Natural Hearing (Aristotle's Physics)
Lecture 89: Zeno's Paradoxes and the Problem of Motion

Transcript
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I wonder if we're going to get each other's attention, right? You know? I've got to shake on somebody, you know, to get their attention, you know? You know? Once you see God face them, I don't know if we're going to be... I don't know if we're going to be preoccupied. Now, Ben de Croceau was saying that Purgatory is the second best place to be. I mean, it is, I can see where it is in a sense, but we'll be the second happiest, so to say. Does St. Thomas say anything about Purgatory? I mean, some people say it's a place of torture and torment, in a sense it is. Yeah, he talks about Purgatory, you know, but doesn't go into great details of it, right? You know, read that St. Catherine of Genoa, she talks about Purgatory, yeah. She seems to say that, I think, that's Rebecca. Yeah, yeah, she gives you some insight into Purgatory, what's like? I imagine in Purgatory you're completely cut off, kind of, from the distractions of this life, right, huh? Mm-hmm. You know? And there's some clarity as to what this is all about, right, huh? You know? And you want to see God, right, huh? You know? And so you must be in some kind of extreme, what, agony, because, you know, you want to see him. But you want to be purified at the same time, see? That would imply some type of knowledge about us, deeper knowledge than we have now, of what heaven's like, wouldn't you say that? Yeah, yeah. But I mean, you know, even as he speaks of the peculiar clarity that hell forts. But the same way, in Purgatory, see, I think what you have to realize, in a sense, is that in a Peteric vision, we not only see God as he is, God is only what we see, but he's also the form by which we see, right? In other words, God is to be joined to our mind, right? Oh, yeah. So he's both that, what we see, and that by which we see, huh? Oh. Okay. God is the form by which we see. Yeah. Yeah. Because he's joined to our mind. Yeah. We can't see him by a created species, right? We'll be able to do that. So, um... That's incredible. He's joined to our mind. Yeah. But notice, scripture speaks metaphorically as a kind of marriage, right? Between our mind, huh? Okay? But it's much more intimate than marriage, right? You see? I think the metaphor is useful in a sense, because you want to unite yourself in marriage to just anybody, right? You know? There's got to be a love between you and so on, right? And, uh, so, um, God's not going to join himself to us until we're completely, what, purified of all these extraneous, what, affections, right? Mm-hmm. All these disorders that we've built up in our, in our life, huh? Oh. Nothing, none of the file type. Yeah. That's right. The St. John of the Cross says, even if a thread is holding you down, it's, that's, it's, you've got to start a break today, a thread, right? Mm-hmm. Mm-hmm. Then how is it that, it's sometimes said that when someone, right when they're baptized, Mm-hmm. if they died, they went out to go to purgatory. They wouldn't have to know. So it's you. But, but they, they died every time. But, um, if I was baptized, 30 or something, I was, after I baptized that day, I still have the attachments to earthly things that I had the day before I was baptized. It's more in your body than in your soul, those things. More in your body. Mm-hmm. But don't I still have some vices in my soul? Mm-hmm. If, if I was, if I had even pride or envy as a vice, and I got baptized, um, I would still be inclined after my baptism. No, but I, I don't, I don't, I don't, you know, there's any impediment there to the vision, right after baptism. But then, then purgatory isn't, then, to purify those. I mean, I mean, Tom, Tom says, you know, I mean, if one's love of God was strong enough, it would, what? Not only eliminate purgatory, but eliminate, you know, the necessity of any, uh, reparation, right? In itself, right? Mm-hmm. That's an essential thing there, to love God, huh? So that love of God was so intense, right? He wouldn't bring up all the, heh, disordered affections, huh? No, it would be possible in that situation that they wouldn't have as high a degree of glory as some saints who maybe spent, maybe some people spent a long period of time in purgatory, right? Yeah, that's true. That's true, yeah. Yeah, yeah. Would it be because maybe, like Father Anki said, I see that that makes sense, that basically they would, after the baptized, before they still have those vices, they could never possibly die when God went out, so to say, quick enough so that they didn't commit some type of sin. I mean, the... I see. I see. I mean, I see. Well, what's that part of the reason why so many people was at concert time, somebody who delayed their baptism until the last minute, you know? A non-binary man. Yeah. Yeah, yeah. There's a true story, a man who was, like, a drunk or something, and he went to confession and killed himself, and he left a note, because he said, if he wanted to die, I have to give me a confession. I guess he was kind of expecting that. Yeah. But isn't that difficult? I mean, when you... Sometimes they explain purgatory as, like, the purification of our attachments and vices and things. Yeah, but there's something about the effect on my soul, though, of my repeated bad acts, right? You know, that the person who's baptized doesn't have, you know. He's born