Natural Hearing (Aristotle's Physics)
Lecture 71: The Continuous and the Problem of Indivisibles

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in my example class I say if the flash has an idea it should be a thought but if your girlfriend says to you don't get ideas she's probably talking about images you're not doing much thinking but you can see a lot of confusion between thought and what image because John Locke is trying to understand you know general idea of triangle like you mentioned this before and so now if you define triangle in general you say it's like a let's say it's a figure contained by three straight lines now so you might say well three straight lines or even two straight lines they can either be equal or unequal don't they what about these three straight lines are they equal or unequal each other well if you say either one you're going to be in trouble right if you make these three straight lines equal it's not going to fit the scalene triangle that's going to be common to the scalene triangle as well as the you know equilateral triangle if I make the three of them unequal they won't fit the equilateral triangle I think just two of them you know and so on okay so Locke doesn't know what to say you know and so he ends up by saying it's all and none of those well that's an apparent contradiction right and then Barclay coming along next he says well that's absurd therefore there are no general ideas that's it now I think I was you know using this to exemplify one thing there before right the fact that he doesn't understand ability right and the proper answer to this is that those three straight lines in the general definition of triangle they are able to be equal or unequal right but they're not actually one or the other in the definition okay so he doesn't understand ability that was one problem right but there's another problem and that is that he's in a sense trying to imagine the triangle in general see now any individual line or pair of lines that you imagine you have to imagine either two what equal lines or two unequal lines right any two lines you imagine will be actually equal or actually what unequal there's no other possibility right you see and so he's in a sense trying to imagine right what he should be understanding and that's where he gets in trouble right if I picture a man right I can picture in my head my imagination a white man right or I can picture a black man or a yellow man or a red man or something brown man I guess right picture green man too for me they don't exist okay but when I understand what a man is right that's a material at that point I'm understanding something that is common to the white man the black man right but can I imagine a man you know without imagining someone you know a male or female right you see but black or white short or tall or you know you see yeah but my image of a man is never my thought of what a man is right so Aristotle's going to be distinguishing between thinking and what imagining right between thinking and sensing too but that's easier to see but you'll be distinguishing between thinking and imagining and it's kind of so the way Aristotle proceeds because he'll start with what is more known to us he doesn't start with the fact that the thought is of something universal the image is of something singular that's true that's kind of hard to see for the average person right at first right where Aristotle begins is very proportion to us he says I can imagine a terrorist in the next room about to come in here right I can imagine that right he's got a black thing he's got a Kleschnikov whatever it's called and but do I think there's a terrorist in the next room no no see I have a certain freedom in my imagination but I have to have some reason to think that there's a terrorist in the next room right I really saw there is that's very simple to see and the second thing Aristotle points out that if I think there's a terrorist in the next room I'm going to be afraid probably right now I can imagine a terrorist in the next room by a man right you see see or else I can imagine myself what winning the million dollar lottery in class right but I don't think I won see I haven't even bought a ticket right so so I have no reason to think I won I even could have won right and secondly just imagine myself winning a million dollars I don't get particularly creatively excited about but if I thought he won the million dollars you know something around you know and you're buying me off for a drink and so on you know you see that is a very concrete way Aristotle has to say there's a difference there right between thinking and what imagining and I think there's that difference there too I'm talking about contemporary belief you know that imagination is better than reason you know but at Disneyland it says you know now people see somebody sees around you know imagination is more important than knowledge oh you see but one thing about imagining this is a freedom of imagining this isn't thinking one of my former colleagues there used to like to quote a passage from Plato I don't know if it's in the public or not but it's um passage from Plato is an opinion without a reason is an ugly thing so he used to quote this thing in class you know and he says don't pawn your uglies off on me so it's kind of like putting the students on guard they've got to have a reason for what they think you see a lot of times people they just what imagine something which is vivid enough it seems real and that's it you know he used to go for walks and you know maybe a Saturday or Sunday afternoon with the three children when they're little and I used to try to kind of spice it up we