be. Popper is correct. There is no way to falsify this conjecture that sound is a wave, making it more what Popper called a concept rather than a theory. To us today, we no longer conceive a sound as being quote analogous to a wave, but rather the concept of a wave has a long sense stretched and evolved and extended to include many types of waves with sometimes very different properties.
[00:27:43] Red: So sound is not like a wave to us today, it is a wave to us today, but only because the concept of wave changed and extended to include a new kind of wave, a compression wave in this case. So of course, there is no chance this analogy could have been falsified, given that we ultimately just changed the definition of wave to include sound. You’ve probably never given much thought to how this expansion of the concept of wave was only made possible because humans can extend concepts via analogies. Hofstadter continues explaining just how significant this is to human intelligence, quoting Hofstadter again now. In a sense, the leap from visibly undulating water to visibly undulating air, though humble in a way, was also the greatest leap in the story of the development of the wave concept because it opened up people’s minds to the idea of making another daring leap across similar lines. One success led to another, each new analogical extension making it easier, easier to make the next one. This highly cerebral game might be called playing analogy leap frog. Okay, that’s the end of the quote. So despite the analogy being strictly wrong, it for sure turned out to be fruitful as an analogy. So fruitful that today you probably can’t conceive the concept of wave without upfront assuming there are many different kinds of waves. Hofstadter continues, quote, the first guess is about light as a wave phenomena were somewhat wrong as they were based on an overly simple simplistic analogy with sound. It was assumed that light just like sound was a compression wave that propagated in an elastic medium such as air. Continuing the quote, it was only in about 1860 that James Clark Maxwell
[00:29:44] Red: came to the astonishing revelation that light waves did not involve the motion of any material substrate at all, but instead were periodic fluctuations at each point of the three dimensional space in which we live of the magnitudes and directions of certain abstract entities called electric and magnetic fields. It was as if the medium that conducts light waves consisted of a gigantic collection of immaterial arrows, one located at every point of empty space and whose numerical values simply grew and shrink, grew and shrink periodically oscillating. Now let’s consider this quote from Popper we started with again, quote, theories are 100 times more important than concepts. Theories may be true or false concepts can at best be adequate and at worst be misleading. Concepts are unimportant in comparison to theories. So by now it should be obvious that this is an incorrect statement. And here’s why. First of all, the idea of sound as a wave gave rise to the idea that there were many kinds of waves that gave rise to an incredibly fertile or if somewhat abstract concept of a wave that quickly proved fruitful across all sorts of different theories. So the idea that a concept can be at best adequate and at worst misleading, it is wrong. Concepts can be far more than merely adequate. They can be incredibly fruitful and fruitful and fertile. Does anyone seriously doubt the idea that sound as a wave proved at best merely adequate? No, of course not. Hofstadter explains, quote, it didn’t take physicists too long before they started realizing how immensely fertile this concept of wave truly was in the explanation of natural phenomena ranging from the most ubiquitous such as sound and light to all sorts of exotic cases.
[00:31:41] Red: For example, moonlit waves in the early 20th century radio waves really just long, long wavelength light waves were used as a host medium for carrying sound waves. Later during the 20th century, temperature waves were discovered. Also discovered were spin waves. And then there are gravitational waves. Last but not least among the very, very most important kinds of waves in all of physics are quantum mechanical waves, sometimes called matter waves or probability waves. As we have seen, this is still quoting Hofstadter, the notion of wave in physics has reached an enormous degree of abstraction and sophistication today. And yet all of the latest and most abstract forms of waves are tied by analogy and by heritage to the earliest kind of extremely concrete, tangible and palpable waves in the bodies of water and in the fields of amber grain. Waves that we can see with our eyes and feel with our bodies. I hope you can see now why I say that the crit -rat claim that observations only help us choose between theories is really just plain wrong. At least one source of conjectures, and if Hofstadter right, this might be the only source of conjectures, I don’t know if he’s right or not, is analogy. That is what Hofstadter believes is the sole source of conjecture. Even Popper admits we notice similarities and build regularities from them, that’s where conjectures come from. But these aren’t initially conjectures of theories, they’re conjectures about whether extending a concept by analogy might be fruitful. Take the idea that sound is a wave, like water is a wave. As a theory, that’s a faultifiable and even fault theory. But as an analogy, it’s incredibly fruitful, opening up whole new ways of theorizing.
