Natural Hearing (Aristotle's Physics)
Lecture 78: Continuous Magnitude, Motion, and Time: Infinite Divisibility

Transcript
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of philosophy. And this is what actually happened in modern philosophy, the history of modern philosophy. There is a revolt from the natural. And basically you'd say they revolted from the idea that there are any statements that we naturally know, right? From this natural understanding. You see this, you know, in popular states, you know, you see them holding all the window holes, right? If I was to write down a piece of paper, the statements which I'm completely sure, I would need to keep her blank. Okay? Now, of course, the question is, is he sure about the fact that he doesn't know these statements? But anyway, that's his problem, right? Okay? Because he in doubt that statements exist. Because when I say statements exist, the proof is right there. And the man who would deny that and say statements do not exist, he can't deny it without making a statement. So that's some statements we know. We know that statements exist, right? Okay, so. So he had that rejection, right? If you read through John Stuart Mill there on liberty, I'm not going to call it that. On the grounds that we don't really know anything. You see? And therefore we've got to be free to think what we want to think and fight among ourselves, but, you know, we never really know anything, right? That kind of dominates, you know, the university nowadays, right? Yeah. In other words, if you're trying to teach the students that some statement is true, you're trying to believe the students that, that would be a violation of the morals of the modern university, right? I've got to present all points of view, right? And allow the student to make up his own life. Otherwise, I am what? Terrorist. Yeah. You see? Okay. So one thing that the mill will not admit is that there's some statements that we, what, naturally know. Okay? So there's a revolt from, we might say, natural understanding, right? When you spoke of that as St. Thomas's intellectus, I would imagine he uses intellectus with many senses. Yeah. Yeah. Okay. Yeah. And the same way loose in Greek is used in many senses, right? Okay. But they use the same word there for the faculty sometimes, right? And for this hobby to us, right? This habit. Because it's one that seems to arise naturally for the mind rather than having to be reasoned out. Right on the habit now that I've, I translate episteme today, as a reasoned out to understand that, then to call the other natural understanding, right? Okay. But Plato, I mean, I play with Aristotle and Thomas understand that use as being something, what, natural. Now, the second thing you find in the moderns is kind of a revolt from this natural desire, right? And it's more explicit in some than others, right? But in the case of the early modern philosophers, you see this desire for, what? Power, right? As you place this desire to know, and, you know, even in Descartes, right? You know, the tree of knowledge, you know? You've got the roots down there, which are metaphysics, I don't know how that works. And you have the trunk, which is physics. Then you have medicine and mechanics and all these practical things up here, where the fruit should be, right? So everything's ordered to the practical, right? You know? So it's an ejection of what? A wonder, eh? When you get to Hobbes, right? Hobbes says it explicitly, right? At the end of all knowledge is to do something, right? To make something. Power. And you see this very much in Marx, right? In Marx, eh? So I ask students, you know, when you read a little bit of Hobbes or even Descartes and Marx and so on, are these men philosophers in the original sense of the word? Are they lovers of what? Power, right? It seems to be lovers of power, eh? So they're giving up this second thing here, right? This natural desire, right? And if you give up those two, of course, they're going to give up the third thing, obviously, right? Right? So that's part of the reason why philosophy kind of collapsed in modern times, right? And I kind of get an image of the history of Greek philosophy from Thales to Aristotle, you know? I say, well, in the philosophers before Plato, you see the seeds of philosophy, especially in the fragmentary form that we have, their words. In Plato, you see the seeds growing into philosophy. In Aristotle, you see the growing plant, to some extent, huh? Nothing like that one in philosophy. You can't say, you know, that you see the seeds in Descartes and they're growing and, you know? The history of modern philosophy is not like a development there, right? It's a zigzag. Each guy takes off with zigzag, zigzag, zigzag. You know, you can call it zigzag if you want to, right? But there's no reason to zig off in that direction, you know? This guy goes here, and this guy takes off with his neck direction, and this guy takes off with him, you know? And I had an interview with a guy the other day there who was kind of a, I don't know, what do you call him, a conchie in a way, I don't know what he was. Anyway, I didn't know what a name was. I was putting him down what a name was. Finally, I got almost insulted. I said, do you have a name? Well, what is a name? And he has all these, you know, complicated things, you know? It's part of a linguistic structure, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah. And, uh, but, uh, so I was talking in the office and I was talking about, uh, uh, we admitted philosophy, modern philosophy was a zigzag, right? You know, they all developed with it. There's something obviously wrong with what's going on here, huh? They're supposed to be standing, as they say, on the shoulders of those who