had a lot of woods around the area there and so on and you'd see on these trees sometimes it's a little red ribbon I guess they put them up for snowmobiles for the winter I don't know what they're there for but I'd always pretend that the Indians had put that up right and try to give a little bit and so as they got older of course they realized that there really weren't Indians around in the neighborhood but that's kind of a game with them see but finally I'd been telling them the story about Indians and we'd kind of traveled just in distance and we were looking down about something we hadn't seen really before I don't know what they really were it kind of quonsan huts you know there's Indian places you know well my oldest son and my daughter were older you know but the youngest one he got really scared we had you know so I think the imagination can seem very real you see well it seems though that even with imagination though it seems as though some of that could be immaterial active because if I were to imagine you know understanding in the universal sense so you have an activity that's outside the material but let's see with the angels that are incorporeal can they imagine things I mean they must be they don't imagine they only know truth no but the angels know singlets but not who senses or imagination but so if you think of the human beings when we die you separate it from your body there's no chance of imagining things at that point I mean you can't let your imagination go about anything you wouldn't come up with a novel or anything at that point no that doesn't come to the next next course that's interesting notice you cannot imagine a thought you see people sometimes you know see the drawings are a little like Boban you know but you can't really imagine a thought it doesn't have any shape you see you you Can you imagine a thought? Is it a circle or is it a square or is it a, you know, is it a cylinder or is it a, you know, circle, I mean a sphere or a cube? What shape do your thoughts have? I don't have any shape. Is it? But there's a real danger, therefore, of what we call false imagination, right? When you try to imagine things that cannot be imagined, right? And try to understand them, huh? So, if you look at Eric Thomas' work on the Dei Trinitati, there are Goetheism, but it's apropos of the text of Goetheism, you know, that in theology, one ought not to, what, try to resolve the imagination, right? You're going to be automatically, what, deceived that way, huh? But notice, the freedom of the imagination is one thing that they, what, like, and it fits kind of democratic customs, huh? But they kind of worship the idea of freedom, huh? So, you may recall the phrase of our style there where you spoke of the Greeks using contrary, or speaking of contrariety and change, right? And they all came up with contraries in some way, right? You remember that? And, you know, when you look at the Chinese, and the Book of Changes there, they're using contraries, too. And the modernists use contraries, huh? And Aristotle says, this seems to be forced on the mind by truth itself, huh? And that's really the perfection of the mind or the reason, when it's, in a way, forced to think something, huh? It cannot be otherwise, huh? Well, the imagination keeps a certain, what, freedom, huh? You can imagine things other than they are, huh? C.S. Lewis says something interesting about that, you know, where he's going to some part of England he's never been to before, huh? And he's picked up by an uncle down there, somebody, you know, that's related to him, huh? And they start, you know, driving back from the station or wherever it is. And C.S. Lewis says, excuse me, Mark, can you know, they didn't think, you know, that this part of England was like that. And he's kind of amazed to see this, right? And the guy says, well, what right did you have to think that, you know? He's kind of a tough-minded guy, right? But, you know, this happens, huh? Even before you go to some place, you know, you imagine it to be a certain way. And when you get there, it's not that way at all. But right that you had to think that it was this way, you see? You've got to have a reason for thinking it that way, right? I'd say, but I've often, you know, I mean, everybody's experienced, I think, imagining things. Even if you're going to meet somebody you've never met before, you know, you imagine them to be a certain way. Yeah? So can you say then that the brain is the organ of imagination? Part of the brain, yeah. Yeah, yeah, yeah, yeah. These ones that are tied to the singular in some way. So. Like the two semicircles, are they, in mathematics, is it right? There's no way to distinguish between continuous and touching. You couldn't have touching in mathematics. It becomes difficult to do, yeah. Yeah, yeah. To distinguish an actual semicircle. Yeah, yeah. But we speak, you know, even in math, the sense of the, you know, circle, touching a circle at one point, you know, there's not really a difference, is that? Not as clear as it would be in the natural world, no? Okay? This answers the question whether the two have become, what, one or not, yeah? Well, it's difficult to say you have two points unless one is here and one is, what, there, right? That happened in modern physics because, in quantum physics there, because they can't pinpoint the particles anymore, not just in practice, but in theory they can't. I mean, they can't, they can't have particles that have both a, what, an exact momentum and an exact position, right? And they have to, and they're related mathematically, the accuracy of these two. And so, as they say, you know, as Schrodinger says, Schrodinger