Wisdom (Metaphysics 2005)
Lecture 14: Anaxagoras on Matter, Continuity, and Mind

Transcript
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A biologist says, well, that's my theory. That's my theory. You see? So they have a mindless matter, right? Bringing things together, right? And you expect, you know, most of these combinations, right, would be bad, right? But eventually it happens to bring them together in a good combination, and that survives, right? And reproduces, and the other one's all pairs, right? So you're saying, really, in Empedocles, is that basically nature produces heaps, for the most part, right? Chaos, disorder, right? And what you see now, where you see good in every animal, almost in every plant, right? Good in every parts, was the rare exception, right? But they survived. And yet it's perished, right? So this is the famous dichotomy, right? It's come down through history, right? Is there a greater mind responsible for the, what, border, right? That you find, which would be suggested by the fact that like effects of like, what, causes, right, huh? Or are you going to try to say that it happened by chance, and, you know, it's more reasonable. But wouldn't, wouldn't they still have to, I mean, let's suppose that that was the way it happened, that things just combined and dissolved at random, and then some survived. Yeah. But survival, I mean, there's some, got to be something, some ordered substrate that, that, you know, to, against which things either survive or don't survive. Yeah, there had to be an environment, you know. In other words, even if you hit upon a good combination, you know, the world is not friendly to you, right? But good in terms of, it has to be in terms of something, right? So isn't there still an order back of that? And also, if you finally do come across this, a good thing by chance, so if you have two bears, they have sex, why on earth do you think that their child is going to turn out good? Yeah. It'd just be, it'd be just as, uh, chancing for that, as, so you can't explain that. So, in other words, if you're acting, some of the chances for bad, you know, almost infinitely outweigh those for good. Mm-hmm. Things should be getting really more disordered, right? Right. Like the physicists say, you know, at the second author of thermodynamics, you just have random action, you're going from an ordered state to a disordered one, you know? Mm-hmm. But, uh, you can see nevertheless, Empedocles' theory is still popular, right? Yeah. Modern biologists, right? The materialists, so. Yeah, yeah, yeah. But it's part, yeah, because if you think it matters the beginning of all things, you're going to have to say that chance, right, is responsible for the order that we see, you know? Okay, now, in the last two fragments here of Empedocles, we see something of his thinking about knowing, right? And he's a materialist here, right? Still. My feelings. By earth we see earth, by water, water, godlike air by air, destroying fire by fire, love by love, and heat by heat. It's because we have these things in us, right, that we know them, right? And, um, there's some truth in what Empedocles is saying, right? That, um, the known must be in the knower before it is known. Okay? Um, but is it in the knower in this material way that he thinks? My favorite example is that of, um, David, right? But he puts the rock right into the forehead there of, uh, Goliath, huh? Did Goliath begin to know stones better then? Right? You know, if I remember you, gentlemen, but, you know, if you cut up with my head now, you know, would you find a little piece of bone or flesh chiseled out and each one of you have a little statue up there for each one of you? At least for me, I hope. What? At least for me, I hope. Not right. Not right now. Now, is your shape, or by recognizing that issue in a sense, is that in my, um, brain even, in a material way, see? No. Right? He's still thinking of it that way, right? See? Mm-hmm. And if that were true, then wouldn't this chair know what wood is, because it has wood in it, right? If it, uh, if being in there in a material way made you know it, right, then the wooden chair would know what wood is, right? And Manhattan would know what sweet vermouth is and what whiskey is, right? And water would know what water is, because it has water in it, right? So, Aristotle would take over the idea that, yeah, the thing known must be in the knower, right, before it can be known. But how is it in the knower, right? Is it in a material way or an immaterial way? And Aristotle will see that it's got to be in there in an immaterial way. And more immaterial in the mind than in the, what, sense of it, right? Even the sense is a kind of, you know, rising above this material way of being in something. Just like with the eye, the only reason we're able to see is because, in a way, there's no color in the eye. Yeah, yeah, yeah, yeah. If it were yellow, I wouldn't be able to see that color. Yeah, yeah. That's what Aristotle says, huh? You know, if the tongue were sugary, right, you would be able to taste all different things. Mm-hmm. And so the, um, Empedocles thinks they're actually composed of the things we know. Where Aristotle says, no, the senses and the reason are inability, you know, to be seen the likeness of these things. But it's not composed of these things. And he still thinks that thought is something, what, material. Now, if you had to choose between bone, flesh, and blood for thought, which would be thought? Yeah. Because thought is, what, you're thinking, you're moving, right, doing your reasoning, right, and blood flows, right? But also the idea, we think of thought