Natural Hearing (Aristotle's Physics)
Lecture 75: The Continuous: Composition, Divisibility, and Circular Reasoning

Transcript
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You know, I kind of summarize this a bit there, and I usually run it together, right? And I say if two things touch, they either touch the whole one part of the other, right? Or part of one part of the other, or else the whole one touches the whole of the other, right? You know, the way to touch, it seems at first sight, not, right? But maybe you could distinguish the edge of a thing from its, what, part, right? Right? So you may not want to call the four lines, you know, a part of the square, right? Or the edge. So sometimes there's four ways things could touch, then, right? And then I eliminate all four, right? But Aristotle has them separated here, right? Further, it is necessary that the points that you make up the continuous be either continuous or touching. There is the same reason in all indivisibles, right? Okay? They will not be continuous on the contrary to the aforesaid reason. In everything touching, either the whole touches the whole, or the part the part, or the whole the part. Since the indivisible is without parts, it is necessary that the whole touch the, what, whole, right? But if the whole touches the whole, it will not be continuous, huh? For the continuous has one part other than another, right? It has part outside of part, right? And is divided into different parts separated in place, huh? In a way, when you say that the two, in the continuous, two parts have a common limit, do you mean that, what, there are other sides of this limit, right? Right? So they're outside of each other, right? So it's the idea that the continuous has a part outside of what part, huh? And I kind of see it a little differently sometimes, I'll say, if two points touch, they, you can't have part of one touching part of the other, or part of one touching the whole of the other, because they have no parts, right? So the only way they can touch is in the way that a whole touches a whole, which means to coincide. But if they coincide, they have no more, what, length than one point, which is no length at all. And if ten or a hundred or a million or infinity of points touch, like the mathematician says, the only way they can touch is to coincide. And if they coincide, they have no more length than one point, which is no length at all. So you can't make a line by putting, what, points together, right? Do you see that? So is Aristotle here proving the second definition of continuous from the first? Because if it can't be made up of indivisibles, that means it can be divided forever. Well, we'll come to that in a moment, yeah, because it's kind of strange, in my opinion, a bit, a little bit. Okay, now the next point he's going to make, and say, he wants to show, as I said in the beginning, that you can't have the continuous made out of points that are next to each other, right? When I was in grade school, you know, in the sister school, you know, down in the playground, you've got to line up to go into class. Yeah. And so you're the next student, and then the next student, and then the next student, right? And just like in a row of houses, you've got a next house, right? But can you have a next point, huh? Well, if you've got two points, you've already got some distance between them, so they can't touch, right? And then you have, potentially at least, there are an infinity of other points between any two points, huh? So you can't put points next to each other, either, right? Okay. But neither is a point next to a point, nor an anau to anau, so the length of time could be from these. For these things are next to each other, between whom there is nothing of the same kind, right? Okay. That was the definition given up there in the first paragraph, huh? So when you speak of the next house, we mean there's no house between this house and your house, right? My next-door neighbor, as we say, right? But there is air, and maybe bushes, and grass, and so on, in between my house and the next house, right? So there's something between us, but nothing of the same, what, kind, right? Okay, but these, but in these, there's always a line between points, and time between, what, nous, right? Okay. Further, if a thing is divided into those things in which it is, it would be divided into invisibles. But nothing continuous is divided into that which is without parts. Now, you know, I don't know, if you look to the Latin text there, but in the Mariette text, you know, there's a little confusion there in the thing, because it doesn't give all the divisions that Thomas Reedy is following, right? Okay. And he says, Aristotle is first, in the beginning here, reasoning from that first definition of the continuous, right? Okay. And then later on, towards the end here, he's reasoning from the second definition, right? Okay. And so he's reasoning from the fact that the continuous is divisible forever, that it's not being made up of what? Indivisibles, right? And the reason why the number is not divisible forever, right, is that it is composed of indivisibles. You know, the definition of what number there that you can use is a multitude composed of units, right? But the units are altogether, what? Indivisible. They're even simpler