Natural Hearing (Aristotle's Physics)
Lecture 41: Aristotle's Arguments Against Anaxagoras and the Second Difference in Quantity

Transcript
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And with Pi, man has a natural desire to do it, too, because they write computer programs to divide that thing as far as that. Yeah, yeah, yeah. I mean, can a man really be aiming at dividing a line forever? No, but he realizes that. Or like with numbers, right? You can keep them going higher and higher, right? But do we have a natural desire to go on forever? No. No, because we have no goal there, right? No. You see? So, sometimes, you know, to kill many birds with one stone, I put these three arguments together because in explaining them, they all seem to in some way have a connection with the principle of Venus, most explicitly the eighth argument, right? And then the fifth, less so, but also, and then the first argument, right? Okay? But it also facilitates a comparison with modern science, right? Now, the second, third, and fourth arguments, the second, third, and fourth arguments, we'll see, are linked together. Because in the second, because in the second, and in the third, and the fourth, he's going to refute three different statements of Anaxagros about the matter. But what he shows in the second one, but what he shows in the second one, he's going to use in the third to overthrow something else he said, and in the fourth to overthrow something else he said. So these three will be linked, right? Now, they also have in common here, the second, third, and fourth, something that Aristotle was the first to discover. And I call it sometimes, at least in our study here, the second difference between quantity in pure math and the quantity naturally. And I call this the second difference, because we already saw one difference between these two. And having seen that first difference, we're open to seeing and discovering the second difference. Now, what is that second difference, huh? I'd better say that in a moment, but I guess, let me start to look at two, three, and four. But the second difference is what distinguishes modern physics, physics of the 20th century, from physics of the 17th, 18th, and 19th centuries. Or one thing, at least, that distinguishes that. And so in my comparison between what Aristotle is doing here and the physical sciences, 8, 5, and 1 are based on something that the whole physical science, from Galileo, Captain Newton, to Einstein, and beyond, what they all have in common. The second, third, and fourth are based on something that doesn't come into physical science in modern times until the 20th century. Now, the physicists in the 20th century, those who worked out quantum theory and relativity theory, the two relativity theories, you read these scientists, right? Like Einstein, or Louis de Broglie, or Niels Bohr, or Heisenberg. They'll often call the physics of the 20th century modern physics. And the physics of the 17th, 18th, and 19th centuries, they'll call them classical physics. But, you know, classical means that it doesn't mean the Greeks, right? It means Galileo, Kepler, Newton, and so on. They'll also call the physics of the 17th, 18th, and 19th century Newtonian physics. Not that he did everything, but he's the man who united Galileo and Kepler's work. And then he was the model to imitate all the way up. So they contrast modern physics, meaning the physics of the 20th century, with classical physics, or Newtonian physics. The physics of the 17th, 18th, and 19th centuries, right? One thing that the physics of the 20th century has, especially its most established parts, is the second difference in Aristotle. Now, what was the first difference that Aristotle pointed out between those two? That we saw in our reading on the difference between natural philosophy and mathematics. You know, they seem to overlap the two, right? Natural philosophy, bodies. Okay, natural bodies. Yeah. Yeah. It's abstract mathematics. Yeah. So natural philosophy is concerned with numbers and shapes and length and width and so on, only insofar as they are the, what? Numbers, or the shapes, or the surfaces, or the length, or the width, or depth of natural bodies, right? By the geometer and arithmetician, they consider number and shape and so on in separation from natural bodies, right? And indeed, in separation from all, what? Sensible bodies, right? So the geometrical sphere really has no matter, huh? It has no, what? Sensible qualities, right? It's neither heavy nor light. It's neither hard nor soft, right? It has no color, no sound, no taste. None of these sense qualities, right? Okay. See that? Okay. Now, having seen that first difference, which Aristotle, in some sense, was the first man to see, really, see clearly, and most people, even after him, have not seen it clearly, though he's good students, like Thomas has seen it, right? But that opened him to, what? Recognizing the second difference, huh? Now, what is the second difference, huh? Well, he discovered that natural quantities have limits, huh? Either in the direction of the large or the small, or both directions, due to the natures of these things, right? Limits that could not be foreseen from the point of view of pure math, right? Which considers these in, what? Separation from, right? The natures of things, right? Okay. Let's look at the second argument, huh? We've got the arguments numbered here, right? Now, basically, Aristotle is going to use here in the second argument, if, then, what? Syllogism, right? Which is a very common type of syllogism when you're refuting a position, right? And you