again, really. It's hard. I think there's still vices that haven't changed. Well, maybe what's infused there overcomes that, right? Infused is so strong there. It's a special grace, the baptism that actually takes care of those vices initially. Yeah, or counteracts. Yeah. Yeah. There's a point there of the spiritual exercises of St. Gertrude the Great. Have you ever seen those? Very interesting, right? One exercise is to regain innocence of your baptismal day, right? Mm-hmm. Very interesting. That's just one of the seven meditations, yeah. The seven exercises she has is to regain innocence of your... So that's part of the grace of baptism. You get this supernatural power to overcome whatever vices you've had. Mm-hmm. Mm-hmm. Wow. That makes sense. That's what I'm talking about. So then you can see that even if you couldn't even really judge of yourself, even though you might perceive that you saw vices and attachments. You get everything about baptism really is. It really is a, what? A birth, right? Like we're saying up there, you know. I mean, they... You know, there's a first incident when you're born, right? I mean, that's not... That's not a exaggeration if Christ says it, right? Unless a man be born again, right? He is. So then there's... Even after someone's baptized, they still require... in this life, purification of things in themselves that aren't purified. They'd have to go through these purifications and things of their soul, but then it seems those purifications that the person says to go through, sometimes it's said those are the same as purgatory in this life, but it seems they're different. You have to purify the roots of these habits and things that you still have, but it would seem from this, just because the person baptized can go straight to heaven, even though the heaven might still need to reach greater sanctity, they have to go through dark night and things like that. But those things really aren't correctly compared to purgatory. It's something different. They're doing something different in their soul than purgatory would, because the person baptized would still need to want them, but they wouldn't need to go to purgatory. But they still need to go through dark nights if they're going to get to the same thing. Kind of like a correlation to that. It seems like there are people who are, at least my person, just getting baptized, getting married. In the name of the Father, and of the Son, and of the Holy Spirit, Amen. God, our enlightenment, guardian angels, strengthen the lights of our minds, order and illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor, help us to understand all that you've written. But tomorrow is the what? Ascension, right? Okay, do you all know who Zeno is? Yeah, he's a pupil of Parmenides. And in this dialogue, called the Parmenides of Plato, Parmenides and Zeno, they come to Athens, and they talk to Socrates, who's a young man. And they examine Socrates, and Socrates getting into contradictions. The same thing that Socrates does in the other dialogues as an older man, right? He's undergoing himself as a young man from Parmenides and Zeno. And there are references to this in other dialogues, too. Like in the sophists, you know, Socrates says, Yes, as a young man, I met Parmenides and Zeno and so on. And so they speak very reverently, they're Parmenides. But what Parmenides insisted upon is the impossibility of what? Change. Of being and not being, right? But because people like Heraclitus had spoken as if change involved, day being night and the young being the old and one opposite being the other, then he said there's what? It's an illusion of change, right? Okay. And that's kind of one of the famous dichotomy, right? Human thought. But if you had to choose between these two guys, if you had to choose between holding on to the impossibility of something both being and not being, right? Or the existence of change, if change involves something both being and not being, which would you hold on to of those two? The impossibility of being and not being. Yeah. But probably in the history of human thought, you have more people holding on, right? to the reality of change than to the impossibility of being and not being. So which is really more known to us, huh? And more certain, huh? It seems as though change is because it's just so strong in our experience. Yeah. It's because, as Shakespeare says, things in motion. Soon you catch the eyes and what not stirs, right? So since our knowledge starts with our senses, and motion is what gets the attention of the senses, most people tend to follow that, right? Okay. But Permanente says no. Permanente says that this is the beginning, among statements anyway. Not that change exists, but it's impossible to be and not be, huh? And he says only a two-headed mortal could think that something both is and is, what? Not, huh? It goes against the very nature of the mind, how to think that. Well, if you had to choose between the two, because change involves a contradiction, in a way you'd be already admitting the principle of Parmenides, because the impossibility of contradiction and change apparently, what? Contradict each other. So, in making a choice, you're already accepting the principle of what? That Parmenides insisted upon as being first. And furthermore, those who are challenging that principle because something seems to contradict it, right? They're saying it isn't so because it is so, right? If something