says, the atoms or the particles become blurred. And we don't mean just in our knowledge, but in reality. There's not identifiable individuals anymore. That's kind of striking when you see that, because, you know, the average person has got kind of a naive view of man as kind of a collection of atoms and molecules, in which case we wouldn't be one thing, we'd be just, what? One, two, one. Yeah, we'd just be a collection of substances, right? But I think, you know, if you talk to students in class, you kind of get them, that's what they think, right? Now, I'll ask them, you know, is man one substance? Or, you know, like Pedocles says, or Anxagos, a mixture of many substances, huh? And they more have to say a mixture of many substances, huh? Not really one thing, huh? And if that's so, then there's no birth or death. You know how Pedocles and Anxagos are saying? And perhaps, oh, all you have is a mixture and separation of things, huh? And therefore, when you go to the funeral home, you say, oh, I see a separation, you know? And you're talking about, you know, a new baby comes into the world, you know, just a new mixture, I see, right? You know, and so, you know, when Brady Russell's running around the world, they're trying to stop the atomic war, you know, in all these conferences. And what's the difference? It's the rearrangement of atoms and molecules, I mean, what's, you know, it's no big deal, right? It's like, you know, Brooke was putting on a black band, you know, at the end of his class because his class has died, you know? You know, that's emotional about just separation, and they're going to be, they still exist, these students, right? They're just going to be, you know, mixed in different combinations and so on. And these guys want to have, you know, their ashes spread over the ocean or something, you know? It's like, you know, all we're doing is mixing these things, you know, and separating them, see? But do you really, you know, there's two things here, right? One is, do you really think of yourself as being many substances, right? Do you really treat yourself or behave that way, right? You know, if I lost an arm or a leg or something, right? Better not give me a tooth pulled once. I mean, if I lost an arm or a leg, I'd really hate that, you know? You know, part of me missing, right? But what will me be, I mean, would it, you know? See? I mean, really, if that comes to a combination of abs and balacus, the losing of my arm is like, you know, part of the city there of Worcester has disappeared or something, you know? But the other part's okay. No, it's a... That's me. Or, you know, the... I give lectures sometimes on the principle of subsidiarity, you know, that the popes talk about a lot. But you really find it in the second book of Aristotle as well. Oh, that's right. And I give them this example, say, to try to bring out that the unity of a man is different from the unity of a, what, family or the unity of a city or something like that, sorry. An example is to use, you know, with college kids especially, I'd say now, suppose, you know, a student from Holy Cross comes over, you know, and beats up some student at assumption. Okay? Now, would it be right for us to go back over and find some... any Holy Cross student and beat the hell out of him, right? You know? Is that just? See? Or, you know, if a Palestinian goes, kills a Jew, and then the Jew will kill a Palestinian, right? Is that just, huh? See? Okay. So now, suppose I hit you, right? You're going to have to hit me back on my fist? Or would you feel that you could, you know, hit me back here or here or somewhere else? Huh? I said, well, you hit me here. My chest never hits you. Huh? Chest didn't hit you. You know, you should hit the knuckles there, right? You see? Well, nobody would take that seriously, would they? You see? I hit you. was in my hand, right? But if I'm just, you know, many substances, there's just another multitude there, right? You see? You see? Like the people of Florida going crazy and then punishing people of Washington or somewhere or Oregon or someplace because people of Oregon went crazy, right? That doesn't make any sense, does it? Frenchmen go crazy and go punish the Spaniards? That's not fair, is it? The Germans run amok there under Hitler and then we go and destroy our Switzerland or something? It's called part of Europe, isn't it? Why not? So you really have a unity that Europe doesn't have, right? That Assumption College doesn't have, right? You know, the individuals make up this, huh? Like later, what's her name? Havisham, they're in different novels, right? So you don't take revenge at all, man, because some man left her at the altar, right? You know the story there, the great expectations. There'll be a little dick in this area. Yeah, he's our greatest novelist, right? He's a novelist, huh? Okay. Now, there is a way you can also kind of, you know, try to lead people back to what they really do know, that they are one substance, huh? And the best way of doing this, I think, is by seeing the difference between activities like seeing, hearing, understanding, reasoning, and so on, and activities like lifting and pushing and pulling. So what's the difference between those two? Well, take an activity like lifting, an activity like pushing, an activity like pulling, compare that now with an activity like seeing, or hearing, or reasoning, or something of this sort of thing. What's the fundamental difference between an activity like lifting and pushing or pulling, and an activity like seeing or hearing or reasoning? Well, it's physical. So, yeah? Seeing and hearing might involve the body, too, right? More fundamental difference