Natural Hearing (Aristotle's Physics)
Lecture 19: Anaxagoras on Matter, Mind, and Infinite Divisibility

Transcript
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After a while, a long critique of Anaxagoras, but it's an extremely interesting critique of Anaxagoras. And he would count the whole argument of Anaxagoras, and then he would give eight arguments against Anaxagoras' position on matter. It's kind of interesting that he singles out Anaxagoras to attack. But in some way, the Anaxagoras' position reveals the difficulties of those who can't quite understand ability. And Anaxagoras is trying to understand ability, but he can't quite express it. He'll be saying everything is inside of everything in infinitely small pieces. That's not even what potency is or ability, but he's trying to get down to the idea of ability. But it's interesting that Anaxagoras' way of speaking about matter came back in the 20th century, in the most advanced part of modern science, about the study of matter, the study of elementary particles. And they began studying elementary particles in the middle of the century here. The common way of speaking was Anaxagoras' way of speaking. They don't have the same difficulties if you take the words, right, that Anaxagoras is in when Aristala gets to look at him. So it's kind of interesting, you know. Now, we can, as I say, reconstruct Anaxagoras' argument by Aristala's account of it. Is there any chance Aristala knew him as an older man or anything? Or were they completely separate? No, I think he probably would have been dead by then, yeah, because Anaxagoras, they say, came to Athens in the reign of Pericles. He was a friend of Pericles. But the charge against him was in piety for saying that the sun is a hot stone, the sun is a stone on fire. Well, the sun is, you know, the god of power, in case you didn't know. So that's obviously impious to say the sun is a stone on fire. Now, they think the reason why Anaxagoras said this was that, you know what we call shooting stars or falling stars? These are really what we call today meteorism. They're not falling stars, but they're meteors, huh? A meteor is what? A more or less a rocky thing, but it hits the atmosphere and it bursts into flame. That's what she called, these things that are falling to the earth. But they burn up before they hit the earth, usually. And they don't come down to the earth except maybe in the form of dust or something, but not something in the form of a rock. But occasionally you have a meteor that's so large that it's still a burning rock when it hits the earth. And that makes one hell of an impression of a lot of people. You know, and I suppose it's fiction now, they talk about disaster. And there's one example that hit somewhere in the southwest of the United States back in Indian times. And apparently they made such an impression upon the Indians that the father would pass on the description of it to the sun and it would go down a number of generations. And then the white men heard about it through the Indians. And they just thought when these Indian things it had no basis for it. But now I guess they go scientifically over that area and they, you know, actually they use the airplanes and so on. They photograph that they actually see the impact on the terrain into this thing. Well, they know that in northern Greece there, where H.A.V. came from, there was one of those things happen to them. So here's a huge rock, which is one of those falling stars, so-called, falling in the earth. So maybe the sun and the stars are really, what, burning rocks. And so this may have been behind us thinking of the sun as a storm and fire, which would be impious, because it's a god of power, right? You can't say those things. And Aristotle himself was, didn't think that the sun was fire because it would have burned out long ago. And I guess the pupil there of Heisinger and Weizsack is supposed to give an explanation of why the sun can go on so long, right, without burning out. I mean, it's quite eventually. I mean, it's incredible. If there was ordinary fire, it wouldn't have burned out long ago. It's incredible how much energy. When you think, you know, of how much energy we get from the sun down the earth here, we're supposed to be, what, 93 million miles, something like that, from the sun. And of course the sun is sitting out in every direction, right? So we're getting just a tiny, tiny fraction. You know, amazing. I mean, how can we do that in a century? Every century, apparently, it never seems to be diminished, although maybe it is, but it's, you know. So that's really a hard thing. It's not surprising that Aristotle thought the sun was something quite different from what's down here. It doesn't make really sense to think. If the sun is stoned on fire, it would bring out much better. Even the Great Fire of London, right, it went on and on, but that thing in New York is still, you know, smoking, I guess, but it's going to go on forever, right? It's going to go on for hundreds of years, smoking and burning and so on. So Aristotle is quite correct in saying it's not ordinary fire. Sun and moon and stars must be something quite different. But anyway, it took quite a second to explain that idea. So, apparently Anna Chavis' thinking about matter begins with a kind of an inductive observation that you can start almost anywhere in the natural world and eventually get everything else. Let me give a kind of an oversimplified version of that. Let's