Natural Hearing (Aristotle's Physics)
81. Zeno's Paradoxes, the Socratic Method, and the Four Kinds of Conversation
https://berquistcourse.com/course/philosophy/3-natural-hearing/081-zenos-paradoxes-the-socratic-method-and-the-four-kinds-of/

[0:03] 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. Saint Thomas Aquinas, angelic doctor, help us to understand all that you've written.

[0:41] 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?

[1:35] 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 Sophist. You know, Socrates says, "Yes, as a young man, I met Parmenides and Zeno, and so on, and

[1:55] so they speak very reverently of their Parmenides, but what Parmenides insisted upon is the impossibility of what? Change of being and not being, right?

[2:11] 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?

[2:29] An illusion, change, right? Okay. And that's kind of one of the famous dichotomy, right, in human thought. 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,

[3:00] if change involves something both being and not being, which would you hold on to, 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.

[3:31] So, which is really more known to us, huh? And more certain, huh? It seems as though change is because it's it's just so strong in our experience. Yeah, it's because Shakespeare says, "Things in motion soon catch the eyes and what not stirs," right? So, since our knowledge starts with our senses and motion is what gets the attention, senses,

[4:03] most people tend to follow that, right? Okay. But Parmenides says no. Parmenides says that this is the beginning among statements, anyway. Not that change exists, but it's impossible to be and not be. And he says only a two-headed mortal could think that something both is and is what not.

[4:35] It goes against the very nature of the mind to think that. Well, if you had to choose between the two, because change involves a contradiction,

[4:57] 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.

[5:27] And furthermore, those who are, you know, 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, can't be true. Why not? Because you can't accept a contradiction. Well, that's what his principle is, right?

[5:52] So it's kind of the very attempt to 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,

[6:08] 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? Okay.

[6:26] 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's 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 in change. We saw one back in Book One, and we see another one here in Book Six, huh?

[7:04] That's kind of the the key to the human mind going forward, huh? In its major steps, huh? That never accepts a a contradiction in the things that'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, right?

[7:31] But before Aristotle, it seemed like you had to choose one or the other, huh? And so people were making fun of Parmenides, you know, and supposed throwing things at him and see if he ducks, which would be a sign that he really knows that change is existing and something is moving towards him. There's

[7:54] somebody like Parmenides, since he doesn't want to accept a contradiction, won't won't people like that? Because why won'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. 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?

[8:25] So he tried to find other right proofs 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, huh?

[9:01] 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's connected with what has just been seen before. But today he's going to enumerate four arguments from local motion, really, and then another argument from

[9:32] 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.

[10:12] So in every now that 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. Aristotle is 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?

[10:50] Okay. Okay, but now he's going to enumerate the four reasons of Zeno. There are four reasons of Zeno about motion, and I think it's locomotion you're talking about here. Change your place. Giving difficulty to those on time now. 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?

[11:24] You think you're going to 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 got to walk half of it first.

[11:49] You're still not out, right? Of course, there's going to be always another half and whatever remains, right? Because the infinite divisibility, huh? So there's always going to be another destination you got to get to before you're going to get out the door. So you never get out the door, right?

[12:11] 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 got to get to, right?

[12:43] 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, 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?

[13:10] Then it's like what counting to infinity, isn't it? Yeah. See, you know as a little child you learn the alphabet, you know A B C D E F G. You go good, 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?

[13:33] 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 if there was an infinity of statements you had to go through, infinity of conclusions you had to draw in order to arrive at some theorem, would you ever arrive at that theorem?

[14:05] 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 or rectilineal plane figure, he defines rectilineal plane figure, right? And before that plane figure, before that figure, right?

[14:41] Now if that went on forever, right? So you have to define an infinity of things before you can define anything. Would you ever define anything? No. No. See. So if you actually had to

[14:58] meet all these points, right, between here and the door, right, since it continues as divisible forever, you'd never get out, right? Yeah. So the solution to that is what? The ability that 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? Dividing it actually, huh? Each one of these, huh? Okay. That's a very interesting

[15:37] difficulty that Zeno has there, right? Yeah. He's making something that's there in ability actual, right? Yeah. But as I said, quoting Weizsäcker there, that when we imagine something, we make it actual in imagination. I am. 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 imagination. So you're making all these points that you could what divide the line into.

[16:12] You're making them actual in your imagination, or trying to anyway, right? And then you got a problem that you can't really what solve, right? Huh?

