Natural Hearing (Aristotle's Physics)
Lecture 81: The Indivisibility of the Now and Motion

Transcript
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so that the difference between the discrete and the continuous is that in the continuous quantity, the parts meet at a common boundary or limit. But in the case of the discrete, like the number 7, the parts like 3 and 4 don't meet anywhere, right? They don't meet at a point or a line or anything else. So if the continuous is that whose parts meet at a common boundary, then parts is the very understanding of the continuous. So how could the indivisible be what? Continuous. Yeah, how could the continuous be something indivisible? Right? Okay. And likewise, if we've shown that the continuous is divisible forever, how could it be something what? Indivisible, right? Okay. But nevertheless, Aristotle wants to make this kind of explicit, right? Because he's shown before that what? The continuous is not composed of indivisibles, right? And you might want to add, nor is it an indivisible. And those are not really the same statement, are they exactly? See? Okay? So having shown that it's not composed of indivisibles, now Aristotle wants to show that it's not indivisible. Right? Okay? And in a sense, you have to have kind of suspension there. I mean, you want to keep your wonder up, right? Kind of suspension of what you've learned before, in a way, right? And you're asking now, can time be something what? Indivisible, let's say, right? Okay? Or magnitude be something indivisible, right? Okay? Can the distance you travel be something indivisible? And the time you travel be indivisible, right? Okay? Like, you know, in the first, I was wondering, does he have some other kind of common notion of continuous because what he's trying to prove is in the definitions, or is he just like thinking of examples without magnitude's time? Well, it's like he's not thinking explicitly of the definitions there, right? You know, okay? So he says, It is clear from the aforesaid, as if it almost comes out of what you've seen before, right? This is the last paragraph now on page five. It is clear from the aforesaid, that neither line, nor surface, nor body, nor time, right? Nor generally any continuous thing will be, what? Indivisible, right? Not only through what has now been said, but also because it will happen that the indivisible will be, what? Divided. Okay? Now, there's a way of showing this, which is similar to what we've seen before, anyway. It shuts off with certain reasonable assumptions here. Since in all time, there's the faster and the slower, right? And the faster, of course, as we've seen, goes through more in equal time, there can be some, what, ratio between the faster and the slower, right? And it's kind of indifferent which ratio it takes, but let's take three to two, right? Okay? It may happen to go through double and one and a half the link. This may be the ratio of the speed. Let then the faster be brought one and a half the distance in the same time, and let the magnitudes of the faster be divided into three indivisibles, A, B, B, C, B, D. So the faster body in this amount of time is going from what? Through A, B, B, C, B, D, which are indivisibles. And the slower, which is only, what, two-thirds as fast, right? Is going through E, F, and what? F, G, right? Accordingly, the time will be divided into three indivisibles. It goes through an equal distance and equal time. Let then the time be divided into K, L, L, M, and N. Okay? So the faster body has gone through the indivisible magnitudes, A, B, B, C, B, D, in the indivisible units of time, K, L, L, M, N, right? Now the slower has been brought the distance, what? It's only gone through two of those indivisibles, E, F, and F, G, the distance E, F, G. So it's going to what? K, M, and F. Yeah, in which case, how do you divide three units, three points, and three indivisibles? You've got to take one and a half, right? So you've got to divide the indivisible. It's, of course, as contrary to what the indivisible is. The indivisible, therefore, will be, what? Divided. And it will go through the partless, not in the indivisible, but in more. And, of course, you can turn it around and divide the other if you wanted to, huh? Instead of that, you could say, what? You could divide the magnitude, E, G, into three parts. Yeah, yeah. The same argument, basically, huh? But then you could do that separate in a sense. You could say that, what? In one unit of time, which is indivisible, right? Let's say the, what? Slower body goes a certain distance, right? That same distance, then, the faster body goes in less than one unit of time. You can't go in one unit of time, because it would be just no faster. Well, what is our less than one indivisible of time, right? Well, let's see. It's not really that different from what's gone before. I mean, it's basically the same, right? But it's a little difference to say that something is, what? Not composed of indivisibles, and it's not, what? Indivisible. Yeah. Yeah. Okay? Because something could be, what? Indivisibles, but indivisible. Yeah. Yeah. Like a point is, right? Okay. A point is not composed of indivisibles, but it is indivisible. Right? The one that's the beginning of a number, right, is indivisible, too, right? It's not composed of indivisibles. See