Natural Hearing (Aristotle's Physics)
7. Nature vs. Art, Rhetoric, Experimental Science, and Mathematics vs. Natural Science (Physics II, Readings 2–3)
https://berquistcourse.com/course/philosophy/3-natural-hearing/007-nature-vs-art-rhetoric-experimental-science-and-mathematics/

[0:02] I ties up with that old prayer to the Guardian Angel, huh? Oh yeah. You know, he's explaining some kind of confusion that people have, and then, but if someone rightly considers,

[0:17] okay, so you're all masters now of the first road in our knowledge, huh? That's something you can look at from time to time, you know, because kind of organizes outlines the whole thing. Now, why does the philosopher follow that natural road?

[0:41] I can give at least four reasons why he follows that natural road. Why he should? One reason, of course, is that he's a man. That is to say, he's an animal with reason. So it's natural for him to follow this road because he's a man.

[1:04] Second, you could say that all of our knowledge is over that road. Has to be, since the road is from the senses into reason. The knowledge that we have is either in the senses or in reason, so it's got to be over that road.

[1:20] But then, as philosopher, as lover of wisdom, he follows this road because as Heraclitus teaches us, wisdom is to speak the truth and to act in accord with nature, giving ear thereto.

[1:35] And finally, you could say that this is also the road to wisdom. You see, how Aristotle describes it—that the animals that have sensation seem wiser than the plants that don't have sensation. But the animal that has memory. And the mechanical arts are about the arts, the order that reason makes in exterior matter. Okay. But when you come to the to what is called rhetoric, Aristotle says that rhetoric, which is defined as the art of persuasion,

[2:15] he says that's an offshoot. It's an offshoot of dialectic, and therefore logic in some way, because there's an argumentative aspect to it. And it's also an offshoot of political philosophy. and of ethics, in a way, huh? Well, Because you persuade men not just by the arguments or parent arguments you give them, but you persuade them by your image of a man of foresight, a man of justice, a man of character, you know.

[2:51] And you have to know about these things from ethics and political philosophy. And you don't talk to people in different kinds of government. Different kinds of political constitutions in the same way. When I was young, I was interested in politics in high school and so on, and you know, listening to speeches and so on, making speeches. And I went back and I started reading Demosthenes' speeches. Huh?

[3:19] Because he's a big authority on Demosthenes, so on and I was reading Demosthenes' speeches, and he's making fun of these opponent, right? Because he came up the hard way. He scrub benches when he was a kid. I said, "Gee, would that be lousy rhetoric nowadays? " Huh? But if you came up, you know, if you scrub benches as a kid, you were a nobody. You were you you're you're ill born, huh?

[3:44] You know, you're kind of a slavish origin, huh? You see, but in America, we admire the self-made man, the man who started with nothing, much more than the man who's born with you know, you know, wealthy or something. Huh? See, the man who had to you know struggle to to open the world. But for Demosthenes, you had to struggle to open the world. That meant that you were ill born, that you were, you know, you'd come from the trash the wrong side of the road and so.

[4:18] Well, you see, you have to understand, you know, whether this is democracy or an aristocracy, right? And and the rhetoric that would work in one. if. Demosthenes was the greatest of the Greek orators, or one of them, anyway. You know, why would he be so flat today? Well, because you've got to know who he's speaking to, huh? And you know, sometimes they follow politicians around and record them.

[4:41] You know, if I'm talking to a bunch of businessmen, and then I go and I talk to a labor union guy, you know, you don't talk the same way to these people. And so you have to kind of adapt yourself, right? Because you don't talk the same way, and you know, this kind of under this kind of government, under that kind of government, and we didn't. A little bit of Edmund Burke recently, you know, the way he speaks in the 18th century, where England is still not so democratic, and some people want to make the House of Commons more democratic, and this is going to destroy the U.

[5:12] S. Constitution, you know. So, so anyway, rhetoric is kind of a mixed thing. It's an offshoot of dialectic, of logic, in a way, because it has arguments, but also it's an offshoot of ethics and political philosophy, because these talk about character and virtue, and they talk about the emotions and so on, and the virtues are concerned with different emotions. In the art of persuasion, I persuade people partly by my arguments, but more so by the image I project to myself as a man, you know, who knows what he's talking about, a man who has your good in mind, a man who, you know, is honest and so on.

[5:55] And by the way, I move your emotions and whatever your prejudices are. And by the way, I appeal to your your customs, so that this is a very powerful art with the Greeks. We can kind of see how powerful the art of persuasion was, even in those great men, Saint Augustine and Saint Jerome, who were both trained in the art of what rhetoric, and you know the famous vision of Christ where he's supposed to, Christ is supposed to have said to Saint Jerome, you know, are you a are you a Christian or a Ciceronian?

[6:35] Make up your mind, you know. And Saint Augustine says in the Confessions, when he first picked up the Bible, he found it unworthy to be compared to Cicero. Have this beautiful style, Cicero, and so on. But they're right; they appreciate the Bible. I mean, you know, you notice how important that art was. And Aristotle does a little history of the art. There it began in the Greek cities of Sicily.

[7:04] They threw out the tyrants, and they got a democratic form of government, and then advancement and power depended upon your ability to persuade a crowd. Well, the crowd doesn't follow you in a elaborate, you know, intricate argument. You need these, you know. Aristotle says sometimes an educated man succeeds better with a crowd than a professor, because a professor goes way back to fundamental principles that existed before.

