Natural Hearing (Aristotle's Physics)
61. Why the Philosophy of the Continuous Matters: Motion, Time, Zeno and the Limits of Imagination
https://berquistcourse.com/course/philosophy/3-natural-hearing/061-why-the-philosophy-of-the-continuous-matters-motion-time/

[0:00] You know how you doing? He says. He answers well. He says the the the better for my enemies and the worse for my friends. He says, "Oh all right, you mean the better for your friends and the worse for enemies, don't you? " No, no, no, no. He says the worse for my friends and the better for my enemies. And he says, "What?

[0:21] What do you mean? " He says, "Well, my my friends tell me I am what my enemies tell me. Well, I'm wonderful, right? You know, and enemies tell me I'm an ass. " But there's

[0:35] you learn something from your enemies, right? Because they're going to point out your defects to you sometimes, and sometimes your friends will not point out your defects out of what friendship, right? But there's an essay of Plutarch, right, on that very subject. Have you seen that one? You know how to benefit from your enemies.

[0:56] It's good, you know, because your enemies don't love you, so they like to point out your defects, and so you learn the truth about yourself from your enemies in a way that you don't. Sometimes your friends, your friends will put up with certain defects and faults you have, right? And you know, you know, the extreme example, of course, is where a man in power is is what flattered by these people, right?

[1:22] And can't get an honest what statement, right? Don't tell him what the situation really is. Right. That's a real problem. Real problem. That conversation there, the argument

[1:56] between Brutus and Cassius there, when things are kind of going against them, and Cassius, Brutus is kind of pointing out Cassius' faults to him, right? Cassius, our friend wouldn't, you know, you're not a friend, you're not a friend. And Brutus says, you know, a flatter would not, he says. You know, I mean, you know, Shakespeare speaks of the sweet breath of flattery. You know, you go to somebody's house for dinner and this is a wonderful meal?

[2:31] Oh, this is delicious. You're always saying that, you know. And I suppose this is a small lie, but I mean it is. And you know, I said, you know, the college people, you got to kind of encourage people, you got to encourage students, you know, but sometimes you got to tell them what their their thing is, you know.

[2:55] The story, you know when Rossellini was presenting his. Draft of his thing, you know, is so mixed up, you know, that the kind just says, "Okay, let's start over again.

[3:07] Let's start over again. " Is that? It's kind of brutal, you know, but but he said that you know, he's just so mixed up, you know, huh? See, just you know, that's that's just you know, forget all that and start over again, huh? You see something like that in the lives of the saints too, you know, where at the end they say, you know, they're always beginning, right?

[3:38] Let's start over again, huh? Know myself when I come back, you know, you know, to think about something that I thought about before, and maybe I picked up things in the meantime, and I see it much better, you know. Now sometimes I, you know, I start to think over again, and I'm doing much better now, you know. If I go back to the one and and try to complete that one, I'd be what?

[4:06] Off on the wrong foot, you know. I'm off on a better foot at least to just approaching it. Yeah. It's like all these, you know, these scandals going on now in the church. You know about, you know, you hear about them or not? Do you? Yeah, yeah, yeah. Pretty more than enough. Yeah, yeah, you get, and they keep on, you know, you know, people they love to pursue these things, you know.

[4:36] But there is something kind of what, you know, scandals about these things, nevertheless, huh? You know, there have been. I was kind of surprised. I was looking in the paper the other day there, and you know, people were calling for

[4:49] laws of resignation, you know, but even Bennett called for it. You know Bennett, you know the former Secretary of Education, you know, yeah, the Book of Virtues, and Riddles. Oh. Yeah. I guess William F. Buckley did, too, before that too. So William F. Buckley. Oh yeah. Yeah, so here you got two, you know, Catholic laymen, you know, pretty solid guys, you know, but you know, it's kind of a strong thing, right?

[5:13] But you know, I'm not trying to, you know, judge whether it should be so or not. That must be the thing. But I think the thing is, there has been, you know, some imprudent thing, you know, done in the past, certainly, and things are not very defensible, and do we resign another question or not? I mean, they're pretty hard things. But but people who are going to, you know, keep on hitting these things, the paper and so on, they're really enemies of the church.

[5:39] Sure. But sometimes your friends won't tell you. In other words, you know, if you say, "What can we learn from this? " You know, well, just go back to Plutarch's essay, right? You know, your enemies are going to be, you know, looking for something wrong, right, about you and and this. Especially, they can get you know money for it and so on. And and so

[6:03] something to be learned from that, right? Yeah, yes. Friends will tell you what's wrong with you. Was that really a friend? Was that a flatterer?

[6:21] By Saint Paul, there's you know that Peter had it that one time. Remember that? Huh? That Peter was being a little bit, about the Mosaic law, Right? Wasn't it? That was a problem. Kind of kind of interesting example there, right?