how modern math follows you up, right? Because they'll think that they're always comparing the, what? You know, number to the continuous, right? And they're really dividing the continuous as if they were dividing the, what? Number. Number, yeah. So they divide the one into two halves, right? But actually, the one that's the beginning of a number is simpler than the point. Yeah. I mean, so sometimes, you know, the Greek German would say that a point is a one having a position. It adds to one an idea of position, right? So if the point is indivisible, then more so is the one. Okay? Now, this kind of ends the kind of general consideration of the continuous, right? Which is very important for many, any time the continuous comes up, right? Whether you're studying the continuous or you're studying what is not continuous because you have to know what you're negating, right? Okay? Now, starting in reading five, he's going to go more in particular, right, into the divisibility of motion, right? And the order, right, therein, of what is found there. But in reading five, as Thomas explains, he's going to establish some things that are presupposed to that consideration. Okay? We might not get all the way through reading five today, but that's preparing the way for this more particular consideration of the divisibility of motion, right? Okay? And really, we want to show here, there's a couple of things, right? He wants to show, first of all, that there's no motion in the now. And in order to show that, he wants to show that the now is, in fact, indivisible, right? And therefore, we'll be able to show that there's no motion in the now. And then, towards the end of this reading, he wants to show a second thing, that the thing that moves, the mobile itself, is what? Divisible, right? Okay? This is important when Thomas, back in the premium, you know, when he's saying, what is the subject of the natural philosophy? And he'll say it's, ends mobile, okay? Sometimes he says, like in the commentary, in the Nicomachean Ethics, he refers to the subject of natural philosophy, he says, res mobile, right? Okay? But in the beginning of the commentary, in the physics, he looked at it, he says the subject ends mobile, movable being, or movable thing, right? He says the subject is not movable body. Okay? Even though we, later on, we say that, what, everything that moves is a body. But he says, we show, like here in book six, that what moves is what? Divisible, and therefore what? A body, right? So it's like a, what? Logically speaking, a property, yeah. Conclusion, yeah. So in the beginning of science, the subject that you're studying, is known without the properties, right? Okay? Just like when, you know, Euclid doesn't define triangle as a plain figure whose interior angles go to right angles. Now that would be the interior angles go to right angles. Yeah, okay. Okay. Someone's never sticking your head. So that would not be the subject, but a property to have your interior angles at two right angles. That's proven not until 32, right? So you define triangle in the beginning, instead of talking about the triangle, you don't have any definition of triangle, do you? See? So you find out that Enz Mobulae is a body, right? Okay. Now the second book of Aristotle, after the eight books of the actual hearing, the so-called physics, the second book, which in Greek the actual title is about the universe, about the cosmos, right? But in Latin, they, which you refer to as the Cheloid window, have you probably seen that? Okay. I think that's due to a confusion there going from Greek to Latin, because in Greek, the word there can mean the universe or can mean what? The heavens, right? And so they translated it by the word for heavens in Latin, De Chelo. Aristotle doesn't just talk about the heavenly bodies, he talks about the earthly bodies, right? And therefore they felt the need to say, De Chelo, Edwin though. Why didn't they see that? If it can be given between the universe or heavens, and he talks about the earth. Well, I'd say there's a lot of chants in these things, you know, I was mentioning before, you know, I used to give it as a title to this book of physics, right? Which is kind of a transliteration, not a translation, of the Greek word fousis there, which is part of the title, right? So it's kind of Greek in its origin. But then they always refer to the three books about the soul as the Dianima. Everybody called this Dianima. So that's from what? Latin, right? So why can't one read one, you know? Why can't one read one, you know? Why can't one read one read? It got loaded in Greek, right? And Sarah called it, you know, Perry suitcase. They call it Dianima, right? Now maybe suitcase is too hard to say, right? You see? So you have to go back, in a way, to the original what? Language. Yeah, to see what the title was, see? And as Thomas explains in the premium to the book on the universe, it's not the universe. And Aristotle talks about the universe as a whole in the first book, right? Whether it's limited or unlimited and so on, right? And then the constituent parts of the universe, right? It's about change of place, basically, right? When you study the place, you realize you have to read it to know what places you have to, what? Eventually know the whole universe. When I was a little boy, you know, in