than a, what? Point, huh? Sometimes the Greek mathematicians say a point is a one having position. So it adds something to the idea of the one, right? Okay. So what's kind of puzzling there is that Aristotle seems to be reasoning from the second definition of the continuous, right? To the continuous not being, what? Divisible into indivisibles. Okay. Now he's reasoning from the continuous being divisible forever, which is the second definition, or that which is always divisible into divisibles, right? In the way of saying it, to its not being, what? Composed of indivisibles, right? Okay. Now, in his commentary, then, Thomas says, and then at the end here he starts to manifest some things that he's kind of presupposed, right? Okay. And, yeah, in the last two paragraphs, I think it is, of this first reading, right? Okay. In the third from the end paragraph, maybe he's giving that second reason, right? Okay. Okay. Which is, but it is impossible that, look at the next to the last paragraph, but it is impossible that any other kind of thing be between points and ous, for if there were, it would be clearly divisible or indivisible. And if divisible, then it would be indivisible, and it would be always divisible. This service is continuous. But now in the last paragraph, it is clear that everything continuous is divisible into things which are always divisible. For if into indivisibles, the indivisible would be touch and indivisible, where continuous things have one edge and touch, right? Well, now, if you compare that with the so-called second argument in the text there that he has, and Thomas gives it the second argument, he's reasoning in the second argument that because the continuous is that which is divisible forever, therefore, therefore, it's not composed of indivisibles, right? It's not divisible into indivisibles. And he gives a reason here later on why the continuous is divisible to things that are always continuous. It is because it can't be made up of indivisibles. Right? You see, it's like a paradox there, you see? Ah, which came first here, right? Which is the reason for which, right? Let's just raise the question here a bit, huh? We have this definition of the continuous. The continuous is that which is divisible forever. Okay. or I stated it somewhat differently, that which is always divisible into divisibles. Okay? That's another way of saying it, right? That which is divisible forever. And then you have the other thing that the continuous is not composed of being divisibles. Continuous is not divided into being divisibles. It kind of corresponds to that way of stating the first definition, right? As I was saying before, if you reason from a definition, right, and this is a definition continuous, you might reason from this to that, right? Okay? But, in the last paragraph there, he seems to be reasoning from this to that, right? Okay? I know myself, and I'm not reading this text, but I'm just teaching the first book there, you know, we're teaching the fragments, right? And we come to the fragment of an exhibition, you've probably seen me do it. And then Xavier says that there's no smalls to the small, right? And I'll say, well, this is true of the mathematical line, and I'll draw a mathematical line on the board, right, and say you can cut that in half, and you can take the half and cut that in half, and so on. And most students are somewhat inclined to accept the fact that you can keep on cutting it forever into halves, right? Okay? And I say, will this ever stop, right? See? Well, you always have something further divisible that you cut it into. But I can't be, you know, willing to accept that you can always cut into things that are further divisible, in which case to admit that it's divisible forever, right? Well, I try to manifest that. Do you remember the way I manifest that? I say, if you didn't cut it into something that is further divisible, right, then either you cut it up into nothing, or you cut it up into something indivisible, right? Okay? And I say, can you cut something up into nothing? See? Well, as Ann Xavier says in the other fragment, what is cannot cease to be by being cut, right? He said, if you could cut something up into nothing, it would be made out of what? Nothing. Nothing, right? I used to quote Nixon's remark one time, you know, He said, any way you slice the democratic program is still the same baloney, right? Let's take a little... Well, I said, well, you cut something up into what it's made out of, right? So if you could cut something up into nothing, it would be made out of nothing, which is absurd, right? Okay? So you don't make that possibility, right? So when you cut a straight line, either you get shorter straight lines, always, right? Unless you could cut it into two points, right? And then you could stop, right? Because the point is not divisible anymore. Well, then I say, well, but could you have a line that's two points long? See? Could you have a line, in other words, composed of points, huh? And then I bring in the other argument, I say, well, if you're going to make a line out of points, the points have to come together and touch, right? And then I say, now, there are these ways things can touch. Hole can touch hole, part can touch part, part can touch hole, and perhaps you can speak of the edge of things