know, when you're trying to overthrow a statement, the form of the if, then, syllogism we use is this, if A is so, then B is so, and B is not so, okay? If you lay down statements in that form, what follows, necessarily? A is not so. Okay. Remember that form? Well, the obvious form was, if A is so, then B is so, but A is so, therefore B is so, right? Well, if A was so, B would have been so, but since you're given that B is not so, then A must, but, not be so, right? So, you reason this way, you say, if your position is true, right, then what follows? We show that something follows that is not what? Yeah. Therefore, your position can't be true, right? Okay. So, you go to reason this form, right? You go to reason against the idea that the parts of an animal, or a plant, or something else, right, can be what? Infantly small, right? Now, if the parts can fall below any size, right? There's no limit as to how small they can get, right? What follows, huh? If the parts make a difference, right? If the parts make a difference, right? If the parts make a difference, right? If the parts make a difference, right? If the parts make a difference, right? If the parts make a difference, right? If the parts make a difference, right? If the parts make a difference, right? If the parts make a difference, right? No more concrete, let's say, for example, of an animal or a plant, let's say, if the parts can fall below any size, then what about the whole? Yeah, then the whole can fall below any size. If the parts get smaller and smaller and smaller and smaller, then the whole, which is composed of the parts, right, can get smaller and smaller and smaller and smaller and smaller, right? And so if there's no downward limit as to how small the parts can get, there should be no downward limit as to how small, right? So if you understand the relation of part and whole, the if-then statement is kind of obvious, isn't it? The Aristotle goes out to what? That cat was just here a minute ago, right? You go out to the natural world. But do we find that different kinds of animals, right, different kinds of plants have just any size? No. We find that there are limits as to how big or how small the cat is, right? There are limits as to how big or how small the elephant is, right? Okay. And for different kinds of things, which means different natures, right, there are different limits, right? Okay. And although there are variations among different cats or different elephants, right, there are certain limits above which or below which you don't find that kind of animal, right? Okay. The same way for plants, although that's manifestly, right? But the trees in our part of the country don't grow as big as these redwoods or sequoia or something in California, right? And the grass doesn't grow as big as the grass doesn't grow as tall as the trees, right? Okay. So the consequence is not in fact true in the natural world, is it? That the hole can be just these heights. But the hole cannot fall below any size, huh? Therefore, what? The part cannot fall below any size, right? Okay. So he's overthrowing what position of annexed area, sir, in regard to that? It's made of parts that are infinitely small. Yeah, but the parts themselves, right, can be infinitely small. They can fall below any size, right? You see that? Okay. Now, he's going to use that consequence of what he shows in the second argument. Therefore, the part does not fall below any size. Which means it must be as small as piece, right? Okay. He's going to use that in the third and in the fourth arguments to overthrow two other positions of annexed area. And in a way, it's like, you know, so-called domino theory, right? You knock over one, you knock over other ones, right? Because annexed area survived this position by a series of steps, right? One of which led on to the next point. You overthrow this last thing and then, You knock over the other ones before. Okay. Now, in the third argument here, once you say that there's a smallest piece of flesh or blood or bone, right, then any time you get something out of that blade of grass, you're going to have to take at least that amount out. Right? You can't take a piece of flesh out of that grass smaller than the smallest piece of flesh. Okay. Now, can you take, can there be an infinity of the same amount of flesh in the finite blade of grass? Now, notice the difference here, huh? To make a comparison here. You said before with the mathematical line, right? You can cut it in half, right? And you can take half of the remains, right? And then half of that and go on forever, right? But the pieces get smaller and smaller and smaller. They fall below any given size, right? You can go on doing that forever, right? If you had to take out the same amount of that straight line every time, however small you make the same amount, right, could there be an infinity of the same amount in a finite line? I don't know. Because you multiply the same amount, infinity, you're going to exceed, eventually, everything. Okay? So the difference between the same ratio, which I can do forever, and the same, what? Amount, right? Now, mathematics can take the same ratio forever because there is, as I said, in one of the fragments, no smallest of the small there. But here, there is the smallest of the small. Namely, the smallest piece of flesh, the smallest piece of bone, and so on, right? So you have to take out at least that amount, huh? Sometimes I give a holy example to bring out this difference, just to speak of it more, bring it back, bring it home. See, if I was going to go into business, retail business, I tell the students I would