[7:30] So our politicians, you know, they talk about you know economic matters. They don't give an economic lecture, do they? They have lost all their audiences that they were able to in the common schools too to make his predictions. So, but this is it's an offshoot of two different kinds of order: the order which reason makes in its own acts and its own thoughts, and which signifies those thoughts, logic, in a way, and it's an offshoot of the order which reason makes.

[7:57] In our will, in our emotions, and in our actions, in the city. So it's kind of a mixed thing. It's a paraphysis, but modern experimental science is a paraphysis of what natural philosophy or natural science and the mechanical arts. And the oldest part of modern science is in what we call today physics. And what's the fundamental part of physics? What it's called. Part of Galileo and Kepler.

[8:31] Mechanics. Mechanics, yes. Well, those that goes back to the word, the Greek word for nature, physis. And mechanics, we saw Thomas using that mechanical arts. That's the union of what natural science and technical science. It's reflected in the words. This one comes from nature, and this one here comes from the technical arts, the mechanical arts, the servile arts. They're called the two great ways: mechanical or servile arts.

[9:05] But these are the arts that transform matter in some way. So there is a union of natural science and technical science, which really begins strong in the 17th and 18th century. And so developments in mechanical arts help us to perform experiments that have been performed before, right? But then developments in theory, more a theoretical aspect, suggests new inventions. And so one helps the other, but it's a kind of intertwining.

[9:38] And you have to understand the theory to understand how the instruments are presumably working and what they mean, what they're telling us, and vice versa. So you have really an offshoot of natural and technical science. So you have kind of a offshoot of the study of natural things and of artificial things. By the Philosophy of nature is like a more like a purely natural knowledge, huh? Besides make comparisons to the art, but it's not really like a union like the way experimental science is.

[10:16] And you know, Kant was one of the first philosophers who really saw this. You know, if you look at the second preface to Critique of pure reason, there he sees that, huh? But but he's seeing that nature here knows, I mean not nature, but man knows here only what he in some way makes. And then Karl Marx, you know, he develops that idea in the theses on Feuerbach, huh?

[10:42] But he generalizes that. See if you if you take the experimental sciences as being the only reliable knowledge of the natural world, well then we have no knowledge of the natural as natural anymore. We only have the naturals in some way transformed by instruments, and therefore we know only what we ourselves have made in some way. And man is the beginning and the end of everything he makes, and we know only what we make in some way.

[11:14] Therefore, see when you take those four orders that Thomas distinguishes, right? The first order he talks about is the order not made by reason, huh? And the the other orders, the ones made by reason, but if the natural order becomes what kind of an artificial order, an order made by man, right? Then you've closed a circle. Man is enclosed in a world entirely of his own making, and that's what Karl Marx does, huh?

[11:44] Well, then he's the beginning and the end of all he makes, and therefore he seems, and he only knows what he makes. Therefore, he's the beginning and the end of all he knows. He's God. I am the Alpha and the Omega. He says, that's it, right? You know, because we get horrible consequences if if if you see or if you think the experimental science is the only knowledge there is of the natural world.

[12:09] This is science, it's unreliable stuff, and then you realize, you know, the nature of this knowledge, right? That that is in a way knowing what you make,

[12:22] and and another making there too, you know, the mathematics, you know, we make like I was quoting Great Niels Bohr, right? Reduce it to order. He didn't say find an order there, right? But reduce it to order. The mathematics is made by us, and then we bring that in to order these other things.

[12:44] In order to order these other things, we have to you know experiment on them, and that's also something artificial. Someone once said, you know, the trouble with modern man is he's trying to live entirely in a world of his own making. That's exactly our problem, right? Because a world of our own making is obviously inferior to us. So, world of our own making can never satisfy us.

[13:09] But if all we know is what we make, then we we are trying to live in a world entirely our own making. But that's necessarily inferior to us, you know. The meaning, you know, of God rested, you know, from everything he had made in the seventh day was he didn't find a satisfaction in the things he made; he found a satisfaction in himself. But even we can't find a satisfaction ultimately in the things we make, because obviously inferior to us, if we're beginning the end of them.

[13:43] So, this distinction between the natural and the artificial is important to see what natural philosophy is about, because it's about the natural and not the artificial. So, you have to distinguish the two, right? But it's also important for understanding what experimental science is like. Everything we do in this course, you know, is important for more than one reason.

[14:05] Now, in the fourth paragraph, he says, "Whatever things have such a cause have a nature." That's obvious, right? And all of these are substances.

[14:24] Now, nature is what is first, and substance is before everything else. And now, when he says nature is always a certain subject and in a subject, he's hinting at the two meanings of nature: the active one and the passive one. And the subject is the passive one, the matter, and the active sense is the form in the subject. But when we go back to the first book, we'll see the distinction between matter and form, right?

[14:55] But he's hinting at that right here. Now the Fifth paragraph is merely explaining how we use these words, huh? And notice how the expression "natural" or "according to nature" or "by nature" is more general than the expression "has a nature."

[15:23] Now, let me explain. that a little bit Make a little comparison too. Natural means basically by nature, or you could say according to nature.

[15:48] Now, has a nature. You could say that what has a nature is by nature, is according to nature. But is everything that is by nature, according to nature, does that have a nature?