touching, right? I say, well, now, can two points touch in this way? So I draw, you know, you probably see me do that, I draw the circles on the board and I say, you know, part can touch part, like these two circles, right? A part can touch hole, like these two here, and a whole part, right? A whole can touch hole, and I say, I can't really draw that very well, but I just go around twice to get the idea, right? Maybe to speak of a fourth way where they touch at their edge, but the edge is really not a part, right? I say, well, now, can two points touch in this way? Well, they don't have any parts, right? So they can't touch in that way. Part touching part. Can part touch a hole? No, they don't have parts, right? Now, can you make any distinction between a point and its edge? See? But then you're really imagining the point to be a little tiny circle or something like that, right? And if you have some distinction between a point and its edge, there'd be something inside that's not the edge, right? And then you'd have some kind of extension and it wouldn't be invisible. So that way is all super possible, right? So two points can touch only like, and I say like, because if you speak, you don't have a hole either. There's a hole in this part, right? But they can only touch like a hole touches a hole. That is to say, coincide, right? And then I say, now, if two points coincide, how much length do you have? Well, as much as one point. Just no length at all. And then I say, if ten or a hundred or a thousand or a million or infinity of points you can touch. The only way they can touch is to coincide. And if they coincide, they have no more length at one point. Therefore, they have what? And if they have no length, you don't have a line, right? So there's no way you can put points together to make a line, right? So it's impossible that when you cut a line, you end up with two points rather than two shorter lines. So you always end up with two shorter lines, and you cut or bisect a straight line, you end up with two points. And there was nothing. So if you always end up with shorter lines, you can cut again and cut again and cut again. So it's divisible into things that are always divisible. It's divisible forever, right? So I'm showing from the fact that the continuous cannot be put together, the line in particular cannot be put together from points, that it's divisible forever, right? But when Thomas explains the way Aristotle's reasoning there in the second argument, and I know I was looking at the Marietta again this morning, and I noticed there's a real confusion there in the text, you know, occasionally you'll find that part of the division or one of the divisions is left out sometimes, you know, whether it's in the original text, you know, probably lost or what, you know. But, you know, Aristotle gives two principal reasons, and one is taken from the first definition of the continuous, and then later on, now there's a second to the one. And then he's reasoning from the second definition of the continuous to its being, what, not composed of indivisibles. I know you could reason from the continuous being divisible forever to its not being composed of indivisibles. Because if it were composed of indivisibles, then eventually you'd arrive to indivisibles and you could go on. But, which is really more basic than the other, right? Thomas doesn't say anything in the commentary about that apparent, what, circularity, right? That's interesting, huh? I know a famous place there in the Postal Analytics, where Thomas points out that Aristotle seems to reason in a circular way, because he's showing that the statements that are necessary are as such, or kap out to, per se. In one place he reasons for being necessary to there being statements as such. In another place he reasons for being as such to there being necessary. But, of course, Thomas notes this, right? There are style of reasons in both directions, right? And especially the fact that it's in the Postal Analytics, where Aristotle is saying one cannot reason circularly. You know? You can't use A to prove, what, B, and then B to prove A. Because then A would be more known than B, and since B is more known than A, then A would be more known than itself, and something would be, what, both before and after itself. You see? So, what is Aristotle doing? Thomas says, right? You know? In the very book where he teaches us, right? And it's kind of interesting because, I don't know if you're in the Nicomachean Ethics there, right? But in the first book of Nicomachean Ethics, Aristotle is about to object and argue against the position of Plato, right? And he gets to that point, he says, it's difficult for us to attack this because it is... It's difficult for us. It's difficult for us. It's difficult for us. then what held by our friends right okay and then he says uh but being philosophers right we should be lovers of the truth right and so he says plato is a friend he says but truth is a greater friend okay um and secondly it says something like that in the phaedo right now if you listen to me you'll hear little about socrates and a great deal about the truth right okay so ourselves said it would be impious to put plato before the truth okay and first thomas coming i said well yeah god is truth itself right okay but then thomas stops and then he