the end of it, it's funny. I'd sign my, give my addresses. Dwayne Berkwist, 1769 Stanford, Ramsey County, State of Minnesota, Midwest, USA, North America, Western Hemisphere, the Earth, the solar system, the universe. What about the galaxy? I didn't know. But the point is, in a sense, if you say, where are we, right? You know, you say, we're in this room. Well, where is this room, you know? The question, where, eventually leads you on to what? The ends of the universe. Yeah, the universe as a whole, right? So it's interesting that the study of change in place, the book that's devoted to change in place in Aristotle, in particular, is called About the Universe. It's if that's the noblest thing, right? Well, one thing I discovered years ago when I was thinking about this, that the four parts of natural philosophy, in a certain way, it corresponds to the four causes, not that you don't talk about one kind of cause in each part, right? But it's in a different part that you go the furthest to respect each of the four kinds of causes, huh? So when Aristotle divides natural philosophy, you know, you talk about change in general in the eight books of natural hearing, the so-called physics, and change of place in particular in the book of the universe, then change of quality leading to change of substance in the books and generation of corruption, and then growth, right? Change of quantity in that sense, and then change the living things, starting with the animal, often the biological books. Well, at the end of the eight books of natural hearing, you arrive at the unmover, right? That's going as far as you go, that third kind of cause, the mover, right? In the books of generation and corruption, it goes all the way down to what? Matter, right? You see. And in the book on the universe, on change of place, you go to the what? Universe as a whole, kind of like the ultimate form, right? The order of the universe. And if you realize what Aristotle says, that in a way, the soul and the human soul is the end of nature, then you do that in what? The fourth part getting with the living things, where you talk about in their purpose, most of all, huh? So it's kind of interesting, the four parts of natural philosophy or natural science in general, that in each of them, one goes the furthest with respect to one of the four kinds of causes, even though you talk about doing more than one kind of cause in each part, but kind of interesting. So Thomas says, this is the subject, and this is like a property, because you prove that the movable is what? Divide, like he does at the end of this year. But most of this, as I said, is taken up for showing that the now is indivisible, and that there's no motion in the, what? Now, huh? Now. Okay. And that really makes us realize how motion and time and so on hardly are, right? Because what really is, is what's going on. Past and future. Yeah, what's going on now, right? Oh, yeah. Yeah, yeah. The past is not really here anymore, right? And the future is not here yet, right? All that's really here is a now. And so if there's no motion in the now, is that a real thing? Hmm? When really is there motion? Okay? When it's already past? Hmm? That's when it really is? Sounds kind of strange, doesn't it? When they say in the Roman Empire, it's really now, right? Because now it's in the past, right? Not got any sense, does it? So when is motion really? In the past? Or is it in the future? Sort of the existence it has? It has in the now. It just certainly makes you appreciate more calling the motion imperfect act. Yeah. Because you really see it's not fully in that. Yeah. Yeah. It barely is, as Aristotle says, you know, about motion, about time, right? The same thing can be said about motion, right? It barely is, huh? It always seems to be in the past, the future, never, never to be. That's why it's hard to understand, huh? And the cause of difficulty is, Aristotle says, isn't it? As Boethius says, after Aristotle, as Thomas says, after Boethius and Aristotle. And yet, as Aristotle points out, In this book of wisdom, motion seems most real to us because it strikes our senses. As Shakespeare says in Taurus and Cressida, Things in motion, sooner catch the eye than what not stirs. So if you're at the airport or someplace and you take a sense of attention, you're away, right? If you don't want to be seen, you try to, what? If you're in the bushes, don't move, right? They might not see you, right? They're looking for you. Okay? So what seems most real to us is what? Least real in this. Yeah, yeah. But to us, God seems kind of unreal, right? Eternity seems kind of unreal, huh? What's most real seems kind of unreal to us, you know? I was lecturing my class and I had a seminary to write, actually, in class. I had some reference to angels, you know, and he's kind of pleasant about angels. And I said, do angels really exist? You know, he asked me. Oh, is it a seminarian, I mean? Yeah, yeah. And I said, they're more real than you are. That's my answer. They really exist, he said. I said, they're more real than you are. My old teacher, Kisurik, used to say, when you die and you see your angel, huh? Your guardian angel, you know, you're going to start, you know, like, this is God, this must be God. And he'll say, no, no, no, no. I just see your angel, you know? But you could be