contradicts it, it can't be true. Why not? Because you can't accept the contradiction. Well, that's what his principle is, right? So, it's kind of, the very attempt to reject the principle is based on the principle, right? It's like I was saying about statements there, you know, the man who says, statements don't exist. He can't say that without, what? Contradicting himself. Yeah, and without making a statement, right? So, it's kind of hopeless, right? To try to say statements don't exist and try to maintain that, huh? So, Parmenides, as Plato says, is a man to be feared, huh? But at the same time, you can say it's obvious that change does exist, right? So, therefore, there must be a way of understanding change which does not involve a, what? A contradiction. Contradiction, yeah. Yeah. But it's not really until Aristotle that they see the way out of these apparent contradictions and change. We saw one back in Book 1 and we see another one here in Book 6, huh? And that's kind of the key to the human mind going forward, huh? It's major steps, huh? That it never accepts a contradiction in the things that it's studying, right? But it's always running into what seems to be a contradiction. And that's always pointing the way to where something is hidden that you have to, what, unravel and discover it. But before Aristotle, it seemed like you had to choose one or the other, huh? And so people are making fun of Parmenides, you know, and throwing things at him to see if he ducks. Which would be a sign that he really knows that change is existing and something is moving towards him. Right. With somebody like Parmenides, since he doesn't want to accept a contradiction, wouldn't people like that, because why wouldn't they see that, well, maybe there is a way of explaining change which doesn't allow the contradiction? Well, it's not easy to unravel these. Oh, oh, I know it's a difficult problem, but nevertheless, maybe he could just leave it at the level of a problem. Well, you see, Zeno came to the defense of his teacher, right? So he tried to find other, right, absurdities in saying that change exists, right? Okay. And so Aristotle will be talking about some of these objections of Zeno, right? Okay. But notice it's more appropriate to bring Zeno and his objections in here in the sixth book than back in book one, right? Okay. There you had some of the difficulties that Parmenides brought out, but Zeno going on to further difficulties. Now, he's going to go through about, or touch upon, anyway, six different arguments of Zeno, right? But he pulls one of them out and briefly refers to it here in the beginning because it connects to what has just been seen before. But today he's going to enumerate four arguments from local motion, really, and then another argument from becoming, and then another argument against circular motion in particular. Okay. So he says, Zeno misreasons if he says everything always either rests or is moving when it is in a place equal to itself. And the thing carried along is always in the now. The arrow carried along is immovable. But this is false. Apparently, Zeno is saying, but in the now, the body is in a place, what? Equal to itself. And so long as it's in a place equal to itself, it's not in motion, but it's at rest. So in every now, it makes up time. it's at rest. So during the whole time it's supposed to be in motion, it's always at rest, huh? Okay. And Aristotle's saying, well, that's assuming that time is made up of what? Indivisible nows, right? And we've rejected that for anything continuous, right? That'd be made up of the indivisible. For time, he says, is not put together from indivisible nows, just as no other magnitude, what, is, right? Okay. But now he's going to enumerate the four reasons of Zeno, huh? There are four reasons of Zeno about motion, and I think it's locomotion you're talking about here, changing place. Giving difficulty to those untying them. The first is the one about not moving because one must arrive at the half before the end, about which we have distinguished in the aforesaid reasons. Let's restate that argument a bit, huh? You think you can walk out that door, don't you? Well, before you can walk out the door, you've got to walk, what, halfway to the door, right? So you're still not out, are you? Now before you can walk the rest of the distance, you've got to walk half of that, right? You're still not out, right? And before you can walk the remaining distance, you've got to walk out of it first. And you're still not out, right? Well, of course, there's going to be always another half of whatever remains, right? Because of the infinite divisibility, huh? So there's always going to be another destination you've got to get to before you're going to get out the door. So it should have you out the door, right? Okay, so don't try to get out. It's obviously hopeless. Okay? Now, Aristotle gave a kind of, Thomas says, a kind of ad hominem reply to that in the earlier part, saying that time is divisible as much as distance, right? So, if you keep on dividing the magnitude infinitely, you're dividing the time infinitely. So you have as many nows as you need in the time, right? For all these places you've got to get to, right? Okay? So in a finite time, you can go a finite distance because they're both, you know, made up of infinity of parts, so to speak, right? Okay? One-to-one correspondence there, huh? Okay? But that doesn't really solve the