as being something fine and what? Thin, right? And so we think of, um, uh, insight, penetration by the mind, right? You see? Fire in some way. Yeah. I mean, if I put a dry bone on here, it wouldn't go through, would it? No. Or a piece of dry flesh wouldn't go through, right? If you put some blood here, it'd go right through, right? So, blood penetrates things like thought penetrates things, right? So if you had to guess, is thought bone or flesh or blood, blood would be the best, what, guess, right? And the modern biologist kind of thinks of thought as being maybe, you know, electric waves in the brain or something, right? But something, you know, even finer and thinner, right, still material, than, uh, than, uh, blood, right, huh? So my high school teacher, you know, biology teacher, you know, I'd call us, what, to know the answer to the question. He'd say, boneheads, you'd call us. Boneheads. But that was not a compliment, right? No. It depends upon his position on thought. So pedicure still thinks, and men before him, apparently, that thought is something material, right? See, and most people, they talk to them on the street there, they think their brain is what thinks, right? Okay, and, uh, you need a course in the third book on soul, right? Okay. So now we've come to the great Anxagoras. Do you want to start him now or not? Do one or two of them, sir? What? Do you want to do one or two of them or something, or how much do you? I begin with the fragments of Anxagoras here on matter, and change, where he says that, you know, when you change a place, it's the only kind of change, right? And then we'll come to his position about the mind. It's interesting, right? If you read the Phaedo, which takes place in the last day of Socrates' life in prison there, when he's going to die, and he gives an account of his study of natural philosophy a bit, and how he became very enthusiastic about Anxagoras. The Aristotele plays a very nice compliment to Anxagoras. He says that Anxagoras introduced mind as a cause of the order in the natural world. He seemed like a sober man among drunk men. It's a very nice way of saying it, right? So there's a lot of admiration that Aristotle has for Anxagoras and that Socrates had for him and Plato and so on. And Anxagoras is the man who brought, what, philosophy to Athens, right? Yeah, he became the friend of, what, Pericles, huh? But then he was accused of, what, impiety, like Socrates was, because he said that the sun was a, what? Burning rock? Yeah, burning rock, rather than the sun was the god Apollo, right, huh? And we think the reason why he said the sun was a burning stone was because in his part of Greece, We know that one of the meteors that came down, usually a meteor is, you know, almost consumed, you know, it's come down in dust or anything. But there's a couple of times, you know, not a couple of times, a couple of times, where a meteor has hit the earth, there was a burning rock, right? Apparently there's one down in the southwest of the United States where this happened, and the Indians would talk to the white men about, you know, this burning rock that came out of the sky, and this is a story that was passed down, you know, from generation to generation among the Indians. And now they can go and kind of study the landscape and see the result of this. And they know that one of the things came down in Asia Minor, where Anne Xavier's came from, north. So maybe he thought that falling stars, or shooting stars as they call them, were what? Rocks, right? On fire, right? Aristotle himself, if it was really on fire, it would have burnt up the sun a long time ago, right? But anyway, for this opinion, he was charged with impiety, right? But they were probably, you know, politically, well, after Pericles, he'll get his friend, you know. Okay? Now the position of Anaxagoras on matter is discussed by some link by Aristotle, some link by Aristotle in the first book of Natural Hearing. And he gives us his reasoning a little more completely than the fragments give us his reasoning. So let's say a little bit about that reasoning, right? One premise that Anaxagoras had is that you can't get something from nothing. Okay? And this is touched upon this fragment here. How could hair come what is not hair? And flesh what is not flesh, right? Okay? You can't get something from nothing. Now to this common thought of the early Greeks, he had an observation as a result of an induction that in the natural world, everything eventually comes to be for everything in the material world. Let's try to just give a little flavor of that induction, right? I take kind of a simple example here. Let's start with grass, right? Okay. Now the cow comes along and eats some grass. So what do you get? A bigger cow, right? So from grass you can get some cow, right? Now Berkwist wants a steak, right? So you get a bigger man, right? You get a man. So you're getting down to more cow, but more man out of that grass, right? Now we find out that Berkwist is a Christian, so we give him to the, what? Lion, right? So now we're getting more lion out of that natural grass, right? Now the lion is punished for eating a Christian. And so now you're getting worms, right? From grass, right? And from the worms you get, let's say, more birds. The bird eats the worms, right? And from the bird you get more cat if you can, it's the worm, right? Maybe the cat dies and the cat's pushing up Daisy, right? Okay? So this seems to go on and on without stop, right? Okay? So you can start anywhere you want in the world, right? And eventually, out of anything in the world, you'll get everything else. But you can't get something out of