Natural Hearing (Aristotle's Physics)
36. Smallest Pieces and Modern Physics: Arguments 2-7 Against Anaxagoras, Locke and Ability
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[0:00] arguments, the second, third, and fourth arguments, we'll see are linked together, because in the second, and in the third, and the fourth, he's going to refute three different statements of Anaxagoras about the matter.

[0:22] 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 throw, overthrow something else he said. So these three will be linked, right?

[0:38] 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

[1:02] between quantity in pure math and the quantity of natural things. Okay. I call this the second difference because we already saw what a difference between these two, and having seen that first difference, we're open to seeing and discovering the second difference.

[1:42] Now, what is that second difference? I better say that at home before I guess. We start to look at two, three, and four. But this second difference. Is what distinguishes modern physics, physics of the twentieth century, from physics of the seventeenth, eighteenth, and nineteenth centuries, or one thing at least that distinguishes them.

[2:10] And so, in my comparison between Aristotle's doing here in the physical sciences, eight, five, and one are based on something that the whole physical science from Galileo, Kepler, 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 twentieth century. Now, the physicists of the twentieth century, those who worked out quantum theory and relativity theory, the two relativity theories.

[2:48] If you read these scientists, right, like Einstein or Louis de Broglie or Niels Bohr or Heisenberg, they're often called the physics of the twentieth century modern physics. And the physics of the seventeenth, eighteenth, and nineteenth centuries, they'll call them classical physics. But no, what classical means? It doesn't mean the Greeks, right? It means Galileo, Kepler, Newton, and so on. They'll also call the physics of the seventeenth, eighteenth, and nineteenth century Newtonian physics.

[3:19] 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, right? So, when they contrast modern physics, meaning the physics of the twentieth century, with classical physics or Newtonian physics, the physics of the seventeenth, eighteenth, and nineteenth centuries, right? One thing that the physics of the twentieth century has, especially its most established parts, is the second difference that Aristotle pointed out.

[3:57] 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.

[4:14] You know, they seem to overlap the two, right? Natural philosophy deals with bodies. Okay, natural bodies. Yeah. Yeah. Is 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? Okay. By the geometer and arithmetician, They consider number and shape and so on in separation from natural bodies, right?

[4:59] And indeed, in separation from all what sensible bodies, right? Okay. So the geometrical sphere really has no matter. 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? Remember 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 these good students like Thomas had seen it, right?

[5:49] But that opened him to what recognizing the second difference. What is the second difference? Well, he discovered that natural quantities have limits, son. Either in the direction of the large or the small, or in 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

[6:41] things, right? Okay. Okay. Let's look at the second argument now. We've got the arguments numbered here, right? Now, basically, Aristotle is going to use here the second argument if and what syllogism, right? Which is a very common type of syllogism when you're refuting a position, right?

[7:17] And as you know, when you're trying to overthrow a statement, the form of the if and syllogism you use is this: if A is so, then B is so. B is not so.

[7:34] Okay. If you lay down statements in that form, what follows is this: A. 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 what not be so, right?

[8:08] 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 is for right. You go to reason against the idea that the parts of an animal or of a plant or something else, right, can be what infinitely small, right? Now, if the parts can fall below any size limits, right, there's no limit as to how small they can get, right?

[8:51] What follows? If the parts make it A little more concrete. Let's say, for example, of an animal or a plant, if the parts can fall below any size,

[9:17] 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?

[9:49] Okay. So, if you understand the relation of part and whole, the if-then statement is kind of obvious, isn't it? Okay. 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?

[10:22] 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 this manifests, right?

[10:50] But the trees in our part of the country don't grow as big as these redwoods or sequoias or something in California, right? And the grass doesn't grow as tall as the what? Trees, right? Okay. So the consequence is not in fact true in the natural world, is it? That the whole can be just any size.

[11:16] But the whole cannot fall below any size. Huh? Therefore, what? The part cannot fall below any size, right? Okay. So he's overthrowing what position of Anaxagoras sir in regard to that?

[11:38] But it 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 second argument. Therefore, the part does not fall below any size. which means it must be a smallest piece, right? Okay. He's going to use that in the third and in the fourth arguments to overthrow two other positions of Anaxagoras.

[12:12] And in a way, it's like you know, so-called domino theory, right? You knock over one, you knock over the other ones, right? Because Anaxagoras arrived at 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.