of looking for in these two, huh? In the ones affecting something outside. Yeah, yeah. Here you're acting upon something outside, right? While seeing and hearing or reasoning are activities that remain within the one seeing or hearing or, what? Reasoning, right? Okay, so there's sometimes called those imminent, but that's just kind of lacking. We're meaning remaining within, right? Remaining within the doer. So if I see you, is that affecting you in some way? No, you may not even know I'm seeing you, right? Okay? But if I push you or pull you or lift you, then you are being, what? Affected upon by me, right? Okay? Now, is it possible for you and I to lift something together that one of us could not lift alone? Now, I know these bad boys who used to, on Halloween night, they'd take somebody's Volkswagen, right? Enough guys, they can lift the Volkswagen and put it up on top of the guy's garage. Hey. So he wakes up on... The hell am I supposed to be? He wakes up on top of the roof, right? Plus, you know, bad thing to do, obviously, it's kind of funny, nevertheless. Or if we're having a tug of rope, right? You see? You got, let's say, five guys on that side, right? Maybe I go myself and put and pull those five guys over the line, right? But if you guys come and help me, right? Together we can pull them over the line, something that no one of us could do by himself, right? Okay? Now, what about these activities, though, right? See? Can you and I together see something that one of us alone cannot see? I mean, suppose you had a painting there, or take this, I'll paint that this you bought, you know? And if we put a curtain here, right? Going like that. So you could see the left side, but not the right side. And I could see the right side, but not the left side. Could you say that that painting has been seen? Someone would have to, one of us would have to see both parts to say that the painting has been seen. Well, in the case of their activity, truly, the Volkswagen has been lifted, as the poor guy discovers, right? Even though no guy could do that by himself, right? And one guy doesn't have to do it by himself to have the Volkswagen lifted, right? And not the one, and together we can pull those, you know, the team over the line, right? Something no one of us could do alone. But one and the same person has to see the whole painting, right? Before the whole painting is been seen. The same way of hearing, right? You've got a nice melody of Mozart, right? And you hear the first notes, and you hear the next notes, and I hear the next notes, right? Has that melody really been heard? It's got to be really one and the same person that what? He hears it, right? The same way in reading or calculating, right? If I know that every mother is a woman, right? But I don't know that no man is a woman, right? And you know that no man is a woman, but you don't know that every mother is a woman, right? Can we together syllogize that no man is a mother? One of us would have to get both of those premises into his head, right? Before that conclusion could be syllogized, right? Or if I knew the length of this table, but not the width, and you knew the width, but not the what? Link. Could we together, with my never knowing the width and you never knowing the length, could we together calculate the area? No. You see the difference between that, right? You and I cannot together calculate the what? Area, right? One of us just knowing one, not the other. One of us at least has got to know both. But you and I can lift something that one of us alone cannot, right? We can do it. Well, it's because you're acting upon something outside of you, right? But the image of the activity, it has to be within one person, right? Now, if I was really, in a strict sense, many substances, right? And each atom and molecule was really a distinct what? Substance, right? Like you and I are distinct substances, right? Then there would be no such thing as what? Seeing, hearing, reasoning, right? But before you before you see this, people really do think of themselves as one thing, right? And therefore, there's such a thing as Aristotle said substantial change, right? And that's very important later on for understanding the soul, for understanding that, right? The first matter, right? Because it's not until you know about substantial change that you see there's a distinction between And that's very important to you. first matter and these actual substances that we call matter too but are matter meaning a secondary sense not a divisional one. And before you see that there's such a thing as substantial form, right? And that division is necessary when you approach the definition of the soul because the soul is going to turn out to be a substantial form. Aristotle was the first man to really see that, right? Is it a consul, was it Vienna or is it got the fake one there? Consul, Vienna, that the church officially said the soul was that substantial form, right? But people had a hard time understanding what the soul was. They either make the soul something accidental like the organization of a house or something. The harmony of the body is as Simeon suggests in the Phaedo. Or else he made it a what? Have an angel. Any material substance imprisoned in the body, right? There were crude notions in that but those are the two ones, right? They couldn't see there's something formal but in the genus of substance. There's something substantial but not like a complete substance, right? So let's come back now to the texture at hand. We'll touch upon these things again I want you to see kind of the fact that these lowly things have to be understood to understand even the what? Higher things