says but there are other books in aristotle like you've been physics and so on where he disagrees in the first book of the physics right where he disagrees with plato right but he doesn't say you know this is to be against my friendship with plato you know and so on why is he why is he stop and make this observation at this point right he says well he's in the ethics right and the ethics friendship is one of the main things to be considered huh if you look at the ten books of nicomachean ethics two of the ten books are devoted to what friendship right which is the main theme there in the nicomachean ethics right and so to be attacking his friend's opinion right might seem to be against what friendship right and so aristotle wants to say this is not really against true friendship right to disagree with your friend right it doesn't matter like this huh okay um so i think it's kind of appropriate that in the uh uh posteriorlytics right when aristotle seems to reason from a to b in one place and from b to a in another place right this time should note this right and say what the heck is he doing because he's told us in this very book the posteriorlytics that this is uh bad reasoning to reason in a circle right and then he's going to eventually try to show that there must be some statements that we know right not to other statements right because nobody should be going on forever right unless you could correct it correctly from a to b a has to be more known than b right and then if you reason from b to a b has to be more known to a so you're saying that a in a way is more known than itself right makes my sense right you may have a little more complicated but as he talks about this he goes on he says well the real demonstration he says is from necessary to as such okay why then does aristotle reason at this other place from as such necessary well certainly in this academy right it would be a common opinion that uh episteme right is about the what as such the path out to right so you can take that as a probable opinion right and then reason from that to its being what necessary right okay in a way that does show that there's a real connection between being necessary as such the fact you can reason from one to the other right okay but he said the demonstration is basically from necessary to as such right and when you reason from as such to be necessary he's reasoning from as such as what a probable opinion right back to that right okay but he doesn't here seem to see this circularity that i seem to see in the way he presents it right because in the commentary thomas says he first reasons from the first definition of the continuous that whose what parts have a common boundary a common limit a common edge is this translation added right and um then the second principle reason he reasons from its the second definition of the continuous that which is to this right okay and then later on at the end of the reading he says aristotle's manifesting some things he's presupposed and then he seems to be reasoning from this to that right okay so thomas doesn't raise the question so it doesn't answer but i'm raising the question how would thomas answer how will we try to answer that seeing the proper demonstration would be from the definition but maybe for some reason like the way you did it you showed it the other one seems to be maybe more known yeah it seems to me that we would prove more that the uh contingent that would be judicial forever from the fact that it's not composed of what indivisibles right okay like in the way i was indicating my reason why discussed the fragrance of that jager right okay now as you read from this simply as something probable right you know solving it the way thomas solves this here right okay that's that's one possibility right okay like with my students they'll say you know when i ask them you know you can take a map line and cut it in half right and cut it in half right and so on and they're kind of prepared to admit it seems you know probabilities to them right that you always get shorter lines right but to really make it all together certain i point out that you can't cut it into two nothings and you can't cut it into two points right okay and so i'm really showing the impossibility from the impossibility of the line being composed of points right i'm really showing from that that it must be divisible forever it's always divisible in shorter lines which in turn are divisible again right right okay is the second um would that really be a property of the first the definition i don't know what i'd say about that but i'm saying is i'm reading from the second here to the first right yeah but our style apparently is reasoning in this reading right first from this to there but at the end it seems to be a reverse right okay now you could you could argue that this first one is as i say um probably that's one way of trying to solve it you know but is there a way of showing that the continuous is divisible forever um apart from this down here could you show that the continuous is divisible forever in some other way independently of the second thing here right and then also be able to reason from it to this huh what's what i would do reason by the way i always do it take a line right yeah you cut it in half yeah then i zoom in from the one half yeah into myself