objection because if you imagine each of these halves you're going to go to as actually distinct, right, then it's like what? Counting to infinity, isn't it? Yeah. See? You know, as a little child during the alphabet, you know, A-D-C-D-E-F-T, you go through it, right? And the kid, you know, what good boy am I or whatever the thing you say at the end, right? But if there was an infinity of letters, right, could the kid ever go through the alphabet and recite it? Okay? In the same way in reasoning, right? You know, if you look at Euclid there, sometimes you use A to prove B, right? And B to prove C, and C to prove D, right? And so on. And so you go through kind of a long chain there to arrive, a large discourse, as Shakespeare might say, to arrive at a conclusion. But there was an infinity of statements you had to go through. Infinity inclusions you had to draw in order to arrive at some theorem. Would you ever arrive at that theorem? See? Okay. In the same way in defining, right? Sometimes Euclid defines something by something, and before he defines it by that, he defines that thing itself, right? So he defines square by quadrilateral, right? But before he defines square by quadrilateral, he defines quadrilateral, right? And he defines quadrilateral by rectilineal plane figure, but before he defines quadrilateral by rectilineal plane figure, he defines rectilineal plane figure, right? And before that plane figure, and before that figure, right? Now if that went on forever, right, so you have to define infinity of things before you can define anything, would you ever define anything? No. No. See? So if you actually had to meet all these points, right, between here and the door, right, since it continues as divisible forever, you'd never get out, right? So the solution to that is what? Oblability. It's able to be infinitely divided. Yeah. Yeah. You're going a finite distance, which is divisible forever, but you're not actually what? Divided it actually, huh? Each one of these, huh? Okay. That's a very interesting difficulty that Zeno has there, right? Yeah. He's making something that's there in ability, actual, right? Yeah. But as I said in quoting Feitzacher there, that when we imagine something, we make it actual in our imagination. Oh, yeah. The senses and imagination, they don't really know ability, huh? And when you sense something, it's got to be actual to sense it. When you imagine something, you make it actual in your imagination. So you're making all these points that you could, what, divide the line into, you're making them actual in your imagination, or trying to anyway, right? And then you've got a problem that you can't really, what, solve, right, huh? Just like, you know, what's his name, John Locke there, right, huh? And he's saying, you know, what is triangle in general? What are the three lines in the definition of triangle in general? Are they equal or unequal, or, you know, are they going to get right angles or good angles? And he doesn't know what to say, so he says, it's all and none of these, right? You know? Well, he's in apparent contradiction there, right? But it's all of these in ability, potency, yeah. None of these in what? Act, right? And the difference makes actual something there that's in ability, right? So when I add equilateral to triangle, right, I make actual something that the three lines were able to be all equal. If I add scatine, I make actual some other ability, right? But in each one of these, I make actual just one of the abilities. I don't make actual, in one of the same triangle, equal lines and unequal lines, okay? So, um, I guess it's in the eighth book, on, that he gives this more full solution to it, right? Okay. Now, the second is the one called Achilles, huh? And I don't know if Thomas gives the, this explanation there of what the word, why it's called the Achilles, huh? Apparently Achilles in the Iliad is a very, what, swift runner, right? You know, he gets in the struggle there at the river, right? He almost gets, the river God gets mad at him, right? Because he's polluting the sacred river with all the bodies he's killing and the blood and so on. And he has to run a big hurry, right? To escape the God, right? To the river, huh? So, um, this was the argument then that Achilles, who's swifter than a turtle, let's say, right? Okay? If you give the turtle a little head start, even Achilles, the fastest runner of all, will never, what, catch him, right? Okay? Now, how does that argument proceed, huh? Whereas I was going to say it's really, in substance, the same as the first argument, but it's based on, but he says in Greek, it's said with a, um, a certain tragedy, he says. As I translated there, speaking tragically, huh? In the Latin it says, you know, tragedy. But tragedy is supposed to, what, strike the imagination with wonder, huh? Strange and wonderful things, huh? Okay? El Madze, you know? So, the argument gets stated with a way to, what, strike the audience, right, huh? More so than the one about trying to get out the door, right? You see, this guy, no matter how fast he can run, no matter how slow the turtle or something else is, if you give it just a little bit of head start, he's never going to, what, catch it, right? So, how does it proceed here, huh? This is that the slowest runner will never be overtaken by the swiftest, huh? For it is necessary that the one pursuing go before to where the one fleeing starts off, huh? And in the time