so impressive, these angels, right? They're really impressive. Much more impressive than you've ever seen. Even, what, Frangelico, right? You can do justice to them, right? But, you know, when my brother Richard came back, and he spent 12 years in Rome, he was working on his doctoral thesis there. But he came back from Rome, you know, or from Italy there. He had, you know, four of these angels of Frangelico, right? And he had them all nicely, you know, mounted and so on, you know, for the boys' room and so on, you know? But they're really impressive angels, the ones you usually see, you know, are very poor, you know? And Frangelico, I mean, he's a mechanic yet, but he's been beatified, right? He hasn't been all the way, I don't think yet. But this in the last 10, 20 years, he's been beatified, right? So, I mean, he's a saintly man, right? I mean, he's, he's, and he really has an understanding of what a magnificent creature these are, but of course you have to put it into painting, huh? You know, used to have another picture, you know, you ever see this one of the saints in heaven, they're kind of in a circle there, Frangelico there, it's kind of doing like stately dance, in a way. You see that one? Used to have a reproduction of that one in, in, in the classroom there, where I study with one of the two of the young, you know, kind of beautiful. But, you know, I used to, before class, look at this one, you know? And he's really something, this Frangelico, you know? And Brother Richard always said, you know, that what impressed him the most in Europe was to San Marco, you know, if you've ever been there. Each cell's got, you know, a painting by Frangelico. Yeah. And then there's some other ones, you know, that are in the halls and so on. And they're very well preserved, I mean, they must have, you know, worked, you know, they've been very well taken care of. And, uh, so that impressed him the most in anything he saw in Europe. You know, he saw all these things and, and the museums and so on, you know? It's really, really, really something like Frangelico. You know, he, I mean, there's something about him, you know, like the, the icons, you know, I guess where they, they fast and, you know, go through a, you know, spiritual, but aesthetic preparation to do this, right? You don't just go in there and, and paint your mistress like a lot of the, the Western, you know, painted their mistress as a Madonna or something, you know? But, but here it's really, you know, trying to get some spiritual understanding of this and, so far as possible, put it into the, uh, into the, uh, the painting, you know, so far as you can get those things. So they were much more real than we are, those angels, right? Mm-hmm. But Sirk used to compare you, you know, trying to make a decision in your life, you know? You know, trying to, you know, you know, to you watching an ankle, or, you know, the angel watching you is like you watching an ankle, or trying to decide where to go. One question, is that, when you go from ends mobile to show it's a body, is that just a before in our knowledge? Isn't the body really, isn't being mobile a property of body? Well, it's in our knowledge, yeah. Yeah. But a reasoning from the former, you know, to the latter, like a property, right? Yeah, but it's more universal to the less universal. Oh, you mean, he's saying, you know, that, uh, it's a property of the body to be a, yeah. You could say that. But it kind of shows, you know, that the, well, fundamental emotion isn't our thinking, right? If you go in this order, right? You know, with a mathematical body, right? Descartes' bodies. Hey, hey, hey, hey. Seems like some people try to make God more real by making him more real. Yeah, yeah, oh yeah. I can't hear him real, yeah. And we falsely imagine eternity to be a frozen now, you know, of time. That's how it is. Okay. So he says, the now, which is not through another, but through itself in first. What does that mean? Well, he's talking about the now in the strict sense, huh? Well, sometimes we speak of the present, what, year, right? Although we know the present year is partly in the past, right? Partly in the future, right? The present month we might speak of. You've got a kiln in there, or you've got the present month up there, right? If you remember to change it, right? But the present month is only present by reason of one day of that month, right? And the other days are in the past or in the future, right? Well, then the present day, right? Well, the present day is not present as he says what? Yeah, to itself, right? But to the hour right now in which we're talking, right? And even that's not present, through itself, right? But only through part of it, right? Okay? So he's trying to find the present or the now in the strict sense, huh? The one that is not present through some part of itself being present, right? Okay? But itself, through itself, right? It's present, huh? And he says, the now which is not through another, but through itself in first necessarily is what? Indivisible, right? And exists in all time, huh? Now, we met the now back in Book 4 when he talked about time, right? But we're going to understand the now better, right? As we study this, huh? Now, he's going to kind of manifest this, right? For there is a furthest extremity, a furthest limit of the