[16:07] Well, think of Aristotle's example: there, tree, a tree, and the growth of a tree. Both of these could be said to be natural: the tree and its growth, right? They could both be said to be by nature, according to nature. You could also say that the tree has a nature, but does the growth of a tree have a nature? No, not as we define nature. But the growth of the tree is due to the nature of the tree, not to another nature inside the growth.

[16:46] So the expression "has a nature" and "by nature, according to nature" are not identical in meaning, are they? Aristotle, in the next paragraph, he says, "We said then what nature is, and what it is to have a nature, to have that kind of a cause, and what natural means, huh? So when he says that natural philosophy is about natural things, we mean it's only about things that have a nature.

[17:14] That's about the tree and not about the growth of the tree. No, it's about both, right? So he's distinguishing nature, has a nature, and by nature, according to nature. Okay. And did you see that distinction? And in some ways, you can say that natural philosophy is more, in a way, about growth or about change in general than about what has a nature, because nature loves to hide, and it's known only through what what it does and so on.

[17:48] So up front is more what change itself, and what we're going to be studying. Now notice this kind of distinction. We can make a distinction between art and what has an art. And what is by art or according to art? Okay. Take me for example, right? Am I the art of logic?

[18:19] No, I'm not the art of logic. I might have some of the art of logic, right? But not the art of logic. I'm very too

[18:31] Okay, You see there's a real difference there, right? Okay. Now, is everything that is by art does it have an art? No. If I construct a what syllogism, right, where the conclusion follows necessarily and so on, this is by the art of logic. Maybe I do this, but does the syllogism itself have the art? No, I have the art. It doesn't have it. Or take the medical art, right?

[19:01] The medical art is one thing, right? The doctor, see the medical art? No, but he might have something of the medical art, right? But a medical procedure, does that have a medical art?

[19:16] The doctor has the medical art. The procedure doesn't have it. But the medical procedure is according to, and is by the art. See that? So, so, you know, if he was talking about these things, he'd say we said what art is, and what it is to have an art, and what it is to be by art, but don't identify these. three yeah In The same way we don't identify nature and what has a nature, and what might be by nature but doesn't have a nature.

[19:48] Although what has a nature could also be said to be by nature, maybe. Okay, but not everything that is by nature has a nature. The growth of the trees by nature, but it doesn't have a nature. The tree has. That's a nature. but the growth of the tree is due to the nature of the tree.

[20:10] And the stop growing of the tree and gets to certain height for its kind of tree is again due to the nature of that tree, the kind of tree it is.

[20:24] So he says in the next or last paragraph. Then what nature is then has been said, and what by nature and according to nature, and also he said what it means to have a nature, right? Okay. What's the last paragraph in this reading about?

[20:46] Well, someone might say, Aristotle, you violated what you yourself taught in the Posterior Analytics. In the Posterior Analytics, he teaches that there are four central questions: Does it exist? And if it does exist, then the question, what is it? And two other questions: Whether this is that, and if this is that, why is this that? Okay. So the question, does something exist, is before the question, what is it?

[21:20] Like in the Summa Theologia, question two, does God exist, right? And after you show that God does exist, then you begin to ask, well, what is God, right? Okay. Well, he's been asking up to this point and determining, in a way, what nature is, but he never took up the question, does nature exist? Right? And tried to show that nature does exist. Now, the reason why he didn't do that is that it's what obvious or known to itself that nature exists, huh?

[21:53] So the fact that we see in my example there, the tree and the stone with the same sun, rain, soil, one grows and the other doesn't, right? Or in the garden, right? You know, I clear the garden and I got the same dirt more or less over the garden, and then I add kind of a common fertilizer and mix it in there, right? And then I plant the row of broccoli and a row of lettuce, right?

[22:18] And I keep it watered and so on. Up comes broccoli, up comes lettuce. It's due to something within those seeds that broccoli comes up here and lettuce comes up there, isn't it? Because they have the same sun, the same water every day, the same soil, the same fertilizer, right? I told you one time, you know, I looked down at broccoli and one of the things came up instead of green and came white.

[22:46] I said, Rosie, is that my wife, is that a mutant? Or what Have I discovered something? but I suspected right away it was going to be cauliflower, and sure enough, I went out and looked, at it. it was cauliflower, huh? But I think that cauliflower seed got accidentally into the broccoli seed. I don't think the broccoli seed became cauliflower seed. But no, it's obvious in our experience, right?

[23:10] With the same exterior things, like the stone and you get the iron grate there. The stone and the wood. The one burns and it doesn't burn with the same fire I'm looking at them both. So it's obvious that there are causes of change within things, right? So if you tried to prove that, you'd be thinking you didn't know what you did know, And that's laughable, he says, right?

[23:33] If you tried to prove the obvious, what is there to prove it by, except what is not obvious? And isn't that laughable to try to prove the obvious by what is not obvious? To try to prove what is known to itself, but what is not known to itself? So he says it would be laughable to try to prove that nature exists, for it is obvious that there are many such things among the things that are.

[23:58] To prove the obvious to what is not obvious belongs to one who can't separate what is known to itself from what is not known to itself.

[24:06] Now that it's possible to undergo this is not unclear. A man might, a man blind from birth, might syllogize about colors so as to have reason about names, while understanding nothing. I know it's the example he gives there, right? The man blind from birth doesn't really know what colors is, but he talks about what he doesn't know as if he didn't know it. Where the man who tries to prove that nature exists, he's talking about what he does know as if he didn't know it.

