Natural Hearing (Aristotle's Physics)
Lecture 74: The Continuous, Indivisibles, and the Axiom of Distinction

Transcript
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Okay, very good. But then I quote this thing about an opinion without a reason. It's an ugly thing. What's your reason for saying that breathing is better than philosophizing? So finally one student speaks up and says, well, if you're not breathing, you won't be doing anything else, right? I said, now, what are you pointing out? Aren't you pointing out that breathing is before philosophizing in the second sense of before? They've had the text here from Aristotle, right? What he's pointing out is that you can breathe without philosophizing, but you can't philosophize without, what, breathing, right? So you're saying that breathing is before philosophizing in the second sense of before, and I agree, but how can you conclude that therefore it's before in the fourth sense? And, you know, my other stock example in class, you know, if you show that Chaucer came before Shakespeare in English literature, because Chaucer's in the 14th century, I guess, and Shakespeare at the end of the 16th, I mean, in the 17th century, could you conclude from that, therefore, Chaucer is a better poet than Shakespeare? No, I mean, obviously they can see that that's wrong, right? Because Chaucer's before in time doesn't mean he's before in goodness, right? Okay, so how can they reason that because breathing is before philosophizing in the second sense, therefore it's before in the fourth sense? Obviously it doesn't follow, right? So Chaucer doesn't know what to do then. I say, well, I'll help you make your argument a little bit stronger, right? Which is worse for me, to stop philosophizing for the next hour or to stop breathing for the next hour? Obviously to stop breathing will be worse, right? To stop philosophizing for the next hour. See, that's quite true, quite true, see? And isn't it, you know, probable that the opposite of the worse is what? Better, right? So if it's worse to stop breathing than to stop philosophizing, then the opposite of stopping breathing, which is breathing, right, must be better than the opposite of what? Stopping philosophizing, which is philosophizing. Oh, yeah, yeah, now they get the argument. See, come on. Help them, see? I said, just like, you know, I said, if you say, it's worse to kill a man than to kill a mosquito, well, then a man must be better than a, what, mosquito, right? I said, oh, if it's worse to kill a man than to rob him, right, huh? Well, then the man's life must be something better than his money, right? Okay, yeah, yeah, yeah, yeah, okay. But there's an exception to the rule. There's an exception to the rule that the opposite of the worse is better, and that is when the lesser good is before the greater good in the second sense of before, when the lesser good can be without the greater good, but the greater good cannot be without the, what, lesser good, right? Then the loss of the lesser good is worse than the loss of the greater good because it entails also the loss of the greater good, why the loss of the greater good can leave you still with the lesser good, right? And sometimes I, you know, go into the famous theological example where Thomas, you know, following, you know, St. Paul and everybody like that, sees that charity is greater than faith, right? It's a greater good than faith. But yet he'll speak as if the loss of faith is worse than the loss of, what, charity, right? Because if you lose faith, you lose hope and charity, because faith can be without hope or charity, but they can't be without faith. So the loss of the lesser good is worse, okay? So that's what the exception is, right? So since breathing and philosophizing in this life, suddenly, are the lesser good there, breathing is what? Before in being, right? Then the loss of it can be worse without it being, in fact, the greater good, huh? I usually take a simple example and I'll say, you know, which is better, just to live or to live well? And they all say to live well, right? But obviously to live is before living well in the second sense, right? So that argument breaks down, see? So I think it's pretty clear that the word beginning, right, is equivocal and that this fallacy of equivocation is being made by Melissa's, right? When he argues that because being always was, right, and always will be, that therefore it must be, what, you know? Go on forever, right? But these are nevertheless, what, much closer to being, what, the same, right? Because one kind of follows upon the other, right? Okay? It doesn't mean to follow upon, you know, something having a beginning in time that has a beginning in size or vice versa. So our Stalin example thought that the universe was, what, you know, had limits in size, but not limits in time. It always was, right? Okay? Okay, so let's come back here again to the first reading a bit and look at it again a little bit. Another kind of another logical point here, too. Another thing we learn in the Mino, you know, in the Mino, if you recall, Mino wants to know whether virtue can be taught. Remember that? And Socrates says, I don't know. Furthermore, I don't know what virtue is. Furthermore, I never met a man who knows what virtue is. And Mino says, well, I know what virtue is. And Socrates says, oh, okay, tell me. And it turns out, of course, in the conversation, like usually happens in the dialogues, Mino doesn't know what virtue is either, right? And so then Socrates is proposing that the two of them put their heads together and try to figure out what virtue is, but Mino's not willing to do this. But later in the dialogue, he still wants to know whether virtue can be