start off with grass out there, okay? Now, the grass is, let's say, eaten by the cow, and you get a bigger cow, right? So, you're getting more cow, not out of nothing, that's impossible, it's not out of nothing, right? You're getting more cow out of grass, right? Now, Perkwist wants to stay for something, so you get more man now out of the cow, but eventually out of the, what, grass. Then get more man, okay? Now, we find out the Perkwist is a Christian, so what you do with a Christian is you give to lions, huh? So, now you're getting not only more cow and men, but more, what, lions out of that grass. And the lion is punished for his iniquity, they're eating a Christian, and he's food for, what, worms, huh? So, you're getting more worm out of grass, huh? And maybe the bird gets the worm, so you're getting more bird out of grass. And then the cat gets the bird, so you're getting more cat out of grass. And the cat dies, and the cat's pushing up daisies, they're getting more daisies, huh? This seems to go on forever, right? Okay. So, by a sort of induction, he arrived at the conclusion that everything eventually comes to be from everything. And to that, he added the thought that we saw already in Empedocles, but it's probably a thought that's common to all these really Greeks. You can't get something out of nothing. You can't get blood out of a turnip, they say. That's an old saying, you've heard that? Why not? There's no blood in a turnip, right? And so, in DK10, he sees some of that thought here, the first fragment. How could hair come from what is not hair, and flesh from what is not flesh? How could you get blood out of a turnip if there's no blood in a turnip? So, how could you have gotten more of all these things out of that grass, unless there was a bit of a cow, a man, a man, a worm, a bird, a cat, and daisies already in the, what? Grass, huh? Okay. Now, before you laugh too much at that, huh? What happened in the study of elementary particles in the 20th century, they noticed in their experiments that out of any elementary particle, you seemed to be able to get, eventually, all the rest. And therefore, the well-known formula among the students of elementary particles was that every elementary particle is composed of all the rest. Because, like the Greeks, they would automatically think you can't get something out of nothing, right? So, just as you can get hydrogen and oxygen out of water, water must be composed of hydrogen and oxygen, right? So, if you can eventually get all the other elementary particles out of any one of them, any one of them must be composed of all the rest. And that's a conclusion that, and I tell you this speech is right, that if everything comes to be from everything eventually, and you can't get something out of nothing, then everything must be inside of everything, huh? So, it's kind of amazing to see it coming back, huh? And every elementary particle consists of all the other elementary particles. Don't know the formula. And I started to study them. Now, to that, Anax Egris added another observation, which was, we think, common, and we talked about it with Anaximander a bit. Things keep on coming to be forever in this world. Every year there's a new spring. And that means new things spring up, right? So, if you keep on getting forever things out of that original grass, how many times... things must there be in the original grass? An infinity, okay? Now, the point is, you say, well, here's the blade of grass, it's finite, huh? How can you have an infinity of pieces of everything else inside that grass, huh? How can you put them all in there? Well, you have to make them infinitely, what? Small, huh? A little bit like the modern mathematician sometimes says that a straight line is composed of infinity of points, right? Okay? But because the points were infinitely small, right, you can think you can fit in an infinity of them, right? So because things keep on coming to be forever, there must be an infinity of pieces of everything inside of everything, and to fit them in there, you have to make them infinitely small. So there's an infinity of infinitely small pieces of everything inside of everything. Okay? And this is what he's talking about here in the famous DK1. All things were together, unlimited in number and in smallness, huh? I use the English word unlimited, but infinite you can use too, there's a Latin word, huh? They're unlimited or infinite in number, meaning in multitude, and in what? Smallness, huh? They're infinitely small, right? Okay? In all things being together, nothing was clear because of smallness, huh? And there he's trying to get the idea maybe of everything being in there in ability, by making them infinitely small, huh? But still, when he's making them infinitely small, he's still making them be actually in there, and he doesn't really have the idea of ability. And notice how a little throwback there to an axiomonez, and maybe an axiomander too, where he talks about the air and the ether, right, huh? And they're unlimited character, huh? You're influenced by that. But his thought is kind of that there's an infinity, an infinite small pieces of everything inside of everything. Now we'll see how Aristotle criticizes this, and there's a very interesting critique of this, but that's his position, right? And in a way, you'd have the same thing in the modern scientist, if he says, every elementary particle consists of all the rest. Well, then inside each company of particles, all