like to sell mathematical lines, huh? And I say, why? Well, it seems to me the pain in the arse in retail business is reordering all the time, right? So you have something on stock, right? And sometimes you run out of something and the customer goes somewhere else, you might lose a customer, right? So I like to sell mathematical lines, right? You never have to be ordered, huh? And so the first guy comes in the door, I sell half the mathematical line I have, right? The second guy comes in the door, I give him half a month's left, right? I can go on selling mathematical lines all day long, right? And they would say about Perkowitz, you know, one thing about Perkowitz is he never runs out. He always has mathematical lines in store, no matter how many customers come through the door, right? You know, it can be a stampede, he's still got mathematical lines. Well, someone else might say, but you know something, they keep on getting smaller and smaller and smaller, right? Then I take my second example, right? Perkowitz is out in the desert there, right? With a canteen of water. He's heard something about, you know, you give somebody a cup of cold water and you get a reward, right? So a guy comes along, right? Oh, give me some water, water. So Perkowitz gives him half of his canteen, right? Okay. Then later on, the other guy comes along, oh, give me some water. Perkowitz gives him half of what he's got left in the canteen, right? Can Perkowitz go on giving water forever? No. Why not, right? Because there's the smallest piece of what? Water. Which is very small, mainly the molecule of water, right? But the molecule of water has a definite, what? Signs, right? And so there was a huge number of molecules in a canteen of water. Can there be an infinity of molecules in water in the same canteen? So Perkowitz eventually will run out, right? You see the difference? Okay. So in the third argument, Aristotle takes the fact of what's been shown in the second argument, right? That there's the smallest piece of flesh, the smallest piece of bone, right? And he uses that to forward throw another position of Anacetorus that there's an infinity of pieces of everything inside of everything, right? You see the argument? Okay. Now the fourth argument, huh? He's going to overthrow now the original position there, the original conclusion, you might say, of Anacetorus, that everything is inside of everything. Okay? Aristotle says now, again using what he showed in the second argument, if you take the smallest piece of flesh, let's say this is the smallest piece of flesh, in the smallest piece of flesh, is there any bone in there? This is the smallest piece of flesh, whatever size it is. Well, if part of the smallest piece of flesh was bone, let's say this is bone here, then only part of the smallest piece of flesh would be flesh. In which case it would be something smaller than the what? Smallest. Smallest, right? So in the smallest piece of flesh, there can't be any bone, can there? In the smallest piece of bone, there can't be any flesh. If this is the smallest piece of bone, and this part here is flesh, then only part of the smallest piece of bone would be bone. And therefore, It can be something smaller than smalls, which is a contradiction, right? So not everything is inside everything, is it? You see the argument? So notice how the second and the third and the fourth are linked together, right? In the second, he shows the falsity of one position of Anaxagoras, that flesh and blood and bone and other things can be smaller and smaller and smaller, how do you live it, right? To the consequence of that, right, which is a contradiction of our experience, right? And therefore he shows in that second argument that there must be a smallest piece of flesh and bone and other things. And then he reasons from that in the third argument, that you can't keep on taking things forever out of a finite body, because you have to take out at least that amount, right? And then you exhaust it. Therefore, the generation would stop. Conjuring what he thought, right? All the Greeks thought. And then in the fourth argument, he shows that not everything can be inside of everything, then. And notice, here's the way in which everything can be inside of everything. Inability, right? But when you make it actually there, right, you're running a difficulty with the second difference in the quantity of natural things, huh? So the second difference, you know, could be stated by saying that there are limits limits in the quantities of natural things, be it in the direction of the large or the small or the bulk, due to the natures of these things, right? Limits, therefore, that we discover in our sense experience, or through our sense experience of natural things, but limits that we cannot foresee from the point of view of pure mathematics, where you consider quantity in separation from the natures of things. Now, in modern science, modern physical science, this first came into what we call chemistry, right? So chemistry, modern chemistry, is based on Aristotle's idea that there's a smallest piece, right? So for every chemical element, for example, there's a smallest piece, which is called a, what? Atom, yeah, yeah. Now, an atom is very small, right? And different atoms are different sizes, right? Okay? But every atom of, what? Hydrogen has the same size, huh? Okay? And for every chemical compound, there's a smallest piece, which is called a, what? A molecule, right? Now, though a molecule is very small, every molecule has the same, what? A water, say, a molecule, right? Right. It has the same size, right? So modern