Natural Hearing (Aristotle's Physics)
Lecture 63: Time as the Number of Motion: Definition and Nature

Transcript
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The actual philosophy and wisdom are both more difficult than geometry, but for different reasons, right? And we used to joke about women you know, huh? They say this is kind of a good line with the woman you know to say that you can't understand her, you know? But I say, it isn't necessarily a compliment if you know why we have a hard time understanding, right? Woman, right? Has it caused the difficulty in us? Or is it reading the woman, right? There's something kind of irrational about that, right? So, there's a compliment. I mean, that's a secret we can't do. They like to be told, you know, I can't comprehend you, you know? You're a mystery. They want to be mysterious, right? Okay, so why don't we stop now so you can go to Mass and I can go through the snow. Okay, now next week, we're going away, my wife and I are down to the airport now, so. We got on the airplane, my wife realized she left her sweater out in the—or jacket was out in the—part of the place, so she runs off and runs out to get it, see? And she didn't take her to prison there, of course, because she always wanted to check your ID again. Oh, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no. Okay, shall we begin? In the name of the Father, and the Son, and the Holy Spirit, amen. God, our enlightenment, guardian angels, strengthen the lights of our minds, order to illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, angelic doctor. Pray for us. And help us to understand all that you have written. In the name of the Father, and the Son, and the Holy Spirit, amen. Because you happen to see the address there of John Paul II there, that he gave in Kazakhstan, to the representatives of culture, art, and the sciences. Do you have the Pope's speech here? Do you have that? It's in that latest Pope's speech, you know, but it's back several months. I was off to bring it in and read some interesting things he has to say, but he's quoting some author there from Kazakhstan. Saying some interesting things, so, but I'll wait till I have the text in front of me, so I'll just read you the little things he said. So, we're up to the 16th reading, I believe, right? In the 15th reading we saw before I went south, they call you people, you know, come down for the winter to escape the snow, and what their nickname for them is? You hear it all around there, they call them snowbirds. Oh, you know, that house belongs to a snowbird, you know, like they come down in the wintertime and they go up. It's kind of a nice name, you know, you can be... It's a funny name. Okay. So, we saw the difficulties in 15, the difficulties about how time even exists, right? And the difficulties about the now, and how it can, what, cease to be, right? And if it doesn't cease to be, other problems. Okay. So, now we've got to start to approach the definition here in reading 16. So, what time is, and what is the nature of it, he says, at the beginning of this, is likewise unclear from the things handed down which you have gone through before. And now he gives two, not too deeply thought out opinions about what time is. For some say it is the, what, movement of the whole, right? The circular movement of the whole, what, sky around us, huh? For others say it's the sphere itself. Now, he gives a couple of reasons against that first opinion. And yet a part of going around in a circle is some time, but not a going around in a circle. That's kind of an interesting thing, right? If you say that time is the circular motion, right, okay, then a part of that circular motion would not be, what, a circular motion. And therefore, a part of time would not be time, okay? But just as part of a line is a line, so it seems part of time is time, huh? For what is taken is a part of going around in a circle, but it is not a going around in a circle. It's not a circulation. Further, he says, if there are many heavens, and time was likewise the motion of each of these, then many times will be together, right? We have these many circular motions, apparently, around us, huh? So if time is a circular motion, then there are many times simultaneous. It just doesn't seem to agree with what we think about time. Now, the other opinion, of course, is more gross, he says, huh? But all things are in time, and all things are in the sphere of the whole. Because of that, it seems to some that time is the sphere of the whole. But this statement is too stupid to look into the possibilities of it. Notice there's obviously an equivocation on two meanings of in, right? All things are in the world, right? So they're contained in the sphere, apparently. And all things are in time, right? Therefore, time must be the whole sphere, right? Well, two different senses of what? In. And incidentally, Melis is there. We didn't look at that part in the first book. But Melis says, he confuses the two senses of in, too. And not the two senses of in, but the two senses of what? Limit, right? He says that being never came to be, so it had no beginning, right? It's without any, and therefore it has no end, right? Therefore it's what? Unlimited in size, right? But he confuses