the rest of them, and inside each one of those would be all the rest. So go on. And they're getting smaller and smaller and smaller, right? Okay. Now the next fragment is just kind of an expansion on this idea. These things being so, it's necessary to think that there are many things of all kinds and all compounds, and the seeds of all things. He calls these small things like the seeds of all things, huh? Again, in DK4, you continue to talk about the seeds and how nothing is distinct, one thing from another, because they're so small. Now, in DK3, a very interesting statement here. Nor is there a smallest of the small, but there is always a smaller. Now this is certainly true of the, what? Mathematical line, huh? And now the expression here. For what is cannot cease to be by being, what? Cut, huh? Okay. Now, let's stop on that a bit, huh? Because when we define the continuous, to go back to logical, when you get the quantity, huh? We distinguish two species, maybe a quantity, a quantity, and one we call discrete, and the main kind of quantity is called number, and the other we call continuous, and there are many kinds of that, like the line, and the surface, and the body, and so on. Sometimes we add time and place to that, too. Now, when Aristotle distribishes these two kinds of quantity in the categories, he does so in terms of their parts, and the difference he assigns is that in a discrete quantity, the parts don't meet anywhere, but in a continuous quantity, they meet. So the two parts of a, what, line meet at a point, then. And the two parts, let's say, of a circle meet at a line. And the two parts of this piece of chalk would meet at a surface in the middle. But in the number seven, do the three and the four meet at a point or a line or something? Do they have any boundary? No. So that's one way of distinguishing discrete and continuous quantity. That's the way the logician does that. But now, in natural philosophy, when he talks about the continuous, Aristotle in Book Six of Natural Hearing, you have the whole philosophy of the continuous there. Then he gives a second definition, he calls this one, but he gives a second definition of the continuous. The continuous is that which is divisible forever. That which is divisible forever. Now, number is not really divisible forever. When you get down to one, you can't divide the matricot one, the abstract one. It's simpler than a point. That's why the modern mathematician confuses you there, right? He divides the one and the fourth tip. Because he's thinking again of the continuous, huh? Now, why do we say that the mathematical line is divisible forever? We say you can cut it in half, and you can cut the half in half, and cut the half of that in half. How do we know that this is divisible forever? How do you know that? Well, when Heraclitus, or what Hank Seguer says, that what is cannot cease to be by being cut, huh? If you cut a straight line into two shorter lines, you still have something you can cut again, right? If you cut it up into nothing, that's impossible, right? Now, the only other alternative, besides cutting it up into nothing, cutting it into shorter lines, would be to cut it into, what, points. Now, if there was a line that, say, two points long, and you cut that in half, right, then you couldn't cut it any further, because the point is indivisible, okay? But is a line composed of points? Can you put together a line from points, huh? Well, we sometimes show that you can't by an either-or, what, syllogism, huh? Okay? So let's give the either-or syllogism here. But notice, this is contrary to what the modern mathematicians sometimes say, especially in grade school or high school, that the straight line is composed, right, which means put together, composed of an infinity of points, huh? We're going to show that you can't put together a line from points, huh? Okay? Now, we're going to use an either-or syllogism, huh? If you're going to put together a line from points, the points are going to have to come up and touch, right? Okay? To make one continuous line. Now, there's really three or four ways, actually four ways, two things can touch. You can have a heart touching heart, like I have these two circles, right? Part of one touches part of the other, right? Or you can have a heart touching the whole, like, say, these two circles, huh? Part of one touches the whole of the other, right? And vice versa, the whole of one touches the part of the other, right? The third way would be for the whole to touch whole, and I can't draw this very well, I just go around twice, huh? And the whole touches the whole. And then the two of them would what? Pull inside, right? Now, is there a fourth way the two things could touch? Besides part touching part, part touching whole, or vice versa, and hold touching whole? All right. We might seem, at first, exhausted because what you've got besides the whole parts, right? But couldn't two circles, say, touch at their edge? Okay, like a touch at a point, you know? So, edge touches edge. The edge is not really a part. So, edge touches edge, okay? So, you've got four ways that two things can touch, right? Now, if the points touched, could they touch in this first way, that part touches part? No, because a point has no parts. In fact, that's the way you could define it, if you recall, right? Okay? The point is the end of a line, right? Does the end of a line have any length? No. They have any length, they haven't come within the line