it looks like it's the same length as the original line but i know that i've zoomed in right and so i do that again it never seems to change although yeah dividing forever yeah i'm thinking of you know i've been away from book six for a while i haven't been teaching for a while then i went to my advanced course but there'd be enough students so okay but when i think about you know kind of a way for the text right what always comes to my mind is our people will meet later on in the in the third reading right where aristotle was showing um together you might say that time and distance are divisible forever right and the way he shows it is from the fact that there are bodies that are what faster and slower right okay okay and that the faster body covers the same distance as a slower body you in less time so that divides the what time right and then the lesser time that the faster body went this distance the slower body necessarily goes a less distance right you can't go the same distance at the same time because it will be slower and therefore you divide the distance right and then that lesser distance the faster body had to go that lesser distance in less time than the slower body did otherwise it would be faster so therefore you got to divide time again right so you might be some way of like that right to show that time and distance together are must be divisible forever right so seeing that to some extent independently right then you can what argue from the first to the second yeah yeah yeah i noticed that you know when i studied um the two sumas you know and the two sumas when he talks about the substance of god i mentioned before all those five attributes of the substance of god in both sumas that he divides the inspiration around and the order in the uh summa theologiae he shows that god is simple right and then that he's perfect right and then that he's infinite and then that he's unchanging he doesn't reason from uh uh he doesn't reason from uh uh he doesn't reason from god being simple to his being unchanging in the summa kind of gentile is the way he reasons in the other one right uh because he shows that god is unchanging before he shows that god is what simple right okay and you can show to some extent that god is unchanging before you show the simple right but you can also show that he's simple before you show fully that he's unchangeable you see and so depending which one he shows first he reasons you know from that to the other one and so i wrote i get a paper on this on this one time you see and on the difference there and there's something to be learned from both orders right you see so um actually depending on theology so um you might be a little more involved this you know than the question he raises there in the postuletics right then you're kicking in in this case right right what's the answer well i'm saying our style of first reasons from from the definition of continuous right to the second right okay but then it seems to me at the end he's always getting from the second to the first right and and basically that's the way i usually do it right seems to be more more basic that reading okay and in in a way you know as you were trying to hint theory the first part you know in a way it sets the stage for the reason right but he explicitly does it towards the end of the chapter there but uh uh you could reason the other way around either taking this as a probable statement right you know like it seems to you imagine that way right the folks in the line that seems my students that way right okay or you might be able to what have some reason to show that this is true other than this reason down here right okay and in that sense the reasoning from the first as known by this other reason right okay although he hasn't shown the other reason at this point yet right you see but later on he does right give an argument that seems to be independent this other one so insofar as you can give a reason for the first independently of the this other reason right then it's not so we can circular reasoning for that back to this and also when i was thinking about the the uh the first road in our knowledge right yeah something like this huh and i say now the students what is the first road in our knowledge huh well i say that the first road in our knowledge is the what natural road from the senses into reason right okay now you ask me why is that the first road right and i'm going to answer the question why i'm going to give a reason in the form of a what syllogism right i'm going to give you the what middle term right okay so i say the first road in our knowledge is the natural road in our knowledge and the natural road in our knowledge is the road from the senses into what reason okay now the minor premise there and the major premise can be manifested further right see the minor premise is that the first road in our knowledge is our knowledge is an actual road right okay okay what do you mean by by nature right in this context what do you mean the last sense of the word nature there what a thing is right okay the nature of a thing is what it is okay and why should the natural therefore be first well a thing must be what it is before it can be anything else so obviously the nature of a thing was first and then so now it's obvious that the first road will be the natural