the sense in which it has no beginning and no end in time with having no beginning and no end in its, what, size, right? So, here you have a somewhat similar confusion there, huh? It's a sense of in as in place and then in time. In time, yeah, yeah. Everything is in time, everything is in place, right? Therefore, everything is in the same thing, right? But in doesn't mean the same thing. When you say things are in time and you say they're in place, right? Okay? Yeah. We're in this room, in this day, in this year. Yeah. It doesn't mean the same thing. But notice, those are not two different central senses of the word in, as we spoke last time. Right. The central sense he gives of in there, the first one, is in place, and then he leads back to that in time. When you say lead back, we don't mean he simply says it's the same meaning, but it has a certain similarity, right? Well, as Plato says, beware of likeness, huh? Likeness is a very slippery thing. And Aristotle, when he writes the book on Cisographitations, he says that in general, deception takes place by means of what? Because of likeness, right? We mix up things, huh? Because they are alike. And that shows kind of a connection, too, between deception and imagination, because imagination is taken with the likeness of things. That's got what Joe come afloat in trouble there, right? You know, and he's trying to see the likeness there between what? But, you know, Christ's prayer, you know, that they may all be one, as you and I are one, the Father and I are one. But the Father and Christ are one in a greater, in a different way, really, than we can be one, huh? And so you get a little trouble overextending the likeness between those two. And so his mistake there was corrected in the, was it, the fourth ladder in the council, right? The one in 1215. The one in 1215. But that's the one where the Lateran Council teaches, that you can never note a likeness between the creature and God without at the same time noting a greater, what? Dislikeness. Unlikeness, yeah. As far as you made that kind of infinite distance there between the creature and God. I told you about the time I had a student from Saudi Arabia in one of my classes. Oh, yeah. And he objected to Shakespeare saying that reason is godlike. And so I wanted to explain to him in what sense we would speak a little like this of these things. I was giving him that text, you know, so that kind of assuaged him a bit, right? That we're not as crazy and as theoretical and impious as we might appear to him. Okay. Now, in the fifth paragraph there, he's going to start to approach in his own now what time is, huh? And the starting point is to see that, what? There's some connection between time and, what? Motion. Motion or change, yeah? And even in those two opinions given before, the one that he considers a little more than the other, right, is the one that ties up time in some way with motion. As if that's more plausible, right? Than to confuse time with place. So that's kind of the loose thread, you might say, where he starts to unravel this. But since time seems especially to be motion and change, this ought to be looked into, right? Okay. Now, let's just stop there for a moment, huh? You know, Sir Isaac Newton and others speak of the flow of time, don't they? And you hear the expression, tempus fugit? Time, what? Flees, right? Well, is that a sign that we see some connection between time and motion, whatever that is? Whether time is a motion or in some way, I'll connect with it. Time waits for no man. See? Seems to imply that, right? Okay. Or take Shakespeare's beautiful, what, simile, huh? Where he says, Like as the ways make towards the pebbled shore, so do our minutes hasten to their end. Each changing place with that which goes before, in sequent toil, all forwards do contend. Okay. So notice he's comparing the minutes of our time to, what, the ways, one of which is crashing against the shore before or after another one, right? So you're thinking if there's some connection there between time, right? Like as the ways make towards the pebbled shore, it's like a motion, right? So do our minutes hasten to their end. So there's many signs in the way we all speak about time that we think of what? It is being somehow connected with motion, right? But now the next step is the question, is time itself a motion, or is it something of motion, right? But not motion itself, huh? Okay. And he's going to what? Reason against it being a motion. But then, because it's connected with motion, if it's not motion, it must then be something, what? Of motion, yeah. And then you'll have to investigate what it is of motion, huh? Okay. But this is the first thing. Is it what? Yeah. Yeah. And I was mentioning something like that when he talked about motion itself, right? Is motion the thing in motion? You know, and Galileo talks about the falling to the earth and so on. Naturally accelerated motion. Is it the falling that falls? See? When they kicked the football, right? Is it the flying that goes flying through the air? The flying that flew through the air was an airplane. To the best of my knowledge, it was an airplane, right? Going through the sky, huh? We were taking off from Melbourne, Indy. And they were running down, you know, to