it takes him to get up to where the other one got the head start, right? The other one will have gone some distance, right? And then, again, before he can go beyond him, he's got to get up to that next place, right? In which time, however short it takes him to do that, the other one will have gone a little bit further, right? Now, how does that, in a sense, be the same as the other argument, right? See? Well, let's just take a simple example here. And then they can give us what the ratio is. Let's say you have something that is twice as fast, right? Okay? So that when one goes this distance, the other would go, presumably, twice as long, right? Okay? So, let's say, you give the slower one, called an S here, you give him a head start, let's say, one of these units, right? Okay? Now, the faster volume now is going to start here, and the shorter one is, or slower one, has been given this head start, right? So, before he can go beyond there, he's got to get up to this line right here, okay? Now, in the time it takes him, we'll call this time one, to get up to that line, right, the shorter, or slower one, I'm going to say short all the time, the slower one will have gone, what, half of that distance, because he's half as fast. So, in T1, he'll be out to here, okay? Now, time 2, the faster body has to get up to that point, okay? And in the slower body, we'll, what, go half of that, in time T2, okay? And, again, in time 3, if you have some time, you get up to that point, and at half of that distance, he will have gone already further, right? In T3, okay? Was he ever going to catch him? Never, right? I'm kidding. But that's what's taking place here, right? If this guy is twice as fast, right, the place where they should meet is at this, what, distance, right? See? In other words, if this slower guy is, you know, he's got this head start, and he's twice as slow, or when half is fast, rather, when the fast body has gone here, this one has just gone that same distance, right? Okay? And then, from then on, he's going to be ahead of him, right? Okay? But, as you're dividing this, what are you doing? See? He's never going to reach that point where they're going to catch up to him, because you're taking, what, let's say this is one mile, and this is two miles, right? I think, okay? Well, he's never going to go two miles, right? Because he's given one mile to begin with, and then he goes a half a mile, and then a fourth of a mile, and then an eighth of a mile, and then a sixteenth of a mile, and then a thirty-second mile. But he's never going to reach two miles, is he? He always takes half of what he means. So, in effect, it's the same thing as, what? He's never going to get to the doorway. He's never going to get to that point where the two of them would be, what? Uh, together. And then one is about to overtake him, right? So, it's the same argument, but it's said with a, what? A sort of trabudia, right? I see. And Thomas says a magnifying of words, right? To move one bit, right? Okay? But, um, I notice that, you know, myself sometimes with, with, uh, uh, some of the theorems in Euclid, right? That if you restate them in a different way, they arouse more wonder, right? Okay? You know, that theorem I like so much there, the one, number five in book two, right? And if you know the theorem there, it says you divide a body into, I mean, a line into equal and, what? Unequal segments, right? The, um, square contained by the equal segments, right? You know, which are, it's two sides and you complete it. Will always be greater than the, a rectangle contained by the equal segments, right? By the square on the distance, what? Between them, right? That's interesting in itself, I think, right? Okay? But, when you stop and think about that, if you think of this as being the, what? Uh, perimeter of a rectangle, right? You can see that you can have two rectangles, and you see a rectangle in the broad sense now to include square and oblong. You can have two rectangles with exactly the same perimeter, but one of them has more area. See, that kind of rouses us into wonder, right? That the same amount of fence, you know, to make it kind of concrete for the student, um, I can impose in a rectangle more property, right? Than someone else with the same amount of fencing, right? And then because of that distance, it's actually possible, you know, to construct a rectangle with more area and less perimeter. See? And that really surprises people, right? You see? It's sort of the quad bellum fragilia, I like to say, right? You see? It's all around wonder, right? See? Now, I told you that proportion I use, and I say that the, the words of the, what? Uh, the words in some sort of what you're saying, something like perimeter is to the area you cover, right? Or contain. And just as it's possible, you know, to contain more area with less perimeter, so it's possible to say more with your words. See? But it's probably more surprising to them that you can say more with less words than a page or two of, or a style or something, you might be getting more than a book than some other course. See? But you see, that's like this other thing here, and they at first would think it's impossible to, what? Have less perimeter, and yet have more, what? Yeah. They said the ancient, you know, crooked geometers, and wanted to use their knowledge to buy and sell land, they would sell by perimeter, and so they give you more perimeter, but less area. So