[00:33:24] Red: That’s why I can’t accept Popper’s claim that theories are 100 times more important than concepts, that’s just wrong. Concepts, at least as Hofstadter says, are built on analogies. And analogies aren’t true or false, they’re valuable because they spark new productive ways of thinking. So once you see that, Popper’s claim that concepts are 100 times less valuable than theories just appears to be incorrect. This also tells us something about the nature of conjectures. Conjectures can reuse pre -existing knowledge while also evolving and expanding it. Chrysophus made a leap of imagination that sound was a wave like water was a wave. He was strictly wrong, but that didn’t matter. What mattered was that sound was somewhat like a water wave. When people began to test this idea, it worked often enough, or we should say it was corroborated often enough, that the times it failed didn’t really matter that much. By the way, this is an example of what we’re going to later call corroboration without falsification. How corroboration can still be valuable even when there is no falsification possible. This is a topic for a future podcast. Instead of keeping wave as one precise falsifiable concept, which would then be a theory, we split into several sub -concepts connected by abstract relationships. And once we did this, it became easy to keep doing it, expanding our knowledge again and again. We could imagine a different reality with very different physics, where sound and water both bounce, but the analogy goes no further. So the analogy is no better than, say, sound is a ball that bounces. There is an analogy there, it’s just not a very fruitful one. In that world, so it’s not a false analogy, it’s just not a fruitful analogy.
[00:35:11] Red: In that world, with this other physics, we might still call sound a wave, because there’s a true analogy there, it bounces like waves do. But the analogy would probably die out because it’s unfruitful. In that reality, we’d likely never extend the concept of wave to include what sound is. Like, Christmas has the thought, says it, it just gets lost because it just isn’t fruitful. Here, fruitful means the analogy is close enough that we treat it as tentatively true. That if we treat it as tentatively true, it reveals something unexpected about reality. Sound is a wave is a fruitful analogy, because of what it reveals. Sound is a bouncing ball reveals little or nothing about reality. Once an imperfect analogy proves fruitful, we expand the concept to include the new case, like expanding wave to cover both water and sound. Over time, the concept evolves to include all kinds of waves. But even in that imaginary world that we’re imagining, where sound and water are barely alike, we might still call sound a wave, because there is at least some analogy there. Not likely, but it could happen. This shows that analogies aren’t falsifiable. Their fruitfulness isn’t about being true or false. It’s about how often they lead to new insights. So the value of an analogy is tied more to the corroboration of it than to its falsifiability. Let’s go back to the claim that an observation can suggest a theory. Now, you might, Nick, pick me here, rightly so, by the way, that since that popper would call this a concept, called this wave concept that we’re talking about, a concept, not a theory.
[00:36:53] Red: So maybe it’s more accurate to say observations can suggest a new analogy or concept, not necessarily that they can suggest a new theory. And I’ve kind of been intentionally muddling those two together. I’m now making it more clear. I would have to admit that strictly speaking, I can’t imagine an observation suddenly producing all of Newton’s theory. I’m really more talking about how observations can suggest a new concept. However, this alone already falsifies the Crittrack claim that we can only use observations to choose between existing theories. That just isn’t true. But can we really say sound is a wave isn’t a theory? Now, this is where Peter, your question comes in. Now I’m going to go back the other way. A wave is a concept, not a theory, but actually it’s kind of a theory. Once we test this idea and we start to say, oh, can we treat sound like a wave, like a water is a wave? We are in that moment treating it like it’s a theory. And it turns out to be strictly false. Yet, it’s corroborated often enough it becomes a useful analogy, leading to the expansion of the concept of wave such that sound becomes included. So sound is a wave is both a fruitful concept and a false theory at the time, but one with a touch of erosimilitude. That’s the problem with trying to draw a sharp line between concepts and theories. This is not something that I kind of see Popper bringing this out because he gives the examples of concepts hiding a theory. He talks about how a concept can lead to future direction on a theory. Like he’s kind of got what I’m saying, but I feel like it’s kind of lost to some degree.