[16:25] 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? The definition, the triangle in general? Are they equal or unequal or you know are they meeting at right angles or acute angles? And he doesn't what to say, so he says it's all none of these, right? You know. Well, he's in apparent contradiction there, right?

[16:50] But it's all these in ability, potency, huh? None of these in what act, right? And the difference makes actual something there that's an 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 scalene, I make actual some other ability, right? But in each one of these, I make actual just one of the abilities.

[17:22] I don't make actual in one the same triangle, equal lines and unequal lines. Okay. So, I guess it's in the eighth book now that he gives us more full solution to it, right? Okay.

[17:45] Now the second is the one called Achilles, huh? And I don't know if Thomas gives the best 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, I guess in the struggle there at the river, right? He always 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?

[18:20] To escape the god, right? To the river, huh? So this was the argument then that Achilles, who's swifter than a turtle, I'd say, right? Okay. If you give the turtle a little head start,

[18:41] even Achilles, the fastest runner of all, will never what catch him, right? Okay. Now, how does that argument proceed, huh? Where else I was going to say it's really in substance the same as the first argument, yeah. But it's based on. But he says in Greek it's said with a. A certain tragedy, he says, as I translated there, speaking tragically. huh In the Latin, it says "quodam tragoedia you know, tragedy.

[19:17] But tragedy is supposed to what? Strike the imagination with wonder, huh? Strange and wonderful things, huh? Okay, So the argument is stated with a way to what? Strike the the audience, right? Huh? Even more so than the what about trying to get out the door, right? You see, this guy, no matter how fast he can run, no matter how slow the the turtle or something else is, if you give it just a little bit of head start, he's never going to what?

[19:54] Catch it. How's it proceed here? 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? Okay. And then again, before he can go beyond him, he's got to get up to that next place, right?

[20:33] In which time, however short it takes him to do that, the other one will have gone a little bit further, right? Okay. 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?

[21:07] Okay. So, say you give the slower one, call him S here, you give him a head start, let's say one of these units, right? Okay. Now,

[21:26] the faster body now is going to start here, and the shorter one is, the 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 said shorter time, the slower one will have gone what half of that distance because he's half as fast.

[21:59] Yeah. So in t one, he'll be out to here. Okay. Now, time two, the faster body has to get up to that point. Okay. And then the slower body will what go half of that in time t two, okay? And

[22:26] again, in time three, it takes some time to get up to that point, and at half of that distance, he will have gone already further, right? In t three. Okay. Was he ever going to catch him? Never, right? Okay. But that's what's taking place here, right? Um, if this guy is twice as fast, right? The place where they should meet is at this what distance, right? See.

[23:01] In other words, if this the slower guy is, you know, they've got this head start, and he's twice as slow or half as fast, rather.

[23:14] When the fast body has gone here, this one has just gone that sitting 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? 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 two one mile, and this is two miles, right?

[23:40] 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 eighth of a mile, and then sixteenth of a mile, and then thirty-second of a mile. But he's never going to reach two miles, is it? He always takes half of what remains.

[24:01] 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? Together, and then one is about to to overtake it, right? So it's the same argument, but instead with a what? Traboudeia, right? And Thomas says a magnifying the words, right, to move wonder, right? Okay. But I notice that you know myself sometimes with with some of the theorems in Euclid, right, that if you restate them in a different way, they arouse more wonder, right?

[24:46] Okay. You know that theorem I talked so much about, the one number five in book two, right? And if you know the theorem there, it says if you divide a body into, I mean, a line into equal and what unequal segments, right? The square contained by the equal segments, right? You know, which are its two sides being completed, will always be greater than the a rectangle contained by the equal segments, right?

[25:17] By the square on the distance what between them, right? That's interesting in itself, I think, right? Okay. But you stop and think about that. If you think of this as being the what perimeter of a rectangle, right? You can see that you can have two rectangles, 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.

[25:50] See that kind of arouses some wonder, right? They have the same amount of fence, you know, to make it kind of concrete for the student. I can enclose 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?

[26:21] You see, it's sort of a quadrum fragulia, I like to say, right? You see, to arouse wonder, right? See, and I told you that that proportion I use, and I say that the the words of the what

[26:39] the words are centered what you're saying, something like perimeter is to the area you 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 fewer words. See, but it's probably more surprising to them that you can say more with less words than

[27:08] a page or two of Aristotle or something. You might be getting more than a book in 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 with less area.