take off, and somebody's seatbelt wasn't working. So they were all the way back and delayed us an hour until they could either fix the seatbelt or get someone to agree to get off the airplane. I said, what the heck? I was going to say, just get a rope and tie him down. If you're worried about him. I want to take the legal responsibility of somebody, you know, to fly into the inner space. Sorry, delayed an hour that time, huh? Anyway. Okay. Notice the first argument, he says, huh? In that fifth paragraph again. But since time seems especially to be motion and change, huh? This ought to be looked into. And now he argues. The change in the motion of each thing, however, is only in the one changing, right? Or where the one moving and changing is, huh? But time seems to be, what? Everywhere and among all things, right? So if you're walking down the hall, and I'm walking in the woods, right? Your walking is, what? In the hall where you are, right? And my walking is in the woods, right? But it's at the same time, right? And it seems to be both. And where you are and where I am at the same time. So that's one reason why he argues about it being simply a, what? Motion or change, huh? Even he said it was the motion, say, of the sun around the earth, right? Where is that motion? It's up there where the sun is, right? You're assuming the sun's going around the earth. Okay? See? Why time seems to be down here and everywhere, huh? Further, he says, change or motion is faster and slower, while time is not faster and slower, huh? Now, let's stop again in that for a bit, huh? Because you hear people say that the time went, what? Yeah. The time went fast. Gee, the time went fast. It seems like you just got there, you know? When the students are seniors now, like around graduation time, you know, you always hear some students saying, listen, I just got here yesterday, you know? As a freshman, now he's graduating and going on other things, right? But it's a common statement of people, huh? Okay? I suppose that's very common people coming back on vacations, too, you know? It's just, they're back on a job, you know? Okay? But notice, if time, the fact that we speak of time as going faster or slower is a sign that we think a bit of time as being a, what? Emotion, right? That could go faster or slower, huh? Just like you could walk faster or slower, so time could, you know, go faster or slower, right? You know, okay? But as he points out, fast and slow are actually determined, what? By time, right? For the fast moves much and little time, and the slow little and much, huh? But time is not determined by time, huh? Neither as regards how much it is, nor as regards how it is. It is clear, then, that it is not motion, okay? And he says, for the present, let there be no difference for us to say motion or change, huh? Notice Aristotle speaking there, right? Just like in the premium there to wisdom, right? When he was distinguishing art or science from, what, experience? And he made no distinction there between art or science, but he says, kind of a footnote there that, quote, in the text, you know, we've spoken in the Nicomachean Ethics, right? In the Ethics there about the difference between art and science and foresight and so on, right? But he's not concerned with the difference between them there, but just the fact that what they have in common, that distinguishes them from experience, huh? Okay? Well, here he's not yet concerned with making any distinction between motion or what, change, huh? So, notice in those two arguments, he's reasoning that time is not motion. or change, right? And therefore, in a way, he's going to conclude that it's, what, something of change, right? But he takes, in a sense, the other, what, alternative that it's, nothing to do with change, right? And he checks that, right? For neither is it without change, right? It's not change, but it's not without change. Okay? Just like we can say about motion, right? Motion is not the thing in motion, but it's not without the thing in motion. Right? Therefore, it's something of the thing in motion, huh? Okay? Just like you might say, the shape of my body is not my body, but it's not without my body, either. Therefore, the shape of my body is, what, is something of my body, huh? Okay? Or you may just, you know, say what I want to say there, my shape. Okay? My shape is not my body. It's not without my body. Therefore, it's something of my body. Okay? Now, what is it of my body? See? Well, it's the termination of my body, or something like that, right? Okay? It's a limit of my body, or something of that sort. Okay? So, likewise, he's saying something like that here, right? It's not change or motion, but neither is it without change or motion. Okay? For when we do not change at all in thought, So, we do not change at all in thought. So, we do not change at all in thought. So, we do not change at all in thought. So, we do not change at all in thought. So, we do not change at all in thought. So, we do not change at all in thought. Hill Mountains, right? Yeah, what's his name? Winkle, Rip Van Winkle. Rip Van Winkle, yeah. It's a very famous story, right? But it appears in the collection called, what? The Sketchbook, right? Yeah. Okay? Just as The Legend of Steepy Hollow. A