chemistry, in talking about the atom and the molecule, is based on the idea that there's a smallest piece, right? But there's something smaller than a molecule of water, but it's not water. You see that? Okay? Now, you'd be in the same difficulty if you said that every elementary particle is composed of all the rest, because then you'd have, like, Alex Sabres has the fifth argument there, right? You'd have, like, it's each elementary particle, all the rest, it's each one of those, all the rest, and it's going differently, so the elementary particles are getting smaller and smaller and smaller and smaller and smaller, right? But that's contrary to our experience of the elementary particles in the lab, that all electrons have the same mass or same size, right? Okay? Therefore, it's not possible that every elementary particle is composed of all the rest, right? It has all the rest in it only in what? Yeah. And it will seem. You see? Same difficulty, right? In the same place, they'd be in. And, of course, Heisenberg saw it, you know? But the kind of natural way of speaking was the common way of speaking, right? It's as if every elementary particle is composed of all the rest, and you get them out of there. And it's easier for us to speak that way, because then, if it's our imagination, right, you speak of every elementary particle, it's composed of all the rest, and so you get them out of there. I mentioned how Louis de Broglie says that, in a different area of that, he said that if you ask the physicist of the 19th century, what happens when white light starts with fism, you get this spectrum of color, they would have said, well, the white light was composed of all those colors, and the spectrum isn't really separating them out, right? See? We no longer think that's all he says. We think those colors that exist in the white light only says there's a possibility. It's a very surprising physicist of the 19th century that we think that way, right? See? But that's, again, the idea of ability, right? Potentiality, possibility, right? Okay? But you might kind of, at first, assume that everything must be what? Actually in there, right? Because you can't imagine something in something without imagining it to be actually in there. So the false imagination there, right? But also the critication, too, because the two different senses be in there. What's the fallacy of simply in some respect, right? You know? Are there chairs in the trees out there? If you answer without qualification, some people say no, right? But in some limited ways, they are, right? They qualify to have an ability to have, right? If they have a piece of clay in the shape of the sphere, is there a cube in the clay? No. Except an ability, right? You have to qualify to have it. So you're confusing the simply in some respect. Several fallacies there. Those are very common fallacies, right? The fallacy of equivocation is the first fallacy in language, and the fallacy of simply in some respect is the second one outside of language. And both are involved here. Now, we mentioned also that the second, third, and fourth have in common something with the physics of the 20th century. But now, just to speak pretty simply about it. See, modern physics begins officially in December of 1900, right? When Planck proposes the quantum hypothesis. In the study of Planck-Potty radiation, and Planck was running into contradictions, applying Newtonian physics to the study of Planck-Potty radiations. He's getting absurd consequences of this. There's infinite energy, you see now. And so on. And he untied the difficulties by hypothesizing that energy, right, cannot be given or received in just any amount. But that there's a smallest amount, right? And you either give or receive that amount, or some multiple of that amount, with nothing less than that amount, or in between some multiple of that amount. In 1905, Einstein showed that you can't understand light without introducing the quantum, huh? Not the character of the theory. In 1913, Boris showed you can understand the atom power of this. This kept on being developed until I was in the late 20s, right? Quantum theory was kind of perfect. What characterizes quantum theory is recognition of a limit in the quantity of an actual thing. Now, Newtonian physics, you assume that you could, what, impart energy and just any amount. You know, I could give half the amount of energy I gave you before, or a quarter of that, or eight of their length, right? There's nothing Newtonian physics opposed to that, right? Okay, so that was a limit in the direction of the, what, small, right? Okay. As long as I compare that to the monetary system, right? The only example I give is you and I go down to the bar, right? Two beers. Two beers. Make a potato chips. Two beers, okay? Then we get into an argument and we get mad at each other, and one of us gets up to leave. And the guy says, don't leave until you pay your share of the bill. Okay? Now, we've been buying, what, two beers, two beers, so we can split the cost right down the middle, right? We also bought that 25-cent bag of potato chips. So what's your share? So we know our friends, see? Your share is 12 and a half cents, right? Now you reach into your pocket, what do you find? There's no way to pay 12 and a half cents, right? You pay either a penny or some multiple of a penny, but nothing less than a penny, nothing between one and two pennies, right? And that's what they discovered about energy, right? It comes in pennies, so to speak, right? You see? Kind of a strange thing. But the penny is something arbitrary in a way, but the quantum is something