taught. And Socrates says, well, I can't really think too well about this without knowing what virtue is exactly, but I'll look on both sides and see what seems to be said on both sides, right? Reasonable on both sides. But he's been pointing out that you can't really know perfectly or reason perfectly that virtue can or cannot be taught before you really know by definition what virtue is, right? So Aristotle here, you know, he's beginning with the definition of the what? Continuous, right? Okay? Now, I think it's a little bit puzzling here, and I'll explain to you in a moment what I think is puzzling here about this. But there seems to be, first of all, two definitions of the continuous. Okay? I think you mentioned that before, right? And the first definition of the continuous is the one that is given originally in logic, right? And then back in the earlier books here of the, well, three, I think it was, he gives the second definition of the continuous. But both definitions are in terms of the what? Parts, right? Okay? Just like the definition of the number that Euclid gives is a what? You know, multitude composed of ones, right? Composed of units, right? He's defining it in a way by its what? Parts, right? Okay? So, the definition of the continuous in logic is that whose parts meet at a common boundary. Remember that? Okay? That whose parts meet at a common boundary. Or you could say that whose parts have a common, what? Boundary. A common limit, right? Okay? That whose parts have a common limit. That's good. That's good. That's good. Sersdell uses this to separate line and surface and body and so on, these continuous quantities in the category quantity, from a number, right, and things of that sort. Because the parts of a line, at the parts, the left, let's say, in the right side of this line, they have a common limit, which would be a point, right? Okay? Which could be considered the end of one and the beginning of the other. That's a common point, huh? In a circle, right, the diameter could be considered the end of one part and the beginning of the other, right? And so on. And the boundary between us and Canada, right? But in a number like seven, the three and the four, do they meet at a point or line or something else? No. So he calls that, you know, discrete quantity, huh? All right. And now, in the third book here of the physics, of the actual hearings, he gives another definition of the continuous. And it's that which is divisible forever. This is the one given in logic, but it's taken over here, because logic is common to all the sciences in some ways. And this is the definition that seems to be appropriate to natural science or natural philosophy. I think we mentioned before how Thomas gives a reason why the first definition here is more appropriate to logic than the second one to natural philosophy. And it's because of something we saw before when we were studying the four kinds of clauses. Remember that? And Aristotle pointed out how all parts that compose something are something like matter. Okay? And so you have a nice proportion there that the whole is to the parts. Something like form is to matter. Remember that proportion? Now what part of philosophy is about matter? Yeah. Okay? While logic is more like, what, geometry. It's about form. Some people go so far as to make all logic formal logic. So the form is like the whole more, and the matter is going up to parts, right? Well, wouldn't you define the continuously, that which is divisible forever, you're going in the direction of what? Parts. And parts of parts, and so, right? So it's like going in the direction of matter, right? Which is the way natural philosophy goes towards matter, right? Usqued elementa, as the Latin says in the first reading. But here you're looking at the what? The way the parts are united to form the whole. They meet at a common boundary, right? Okay? Because if you, what, in that circle there, you put these two semicircles together, right, then? To form this whole, what, circle, right? So it's more appropriate for logic to define it this way, and natural philosophy, what? That way, right? Okay? But now, we're back to what we learned in the Meno there, but, you know, it's taught more explicitly in logic, in the prior and past analytics. Reason out of knowledge is based ultimately upon definition, right? Okay? So in a way, it's going to reason from these two definitions, huh? Which does he reason from first? The first one. Mm-hmm. Okay? So let's go back to the first paragraph and just look at this again a bit. He says, If the continuous and the touching and the next star has been determined before, continuous whose edges are one, touching whose edges are together, next of which there is nothing of the same kind between, it is impossible for anything continuous to be from indivisibles, huh? As a line from points, huh? If the line is something continuous, that's what you mean by line, and the point is something, what? Indivisible, right? Okay? Now, what's he going to try to prove here? You can't put together something continuous from indivisibles. Okay? And also, in a way, you can't put together by having them touch either. Okay? And you're going to touch upon the fact that, in a way, you can't put together points that are next to each other. See? Like when you have a row of houses, right? And each house has a house that's next to it, right? I mean, one next to it on this side, one next to that side, but there's a house that's next to it, right? But two points cannot be continuous, he's going to argue. They can't, what? Touch and remain distinct, right? And they can't even be, what? Next to each other. Okay? So in no way do they seem to come from something indivisible. It's kind of