[6:42] Aristotle teaches us a component of friendship that that you will tell be able to tell. Yeah, I mean, you don't have to be carping all the time. I mean,

[6:57] and some things you realize your friends won't probably never change, right? Prejudicial judgment and how to apply it. Yeah. The general principle. Yeah. Yeah.

[7:12] I mean, the opposite extreme, obviously, of course, is to be encouraging your friend. You know, in their vices, huh? You know, but. I mean, it's such a common thing, in other words, that the friend is a flatterer and not be your friend, really. The Plutarchian is just saying how to benefit from your enemies, right? Yeah.

[7:50] So we're going to go in now to the philosophy of the what continuous, huh? And my particular, reproduce these for us, okay? Okay. Fifteen pages here, okay? It's going to be on there for a while, okay? Just say a few words here before we go. Make me three or four copies, me too, just so I can. Um.

[8:18] Yeah, I like to call this. This is for the sixth book. This is a large part of the sixth book of natural hearing, huh? I like to call it sometimes to give it a kind of a selfie. I like to call it the philosophy of the continuous.

[8:45] Now, someone might be surprised at that because what other part of philosophy might be? Seem to be even more a philosophy of the continuous. Geometry. Yeah, geometry, right? Remember the distinction in logic between two kinds of quantity: continuous quantity, like width and breadth and depth and so on, and then discrete quantity, like number, right? Okay, remember that distinction. Okay. And we talked a little bit about the definitions of the continuous and the discrete and so on.

[9:21] We'll read them again. Continuous is that which is what parts meet at a common boundary, like the parts of a line meet at a point, let's say, or the parts of a surface meet at a line, or the parts of the body meet at a surface. Or the other definition that you read in this book, in fact, that the continuous is that which is divisible forever, right?

[9:47] Okay. By number, its parts don't meet at a common boundary, right? It's not divisible forever, right? So when you distinguish between the two parts of mathematical. Philosophy, geometry, like in the first six books, say of Euclid and later on in the solid geometry, and then in the seventh and eighth and ninth books, the books on numbers, right? Well, geometry is about the continuous quantity, and arithmetic is about numbers, right?

[10:17] The non-continuous quantity. So, what does it mean to to speak of book six as the philosophy of the continuous, huh? And how does it differ from geometry, right? You know, or why should there be this consideration here, and this one in geometry, huh?

[10:49] Euclid doesn't, for example, define the continuous, right? In some ways, you're going to see that this is more basic, right, than geometry, huh? But notice, does geometry consider everything that is continuous? Oh, no. See, it considers a line, which is continuous in one dimension. Considers a surface, which is continuous in two dimensions. Considers the geometrical body, right, as length and width and depth, right? But it doesn't consider what?

[11:32] Motion. Motion. Now, if motion is over a line or down the line, the motion over a line will be also what? Continuous, right? And also divisible, but forever, right? Okay. And then the time that it takes, right, will also be what? Continuous, right? So, in a way, the continuity of motion over a line follows the continuity of the line, and the time follows the continuity of motion, right?

[12:16] There's a connection between those three, right? So, in one sense, this is about everything that is continuous, right? And geometry is not, right? That's that's one difference we see, right?

[12:35] And the reason why each of these is divisible forever is somewhat the same, right? And we'll see that nothing continuous is composed of what? Indivisibles, right? We'll see, for example, that the line is not composed of what? Points. And time is not composed of what? Now, Now right. And we already have a good. Common word image for the indivisible in motion, but they call it the Latin momentum, but has taken on different meaning in modern physics, right?

[13:12] Okay, but again, motion is not composed of indivisibles, huh? But in a way, it's the same reason why none of these is composed of what indivisibles, right? And also, if you see it in one, you can see it in the others because of that.

[13:33] I think I mentioned how sometimes Aristotle will, you know, reason from one to the other, and sometimes reason about both together. Like example, I gave of time and distance being divisible forever Because there's a faster and a slower. Remember that? Right? The faster body covers the same distance in less time. In that lesser time, the slower body would cover a lesser distance, right? And so on. So you can divide them forever, right?

[14:02] So it seems, in a way, to be the same knowledge, or pertain to the same knowledge, of all continuous things, right? As far as they're being divisible forever, right?

[14:14] And as far as they're not being composed of what indivisibles, okay. So according to what he teaches in the Posterior Analytics, right, if you have a common reason for many things, you should what bring them together, right, huh? In that one thing.

[14:38] And some of these things are so basic that, in a way, the geometry supposes those things to be true, huh? Take for example, you have a postulate in geometry that between any two points you can draw a what straight line, right? Now, if two points could could touch without coinciding, right?

[15:11] Could you draw a straight line between them? No, because there are no points between them. Yeah, yeah. So, in a way, saying that between any two points you can draw a straight line is assuming that what two points cannot what touch, touch, yeah. And then we made the same right, okay? Which is tied up with the idea that you can't compose a line of points, right? So in a way, that is what assumed geometry, right?