so far as we can. So the continuous is that whose edges are one touching whose edges are what? Together but they're not one and the same next of which there is nothing of the same kind between. Now notice in a way things that are continuous or things that are touching are next to each other too, aren't they? right? But sometimes you might keep the word next for something that is not continuous or touching but it has nothing of the same kind in between right? Okay? So my house and the neighbor's house are not continuous and they're not contiguous they're not touching right? But there's no house in between my house and the next house right? Okay? The same way you two are not what? Continuous right? You're not what do you call them Siamese twins or something right? Okay? You're not touching right? But you're the next okay next Okay? Like they say at the doctor's office next They're all lined up there right? Whatever office it might be huh? Okay? See? You see that? And in the strict sense thoughts are more what? There's a next thought right? And maybe a next topic and a next thing to be done and so on right? But not a continuous thing maybe or touching thing in many cases Now he says given those definitions it is impossible for anything continuous to be from what? Indivisibles right? As a line from points right? If by line you mean something continuous and by the point what? Something indivisible right? Now as Thomas explains in the commentary he's going to be developing this reason for everything that is continuous not just for a line right but also for the what motion down that line right that is continuous and the time it takes to go down that right okay but kind of emphasis here in the first reading is upon the line right the magnitude being continuous huh and not being composed of indivisibles right and he's going to kind of elaborate you know more about motion about time in the next readings right although really the basic reason is seen here too right okay you're going to have extra ways of seeing it just so you're to be sure that everything continuous right is not composed of indivisibles huh now sometimes when I do this I'll say you know well if you want to put something continuous together from indivisibles right that were possible if you wanted to put a line for example together from points the points would have to what come together right okay okay but can they come together at their edges see could two points have a edge or limit in common right see like the two semicircles right have that diameter you might say right it's the end of one and the beginning of the other right they have that or could they have two edges together two points why not see okay so is there any distinction between a point and its edge or in that case you're imagining the point to be like a little circle where the circumference is what not the same as what's inside right but then you're giving the point somewhat yeah yeah yeah okay now in a way you could say sometimes sometimes I have a student in class who deny that there is such a thing as a point and you know as you know as you know as you know as you know as you know as you know as you know some of the ancient greeks that if you add a point to a line is the line any longer so the point seems to be nothing right but in a way that that is assuming that what is is what continuous right but I mentioned how Thomas uses that though when he's person mani dexio there when he's talking about how the goodness of the creature adds nothing to the goodness of God because the goodness of the creature is to the goodness of God not like a shorter line is to a longer line in which case if you add the goodness of the creature to the goodness of God you'd have a what greater good right but there's an infinite distance between what God's goodness and that of the creature so the creature's goodness is to God like a point is to a what a line and a point added to a line is no more okay that's kind of an amazing thing to see right that how purely gratuitous on his part right and how generous on his part the great era philosopher Alicena there you know Thomas will quote him Alicena you know God he's talking about the virtues of God right God alone in a way is liberal right because when you talk about the virtue of liberality or generosity in ethics it's not when I give you something expecting something in return right or demanding something in return right but just sweat you know it's yours you know I don't expect you to pay me for it no I expect the return it's yours really yeah yeah you know that's generosity right but but God gets sweat nothing out of what he gives us huh you know he doesn't even get a good act out of it right you see so if I give you something you know gratuitously today or tomorrow or something like that uh at least you got a good act out of it right you see but when God gives us something he doesn't get a new act out of that he's completely liberal he's completely generous right astounding right you see a lot of times students have a hard time understanding you know God right you know utterly uh independent he is in the way of us right anyway so certainly as I say students would deny that there's such a thing as a point huh I thought Do you know how I try to lead them to see that in a way there is a point? Well, I start off with that there are bodies, right? And they know there are bodies, right? Okay, they don't doubt that. That follows a Barclay or something. Okay? And secondly, they know that there are bodies that don't go on forever. Like this table comes to an end, right? So there's an end of bodies, right? And what do you call the end of a body? Surface, yeah. Okay, so now