yet. Okay? So, two points cannot touch as part, well, one touching part of the other because they don't have any parts. For the same reason, part cannot touch, what? Of one touch the whole of the other. So, these two ways are eliminated, huh? Now, can you make any distinction between a point and its edge? Then you're making the point a little circle, right? You've got something inside this, you know, not the same as the edge, right? So, this way is impossible, right? So, the only way two points can touch is like when the whole touches whole. That is to say, the only way they can touch is to coincide, right? Okay? Now, if two points coincide, you have no more length than with what? One point, which is no length at all. And if ten or a hundred or a million or an infinity of points are to touch, the only way they could touch would be to coincide. And if they coincide, they have no more length than one point, which is not at all. So, there's no way to compose a line, right, from points. The points that have to touch, if they touch, they coincide, they coincide, they have no more length than a point. There's no length at all. So, when you divide a straight line, you never get two points. And you never get nothing, you can't make something out of nothing, right? So, when you divide a straight line, what do you get? Two shorter lines. And as long as you've got a line in length, you can always divide that in half, right? And what do you get? Same thing. Two even shorter lines. There's no smallest of the small. No shortest of the short, huh? You see that? And that's true about the line, but the same is true about a square, right? Because the lines can be shorter and shorter, and the square is smaller and smaller, huh? Okay? And the same about the circle. You get a circle by rotating a straight line around itself, one of its endpoints, huh? Okay? So, this is one way we see the infinite visibility, the continuous, huh? But in the sixth book of natural philosophy there, of natural hearing, Aristotle would give me the other ones, huh? Because he's showing, you know, how, he shows, for example, in one argument, how distance, like a line, and time are both continuous. They're both divisible forever. You know the way he shows that? We take something we all know, that one body moves faster than another body, right? Okay? So, the faster body moves the same distance as the slower body in less time. In that less time, the slower body would lose, move a, what? Lesser distance. In that lesser distance, it would take the faster body even less time. So, just by alternating the two, you can see together that time and distance are, what? Divisible forever, huh? Because the faster body always covers the same distance in less time. In that less time, the slower body will always cover less distance. In that lesser distance, the faster body will cover even lesser time. So, the two are divisible forever, right? You know? So, Enx Egrus, the great, Enx Egrus, seeing something of this. Nor is there a smallest of the small, right? But there is always a smaller. For what is cannot cease to be by being, what? Cut, huh? We have to point out, you know, that you can't cut into points, too, to be complete there. But there's also something greater than the great. Now, why, what's the connection between that? The fact that there's no smallest of the small, and there's no greatest of the great. How can you reason from there being no smallest of the small, that there's no greatest of the great? as you divide the line you keep on dividing the line what is getting greater the number of lines is getting greater so if the if the continuous is divisible forever then the numbers can get greater and that's one way that's one way of understanding the infinity there of numbers you can say that number arises from the division of the continuous now strictly speaking the first meaning of number one is not a number is it because number is a multitude composed of units so if you have a continuous straight line there you've got one line there you don't have a number yet but you divide that and now you have what the first number two now you divide again and you've got the next number three right if you can keep on dividing forever then the numbers will keep on going up forever so if there's no smallest of the small you never get to an invisible line then you never get to a greatest what number that's why number when you speak of the trinity means something quite different because there's nothing continuous there in God God's not a body okay now a little confusion there at the end of the fragment each thing to itself is both great and small does he understand the category of prosti towards something is great and small to itself or to another yeah it's not something absolutely in itself is it in the categories Aristotle gives example you know if if I had a hundred people in my house something like this right you'd say oh big dinner there's a big dinner part of your house breakfast a hundred people but if you had a hundred people there watching the world series you'd say oh you know I'm just a terrorist that's really getting into the the business right that'd be a small crowd in a world series a hundred people right but no it'd be the same number absolutely speaking a hundred people in my house if I had a hundred people in class that's a big class oh gosh a hundred people I'm going to correct all these papers you see but if I'm out if I'm running Yankee Stadium or something you know a hundred