lot of times, you know, they pull out The Legend of Steepy Hollow or Rip Van Winkle and you get them in a separate, what? Edition, right? Story, right? So if you go down to the Hudson, one of the main bridges across the Hudson is called the, what? Rip Van Winkle Bridge. And it's near where the Catskills are, right? Where the story's taking place. And in that area sometimes they buried, you know, a treasure that people can try to find. So it's sort of interesting, huh? But notice, what happened to Rip Van Winkle? You know the story, huh? He went up where? Up into the mountains, right? To hunt or something. Okay, yeah. He ran to these strange characters, right? And he had a slug of their whiskey and so on. And he fell asleep. And this is sometime before the, what? American Revolution, right? And he was asleep for what? Ten years, I guess it was, huh? See? And so he wakes up. He thinks, what? Oh, my God. I say, I'm going to be in trouble with the mistress. And, you know, his gun is rusted and everything, right? And he goes down to the village and things look different, right? Things have changed and different people living in their houses and so on. And they kind of think he's kind of a madman, right? And the old sign used to be there of Kim George, huh? Oh, yeah. Now it's got some guy called George Washington, you know, on the side. They paid it over. Hence George Washington. Instead of George III, was it? And, you know, there's some kind of a political rally going on. And, who are you for? I'm for the king, he says. He's trying to get in trouble with, you see. It's only gradually that he begins to realize that he spent, all this time has passed, huh? See? I knew a man who was in the Second World War. I was in the airplane flights over, what, Normandy, huh? And he's only, like a kid, 17, I guess, at the time. And Gunner, I guess, is his position. But he says the first day we went over there, we didn't hit too many targets because you were flying pretty high. Second day we went over there, they told us to fly low, huh? Hit your targets. So he said you would, you know, go to confession and communion maybe, but that's it. You wouldn't really eat anything to speak of because you were just, what, you know, you get so tense, huh? And then when you get off the airplane, you know, as you walk off the air, there's little cups of scotch for you to drink, right? To calm you down. And he didn't really care for scotch, you know, but one time I come back and he takes the two scotches, right? And goes to bed, you're just exhausted, right? And he's stuck for two days. So, sometimes people in the hospital or something, you're wrong, you know, they sleep for a couple days. I mean, you don't know this is possible, but you wake up and you think it's, what, the next day and it's actually, what, two days. But you're not aware of any, what, motion going on. So it's as if, what, there's been no passage of time, huh? For he says, for they joined together the later now and the earlier now, making them one, right? So when he fell asleep, right? And when he woke up, right? They take as being more or less the same now, huh? And if it's the same now, then there's really no, what, time in between, right? Just as if the now was not other but one and the same, time would not be, right? So since it's being other is hidden, huh, you take it as being one and not two, there does not seem to be time in between. That's interesting, huh? Because you've got to see the earlier and the later now as being two nows, right? Before you're aware of time, right? And that's going to be connected with time and, what, number in some way, because two is the first, what, number, right? Unless you have two nows. You don't have any, what, time, right, huh? If you're just one now, you'd have no time, right? And the person's been asleep, right? But now when he, he falls asleep now, and he wakes up now, and there are two different nows, but he's, what, things are the same now. Did I go off? I'm sorry. I'm apologetic like that, huh? When I was in college there, there was a, used to have these kind of windows where he kind of cranked them out like that. And this one classroom had a kind of a loose window, and this one student had fallen asleep, you know. And the wind blew the window and banged like that, right? And he, oh, don't look at this, with some kind of a swear word, you know. As a priest teaching the class, oh, oh, oh. So he's apologizing for it. But some people, you know, they doze off, and they don't realize they've dozed off, right? And so they think, you know, it's the same now, right? And so we do it later now. So not aware of the passage of what? Okay. So he's at the top of page five now. If then it happens to us not to think there is time when we do not distinguish any change, but the soul seems to remain in something one and indivisible. And when we sense and determine, then we, they're true nows, right? Then we say there has been time. It is clear that time is not without motion. That should be or, I guess, without motion or change, huh? Okay. So the conclusion then is it is clear then that time is neither, what, motion nor without motion, right? As I said there with the definition of motion itself or with my shape and so on, right, huh? You could