nothing. Therefore, there must be a bit of everything inside of what? Everything. Yeah. So that's one of his first major conclusions, huh? Everything is inside of everything, huh? Well, there's a bit of everything inside of everything, right? But then things keep on coming to be forever, right? So there's got to be an infinity of pieces of everything inside of everything, right? But now how do you fit an infinity of pieces of everything inside of a plate of grass? They're darn small. Yeah. You make them infinitely small, right? Okay? So now the grand conclusion. There's an infinity of infinitely small pieces of everything inside of everything, right? Very complicated, right? Okay? And that's what you come to the next fragment there. All things were together, infinite or unlimited, in number, right? And in what? Smallness, right? Okay? Now, it was clear, huh? Now, what's striking is that this way of speaking of matter came back in the 20th century. When they began to study the elementary particles, huh? And if you read, you know, like I have an office at school there, Heisenberg's book, you know, on the unified field theory of the elementary particles. I'm not concerned with that particular theory. I'm tempted to try to understand them, you know? But the way they were speaking in their experiments of what they saw, right? Okay? What they saw was that out of any elementary particle, you could eventually get all the other elementary particles. And therefore, the common way of speaking was that every elementary particle is composed of all the rest. That's the same thinking as Anaxagoras, right? They thought if any elementary particle can get all the rest, and like everybody else, you can't get something or nothing, right? Then every elementary particle must be composed of all the rest. Right? And so the same way of speaking as Anaxagoras had, huh? They said, there's some difficulties in that thought, right? And Aristotle points them out in the ninth reading there of the first book of natural hearing. I don't know if you want to go back to that or not. That's in the natural philosophy course, right? But the same difficulties would be in the modern physics, right? If you said that what everything is instead of everything, there's only small pieces, huh? Let's just take one difficulty, huh? If flesh and blood and bones and everything else could be infinitely small, they could fall below any size, huh? Then the hole that they make up could fall below any size, right? Aristotle says that the parts of animals and plants can get smaller and smaller and smaller, and there's no limit to how small they can get, right? Then the whole thing that is made up of them, right, can get smaller and smaller and smaller, and there'd be no limit, right? But then Aristotle goes out to the natural world and says, but does a cat and a dog and a tree and a grass of just any size? No, different kinds of animals, different kinds of plants, as soon as a limit says to how big they get and how what? Smaller they get, right? Okay? So if the hole doesn't have just any size, then the parts don't have just any size, right? And therefore, Aristotle comes the idea that there's a smallest piece of flesh and blood and bones, right? And therefore, this position is wrong that they can be infinitely small, right? The same way in modern physics there, if every elementary particle was composed of all the rest, then inside each elementary particle would be all the rest, and inside each one of those inside of that original one would be all the rest, and inside each one of those would be all the rest, and so on infinitely, right? And therefore, the elementary particles would be getting smaller and smaller and smaller and smaller, and smaller. But in our experiments, all electrons have the same size, yeah. All protons have the same size. So, they can't really all be in there. They can only be in there in what? Ability. But you see here in the modern physicists, like in Anxagoras, the difficulty of understanding what it is to be in there in ability. And this runs across the board. with other kinds of ability, that there's a tendency in our mind to imagine what is in something, only an ability to be actually in there. And like Weizsacher, the pupil there, Heisenberg, said, when we imagine something, we make it actual in our imagination. So there's the great source of error there, Thomas talks about it in the epistles to Timothy. You know, false imagination, right? The great cause of error, imagining things other than they are, or imagining what cannot be imagined, right? You imagine the soul to be an error like substance, right? It's your imagination. It deceives you there, right? People imagine the Father, the Son, the Holy Spirit, you're going to be parts of God. God has no parts. He's not a part of anything. Do you know what? God's not a part of anything. Everything else is, almost has parts, and it's a part of something. But God has no parts. He's not a part of anything. He's kind of interesting, God, you know. God has no end or purpose. He's the end or purpose of all other things, right? But He has no end or purpose. Then He'd have a cause. That's one of the causes, huh? But God has no parts, not a part of anything. So, Anaxagoras can't quite understand ability, right? He says nothing is distinct. He's trying to get the idea of ability. Herstal says, we listen to what he's trying to say, but it doesn't say, exactly. You can see he's trying to get the idea of potency, right? Because in making these things infinitely small, it gives them about as little actuality as he could, right? But it's not quite the idea of ability yet, right? He can't quite