road right now why is the natural road the road from the senses into reason well of course you mean the natural road for man obviously what's the nature of man what is he he's a two-footed animal with reason right okay now because he's an animal of course he has senses that's what defines animal right but he's not just an animal it's an animal that has reason right and as we know in the generation and development of something what is generic or general comes before what is particular so he obviously or naturally goes from what his animal nature right from the senses into his what reason right okay did you manifest that well you know we usually go into biology a little bit there right now okay and so you know you know when you have a fertilized egg you know the first thing you see is not sensation but you see what cell division and growth right you see what we have in common with the the plants right and then the senses you know develop much later right and then finally the reason comes huh now now now sometimes you know i i argue though that if the road from the senses into reason is a natural road in our knowledge then it must be the what first road right so my mind kind of goes around this huh is it the first road because it's an actual road or the natural world because it is the first road i think so yeah yeah that's why the middle term is basically that but it's the other way right now you're going to reason though from it's being the natural road to it's being the first road what could you reason from it's being the first road to it's being the natural road it's being the natural road to it's being the natural road to it's being the 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first, don't you? What is the road that's before every other road in our knowledge, right? And so I want to reason from its being the first road to its being what? Naturally. But if someone, you know, without even asking the question about what is the first road in our knowledge, right? If you ask, you know, out of the blue, is there some road we naturally follow in our knowledge? And he figured out what the natural road was, right? So now he knows the natural road in our knowledge is a road and sense into reason, right? Then he might syllogize, huh? The natural road in our knowledge, excuse me, the road from the senses into reason is a natural road in our knowledge and because it's a natural road in our knowledge it's got to be the first road in our knowledge. Therefore. But again, you might know from experience to some extent that the first road that a child follows is what? From his senses, right? The child is sensing, right? And he's doing the thinking at all he's thinking about what he senses, right? Okay? So you might in some way know that the road from the senses into reason is the first road that the child travels, right? Without thinking explicitly yet that this is a natural road for him to travel, right? So you might go from it's being the first road to it's eventually being the natural road, right? But they're kind of convertible in a way, huh? You know, to reason from philosophy being a knowledge of what and why a knowledge of causes that its beginning must be wonder because its beginning is wonder it must be a knowledge of causes. You can do both ways. I was talking to the students there in Wisdom there the other day talking about the private road of science, right? And I say you know, basically when you talk about the private way of proceeding in the midst of that science you talk most of all about the way of defining and the way of what? Demonstrating, right? Now why are those the main things to talk about, right? Defining and demonstrating how you define how you demonstrate in the science? Well, defining I said answers the question what? What is it? Demonstrating answers the question why is it so, right? Now why are the questions what and why the essential questions for the philosopher? Well, you all learned, you know from the Theotetus and from the Marketis that philosophy begins in wonder, right? Wonder about what things are and why they are and why they are, right? Okay? So you might reason from wonder being the beginning of philosophy and wonder being a desire to know the cause to know what and why well then philosophy must be a knowledge of what? Why? Yeah, it must be a knowledge of causes, right? If it's accessible, right? Okay? But in the premium to wisdom that we saw earlier in together Aristotle shows that wisdom is a knowledge of causes and even a knowledge of the first causes before he talks about wonder being the beginning of philosophy, right? You know? So could you know that philosophy is a knowledge of causes without having considered that wonder is its beginning? And so I said if philosophy is a knowledge of causes and it's a knowledge of desire for its own sake as he says it points out there in the premium too Remember that he's comparing the man of experience and the man of art or science He says the man of experience might succeed in doing something better than the man of art or science Remember that? And the reason for that is that the man of experience is close to the singular, right? And when you take this example when you cure somebody you don't cure a man but you cure this man here you know? And I took the example you know of how sometimes