past, beyond which there is nothing of the future, and again of the future beyond which there is nothing of the past, huh? Which we say is the limit of both. Now, what is he saying there, huh? When does the past extend forever? Well, maybe in that backward direction, it might. We don't know, right? We know from faith, it doesn't know, okay? But the reason we might not know, right? But it comes up to the what? The now. The now, right? So the now, you could say, is the end or the limit of the what? Past. Past, right? None of the past extends beyond the present, beyond the now, does it? Mm-hmm. It's all bound, on this side at least, by the now, right? Okay? Now, the future, right? We don't know how far it's going to go, for a reason. Even by faith, I don't know how far it's going to go, but, you know, it's going to come down in. But by reason, we don't know how far it's going to extend, right? See? But coming back this way, right? Right. It doesn't extend beyond the what? Present, right? Otherwise you have some of the future and the past, and some of the past and the future wouldn't make any sense, right? So the now, then, is the what? The limit of both. Yeah, it's the end of the past, right? Beginning of the future, if you want to say that, right? Okay, now, it concludes that. It's necessary that the now, the same now, be the limit of both times. He's going to go on and develop this and show it more fully, but notice how that fits in with the definition of the continuous. Time is something continuous, right? And continuous means that whose parts have a what? Common boundary. Common boundary, right? Like in the circle, right? The diameter, right? Common boundary of the two sides, the end of one and the beginning of the other, right? Okay? So the time being continuous, continuous, the future and the what? Past, got to have a common what? Boundary, and that common boundary or limit is the what? Now, huh? Yeah? That's the definition of the continuous from logic. Yeah. So then, would you then bring in, regarding the definition of the continuous from natural philosophy, are they, you really can't use them interchangeably? In the same, I know this is kind of a step back here, Russell. Well, you can show that it's the same thing, right? This is like a table with continuous quantity. Yeah, yeah, yeah, yeah. This table with continuous quantity. So is the table then as a body, truly divisible forever? Well, you see, you're looking in a way at the same thing, which divides the continuous, right? And which is the limit of the parts of it, right? So if you wanted to divide a circle, let's say, in the two equal parts, right? You do it by a line, right? Okay, so the line is what divides the circle into two parts. But it's also the limit of the two parts that are continuous at, right? Okay, or in the case of a line, when you divide it, you have a point there, right? So the point is the division of the line, right? That point divides the line into two parts, but you could also consider that point as being the limit that the two parts have in common, if they meet at that point, okay? But you're looking at it in the one way of from the whole going towards the parts, right? Which is like going from form towards matter and therefore appropriate to natural philosophy. Or you can look at it from the point of view of the parts going to the whole, right? I mean, suppose I said that the word cat, right? Cat is a word divisible into C, A, and T. And someone else said the word cat is a word composed of C, A, and T. We're talking about the same reality, right? In one case, we're going from the word cat and dividing it into its parts, right? In the other case, you're going from the parts and seeing them as, what, composing the whole, right? So the definition of logic is more in terms of the wholeness of it, how they come together, right, to make the whole. And the natural philosophy, the one that's about new in actual philosophy, or use the one from the logic too, is in terms of what the parts in which it can be divided, right? If you go back to the proportion that Aristotle gives this in the chapter we saw it earlier, of course, the chapter on the four kinds of cause, right? If you recall that chapter, that reading, it had three parts, right? He distinguished the four kinds of causes, you know, naming and defining and exemplifying each of them. Then he gave the three corollaries, right? And then the third part, he comes back to the four kinds of causes and shows that he can understand them in a very universal way. And then he makes that proportion that the form is to the matter as whole is to parts, okay? So that all parts, composing parts, that is, are something like matter. So even in our friends here, the angels, we could speak of, you know, the three orders as being the matter out of which the hierarchy is made, right? Okay, but it's not matter in any ordinary sense of the word, right? Okay, but it's in a very broad sense, huh? So, when you define the continuous, looking at it in the direction of the whole, right? How the parts come together to make a whole, it's one whose parts meet at a common boundary, right? So if you look at those two semicircles and you're putting them together, so to speak, so they have a common boundary, right? Then they form a, what? A circle, right? Or like you learned in