[24:35] Now, why does Aristotle manifest it by the opposite example? That's the way he's reasoning, huh? Suppose, huh? It's like this. Suppose someone makes a mistake of thinking that a man. Is a what woman? Suppose you see, let's say Michael Jackson, right? Okay, and you think he's a woman, right? You need to make that mistake, right? Okay. Now, if someone does in fact make that mistake, could someone else possibly make the reverse mistake of thinking that some woman is a man?

[25:21] Okay. You can see how you could go from one to the other because if you make the mistake of thinking a man is a woman, it's because in some case at least you can't tell them apart, right? If you can't tell them apart, you can make the mistake going in the reverse direction, okay? Now Aristotle was saying that the man who tries to show that nature exists, he's taking something he knows, something that's obvious to him, and he's thinking that it's what not known.

[25:49] That's why he's going to try to prove it. Okay. And he said that someone can make the mistake of thinking that something he knows he doesn't know is shown by the fact that men sometimes think they know what they don't know. But isn't it more known to us? It's more common this kind of mistake than that. And Socrates, who came before, is famous for finding out that men are in this position all the time.

[26:21] They think they know what they don't know, right? Well, if men can make that mistake, you can make the reverse mistake. You make this mistake because sometimes it's hard to separate the two, and therefore you can make the mistake going either way, right? If somebody could think that Budweiser is Miller, then someone could make the mistake of thinking Miller is what Budweiser, right? But this is more known.

[26:48] This is more frequent. And you could say most men are making this mistake, but many thinkers make the opposite mistake. They're trying to avoid this. They're trying to avoid claiming to know what they don't know, and they go to the opposite extreme and say they don't know what they do know. And this is this is the characteristic of modern philosophers. My old teacher Kasurik you know, was teaching the modern philosophy course, and a student comes in the class one day and says, "How do you argue with someone who says that material things don't exist?"

[27:23] Kasurik replied, "Was kick him in the ass." It wasn't just a jocular reply. It was very precise. Because if your senses don't convince you that material things exist, right, it's stupid to try to argue. Because the senses are closer to these things than your reason is, huh? And if the senses touch you, the most, certain of all senses are going to convince you.

[27:49] So the modern philosophers, very often and thinkers, they end up thinking they don't know what they do know, and so they deny the obvious as if they didn't know what they do know, and they already try to prove, right? Immanuel Kant says it's a scandal that philosophers have not been able to prove the existence of the external world. But the scandal is that they should have tried to prove the existence of the external world.

[28:17] The scandal is that they all thought they didn't know what they did know. Bishop Berkeley, the Anglican bishop, he thinks that what matter doesn't exist, right? So I used to say, even Bishop Berkeley opens the door to his study before he tries to leave.

[28:40] So, so notice, huh? In order to to really make to go forward, you have to distinguish what you know from what you don't know, right? And either kind of mistake is going to be fatal to the life of the mind.

[28:58] Whether you think you know what you don't know, or you don't know what you do know. If you think you you know what you don't know, you won't bother to investigate it, right? But what you do know, if you think you don't know what you do know, you have nothing to to use to know anything. So, and see Aristotle's common sense here. But it's very important that he sees this, huh?

[29:22] Okay. I guess we have we have to stop now. We have five after five. Now, next time we're going to look at reading three here, right? Okay. And here Aristotle is going to be distinguishing between the natural and the mathematical. The reading we just had the natural and the artificial, nature and art. But in this third reading, he's going to show there is a difficulty about this, right?

[29:51] And he's going to propose a solution, and then he's going to prove the solution is correct. He's also going to touch upon the central question of philosophy. Which is really a question for the wisest men, but he touched upon it here, so we'll touch upon it. Okay. Now, after that, we're going to, before we look at Aristotle again, we're going to look at the first

[30:17] natural philosophers. Okay. And so, give you ten copies of this again. Ten, right? Okay. So we're going to do that third reading, and then before going back to Aristotle, we're going to look at the first philosophers, the, the, we call this here the natural fragments, the first philosophers. I might mention as a point of fact there that for the philosophers before Plato and Aristotle, we have no complete work by them.

[30:56] All we have is what fragments, huh? And they're usually preserved in the form of quotes from later authors and so on. And the German scholars, with their, you know, their, their scholarlyness, they would go and gather all these, right? And one of the most famous one, of course, is the Diels Kranz, Diels originally Kranz, huh? So I have a copy of the Diels Kranz in my office.

[31:23] There, it's in Greek. You know, get all the Greek fragments, huh? And they give them a number, but the number has no significance; it's a way of referring to particular fragment, huh?

[31:34] Now there are. I made a number of collections of these fragments, but these are what I would call the natural fragments, the fragments in natural philosophy, huh? Okay. And we're going to look at these, and then go back to Aristotle and see how he proceeds from them, huh? Okay. And in reading these men, we don't read them as being the truth. We read them as as nevertheless making reasonable guesses, huh?

[32:02] And here we're going to be introduced to the what the second road in our knowledge, huh? Which is the road of reason as reason. And that's the road from reasonable guesses towards reasoned out knowledge, huh? We're going to go through the reasonable guesses of these philosophers before Aristotle, and then we're going to see how that gradually leads to the beginning of reasoned out knowledge in, uh, in Aristotle, huh?

[32:30] Okay. let's see how that how that's done, huh? Okay. But these are very important. These these natural fragments, but you have you know other collections of these fragments that I've made, you know, like the ethical fragments or or fragments on on method and so on, and and I have the natural theology fragments, too, which are very interesting. But these are perhaps the most basic ones, the natural fragments.