[12:30] Now, in the third argument here, once you say that there is a smallest piece of flesh or blood or bone, right? Then, anytime you get something out of that blade of grass, you are going to have to take at least that amount, right? You can't take a piece of flesh out of the blade of grass smaller than the smallest piece of flesh. Okay. Now, can you take?

[13:09] 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.

[13:29] 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 half of that, and go on forever, right? But the pieces get smaller and smaller and smaller. They fall below any given size, right? And you 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 that same amount, right?

[13:56] Could there be an infinity of the same amount in a finite line? I don't know Because if you multiply the same amount infinitely, you are going to exceed eventually. Yeah, they can. 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 Anaxagoras said in one of the fragments, no smallest of the small there.

[14:28] But here, there is a smallest of the small, namely the smallest piece of flesh, the smallest piece of bone, and so on, right? And so you have to take out at least that amount, huh? Okay.

[14:44] Sometimes I give a whole 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. 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?

[15:20] And suddenly you run out of something, and the customers go somewhere else. You might lose a customer, right? So I like to sell mathematical lines, right? Never have to reorder. And so the first guy comes in the door.

[15:35] I sell him half of the mathematical line I have, right? Second guy comes in the door, I give him half what's left, right? I can go on selling mathematical lines all day long, right? And they would say about Berquist. You know, one thing about Berquist is he never runs out. He always has mathematical lines in store, no matter how many customers come through the door, right? You know, can be a stampede, he still got mathematical line.

[15:59] Though someone else might say, but you know something, they keep on getting smaller, smaller, smaller, right? Okay. Then I take my second example, right? Berquist is out in the in the desert there, right, with a canteen of water. I just heard something about you know, give somebody a cup of cold water, get a reward, right? Some guy comes along, right? Give me some water. So Berquist gives him half of his canteen, right?

[16:27] Okay. Then later on, the other guy comes along. Give me some water. And Berquist gives him half of what he's got left in the canteen, right? Can Perkowitz go on giving water forever?

[16:41] No. Why not? Because there's the smallest piece of what? Water. Which is very small. Maybe the molecule of water, right? But the molecule of water has a definite what? Size, right? And so if there was a huge number of molecules in a canteen of water, can there be an infinity of molecules of water in the same canteen? So Berquist eventually will run out, right? You see the difference?

[17:12] Okay. So in the third argument, Aristotle takes the fact of what's been shown, the second argument, right? That there's a smallest piece of flesh, a smallest piece of bone, right? And he uses that to overthrow another position of Anaxagoras that there's an infinity of pieces of everything inside of everything, right? You see the argument? Okay.

[17:43] Now the fourth argument, huh? He's going to overthrow now the original position there, the original conclusion, you might say, of Anaxagoras 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?

[18:14] 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, 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? And the smallest piece of bone can't be any flesh.

[18:45] 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. there'd be something smaller than the smallest which is a contradiction, right? Okay. So not everything is inside everything, is it?

[19:07] See the argument? So notice how, the second and the third and fourth, they're all 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 limit, right? Through the consequence of that, right? Which is contradicted by experience, right? And therefore, he shows in that second argument that there must be a smallest piece of flesh and bone and other things.

[19:41] And then he reasons from that in the third argument that you can't keep on taking things forever out of a finite body. That they 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.

[20:07] Okay. And notice there's a way in which everything can be inside of everything, in ability, right? Yeah. But when you make it actually there, right? You run into difficulty with the second difference in the quantity of natural things. So.

[20:27] So the second difference, you know, could be stated by saying that there are limits in the quantities of natural things, in the direction of the large or the small or both, 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.

[21:06] 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 atom is very small, right? And different atoms are different sizes, right? Okay. But every atom of what hydrogen has the same size, huh?

[21:50] Okay. And for every chemical compound, there's the smallest piece, which is called what? Molecule, right? Now, though a molecule is very small, every molecule has the same what? A water, it's there. What? Has the same size, right? So modern chemistry in talking about the atom and the molecule is based on the idea that there's the smallest piece, right? But there's something smaller than the molecule of water, but it's not water.

[22:21] Do you see that? Okay. Now you'd be in the same difficulty if you said that every elementary particle was composed of all the rest, because then you'd have like Anaxagoras has the fifth argument there, right? You'd have what? Instead, each elementary particle all the rest, and each one of those all the rest, and things would go on differently. So the elementary particle getting smaller and smaller and smaller and smaller, right?

[22:44] 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, ability. You see? Same difficulty, right?

[23:12] 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.