[27:42] So if you trade a piece of property, it's got more perimeter for less perimeter. You think of you, I make an L, right? Yeah, I mean, you're getting a you know more perimeter for less perimeter. Actually, the guy who's getting the less perimeter might be getting more area because he knows geometry, right? See, so it's kind of contrary to what people would think, and it kind of surprises them, right?

[28:03] So I get a lot of things out of that with the theorem, you see, but kind of restating it in different ways becomes kind of striking, huh?

[28:14] Even the theorem it stated there, you know, it seems to me we stated that the rectangle contained by the equal segments plus the square on the side on the line between the points of 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?

[28:47] 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 equal segments will always be greater than the one contained by equal segments. That's that's interesting, isn't it itself, isn't it? Right. You see,

[29:12] and then when they're still in admiration for that, but by 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, 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?

[29:41] 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 got to be that square, 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?

[30:12] It rouses more what? Wonder, huh? But substantially, though, the same foundation as 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?

[30:48] For when it is ahead, it will not be overtaken. But nevertheless, it will be overtaken if one grants that the limited can be gone through. So should be the limited, limited there. Okay. You know, it's the same reason fundamentally, right? In a limited time, right?

[31:08] It's unlimited in potency, right? But limited in distance. Okay. 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 later books by the maintaining that the what? All those divisions are not what? Actual. Actual, yeah. Not to count them all, right? Okay. So you

[31:46] got to take account of that 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 it is, right?

[32:03] It's in danger. Considerable danger in doing that, huh? Monsignor Dion used to talk about this tendency of human mind to want to make words univocal and kind of avoid this equivocal.

[32:25] I was first got 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

[32:43] John St. Thomas makes sign kind of univocal, huh? to the sensible sign and to the the mental sign. And go back to Thomas. It's always an objection, you know. 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, right?

[33:12] And you know the classical definition of sign is the one that goes back to Saint 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? If you use the word sign for something you can't sense, you're not using the word in exactly the same meaning anymore.

[33:39] So even John St. Thomas, who tries, you know, gets his name because he's always following Thomas. He is trying to make something univocal, right? That's really equivocal, equivocal by reason, huh? So you find that

[34:02] reminds me of this here, right? This is a different thing, but there's something like that, huh? Yeah. Trying to make what is there an ability actually there.

[34:21] Now the fourth argument is somewhat quite different, though, from the what's gone before. 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.

[34:49] 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 is at rest in each now, right? And if time is composed of nows, then the whole time it must be at rest, even when it's supposed to be what moving, right?

[35:18] Okay. This is on that he began. Yeah, yeah. He says Zeno's reasons. 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?

[35:47] Oh yeah. Yeah. Okay. That the continuous is not composed of indivisibles, right? Yes. But apparently it was the third reason among the ones that Zeno gave. Okay. Louis de Broglie,

[36:05] 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 preface to 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, because in a way, you know, with things like instantaneous velocity, right?

[36:32] 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 is some connection between the problems in the in quantum theory and the difficulties that Zeno was bringing out, huh?

[36:55] And Schrödinger says, you know, there was reason to wonder whether there wasn't something fictional about this instantaneous velocity, right? But they used in Newtonian physics, huh? And they tried, you know, put together straight line motion and motion in a what, circle, right? And straight line is, you know, in geometry, is tangent to the circular at one point, huh? So there you've got, you know, a coinciding there, right?

[37:24] A straight line motion and what circular motion? If there is any motion there in the indivisible, right? You know, but there isn't such a thing, huh? So it's kind of interesting that Einstein singled that out as something he particularly what liked, huh?

[37:46] First, in English edition, they don't translate that whole chapter, that whole chapter, which is unfortunate. I got the French edition there and got the Zerox copy of that particular chapter, but

[38:01] okay. Now the fourth argument, boy, is 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 moved contrarily alongside equal ones, some from the end of the race course and others from the middle, in which he thought would happen that the half times equal to the whole.

[38:30] 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 should do a puzzle over exactly how the example is set up, but I think the point is easily enough to see, and this may not be exactly set up, but let's do it this way anyway.

[39:02] Let's say we have these magnitudes simplified here, A, A, you know, equal, and then we have, let's say. These two here, B and B, okay, and then we have

[39:27] C and C, so that A, B, and C are all equal, right? 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?