a very fair way. The main thing might be that it can't be continuous, right? Okay? Now, when he... And notice the definition given there, of course, is the one from logic, right? Okay? He continues there, whose edges are one. That's the same one, basically, that we got up on the board there, the top one, right? Now, in the second paragraph, how is he reasoning? For neither are the edges or the limits, the boundaries of points one. In fact, you really speak, he's saying, of the, what? Edge of a point, or the boundary of a point, or the limit of a point, or the end of a point. Does a point have an end? See, a line has an end, right? But there's a point of an end. If a point had an end, would it be a point? Because the end would be something, what? Different. There'd be something outside of something, right? It wouldn't be, you know, indivisible, right? Okay? Again, can you speak of their edges being together then? Their ends together, right? So in a way, you're excluding both it being continuous there, and it's being, what? Touching in that sense, that the edges are touching, right? For there is no edge, he says, of the parkless, right? There's no boundary, right? There's no limit. There's no end. And for the edge, and that which it is an edge, are other, right? Okay? I think that's very interesting what he's saying there, right? And you notice he's going back, in a way, I think, to an axiom, right? Okay? And notice, when Thomas talks about what an axiom is, if you read Thomas, and all my teachers, you know, all follow Thomas, huh? The standard example of an axiom is, the whole is more than one of its, what? Parts, right? And it's kind of interesting, Thomas always uses that as an example, and Connick would use it as an example, or a certain teacher. I use it as an example all the time, right? It's, because whole and part in their first sentence are tied up with the, what? Continuous, right? Okay? And it's only a very obscure way people see this as being true of other kinds of all those and parts than the continuous, huh? They see it with the continuous first, huh? Okay? Now, no one has ever made, really, a list of all the axioms, to my knowledge, huh? But the whole is more than a part. That's always taken as an example of an axiom by Thomas, okay? Now, Aristotle has, in the fourth book of the Metaphysics, the fourth book of Wisdom, he has a long defense, right, of the, um, you can see it as two axioms, the axioms, um, about being and non-being, right? Okay? These beginnings about being and non-being. And usually we state it as, what? It's impossible to be a not-being. Okay? It's impossible to be a not-being. Be and not be at the same time, in the same way. And it's necessary to be or not to be. So sometimes I popularly quote Hamlet there, right? To be or not to be, that is the question, right? I say, it wouldn't be a question if you could both be and not be. If you didn't have to either be or not be. You can't really avoid that, right? You can't both be and not be, and you must either be or not be, right? That's why it's a question. But you say it's a question because of the two, what? Axioms, right? Now, I'm a man who's thought a lot about before and after, right? And those are words that you find in the fifth book of wisdom, too. And is there an axiom of before and after? Before itself. Nothing is before or after itself, right? Everybody, in a way, understands that, huh? Today can be before tomorrow and after yesterday. But can it be before itself or after itself? No. Not strictly speaking, can it? Morning, one part can be before, right? The morning can be before the afternoon, but it can't be the morning before the morning. When the morning comes after the morning, right? There's always a distinction there, right? Now, although I never heard them say it exactly, when Aristotle is talking in the first book of natural hearing, and he's talking about how Melisius and Parmenides say there's only one thing. There's no multiplicity at all. He says they're really doing away with beginning, he says. Because the beginning is always the beginning of something, right? Other than itself, right? There's always a distinction between a beginning and that of which it is the beginning. Nothing is the beginning of itself. It would be an axiom about beginning. Yeah? There's always some kind of distinction there. Because there's always like the axiom there of before and after, isn't it? Now, those two words are related very closely. Because in Aristotle, in the fifth book of wisdom, distinguishes the senses of before and after. He does so, starting with the common notion of beginning. So it's very closely connected, the two. And when he gives a common notion of beginning, he says what's first in being or becoming or in knowing. But first is defined by before, right? So the two are very tied together, those two. But then when you get to the third part of book five, right? You come to the famous word end or limit, huh? And Aristotle points out how sometimes you distinguish the beginning and the end. Like this is the beginning of the death, that's the end, right? The beginning of the day, the end of the day, right? But then sometimes we call both ends, right? Okay, the ends of the desk, right? The ends of the day, the limits of the day, right? Okay. But would it be also an axiom that nothing is the end of itself? A surface is the end of a what? Body, right? A line is the end of a surface. A point is the end of a line, right? But a point is not a line, a line is not a surface, and a surface is not a what? A body, right? Okay? So there's always a distinction there, right? Of the end and that which it is the end. Or the limit and that which it is the limit, huh? Do you see that? Okay? And