[15:51] So in some sense, geometry assumes. This is more basic, right? It's kind of interesting, right? It shows in a way that actual philosophy is more the character of wisdom, in a way. And geometry does, because this doesn't depend upon geometry, but geometry in some way depends upon this. So

[16:31] you can see too that we saw back in the beginning of Book Three, Aristotle says we're going to talk about motion. We're going to talk about what place. We're going to talk about time, right? Remember he had two ways of showing that. One was he goes back to the definition of nature, right? And obviously, natural philosophy is about things that depend upon nature, and nature is defined as the beginning cause of motion, right?

[17:02] So that's he's been talking about motion here, right? But then he talks about how motion maybe takes time, right? So it makes sense to talk about time when you talk about motion, and motion is also what

[17:18] falls a thing in motion, and that thing in motion is somewhere, right? That involves a place, right? Okay, that's one way we see us talking about these things, but also he gives a second reason that these seem to be common to all what natural things, right? They're somewhere at some time, right? They're all subject to motion, and we're talking here in this first book of natural philosophy about those things that are common to all natural things.

[17:54] Of course, to the first philosophers, they seem to be common to all things. They're somewhere and in some what time, right? Okay. So the question: Where is heaven? Right? I was always asked in grade school, you know, where is heaven? You know, and what's up there? Is it you know? And and the poor frustrated nuns used to say, you know, well, the answer was heaven is where God is.

[18:25] Because then somebody asked, where is God? But God and an angel, that matter, they're not in place. Yeah, but in grade school, you know, you'd say, you know, sister would say, you know, now leave a little room for your angel there, right? I had Saint Joseph's sisters, you know, and they were

[18:49] pretty good, you know, the ones I had anyway, you know, and Sister Carolyn was the principal my time. We were all kind of afraid of Sister Carolyn, and at least they have on Sunday. You'd have like nine o'clock mass. You're supposed to go to that mass, but it's a children's mass. And if you didn't go there, they knew it, you know. I get called down to Sister Carolyn's office, right, where Kurt's getting all talking to, and he'd always try to get you some in the back of the other kids, you know.

[19:20] But I can remember one time my brother Marcus was was sick and he'd miss some classes or some days, you know. And I was coming up the stairs to Sister Carolyn, and she went to ask me about Brother Marcus, and so looking down, you know, says, "Look at the person to whom you are speaking."

[19:45] So, Sister was a pretty tough. There was one whose name, the nickname was Sister Corona, but her nickname was Cannonball Corona. Wham, you know. Yeah. But uh. So, um why talk about the continuous, right? Well, continuous is common to those things, right? That motion and place and time, right? These things are what continuous, right?

[20:24] And because the distance from here to there is continuous, the motion over it and the time over it, right? So they're all closely connected with that.

[20:38] But another reason why I want to talk about the continuous here is that it seems to be the most, almost the most basic thing in our knowledge, huh? I mean, I'll begin the text there from the the book on sense and sensible, the book on memory and reminiscence. But Aristotle says, you know, we we don't think without an image, and therefore we don't think without the continuous and time, right?

[21:16] Okay. And if you take, you know, these basic words like beginning and before and after, and things like this, they all seem to have a connection with the what continuous, right? You know, the beginning of the table here, right? Beginning of the table. time, the before and after, for us to see it in time and so on.

[21:49] Don't realize how fundamental the continuous is in our what in the very words that we use, huh? When you study later on in the three books about the soul, you study the what they call sensible, right? And Aristotle will distinguish between the sensible as such and then the accidental sensible. Okay. When someone says, "I can see you're angry," does he see your anger? Have you ever seen anybody's anger?

[22:35] No, no. That's accidental, right? You're not really sensing it, right? But you know it by something else in you when you sense, right? certain things, huh? Okay. But then the sensible as such divides into what two? And one's what you might call the proper or the private sensible. It's private to one sense. Like color is to the eye, or sound to the ear, and smell to the nose, and flavor or something like that to taste, and so on.

[23:11] And then he speaks of what he calls the common sensibles, something that's sensed by more than one sense. Like, for example, what surface? Right? I can know the surface through my what sense of touch? Right? I can know surface by my eye, and

[23:33] or the shape. Right? I can know the shape of this table without my eyes. Right? I can feel the shape of this glass. Right?

[23:45] I can feel the shape. Right? It's round. You know, if you put in my hand, right? But I can also see it. Right? So he calls those the common sensibles. The common sensibles are tied up with the what? Continuous, right? Okay, like the surface here is continuous, and and even the shape is kind of the the limit of the continuous, huh? Okay. So,

[24:12] how many words are tied up? The basic words that are thinking are tied up with continuous, huh? As opposed to the to the the private sensible, huh?

[24:26] Take take something like the word red or green, right? Or I might call communist or red or something, but does red get extended much? Anything else than red? Doesn't seem like.