if you trade a piece of property that's got more perimeter for less perimeter, you think, well, you, I'm making out, right? I mean, if you're getting, you know, one with more perimeter for less perimeter, and actually the guy who's getting the less perimeter might be getting more area, because he knows his geography, right? See? So it's kind of contrary to what people would think, and it kind of surprises them, right? So I get a lot of things out of that one theorem, you see, but kind of re-stating it in different ways, huh? It becomes kind of striking, huh? Even the theorem where I could state it there, you know, it seems to me, we've stated that the rectangle contained by the equal segments plus the square on the side on the line between the points and section is equal to the square on the half, right? It's not as striking as if you say, I ask this question, now, will the rectangle contained by the equal segments be greater than, less than, or equal to the rectangle contained by the equal segments? See? And they probably wouldn't know at first what to say, right? See? And so, the first kind of surprise is, the rectangle contained by the equal segments will always be greater than the one contained by the equal segments. That's interesting, isn't it, in itself, isn't it? Right? You see? And then there's still, you know, an admiration for that. But how much more do you think it will be? I don't know. Always by the square on that line right there. How simple that is, right? The square on that line, huh? The distance, the difference in length between either the longer and the half line, or the shorter and the half line, you know what? It's the same distance here, right? Between this and this, and between this and this, right? It's an amazing thing, right? You know? You can take the difference and always be the same, you know? And it's kind of amazing to see that, huh? It's like you've got a square in that, huh? So sometimes when things are stated in a little different way, they're substantially the same truth, right? You're dealing with. But it's more, what? It arouses more, what? Wonder, huh? Wonder, huh? Wonder, huh? Wonder, huh? Wonder, huh? Wonder, huh? Wonder, huh? So substantially though the same foundation is the first argument, right? Because you're making actual, right? All those divisions, right? And so you never reach a certain limit, even in a finite what? Distance, right? For when it is ahead, it will not be overtaken. But nevertheless, it will be overtaken if one grants it the limited can be gone through. That should be the limited there. Okay. It's the same reason fundamentally, right? In a limited time, right? It's unlimited in potency, right? But limited in distance. So those first arguments are solved in the same way, right? As far as the truth is concerned, they're going to be solved later on in the later books by the maintaining that the, what? All those divisions are not, what? Actual. Actual, yeah. Not to count them all, right? Okay? Okay. So you've got to take account of that tendency of us to want to make, what? The potential, right? The possible, the what is able to be actual, right? To make it more actual than us, right? It's in danger. Considerable danger in doing that, huh? Monsignor Dion used to talk about this tendency of the human mind to want to make words univocal and kind of avoid this equivocal. I was first, in fact, Monsignor a little bit concerned about John St. Thomas, right? Because he was teaching, you know, the sacraments and the genus and sacrament there is sign, right? And John St. Thomas makes sign kind of univocal, huh? To the sensible sign and to the mental sign. If you go back to Thomas, it's always an objection, you know, huh? Do the angels have signs? Can they signify to each other what they think? Well, sign is something you can sense, and they don't have senses, so... So it's always, you know, an extended meaning, right? But a different meaning of the word sign, huh? Right? And, you know, the classical definition of sign is the one that goes back to St. Augustine, right? You know, a sign is that which strikes the senses and brings to mind something other than itself, right? Okay? But it's always, in its original meaning, something you can, what? Sense, huh? And if you use the word sign for something you can't sense, you're not using the word in exactly the same meaning anymore. See, even John St. Thomas, he tries, you know, gets his name because he's always following Thomas. He's trying to make something univocal, right? That's really equivocal. Equivocal by reason, huh? So you find that, huh? It reminds me of this here, right? This is a different thing, but there's something like that, huh? Trying to make what is there, an ability, actually there, huh? Now, the fourth argument is somewhat quite different, though, from what's gone before, huh? The third reason, right? The third, yeah. Well, the third was the one he spoke about just at the beginning of this because it was connected with the thing before. The third reason is the one spoken about just now, that the arrow carried along stands still. So, this results from taking time to be composed of nows. This not being given, there will not be a, what? Syllogism, right? So if you look at time as being composed of nows, it would seem that in each now, there's no, what? Motion, right? That the body's at rest in each now, right? And if time's composed of nows, then the whole time, it must be