went before us. They're supposed to be building, right? They're supposed to be gathering, you know, whatever part of the truth the man before us saw, you know, and, you know, bringing these parts together and building them and so on. They don't have any sense of that at all in one philosophy. As it goes on, it gets even less, what, understand what they're even saying, you know? So, well, Hegel is just like, I don't think I've ever understood it. One of the things where Hegel says, he was on purpose writing so he couldn't understand it. Because people would not admire him if they couldn't understand it. But, uh, when you read, you know, what my standard joke about Heidegger was when I was teaching at St. Mary's College, huh? I taught that for three years between my two sessions in graduate school. When I arrived there, one of my colleagues there in the department was trying to figure out what Heidegger meant by being. Three years later when I left, he was still trying to figure it out. Well, see, the race is all, you know, it's all wrong. You should be able, you should spend more time trying to judge whether what somebody says is true or false. Then what does He mean, right? And you have to spend all your time trying to figure out what He means, and you still know what He means. Oh, right, right, right. Uh, the fortune of all, right? Yeah. See? I mean, you still have to come out and say, water is the beginning of all things, I know what He's saying. Now we can discuss that, right? And even if we disagree with Him, we can develop our mind in critiquing our reasons for rejecting that, if we do. It's a pretty good guess, I think, but he might. But these guys, you know, he's been all the time, and you still don't know exactly what they mean, huh? My brother Richard got his doctorate from the University of Notre Dame, right? And one professor he knew there in the graduate school, one of his tricks was he had quite a vocabulary, right? So in conversation, you know, conferences and, you know, disagreements and so on, he would use these words, right, which are so extrused that even the other, what, professors don't know what they mean, right? Well, professors, as you know, are vain and private and so on. So, what does that word mean? You see, they're not going to ask that, because then they look a little bit naive, you see. So you don't know what the guy is saying exactly, so, you know, you can't really tap what he's saying. And then they're so wordy, too, you know. John Locke ends up at the end of the essay of Human Understanding apologizing for the work, and saying it's too lazy to go back and pare it down. So you've got to read so many words, you know, to get anything. Maybe she was a city, and it's kind of hard to attack them, because I may attack a whole cloud. So, that's kind of it, the tracks of philosophy. I gave a talk about St. Mary's College one, not St. Mary's College, on the one fragment of the Great Heraclitus, where he said, Wisdom is to speak the truth, and to act in accord with, what, nature. You get an ear there, too, right? But as Kant says there in the, you know, the second preface, the critique of pure reason, right? We shouldn't listen to nature like a student listens to his teacher. We should summon nature to obey us, like, what? The judge, someone's with us, to respond to only what the judge decides to put to him. Yeah. There's some truth, that's what's a lot of us, but I'll say it, so. Yeah. You know? But that's not philosophy. It's not really listening to nature, at least not in that full sense. I think this is a pretty good summary there of the complete dependence of philosophy upon the natural. And you see that those first two things are, that they revolt from that in modern times. And you can see that philosophy is going to be in a very serious position. So, notice, huh, in the second paragraph of that first reading, I'm not going to go through the whole reading again, but just at the end there of the second paragraph on page one. For the edge and that of which it is an edge are other, right? Or if you want to use the word end or limit. The end and that of which it is an end. Or the limit and that of which it is a limit, huh? Or other, right? That's a statement. And it's a statement that we naturally, what? Know. See? Or naturally come to know, anyway. You see that? And so, it's through things that we naturally know like that that we eventually come to know other things, huh? So, let's go now to the second reading here. Now, as Thomas explains in the commentary, in the first reading, Aristotle has really shown this for everything continuous. But it's more clear in the case of the magnitude from what he said. So, he's going to come back upon the motion over the magnitude, right? And show that that is more fully, that that is continuous, huh? And then, in the third reading, in the fourth reading, he's going to show the same thing for, what? Time, right? Okay? So, he says in the first sentence, there is the same reason for composing magnitude, time, and motion of indivisibles, and dividing into indivisibles, which, of course, is what we found was false. Or none of them, right? Okay? Now, he's going to start to develop the presupposed things to showing this. And he's going to, later on in this reading, deduce the, what? Absurdities, right? Of composing the motion from, what? Indivisibles, huh? Yeah. So, he says, it is clear from these things. For if a magnitude is composed of indivisibles, the motion over it will be from equal indivisible motions. As if the magnitude, for example, A, B, C, is from the indivisibles A, B, and C. Then the motion D, E, F, over it, according to which is moved O, that's the mobile, over A, B, C, has each part, what? Indivisible. Okay? I take some