people gosh gee I'm going to pay the hot dog stands for this kind of a crowd I'm going to pay Clemens the rest of these pitches I'm going to pay for him you see what I mean so great and small is toward something so you know a seven foot man is tall compared to us let's say but compared to a what redwood tree he's small so when I was first you know studying astronomy and you'd read about Betelgeuse and of course this is after you learned the dimensions a bit of the solar system and then you you realize how huge the solar system is you're like you know we're 93 million miles and the sun and I said the whole solar system would be fit into Betelgeuse wow you know but now I realize it's all relative I'm not impressed with that too much anymore right you know because just think of the number of molecules inside of you know me or the number of molecules inside of my glass of water see you know you know no big deal you know it's all relative right I'm first very much impressed because I think I'm an absolute thing right the whole thing in there or there's some star I guess where you bring bring back that thimble full of the star you know it'll weigh a ton on the earth it's like my children when they're little you know daddy can you count to a hundred yes wow you know they're really impressed you know then they get a little bit older you know daddy can you count to a thousand yeah wow see now they're not impressed at all so I can count it would make any deal count to a million they're not going to be impressed it's relative huh you know You know, when the scientists call man the Homo sapiens, sapiens means wise, and I say, well, is that contradicting what Socrates or what Pythagoras said, you know, don't call me wise, God alone is wise? Then you have the proportion, though, you see, of Heraclitus, that as the ape is to man, so man is to God, right? So man compared to God is not wise, but man compared to the ape is wise. That's what Homo sapiens really means, the wise ape. Or he says, as a child is to a man, so is man to God. So to the little child, daddy seems to know everything. In comparison to God, daddy seems to know, what, nothing. You see, kind of relative, huh? So we're wise in comparison to ape, but not in comparison to God. That's a very interesting fragment, but later on we'll come back to that, because there is a difference between quantity and pure mathematics. Anics and quantity of natural things. And Aristotle will point that out when he starts to argue against Anaxagoras. Aristotle was the first man to talk about this, to discover, in a sense, that there are limits in the quantities of natural things, due to the natures of things. But in pure math, we're just considering quantity and the abstract and separation from natural bodies, nothing prevents you from dividing these things forever. But we'll come back to that when we see that in the second, third, and fourth arguments against Anaxagoras. But they involve what I call sometimes the second difference between quantity and natural philosophy and quantity and math. But Aristotle was open to discovering the second difference, because he saw the first difference. He realized that in mathematics you're considering quantity and separation from matter and motion, and separation from all natural bodies. And that left him open to discovering that there could be something in the quantity of natural things, due to the natures of these things, that could not be foreseen from the point of view of pure math. But we'll see that when you get to his critique of Anaxagoras. But it's still very interesting, and it reveals an understanding of the continuous, and maybe even of the connection between the continuous and number. Now, in the next fragment, DK-6 and DK-8, Anaxagoras is talking about how nothing is really entirely separated from anything else. And especially in DK-8, the things in the one world are not separated from each other, and they're cut off with an axe, neither warm from the cold nor the cold from the warm. Well, again, if you don't understand debility, this is even more radically true. See, we could say, you know, that a piece of clay, let's say, that is a sphere, is able to be a, what, cube, right? So in that sense, sphere and cube are not cut off. But if you make it actual, yeah, a sphere is never a cube. If you, if the lion ate me, right? If the lion had it on the board there. If the lion ate me, my matter would become, what? A lion. If the worms eat me, like Hamlet says there, huh? Philonius said, dinner? Where? Not where he's eating, but where he's being eaten, right? Or that, that, oh. Kind of horrible sense of humor of Hamlet there. After he's killed Philonius, huh? So there's something in me that's able to be, what, a lion, able to be a dog, able to be a worm, huh? Able to be dust, huh? See? But it's not actually all these things, is it? See? Actually, I'm cut off, but not completely, from lion and from worm, huh? Because there's something in me that, in a way, is my enemy, in that it's able to be something other than me. A lion, a worm, a dog, hmm? You see? But not seeing the idea of potency, he has everything inside of everything, actually. Absolutely. And therefore, very much so, one thing is not cut off from another. Aristotle will also raise some problems here about the multitude of things that he has there. If there's an infinity of them, they cannot be known in word or in deed. Now, starting at DK9 there in 15 and 16, Xavier was talking about at