at rest, even when it's supposed to be, what? Moving, right, huh? Okay? So this is the one that he began? Yeah, yeah. And he says, you know, this reason. Yeah. And Thomas says he referred to that in the beginning because it's connected with what has just gone before, right? But then he puts it in order among the various reasons of Zeno, right? As being the third reason he gave. He refers to it at the beginning of the reading because it's related to what we have said before, right? Oh, yeah. Yeah, okay. That the continuous is not composed of indivisibles, right? Yes. But apparently there's a third reason among the ones that Zeno gave. Okay. Louis de Broglie, the great French physicist there, the father of wave mechanics, refers to this Zeno, right? One of his books, huh? Physics and Microphysics. And Einstein wrote the purpose of that book, right? And so that's what he really enjoyed in the book. This discussion of, you know, what happened in physics and quantum theory. And it kind of looks back to the problems of, what, Zeno, huh? Because in a way, you know, with things like instantaneous velocity, right? You were kind of having motion in the, what, indivisible, right? And so that, you know, fully maybe unfolding it, Louis de Broglie was aware of the fact that there's some connection between the problems in quantum theory and the difficulties that Zeno was bringing out, huh? And Schrodinger says, you know, there was reason to wonder whether there wasn't something fictional about this instantaneous velocity, right? But they used it in Newtonian physics, huh? And they tried to, you know, put together straight line motion and motion in a, what, circle, right? And the straight line, as you know, in geometry, is tangent to the circular at one point, huh? So there you've got, you know, a coinciding there, right? A straight line motion and, what, circular motion. If there's any motion there in the indivisible, right? You know, but there ain't such a thing, huh? So it's kind of interesting that Einstein singled that out as something he particularly, what, liked, huh? Of course, in English edition, they don't translate the whole chapter, that whole chapter, which is unfortunate. I've got the French edition there and got the Xerox copy of that particular chapter, but... Now, the fourth argument, huh? I've always puzzled exactly how you should understand that, but I think I'll give one explanation of how you could understand it. The fourth is the one about the equal masses in the race course move contrarily alongside equal ones, some from the end of the race course and others from the middle, in which he thought it would happen that the half-time is equal to the whole. The misreasoning is in thinking that the equal magnitude and equally fast is moved alongside the moving and the resting in equal time, but this is false, huh? And then he starts to exemplify it in the next paragraph, huh? Now, it's kind of, I seem to be a puzzle of exactly how the example is set up, but I think the point is, it's easy enough to see. And this may not be exactly how you set it up, but let's do it this way. Let's say we have these magnitudes, simplify it here, A, A, A, okay, you know, equal. And then we have, let's say, these two here, B and B, okay? And then we have C and C, so that A, B, and C are all equal, right? Okay? Okay? So, the B's are moving in the contrary directions from the C's, right? Okay? Now, when the B gets down to the end of the A's, where will the C's be? Yeah. Okay? So, B will have gone by one A, right? Okay? But the B will have gone by how many C's? Two. Two. Yeah, yeah. So, you've got the double and a half there, right? Uh-huh. You know? It's going, what? Things that are... Equally fast, right, are going what? One twice as fast as the other, right? Okay? How does it follow that it's twice as fast? Just because it's moving too? Yeah, because he's going to go beyond this C and beyond that C, right? So he's going to cover a distance of two C's, right? While the C's here, compared to the A's, anyway, will have covered what? One A, right? Okay? Okay, so equally fast bodies, B and C, right, traveling equally fast, B will travel twice as far, right? Okay, so equally fast will be twice as fast as the... In relation to what? That's the point, that's what I'll say, right? Because in one case, you can take it in comparison to a what? Body in rest, right? In some case, to a body in what? Contrary motion. Yeah, yeah. And it makes you think, you know, if the other thing makes you think of quantum theory, it makes you think of relativity theory, right? Yeah, yeah, yeah. That's that, right? You know? Where something, you know, relative to one thing is at rest, relative to something else is in motion. Mm-hmm. You know? But Aristotle says the fallacy, of course, is in taking it in comparison to something at rest, in comparison to something, right? In motion, right? But if you measure, you know, the B by A, it's gone this distance, right? If you measure it by C, it's gone two Cs. Mm-hmm. Okay? So those four arguments are in terms of what? Difficulties in the most known kind of motion, which is change of place, right? And often in English when we say motion, we're thinking of change of place, huh? Now, in the next paragraph, towards the bottom of page 14, nor is there anything impossible. Now he's talking about change between, what, contradictories, right? Nor is there anything impossible for us in the change between