you know that there are surfaces, right? And then I say to them, now, the surface has length and width, right? But does the surface of the ice cube, does it have any depth? Because if you give it some depth, you're taking part of the body, aren't you, right? So you haven't quite come yet to the end of the body. So there's an end of the body, right? Maybe the surface, but it has no depth, right? So now they're admitting that there is something that has length and width, but no depth, right? And now I say, now, in this finite cube, let's take that as an example, right? The surface, which is squares, right? They have length and width, but no depth. Now, do those go on forever? If it's gone on forever, then the body would have gone on forever, right? So there's an end to surfaces, too. And now I say, now, does the end of a surface, of a square, for example, does it have any width? No. In that case, you would not have come to the end of the, what? The surface, right? But that's an end, right? It's gone forever. So now they've got something that has length, but no width, right? Now they have the existence of that. And then finally I say, now, is there, is that line that is the end of the square, any one of those lines, do they go on forever? If they went on forever, then the square would have gone on forever, right? So they have an end, right? Now, how long is the end of a line? No, if you give it any length, you haven't quite come to the end, right? But it does have an end. So now you've got something that has neither length nor width nor depth, right? So it has no, what, magnitude at all, right? So how can you distinguish between the point, which exists, by this argument, and its edge, right? Because then you'd be giving it some kind of, what, length, right? And even width, wouldn't you? So two points couldn't really, what, have an edge in common and that's it? And the rest not, right? Or you could have two edges touching, right, but the rest of them not touching. Now, I'll make another little side of it, I'm interested in what I think. When Aristotle talks about the four kinds of causes, he argues that there's a first cause in every kind of cause, and we'll see these arguments eventually. He gives them individually in the different particular parts of philosophy, but universally in the second book of wisdom, right? But he also says in the beginning of the fifth book of wisdom that every cause is a beginning, but not every beginning is a, what, cause, right? And then when he gets to the word end, or limit, he says that we first, you know, speak of the beginning is here and the end at the other end, right? But sometimes we speak of both as being a, what, end, the end points of a line, right? Okay. So in some way, beginning is more general than cause, and end or limit in some ways, what, more general than beginning. What's kind of interesting, you have something like what you say about causes that are on the limit. Just as there's a cause that has a cause, right? So there's a limit that, what, has a limit, right? So the surface is a limit of a body that has a limit, right? So the square that is the limit of a cube has limits which are lines, right? The lines are also a limit that have a limit. Because the four lines that are the limits of the square, each of them has a limit which is the point, right? But now is the point a limit that has a limit? No. It is a limit, just like God is a cause. But just as God is a cause that has no cause, the point is a limit that has no limit. Kind of interesting, right? Something similar to what you have there. You sort of see that here. So he says there is not an edge and some other part of the invisible, or a limit, you could say, right? So you can make some distinction between the end of a body and the body, right? They're not identical, right? You can make some distinction between the end of a surface and the surface, right? And between the end of a, what? Line and the line. The end of a line is a point. It's not a line. But can you speak of the end of a point? And the point makes some distinction between the... Kind of marvelous, right? There's not an edge, he says, in some other part of the invisible. But there's no difference between the indivisible there and a limit. You can't make that. It is a limit. Nor are there edges together, for there's no edge of the partless. For the edge and that of which it is an edge are other. Or the end, in that of which it is an end, or other, right? Or the limit, in that of which it is a limit, or other, right? Okay? Now, setting that aside, he's going to give a kind of either-or syllogism in the next paragraph here, huh? He's going to reason against the idea that a line can be put together from points, either by the points being continuous, right? Or by the points, what? Even touching, right? Okay? And he says, there is the same reason all indivisibles. And Thomas would note that, right? Okay? But it's a little more explicit here about the line and so on here, so that he'll kind of more fully satisfy the mind, right? Gives some more particular reasons for thinking that the motion, right? Over the line, right? And the time it takes are also continuous, right? But it's basically the same reason here, huh? It's interesting that he does something like that with the causes, because he gives a reason that's common, really, to all four kinds of cause, right? Although maybe it's a little more explicit with the cause and sense of mover, right? But then later on, he gives special reasons for the form, and special reasons for the end, right? And so on, right? And look at what he's doing here, right? Except it's with limit, you know? Another little analogy