[32:55] And so we're going to talk about that, but we'll talk about that again after we do the third reading in Aristotle, okay? But in the second reading of the first book of Natural Hearing. Aristotle begins with a logical division of everything that they say, and then we'll see the dilemma that leads you in, and then how Aristotle goes forward. But we'll do reading three first. Okay.

[33:23] Here you go back to the very beginning of philosophy, and it's also regarded as the beginning of natural science. Einstein says we reverence ancient Greece as the cradle of Western science. Heisenberg goes back very often to them, and other scientists have talked about this. Science is the Greek way of looking at things. No one has ever had science as a conquistador. So they have great respect for the Greeks.

[33:54] Okay, now this is my extra copy. Are you an ear or a nose? Getting up. What? So the higher things are, you actually understanding them when Thomas or Aristotle explains them.

[34:24] Give back the exam. I see at the end of the honeymoon period, the rest is going to give back the exam. You know. What is the which sense of "in" is in the definition of nature? There's more than one sense. Well, it's in a subjectuminate sense. Yeah, the third part of the encircling in that in which it is.

[34:58] I suppose it'd be. Well, generally, it resembles. It seems like a part in the whole, right? But then, when you talk about form and matter, right? Then you have the other sense there too of form and matter.

[35:43] But you know the proportion Aristotle has that matter is to form as parts are to the whole. Parts are like matter. Then form becomes more like the whole, form and matter.

[36:04] The whole soul is in each part of the body. in a sense, right? That's very hard for us to understand, you know, because we want to try to we want to try to picture the soul or imagine the soul.

[36:23] Yeah, I think I talked to you about the four senses of part and the four senses of whole in the metaphysics. And what's interesting is that

[36:36] the sense in which what they call essential parts, matter and form, are parts of the thing. That's in some ways it seems the one that escapes people the most. And if you look at Aristotle here in the first reading, there he talks about the sensible composed whole and the you know understandable composed whole. And there's really touching between two senses of whole and part there.

[37:04] Okay, the way in which maybe olive oil is a part of the salad dressing, and the sense in which genus and difference are parts of the definition. Right? Those are two different senses, right? Okay, and then he talks about the universal whole. When he talks of the general and the particular, he says the general is the particular, something like the whole is to the parts. So if the whole is more known than the parts, than the general, right?

[37:29] We're talking about that a bit, right? We're talking about the general sensible, which is like that, right? But the kind of whole and part that doesn't appear there and all that is matter and form. But when he goes from a confused knowledge to what changes to more distinct knowledge, he's going to be coming to matter and form. So the one he's after most of all doesn't appear there in the beginning, right?

[37:53] It's just not so clear. And the other place where I noticed this in my thing there when I'm teaching the third book of wisdom. And this is the dialectical book, the third book of wisdom, metaphysics. And when he gets to the point there, he's talking about

[38:17] getting the beginning of things. Thomas points out that he has three opinions there, and they correspond to three kinds of division. And again, those three that we've mentioned already.

[38:34] In other words, you have to divide, or to get to, you know, take things apart to get to their beginning, right? Okay. well, and if you divide in the way in pedigrees divides, you end up with earth, air, fire, and water, let's say. But if you divide the way we do when you define, you end up with the most universal. You know, you define square and then you define quadrilateral and you define you know you get somewhere universal all the time.

[38:59] But if you divide the way we divide genus into its species, you end up with the least universal. So the question is: Are the beginnings of things like earth, air, fire, and water, are they like body, Or like the least universal? huh? Well, the one he's really going to conclude to the twelfth book of wisdom is matter and form or act and ability. It doesn't even appear in the Dality, right?

[39:27] See? Now I I ask myself, why is that so? Well, now it's clear that if I got one thing here and one thing here, they're not the same thing, right? If I can put one thing here and one thing there, it's easier to separate them, right? So I mean, it's easier to see how, let's say, a man and a dog are two different things. I can put the dog in there and the man in there, but is the man in his shape two different things?

[39:56] Not clear, right? I can't put the man in there and his shape in there, right? But even if I divide the genus into species, well, that's kind of in the mind; it's kind of hidden to us, right? When I divide animal into man and dog and cat and horse and elephant, I could put the man in one room, the dog in the room, the horse in the room.

[40:15] You know, it's more clear they're distinct, right? Parts of animal. And the definition, of course, of that's really maybe up in the mind, but the definition that we know more is is the the one in speech, huh? And we can separate, you know, and put, you know, quadrilateral here and equilateral here and right angle here, right? We can separate the words, right? Okay. But now, just take a very simple example of something like matter and form.

[40:48] Take the word cat, right? Can you put the letters here and the order them over here? Well, it's kind of hard to say they're two different things, right? You know, and if it's the order, you get to something that is much further removed from the senses than the order of the letters, huh? Or in a rubber ball. can. I put the rubber here and the shape over here.

[41:13] You know, right? The other three parts of whole parts, to some extent, I can put one here and one there, right? The mind, the mind. It doesn't really understand that very well, right? Or has a hard time getting a hold of that, huh?

[41:33] And to say that the parts of the word cat are the letters and their order sounds kind of strange, doesn't it? The two parts, I mean, two parts. I mean, C and T are the parts of it. They can't see that that the letters, in another sense, of the word though, it is another sense, of, the word that the letters and the order of them are the two parts of the word.