[24:45] But now take the word like beginning, and the word end. The first meaning of beginning and end is like this: is the beginning of the desk, and that's the end down there. But how how many senses there are on does the word beginning take on?

[25:05] Aristotle talks about the foundation of the house is the beginning, right? And he talks about how the the the prince and the city is the beginning, right? The principle is the beginning. This Sister Carol I was talking about, but principle comes from the Latin word for beginning, right? And then you speak of what the axioms as being the beginning of geometry or something, the definitions being the beginning of a science, huh?

[25:32] You have all these different meanings of beginning, but they all involve carrying over that first meaning of beginning, which is beginning of something continuous, right? Then you take the word end, right? First meaning of end is the end of something continuous, right? Then we speak of the end of a motion, right? Then we speak of end in the sense of purpose, right? And then even the Greek word for definition, the Latin word, they use horos, terminus, limit, end.

[26:04] You see? So we take words that name something in the continuous, right? And we carry them over to other things. I'm always talking. I'm I'm going to tell you the Greeks here when I say this. I'm using the word road all the time, right? The first road in our knowledge is the road from the senses into reason. The second road is the road from reasonable guesses towards reasoned out knowledge.

[26:36] Then there's a private road of each reasoned out knowledge and so on. But this word road first comes from something what? Continuous. The road upon which I drive here, or walk here, right? Then we carry it over and apply it to the mind.

[26:57] So in and out. Well, in is the first meaning of the place, right? The place again is something what? Continuous, right? Don't stop and realize how how fundamentally continuous is in all

[27:15] That's why in the De Trinitate you know, when Boethius is talking about these things and so on. Well, if we never think without an image and therefore about the continuous, how can we think about something that is not continuous? Well, we have to negate the continuous, right?

[27:36] God is incorporeal. He's not a body. He has neither length nor width nor depth, right? Now another way that's going to be very important is when we get to the three books on the soul, because there we want to eventually talk about whether man's understanding or his reason is a body or not, right?

[28:21] And if we can show that reason is not continuous, right, then we can syllogize that it's not a body, right? So we have to understand what the continuous is before we can see that reason is not continuous, huh? And you'll see even in the dialectic of the first book about the soul, that Aristotle is arguing against thinking right being something continuous, huh? I notice we do speak of of a line of thinking, don't

[29:00] we? There's some likeness of thinking to a line, right? But is it really continuous like a line is? We have to understand the continuous before you can see the reasons for thinking that thinking is not continuous. You have to see that before you can see why we think that reason is not what a body, right? Okay.

[29:33] And we have to know that before we know that the human soul has a power or an ability that's not in the body, right?

[29:43] And that's a sign that its existence is not entirely what immersed in the body, right? Okay. If it had existence only in the body, Right it would only what. Operate in the body, right? Okay, right, yeah, yeah. Okay.

[30:08] So, if thinking is not in the body, if understanding is not in the body, then the soul's existence is not over only in the body. So you have to, but in order to see if the understanding is not in the body, you have to see how understanding is not something like continuous, right? And how even in understanding a continuous thing, we understand a continuous thing in a non-continuous way.

[30:42] My mind is not false in doing that, right? Because it's not it's not saying the continuous thing is not continuous that would be absurd, right? But the way in which it knows the continuous is not continuous.

[31:06] Just as the way I know the past, which is now, not the way the past is. But I don't say that the past is now, do I? Past is past. That's gone. That's over, right? My youth is gone. You know, but I remember my youth and all the way back to kindergarten, right?

[31:30] Each had a little drawer in the kindergarten, right? Each student, you know, each student was going to have a drawer. So sister said, "I'll bring a little toy from home and and we'll tie to the to your drawer so you'll be able to recognize your drawer, right? " I brought some toy soldier home and tied to the thing, but then I wanted to play with that soldier, but I couldn't because it had to stay in school because it wasn't education.

[31:57] Yeah, I didn't foresee that. So I mean that that frustration. You know, what kindergarten teacher was? Did I tell you who she was? Yeah, Sister Aquinas.

[32:19] Yeah, yeah. So sometimes I tell people about you know what first teacher was? No. You was though? Yeah, yeah. Sister Aquinas getting a they call it a coconut shell, you know, thing a little thing for it. But it's very hard to open a coconut, right? It's just hard. Get the thing open, you know. I'm breaking it. Finally, he's kind of broken. So I can know the past now, right?

[32:55] The now is in my what? I know it, right? Not what I know. I don't. I don't think that Sister Quiness is still trying to get that thing open. That cooking, right?

[33:14] My toy soldier is still in Timothy Grade School in the kindergarten. Timothy Grade School. right So how did everyone pronounce your name? So again, here you'll find out that our reason knows the continuous in an uncontinuous way. It doesn't say that the continuous is not continuous, but the way in which it knows it is not continuous. That's Aristotle's discovery, right? Recognition there that the way we know doesn't have to be the way what things are, right?