say it, right? And I'm going to go through the history of philosophy and show people having difficulty understanding the ability of matter, right? But also understanding the ability of other things, huh? You know, if you read that famous dialogue, Domeno, right, huh? Socrates thinks what? He's trying to claim that the slave boy already actually knew how to double the square, see? Why? Because the way to double the square comes out of what the slave boy knows. Out of his answers, not out of Socrates' answers. And therefore, he imagines that what the slave boy is able to know, he already actually knew. But it was hidden, right? Yeah. The inability to understand ability, huh? You can see what Aristotle has in the ninth book of Wisdom, which he'll be looking at eventually. The whole book, The Boy, to ability and act, right? Or it's like, you know, what passage I had given to you before from John Locke there, you know, in the essay of Human Understanding, where he's trying to understand the definition of triangle in general, right? And is it equilateral, scalene, or isosceles? What's all or none of these, he says. That's the same idea, right? You can't understand the ability of the genus, right? See? When you define triangle in general, you see it's a plain figure contained by three straight lines. Now, if you try to imagine those three straight lines, you have to imagine them as equal or unequal and so on. So which are they, equal or unequal? Well, you say it's one of these, then you exclude the other ones, right? So it must be all of them, or none of them. You can't say, well, it's all of them in ability, none of them in act. You can't make the distinction between ability and act. And so then Barclay, in his principles, quotes this passage and he says, well, now, who can make any sense out of that, you know? It's all none of these, right? So he denies that we have any general ideas. Neither one can understand the ability of the genus, right? So the three straight lines in the definition of triangle in general are the equal or unequal. Well, it's both of them in ability, but none of them in what? Act. When you add the difference, you make actual what is there in ability. So the different kinds of ability, they're talking about in the Mino and in Locke there and here, but in all of them, there's a tendency to want to make actual something that is there only in what? Ability, right? It's like, you know, what does C.S. Lewis say that pantheism is the oldest thinking of the human mind about God? But in pantheism, you're saying that what? God is made up of all things, right? You're making, you know, actually distinct everything that's in the ability or the power of God, right? And that's the same kind of mistake, you know? But the imagination tends to deceive us there, you know? So, now I'm going to be away for a couple of weeks. I'm going away on Wednesday if the snow doesn't. In the name of the Father, and of the Son, and of the Holy Spirit, Amen. God, our enlightenment, guardian angel, strengthen the lights of our minds, order and illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor. And help us to understand all that you have written. Father, and of the Son, and of the Holy Spirit, Amen. So, I guess we are talking about the position of Anaxagoras about matter. On page 7 there. And this is very fragmentary there, but Aristotle, in the first book of Natural Hearing, the first book of the so-called physics, gives us the argument of Anaxagoras, which I'll repeat here again briefly. He saw that, by induction you might say, that everything in the natural world comes to be from everything else. Eventually. I was getting kind of a simplified form of that, right? Cow eats the grass, you get more cow from grass, right? And the breakfast eats the steak, so you get more man from cow, but originally from the grass, right? And the lion eats burqus, huh? You get more lion. And the worms eat the lion, and so on. So this goes on and on, huh? And then, added to that, what he's saying in particular here in DK10, how could hair come from what is not hair? How can you get something out of something that's not in there, right? Can you get any money out of my pocket? Well, if there's no money in my pocket, you know? Or can you get blood out of a turnip, as the old saying goes? Well, you can't, because... But why not? Because there's no blood in there, right? So how can you get more cow, and man, and lion, and worm, and bird, and cat, and daisies out of that original grass? They've got to be in there, right? So, it seems like everything is inside of everything, right? And then, like the other Greeks, and as experience seems to tell us, things keep on coming to be forever in this world, right? So there's got to be an infinity of pieces of everything inside the original grass and everything else, huh? And how do you fit an infinity of pieces of different things inside a blade of grass, which is limited or finite, huh? Well, by making them infinitely small, right? Something like the modern mathematicians, you know, will speak of a line, a finite line even, is composed of an infinity of points, right? So, ends up with the grand conclusion that there's an infinity of infinitely small pieces of everything inside of what? Everything, okay? And you see this a little bit in the beginning of this DK1 here, the second quote here, the second fragment on page 7. All things were together, unlimited or infinite, in number and in what? Smallness, right? There's an infinity of things that are infinitely small inside of everything. And nothing was clear because these things are so small, right? And Aristotle sees this as trying to express