[39:52] The other end of the other A. Yeah. Okay. So B will have gone by one A, right? Okay. But the B will have gone by how many C's? Two. Yeah. Yeah. So you 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.

[40:26] How does it follow that it's twice as fast just because it? Yeah, because. He's gonna be on this C and be on that C, right? So he's gonna cover a distance of two Cs, right? Why the C's here compared to the A's, right? Will have covered what? Only one. One A, right? Okay. So equally fast bodies B and C, right? Travel equally fast. B will travel twice as far, right?

[40:59] So equally fast would be twice as fast. 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. It makes you think, you know. If anything, makes you think of quantum theory. Makes you think of relativity theory. That's right.

[41:25] Where something, you know, relative to one thing at rest, relative to something else is in motion. You know. But Aristotle says the fallacy, of course, isn't taking it in comparison to something at rest and comparison to something right in motion, right?

[41:47] But if you measure, you know, the B by by A, it's gone this distance, right? If you measure it by C, it's gone two Cs. Okay.

[42:10] Okay. Those two 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?

[42:31] Now, in the next paragraph, towards the bottom of page 14, nor is anything impossible. Now he's talking about change between what? Contradictories, right? Nor is there anything impossible for us in the change between contradictories. And 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?

[43:06] Okay. Now you're changing from being a man to not being a man when you 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.

[43:26] So you have to both be and not be a man, apparently, right? When you are changing, right? Okay, 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?

[44:00] If you are changing from the 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, Book Eight deals with the other part more. But

[44:22] does the change from being a man to not being a man take any time? No, unless you you take with it, what Aristotle says is these changes in something else, right? That is disposing for death, right? Okay. So I am out there in the snow. They're freezing to death, right? Huh? You know, my temperature is going down, right? It's taking some time for my temperature to go down from here to to here, right?

[44:51] 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 in which I am freezing to death, right? The end of that time is a now in which I am what? Dead, right? See, and there is no last now in which I am what? Alive. Alive, yeah, yeah. So will death ever come to you when you are alive?

[45:23] That's a great consolation of the of the of the uh the uh the Epicureans, right? Don't worry about death; it never happened to you during your life at all. You never died during your life.

[45:38] Son, 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 when you die. So when you actually become dead, you will not be alive. So don't let's hope that consoles you.

[46:00] Every Epicurean wants to enjoy life, right? How can you enjoy life if you are going to die, right? You know, it's going to happen to some someday. You are going to die. Well, no, you never going to die. Don't be around there to experience your own death.

[46:22] Now the last argument. In the way is somebody's very weak. What is he talking about? 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?

[46:47] So how can you have motion when something remains in the same place? One part very takes place in the other part. Yeah, yeah. I mean, it seems to me kind of very simple to solve it, right? The one part is succeeding to the part of the other, right? Okay. Thomas says the same thing. If you imagine a a column or something, you know, rotating, right? One part is entering into the other part, is right?

[47:16] Okay. Now, of course, there is 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, so it's a strange kind of change of place, isn't it? Yeah. You know, but still, there is what one part succeeding to where the other part was as it goes along.

[47:42] So Zeno's here not to come back and give us 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? With that historical, I don't think is the most important point, right?

[48:15] I think the point is that the Socratic method involves seeing whether what what do you think fits together the other things you think, right? Or whether something you think eventually contradicts something else you think, right? Okay. A 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.

[48:48] 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 this doesn't matter what the example is, but you take what two, let's say, and four, right?

[49:22] And obviously four is. Double two, right? Okay. And he thinks that the square whose side is twice as long is twice as big. Therefore, this 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.

[49:53] 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?

[50:09] Okay. So what you need is really three admissions, huh? Two of which. You can reason to or calculate would give you the contradictory of the what third thing right you see just like you know take a simple example now if I say that the the width of this rectangle is two and the length is six you can't just mean contradiction

[50:41] but then if I add but the area is ten now something's wrong right see and this doesn't tell me which is wrong but can these three be all correct no because two times six would be twelve ten divided by two would be five you see so any two of these contradict the third one right okay

[51:13] of course you reject the one which is least known right or unknown right so if the slave boy is very sure that four is double of two and very sure that sixteen is not double of four then he's going to reject the idea that doubling the side will double the what area look at Einstein there in the evolution of physics he says that the theory of relativity arose from a contradiction right and he points out the statements that are really the contradiction right and then the reason why they rejected this one because it didn't have the experimental evidence that the other ones had right you see so this is what Socrates does with the man right he examines he says he doesn't say you're true