[23:32] I mentioned how Louis de Broglie says that in a different area, but he said that if you ask the physicists of the 19th century what happens when white light strikes a prism and you get this spectrum of color, they would have said, "Well, the white light was composed of all those colors, and the spectrum has merely separated them out, right? " See? We no longer think that so.

[23:54] 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, ability, right? Potentiality, possibility, right? But your mind kind of at first assumes that everything must be what? Actually in there, right? Because you can't imagine something in something without imagining to be actually in there.

[24:27] So false imagination there, right? But also equivocation 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 a sphere.

[24:58] Is our cube in the clay? No. Except in ability, right? You have to qualify them. So, confusing this simply in some respect. Several fallacies there.

[25:19] 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.

[25:39] Now, you mentioned also that the second, third, and fourth have in common something with the physics of the 20th century. So now, just to speak very simply about it,

[26:03] see, modern physics begins officially in December of 1900, when Planck proposes the quantum hypothesis in the study of black body radiation, and Planck was running into contradictions applying Newtonian physics to the study of black body 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 is a smallest amount, and either give or receive that amount, or some multiple of that amount, with nothing less than that amount, or even between some multiple of that amount.

[27:03] In 1905, Einstein showed that you can't understand light without introducing quantum. In 1913, Bohr showed you could understand the atom this. This kept on being developed until it was the late 20s, right? Quantum theory was kind of perfected. What characterizes quantum theory is recognition of a limit in the quantity of an actual thing. Now, Newtonian physics assumes that you could what? Impart energy in just any amount.

[27:50] You know, I could give half the amount that I gave you before, or a quarter of that, or eighth or an eighth, right? There's definitely quantum physics opposed to that, right? Okay, so that was a limit in the direction of the what? Small, right? Okay.

[28:13] Sometimes 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, bag of 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. The other guy says, "Don't leave until you pay your share of the bill."

[28:33] 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 twenty-five cent bag of potato chips, so what's your share? So we know we're friends, right? Your share is twelve and a half cents, right? But I reach into your pocket, what do you find? There's no way to pay twelve 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?

[29:06] And that's what they discovered about energy, right? It comes in pennies, so to speak, right? Isn't it? Kind of a strange thing, but the penny is something arbitrary in a way, but but the quantum is something natural, right? Now, in 1905, Einstein also proposed the special theory of relativity.

[29:38] And one of the cornerstones of 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. It was the speed of light, right? But the speed of light was the maximum speed in the universe, right? And it was impossible to go what faster than that, right?

[30:05] Okay, that's part of the special theory of relativity. Now, Newtonian physics, there is no what limit to how fast something can go, right? You can 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?

[30:39] 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.

[31:11] And to a large extent, it may be true. So if in pure math, four minus two equals two, right? Then I expect that a dog has four legs, and you cut off two legs of the dog, you'd have what? Two legs left, right? If the chair is four legs, and you cut off two legs, the chair has two legs left, right? You kind of assume what's true of quantity in math is true of quantity in the actual world, don't you?

[31:41] See? But you forget that there are what? You're considering quantity in abstractly 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? See, now pure mathematics is there such a thing as the shortest line? Is there such a thing as a what longest line? See, you always just get the line longer, right, or make it shorter, right?

[32:18] And therefore, triangle or square or circle can be bigger. Geometry is based upon that, right? Like in the what the fourth book, when you inscribe a circle in a square, circumscribe a circle around the square, and vice versa, well, that implies that circles and squares would get smaller and smaller and smaller without limit, right? And bigger and bigger and bigger. You can always inscribe and circumscribe in pure math.

[32:47] 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, Heraclitus said, "nature loves 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?

[33:18] 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 in pure math. That's a sign we're getting closer to the natures of things, right?

[33:42] It also explains why, for so many centuries, we kind of assumed everything that's true of quantity in pure math is true of the quantity of what of natural things, huh? Do you see that?

[33:57] Why we should have you know assumed that mathematically, right? Because they didn't really see the first difference. And it's interesting with Democritus, right? Democritus

[34:20] in the text that we saw before, Democritus 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?

[34:33] But I think it's in the in the De Generatione, in one of the later books, when Aristotle is describing or talking about Democritus, he speaks as if Democritus spoke of the atoms as being points. Okay. Now you recall Democritus arrived at his position by a what thought experiment, huh? He said, "Imagine a body cut in every way a body can be cut. Was there nothing left over, or something uncut left over?