[34:03] And now, let's take a little different example here, but something like that. I could know the shape of this glass, right, by the sense of touch, right, and I could know it by what my eyes. Right, I can know the shape of this table here by my sense of touch, but the way we know this is different, isn't it? The eye and the touch. The eye knows shape through what color, right?

[34:33] Color extends as far nor further. The sense of touch knows shape through hardness, right? So, if the way of knowing had to be exactly the way the thing is, you couldn't have two ways of knowing the same thing, could you?

[35:04] Sometimes people think, you know, hey, the theologian talks about the immortality of the soul, but the philosopher can't talk about that. But it's possible sometimes the same thing be known in two different what ways, right? You see that already in the senses, huh? The senses.

[35:26] So, the better you understand the continuous, the better you can understand later on what what is not continuous, right? Just like we saw with the example there of what time. The better you know time in the now of time, the better you can understand the definition of eternity, right? Okay, so a lot of reasons why it's important to know the what continuous, huh?

[35:56] Now, when you look at the definition of reason before it's the ability for what large discourse, looking before and after, and then we had a text of Aristotle around before and after. But the first meaning of before and after is in the continuous, right? And then the second one he gave, he took an example from the discrete, right? One is before two. Remember that. You know, yeah.

[36:23] So you have to, you know, understand the first meaning of before and after, then see how the word is moved forward according to certain connection with the meanings. So you don't realize how basic the continuous is in our thinking, and most people can't transcend it at all. Whatever is must be somewhere. They can't transcend it continuous.

[36:47] See, I mean, I think if you if you ask most people, you know, what eternity is, they think and say what endless time, right? But endless time, like an infinite line, there is such a thing. It's still something continuous, isn't it?

[37:06] They they can't transcend the continuous. And the imagination is tied to the continuous, as are the senses too. You know, senses and imagination, right? You can't sense or imagine without the continuous. So fundamental, I know it.

[37:39] So the philosophy of the continuous is important for what for understanding motion, place, and time, right? And if you ever look at at you know the Summa Theologiae, is not as complete as the Summa Contra Gentiles as far as the reasoning from motion to God, right? Now, if you look at the Summa Contra Gentiles, it's much more complete, huh? And when he's arguing, you know, to the proposition, say that whatever is in motion is moved by another, right?

[38:17] You know, he has you know three different syllogisms to show it in the Summa Contra Gentiles, taken from the Aristotle, and in the Summa Theologiae, just as one, right? You know, but some of the ones are drawn from the sixth book. We'll see. Some of the reasons for saying that something can't move itself are drawn from an understanding of the continuous character of what motion, right? I think we talked about that that that problem that the kind of what the article paradox of Duvener product on Dixon, right?

[38:56] And how do you have this change between what non-being and being, right? Suppose what is not a circle becomes a circle, right? Well, there's a period of time which it is what

[39:24] not a circle, right? There's a period of time in which it is a circle, right? Now, is the last instant which is not a circle the first instant in which it is a circle? Well, if you say that, that it both is and is not a circle. That's what Hegel says, right?

[39:52] Now, if they're not the same instant, right? The? Last instant, which it is, then these are two different instances, two different nows, right? And just like with two different points, you have to have a what? Timing between them, right?

[40:14] Okay, unless two what? Nows could be what? Adjacent. Yeah, nothing between them, right? Okay, but is that possible? No. See? Or is it like two points? See, well, that's something to learn. We just studied this, right? That if two points touch, they coincide; they'd be the same one, right? Right. So if you really have two distinct points, there's got to be a line between them. I can always draw a line between them.

[40:43] So if you have really two distinct nows here, the last instant in which it's not a circle, and which it is a circle, then there has to be a time in between, right? And now either are a circle or now is a circle. so why do you have this time in between? Well, if it's not a circle, well then this pertains to that time over here, right?

[41:03] If you are a circle in this time, it pertains to this time, right? So you can't have any time in between the two. So it seems you're going to be forced to say that the last instant in which it is not a circle is the first one which it is, and then you got the contradiction, right? And that's uh what Hegel argues. you know, that becoming is a contradiction, right?

[41:23] Okay. Now Aristotle is going to solve that problem in the what? Sixth book, right? He's going to bring out that there is not a last what? Instant in which it is not a circle, but there is a first instant in which it is a circle.

[41:47] Okay. That might seem arbitrary at first, but it's not. We'll see when we get into the book. There's a reason why you why it makes sense to say that there is a first instant in which what is becoming a circle is a circle, right? But there's not a last instant in which it is what? No. Not a circle, right? See.

[42:23] Just like when you when you're dying, right? See, okay. See, so and so is dying, right? It takes some time to die, apparently. Sometimes, okay. You're dying, right? Okay. Now, is there a first? Is there a last instant in which you're still alive?