[51:59] or false he says what do you think you know you tell what you think right I I want to say that third admission can be dangerous right because he may be able to take two of your admissions and deduce the contradiction of the third one so this is some example of the dialogue he's doing that thing basically again and again so the Socratic method of examination is in a way based upon the truth of what Parmenides insisted upon that something can't both be and what not be right according to what he said that the way double squares double the side and four is double of two this square is now double of that right but it's not double that because sixteen is not double so

[52:50] from some things he says it is and other things he admits it is not double of that right but can't both be double and not double look at it so Socrates' method is based upon the possibility right that something can both be and not be right okay same time same way and the same so in that sense it's Illuminating, right? That Plato represents Socrates as learning the Socratic method from Parmenides and Zeno, right?

[53:25] Because it does have a connection there. It's interesting that sometimes they accuse Socrates of being a sophist, right? If he's trying to get you to refute your, you know, contradict yourself, right? Well, when Aristotle talks about the four conversations, these four logical conversations, argumentative conversations, he distinguishes between the examination conversation, which Socrates is very fond of, and the sophistical conversation, right? And he wrote the book called "On Sophistic Refutations."

[54:09] Refutation involves what contradiction, right? But a sophistical refutation is not a true refutation. You didn't really contradict yourself, but I give the appearance to people watching that you have contradicted yourself, okay? And so, but in the examination conversation, the idea is to find out if you really are contradicting with yourself, right? You see, and therefore, the examination conversation is is could lead to a true refutation, right?

[54:40] Okay. So, what are the other two? Demonstration. Yeah, the teaching conversation and the dialectical conversation, right? Okay. You see, they're all found in the dialogue called the Meno. Because in the first conversation that Socrates has with Meno, Meno

[55:16] claims to know what virtue is, right? And Socrates says, "Well, tell me what it is, right?" And eventually, we see that what Meno does not know what he claims to know, right? Okay. Now, at the end of that, Socrates proposes that they put their heads together and try to figure out what it is. He's proposing really a dialectical investigation of what

[55:44] virtue is, because Socrates says, "I don't know what virtue is either," right? Okay. Now, if you have two guys, neither of whom knows, then they should put their heads together in the sense that two heads are better than one. And now, what does it seem to you? You know, go back and forth dialectically, right? But at that point, Meno comes in with a sophistical objection against the very possibility.

[56:16] Of investigating what you don't know, and he says, "How can you direct yourself to what you don't know? " Right? Think me coming into the the filling station, gasoline station, saying, "How do you get there? " Where do you want to go, buddy? See? Why? How do you get there? I don't know where I'm going.

[56:42] See? How can you possibly direct yourself to what you don't know, right? See? You can't do that, right? See? So this is an objection that would seem to destroy the very possibility of logic and logistic, these arts that direct us in coming to know what we don't know. Okay. And Socrates tries to reply to that, but he falls into the same kind of mistake that Mino made.

[57:12] Okay. Then later on, he has two conversations with the slave boy. And the first conversation is an examination conversation, like I was repeating here on the board, huh? Okay.

[57:25] Now, notice, huh? An examination conversation is necessary sometimes because it's not always clear who knows and who doesn't know. So sometimes you have a would-be teacher, like Mino is going to teach Socrates what virtue is, right? But the would-be teacher doesn't know what he claims to know, right? So he should be a co-investigator rather than a teacher. But then you have the should-be student, but he also thinks he knows, but he needs to be taught, and so he what?

[58:02] Has an impediment to being taught until you convince him that he doesn't know what he thinks he knows, and now the should-be student will maybe be a student, right? At least he's as humble as a slave boy, right? But now the second conversation that Socrates has with the slave boy is, although he denies it, right, he's really teaching the slave boy how to double the what? The square, right?

[58:27] Okay. He helps the slave boy order his thoughts, right? And eventually, the slave boy can see that the the diagonal of the original square, right, would be the side of a square twice as big, huh?

[58:42] But notice, on the teaching conversation, should take place when one man knows, right, and the other man doesn't know, right? And then the man who knows should teach the man who doesn't know, right? So Socrates, although he may not know what virtue is, right, he does know how to double a square, right? The slave boy doesn't know how to double a square. In fact, he's mistaken about how to do so, right?

[59:10] But after he's purged of that mistake, right, now he'll want to know, right? And Socrates says to Mino. And then Socrates can teach him how to double square.