what ability or potency is, huh? Where nothing is distinguished from the other. Just like you might say all the shapes can be in the wood, are in there in ability, and you can't see them one that's distinct from the other. Now, I mentioned how in the most advanced part of physics in the 20th century there, as regards the study of matter, huh? You had a well-known saying among the students at elementary particles, which at that time were the smallest things they knew about, and therefore the closest thing to the first matter. But they saw in their experiments that out of any elementary particle, you could eventually get the rest. So the well-known saying was that every elementary particle is composed of all the rest. But notice, if you took that for what it's actually saying, then inside each elementary particle there'd be all the other ones, and inside each one of those inside that original one would be all the rest, right? And inside each one of those, all the rest, if every one is made up of all the rest, and they'd be getting smaller and smaller and smaller without, what? Limit, right? Okay. Now the rest of that DK1 there shows maybe he's influenced a bit by an axiom and as an axiomander, the man who has spoken about the infinite as being the beginning of things, huh? Now the next fragment there is just an elaboration upon what we've seen already, right? Calls these infinitely small pieces the seeds of all things, right? Okay. But now in the fragment next to the last one, DK3, you have a good introduction to the philosophy of the, what? Continuous, huh? Now the continuous is talked about by Aristotle, especially in the sixth book of natural hearing, the sixth book of the so-called physics, huh? But you also talked about it in the chapter on quantity in the categories, huh? Where he distinguishes between continuous quantity, like a line, a surface, a body, time, place, and discrete quantity, like number, huh? Okay? Now in the categories, he defines a continuous quantity as one whose parts meet at a common limit, or common boundary. Like the left and the right sides of the straight line meet at a point, and the left and the right sides of the circle meet at a line, and the parts of a body meet at a, what? Surface, huh? Why the discrete quantity, like number, the parts don't meet anywhere. So in the number seven, the three and the four, or the two and the five, don't meet anywhere. But in the sixth book of natural hearing, Aristotle will give another definition of the continuous in terms of its, what? Parts, huh? And he'll define the continuous as that which is divisible forever. And he's going to, and he shows actually in the sixth book of natural hearing, that you can cut a straight line in half, and you get smaller lines, and cut those in half, and always cutting them in half, this will go on forever. It'll never come to an end, huh? Now, Anaxagoras, in that way, is seeing something of this, huh? Nor is there a smallest of the small, he says. But there is always a smaller. For what is, cannot cease to be by being kata. Now, let's just stop a little bit on that, huh? If you cut a line up, could you cut a line up into nothing? No. Now, what would be the objection to saying you cut a line up, you cut a line up and you've got nothing left? Instead of two shorter lines, you have nothing left. Well, you cut a thing up into what it's made out of, right? And so, if you cut a line up into nothing, it would be what? Made of nothing, right? Now, the only other way you could maybe end up with an end to this cutting would be if you cut a line into two points, huh? Now, the point you can't divide, right? And if a line could be put together from points, right? Then you couldn't cut it forever. It would take two points next to each other, right? Okay. But now, is it possible that a straight line be put together from points? Well, how do you know that it can't be put together from points, huh? That's the way the modern mathematician sometimes in high school talks that way, right? As if a line is composed of an infinity of points. Composed is a Latin word for put together from, right? Mm-hmm. Well, Aristotle, in the sixth book, has a number of ways of showing this. One way to show it is by a disjunctive or either-or syllogism, right? And we say that there are, what, three, perhaps four ways that things could, what, touch. Because you're going to put a line together from points, they have to come together and touch, right? Well, one way they can touch is where part touches part, like these two circles, right? Part touches part. Or you could have part touching the whole, or the whole one touching part of the other, right? Or then you could have, it's so hard to draw, the whole touching the whole, right? So I just kind of go around twice and, you know, let me come at that, okay? Mm-hmm. Whole touches whole. That might seem to exhaust the possibilities, because what you have besides the whole and the part, right? But maybe you could make a distinction between the limit of a circle, right, and a part. It's not really a part in a strict sense, huh? So you could have a what? Yeah, at a point? Yeah. Limit, touching limit, right, huh? Okay. The limit's touching. Now, does a point have any parts? No. No, in fact, that's the way Euclid defines a point in there, which has no parts. So part of one point cannot touch part of the other point, right? And part of one cannot touch the whole of the other, because a point has no parts, huh? Okay? Okay. Now, can you make any distinction between a point at its edge or limit? So there's a little bit of a point inside that's not the same as the edge or limit? Well, then you're making