proceed in a somewhat similar, what, way, huh? Okay. That it's not this, but it's not without this, huh? What is poetic meter? Hmm? Is it syllables? Just syllables. Say? Some kind of syllables? Mm-hmm. Say? But is it without syllables? Poetic meter is not syllables, but it's not without syllables. Therefore, it's something, what, of syllables. Yeah. Okay, the next question is, well, what is it of syllables? Well, it's an order, right, of accented and unaccented syllables, huh? Or it's an order of long and short syllables, maybe in Greek or Latin, huh? But in English meter, it's an order of, what, accented and unaccented syllables, okay? You have one accented syllable and one accented, or vice versa, right? Or two unaccented and one accented. Or the reverse of that, huh? Those are the main ones, huh? So there's a lot of things that have to be defined in this way, huh? And even when we study the definition of soul sometime, right? The soul is not the body, right? But it can't be defined without the body. That's why it's difficult to understand the human soul, because the human soul can be without the, what, body, right? Unlike the other souls, huh? So it's kind of a special thing, isn't it, right? It's not a body, but it can't be defined without a body. It's not a body. It's not a body. It's not a body. It's not a body. It's not a body. It's not a body. It's not a body. It's not a body. It's not a body. But it can be with our body. It's kind of strange, huh? Well, with Thomas in the commentary on the soul there, he compares the definition of what? The soul to the definition of an accident, not because the soul is an accident, right? But because, like an accident, it has to be defined as something, what? Of another, right? That's why Aristotle, in the seventh book of wisdom, when he's talking about definition, he says that either only substance can be defined, an accident cannot be defined, or accident is defined in another sense of the word definition than substance, huh? Because the word definition means what? It comes from the word limit, yeah. Phinis in Latin means end or limit. And in Greek you see sometimes the word oros, O-R-O-S, or Omicron, or O-O, but it was an H with an accent, ah. But that means limit in Greek, right? See? Or sometimes they call it a horizmos, huh? It's like the word for, what, horizon, right? The horizon is that line that, what, separates the sky from the earth, right? Okay, so it's the idea of a limit here, huh? But the idea of a limit seems to mean what? When you draw the city limits of Worcester, all Worcester and every bit of Worcester is inside those city limits. And no bit and no part of Worcester is outside those city limits. And no other town whatsoever, right, is at all within that, what, city limits of Worcester. I live in Shoesbury, but no part of Shoesbury is within Worcester. Worcester tries to, you know, time to swallow something because we're kind of a wealthy suburb, you know, but Shoesbury always says no. It would be a much better, you know, snow shoveling that than the city of Worcester has, you know, on our side streets and so on. So, but when you define an accident, you have to, what, put in its limit, something other than itself, because you have to define it as something of another. It's something of something that isn't. And so you have to bring in something other than itself into its definition. Well, that seems to be contrary to what a definition is. So you don't really have a definition of accident, or if you want to say you have a definition of accident, it's a little different meaning of the word, right? So those things that have to be defined as something of another, they have to be defined that way because that's what they are. And that's why we say, in logic, as Monsignor taught us, you can't, what, entirely divorce logic from things and have a purely formal logic like the modern magicians want to have. Because something as basic as definition, you have to take into account the difference between something that can be defined just by itself, right, and something that has to be defined as something of another. You see that? And so you have to take into account somewhat what it is that you're defining. Not every difference in things gives you a different kind of definition, right? But surely there's a difference in the kind of definition you need for, what, defining a substance and for defining an accident or defining something that is something of a, what? Of another, right? Okay. And maybe when you define something like blindness, that's, again, another kind of definition. Because that's really the negation, the non-being of something else, right? It's not something of another, but it's the negation of it. So notice how the connection now between the last sentence in the 16th reading, it is clear then that time is neither motion nor without motion. And now the starting point in the 17th reading for the next part of the investigation. Since we seek what time is, right, we must begin to grasp what it is of motion, right? Okay. It's not motion, but it's something of motion. What it is of motion, right? For we sense motion in time, what? Together, right? Notice Aristotle's way of proceeding here, you know, I kind of borrowed and imitated back in the first book