[59:24] Now, finally, in the dialogue, the third part of the dialogue, Meno still wants to know whether virtue can be taught, even though he doesn't know what virtue is. And Socrates says, "Well, we can't really fully know whether it can or not be taught until we know what virtue is, right? But if you twist my arm, right? I'll examine the matter, right? And so he reasons with probability that it can be taught, right?

[59:51] And then he reasons with probability that it cannot be taught. And this is the way Aristotle describes the dialectical conversation. It's reasoning from probable opinions, right, even to contradictory what conclusions sometimes. Okay. So Socrates reasons to. So you have a really example there of the dialectical conversation, right? Though Socrates kind of conversing. with himself right? But yeah, that kind of conversation there in the third part, reasoning from probable opinions to even to contradictory conclusions.

[1:00:29] So in a way, you have all four conversations there in the Meno. Plus, you see the order of the examination conversation, right? It should, in some cases, prepare the way for a dialectical conversation, and other times for a what teaching conversation, right?

[1:00:52] So what are the four? I got examination, dialectical, teaching. Well, I give them the proper order there. You have the teaching conversation, right? Okay. Then the dialectical conversation, and then the examination conversation, and then the sophistical or contentious, they sometimes call, it conversation, huh? Now why do you put it in this order? It's from the more perfect, yeah, down to the thing. Because the sophistical conversation is really a bad one, right?

[1:01:23] Because it's not really ordered to knowing, but to what? To victory or to the appearance of knowing. Okay. I see. One way of examining this is in terms of the fact that a conversation is between two people, right? And as far as knowing anything, two people can be in one of three conditions: either both know, or neither knows, or one knows and the other doesn't know, right?

[1:01:52] Now, both know, you don't really need a conversation about that, right? Okay. If one knows and the other doesn't know, then you should have a teaching conversation. If neither knows, you should have a dialectical conversation. But it's not always clear who knows and who doesn't know. And sometimes it would be teacher doesn't really know, but he thinks he knows. And sometimes a should be student doesn't know either, but he thinks he knows, right?

[1:02:27] So you may need a what? Examination conversation before you can have a dialectical one. And so after the examination of Meno, where it becomes clear that Meno doesn't know what virtue is, and Socrates admits he doesn't know, right? Then Socrates proposes a dialectical conversation, although it doesn't take place because of the sophistical tendency of Meno, right? With the slave boy, right? Socrates really does know how to double square.

[1:02:59] The slave boy really doesn't know. In fact, he's mistaken, right? But when Socrates shows him by an examination that he doesn't know that you don't double square when you double the side, you. quadruple, right? And the slave boy says, it's a guess. Well, how, about three, you know. Well, it's a closer nine, you know. But he still hasn't got it, right? And then Socrates, since he does know and knows that he knows, right, he teaches this slave boy how to do this, right?

[1:03:29] Okay. Okay. Do you see that? Yeah. Sophistical, no one knows. Well, sophistical, I mean, is kind of like a bad thing, right? But notice now the sophistical and the examination conversation can resemble each other, right? See. And sometimes in some of the dialogues, you know, someone will get kind of irritated. Socrates, you know, and

[1:03:56] say, "You are trying to refute me, right?" Well, Socrates says, "What difference does it make whether you are refuted or I am refuted, right?" Now, neither case will get closer to the truth, right? But he might appear to somebody, you know, like he's trying to be a bit of a what? A sophist, right? He's trying to.

[1:04:21] He's trying to. What kind of conversation was that? Irrational. Well, no, I see the. clearly Aristotle, they use the term "theruan the ruin." when you're hunting down a definition. Oh. It comes to the word for a wild beast, I got a wild beast, So the cat is kind of a you know a lazy hunter, right? And John Locke, in the Essay Concerning human understanding, he compares the philosophical life to a hunt, right?

[1:05:10] It's kind of appropriate because the English gentleman, right, like to go hunting, you know. You know. And so this is kind of a mental hunt, right? But as I say, Plato does that even before. And kind of reminds me, you know, of you know you see this in the in India there when they're trying to get a you know a man-eating tiger, whatever it is, and they kind of what get a whole bunch of the natives together and they beat their drums and they kind of you know advance here and they're kind of cornering the animal until they can shoot it, right?