natural, right? Now, in 1905, Einstein also proposed the special real relativity. The cornerstones of the special theory of relativity was another limit. But in this case, instead of a limit in the direction of the small, there's a limit in the direction of the large. And you've all heard what that limit was, huh? It was the speed of light, right? But the speed of light was the maximum speed of the universe, right? And it was impossible to go, what? Fastly minutes, right? Okay? That's part of the special theory of relativity. Now, in coding physics, there was no, what? A limit to how fast something could go, right? It could always go faster and faster and faster, right? But Einstein's special theory of relativity is based upon the idea that there's a maximum speed in the universe. So here you have a limit in the direction of the small, quantum theory, and the special theory of relativity, a limit in the direction of the large, right? So these are considered the fundamental parts, the most well-established parts of the physics of the 20th century, huh? Quantum theory and special theory of relativity. Now, you see, with Newtonian physics, it's a mathematical science of nature. And what does that mean? It means that you're applying pure math to the study of the natural world. Now, that kind of implies that what's true of pure math is going to be true of the natural world. And to a large extent, it may be true. So, if in pure math, 4 minus 2 equals 2, right? Then I expect that if a dog has four legs, and you cut off two legs of a dog, you'd have what? Two legs left, right? If the chair has four legs, and you cut off two legs, the chair has two legs left, right? You kind of assume that what's true of quantity in math is true of quantity in the natural world, don't you? See? But you forget that there are what? You're considering quantity an abstract way here in pure math, right? And if something happens to quantity due to the natures of things, right, that's going to entirely escape the vision of the pure mathematician, right? Now, in pure mathematics, is it such a thing as the shortest line? It's such a thing as a, what, longest line, huh? You can always extend the line longer, right? Or make it shorter, right? And therefore, a triangle or a square or a circle can be greater, you know? And geometry is based upon it, right? Like in the fourth book, where you inscribe a circle in a square, and circumscribe a circle around the square, and vice versa. Well, that implies that circles and squares get smaller and smaller and smaller, and bigger and bigger and bigger and bigger. You can always inscribe and circumscribe, right, in pure math. But the discovery of these limits, huh, is a sign that modern science is getting closer to the natures of things. As the great common teacher there, Herak Haidt, said, nature allows to hide, right? Okay? But the discovery of limits, right, that could not have been foreseen from the point of view of pure math, the discovery of limits experimentally and so on, in the quantities of natural things, limits therefore due to the natures of these things, right? The discovery of such limits is a sign that we're getting closer to the, what, natures of things, right? When we discover limits, huh, they're due to the natures of things, huh? And they could not be foreseen in the abstract consideration of quantity and pure math. That's a sign of getting closer to the natures of things, right? It also explains why for so many centuries we kind of assumed everything that's true of quantity and pure math is true of the quantity of what? Of natural things, huh? You see that? Why you should have, you know, kind of assumed automatically, right? Because they didn't really see the first difference. And it's interesting with Demarchitus, right? Demarchitus, in the text that we saw before, Demarchitus sometimes speaks of the atoms apparently as having a shape, right? They're very small, but they have a definite shape and so on, right? But I think it's in the Degeneratione. In one of the later books that Aristotle is describing or talking about Demarchitus, he speaks as if Demarchitus spoke of the atoms as being points. Okay? And you recall how Demarchitus arrived at his position by a, what? Thought experiment, huh? He said, imagine a body cut, in every way a body can be cut. Well, is there nothing left over or something uncut left over? We can't make something out of nothing, so there must be something uncut. That's what Adam means, uncut. But is it interesting, if those two texts, I was talking to Warren Murray one time, I was pointing out how in this one text, her style speaks as if Demarchitus said that the atoms were like points. In other texts, he speaks as if the atoms are having some size and having some shape, right? But maybe there's an ambivalence in the thinking there, Demarchitus, right? Because if you think of quantity from a mathematical point of view, the only thing indivisible in geometry is what? The point, right? So that doesn't have to be, right? You think of it mathematically, right? But if there's a problem about how you can make a line or anything else out of points, like we showed before, right? Then you've got to have some size for the atoms, right? And then you introduce the idea that they have a limit, right? The direction of the small, right? But they're not infinitely small. They're very small, but not infinitely small. Do you see that? And in the, he has another thing in the old position there, of the Greek mathematical works, right? There's a fragment there that they attribute to Demarchitus. And it kind of shows maybe he's a little