[00:38:41] Red: Okay, we can treat concepts as theories or theories as concepts. Each approach has its own advantages and disadvantages depending on the context. Recall from the previous episode that even Popper admits this. He says concepts often contain implied theories or summarizes them. Quote from Objective Knowledge, page 123, for concepts are partly means of formulating theories, partly means of summing up theories. Popper also admits the fruitfulness of concepts. Quote, concepts may have great suggested power and may influence the further development of the theory. But Popper misses the deeper significance of how concepts and theories relate. He’s right that we can conceptualize theories in multiple ways. And I will show that as examples of that in a future podcast. I don’t think you will ever come across a theory that can’t be, the same theory can’t be said in entirely different conceptual ways. Okay, so I actually do think Popper’s right about that. But then he claims, quote, in many cases their significance is mainly instrumental and they may always be replaced with other concepts. That’s from Objective Knowledge, page 123. Yet theories can’t easily be divorced from the conceptual frameworks like this. They can be done. It’s just not easy. Once the theory of sound waves was created, we could, in theory, have said, okay, waves are only water waves, but let’s invent a new concept for sound that’s not related to water waves because we know they’re somewhat different. But that would have been counterproductive and likely slowed progress in many future theories. It’s hard to imagine a world in which that happens that you would then be able to see that light is also a wave. There’s a reason for this. Concepts have shelling points.
[00:40:21] Red: There’s never one true concept for understanding the world, but some concepts are so much more fruitful than their alternatives that human societies either latch on to them and they propagate well or they reinvent them independently. For example, the Mesopotamians, Mayans, and Indians all independently invented the zero positional number system. Even deductive reasoning and mathematical proof were invented more than once. And the idea that sound is a wave, like water is a wave, was partly discovered by Hindus drawing analogies between sound and breath. That analogy was so fruitful, these analogies were so fruitful, they independently moved partway towards the same concept. So some concepts simply prove so fruitful that they endure and spread. They can’t be dismissed as merely instrumental like letters are for a word, even if they aren’t falsifiable. Okay, quick summary to kind of bring everything together at the end here. Crit rats claim that observations are only used to choose between existing theories. That is actually incorrect. We also use observations to create new concepts, to suggest to us new concepts. What’s going on behind the scenes is a different question, and we’ll have to talk about that in a future episode. Hopper’s idea that theories are 100 times more important than concepts may hold for criticism, but it’s false overall because concepts are essential for conjecturing new theories. Concepts can be more than merely adequate, they can be fruitful. While Popper is right that a theory can fit within, a theory can fit within different conceptual systems, I feel like that’s a misleading though true statement. Some concepts are so fruitful, they act as shelling points.
[00:42:04] Red: Universal explainers will inevitably rediscover those concepts because they all should, because universal explainers all share similar problems, so we have to solve these problems using certain more fruitful concepts. We will rediscover them because of that. Concepts when treated as unfalsifiable fuzzy categories rather than theories, they evolve by analogy. Popper was correct that such fuzzy concepts can’t be strictly falsified. Instead, we extend them over time by analogy. The point is that you don’t falsify them. The point is that you extend them over time and evolve them to be more fruitful. But there’s no sharp line between a concept and a theory. A concept can become a theory when made precise and tested, and sometimes that’s useful and other times it’s not. We often move fluidly between treating a concept as a theory and treating it as a flexible idea. For example, once we hypothesized that sound is a wave and tested it, we found it sometimes fits and it sometimes doesn’t. Instead of discarding it, we reconceived it as an extension of the fuzzy concept wave, creating a richer abstraction of the concept wave than existed prior to that point. This shows that corroboration without falsification is possible. Croboration isn’t just a failed falsification in all cases, at least not what it comes to concepts. Concepts play a crucial role in how we make conjectures and develop new theories. Okay, that’s the end of my presentation. If it’s okay, let’s get back to your question now. Okay,
[00:43:36] Blue: here’s an addendum. I don’t know if this relates to your main point or not, but it’s what I’m thinking about a lot. Let me ask you this question. Do we live on a compact disc or a vinyl record? Is one explanation for reality better than the other? Oh, interesting. Is this reductionism and a philosophical error? If it is reductionism, if it’s not right to even think of it as one or the other, what does it even mean to say, as John Wheeler does, that we get it from bit?