[1:05:42] Yeah. But the way you are doing that, you know, Plato will compare that because you start to divide, you know, you start to you know don't let escape, you know, you know, beat that way, you know, like because an animal is trying to escape you, right? And it's kind of hard, but as you divide, you start to what narrow down. It doesn't have much room to go, right?

[1:06:03] The thing you are trying to define. There's a very, a very vivid way of speaking about this, huh? So the cat there is, huh?

[1:06:12] I always say, you know, I had this. Like this is a cause of love, see. So I like cats because the cat's a lazy hunter. That's what a philosopher is. I'm kind of a lazy hunter. What is the Greek word? Huh Thereuein. Yeah, you find that in the postanalytics, and you find it in the sophists and so on. When you're trying to arrive at definition by division, right?

[1:06:38] Hunt it down, right? Investigate that origin too, to some extent, huh? Vestigium, you know, means a footprint. You know, so you kinda track an animal by its footprints, huh? Investigate, huh?

[1:07:01] Aristotle is very concrete with you, you know. So you have those four kinds of conversations, huh? As I say, sometimes he accused Socrates of being what? Trying to refute them, and he says, "No, I'm just trying to see whether what you say fits together with other things you say, and like you to do the same for me." Okay. But as Aristotle says in the in the first book of Nicomachean Ethics, with the truth, everything what harmonizes, huh?

[1:07:35] Everything what fits together, right? It's kind of marvelous to see the way that turns out, huh? I was just talking there. We're finishing the ninth book of wisdom there in the metaphysics, and and from what Aristotle shows in the ninth book of wisdom, you can see that the first cause is the best thing. And I was mentioning how you know we can show, like in the *Premium to Wisdom*, that the end or goal of our knowledge is to know the first cause.

[1:08:21] Our mind's not satisfied to know the way things are; wants to know why they are the way they are, right? Therefore, wants to know the cause, right? And if the cause has a cause, it naturally wants to know the cause of the cause. And so the final thing it wants to know is the very first cause. Okay. But then he he argues in the *De Anima* that a knowledge of a better thing is better, right?

[1:08:47] And therefore, a knowledge of the best thing must be the end of our knowledge. Well, you see, the ninth book of wisdom there, it's very clear that the first cause is the best thing, right? But those who say that matter say is the first cause, they make the most imperfect of things the first cause. So what's the end of our knowledge? A knowledge of the first cause has pretty good reasons to say that, or is it a knowledge of the best thing?

[1:09:16] And they have two different what? Ends right. It can't do ends. You got schizophrenia, right? But when you see the truth, it all fits together, right?

[1:09:37] Aristotle reasons, you know, there in the ninth book, that simply speaking, act is before ability, before the passive ability, right? Because what goes from ability to act does so because something already in act. And from that he's going to reason that the first cause must be pure act. But he also shows that act is better than ability, so the pure act must be the best thing, also.

[1:10:00] And it fits together, right? You know that the end of our knowledge is to know the best thing, or is it know the first cause? Well, which is it? If they turn out to be the same thing, well then everything fits together, right? But if the first cause Is not the best thing, then you've got schizophrenia. That's What you have in the modern thinkers? Those who say matter is the beginning of all things, huh?

[1:10:28] I mean, our comrade Lenin says mind is the highest product of matter, right? You know, but mind is something better than than matter, right? But if the first cause is matter, then the best thing is not the first cause. So what's the end of our knowledge? To know the best thing, or to know the first cause? They can't put the two together. So it's a sign that you have the truth that everything fits together.

[1:11:00] Or if you're saying something false, it's not going to fit together, right? Oh, what a tangled web we weave! When first we practice to deceive, right? Now the kid is lying to his parents, right? You know, you know, or lying to Perry Mason, right? And they went to stand. Eventually, something it's going to contradict something, right? And now you're deep, deep, deep, deep trouble. You see?

[1:11:32] So, yeah, give a little bit of my lecture the other day, okay? But next time we're going to look at the. Did you have the English text there of the of the Summa Contra Gentiles Yeah, we have one. Yeah, yeah. Just just the first two arguments for the existence of God that are based upon motion, right? Okay. We're not going to go into theology at this point in our studies, but I think might be good to look at that just so you see the connection, right?

[1:12:04] It does give a summary of some of the things in books Seven and Eight, but also you see the connection between what we've just studied, the definition of motion and the continuous character of motion, how you reason from that to the unmoved mover, right? Okay. So when we come to theology later in our studies, we will already see the connection to some extent, right? Okay.