[35:08] You can't make something out of nothing, so there must be something uncut. That's what atom means, uncut. But isn't it interesting if those two texts? Sorry, Warren Bray. One time I was pointing out how, how in this one text, Aristotle speaks as if Democritus said that the atoms are like points. In other texts, he speaks of the atoms having some size and having some shape, right?

[35:35] But maybe there's an ambivalence in the thinking there of Democritus, right? Because if you think of quantity from a mathematical point of view, the only thing indivisible in geometry is what? Points. The point, right? So that's the answer has to be, right? If you think of it mathematically, right? But there's a problem about how you can make a line out of something like points, that we showed before, right?

[36:04] Then you got to have some size for the atoms, right? And then you reduce the idea that they have a limit, right? The directions are 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 Loeb edition there of the Greek mathematical works, right? There's a fragment there that they attribute to Democritus, and it kind of shows maybe he's a little bit on to the difficulty of thinking that you can make a point out of a line out of points.

[36:45] But you know, some of the analogy is making a surface out of lines, or making a what a body out of what surfaces, stacks of surfaces, right? And I think I gave you that one that he gave before, but Democritus took the example of a pyramid, something like that.

[37:12] Now, if you look at that as being a series of of surfaces one laid 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 unequal? Equal. I think it's just a pyramid, but a cone, right? Okay. Well, if they were equal, then any place you cut into they're equal. Then what would you have?

[37:45] You have a stack of equal things, right? So would you have a cone, 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 what the paradox, right? Because the Greeks are thinking of a cone as what, and a body as a what, pile of surfaces, right?

[38:14] Just as a lot of mathematicians think of the line as composed of points, right? But there you show a difficulty in it, right? So he might, in some sense, be a little bit on to the idea that there's inherent difficulty in making the divisible out of the indivisible. You know, if you put lines next to each other, you get a surface, right? Well, if you're going to compose a surface of lines, they've got to come up and touch each other, right?

[38:41] And if they touch each other, they're going to what? Coincide, right? The same way here, if you try to make a body out of surfaces, right, they have to come down and touch each other, and then they coincide 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 Democritus there is some, you know, anticipation of difficulties that will lead Aristotle mentioned to see that the difference between the quantity of pure math and quantity of natural things, right?

[39:18] And then to see the second difference here, that to see limits in the quantities of natural things, the directions are large and the small, right? No, if that idea is already in chemistry, right, with the proton, with the electron, and the atom and the molecule, right?

[39:41] Now, after this, the quantum physicists, I mean like Planck really and Heisenberg and Bohr, so they went on to the study of elementary particles, right? Okay, and that work is still working on now. It's still not complete, but Heisenberg and others like Gell-Mann, who also got the Nobel Prize in development of quantum theory, they were looking for what? They were looking with the hypothesis that there was a minimum length in the universe, which was ten to the minus thirteen centimeters.

[40:16] Now I say that's not established, but I mean it's interesting. 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, a length below which there's nothing, right? Because that's so contrary to pure math, a minimum length, right? You know. Will not be the truth, Adam. Yeah, yeah, yeah. See, But something below which there's nothing.

[40:43] I mean, they should even attain that as a sign that their their thinking has now been changed, right? Quantum theory and relativity. In the Einstein, ten years later, in ten and nine fifteen, I think fifteen, he proposed a general theory of relativity, right? Which was confirmed somewhat after the Second, World War, first world war. But that was going in the opposite direction towards the large, right? But that led to an explosion in cosmology, right, in the study of the universe as a whole.

[41:15] As they started to study the cosmos more intensely with this general theory of relativity, it seemed more plausible that the universe was what finite, as Aristotle had thought, rather than infinite, like the early Greeks thought and like the Renaissance physicists. Koyré's book? Is that the name of it? Koyré, 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?

[41:44] But now they seem to be returning to a what? A cosmos that was what finite, you know, again. Cosmology is is more the you know the along with elementary 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 the limit in the direction of the what large and then after the discovery of you know the expansion of the universe and so on and the big bang theory and so on begin to entertain the hypothesis the universe might be limited in time too

[42:32] Did you ever hear something called a plank Planck particle and plank time Okay. So it certainly characterizes the two well established parts right but also in the study of elementary particles which going on from there right and the study of the universe as a whole right both of those might also reveal what limits right so Aristotle in one way would be less surprising than anybody else in the twentieth century right in a sense his mind was open to the discovery of what limits in quantities of natural things due to their nature huh limits that could not be foreseen in the point of pure math but he's in a sense open to that because he saw that first difference huh it's reference to the quantity and

[43:28] abstraction so as somebody put as you say eight five and one together because they have something in common right and then two three and four together because they have something else in common right eight five and one have in common principle of fewness. and two three and four tied up with this second difference of quantity in pure math and quantity of actual things but also as they say eight five and one bring out something in common with the whole physics from Galileo to Newton to Einstein and beyond but two three and four has something in common with the physical sciences in the twentieth century modern physics is called

[44:31] 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 the chicken skin from the bone because they're both something substantial, right?