[00:44:17] Red: That’s a really interesting question. I honestly think that Deutsch would answer that we live in a vinyl record that can be turned into a CD. I may be wrong about that.
[00:44:30] Blue: Okay, so reality is computation, not all, but not a computation.
[00:44:37] Red: Yeah, so it is possible that new physics, it will turn out that reality is entirely quantized, where absolutely everything is digital. Roger Penrose believes that’s the case. Like, there are really good cosmologists out there that think our future theories of physics will show, just like quantum physics did, will show that everything, even time, for example, is something that can be quantized and turned into digital steps, right? That’s what Roger Penrose thinks? Yeah, actually it is. Then why would he think that
[00:45:16] Blue: consciousness can’t be simulated?
[00:45:22] Red: So, it’s not true he doesn’t think consciousness can be simulated. It’s true that he thinks a digital computer today can’t simulate it. Do you see the difference between those two?
[00:45:32] Blue: Oh, so it would take like some kind of future understanding of - Quantum, quantum gravity computer or something like that. Right,
[00:45:39] Red: right,
[00:45:40] Blue: okay.
[00:45:41] Red: I think that the problem is, is it okay to look forward to theories that don’t exist yet and act as if they’re true? And I, I mean, like, Deutsch being a critical rationalist, he’s sort of not okay with that, right? And he’s right. If you go off the theories as they exist now, not everything is digital, right? So, you would have to assume that the world under current theory is more like a vinyl record. And like a vinyl record, you can make a CD out of it with the same music because a vinyl record can be simulated to any level of, the music on a vinyl record can be simulated to any degree of precision you need. And it, and once it is, it’s, they’re indistinguishable. I mean, here I’m ignoring the fact that vinyl records pop, right?
[00:46:36] Blue: Yeah, there’s a lot of, there’s a lot of distortion in there that’s added, but you know, we’re talking, I think we’re more talking about a vinyl record as an abstraction.
[00:46:44] Red: That’s right. A vinyl record as an abstraction. So the vinyl record is the source of the original music in this abstraction, right? It’s, it’s the thing we’re trying to digitize. So that is, I think the, the Deutsch, the current, I don’t know for sure, but that’s what I would guess the current Deutschian answer would be. But I think it’s actually a very interesting question. Let me also get back to your question about waves. The fact is, is that waves as a concept, it, it evolved not only into a fruitful concept that we then reused in all sorts of ways. Hofstra gave tons of examples of theories that rely on this concept of wave, right? Today. And even the concept of wave itself has been math, mathematicized in ways that we could rightly think of it now as a theory. Okay. And I do think this is one of the areas where I, because Popper’s not super specific, I can’t say I necessarily disagree with him. It may just be that he didn’t dig into it as deeply as I became, you know, it’s not his area of interest. It’s my area of interest. So it’s, so it’s understandable that he didn’t dig into it and that I’m now digging into it. Okay. I get the feeling though that he had a negative enough view of concepts because he thought of them as instruments in the same way he thinks as letters as instruments. And that just isn’t right. Okay. But I think he just didn’t have that much interest in things like meaning, concepts, things like that. And in a way that makes sense because they, they didn’t really impact his critical method in any way.
[00:48:21] Red: Let me put this in, in Bruce terms now, right? Humans have this amazing ability. And I’m going to give examples of this in future episodes. This amazing, beautiful ability to move out into abstractions and to move down into specific theories. And we confuse the fact that we’re doing this like we fuzz out and we look at things in an abstract way and then we focus in and we become precise and we test a precise theory that comes from that abstraction. This ability for humans to do this is just stunning. There’s no animal can do it as far as we know anyhow. It’s, and I do think that this is directly, I’m guessing, but I think this is directly related to what AGI is. Whatever the algorithm is that allows humans to say, I’m going to treat waves as a concept. I’m going to fuzz it out. I’m going to extend it instead of just saying, oh no, sound is not a wave because waves are things on water. We go, oh, I’m going to extend this concept. I’m going to make this way of thinking. I’m going to invent that new way of thinking. And that’s going to allow me to start testing things, learning things about reality, coming up with new theories to solve the problems that come from the fact that it’s only an analogy and it’s an imperfect one at that. Which leads to this fuzzier abstract deeper, we might say, concept of a wave. And you get into this really kind of cycle where we’re constantly fuzzing out, looking at the big picture, looking at things as concepts to make conjectures.