Euclid, you know, every parallelogram there, you know, you can draw a diagonal, right? And get two triangles, right? Okay? And the two triangles come together if they have a common boundary there and make a, what? A parallelogram, right? So you're looking at it towards the whole, therefore towards the form. Well, logic is a formal science, huh? It's dealing with what's only in reason, you know? In material, but formal. Just like math, dealing with form, mainly. But in natural philosophy, it's appropriate in natural philosophy to talk about matter, right? And natural philosophy goes towards matter, right? So if you go from these books to the book on the cosmos towards generation of corruption, you're going down into matter. If you go again to the Dianima, to the way Thomas orders all the books and the, you know, on life, you go down towards what matter, end up in anatomy and things of that sort. You see? So it's appropriate in natural philosophy to define it looking towards the parts, right? And therefore, you define it as what's divisible forever, right? Divisible and always divisibles, right? Okay? But you're really kind of talking about the same thing in a way, huh? Okay? The mind can go from the whole to the parts and from the parts to the whole, right? I mean, but there's a difference in the mind going. What does Herac Cletus say? It's the same way up and the same way down. But you're going in contrary directions, huh? Yeah. Any body then be divisible at the table? Is it divisible? Well, again, Thomas, you know, raises the question that how does this harmonize with what Aristotle said in the arguments against Anaxagoras, right? And elsewhere, right? And he says, well, he's considering the continuous here, right? In a very general way, right? Not yet, what? Applying it to particular kinds of, what? Bodies and so on, right? Yeah. And so something can be true on this general level, right? There might have something impeding it when you get down to the, what? Particularly, right? Okay? Okay. I forget, how exactly is it that he defines, Aristotle defines continuous in logic? Well, that whose parts meet at a common limit. Okay. A common boundary. So the parts of a line meet at a point, parts of a surface at a line, okay? Parts of a body at a plane or surface. In time, it's the past and the future. You have a common boundary there. If you're saying that the, going back to the axiom you talked about last time, that the limit of something is not a, what? You have a common boundary there. You have a common boundary there. You have a common boundary there. You have a common boundary there. You have a common boundary there. You have a common boundary there. Same kind of thing as that of which is the limit, isn't it? So we say the limit of a body is not a body, but a what? Surface, right? A surface has length and width, but no depth. Why, a body has length and width and depth. So the limit of a body is not a body. And the limit of a surface is a what? Line. A line, and a line is not a surface. A surface is length and width, and the line has length, but no width. And the limit of a what? Point. And a point has no length, so a point is not a line, right? What's the limit of a point? It has no limit, right? Not lacking a limit, though. It is the first limit, right? These matters. So, would the limit of time be time? See, I might say that the morning is the beginning of the day, let's say, right? Or the evening, or whatever it is, is the end of the day, right? But is that really the end in a strict sense? No. So, the 12th hour is the end of the day? The 11th, 11th, 12th? That's the end of the day, right? That hour, right? If you're not coming into the day, you know? When it's 11 o'clock, you're talking about an hour to go, right? So, can the end of the past, which is a time, right? Be itself a time? No. And being the end of the future, you know, the beginning of the future, just like the beginning of the day. Can the beginning of the day be an hour? Well, how about a minute? In a strict sense, the beginning of the day can't be any time at all, can it? Because if I had any time, it wouldn't be all there at the beginning, would it? Okay? So, can the, just from that way, it would seem to make sense, right? I was going to manifest it more, that this now is going to be what? Yeah. Because if we're divisible, it would be some time, wouldn't it? Yeah. And then time would be the end of time, right? The limit of time. Makes sense, doesn't it? And sometimes, you know, we speak more loosely, we say that if you had a laminated surface, you know, like in that counter there in the kitchen, something like that, you say, well, this is the surface of the counter, right? I mean, probably, I get the repairman or his, man, if I did that, that was a surface, right? Because it has some thickness, but that's really something you can peel off, it has a body, right? So a surface you can peel off is really a what? A body, right? And it's really not that whole body that you can peel off, the end of the upward extension of this thing, right? It's only the indivisible, right? The depthless, huh? Okay. But anyway, he goes on to say, first of all now, that it is necessary that the same now be the limit of both times. Now, it's, could the end of the past and the beginning of the future, could they be two different