[42:46] Sounds like no. See. Or just a first instant which you are what? Dead. Yeah, yeah, yeah. Huh. But the end of the time in which you are dying, right? At the end of that time, you're dead. So that the end of that time is an instant, right? But the end of the time which I'm becoming, when I'm dying, I'm dead. So there's a first instant which I'm dead, but not a last instant which I'm still what alive, right?

[43:29] But at the other end of my life, when I was coming to be, right? Was there a last instant in which I was not? No. But there was a first instant which I am, right?

[43:45] So we're just about there. That's very important, right? For understanding becoming, right? And for understanding it as being without a what kind of addiction, right? Now, the Zeno, you also have probably heard of Zeno's paradoxes, and they'd be texted upon some of the sixth book, but he comes back to them in the eighth book. But Zeno had certain problems. Zeno was a pupil of Parmenides, right? And Parmenides was denying change because it seemed to involve a what contradiction, right?

[44:36] Okay, the one that we saw solved earlier, right? In day becomes night, right? The sick become healthy, right? We all say that one opposite becomes the other, right? Right. Now, if one did come to be the other, you'd have contradiction, right? Day would be night because day becomes night, and night becomes day, right? Right. Okay. Well, this is another example, you know, this one that Hegel made you so, where you seem to have a contradiction in becoming, right?

[45:11] Okay. But Zeno raised other problems. Zeno, being a pupil of Parmenides, wanted to show the difficulties, right? Well, his problem was what? Since the continuous is divisible forever, right? Before I can get out the door, I got to go half of the way to the door, right? Before I can go half the way, I got to go half of the half. Before I can go half of the half, I got to go what half of that, right?

[45:39] No. And never you can get out the door then. Okay. Or other paradoxes, Zeno, you know, where you know can the Achilles, who's a fast runner, catch the The turtle or something, you know, it's very slow, right? Well, now the turtle has a head start.

[46:06] Because if the turtle has a head start, before he can pass him, he's got to catch up to where he was, right? And that time, you will go a little bit further, right? Yeah. And before you can catch up with that,

[46:23] and surpassing that, catch up to where he is, and that time he'll go a little more, right? See, various ways, you know, the continuous, continuous character of motion, to say that it can't be, right? And kind of defending his master Parmenides, who people are saying, "Well, you're ridiculous, right? Denying that motion exists. " He said, "Well, you saying that it does exist involves all these impossibilities. " So now this is a very fundamental thing for understanding change and and for understanding it as something possible rather than something that involves a contradiction.

[46:57] So it's an awful fundamental consideration here. This philosophy of the continuous. So you've got to reproduce some, common sense, right? We'll be spending some time on that continuous, huh? That's going to be a key thing, now.

[47:17] All right. Sounds like also the argument against, or or to show that it's a miracle to have a deathbed conversion because there is no last moment. Why you don't? The last instant comes, it right, and you go down. And the tree falls. There it's all on. Okay. Extend. We extend more

[47:40] the words that are in the commons. Yeah. You don't extend green or red too much, except metaphorically, you know. A word like "sweet" is extended, you know, using metaphorically, right?

[48:05] Taste and see how sweet is the Lord, right? Thomas explains the metaphor, right? But but the words drawn from the continuous are extended what elegantly.

[48:17] Why is that more common? Is that? Why I think part of it is is this more, it's more understandable. More comprehensible. Yeah. Because you can see in the moderns, so

[48:34] you know that you know how would you define the redness of red, right? It's kind of hard to define red, isn't it? I can define the continuous in a number of ways, right? It seems to be more understandable the continuous, huh? You can see that too, you know, and how geometry is said clearly, right? You know, what is what is red?

[49:00] I mean, I can point to it, but but what is red? Of course, you know the moderns. When we talk about wavelength, but then they're talking about something continuous, right? But you don't go into mathematically that continuous aspect. What is red? I can't, you know, over here. What is red?

[49:31] Why is that? That it's not something I can imagine. Red, I can just like I can imagine continuous. Yeah. But again, you know, go back to the distinction they make between math and natural philosophy, right?

[49:47] Sensible matter is something more, what? Material, right? So because I can. But it's a sign, yeah It's more tied to matter, the sensible qualities. So

[50:24] sometimes, you know, we'll say that mathematics abstracts a matter, right? Other times, Aristotle will speak of an understandable matter, right, as opposed to sensible matter. But that seems to be not matter in the in the

[50:41] fundamental sense, right? So just you know, if you look at the first, excuse me, the first chapter there in the fifth book of the metaphysics, there, just in the word beginning, take that one, you know, or look at the word before and after, in the before in the categories, right? Comes up again in the fifth book of wisdom too, but see how important those words are, right?

[51:16] Or look at the word in, you know, look at the word in, like we're talking about, right? They're all tied up with the continuous, huh? See, and and how those words are so extendable, right?

[51:31] But you can't, You know. we've had eight meetings, have you ever been, remember the other day? you know, and they're all ordered, right? From that first meeting, you know, by certain likeness and proportion and so on, and like you do with the word red, you know, huh? Can't can you?