of natural philosophy there when I was pointing out that changes between contraries. And the first way we see the changes between contraries is by induction, right? And we see in the fragments of Heraclitus how he's already making that induction, dry things, you know, wet things dry out and so on, healthy become sick and so on. And then you see Plato in the Phaedo giving that induction, right? It's more full than you find it in the fragments, but the same thing basically. And that's really the basic way Aristotle was coming to that, by induction. But then sometimes I give a second way of kind of manifesting this. Remember what I did? My 10 o'clock, 11 o'clock example. Remember that? I said, if you're told that X is, let's say, soft at 10 o'clock and it's what? Cold at 11 o'clock, would you recognize that a change had taken place? X, whatever X is, right? X is what? Soft at 10 o'clock, it's cold at 11 o'clock. Would Sherlock Holmes know that a change had taken place? Well, the same thing could be what? Soft and cold, like ice cream, let's say. Likewise, if you were told that at 10 o'clock X is what? Hot, right? And at 11 o'clock it is hard, right? Would you know that a change had taken place? No. Because it could have been all along a hot stone, right? So it would have been hot at 10 and it would have been hard at 11, right? Without having changed at all. But if you were told that X was soft at 10 and hard at 11, then you'd know a change had taken place, right? Yeah. Okay? Well, oh, if you knew it was what? Cold at 10 and hot at 11, right? Okay? But it's because they're opposites, right? So in a sense, I was saying you don't really perceive change unless you see some kind of what? Opposition, right? And that's kind of a sign that, what, change involves opposites, right? Okay? That's kind of imitating what Aristotle does here, right? Where he says that we don't, what, we sense motion and time together, right? Okay? So it's not exactly a proof that they're together, but... Well, it is a proof, but it's only a sign of it, right? A proof in the sense of a sign, right? That we don't perceive it any other way, right? The two are somehow connected, huh? Mm-hmm. Okay? Just like if I said, you know, we never perceive motion without perceiving something in motion, some body or something, right? Okay? The guy whacks the ball and presumably in the infield there you don't see the ball at all. How would you know that they're knocked out of the ballpark, right? You wouldn't know, would you? I listen to the St. Paul Saints and other little kids, you know, you had on the radio, and that ball is way, way up in the Coliseum! Of course, I know what the Coliseum do is kind of a Greek temple, you know? I imagine this ball going to top this Greek temple, you know? But it's some kind of roller going to go right outside the Lexington ballpark, right? So the ball got knocked out of the ballpark. Yeah, it'd be... Right there in the Coliseum, you know. But if you couldn't in some way, what, see the ball going down the ballpark, right? Or, you know, if it's going into the stands at the other side, right, trying to grab the ball and so on, you wouldn't perceive the motion, right? You know, okay. If it was dark and underwent nothing through the body, that's again the, not he, but some motion was in the soul, right away it would seem that some time had been, huh? Now, you're reminded there a little bit of what, Richard II there, right? Richard II, you know, loses his throne, right, to Henry Bodenbrook in the play, right? And he ends up in, what, prison eventually, right? Eventually he's killed, right? Prison there, but he's, what, weeping, right? And so, this is the way he's aware of the passage of, what, time, right? And Shakespeare actually says, now has time made me her, what, numbering clock, right? Oh. And we'll see the importance of number here later on as he gets into talking about time, huh? But also, when there seems to have been some time, at once some motion seems to have been, huh? So we see where the sun has gone down the sky, right? Or the clock has gone around more, right, huh? Or the sand has fallen through the, what, through the thing, through the lower one, yeah. Thus time, he says, is either motion or something of motion, huh? Since it is not motion, as we saw in the previous reading here, it must be something of motion, okay? Okay, now, in the next paragraph, right, he's going to point out how distance, right, and the motion over this distance, and the time it takes to go that distance, right? How, in a way, the before and after, the continuous character of one of these follows upon the continuous character, right? And the before and after and the other, so if I start down this road from here to there, right, my motion from here to here will come before my motion from here to here, right? Okay, and you can divide it similarly, right, huh? Okay, and this, just as this part of the road is before that part of the road, so the motion over this part is before the motion over that part, huh? And likewise, the time it takes me to get from here to here is before the time it takes me to get from here to there, right? Okay. Now, this is something that he's going to examine more fully in the, what, sixth book, right, which I'll