things that are kind of obvious. If motion being present, something necessarily moves or isn't motion. And vice versa, if something is moved, motion is present, right? To be moved, in this case, will be from indivisibles. For A has moved on A, having moved by the motion D. And on B, by that of E. And on C, likewise, by F. And now the fourth paragraph, huh? The other thing he's going to take into account here, which is going to get us into some troubles, right? Making motion composed of indivisibles. And if it is necessary that the thing moved from one place to another, not at once move and have moved, right? To where it is moved. As if someone walks to Thebes, it is impossible at once to walk and to have walked to Thebes, huh? Okay? And incidentally, Aristotle will come back to that in the ninth book of Wisdom, right? When he's distinguishing between an activity like walking home and an activity like understanding, or an activity like loving, or even an activity like seeing, right? That when I'm walking home, have I walked home? When I'm coming into this room, have I come into this room? Not fully. But when I'm understanding what a triangle is, have I understood what a triangle is yet? Yeah. When I'm loving you, have I loved you yet? I used to use the students, you know, by saying, what do you say to your wife or your girlfriend, right? Have I loved you yet? I'm just loving you. I haven't loved you yet. But even in the case of seeing, same way, right? When I'm seeing the painting, have I seen it yet? Yeah. Or when I'm walking home, have I walked home? See? When I'm building the house, have I built the house? Okay? So in motion there, there's what? You haven't, you're not moving at the same time that you have moved, or vice versa. You haven't moved when you are, what? Moving. Moving. You haven't moved that distance that you're moving when you are moving that distance. Okay? So you take the example of walking to Thebes. I always take the example of walking home, right? So when I'm walking home, I haven't walked home yet. Okay? Well, those two paybacks are those old statements naturally understood? They're close to it, yeah. Yeah. A little more particular, right? Okay? O is then moved on the part to say, as the motion D is present. So that if it has come later than it comes, it will be divisible. There'll be a problem there, right? Okay? For when it came, it neither rested nor had come, but was between. But if the one walking when he walks goes and has gone at once, he will have walked and moved to where he moves. If then something is moved, the whole A, B, C, and the motion according to which it moves is D, E, F, and in the part to say it is not moved, but has moved, motion will not be from motions, but from what? Having been moved. Okay? Now, in Latin there, even in Greek too, you have one word, right? Which is the old word momentum, but it has a much different sense in modern science, huh? There's a little problem here, right? I've gone to A without having gone to A. Or if, when I'm going to A, I haven't gone to A yet, then A is not indivisible, is it? But if A is indivisible, you're going to have a real problem here, right? Because I will have gone to A when I'm going to A or without having gone there, right? And he goes on there, in the sentence there. Very good. And something will have moved without, what? Moving, right? I have gone home without going home. I will move to A without moving to A. And then I will move to B without moving to B, right? Okay? For it will have gone through A without going through it. So that something will have walked without ever walking. He has walked the same without ever walking it. If then it's necessary that everything move or be at rest, and it rests according to each of A, B, and C, there's no motion there, so that something continuously resting will at the same time be moved. For he's saying it moves the whole A, B, C, right? And it rests in each part and hence in the whole. See all the difficulties that arise, huh? And if the indivisibles of D, E, F are motions, it will happen that motion being present, something is not moved but is at rest. And if they are not motions, motion is not from motions, which would be like saying the line is not from what? Lines, right? Now in the third reading, he's going to start to show this about what? Time, huh? Time, he says, must be indivisible and composed of indivisible nows in the same way as magnitude and motion, huh? For if every magnitude is divisible, and in less time the equally fast goes less, time will be divisible. And if the time is divisible in which something moves at distance A, A will also be divisible. And notice, he's first going to reason, I guess, from what, two things that are equally fast, right? Okay? And then he's going to reason from, what, two bodies, one of which is faster than the, what, other, right? And then he's going to reason from even one body moving, right? Okay? And my favorite one is the middle one, right? I think it's more illuminating, right? Okay? But now, let's, let me dive in a little bit here. Blending a bit of what Euclid does in the second book, where you take two lines and show something, and then you'll take one in the same line and cut it away, right? And I just think, you know, Heath or something will say, you know, that he does this because it's easier to see the two first, right? The one, right? That's kind of a similar principle, right? So, if you have two equally fast bodies, right? And one of them, let's say, goes this distance in, oh, this distance, and it goes in this time, right? Okay? Now, a body equally fast is going to go part of that distance, right? In the same time, an equally fast and it goes in this time, and it goes in this time, and it goes in this time, and