bit out into the difficulty of thinking that you can make a point out of, a line out of points. But you know, similar to that, it's actually making a surface out of lines or making a, like, a body out of, like, stacks of surfaces, right? And I think I gave you that one that he gave before, but Demarchitus took the example of a, you know, a pyramid as he was, yeah. Now, if you look at that as being a series of services, one way upon the other, right? Okay. Now, if you cut it parallel to the base, and you look at the two sides, right? Are they equal or aren't equal? Equal. I think it's just a pyramid, but a colon, right? Okay. Well, if they were equal, then, any place you cut into the equal, then what would you have here? You know, a stack of equal things, right? So would you have a colon or what would you have? Cylinder. Cylinder, yeah. Yeah. Now, if they're not equal, then it's not going to be a straight line going down, is it? It's going to be chit-chit-chit. You see? Because that's been interesting framing, right? He's kind of presenting with the paradox, right? Because the Greeks are thinking of a colon as what? And a body as a what? A pile of services, right? Just as a lot of mathematicians think of the lines composed of points, right? But there you show a difficulty in it, right? So you might have, in some sense, been a little bit odd to the idea that there's a difficulty in making the divisible out of the indivisible. You know, if you put lines next to each other, and you get a surface, right? Well, if you've got to compose a surface of lines, they've got to come up and touch each other, right? And if they touch each other, they're going to do what? Go inside and get none, right? The same way here, if you try to make a body out of surfaces, right? You have to come down and touch each other. And then they'd be called inside. Because you can't make... There's no... depth in the surface, then you can't touch at your surface, you have to touch as a whole, right? So, maybe in the market, just to have this some, you know, anticipation of difficulties that will lead Aristotle eventually to see that there's a difference between the quantity of pure math and quantity of natural things, right? And then to see the second difference here, that, you see, limits in the quantities of natural, the direction of the large and small, right? But if that idea is already in chemistry, right? With the proton, with the electron, and the atom in the molecule, right? Now, after this, the quantum physicists, I mean, like, Planck, really, and Heisenberg, and Bohr, and so forth, they went on to the study of elementary particles, right? And that work they're still working on now, it's still complete. But Heisenberg and others, like Gamal, who also got the Nobel Prize in development of quantum theory, they were looking for what? They were working with the hypothesis that there was a minimum length in the universe, which was 10 to the minus 13 centimeters. Now, I say that's not established, but I mean, it's interesting that these great physicists, right, who got the Nobel Prize in quantum physics, were now looking for a minimum length in the study of elementary particles. He thinks below which there's nothing, right? Because that's so contrary to pure math, a minimum length, right? You know? It's the true pattern, right? Yeah, yeah, yeah, see? But something below which there's nothing. I mean, they should even obtain that as a sign that their thinking has now been changed, right, by quantum theory and theory of relativity. And then Einstein, 10 years later, in 1915, 1915, he proposed a general theory of relativity, right? Which was confirmed somewhat after the First World War. But that was going in the opposite direction, towards the large, right? But that led to an explosion in cosmology, right, to study the universe as a whole. As he started to study the cosmos more intensity with this general theory of relativity, it seemed more plausible that the universe was, what, finite, as the rest of the thought, rather than infinite, like the early Greeks thought and like the Renaissance physicists. What is it? Quarri's book, is that the name of it? Quarri, the author of From the Closed Universe to the Infinite Universe, right? Describing, you know, leaving the Middle Ages, going into the modern world, right? But now they seem to be returning to a, what, a cosmos that was, what, finite, you know. Again, cosmology is more the, you know, the, along with how many particles, the two frontiers, you might say, right? I mean, they might very well be characterized by the discovery of, what, limits, right? Again, in elementary particles, a limit in the direction of the small, and cosmology, a limit in the direction of the, what, large, you know. And then after the discovery of, you know, the expansion of the universe and so on, and the Big Bang theory and so on, began to entertain the hypothesis the universe might be limited in time, too. You hear something called a Planck particle and Planck time? No. Okay. So, it's only characterizing the two well-established parts, right? But also in the study of how many particles, which went on from there, right? And the study of the universe as a whole, right? Both of those might also reveal, what, limits, right? Okay. So, Aristotle, in one way, would be less surprising than anybody else in the 20th century, right? In the sense that his mind was open to the discovery of, what, limits and quantities of actual things due to their natures, huh? Let the second not be foreseeing the point of pure man. But he's in a sense open to that because he saw that first