contradictories. Now, what was the argument, apparently, of Zeno in this case, huh? Well, he says if you have a change between contradictories, let's say when a man dies, you go from being a man to not being a man, right? Are you changing from being a man to not being a man when you're still a man? That's before the change has begun, right? Are you changing from being a man to not being a man when you're not a man anymore? Change is complete, then. Yeah, yeah. So, you have to both be and not be a man, apparently, right? When you're changing, right? Okay, you're back to this kind of contradiction there, right? Okay. Now, the way Aristotle solves it here is more in terms of the fact that we saw before that what changes is a body, right? Something that has extension, right? So, it's possible to be white and not white because in between being fully white and being what? In no way white, huh? If you're changing from one to the other, right? Okay. So, if you have something that is divisible like that, right, then you can have what? Something in between, right? Okay. But later on, in book 8, they'll solve the other part more, but does the change from being a man to not being a man take any time? No, unless you take with it, what Aristotle says, is these changes in something else, right, that is disposing for death, right? Okay? So, I'm out there in the snow, they're freezing to death, right, huh? You know? My temperature's going down, right? It's taking some time for my temperature to go down from here to here, right? But, the change from being alive to being dead is going to be what? Instantaneous. Yeah, yeah, yeah, yeah. And in that, if you take that time which I'm freezing to death, right, the end of that time is a now in which I'm what? Dead, right? See? And there's no last now in which I'm what? I'm alive. Alive, yeah. So, will death ever come to you when you're alive? That's a great consolation of the, of the, of the, of the, uh, of the Koreans, right, huh? Don't worry about death, it never happened to you during your life at all. You'll never die during your life. So, you'll never be dead during your life, right? And you become dead in that, the last instant, right? The last, the now which is the end of that time which you die. So, when you actually become dead, you will not be alive, so, don't, that's, uh, hope that consoles you. I think Koreans, you see, want to enjoy life, right? How can you enjoy life when you're going to die, right? You know, it's going to happen to me, some day I'm going to die. Well, no, you're never going to die. Don't be around there to experience your own death. Now, the last argument, in a way, is, uh, in some ways very weak, huh? What is he talking about in the last argument? About a circular motion, right? You imagine a sphere revolving, right? Okay? The sphere is remaining in the same place, isn't it? So, how can you have motion when something remains in the same place? It remains in place in the other part. Yeah, yeah, I mean, it seems to me kind of very simple to solve that, right? The one part is succeeding to the part of the other, right? Okay? Thomas does the same thing if you imagine a column or something, you know, rotating, right? One part is entering into what the other part is, right? Okay? Nevertheless, there's a difference between that kind of motion and the motion of something which, as a whole, is going from one place to another, right? You know? It's a strange kind of change of place, isn't it, huh? Yeah. You know? But still, there's, what? One part succeeding to where the other part was. It goes along, you know? So, Zeno's here not to come back and give us some more things, more objection, but apparently he was picking up these things, you know, one after another, right? In order to defend his, what? Mentor. His master, yeah, yeah. The great, the great parmenides, huh? Okay. And, you know, when Plato says that, or represents Socrates as learning what we would call the Socratic method, right? Whether that's historical, I don't think is the most important point, right? I think the point is that the Socratic method involves seeing whether, what? What do you think fits together with other things you think, right? Or whether something you think eventually contradicts something else you think, right? Okay? The simplest example of that is the, what? The slave boy, right? Okay? But you can see in the slave boy there that three admissions is all Socrates needs to get you in a contradiction. Because people don't maybe contradict themselves directly, right? Immediately. But from two things they say, you can syllogize to the contradictory of a third thing they say, right? Okay? So the slave boy is saying that the way to double a square is to double the side, right? Okay? Then you take an example of that, and it doesn't matter what the example is, but you take, what? Two, let's say, and four, right? Three, and obviously four is double two, right? And he thinks that the square whose side is twice as long is twice as big, therefore the square should be twice as big as that, right? But you calculate this out, and it turns out to be four and sixteen, right? And the slave boy doesn't think that sixteen is double of four, right? Okay? So sixteen is not double of four, but four is double of two, and the square whose side is twice as long is twice as big. Do those three things fit together? Okay? So what you need is really three admissions, huh? Two of which...