it goes in this time, and it goes in this time, and it goes in this time, Because if the equally fast body, if body A, in this time goes this distance, right? Then the equally fast body in a lesser time will have lesser distance, right? So you can see that these are going to be divided in a similar way, right? But there you're taking, you know, as known that the distance is, what, divisible, right? If the time must be. Or if you take from the first reading, the paragon does in a way apply to time as well as to distance, right? Then if you say that the time is divisible, you're going to have to say that the distance is divisible, right? Now, we're kind of maybe a little bit of overkill here, huh? Aristotle's going to start now in the third paragraph to reason from a faster body and a slower body. And this is the one I often give, huh? He's going to develop first some things he's going to reason from. Since every magnitude is divisible into magnitudes, it has been shown that it is impossible for something continuous to be from indivisibles. Neri seems to obviously, what, be proceeding from its not being from indivisibles to its being, what, always divisible into magnitudes, right? Continuous. Yeah. But that's another way of saying, it's always divisible into magnitudes, it's always divisible into something indivisible. Which is another way of saying, in fact, it's always divisible, right? Okay? So he seems to be arguing more from it not being, what, being impossible for it to be from indivisibles, right? And every magnitude is continuous. The faster moves in equal distance in less time, right? Because that's the way we think at first. But even more distance in less time, as some define the faster, right? Mm-hmm. Okay? And that reminds me of my favorite, what, theorem there in book two there, that proposition five, right, huh? That theorem, proposition five in book two, Euclid? Yeah. Yeah. It says that if a straight line be cut into, what, equal and unequal segments, right? Oh. Yeah. The square contained by the equal segments, right? Mm-hmm. It's always going to be greater than the rectangle contained by, or oblong, by the unequal segments, by the square on the, between the points of section. Okay? It's a very interesting theorem, right? Okay? Now, sometimes, you know, to make that interesting, I transcribe that and I say to the students, now, if you take rectangle in the broad sense, where it includes square and oblong, right? Um, can you have a rectangle with the same perimeter but more area? Well, this shows you can. Mm-hmm. Because this square would have the same, what, perimeter as this, what, oblong. Um, see, it's possible to have a rectangle, in the broad sense now, um, with the same perimeter but more area. Okay? But then the amazing thing is, it's possible to have a rectangle with less perimeter and still more area! square. You see? So, you know, if you have a, a square, five by five, huh? Quite that theorem, as you depart from that, you take, let's say, a rectangle of four by six, you're keeping a perimeter of, what, twenty, they both have a perimeter of twenty, but the area of one is greater, right? Mm-hmm. And as Euclid shows in that theorem there, the difference in the area is always the square of the difference between the sides, right? Mm-hmm. So five and six, or five and forty-one, the difference is one, and that's the difference in the area between twenty-five and twenty-four. Now, if you go out to, let's say, seven by three, then you get a perimeter still of twenty, but now the area's dropped to, what, twenty-one, right? And again, it falls what you talked about, the square and the difference between the points of section there. Between five and seven, the difference is two, and two squared is four, and that's exactly the difference between twenty-one and twenty-five. Mm-hmm. And then, let's say you get down to, let's say, two and eight. Well, now the perimeter is still twenty, isn't it? But the area's now dropped to sixteen, and notice, huh? The difference between five and eight, or five and two, is three, right? Three squared is nine, and sixteen is exactly nine less than twenty-five, right? Now, once you see that, then you realize the possibility, though, because of the infinite divisibility, the continuous, you could actually have a square with what? Less perimeter, but more area. So, if you take one, let's say, two by ten, well, now the perimeter is no longer twenty, but it's what? Twenty-four. Twenty-four. Ten by two. Twenty-four. But the area is, what, twenty, huh? So, now you have less perimeter and more area. Yeah. Okay? Here you have the same perimeter, but more area. Once you realize that possibility, because of infinite divisibility, you could take something in between, right? Or you'd have actually, what? Less perimeter, but still more area. That wouldn't happen always, but I mean, you can take that kind of example, right? So, Aristotle's saying something like that here, huh? Once you realize that there is a, that the faster body is covering the same distance in what? Less time. Or covering, let's say, a greater distance, right? Yeah. In less time, huh? Greater distance in the same time. Yeah. Oh, excuse me, it's covering a greater distance in the same time, okay? Yeah. It can also cover a greater distance even in a lesser time. Yeah, right. Because of the infinite divisibility of those two, right? Yeah. Once it's doing one, it's doing the other. Yeah. But it would always cover a greater distance in less time. No, but isn't it true that if you have it covering a greater distance in lesser time, or excuse me, equal time, it will always cover a greater distance in lesser time? Yeah, at a certain point, yeah. Yeah. Oh, yeah. Yeah. Yeah. Okay. It only goes so