difference, huh? It's rotten to the quantity and kind of abstraction there. So, I sometimes put, as I say, eight, five, and one together, because he has something in common, right? And then two, three, and four together, because he has something else in common, right? Eight, five, and one have in common principle of fewness. And two, three, and four are tied up with this second difference of quantity in pure math and quantity of actual things. But also, as I say, eight, five, and one bring out something in common with the whole physics from Galileo, Capri-Luton, to Einstein, and beyond. But two, three, and four have something in common with the physical sciences in the 20th century, modern physics is called. Now, six and seven are more particular difficulties, but they're interesting to consider. Apparently, in his fragments, and if you go back to his fragments, maybe you can see this. But he speaks of a mixture of everything, of flesh and blood and bone and color and taste and odor. Okay? And then the greater mind is separating these things, right? See? Well, you can separate, you know, the chicken skin from the bone, because they're both something substantial, right? Can you separate the bone and the color of the bone? No. See? So he has a mixture of substance and accident, right? And the greater mind is trying to separate these things, right? So he's trying to separate accidents from substance, right? Well, you can separate one substance from another, but not accident from substance, huh? You see? So you can put my arm in there and my leg in there, right? But you couldn't put the shape of my arm in there and my arm in there. You see? So it's kind of a stupid mind that's trying to separate the bone. Accidents, right? From substance, right? But notice that in a way reveals that an extinguished business see clearly the distinction between substance and accident, right? Now, he has a mixture of everything. So he has accidents mixed with substances, huh? Without realizing the difference between the two, right? But now, when you get into wisdom, huh? Those are the two main divisions of being, right? Being in act and being in ability, and then being as substance and being as what? Accident, huh? Substance, quantity, quality, more precise, but basically substance and accident, right? Those are the two main divisions of being, okay? So in a way, he's confusing act and ability, right? Because everything that's in the ability of matter, he's putting what? Actually in there, right? In a way, he's confusing matter and what? Form. Because form is act and matter is ability, right? But he's also not seeing the difference clearly between substance and what? Accident, right, huh? Okay? You've heard the witty remark of Lord Richard Russell, you know? He says, the accidents of Mr. Smith have no more need of a substance to inherit than the earth has need of an elephant to rest upon. You heard that? The accidents of Mr. Smith have no more need of a substance to exist in, right? Than the earth has need of a, what? Elphant to rest upon. But the point is, if accidents do not exist in something, right? They exist by themselves, right? Then what he's calling an accident is really a, what? A substance, right? So it says he doesn't understand what an accident is. So it's not just the ancients don't understand the distinction between a substance and accident, right? And substance sometimes starts to disappear in modern philosophy, right? You know, you get to Berkeley and Berkeley doesn't think that matter exists. You know, everything is mind and thought, and then Hume does away with that. No substance at all left, right? See? Well, it makes some sense to say only substances exist, right? But to say only accidents exist, it makes no sense at all. So, I mean, it's actually the ancients thing that's confused about these things. And, of course, the bottom is used to say with the, uh, the, uh, stozylmetic particles, right? And they say there were three particles composed of all the rest. They were... ... ... using act and ability, right? You know? But those are very fundamental distinctions, right? Being as such, those are the two fundamental distinctions of it. You can also bring in being as a reason with their secondary, accidental being, with those two divisions. But this is kind of a little, you know, you could have avoided this more particular difficulty, right? Okay? Because even with substances like flesh and blood and bones, not everything is inside of everything, isn't it? In the smallest piece of flesh, which we've shown exists, there is no bone, right? Otherwise, it'd be smaller than the smallest. In the smallest piece of bone, there'd be no what? Flesh. Otherwise, there'd be something smaller than the smallest piece of bone. Okay? But Heisenberg doesn't see that? Well, I think he does, yeah. I mean, he's, um, he had to read his other writings, you know? I say, in the, that one, he, he, uh, he says, it seems to be a good description, right? You know? And he says, the well-known formula. He used that phrase several times in the book, you know? The well-known formula. I assume it's, you know, a common way of speaking, right? I remember one time, Pindell and the chemist, there was an assumption there. He was saying, well, it's easier to speak that way, anyway, as if it's composed of this. They realize in the sense, this is a goody-cat bee, but, you know, it's easier to speak that way, right? It's easier to see the way that animal is in man, than man is in animal. Right? Yeah. Now, the seventh objection there, apparently Anaxagoras spoke as if all coming to be was the addition of light to light, and