the patient doctors himself better than the nurse or the doctor You know? I took that as an example that my wife and Demerol, right? You know after one gives birth to a baby they they got discomfort so they gave him this Demerol which is kind of a painkiller or something, right? So they gave my wife the usual dose of Demerol and gave her this violent headache, right? So she got to know herself, right? And so the next time she had a baby you know just give me this amount not the regular dose and that relieved her discomfort but so the nurse the doctor would be what? Not relieving her discomfort as well as she herself, right? Even though they possess the art of science, right? But the point is the art of science is kind of universal this is the standard dose and everybody gets that, right? I was telling the example of the psychologist that I knew when I was a freshman in college you know where he said there were enough psychologists to get to know the patients so when they put you in the mental home you know you were what? They would classify you, right? And you get the treatment for that type, you know? And he thought it often made them worse, right? And better and quit admission, right? You see? But no, in a sense what they would give my wife there in Demerol would actually make her what? More uncomfortable you know? You know? So but then Aristotle goes on to say but the man of art or science we think is more knowing and wiser because he knows why, right? And then he stops and manifests that you know in many ways you know that the chief artist we all think is wiser you know the doctor than the pharmacist right? Because he knows why, right? So he's manifesting that wisdom consists not so much in doing, right? But in knowing, right? And in knowing why, right? Okay? If wisdom is more knowledge for its own sake then what? Practical knowledge, right? And all that's being shown independently of wonder being the beginning of philosophy and Aristotle shows later on in the third reading there in the premium he reasons from wonder being the beginning of philosophy to philosophy or wisdom being a looking knowledge, right? if it had begun in hunger or thirst or the desire to get wealthy or the desire to be warm or something, right? It would have been something practical, right? But the fact it began in wonder, right? But could Aristotle have reasoned that because wisdom is a knowledge that's desirable for its own sake and not for the sake of making or doing, right? that the desire to give rise to it must be wonder rather than hunger or thirst or something else for any reason that way, you know? Wonder is the desire to know for its own sake because wonder is the desire to know Yeah, yeah but if you knew what you had heard you know that wonder is the beginning of philosophy, right? and you've read you know Plato and the early Greeks and it's all a wonder in these men, right? You could reason from wonder being the beginning of philosophy that it's going to be knowing causes, right? You know? A little more complicated, right? Mm-hmm. I was at the School of Orbitos again, you know. I can't agree with these things too much, you know. But DeConnick, you know, was DeConnick when I had him. DeConnick had been teaching the physics, you know, since the 1930s. When I had him, I was up there for the first time, 58 to 60, you know. Then I went back, went out a few years at St. Mary's, then I went back for 63, 64 in the school year. But he had been teaching these things for 25 years, and he said, he always saw something new every time he, what, went through it, right, you see, you know. And he says, went out to the side, and he says, you know, he says, they read the physics, you know, they books on a weekend at Columbia, did you know that? There's no idea, you know, of these things, eh? And it's always a question of how much time you spend on reading, you know, with students sometimes, because sometimes they, they, you don't realize how much is in a text, right, or how important it is, right? And they want to, you know, cover more words, you know. That's sort of a thing, you know. So I said, look, he wrote this again, and I was kind of struck by it, but it seemed to me something kind of what? The way Thomas explains the commentary, that Aristotle's reasoning first from the first definition continues, and then from the second definition, right? And then at the end there, when he's bringing out something that can't be supposed, when he says the very, in the last paragraph, it's clear that everything continues to be divisible to things which are always divisible, right? And then, for if indivisibles, right, the indivisible will be touching the indivisible, that's impossible, right? So there he's kind of, what, arguing from it can't be divisible into indivisibles, right, from the absurdity that follows on that, that it's not divisible into indivisibles, therefore it's always divisible into things that are divisible, right? So he's arguing this in the reverse way, right? But now look at the third paragraph from the bottom there. Further, if a thing is divided into those things in which it is, it would be divided into indivisibles, right? But nothing continuous is divided into that which is without parts, see? He's giving us a reason, right? That nothing continuous is divided into that which is