[45:04] And 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 it's trying to separate accidents from substance. Right, we can separate one substance from another, but not accident from substance. You see, so you could put my arm in there and my leg in there, right?

[45:31] But you couldn't put the shape of my arm in there and my arm in there. You see, so it's a kind of stupid mind that's trying to separate accidents, right, from substance, right? But notice that in a way reveals that an examination doesn't see clearly the distinction between substance and accident, right? He has a mixture of everything, so he has accidents mixed with substances, huh? Not realizing the difference between the two, right?

[46:04] But now, when you get into wisdom, huh? Those are the two main divisions of being, right? Being an act and being an ability, and then being as substance

[46:29] and being as what accident, huh? Okay, substance, quantity, quality, more besides, basically substance and accident, right? Those are the two main divisions of 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. His form is act, and matter is ability, right?

[47:04] But he's also not seeing the difference clearly between substance and what accident, right? Okay. You've heard the witty remark of Lord Bertrand Russell. You know, he says, "The accidents of Mister Smith have no more need of a substance to inher in than the Earth has need of an elephant to rest upon."

[47:38] You heard that? The accidents of Mister Smith have no more need of a substance to exist in, right? Than the Earth has need of a what elephant to rest upon?

[47:51] Well, the point is, if accidents did 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.

[48:11] See, so it's not just the ancients don't understand the distinction between 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, and all he thinks is mind and thought, and then Hume does away with that. No substance at all, right? Well, it makes some sense to say only substances exist, right?

[48:38] But to say only accidents exist, it makes no sense at all. So I mean, it's actually the ancients who are confused about these things, and of course the moderns used to say with the the subatomic particles, right? And they said every material particle is composed of all the rest. They were. confusing. act and ability, right? No. So, but those are very fundamental distinctions, right?

[49:08] 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. It's a more particular difficulty, right? Okay.

[49:34] Because even with substances like flesh and blood and bones, not everything is inside of everything, is it? In the smallest piece of flesh, which we've shown exists, there is no bone, right? Otherwise, there'd be a smaller than the smallest. In the smallest piece of bone, there'd be no what? Flesh. Flesh. Otherwise, there'd be something smaller than the smallest piece of bone.

[49:59] Okay. But Heisenberg doesn't see that. I think he does. Yeah. I mean, he's. You have to read his other writings, you know. I say in the that one he he says it seems to be a good description, right? You know, he he says the well-known formula. He uses that phrase several times in the book. You know, the well-known formula. I assume it's you know common way of speaking, right?

[50:28] 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.

[51:05] 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? Well, you you bring in more pieces of man, right? Aristotle, that's not the way things come to be. Sometimes we bring unlike things together, right? So we we you know.

[51:37] We screw wood into into cement, right? You know, in the basement. See, sometimes you make things by adding unlike things, right? Okay. Those are more particular difficulties, huh?

[51:58] I 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? 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?

[52:28] And the same way with the modern physicists, 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 run into contradictions. 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.

[53:00] Seems to be the same kind of theory too. No, but I mean the thing about that is that that there the physicists begin to think that the universe might be limited even in time, right? Oh, yeah, yeah. I know 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.

[53:25] No argument demonstrates so that it had a beginning, right? Okay. He said none of the arguments had demonstrations for or against this, right? By faith, right? Thomas believes that the universe had a there was beginning in time, right? Right. But he's by faith he believes it, right? The the arguments that reason gives for or against that, right? And Thomas examines all of them in the *De Aeternitate Mundi*, right?

[53:49] In other places, he shows that none of them are what necessary, yeah, yeah. None of them are demonstrations, right? Yeah. I mean, even about the big bang, and this here again is not conclusive, right? But I mean, it it it's more in accord with this to think of the universe as being limited in time, right? Okay. So

[54:15] 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 of the actual world, but that we couldn't foresee from the point of view of the abstract consideration of quantity and what pure math, okay?

[54:46] But notice now, take an example again of Locke, right? Locke's difficulty is really about things that pertain to logic, right? Okay. And what he doesn't understand there is that the genus, right, is in a way to the differences.