[41:54] Sounds kind of strange to them to even say that, huh? But in some ways, it's made up of those two, isn't it? In some sense, or but in a different sense, but kind of a strange sense,

[42:07] They say the tragedy and comedy are the parts of drama. Well, I think we'll see a tragedy one week and comedy next week or something, right? Or I can go read Hamlet and then go read The Comedy of Errors, right? You know? Here's a comedy of errors, I've got a copy of Comedy of Errors. They're kind of here's the one, here's the other, you know. But I can't do that with with matter and form.

[42:30] They use the form. If we're talking about substantial form, you know, substantial form, the soul, see? And in a sense, whoever thinks, you know, the soul is being distinct from the body, they think of it as being kind of a different substance from the body. Primitive people think of with the the soul is kind of an air-like substance with the same shape as a man. You got this, you got this solid gross body, right?

[43:07] You got this kind of air-like body, but even Plato, I think that you know, it's like the sailor in the boat, right? You know, this is the the soul. You know, it's kind of the immaterial substance, and you have the material substance. You know, material substance, immaterial substance. sounds kind of separate. right? You can't really, can't really, uh, It's very hard for us to get that, huh?

[43:29] And yet, that's the key thing: finding and understanding change, and the thing that changes that has these these two parts, right? Yeah, and understanding the soul, you know, union of soul and body in man, huh?

[43:44] I mean, you know, when you say that a man is composed of body and soul, we're told that as children, maybe, huh? You know, by the priest or the catechism or something. So put together from body and soul, but very hard to even see what that means, let alone to you know accept it, huh?

[44:09] Marking my car there. The light was coming on. I want to see if the brake light is off. will you? Mm-hmm. Let me just get somebody else to stand behind there. That's because it's closer to what we sense. Eye is wiser than the man and very experienced, so you can see that the road is going in the direction of wisdom. That's a fourth reason why the philosopher follows it.

[44:37] He's a lover of wisdom. This is the road to wisdom. Okay, so let's come back to natural philosophy here in the third reading in the second book of natural hearing.

[44:53] Now the division of this reading is kind of a classical one, but Aristotle does. In the first three paragraphs, is to raise a problem or a question. But there seems to be some kind of overlapping of natural philosophy or natural science and mathematics, and therefore there is some problem of are they really distinct, or is one in some way a part of the other? So he raises the problem in the first three paragraphs, and then in the middle paragraphs, actually in the first of the three middle paragraphs, he solves the problem.

[45:35] Okay, but in the second, actually the fifth and sixth paragraphs, if you number them, he touches upon the central question of philosophy, and it's really a question for wisdom. But because he touches upon, it, we'll touch upon it. Okay, and then in the last two paragraphs, he proves that his solution proposed in the fourth paragraph is in fact correct, and he gives a reason and then a sign to show that it is so.

[46:10] So you see the way it's divided basically, huh? The problem or the question, the solution, the proof of the solution. Very classical. He says, since it has been determined in how many ways nature is said. Now we didn't go into that, huh? But after he defines nature, he shows that nature is said of both matter and form.

[46:36] Next after this, it should be considered by what the mathematician differs from the natural scientist. Now, if there's a reason for taking up this, is shown in the next two paragraphs. For natural bodies, he says, have surfaces and solids and lengths and points and so on, about which the mathematician considers. So here, mathematics seems to be talking about something found in the natural world. The mathematician talks about number, for example.

[47:07] There's a number of things here in the natural world. I have five fingers. He talks about what shape. Natural bodies have shapes, huh? He talks about surfaces. Natural bodies have got surfaces. He talks about length and width and depth and natural bodies have length and width and depth. So it might seem that the mathematician is talking about something found in the natural world, and therefore mathematics is like a part of natural science, talking about at least some of the things found in the natural world.

[47:43] Okay, then he turns around in the next argument and says, on the other hand, natural science or at least some parts of natural science seem to come under the mathematical sciences, and the great thinker there, Pythagoras, huh? Pythagoras divided the mathematical sciences that we should really study for their own sake into four, and they were arithmetic, geometry, astronomy, and music. This is where we got the quadrivium later on in the Middle Ages.

[48:23] Those four. Now astronomy and music, but especially astronomy, would seem to be talking about natural things. So here you have a mathematical science of the natural world,

[48:42] and we're of course acquainted with this even more so in modern times because we have much more mathematical science in nature. But take, for example, Sir Isaac Newton's major work, which is usually called the Principia. It was such a famous work that the physicists of the 20th century call the physics of the 17th, 18th, and 19th century classical physics or Newtonian physics. Not that he did it all, but he was kind of the model for everybody else, and what he did united Galileo and Kepler.

[49:19] But what is his major work called? Well, the actual title, the Latin title, is Principia Mathematica Naturalis Philosophiae, the mathematical principles of natural philosophy. So you've got mathematical principles, you've got a mathematical science, don't you? And yet you're studying natural things. So now at least some part of natural science seems to come under the mathematical sciences. So Aristotle asks this kind of concretely with the question of astronomy.

[49:54] Further, he says, is astronomy other than or a part of natural science? It would be strange if it belonged. to The natural scientists to know what the sun or the moon is, but nothing of what happens to these as such. Especially seeing that those speaking about nature also speak about the shape of the moon and the sun, and besides that also whether the earth itself or the universe are spherical or not.