look at after this, because the sixth book is the book about the continuous, huh? But there we'll see how close is the, what, the continuity of distance and the continuity of the motion over that distance and the continuity of the time it takes to go over that distance. And the, the, how the way the before and after one is followed by the before and after in the, what, other, right? Okay? And, uh, but here he's not trying to go into this fully like he will in book six, but here he wants to get the idea of the before and after here, right? Because that's going to be important for, what, understanding time, right, huh? Okay? Since the moved is moved from something to something, and every magnitude is continuous, motion follows the magnitude. Because the magnitude is continuous, motion is also continuous, huh? And because motion is, time is, huh? As much as the motion, so much does the time always seem to have been, huh? Okay? And of course, sometimes we, what, measure the motion, it seems, by the, what, time, and sometimes in a way vice versa. Okay? Because we can go, what, a longer distance and more time, right? And vice versa, to go a longer distance, it takes more time, right? Okay? Now, remember what the continuous is, huh? What is the definition of the continuous, huh? Divisive and forever. Yeah, yeah. And actually, as we said before, there's also a definition of the continuous that we give in logic, right? Okay? Common room. Yeah, that, it's a quantity whose parts meet at a common, what, boundary, right, huh? Okay? But then we meet this other definition in book six, but he's touched upon it several times already, that continuous is that which is divisible, what, forever, right? Okay? Now notice, huh? If you can divide forever this line, this road down which you're moving, right, won't you be able to divide the motion forever, right, and therefore the time forever, right? Okay? Now, I think we showed a little bit of that before, we'll come back to just a little bit here. Sometimes Aristotle will show that the magnitude is divisible forever, and then the reason for that, that the other two are divisible forever, right? Sometimes he will, what, take a couple of these together and use them, right? So he uses the idea of the, what, faster and slower, right? Okay? And we all know that some bodies are faster and some are slower. In race, you can see this, right? Okay? And you say, now, what does it mean to say that this body is faster? Well, it means that it, what, covers the same distance in less, what, time. And the slower body covers the same, what, yeah, yeah. Now, could you use that to show that both time and distance are divisible forever? Or you can say, okay, we're present by a line in both of these, time and distance. And you say, okay, this distance is covered by the, what, faster body in that time. Okay? Or let's start the other way around. Oh, okay, let's do that, okay. Now, at that same time, the slower body is going to cover the same distance? Less distance. No. If it covers the same distance in the same time, it would be just as fast, right? Right. So if it's slower, it must cover not the same distance, but a lesser distance, right? I don't care how much lesser that is, but it's got to be lesser, right? Okay. Now, if the slower body is covered this distance in that time, how long do you take the faster body to go this lesser distance? Less time. You can't say the same time, because then it would be a clean path. You'd be contradicting yourself, wouldn't you? Mm-hmm. Okay. Therefore, it must be in a, what? Lesser time. Okay, how much lesser, but it's got to be a lesser time, right? Okay? Now, if the faster body in this lesser time covered this distance, then in this lesser time, the slower body would cover what? Less distance. Less distance. Now, did the faster body cover that lesser distance in the same time? No. It could be fast, right? It could be contradicting, right? So that's the one I'd say. So all you have to do is alternate those two, and you realize that the time, the distance, must be divisible, what? Forever. Forever, right? Okay? Okay? Notice you can kind of make an analogy there when you start to talk about thinking, right? See? Um, if thoughts were, what? Continuous, right? Then the thinking would be, what? Continuous, right? But if the thoughts... If we're not divisible for our right, then the thinking is not what? Continuous, huh? And our thought's divisible forever. And one way we saw that was in reasoning or defining, right? If you know something by reasoning or defining, not every part of the definition, not every part of every definition, is what? Able to be defined, right? I know, so when you define something, you in a sense break it into more particular thoughts, right? You see? So when I define the square as an equilateral and right-angled quadrilateral, I have three thoughts there, quadrilateral, equilateral, and right-angled, right? Now, if each of those could be broken down into other ones, as some of them so they can, and this went on forever, then thoughts would be what? Divisible forever, right? Okay. But if that were so, would you really ever understand what anything is, huh? No. So thoughts are not divisible forever. Now, likewise, the syllogism, right? If you have