[00:49:58] Red: And then we’re focusing in to be able to do criticism and to be able to actually decide what specifically does this mean? What precisely does this mean? I do mean precise. I do mean getting precise now, because now we’re talking about criticism to solve specific problems. And you’re trying to define your things more precisely and you’re trying to mathematicalize it and make it axiomatic so that you know exactly if it’s right or wrong and you can test it with empirical tests. And humans are constantly moving between these two ways of thinking just fluidly. And I think that is the essence of what makes us general intelligences, universal explainers. This is my guess. I don’t know. We won’t know until we actually have the algorithm in hand. This is where my research interest is anyhow, because this is my gut feeling of where to go next. And I think that this is one of those things that I think people get very confused over. And I’m going to argue in future episodes that a great deal of the CritRat community kind of going off the rails at times in my opinion is because they are confused between theories and concepts that the two seem so similar to them, they can’t tell when they’re trying to fuzz out and conceptualize things and when they’re trying to focus in and treat it as a theory. And one of the big secrets that comes out of this is the realization that there is no single theory. Like if we talk about, I’ve said this on the past in the podcast, but I’m hoping people will now see why I feel it’s so important. Think about the theory of Darwinian evolution.
[00:51:30] Red: There is no such thing as the theory of Darwinian evolution. It does not and has never existed. There is a concept of Darwinian evolution that links together a giant group of theories that are constantly getting falsified, tweaked, new conjectured versions of it, linked together by a concept of this survival of the fittest or something like that that runs between all of them and that kind of inspired each of the sub theories. And if you don’t believe me, think about Darwin’s book back when he first writes or origin of the species. Think about how Darwinian evolution was conceived in that book at that time. Then think about modern synthesis or neo -Darwinian evolution. Those are vastly improved, vastly more empirical theories than Darwin’s original theory, precisely because they do have this connection. We may call it neo -Darwinian evolution to call out that it wasn’t quite the same as the original Darwinian evolution, but we know there’s this conceptual connection between them. We fuzz out, we look out, and we say, oh, I see a connection between neo -Darwinian evolution, modern synthesis today, and Darwin’s original theory, so I still consider it to be part of that overall concept. Even though they’re really very different theories at this point. There’s a giant evolution of greatness that went from Darwin’s original theory to what we actually call Darwinian evolution today. This is true of all theories. All theories are collections of theories, and we connect them through various concepts. It’s not even clear when you’ve left one theory and you’ve moved to another. I’ve argued on this podcast that you could call general relativity a new paradigm distinct from Newton’s theory, or you could just call it neo -Newtonian physics.
[00:53:34] Red: It depended on how you conceptualized those two theories. If you conceptualize them as both being about gravity and both trying to explain why things move together or something like that, you’re probably going to perceive them as the same theory, but one’s an expansion and an improvement on the other. Whereas if you instead think of them as a force of gravity versus warping of space, then you’re going to think of them as distinct theories. When you’re doing that, when you’re deciding, if like Tipler does, you think of them as the same theory in Einstein’s Just Footnotes to Newton, or if you think of them as distinct theories like almost everybody else but Tipler does, it’s actually a choice of how you fuzz out the concept and which aspects you’re going to concentrate on and how you conceptualize those. And there isn’t one way to do it. There is no correct way to do it because that is not the nature of concepts. They don’t get falsified. And okay, that’s really all I had for today. Any final questions or comments there, Peter?
[00:54:35] Blue: Well, not really, Bruce. I’m just thinking about how there are artists, thinkers, podcasters, however you want to put it, who strive to please their audience. And then there are those that expect their audience to come along for the ride. You, for better or for worse, may be the latter. But I really appreciate that and I’m sure there’s other people out there who appreciate you and think you’re doing something valuable and I’m really proud to be a small part of this.
[00:55:14] Red: All right. Thank you very much.
[00:55:15] Blue: Thank you, Bruce. Hello again. 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 B. Nielsen 01. Also, please consider joining the Facebook group, The Many Worlds of David Deutsch, where Bruce and I first started connecting. Thank you.
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