[50:21] Incidentally, Aristotle thought the earth was a sphere. He didn't think the earth was a flat disk, and he had more than one reason for thinking the earth was a sphere.

[50:31] So, isn't this a part of natural science, astronomy, and isn't it talking about these things, the shape of these objects, and so on? I guess one argument Aristotle used is that the earth casts a circular shadow upon the moon now when it comes between the two, and that's one way. Other reasons for thinking this too. So, there's no problem now. Do these sciences it seem at least to overlap, or are they really distinct?

[51:02] Now, in the fourth paragraph, he's going to propose a solution now to this question that they really are distinct, and the solution he gives is one that is somewhat puzzling to the Platonists, and it does touch upon the central question, but we'll save that to the last. So, look at the fourth paragraph. He says the mathematician then, and he's thinking what we call the pure mathematician. The mathematician then also treats of these things, but not in so far as each is the limit of a natural body.

[51:46] And then likewise, nor does he consider the things that happen in so far as they happen to such existing things. Let's state that a little more fully. What he's saying is that the mathematician considers number and shape and surface and length and width and depth in separation from natural bodies, and even more generally, you could say in separation from all sensible matter. While the natural philosopher is concerned with number and surface and shape and length and width and depth only in so far as they are the number of a natural body or bodies, the surface of a natural body, the shape of a natural body.

[52:38] Okay, but mathematician considering these in separation. Likewise, he says he doesn't consider what might happen to these things in natural bodies or in sensible matter. The mathematician. So, for example, you may be aware of the fact that many scientists say that the earth is more or less a sphere, but it's sort of flattened at the poles. I don't. The reason for that is exactly when something happens to the sphere in matter, and sometimes I take an example from artificial things.

[53:17] If you look at a tire from the side, you say, "What is the shape of a tire from the side?" What's circular, huh? But you go out to the parking lot and you see that the the tire there is what kind of flattened there at the bottom where it touches the pavement, and that's why you can't leave a car for the winter there on its tires. You gotta kind of prop it up, otherwise the tires will be what ruined, huh?

[53:42] You see. But does the geometer consider the fact that his circles might be flattened by the force of gravity there or something? See, or that the sphere might be flattened at the poles, huh?

[53:56] Um, no, huh? See, he doesn't consider what happens to these things in so far as they are in matter, in so far as they are in natural bodies, and so on. Yeah. Do you see the solution Aristotle is posing to this question? Right. The mathematician is talking about all these things, but in separation from natural bodies, and indeed from the whole sensible world. But the

[54:28] mathematician, but the natural philosopher is considering them only in so far as they are the numbers and the surfaces and shapes of natural bodies. Do you see that?

[54:40] Now we're going to skip temporarily the fifth and sixth paragraphs, which touch upon the central question of philosophy. But we'll come back to those shortly.

[55:00] Ah, now. In the last two paragraphs, Aristotle is going to give a reason and a sign for the truth of his solution. Now, the reason is drawn from the definitions, the kind of definitions that underlie geometry or some mathematical science, and the kind of definitions that underlie natural philosophy or natural science. Now, why does he draw his reason from that? Well, natural philosophy and geometry are two forms of reasoned-out knowledge, and reasoned-out knowledge is fundamentally based on definitions.

[55:51] And you can see that from your study of Euclid that the definitions are what are most fundamental in the science. So Aristotle looks towards the definitions, and he says the definitions in geometry. If you examine those definitions, like the definition of sphere or cube, you'd find no reference to matter and no reference to motion or change. Now, sometimes when he talks about this difference, he says there's no matter in the definition.

[56:22] Other times he'll say there's no motion in the definition, but he's understanding both because matter and motion or change go together. So when you talk about the geometrical cube, is it an ice cube made out of ice, or is it one of those wooden cubes you had as a little child in your your blocks? Or I have a plastic kind of a paperweight cube in my desk.

[56:51] Is there any kind of matter in that definition of the geometrical cube? And likewise, geometrical sphere. Is there any, you know, is it a steel like a marble? I mean, glass, or is it a steel one, or is it rubber? Or there's no matter in the ordinary sense, no sensible matter in the very definition of the geometrical sphere or cube. And then, consequently, there's no reference at all.

[57:27] He says to to motion. And you know, if you have a material sphere, if I had say a lead balloon here and let go of it, it would go down. If I had a helium balloon and I'd go of it, it'd go up, huh? Because the helium is lighter, I guess, than the air or something, and the lead is heavier. But now, would a geometrical sphere go up or go down if you let go of it?

[57:53] No answer to that because it's neither heavy nor light. There's nothing of that sort. You probably know there's a melting point for an ice cube, and different things have different melting points and maybe freezing points and so on. What's the melting point of a geometrical cube, or the freezing point of a geometrical cube? I wasn't having any, no reference to that at all. If I had a rubber ball and I threw it against the wall, there it probably bounced back.

[58:27] If I had a glass ball and I threw it against the wall, it might break or shatter. If I had a steel ball, maybe it would go through the wall or stick in the wall anyway. If I had a geometrical sphere? Would it bounce back or would it shatter or would it? There's obviously none of these applicable to it, so there's nothing that pertains to to change there because there's no matter there.