far, but... Yeah. So this is going to manifest this a bit. Let A be faster than B. Since then, the faster is what changes before. In the time A has changed from C to D, as in the time, let's say, FG, in this B, which is the slower body, will not yet be at D, right? But will fall short, right? So that in an equal time, the faster has gone, what? Further, right? Okay? But also further, in less time, right? So he says, in the time A has come to be at D, B will be at E, some shorter distance, right? Being the slower. Since then, A has come to be at D in the whole time FG, it will come to H, somewhere in between there, in less time than this. And let this be in FI. The CH, which A has gone through, is greater than CE, in the time F1 less than FG. So it has gone further in what? Less time, right? Now, you know all those letters that you kind of... I mean, it's tough, huh? Let's just, you know... So the diagram on the board here, so... Let's say that the faster body goes this distance, right, in this time, right? What's going on? Okay? Now, can the slower body go the same distance at the same time? No. So let's say the slower body, however you put it, it's got to be somewhere on here. Less, huh? Let's say it goes that far, right? Okay? Now, if the faster body has gone this whole distance, in this time here, what about this distance right here? It's going to go that distance, which is greater than what the slower body has gone. It's going to go that way. It's going to go that way. It's going to go that way. It's going to go that way. It's going to go that way. It's going to go that way. Is it going to go this distance in all this time? No. So it's going to be in less of this time, right? So in less time, it has gone further. I don't know if it's on the tape, but there's more here, right? Okay. You see that? It's almost like overkill, right? It's clear, then, from these things also that the faster goes an equal distance in what? Less time, right? You could argue for that, too. Because if the faster and the slower went the same distance in the same time, one would be faster and slower, right? So you're forced to say that two bodies go the same, the faster and slower body go the same distance in what? Less time, right? Isn't that the same as saying that the faster is what changes before? Yeah. I mean, it's a little different way of stating it, right? One consequence of my being faster, say, than you, right? Which I don't think is true, but one consequence of that is that in the same amount of time, I will go further than you went, right? Okay? But that you and I will go, what? The same distance, take you, what? More time. Yeah. I mean, last time, go the same distance, right? Okay? Now, what is he going to do on the basis of those facts, right? Well, he's going to show, by alternating those two truths, right, that the time and the distance are both, what, divisible forever, right? Okay? So, you start off and you say, well, the faster body goes this distance in what? This time, right? Okay? It's the time, and it's the distance, and it's the time, okay? So, the faster body has gone this distance in this time, right? Okay? Well, then the slower body, in that same time, has gone a what? A lesser distance, right? So, now the distance is being divided, right? Now, if the slower body has gone this distance, in this time, right, would the faster body go this lesser distance in the same time as the slower body, did it? Lesser time. It's got to do it in lesser time, right? So, now we divide it in what? Time, right? Now, if it took the slower body, this whole line, to go this distance, right, the only part of that time can go the same? No, it's going to go only part of that, so it's going to divide the distance again. Okay? Now, if the faster body went this distance in this time, it's going to do this distance, which is less, and less time, it's going to divide that, right? So, just by alternating those two truths, we're going to go on, what? To die. To die. Invisible forever, right? I was talking about that argument against Anaxagoras, right? In the ninth reading, Aristoto argues, you know, against the position of Anaxagoras that the flesh and blood and bones can be infinitely small, they can fall below any size, right? And he has an if-then syllogism, you know, he says if the parts can fall below any magnitude, right, then the whole, which is composed of the parts, could fall below any magnitude. And then he goes out to nature and he says that different kinds of animals and plants don't have just any size, okay? Therefore, the parts don't have just any size, right? So, anyway, I was contrasting this difference between the quantity of natural things, which have limits, huh, as to how big or how small they are, due to the kind of thing, right, that it is, huh? So, the trees here don't grow as big as the redwood trees, say, in California. And the ant doesn't come as big as the elephant, right? And the mature elephant is not the size of the ant, right? Okay? But in geometry, is there a smallest or a largest, huh? And so, I was just, you know, to the fun of it, taking these things, the terms in the fourth book, the circumscribing and inscribing, right? And you have a theorem there that inside of any square you can, what? Inscribe a, what? Circle. Circle, yeah. You know what that means, huh? It just touches one point in each side and so on. But that's proven there, right? Okay? Mm-hmm. And it's proved universally. Inside any square, you can inscribe a, what? Circle. But the reverse is also proven that inside of any, what? Circle. Circle, you can inscribe a square, okay? So inside of this circle, you can inscribe a square. But you can always inscribe a circle and a square. So inside of this square, you can inscribe another