without parts. Or to put it in a more affirmative way, everything continuous is divided into that which has parts. Everything continuous is divided into that which is, what? Divisible, right, huh? It's always divided into something that is divisible, which is another way of saying that it's always, what, divisible forever, right? And because of that, it can't be divided into indivisibles. He seems to be arguing in the reverse order in that third to the bottom paragraph, and then in the very bottom paragraph, right? You know? So, I don't know, Thomas missed that circularity. It doesn't seem to stop in remark. It's kind of, you know, you see the way that the thing is laid out, you can see that there seems to be there a circularity, right? And then, you know? I mean, what I would say is that, you know, say I myself, I reason more from the second here to the first, right? In the reverse, right? Okay? When I try to understand this, I actually do that. It's the way he's reasoning at the bottom line, right? But the first one, right, could be taken as probable, right? Okay? I'm sure you can see it before, back in Book 3, right? Or, as I was saying earlier, right? There are reasons that can maybe be given for the first one independently of the second one, right? Okay? I think there's a little bit of that in our thinking, right? You know? You know, as I said, I saw that when I was studying the five attributes of God, right? You know? See, Thomas in Summa Theologiae, he will reason from God being simple to God being unchanging, right? And I talked about that way of reasoning a little bit when we're doing that in The Philosophy of Nature, right? Remember how Aristotle shows in the 11th reading there, the first book, that there must be a third thing in change besides the two contraries, remember that? And that, you know, if the hard becomes soft and the soft becomes hard, there must be something in the hard besides the hardness. The hardness itself cannot become soft, can it? There must be in the hard, not only hardness, but some subject in which the hardness exists, right? They can lose the hardness and acquire the opposite body. Softness, something like butter, for example, right? Okay? And if there wasn't a real distinction between butter and its hardness, could the butter ever become soft? Mm-hmm. See? No. See? Or take, you know, in those examples, you know, can the healthy become sick? Okay? Can health ever become sickness? See? But something that has health can lose the health it has and acquire the contrary, what? Sickness, right? So that when you say the healthy becomes sick, as we do, right? See, if you say the healthy cannot in any way become sick, then the healthy will always be healthy, right? And if the sick in no way can ever become healthy, because the sick cannot be healthy, right, then the sick will always be sick. Tough luck. Maybe it's sick. Right? See? So you're forced to see that there's a third thing in change, right? And it might be the body in this case, right? That is able to be healthy, able to be sick, right? But not at the same time, right? And when it's actually one, it's still able to be the other. But if it becomes the other, it seems to be the first, right? And that way we saw that what changes is necessarily composed, right? Okay? And you're going from, you know, also confused knowledge of what you mean by healthy or sick, right? Because the word healthy, the word, the single word healthy, doesn't distinguish between health and that in which the health is. And it's not really the health that becomes sick, but it's that in which the health is that becomes sick, right? So you're forced to the truth that what changes is composed, right? And so if you can show that God is simple, which means not composed, right? Then you can syllogize in the second figure that God does not change, right? So the major premise is whatever changes is composed. God is not composed, therefore, right? And the great, you know, Socrates, the great Plato there, sees that in a way in the Phaedo, right? And he says at one point, what sort of thing is it that can change? Well, it's the thing that's composed, he says. And what thing would seem to be unchangeable is something that's simple, right? And it makes some sense, right? Because you destroy things by, what, taking them apart, right? And he's kind of hinting, maybe the soul is something simple and therefore indestructible, right? But he doesn't really, you know, bring out argument to prove that the soul is simple, right? But, you know, he sees that connection between simple and unchangeable to some extent there, and changeable and composed, right? You see? So Thomas, you know, in the Summa, you know, the second question he shows the Summa Theologiae now. The second question he shows the existence of God, right? The third question is the, what, simplicity of God, right? And then, later on, after he takes the perfection of God, he argues to God being, what, infinite, and then God being, what, unchanging, right? But he reasons from his being simple to his being unchanging, and he reasons from his being infinite to his being unchanging, and he reasons from his being universally perfect to his being unchanging, right? But he's shown all those things before, he's shown that God is unchanging. He can't quite do that. He can't do that.