[58:54] Why we saw the very definition of nature is change. Nature is defined as the beginning and cause of motion or change and rest in that which it is, first as such and not by happening. Of course, the Greeks at first identified nature with with matter, and then later on with form and the genus of substance. So,

[59:23] and this is if you go even further in natural science, you're going to be bringing in the matter. So, if you wanted to define what bone is or what flesh is and so on, you'd have to talk about a different kind of matter that the bone is made out of. The bone is harder than the flesh. Don't try to be too profound about what it's made out of.

[59:45] So, the definitions in math in natural philosophy involve matter and motion, which is what's essential to natural things. The definitions in geometry have no matter, no reference to motion. So, since the definitions are the foundation. We just had the definition of nature the other day, and you can see from Euclid, there the definitions, are the fundamental things. If the geometry defines without matter and motion, then he's considering these things in separation from our natural bodies, a sensible world, Why the natural philosopher is considering them in matter and with motion.

[1:00:26] See that's his reason. Did he say all that? Aristotle's always taking an example, you know, the snub nose and the curve, because apparently Socrates had a snub nose, so of course the nose stands out right in the center of your face there, and the definitions in natural philosophy like that of snub nose involve a certain kind of of matter, but the geometry would just have the curve without the flesh and the cartilage or whatever the sensible matter is.

[1:01:01] So that's kind of a standard example in Aristotle. So Socrates' snub nose lives on in Aristotle's examples. Then in math, when you wanted to say, I'll get a sphere by rotating a circle, but that's imagination, you know. using the word motion equivocally? Okay, it's not a motion of matter, huh? It's just the act of imagination to help imagining things correctly. Now, in the last paragraph, he's going to give a sign, and the sign is taken from the mathematical sciences of nature.

[1:02:02] Now, sometimes in the Middle Ages, they would call the mathematical sciences of nature middle sciences because they're kind of in between math and natural science. But what he takes, the way he takes a sign, is this: that in a mathematical science of nature, you take something from math and then you apply it to the natural world. And the fact that you have to apply it is a sign that in mathematics it's what separated from the natural world; otherwise, you wouldn't have to apply it.

[1:02:40] Um, I used to take I take sometimes a very simple example in class here to just give the force of that sign. When I was a little boy, it used to be common in the post office you could buy. Envelopes to mail a letter in, and you can buy stamps, and then you lick the stamp and put it on there. We could also buy a letter envelope that already had the stamp built into it.

[1:03:14] Did you ever see those? Some people see them, some people haven't, but they're very common. And I remember my mother would send me up to the post office and so on. She kind of liked those envelopes already had the stamp in them, because the glue never seemed to be very good in the old stamps, and the stamp would fall off. And you're getting out your own glue, you know, and trying to fasten it nice and strong to it.

[1:03:38] What's the point I'm trying to make? Well, if you buy a letter envelope with the stamp in the envelope, it's part of the texture of the envelope itself, not space it on there. You don't have to apply the stamp do you. But if you buy this other, then you have to lick and apply the stamp to the envelope. So obviously, if you have to apply this other kind of stamp before you apply it, it's not in the envelope.

[1:04:06] It's in separation. So if in the mathematical sciences of nature you have to take something from math and apply it to the natural world, then in mathematics it must be what separated. If I have to apply my hand now to the desk before I apply it, it must be separated. You see the force of that? Of course, if you know the history of the mathematical sciences of nature, that sign becomes even more clear, because often the math is worked out by someone other than the man who makes the application, and sometimes the man has no idea that there's a possible application of it.

[1:04:48] So I guess when Kepler was studying the paths of the planets and so on, he was, you know, making observations of the planets and reading the observations of what was it, Tycho Brahe and so on, and He was rummaging around in Greek pure mathematics, I guess, in Apollonius, the conic sections, and things like that. And he found a geometrical figure which we call today the ellipse. The Greeks named the ellipse, and that he was able to what apply to the paths of the positions of the planets.

[1:05:24] But the Greeks had no idea that the planets traveled in ellipses, and they were trying to, as you know, trying to explain the movements of the planets in terms of circles and circles on top of circles and so on, the epic epicycles. So here, the math worked out by a man who had no idea of this application, and then somebody else takes the math and then applies it, or like Einstein, I guess, in the in the nineteenth in the twentieth century, he took some strange kind of math that Riemann had worked out in the nineteenth century, and he used that in one of the theories of relativity.

[1:06:05] Say, and when Heisenberg was trying to mathematize the quantum theory there, and he was kind of he had some kind of idea, and Max Born said, and George said, it reminds us of this kind of weird math they have over here in in Göttingen, there in Germany. And sure enough, this matrix mathematics and so on was a quick. So there is very clear that the math is worked out separately from the application, and the man who makes the application is not usually the man who who did the math in the first place.

[1:06:48] So the fact that you have to go get something and then see if it can be fitted into this is a sign that that when you go get it, it's not in there, but it's outside. You see the force of the argument. So that's the sign he gives. But the the basic reason is the definitions, which are the foundation of everything in science. The definitions in natural philosophy have reference to matter and motion, but the definitions in math have no reference to matter or motion.

[1:07:22] Okay. Any questions then about the basic thing, the problem and the solution? Okay. Now. About the application when you apply the math. Yeah. Then it would that have to do with what you were talking about the idealization because it's not. Those mathematical shapes. Yeah, it may involve that too. Yeah, but that's another, another thing to consider. Okay. But the fact of making applications is a sign that up there in math, it's separated.

[1:08:12] And even today, we sometimes use the expression "applied mathematics." You wouldn't have to apply it if it was in the thing to begin with.