there between the two treatments, huh? Okay? So he says there is the same reason all indivisibles. They will not be continuous in account of the aforesaid reason. In everything touching, either the whole touches the whole, or the part the part, or the whole the part, huh? So like two circles, right, huh? Two circles can touch. Part can touch part, right? Or the whole can touch part of the other one, and vice versa. Or the whole can touch the whole. I just draw the circle twice, because we didn't think. Okay? Now sometimes when I put that earlier part with this, and I'll say maybe there's a fourth way of touching, which is what? To touch it therein, right? Okay? Then you start to eliminate these to the point, right? Because the point has no parts, right? So that's impossible. And this is impossible, right? Therefore the two points touch, they're going nowhere. Go inside the chords. and therefore they have no more length than what? One point. One point, there's no length at all. So how are you getting any line out of two points touching, right? And if a hundred or a thousand or a million or infinity of them touched, the only way they could touch would be to coincide. And if they coincide, they have no more length than one point, which is no length at all, so you can't be put together. You could have a series of points, but that would be continuous, right? But then, now look at this, like we said before, because you can't have any distinction between the point and the edge, or in their limit of the point, huh? With the small circle inside, that represents what again? The whole of one is touching part of the other, right? And vice versa, right? But both of those first two ways imply the media parts, right? So he says, since indivisible without parts, it is necessary that the whole touch the whole. But yeah, you have to be careful when you say that, because whole might imply that you have parts, right? But it means that the two would have to coincide, right? Okay? Which would be like the whole touching the whole, coinciding, huh? But if the whole touches the whole, it will not be continuous. For the continuous has one part other than another, right? And is divided into different parts separated in place, one part outside the other, right? Because that's part of the understanding of what continuous is, right? That is part outside of part, huh? So that's the way he develops it there. A little different than the way I was developing it there, right? Then he goes on to point out, But neither is a point next to a point, nor a now to a now, huh? So that length or time could be from these. For those things are next to each other, between whom there is nothing of the same kind. But these, maybe that should be there. But there is always a line between points, huh? And time between now, huh? So, you know, in a straight line there, the end points are the points that are furthest apart, right? But is there a point on this line that is the closest to, and not the furthest apart, huh? Or is any point you take, there's always another one closer to that, huh? So is there a next point on the line? Is there a next now in time, huh? So if you try to imagine two points being next to each other, you are falsely imagining, right? I think, aren't you? So do you have the next thought, though? But not the next point? What am I? Professor says, my next point? You've heard the definition of reason that Shakespeare gives, right? Okay. Now, in English, there's another meaning of the noun, reason. Now, if I... Let me just put a couple of statements before you. Let me take my mother there a little bit. You know, she'd say, I see, said the blind man, but he couldn't see at all. You know, you have to see, well, there's two different meanings of the word to see there, right? Okay. Now, if I say that reason is able to give her reason, does reason have the same meaning in those? Now, which of those is the ability for life discourse, looking before and after, which is that? First one. Okay? So this, here, the genus, is ability, right? The differences are what it's an ability for, right? It's an ability for large discourse, looking before and after. Okay? How about this here? Reason, okay, reason over here is not an ability, is it? Reason is the reason why a beast, huh? Reason is the reason why man is more than a beast. Same two meanings of the beast there? Same two meanings of that sentence or with the first one? First one, yeah. Yeah, two different meanings here, reason, right? Yeah. Reason is the reason why man is more than a beast, okay? And which is the ability, okay? So the reason why man is more than a beast is that he has this ability called reason that Shakespeare defined, right, for us, huh? Now, this reason, what is it? It's a cause. It's a cause, the genus of it? No. It's a statement. You've got to define it as a statement? Yes. You complete your definition, then. Is every reason a statement, but not every statement a reason? Yes. Okay, so what separates the reason that is a statement from other statements? Okay. Which gives a cause. Well, do you always say, do you have a cause as your reason? I think so. Sometimes, do you like a species making a difference or something? Yeah, we're looking for the difference, yeah, a species making a difference there, right? Sometimes I say to students, you know, I'll say to students that the best reason they can give, right, is the reason why something must be so. So, and Socrates and Aristotle teaches that, right? You know, I need to exemplify all of it, you know, the simple thing in Japanese, you know, I'll say it. When straight lines intersect... You know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know