circle, right? Because you can always inscribe a square and a circle. Inside of that circle, you can inscribe a square. That's even smaller. And because in every square, you can inscribe a circle, right? Mm-hmm. Okay? Because then it's a theorem that ceased to be true. Mm-hmm. And if you're on a circle, then I can keep on, what? Just doubling those two, and I get bigger and bigger and bigger, right? There's no such thing as a, what? Largest. Largest, huh? See? Well, something like that here, right? Except you're going in the direction of the small, right? Mm-hmm. See? If it's always true that the faster body, right, goes the same distance in lesser time, right? It's going to always be true if it's faster, right? And it's always true that the, what? Slower, what? The faster body, the faster body goes at equal distance at less time, or, I'm missing it. Yeah, or you may be, you may see, some of the slower body. The slower body always goes at lesser distance at the same time. That's always true, right? Mm-hmm. Okay? So you can help it in, like I was doing this earlier, right? And you can say that we can always divide the distance, always divide the time, right? See, that's kind of a marvelous way that Aristotle has to show him. And since together, right, that both of these things are, what? Divisible forever. And that's the second definition of the, what? Continuous, right? It's kind of marvelous that he does that. And it kind of shows, too, how wise Aristotle is in making one knowledge, right? Of all continuous things, as far as they're being divisible forever, right? It's a way to save knowledge of both, right? And since, to these very simple statements, that the faster body carries the same distance in less time, or the slower body in the same time carries a lesser distance, on those simple truths, you can show together that the distance and time are divisible, what? Forever. So it seems to be the same knowledge of both, right? Mm-hmm. And actually go on to the same science. And in geometry, you're really, what? Assuming that, right? That these things are divisible forever, right? So in that sense, the natural philosopher is wiser than the geometry, right? He's, in a way, proving, right? But the geometry has to, what, assume, right? Okay? The same way, though, the geometry is a theorem that you can bisect a straight line, right? You know, you can bisect a half and go on forever, but geometry is supposed to be divisible forever. And, um, you know, I mentioned before. For how the geometer says that what? Between any two points you can draw a straight line. That implies that you can't what? Put points touching. Yeah. If you could bring two points close enough to touch without coinciding, you couldn't draw a straight line between them, right? If you could put a house in between my house, the next neighbor's house, I wouldn't want you to do that because I like these little bigger lots, you know? You don't have the noise there. But if you moved my house up, you know, like in old Quebec or some place, you know, where my wall was touching his wall, then you couldn't put another house in there, unless you had two-dimensional creatures on that house. You couldn't put a house in there, right? Because they're touching, right? So really, the idea that between any two points you can draw a straight line depends upon this here, right? So if the natural philosopher is wiser, then the, what, mathematical philosopher, huh? Another sign of that is what we saw earlier in the course there, where in the second book of natural hearing here, Aristotle distinguished between natural philosophy and, what, mathematical philosophy. And there's the distinction between natural philosophy and mathematical philosophy. Does it belong to mathematical philosophy or natural philosophy to do that? It would be more natural philosophy, I'm thinking, but it would be properly metaphysics because it's key. Well, you see, when you get to the sixth book of wisdom, right? The sixth book of metaphysics. Then Aristotle distinguishes between mathematical philosophy and natural philosophy and wisdom, right? Okay? But the principle here, I think, is of universal importance. And that is that it always belongs to the higher knowledge, right? And the knowledge which has more the character of wisdom to distinguish between itself and the lower knowledge. And secondly, then, to consider the order of the two, right? So natural philosophy can distinguish, you know, because there's something of the character of wisdom in comparison to mathematical philosophy. It can distinguish between itself and mathematical philosophy. And it can also determine to what extent mathematics is, what, useful in natural philosophy. Okay? And sometimes when I present that principle, I go back, you know, to the starting point and I say, does it belong to the senses or to reason, to distinguish between the senses and reason? The senses can't do that. The eye, the ear, right? Okay? And to distinguish between reason and imagination belongs to the imagination or to reason. Now, there it's very clear that only the reason can distinguish between itself and the senses or between itself and the imagination. But reason has more the character of wisdom than the senses. Wisdom is a knowledge of reason. That's why we call it homo sapiens, right? Because we have reason, right? Okay? But then you see how natural philosophy distinguishes between natural philosophy and mathematical philosophy and talks about their order. But wisdom, right? Distinguishes between itself and what? Both natural and mathematical, right? And belongs perhaps to political philosophy to distinguish between political philosophy and rhetoric, right? Okay? And between political philosophy and domestic philosophy. Like Aristotle