[51:54] We're in this room, right? Teeth in my mouth. Genus and species, species and the genus, right? All these things, right? You know, I can move the word in to all those eight meanings, huh? I left my heart in San Francisco, right? Correctly, I move the word red.

[52:25] That's because it's less sensible. Well, I said prior to nature, yeah. I mean, I think it's it's easy to see that it can't be moved, right? Exactly why, you know, but it's something to do with the fact that the sense qualities are more what tied up with matter, right? Even the continuous, huh? And

[52:49] that's why you have one species of motion is alteration, right? But alteration is always spoken of as being the third species of quality, right? Sensible qualities, huh? Nothing in the fourth species figure shape,

[53:11] but don't worry too much about exactly why it is so. You know, at first, but just see how important you know that is. Sorry, how we can extend the word in in a way we can't extend the word red or green. Though, wonder if if you can, you know, the words. I am going to take off with this guy. I was going to sit down there. The words like like in sense of touch, like hard and soft, right?

[53:50] They seem to be almost more movable than red or green, don't they? You know, it's a hard proposition. Yeah. Yeah. Soft headed, you know. Soft, hardy, right? It's a touch. of course, of the most basic, kind. You kind of used to something else, you know. The other thing is, talk about

[54:19] something we've actually. I sit therefore I am. And how we're so tied to the sense of sight, you know, but other basic notions like substance and nature and good are tied up to the sense of like touch yeah.

[54:36] You get the idea of good more from a sense of touch than, from the sense of sight, right? From the sense of nature, the sense of the interior, right? Tied up with touch is the sense of the interior, right?

[54:51] But the eye is superficially. One way is that in heaven, everyone does the will of God. It's never contrary. Like God, so like the angels. So the prayer is that, as it is in heaven, may it be on earth. Okay. So since those who are in heaven, their wills are completely conformed to God's will, right? They're asking something, you know, approximately that for our wills down here on earth, right?

[55:35] But as Saint Augustine says, and Thomas Aquinas says as well, in the sense of the letter, even the sense of letter, not only the spiritual sense, but the sense of letter, there can be more than one what meaning, yeah, yeah. Now, going back to it, my old teacher Kasurik used to say, you know, he says you are going to give glory to God willy-nilly, right? Yeah. If you be good, you are going to.

[56:04] Give glory to God's mercy, right? And if you are bad, you are going to glorify His justice in the end. So you can't avoid glorifying God, huh? So maybe another sense in this petition, you can say that God's will is done, not only in heaven, but also in another way, His will is done in hell, right? Okay. And in heaven, it's His what? His mercy, right? That is being

[56:38] His merciful will that is being fulfilled there, right? But in hell, His what? Just will, right? Okay. So when we say that will be done on earth as is in heaven, we're asking for His what? Mercy rather than what we deserve. Which is asking that His will be done on earth as is done in hell, right? In other words, punish us for you know as much as we deserve or something like that, right?

[57:08] And. Right. Is it a way of understanding it? Huh? Yeah. Merciful of God. So that's extra today, okay? Okay. Let's look now here at the philosophy of the continuous here.

[57:44] Aristotle begins with the statement here: if the continuous and the touching and the next are as has been determined before, these have been defined earlier in the book, back in the fifth book. Now, how are those three things related? The continuous, the touching, and the next. Okay. I'll have a boundary. Are they defined in terms of a boundary? Not necessarily. Necessarily.

[58:24] The one adds to the other. Yes. Yeah. For next, they add touching. Add something. Yeah. Continuous. Add something to. Yeah. Touching. I notice, son. The continuous is in one definition the continuous that whose parts have a what? Common boundary, right? Okay. So if you imagine, say, a circle and the diameter of a circle, right? The two semicircles are continuous, and that diameter could be considered to be the end of one.

[59:02] Semicircle and the beginning of the what other right, but it's one and the same end or limit that is the end of one and the beginning of another, and presumably the border there in the strict sense between Canada, say, the United States, that border there, wherever exactly it is, all the United States is south of the border, as you think of Mexico when he sings south of the border, but the Canadians were south of the border, and everything above that line is what Canada, yeah.

[59:45] Now if there's no no man's land, is yes, I'm just having the military, yeah. Then that line that divides the two countries is the what upper limit of the United States, but at the same time it's the What? Lower limit Yeah. Yeah. And strictly speaking, what is that line called, the horizon?

[1:00:13] The boundary of the earth and the sky. Yeah, and it's the same what line that is the upward limit, so to speak, of the earth and the lower limit of the what? Sky. Yeah, yeah.

[1:00:32] Now, as I say, sometimes we use the word "continuous" in a equivocal way, right? But by reason of a certain likeness, for example, when the Arab philosophers say or that man's soul is on the horizon, or man is on the horizon in a way between the material world and the immaterial world, huh?