least the partial separation of these things due to a circular motion. And eventually he's going to say the circular motion was caused by the greater mind. Now, two things about that. One is that when you look around the world, it seems like the whole sky is revolving around us, right? It appears to be doing that, right? So you still see that there's still, what? The remnants of a circular motion, huh? And the heavy things like the earth seem to have settled down in the center of things, and then on top of them the water, and then the air, and then these fiery things up in the top there, right? Okay? Now, does man himself use circular motion to separate things? I always take this simple example. If I want to break your window, let's say, with my rock, I might tie my rock, stick around my rock, and then I'd, what, spin around and then let go, right? And get more force, huh? And my friend Jim Fransok there, the great boxer, he was a golden gloves boxer, you know, one night he puts the gloves on me, right? You know? Ties my hands, puts the gloves on me, he's going to give you a little lesson, right? I'll take it easy, Jim, because these guys, but no, it's, you know, the first thing Jim says, you know, you don't sit like this and walk like this, right? He's down like this, right? But that's what you're doing there. You're using the circular motion to, what, get force on that, okay? And, you know, when they use what they call a cyclotron, right? You know? They, what, accelerate the particles and then they shoot them at something and they split the thing open, right? Okay? So we tend to use the circular motion, don't we, to divide things and separate them, right? And there seems to be some evidence that in the natural world, huh? Things have been separated and that's why the heavy things like the earth are at the center and the light things go flying off, huh? And I can remember being, as a little boy there, an altar boy in the altar boy picnic, huh? And they go out to the amusement park on the altar boy picnic. So I'm with my brother Mark, huh? And I got my little baseball hat on, see? And one of these little machines, you know, whoop, whoop, they're in a circle. Well, off goes my little baseball hat and I could see it flying off and being ground up in the machines and so on. But I stayed on. See, I didn't go flying off, I'm ground up, see? So the heavy stayed at the center and the light things went flying off, huh? You see? Well, that's happened in the universe apparently, right? Because you've got the heavy earth there settled down the middle, right? And then you've got the water, which is maybe a little lighter, and then the air, and then the fire, which is very light, you know, around the periphery there of the sun when the stars, that's fire, right? What else could it be? And then you have air and so on. So the circular motion separates to some extent the heavy things from the light things. The biology has something like that, don't they? They use two and they separate the... Okay. Yeah, yeah, see? So it's a common thing to use the circular motion to separate things, huh? And so greater mind is like the lesser mind, huh? It's very clear. Yeah. But notice, this is still really change of place, isn't it, huh? See? And now on the top of page 8, you'll see Anax De Agra saying something similar to what Empedically said. You know how he was saying, you know, men shouldn't speak of coming to be and dying and so on, right? Okay. Well, he says something similar. The Greeks do not rightly take coming into being and perishing. Nothing comes to be or perishes, right? If something really came to be, you'd be getting something out of what? Nothing, huh? And if something really perished, you'd be cutting something up into nothing, huh? See? I might be able to cut you up until we couldn't find the pieces of you, but could I really cut you up into nothing? It might seem so, because I can't find the pieces, but, you know, you've got no... A far-reaching mind is, you fool, as Empedocles says, huh? But it's mixed and separated from existing things. Do you see that? Same thought, huh? But we think this thought runs through all of these guys, these early guys. But you find explicitly here in the fragments we have of Empedocles and Anxagoras. And thus they'll be right to call coming to be mixing and perishing separating. So I go down to the hospital and the wife has a new baby, right? Oh, a new mixture, huh? And when I go to the funeral house and, you know, oh, I see, a separating, huh? You know? Separation of elements, right? But nothing's really come into being or perish, right? Something in the back of our minds is something wrong with that, right? But they can't really quite understand how it's possible, right? Without getting something out of nothing, right? But notice, huh? If we didn't have enough chairs in this room, we might go into another room where you've got some other chairs and bring them in here, right? Okay? And we're not getting something out of nothing in that case, are we? Because there really are chairs in the other rooms, huh? But maybe we got chairs out of the trees originally. At least the wooden chairs, right? And were there already chairs out in the trees out there? Potentially. Yeah, potentially, yeah, yeah, yeah. And when you've got chairs out of the trees, are we getting something out of nothing? No, no. But it's not the same thing, you get chairs out of trees and you get chairs out of the next room, huh? Chairs out of