every C is B and every B is A, therefore every C is A, you can kind of break down every C is A into every C is B and every B is A. But if they are turned broken down into something and then into something else, then these thoughts would be divisible forever, right? But in that case, you'd never come to, what, know anything by reasoning. Now, there's other ways of kind of seeing that thoughts are not continuous, because, because of this infinite divisibility, you never have a next longest line, right? Or a next, what, shortest line, right? This line is longer than that, right? But whenever length is longer than that, you can cut that in half, right? So which is the next longest line? There's no simply next of those, you could say. Yeah, this is, yeah. This is not, but you put another line there between those, right? Because it continues indivisible forever, you never come to a next longer line. Yeah. Or a next shorter line, right? And that's the difference, a difference between lines and numbers, right? Because if you have the number seven, there's a next greater number, right? Sure. Which is eight, and there's a next lesser one, right? Mm-hmm. Okay? But in the case of lines, there's no next longer than next, right? Yeah. As you ever notice in the text of Aristotle sometimes, or in Thomas, you know, we'll use the word next, right? Next. But in the case of the definition, in the case of syllogism, is there a next thought, huh? Let me take my example here. Every, every mother is a woman. No man is a woman. Every mother is a woman, and no man is a woman. What's the next thought? No man is a mother. No man is a mother, right? No man is a mother. Is there some statement that comes between these two? Between the premises? And I'm getting to write this very clearly, huh? Every mother is a woman, and no man is a woman. Is there some statement that comes between the premises and the conclusion? So there is a next thought, right? Okay. Now, the same way in defining, right? You start off with quadrilateral, and then you add to that equilateral, and then you add to that right-angled, and now you've got to what? Square, right? Is there some thought that comes between these three and square? No. So you see, the likeness they're defining and what? Syllogizing, right? So there is a next what? Next thought, yeah. So thoughts are not, what? Continuous, right? They're not divisible forever. That's one sign. That's the basic reason. But also the fact that there's a next thought. But in the case of continuous, there is no next. So if you, you know, by kind of analogy, say that thinking is moving over your thoughts, right? But the thoughts are not continuous, therefore the thinking is not, what? Continuous, huh? Now, sometimes we do speak, and I do, I think it's an interesting way of speaking. We do speak sometimes, I do, of continuous definitions, right? And I do speak of continuous syllogisms, right? But sometimes we use the word continuous in talking about numbers, too. Even an example I gave you there. We speak of, like, you say 4 is to 6, as 6 is to 9. 2 is to 3 is 4 is to 6. You might say that 4 is to 6, as 6 is to 9 is in continuous, what? Proportion, right? What does that mean? Well, it means that the end of 1 ratio is what? Beginning of the year. Yeah. By here, the end of 1 is not the beginning of the next, right? But this doesn't mean it's continuous in the way we define continuous, right? But there's a certain likeness because of what? What's in an aspect of the continuous? The same. The parts meet at a common boundary, right? So you might say, you know, that this point here is the end of this line and the beginning of that, right? Or the line, the border there between the United States and Canada. Well, it's the end of America, the United States rather, and the beginning of Canada. Right, right, huh? So at the end, you're one being the other. So when the conclusion of a syllogism is a premise in another syllogism, right? You see it all the time in Euclid, right? You know, you've done the first book of Euclid, right? The conclusion of one syllogism or one demonstration is a premise in the next one, right? So it's a continuous reasoning, we say, right? But you've got to be careful that the word continuous there is not in exactly the same sense, is it? And the same when we speak of a line of thinking, right? Or I'm always following Heraclitus and the other Greeks and Aristotle and Plato and speaking about a road in our knowledge, right? But a road, in the original sense, is something, what? Continuous. Continuous, yeah, yeah. But that's a certain, what, likeness, not because it's a before and after in our knowledge, right? Yes. And we first see before and after in the, what? I can go back to the basic text there on before and after, on the word before in particular, in the categories we read there, remember? The first meaning of before he gave was before in time, right? Okay. Now to that sense would be reduced before in, what, motion, and before in, what? Magnitude. Yeah, in place, yeah, yeah. And notice again, to go back to that simile of Shakespeare, how closely there we did, right? He's talking about time, right? He says, like, like, like is the ways make towards the pebbled shore, so do our minutes hasten to their end.