the point into a what? A circle. Yeah, yeah. A small circle. So the only way two points can touch is for the whole of one to touch the whole of the other. Now, if two points touch, they're going to coincide then, right? Mm-hmm. In which case, two points would have no more length than one point, which is how much length? No. No, yeah. And if ten or a hundred or a million or an infinity of points are to touch, right? The only way they could touch would be to coincide. And if they coincide, they have no more length than one point, which is no length at all. So you can't make a line which is something which is length without breadth by putting points together, right? Okay? Incidentally, sometimes, you know, you have a student who will say, well, the points really exist, right? And I say, well, this is the way we show you that a point really does exist. Are there bodies that don't go on forever? Yeah. So this table doesn't go on forever, right? So there's an end to the table, right? An end to the body, right? Which is the surface of the body, right? Now, is the surface of the body, which is the end of the body, does that surface have any depth? Well, if you give it any depth, you haven't come to the end, have you? Okay? So it does come to an end, but you haven't come to the end so long as you've got any depth. Therefore, the surface must have no depth, although it is length and width, right? Okay? Now, if you take the surface of that door, right, huh? It has length and width, but no depth, right? Now, does the surface of the door go on forever? So there's an end upwards and this way and so on, huh? And does that end have any width? Now, if it had any width, you hadn't come to the end yet, had you? So now you have length without what? Width. But does that line, let's see on the right here, that has length without width, does that go on forever? So it has an end. How long is the end? But if the end of the line has any length, it's what? Not the end of the line yet, right? Yet, it has an end because it doesn't go on forever. So the end of the line has no length. And obviously, therefore, no width or depth, right? And we call that end of the line any what? Yes, Euclid tells us there, right? You know, I think the first definition in Euclid is that of the point, the second one that of the line, the third one points out that the end of the limit of the line is the same point, right? So, if points were to come together and touch, they would have to coincide, huh? This argument shows by elimination. And if they come together and touch or coincide, they have no more length than one point, which we already saw has what? No length, right? So it's impossible to put together a what? Yeah. So, therefore, when you cut a line in half, either you end up with what? Two shorter lines, always, which case would be divisible forever, or you end up with two points, but we saw that's impossible, right? Because then a line would have been put together in two points, right? Or you cut it up into what? Nothing. And that's there, right? Okay? Because then the line would be what? Put together from nothing, right? So, it must be that the line is divisible forever. And he, in a way, sees this, right? When we speak about the point, does the point exist? Is there, do we have to understand, exist in a certain way? Yeah, maybe the point exists in the way that an accident exists, rather than a substance, right? Yeah. And so, just like I was saying about the surface of the body, right, huh? It exists maybe more as an accident, as a substance, huh? So, you couldn't cut off that surface without taking some of the depth, in which case you'd be cutting a body off from a body, right? But you couldn't cut the surface and have it exist by itself, huh? So, he says, Nor is there a smallest of the small, but there is always a smaller, for what is cannot cease to be by being cut. But then he adds a new sentence, But there is also something greater than the great. Now, he seems to be saying that you never come to a greatest, either. But how does that, in a way, follow from there being no smallest of the small? Well, no, not so much that, but if you can cut a line in half, and you always get smaller lines, and they can be cut in half, and this goes on forever, what is getting greater the more you cut the line? The number of lines. Yeah, the number of lines, right? And so, sometimes we say, and this is really the basic meaning of number, that number arises from the division of the continuous, huh? Continuous, as we saw, is divisible forever, right? But therefore, numbers can increase forever, right? So, in a way, if someone says, How do you know you won't eventually come to a highest number, right? And my grandchildren are cutting up to 100, you know? You can count to 100, I say? Wow. I remember my own children being impressed that I began to count to 100. But how do you know you won't come to a greatest number, right? Well, if number arises from the division of the continuous, and the continuous, as we've seen, is divisible forever, then numbers can increase, right? And so maybe the great angst, I guess I saw something of this, right? But there's also something greater than the great. Okay? There's always a greater number. And it's equal to the small number. Well, that really shouldn't be said exactly that way, maybe. But he's saying they correspond, right? Okay? But the division of the continuous going on forever corresponds to the number of lines going up forever, right? But now, each thing to itself is both great and small. It shows he doesn't quite understand what relation is, right? Relation is what? As Aristotle calls it in the categories, Pro...