you get, you know, how do you get a man here rather than a dog where you bring in more pieces of man, right? Anaxagoras, well, that's not the way things come to be. Sometimes we bring unlike things together, right? So we, you know, we screw wood into cement, right? You know? I do it myself in the basement. Right? You know? We screw wood into, you know? See, sometimes you make things by adding unlike things, right? Okay? But those are more particular difficulties, though. I'd like to emphasize two, three, and four because they really give us something new we haven't seen before. But notice that all of this you want to take into account, you know, why does he have this difficulty, right? See? It's because he wants everything that comes to be out of something to be actually in there, right? And then to fit it in he's got to make it infinitely small and then he gets into these difficulties, right? Yeah. And the same way with the modern physicist there. If he wants to put actually into any elementary particle all the things you can get out of this elementary particle, right? Well, then he's going to have to make them smaller and smaller and smaller and that's going to take contradictions. Yeah. This is also the same thing with the big bang theory, too, where everything like whatever, whatever time was all compact there such that the density was so great, the gravity was so great. It seems to be the same kind of theory, too. Well, I mean, the thing about that is that there the physicists are beginning to think that the universe might be limited even in time, right? Oh. Yeah. Okay. Yeah. I know it's Aristotle. I mean, he thought the universe always was, right? And Thomas, you know, examines all the arguments for and against and says there's no argument, you know, that really demonstrates that it always was. No argument demonstrates so that it had a beginning, right? He said none of the arguments are demonstrations for or against us, right? By faith, right, Thomas believes that the universe had a beginning in time, right? Right. But he's by faith he believes it, right? The arguments that reason gives for or against that, right? Yep. And Thomas examines those in the Tirnitatimundi, right, in other places. He shows that none of them are, what, necessary, yeah. Yeah. None of the demonstrations, right? Yeah. I mean, even you're talking about the Big Bang and this here again is not conclusive, right? But I mean, it's more in accord with this to think of the universe as being limited in time, right? Okay. So, we're discovering limits, right? But they fall under this general second difference, right? That there are limits in the quantities of actual things due to their natures, right? Limits that we discover in our sense experience in the natural world but that we couldn't foresee from the point of view of the abstract consideration of quantity and, what, pure math, huh? But notice, now, take an example again of Locke, right? Locke's difficulty is really about things that pertain to Locke, right? Okay? Okay? And what he doesn't understand there is that the genus, right, is in a way to the differences something like matter is to form, right? Okay? But in a way, the reason why we have genus and difference in logic is because the things that we know fundamentally have something like matter and something like form, right? And the genus is taken from matter and the difference from what? Form, right? Okay? So it's a similar confusion, right? To make the forms matter be composed of the forms that it can receive, right? It's like trying to put the differences actually into the, what, genus, huh? Okay? So in a way, matter is all of these things, according to Angebrus, that can come to be from it, but in a way it's none of them, right? Because none of them are really, what, distinct, right? And infinitely small and so on, right? In a way, Locke is making the summary difficulty saying that, what, the general idea of triangle is equilateral or isosceles or scaven, is it right angled or obtuse? Well, it's all and none of these, right? See? He can't quite understand the fact that it's all of these in ability but none in act, right? And the difference will be equilateral or scavenous asosceles will be actual but it's in the genus only in what? Ability, right? So these two things are similar in a couple ways, right? One is that you're confusing act with ability, right? In both cases, this is to that is ability to act and this in a way is not ability to act. And notice, you know, you go back to porphyry, right? And a strict name for difference there is the species making difference, right? It goes back to Aristotle in the sixth book of the topics, right? He speaks of the aido-poias, the Greek and the aido-poias, the species making difference, huh? Okay? And notice, the word species there or the Greek word aido-poias, they both are names for what? A form which you can see, right? So in a sense, it's like form to matter, right? In fact, in English, we sometimes use the word form for what? Species. I would say the democracy is one what? Blank of government. It's one form of what? Government, right? Okay? Sometimes I speak of the forms of fiction, right? You know, drama is one form of fiction, the novel is another form of fiction, the short story is another, and the epic is another form, right? See? Well, form there, you see the analogy, right? Between the two, right? Okay? So you can say that these mistakes are analogous or proportional, right? But you can also say in general they involve a confusion of act and ability. And putting what is in something only an ability actually in there. Yeah.