the next room, they're actually in there. Chairs are not actually in the trees out there. But there's something in the tree that's able to be a chair, right? It's a very strange thing, isn't it? Tough to think about that. But if you can't quite understand ability, then it's like, how can you get blood out of a turnip, right? There's got to actually be blood in there, huh? How can you get chairs out of a tree if there aren't chairs in there? It's a little hard to understand ability. Now, the next marvelous fragment there. These things having been thus separated, it is necessary to know that all things are neither more nor less. And notice, the reason why there are never more is that something would have come into existence out of nothing if there ever were more. Nor can there ever be less, because then something would have gone, what? Out of existence, right? For it is not possible for more than all to be, huh? Okay? And if there are neither more nor less, then you could conclude that all things are forever, what? Equal. Now, sometimes I tell the students now, the whole modern mathematical science of nature is based on this one statement here, that all things are forever equal. Why do I say that? Well, the characteristic way of speaking of the natural world, expressing the natural world, is in something we call the equation, right? Okay? And the equation comes from the word, what? Equal. So that all things are forever equal, is underlying all knowledge expressed in what? Equations, huh? Now notice, even in simple algebra, it's based upon this idea, that nothing comes into existence, and nothing, what? Goes out of existence, huh? So, I'll take a simple example here from algebra. What's my algebra teacher going to do with that? Are you going to mark that correct or incorrect? Incorrect. Incorrect, right? Okay? Now, if I'm really stupid, he's going to say, Perkowitz. When you say 2x plus y, right, it means you have 2 of this x plus y's. Okay? So you've got an x plus y, you've got an x plus y. So you have 2 x's and 2 y's, don't you? See? Now over here, you've got what? 2 x's plus y. You've lost a y. A y has gone out of what? Existence. Existence. That is not allowed. Nothing goes out of existence in algebra. Okay? And you won't allow me to say, well, we're out of existence when you want to go to science. That's not allowed. Algebra is basically the idea that all things are forever what? Equal. Equal. Then you can mix them and separate them in various ways, huh? Now suppose you're giving Berkowitz the reverse. Suppose you're giving Berkowitz 2x plus y. And Berkowitz is put over here in 2 in parentheses x plus y. Now would he have correct or incorrect? Incorrect, yeah. And he would say, well, now, he'd point out that I have what? I've got two x plus y's, so I've got x plus y and x plus y. I've got two y's over here. And I started out with only what? Well, I got out of nowhere. It came out of nothing, right? You know, just, you're not allowed to do that, you see? Nothing, it can't be anything out of nothing in algebra, right? So all you can do is what? Mix these things and combine them in other combinations, separate them. Here I, what, put x plus y together, and then I separate them, the x's and the y's, right? If I wanted to, I could, you know, put x plus x plus 2y and do all kinds of things, right? But nothing can ever come into existence, really. Nothing really dies or comes into existence, right? All you do is mix and separate things that always were and always will be and forever equal. But you see, that's underlying the idea of the equation, isn't it? An equation, huh? Is saying that all things are, what, forever equal. It's kind of an interesting world in some way. But you could say it's all based on this one statement here, that all things are forever equal. And it certainly fits in with thinking that change of place is the only change in the world, huh? Because in change of place, you know, if you and I start changing our seats here and so on, it's not going to change the number of people in the room, it's going to remain the same, huh? It's going to be neither more nor less if we just change places, right? We've got to kill somebody or divert to somebody or something to get more people here, right? But if you just change places, you're not going to have anything more or anything less, huh? It's interesting, too, that he goes from neither more nor less to being equal. Aristotle speaks that way in the Tenth Book of Wisdom that equal is after more or less in meaning. Two lines are equal when one is neither longer nor shorter than the other. What's kind of interesting, we go back to the argument in the Phaedo, right? Because Socrates in the Phaedo, he argues in the new kind of recollection he has there, that the idea of equality was not gotten from the sensible world. And the argument is that, if you recall, that the things in the material world, like these two chairs here, they approach equality, but they're not exactly equal. And if you recognize that these material things approach equality, but not exactly equal, you must have a knowledge of equality not derived from them. And that when you see them approaching this, it reminds you that your knowledge already have of equality. But when you recall what equality really is, you judge these things to be somewhat unequal, right? To somewhat fall short of it. And it's kind of a beautiful comparison there, you know, if you showed somebody a painting, and it's a painting of you or