does in the first book of the politics, huh? No? But that's another reason why modern philosophy got in such bad shape. was that in the middle of the period and after Christ and so on, theology came on the scene, right? Revealed theology, huh? And as Thomas shows in the first question, the Summa, revealed theology has more the character of wisdom than even metaphysics does. I think it's, you know, reasons from what we know about wisdom. So the distinction between philosophy and theology belongs to... Theology. Yeah. Not to philosophy. And consequently, the order between philosophy and theology belongs to theology, right? Now, what happened in modern times was that the famous thinkers, anyway, right, gave up revealed theology, right? They discarded it, huh? Okay? And some of them became atheists, but they suddenly gave up to reveal theology. But they lived in a world where there were believers, right? Where they were exposed to all these things, right? But now they're, what, giving up the knowledge whereby they could sort these things out and see their order. So, what you find the modern philosophy is doing sometimes is trying to do in philosophy what should be done in theology. And that follows up philosophy in another way. You see? And they can't get out of it because they'd have to have theology to sort them out, and they've given up that. They'd have to look at something. Yeah. So, what's very clear is, you see, the difference between modern philosophy and Greek philosophy. Greek philosophy is before revelation, at least before the revelation of Christ. And the Greeks are kind of philosophizing independently of what? The faith, right? And without being exposed to it, right? Right. See? And the only religion they're exposed to is maybe the imaginative religion of Homer, right? And the poets. But they can judge that because reason judges the imagination. And you see this in the great thinkers like Xenophon and so on, huh? Xenophon says, you know, he says that horses could make statues and paint things that make their gods look like horses. And the cattle could make statues that make their gods look like cattle. And he says that the Ethiopians, their gods are black and so on. And the Thracians, they're blonde and so on. But he's showing that the poets are, what, don't really know the gods, right? They just, you know, imagine the gods to be something like us, but, you know, more powerful and so on, huh? And so there's a big difference between the Greek philosophers judging the theology, you want to call it that, of Homer, right? Which is based in the imagination, which is inferior to reason and can be judged by reason, right? And the modern philosopher is trying to judge a theology based on the word of God, huh? So not back in the position of the Greek philosophers, right? And their skepticism is not of the same sort at all. And so when they give up theology, they didn't simply go back to the Greeks and start to philosophize in the absence of this, right? And one of the key turning points between Hegel and Marx is a very slow work by Feuerbach called The Essence of Christianity. You know that? It used to be on the index in the old days. I remember when I was teaching at St. Mary's College, you know, of course Marxism was still in power in Moscow and I was supposed to give a course on Marx, right? You know, so I wanted to use a little bit of The Essence of Christianity, right? The connection between Hegel and Marx. And in those days, you know, you had to get permission to use a book like that. And the registrar would handle it, you know. He'd send the books that he'd send down to the thing. But when that came back, you know, the bishop called me in, you know, he says, he says, you've got permission to use that book, he says, but it says here you're responsible if anybody loses their faith. Which is, you know, which is a good thing to tell a professor, right? Of course, I didn't intend to use actually the text of it. I just wanted to make a few references to it, huh? You know. And, but no, it's nothing like The Essence of Christianity. You know, what Vorabach is maintaining in there is that Christianity, God became man, right? It's a kind of poetic way of saying that man himself is God. You see? And, uh, so it's kind of, you know, obviously a perversion of that, right? You see? You don't have any perversion of the mysteries of the Christian faith in the Greek philosophy that they never presented with them, right? You see? Um, it's only four bucks. It's only four bucks. Argument is based on the fallacy of equivocation. He quotes theologians who say the infinite is God. And then he says man's mind is infinite. Every man's mind is God. But the word infinite instead of God, right, instead of our mind is equivocal. When we say God is infinite, we mean there's no limit to his perfection, right? He's universally perfect. But when we say our mind is infinite, we mean our mind is always able to learn something more, right? So it's a much different kind of infinity. But the average person can't distinguish those kinds of infinities, so it's not a good argument. Karl Marx and Engel said they became enthusiastic for Wachians. The same way about love, right? Juliet says my love is infinite, right? The more I give, the more I can give. There's something infinite about love, but again our love is not infinite in the way God's love is infinite. So they're not seeing that with the kids. That's what they sort of built there. Yeah. It's part of their system on it, really. Yeah. He's a link between Hegel. But Hegel's really getting that point, too, see. Hegel's philosophy of history is more like, what, the city of God trying to do in philosophy something that the Greeks never tried to do, you know, in philosophy. But