[55:18] 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?

[56:00] Is 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 Aristotle, 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 a similar difficulty, saying that what the general idea of triangle is it equilateral or isosceles or scalene?

[56:32] Is it right-angled or obtuse? Well, it's all and none of these, right? He can't quite understand the fact that it's all of these in ability, but none in act, right? And the difference, well, equilateral, scalene, isosceles, will be actual but it's in the genus only in what ability, right? Okay. So these two things are similar in a couple ways, right? One is that you're confusing act with ability, right?

[57:04] 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? You know, the name for difference there is the species-making difference, right? This goes back to Aristotle in the sixth book of the Topics, right? He speaks of eidopoios the Greek, and the eidopoios, the species-making difference, huh? Okay.

[57:41] But notice the word species there, or the Greek word eidos, they both are names for what? A form that you can see, right? So in a sense, it's like form to matter, right? Okay. In fact, in English, we sometimes use the word form for what? Species. I would say the democracy is one what? One kind of government. It's one form of what? Government, right? Okay. Sometimes I speak of the forms of fiction, right?

[58:19] Well, 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.

[58:37] 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. In a way, pantheism is doing that with another kind of ability, right? Because everything is in the ability of God to produce, right?

[59:07] But the pantheist, in a way, puts everything but that God's able to make actually in God. It's end up by saying God is a composition of what? Anything, yeah. That's a pan means all things, right? Pan means all things right so, that's a different kind of ability, because they're getting actual ability, right? But you're still, you know, making similar mistakes. Now, in another way, you see in mathematics, like we were saying before,

[59:39] anytime you cut a line, what do you get? You get a point. We'll see. Now, Nixon was first running against the Democrats. There, he said, "Any way you slice their program, it's still the same old baloney." Well, any time you slice it, you have baloney. What's it made of? Come on, there you go. Well, any time you cut a line, you get a point. It must be made out of what?

[1:00:08] Points. Yeah, we saw the difficulty in making a line out of points, right? If the points would have to touch, right? And if they touch, they're going to have to what? Coincide, right? And if two points coincide, then they have no more length than one point, which is no length at all. And even if a hundred or a million or infinity of points were to touch, they would have only one way of touching, which is to coincide.

[1:00:40] And therefore, they have no more length than one point, which is no length at all. So you can't really make a line out of what? Points, huh? So there, we can say there's infinity of points on a line in ability, right? But they're making actual what is on the line in what ability? And this is very common. You know, most kids, you know, coming up to here in grade school, high school, that a line is composed of infinity points, right?

[1:01:10] Well, you're making actual what's there only in ability. That's it shows that same difficulty, right? It's not an unusual difficulty to be mistaken about ability. The inability of man's minds, they say, to understand ability, is a common, common inability. Inability, in the sense, they're very difficult to understand, right?

[1:01:35] But here's in mathematics, and here in logic, and here in what? Natural philosophy, right? So I want to know the reason why, and it's said who said the difficulty, right? That's why I attach this ninth reading to the reading we had before, because it enables us to go a little bit into what Aristotle said about the first matter. But it's pure ability, right? Substance and ability. It's divisible by its proportion by its proportion.

[1:02:06] You see the difficulty of understanding such a thing. But in general, you can see that it has a great difficulty in understanding ability. The study of elementary particles, as we said earlier, is the most advanced part of modern science as far as the study of matter is concerned.

[1:02:41] You see, now you come back and you see, well, gee whiz, you can get hydrogen, oxygen out of water, and maybe, maybe a little bit careful there, right? Hydrogen, oxygen actually in the water, you know. Well, maybe they are, but the mere fact that you can get hydrogen, oxygen out of water is that enough to say that it's composed of those two? If that was enough, then you could say what's enough then to say that every elementary particle is composed of all the rest because you can get them out of there, right?

[1:03:14] But that runs into obvious difficulties, right? Especially when you're not an elementary particle, but big ones that are bigger than the original one. Doesn't make sense to say it's composed of that, right? See, as long as you've got things that are smaller in size, it makes all right. Say difficulty, right? But then you realize the argument itself may be not as strong as you thought it was.

[1:03:43] But this goes back to what we said about the Greeks, and we saw explicitly in the fragments of Anaxagoras and in those of Empedocles, but it runs through all of them that they try to understand every change as a change of what place, right? That doesn't involve any radical understanding of ability. It's in change of place something already actually exists, right? Just an extensic way of being put here or there, right?