me, and we're looking at the painting, so that's a painting of Socrates or a painting of Berkwist or somebody. But it's not exactly the way he looks, you know. You must have a knowledge of Berkwist not derived from the painting. Like when Lafayette came back to the United States, you know, after Washington had died, and he found all these statues and paintings of Washington. They were very good friends, Lafayette, and one of the closest friendships there were. And that's why when Lafayette went back to France and got into all trouble with the French Revolution, right, you know, Washington had agents there with money trying to extricate him, you know, from his situation. But when Lafayette came back to the United States after Washington had died, he came back finally after he got out of his troubles. He came back and he'd see these different statues and paintings, and he'd say, ah, you know, well, that's not exactly what he was, ah, that's the man, you know. But he'd have to have a knowledge of Washington not derived from the statues or the paintings to say that they, what, are like him, but they don't quite equal him, huh? So Socrates is arguing that the things in this world that we call equal aren't really, strictly speaking, equal. And the same thing you'd say about the flat surface and so on. But certainly the things we see in the material world are, what, larger or smaller than each other. And if you get your idea of equal from larger and smaller, then the argument would collapse, huh? But it's kind of an interesting thing to see, the way he proceeds here. Because in English, when you say equal and unequal, unequal, of course, seems to be the negation of equal. So you think of equal as being before unequal. But maybe we get the idea of equality by the negation of more and less, in which case then the argument would collapse in the fate of that particular argument. So you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the fact that you think of the Okay. So I could tell students how the whole modern science is based on this one statement. Well, it's kind of an exaggeration in a way, but I mean, in a way it's true, right? See, I mean, the idea that you can express the world in equations, right? Means that, what? Basically things are always, what? Equoid. You never gain or lose anything, huh? And you see that it's firstly in the fundamental laws and the conservation laws. So the example I was giving you last time was the conservation of energy, if you recall, right? The amount of energy in the universe is always, what? Equal. There's never more energy in the world. You may think you have more energy, maybe you do. But someone else has less energy, right? That's the old joke, you know, about how do the kids have as much energy to get it from us? That's the same as the parents. But the children are gaining, the parents are lost. So, but no, the conservation laws are saying that the amount of energy is always equal one day to the next, right? It may be a different form, right? It may be kinetic energy, it may be potential energy, it may be heat energy, it might be some other kind of weird kind of energy, but it always remains equal, huh? So, we have to understand in the way that we understand algebra here. It always remains equal. We just mix and segregate these things in different ways, huh? But that seems to fit, especially with this idea that the universe has only change of what? Yeah, yeah. But then again, they say, what's the problem there about knowing, right? Is knowing increasing, huh? Is there more knowledge in the world now because of my teaching? You see? Or are we just, you know, taking some knowledge out of me and put it into you and I've got it dumber, you know? Or is the amount of knowledge? I mean, people are really discovering things, you know, huh? Is the amount of knowledge really increasing? I go through Euclid there, you know, and I learn another theorem, right? I have some knowledge I didn't have before now, right? Are all things forever equal? What do you think? Materialist. Well, if you're a materialist, right, you might say as you are wist, all you're doing is rearranging atoms and molecules in your head, that's what you're doing, right? Shifting them around, right? Energy you gain here, some other thing loses, or vice versa, huh? But that is an interesting statement, all things are forever equal, isn't it? When you think about it in terms of modern science, especially. But to see the connection between that and change of place is the only kind of change in the world. Lends itself more to that, huh? Now in the next three fragments, you see the beginning of his starting to talk about the mind here, huh? As being responsible for the circular motion. And he's going to see the mind as being separate from this collection of all things, inside of everything, right? Okay? Maybe we should stop here, huh? And for next time, a discussion here of the great fragment on the mind here, which is DK-12, huh? This whole wrong fragment here. And this great fragment is really like a book adventure about the mind, huh? Now to some extent, what he says about the mind, he's getting from an understanding of the human mind, which he knows, huh? But some things will be said of the greater mind, huh? But our mind may be in a lesser way, huh? Okay? So you have to kind of, you know, understand what he says about the mind to understand your own mind. And see if you, when you read through this fragment, see if you can see...