[1:01:02] Okay. In a way, he's the what end of the material world, right? And the beginning of the what immaterial world, like when Democritus said man is a microcosm, a little universe, huh? Because he seems to have you know one foot in the material world, so to speak, another foot in the immaterial world. He's right on the on the border. That's so interesting.

[1:01:35] Or sometimes when we're talking about natural philosophy and metaphysics, huh? Or wisdom, Aristotle usually calls first philosophy. But metaphysics in Greek is actually three words, huh? Meta, meaning after, and ta, which is the article, and physika, right? After the books in natural philosophy. But

[1:02:05] natural philosophy is about things that involve matter and motion. But when you study motion, and later on in this seventh and eighth books, when you see that motion depends upon a mover,

[1:02:19] but the movers that we are familiar with most of all are moved movers, right? And then you see that moved movers depend upon the unmoved mover, huh? And then you reason out that the unmoved mover cannot be a body because a body doesn't move other things without being moved itself.

[1:02:42] Well, you're at the end of natural science, and in a way, at the beginning of what? Metaphysics. Yeah, science, which is going to be about immaterial things, huh? So you could say the the proof. Of the existence of the unmoved mover and of the incorporeality as not being a body, that in a sense is the the border, like between United States and Canada, right?

[1:03:20] Do you see that? Yeah. And the same way in the third book about the soul, when Aristotle proves the immortality of the human soul, that the human soul can exist without the body

[1:03:39] after death and so on. Ah, where are you? Well, you are at the end, in a way, of natural science, huh? One of the borders, right? Not the same border the other one was, but it's another border. Just like we have a border up here in Canada and one down there and with Mexico and so on, right? But you are at at the borders, huh? Between, though, in this case, at the same time, between the what?

[1:04:12] Natural philosophy and what first philosophy. Okay. And then, as we said before, sometimes even in talking about numbers, right, which are not continuous as they're going to be defined here, but we sometimes speak of a continuous what? Proportion, right? Okay. So four is to six as six is to nine, right? As distinguished from saying two is to three is four is to six, right?

[1:04:52] What two is to three is four is to six? Well, you don't find three with the four and the six at all, right? But if you have four is to six as six is to nine, right? The end of one six is the beginning of the next. So there is a certain what likeness there, okay, to the continuous, but it's not what as we'll see continuous in the strict sense here, right?

[1:05:19] Because numbers don't have any limit in that sense, huh? And Aristotle say the number seven, for example, the three and the four, or the two and the five, or any way you want to divide it, they don't meet anywhere, right? So it's not a continuous quantity, but there is something in that four is to six, six is to nine that makes us call it a what? Continuous Proportion.

[1:05:46] Yeah. And a little bit like you know if they would they double the dyad, right? Two, four, eight, you know. You know, but you have this two is to four is four is to eight is eight is to so on so on so on. You may have it going on for some time, right? Yeah. And then I think you can,

[1:06:13] in the same way, speak even in definitions and in divisions and in demonstrations or syllogisms or arguments. You can speak of what continuous arguments or continuous syllogisms. What does that mean?

[1:06:34] The result of one of these premises for the next. Yeah, yeah. So you have two syllogisms, and the conclusion of one is a premise in the other. You might, by certain likeness here, say that they are what continuous, yeah, yeah, because the end of one is the beginning of the other. And if what is defined by one definition is a part of another thing's definition, then we'd say that those definitions are what continuous, right?

[1:07:07] So the definition of quadrilateral and the definition of square, we could say, are what continuous, right? And maybe there'd be many things. Now, the definition of of plane figure and rectilineal plane figure and quadrilateral and square, they're all what continuous, right?

[1:07:29] And so, but like when you say that a chain is no stronger than its weakest link, huh? And so, it seems to be something like that, right? Okay.

[1:07:46] With the arguments of the definition, you can have the same thing with divisions, huh? So if I divide, you know, rectilineal plane figure into triangle and quadrilateral and so on, then I divide quadrilateral into the square and oblong and rhombus, rhomboid, trapezium. Those divisions seem to be what continuous, right? Okay. And in most, and I would say really any reasoned out knowledge, you're going to have continuous definitions and continuous divisions, right?

[1:08:23] And continuous syllogisms, or sometimes you know, an induction will be continuous, right? Very often, I mean, we have an induction whereby we arrive at a general statement that is used then in a syllogism, huh? And so you can say, in that case, the induction and the syllogism are what continuous, huh?

[1:08:48] And so, just as we we we transfer words like square and cube to numbers, huh? Speak of a square number and a cube number.

[1:09:02] If you've done the theorems in Euclid for for those and for squares and so on, you see a certain likeness even, signs in the arguments, right? But I think we we tend to transfer the words from geometry to arithmetic more than the reverse, because geometry is more sensible and it's continuous, right?

[1:09:28] As well as the fact that number arises maybe from the division of the continuous. So, but now in this text, what does he continuous in this strict sense?