2021-06-06 ToKCast A question for David. 1
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Duration: 00:09:32
Transcript
Brett Hall
In Chapter 5, titled The Reality of Abstractions, David explains how not everything that exists can be reduced to the motion of atoms and physical forces acting upon those particles. That is the error known as reductionism. And although it is easily refuted, it, or at least echoes of it, nevertheless holds sway in mainstream academia. Yes, what happens is determined by the laws of physics acting upon particles moving in space-time. But that is just one kind of explanation. One level, if you will. There are emergent levels of explanation where things come into existence that are equally as real as particles, space-time and forces, but which can be fundamental. Importantly, among the things our best explanations of reality refer to are abstractions. Not only things like the objects of pure mathematics, numbers and sets and infinities of various kinds, but also knowledge itself. And these things can actually affect the physical world. I discuss this in my exploration of Chapter 5. Today I’m doing Chapter 5, The Reality of Abstractions. Here we learn about the fact that there’s not only physical material in the universe, but rather there’s also some other kind of part to reality. Namely, there are abstractions. And these abstractions can have real causal effects on physical things like atoms. The reason why something like that ends up taking the shape that it does has nothing to do with self-organization and physical forces. It cannot be explained purely in terms of the motion of atoms. And it can’t be reduced to laws of motion or any kind of law of physics. Instead, the explanation is that a great architect called Gaudi, some 100 years ago, decided to create something like that. The idea was originally represented inside of his mind. The idea was originally some kind of neural firings inside of his brain, but they can’t be reduced to that either. It was an idea, an abstract idea. He had plans, he put it down on paper, and then over many, many years, it’s beginning to take form or beginning to be instantiated in the rock and stone and mortar and other materials that make up an absolutely phenomenal building like this one. It’s only partially complete, and apparently, it’s going to be some decades before it finally is. This is in Barcelona, Spain. So with a great building, something like Gaudi’s Cathedral, what we have is an idea that has somehow taken physical form. So what we’re saying there is ideas, which are abstractions, knowledge, which is an abstraction, can have real physical effects in the world. Ideas can take physical form. Abstractions can be instantiated in the physical world. But are there different kinds of abstractions? Does an abstraction have to be instantiated, so we say, in a physical substrate in matter or something like matter, like light or sound waves? Does it have to be instantiated in order to be an abstraction?
Brett Hall
Well, I asked David about different kinds of abstractions. Now, you mentioned in the answer there the concept of abstractions, and you actually invoked abstractions in talking about it, of course, pure mathematics is about abstractions. And I don’t know what might be the most controversial chapter in the book, but I think among intellectual types, to at least some extent, it would be chapter five, if it’s not going to be the Why Are Flowers Beautiful chapter, it’s going to be the one that claims there is a reality to abstractions. Because to some people, this seems, weirdly enough, not to me, I think not to most people listening to this, but it can sound like an appeal to the supernatural or some sort of woo, because some people are physicalists. They think that everything just has to come down to the behavior of atoms. But I wanted to ask you if you distinguish between kinds of abstractions, rather than defending the thesis that abstractions are real. I know this is not necessarily a well-defined area, but for example, something like numbers, they’re abstractions, are they different in kind to, let’s say, knowledge? Because after all, there may be infinitely, well, there are infinitely many prime numbers, and not all of those prime numbers ever need to be instantiated in a physical substrate anywhere. Nevertheless, they still exist. But knowledge to be knowledge has to be instantiated in a physical substrate. It’s also abstract, but, well, I might pull the brakes there. Can you explain if there are these different species of abstractions, and if so, how do we understand the differences in their existence?
David Deutsch
Yes, there are different species of abstractions. I mean, maybe it’s better to say there is a classification of abstractions, and some classifications are quite useful, because abstractions within the same category of classification have similar properties and can be understood with similar explanations or the same explanation. But then with the different problem situations, you might want to classify things differently. Like, you know, just like in biology, we may wish to, sometimes we want to classify things as mammals and birds and reptiles and so on. And on other occasions, we may want to classify them as aquatic creatures and terrestrial creatures and aerial creatures and so on. So classifications are useful relative to the problems that you want to talk about. And it’s the same with abstractions. It’s definitely true that some abstractions, as you say, like knowledge and information more generally, don’t exist unless they’re instantiated. So they have to have this extra element of being instantiated. But that’s also true of, there are more classifications than that, even among pure abstractions. There are abstractions that, it seems to be important in mathematics to, like I said, to distinguish between abstractions that involve infinite sets and abstractions that don’t. And then the whole idea of a set is not universally applicable. So the set of all sets, it famously turned out even before Gödel, it turned out that this, from Russell, that it turned out that the set of all sets isn’t a set. So then you have to invoke a class. It’s just a class of things.
Brett Hall
Or the set of all sets that don’t contain themselves.
David Deutsch
So that’s right. But it doesn’t help because it doesn’t help with everything because there’s no such thing as the class of all classes either. Right. So yes, there are different kinds of things. And another thing which I think is still slightly mysterious is what kind of an abstraction the laws of physics are.
Brett Hall
So there’ll be more to say about that, the laws of physics, in another episode. But for now, for more on this, see the rest of my two-part exploration of The Beginning of Infinity, Chapter 5, The Reality of Abstractions, that’s available on YouTube and via podcast. As I say, it might be one of the more controversial chapters of the book. I don’t know why exactly, but like I hinted at, there may be echoes that remain of a physicalist notion, which was, I guess, a reaction against people who invoked the supernatural. And people who reacted against religious or magical type thinking, they threw out the gods, the spirits, the magic. But with that bathwater went, I think, the baby of a whole class of things, quite real and yet not reducible to fundamental particles. Accepting the reality of abstractions enables the explanation of many phenomena that are otherwise entirely mysterious and inexplicable. The denial of them is just a kind of reductionist or empiricist mistake. It solves nothing and ruins what we do know about the nature of reality. It reminds me a little of the shut up and calculate people in physics who are supposed to be the hard-nosed macho skeptical types who say quantum theory allows predictions. What more do you want? Well, what we want is to understand what’s going on. It’s not very skeptical, scientific or macho to give up on that. In fact, it’s anti-rational. It impedes progress. Abstractions are real, as real as atoms are and dinosaurs were. Get over it.
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