it's kind of like, you know, they say, it's one thing to never have had anything, another thing to have had something and given it up, right? Or lost it, right? And so the modern philosophers, they seek a substitute for theology, right? And the Greeks are not, because they never really had this revealed theology. You know, when Thomas talks about the certitude of revealed theology, it's much greater than the certitude of philosophy, because it's based on the Word of God, huh? Well, then you have the modern philosophers seeking in philosophy a certitude, right, more than, what, human, right? So that the, you know, the defect of, let's say, the senses, right? The senses are imperfect means of knowing, huh? The Greeks were aware of that, right? But it becomes an obsession with the modern philosophers, right? To the point that they're not going to, what, trust the senses at all, right? Well, that's the beginning of our knowledge. You can't really know anything, except you can't even understand the words you're using, because they all start with the, what, senses, right, huh? I wanted to tell this character we had on campus the other day, I said, why do you use the words like teleological, you know? Why do you understand the word telos? But, you know, as I say, you know, teleological end, you know? I mean, just... In general, you know, I always object to people calling something by the name of the, what, science that studies it, when it's what the science studies that really makes you know what the science is. People say, you know, you have a psychological problem. You've got a problem in your soul, buddy. You've got a medical problem. You've got a problem in your body. I say, I remember even my friend there, William F. Buckley, you know, speaking of life biologically defined. He's thinking of, you know, the way the, you know, what they call biology studies, life, right? But even so, I mean, life biologically defined, no. I mean, biology is defined by life, huh? It's the logos of bios, huh? Life, the study of life. I don't want to forget the side here, okay? So, I don't have to go through every paragraph here, but he's, um, it's all the way down to almost the last paragraph, right? He's developing the argument that I'm saying, huh? It's that last big paragraph, the final part of the argument is there. Okay, so, no, it's just here to go through it word by word. Understand the argument? It's based upon two simple truths, right? The faster body moves, what? The same distance as the slower body in less time. And in the same time, the slower body moves a lesser distance. Now, would you admit, do you trust your senses enough to admit that some things are faster and some are slower? In this world, right? For the sake of argument. Technical matter. So, once you admit that there's a faster and a slower, then you're going to have to, you know, you spell out what faster and slower means, right? Then you're going to be forced to say, what? That distance and time are divisible, what? Forever, right? And if the motion takes time, and time is divisible forever, you could argue that the motion must be, what? Divisible forever, right? So, for Aristotle, it's the same knowledge, in a way, that the magnitude and the motion over that magnitude and the time it takes to go over that, that they're all divisible forever, right? And that none of them are, what? Put together from the indivisibles of their... Indivisibles. Yeah. Yeah. Some modern thinkers want to put them together from indivisiboses. Is that because it seems easier to understand? Well, maybe, you know, I'll hear some readings later on, if I can find them in my files there, you know? But, you know, the most common example of that is the mathematician saying in high school that a straight line is composed of infinity of points. Okay? Now, why do they say this, right? Say, well, you have a straight line, huh? And you cut that straight line, what do you have there? What do you cut? Two lines now. Yeah, you've got a point right there, right? Oh, yeah, okay. Okay? Now, sometimes I'm in an aggressive mood, I quote Richard Nixon, right, when he was first running for office, right? And he said about the democratic program, right, any way you slice it, he says, it's still the same old, what? Baloney, right? Mm-hmm. Right. Now, if every time you slice something, you get baloney, right? What's it made out of? Baloney. Baloney, it seems, right? Mm-hmm. Okay? So every time you cut a line, you get a point, it must be what? Composed of points. Does that make sense? Mm-hmm. It would seem to, right? Mm-hmm. Yeah. Yeah, yeah. Now, the question is, was that point there before you cut? And if it was there, was it actually there, or was it there in ability? Mm-hmm. It wouldn't contradict this, right? Mm-hmm. And you can say that when you cut the line, you make it actual, right? But the human mind has a difficult time understanding ability. Mm-hmm. And it wants to imagine, right? What is inside of something, only an ability to be actually in there. I always quote Weissacher, who was the physicist in the 20th century there, who apparently perfected Kant's theory of the origin of the solar system. Mm-hmm. And I guess he also was the scientist who showed fully how the sun can, what, put forth so much energy without being exhausted, right? Mm-hmm. See? You know, here, I mean, Anaxagos had thought the sun was, what, a stone on fire, right? That's what he's charged with impiety in Athens there. But Aristotle knew that the sun couldn't be a stone on fire, because fire as we ordinarily know fire down here could not possibly burn as long as the sun is burning, right? Mm-hmm. Okay? So Aristotle rightly, I think, thought that the sun is something much different from fire, right? Mm-hmm.