limits? If they were different, you'd have time between them. Yeah. And the past would not be next to the future, would it? Is the limit between the United States and Canada, is that limit? The northern limit of the United States, in the direction of Canada, and the southern limit of Canada, in the direction of the United States, are they the same limit? If they weren't the same limit, what would you have? I could have a no-man's land, right? And then Canada would not be next to the United States, but no-man's land. I'd probably end up having over there in Palestine, right? I could have a no-man's land there, right? I mean, it's either Palestine nor Israel, right? And it's about the only solution that they seem to be able to come up with, right? Or even propose. I mean, they haven't realized it, obviously, right? But they're not going to have another bullet in the wall, right? But it's going to be a little, it's going to be along those lines, right? It's going to be the Great Wall of China, you know, it's going to go on, on, on, all the way around, you know? And the actual collection to build this water, what they're going to do, but... Because they won't solve it, probably, they'll be shooting things over, you know? Getting rockets from other countries and shaking each other, so, I don't know. Man has his own way of being endless, right? There's something about our fights. There's something endless about our fights. I don't know what it is, huh? I don't know, I don't know. For, he said, notice that phrase, it will not be the now to itself, but to another, right? Which is really not the now in the, what, strict sense, right? Which is what we're, we're after, right? Now, notice, there's something puzzling about this thing, because, is the now in the past? No, because the limit can't be. Well, you see, go back to the line, you see. Is the end point in the line? In the line, I guess not. Well, if you see the end point, the end point's not in the line, then they're outside the line. Yeah, it is in the line. Yeah. Right? Yeah. Okay. Now, just to make an allusion there to the, we were going to talk about the sense of the word beginning, right? Have we, in the metaphysics? You know, when Esdala talks about the word beginning, which is the first word in the fifth book, kind of, the whole book five is devoted to the words that are especially used in wisdom. And these are the words that pertain either to the subject of wisdom, or the parts of that subject, or they pertain to the properties of that subject, or they pertain to causes, right? The causes of the subject. And as Thomas explains in his commentary in the fifth book, in every science you have a subject, right? And you have certain causes of that subject, and then you have properties that you show that belong to that subject. And so the words that are used in talking about causes, or talking about the subject of wisdom, or talking about its properties, Aristotle has discovered that all these words are equivocal. But they're equivocal by what? Reason and not by chance, huh? And so he spends a whole book, the whole fifth book of wisdom, distinguishing these words, right? Into their central meanings, but also ordering those meanings, right? And so when he takes up the word beginning, the first meaning he gives a beginning, is the beginning of a magnitude, right? Like the point is the beginning of the line, right? This is the beginning of the desk here, right? The curve is the beginning of the campus here, I think, in students, and so on, right? And then he says, sometimes you don't begin, though, at the beginning of the magnitude. If I'm going to take the road, let's say, into Boston, I don't necessarily go out to the beginning of the road to take that road, do I? If I live, you know, halfway down the road, right? That's where I want to begin, right? Yeah. That's still very similar to the first meaning, okay? But then he comes to a third meaning of the beginning, which is the... A fundamental part of something, like he says, the foundation is the beginning of a, what, house, right? And then finally he goes to the fourth meaning of the beginning, which is the mover or the maker. Why does the mover or maker, why does the sense in which a house builder is the beginning of a house, right, come after the sense in which the foundation of the house is the beginning of the house? Why is the sense in which the foundation of a house is the beginning of a house more like the way that a point is being in the line than the way that a, what, house builder is the beginning of a house? Because it's still part of the thing. Yeah, yeah. So Thomas says the house is a part, the foundation is a part of the house, right? The house builder is not a part of the house. At least he shouldn't be. So the foundation is the beginning of the house is more like the way that a point is the beginning of a line, or a line is the beginning of a surface, or a surface is the beginning of a body, right? That's because the point is in that which is the beginning of the house, right? The line is in that, right? Okay. So this is when you speak of a circle, right? The circle is not just that line, right? It's this whole thing here, the circle, right? But that line is what? The limit. The limit. Yeah. But is it a part of the circle? Yeah. Okay. Or is it a limit of the circle? Both. Both. Well, now! See? Uh-oh. Do you want to make that which has no width a part, or that which has width? No. Well, not strictly. No. See? Yeah. So, but yet you want to say that that line is in the circle, right? So, if the now is the limit of the past, then the now is in the past. And if the now is the limit of the future, then the now is in the future, right? And the past is in the future, and the future is in the past. Yeah. Well, I would have a problem, you know. Automatically, if you say that it's the same now, right? Yeah. See? Maybe there's no time in the now, right? Because the now is indivisible, right? And a past means what? Time. Some time. It's a part of time. And a part of time is something divisible, right? Mm-hmm. See? The indivisible is not a part of the continuance. So, if the past is a part of time, the past is a certain amount of time, right? Okay? In the same way, the future, right? So, what are you going to say? There's no time in the now, right? So, although the now is in the past, it's not part of the time that is the past. Time, we call the past. The end of the year, right, is not December. It took me speaking, right? The whole month of December. That's not the end of the year. They're talking about, what, April 15th. You guys don't know about this, but... April 15th is a deadline, right? See? You know, more or less the taxes, right? Oh, true. But, April 15th fell on Monday and on Patriot's Day in Massachusetts here, right? So, Massachusetts said you don't have to file your state income tax on the 15th. You have, what, extended the day, right? Okay. And the question was, what about the federal tax, right? And someone asked me, I wasn't sure, you know, would the Fed apply to them, right? Anyway, they had this thing about, it's going to be postmarked by midnight on this last day, right? You see? Or else you have to file for extension, right, and so on, right? I guess there's an automatic extension you can get when you get a file, right? You see, the penalty for not filing is worse than the penalty for not paying. Oh, my God. You see? You know, if I owe the money, I have to check in. That can be, you know, you know, realized in some way. But if I haven't filed, this would be more of a group penalty, right? Because I want the information I do, right? See? So, I've got it until midnight, you know, to get my thing stamped, right? You know, postmarked, right? So, that's the end of the period. File it. I filed it, by the way, so. We're all teaching a series to file in the last day. Yeah. Give them their money to, you know, hold off as long as your kids are giving their money. You see? Well, the, it's not the last hour, is it? The last half hour? Last minute? You know? So, no, it's the end of the day. There's no time at all, is it? Is it? So, if the past is time, and the future is time, right? And the now is in both, is the past and the future, and the future and the past? It doesn't seem so. So, but if you give the nows, you may give it some, what? Extension, right? And then the now is in the past and in the future. Then you'd have, what? Time, both in the past and in the, what? Future, huh? Right? Right? Doesn't have much sense, though, does it? But, of course, as he points out, it wouldn't, wouldn't all be now, would it? In the strict sense, would it? Because, if it had any extension of time, part could be before and part afterwards, right? And that would not make it all at once, would it? Okay? It wouldn't be the now, as he says, what? To itself and first, right? But the now, by reason of only a part of itself, right? Or something in itself, right? Yeah. And so long as that something in itself that you're looking for, that's going to be now, to itself, and first, to use that phrase I used at the beginning of this reading, right? So long as you're looking for that, it can't have any part, can it? It's only, part of it would be there. Right? Unless you want to say the past and the future are there together, but that's obviously absurd. So you've got to have the same now, and it's got to be, what? Indivisible. So it kind of turns it around now, and the next page here, it looks the other way around now, see? Could we just give you a second? What was the second meaning of beginning? Aristotle says where it's most convenient to begin along the road. So, really, just because... So it's supposed to be the road that begins here, right? Sure. And goes here to Boston. Sure. It begins in Springfield and goes to Boston, right? Sure. The road actually starts at Springfield, right? There's no pain in the outhouse, there's just dirt down there, right? No road. It's the road begins. But I... If I start from here, that's the beginning of the road, right? Yeah. But if I live here, the beginning of my trip to Boston is going to be, what? There. That's where I'm going to be the beginning of my trip to Boston. It would be a sense for me to go out here and go out and start there. You know, you've heard of it, you know, various neuroseses, you know? Amen. This would be via neuroses, you know? I mean, you have to very road, you know, it's all right. It's just where the road begins, you know, to take that thing. Just being a consistent philosopher, he's sitting there with... And you've got to be careful, you know, that takes the first time, by the way, see? Because...