that's why you've got to be very careful, you know, sometimes Aristotle and Thomas will use that phrase, kao za sui. You've got to be very careful with that phrase, right? Because in a strict sense, can anything be kao za sui? Because if every cause is the beginning, then if a cause was kao za sui, it would be the beginning of itself. That's impossible, right? Yeah? You can't even speak of God in that sense. Yeah. You have to be understood negatively, right? You see? You know, that God has no cause. Yeah. Okay? You see? I mean, sometimes we state something negatively, grammatically, in an affirmative way, right? You know, like I was saying before, when we talk about statements, some statements are known to other statements. But then there's got to be some statements that are not known to other statements. But instead of saying that they're not known to other statements, or they're known not to other statements, right? We say they're known to themselves. Now, if you understood that in an affirmative way, because grammatically it's affirmative, right? They are known to themselves, then you say it's a statement that proves itself. And that would be what we call circular reasoning in logic, right? Okay? What you're talking about is a statement that is known, and truly known, right? But not known to other statements, right? Okay? You see? So when I say no odd number is even, right? If I know what an odd number is, what an even number is, it's obvious to me that no odd number is even, right? I don't have to prove that statement. If I know what a whole is, I know what a part is, it's obvious that the whole is more than a part, right? See? Not to prove that, right? Through some other statement, huh? Okay? It's just maybe known to its parts in this example, right, anyway? You know? But it's not known through other statements, right? You have to be careful of that, right? Okay? You ever look at the end of Sartre's work, there being in nothingness? You know? And of course, he's saying, kind of crazy ending, because he says, a man is the attempt to be kawuzasui, to be God, which he calls kawuzasui, right? But that's a contradiction, he says. Therefore, he says, the last sentence almost in the book is, therefore, a man is a useless passion. But if you read, you know, Marx, you know, saying these sort of things like that before him, right? Now, Marx is trying to what? Make himself. There's an expression in English, you know, in America, self-made man, right? You've got to be careful what you mean by that. I mean, Marx is trying to what? Have man make himself, right? These people that are, you know, fooling around with clones and other such things, right? You know? They want, for instance, for man to really make himself, right? And if I made myself, I don't have to worry about God. I'm my own God, right? But strictly speaking, it's impossible for something to make itself, huh? You see? So be careful with that expression. There's a legitimate sense if you speak of a self-made man, a man who, you know, wasn't born wealthy and a man who, you know, worked his way up, et cetera, et cetera, right? But strictly speaking, the man didn't make himself. And Father and God made you, but you didn't make yourself, right? You see? So nothing is before or after itself. Nothing is the beginning of itself, right? You see? Now, there's a way which you can say that the foundation of a house is the beginning of a house, right? Some might say, well, isn't the foundation a part of the house therefore the beginning is the beginning of itself? Well, no, no. We don't say the foundation of a house is the beginning of the foundation of a house, do we? No, we say the foundation of a house is the beginning of a house. And there's a distinction, after all, between the part and the whole, right? There always has to be some distinction, some otherness there between the beginning and the which it is the beginning. Now, if you go to the word end or edge, right? Which is the same word here, basically. End or limit. It's always, what? The end or limit of something, right? But you might say as an axiom that nothing is a limit that nothing is a limit. of itself. Nothing is the end of itself, huh? And so, if a point really had an end or a limit, then it would have what? Parts. Yeah, it wouldn't be indivisible, right? There'd be some multiplicity there, right? Between the end and that of which it is an end. Okay? There'd be something outside of something, right? You'd have some extension there, right? Okay? So, if the point has no end or no limits, how can it have a common boundary, a common edge, a common limit with something else? It doesn't have any. Right? Okay? Notice, as Thomas points out at the beginning of the second reading, in a sense, this is also the reason why two nows, right, cannot be, what, continuous, right? You see? But, again, it's a little different meaning there. I know we'll speak of one time, touch another time, right? Seems to be said more of the continuous, it has a position, like a line, right? Or as parts of a line, the parts of a surface, right? And that's why he'll go in and try to manifest more in the second reading that motion also is continuous, right? And in the third reading and so on in the fourth reading, the time is continuous, right? But, in a way, the reason here is the same for all three, proportionally speaking, at least, huh? So, he says here at the end of the second paragraph, for the edge, and that which is an edge or other, or you could say the end, and that which it is an end, or the limit, and that which it is a limit, in those words, that's really an axiom, something that we know without having to prove it, right? Once you understand what you mean by this, huh? Okay? And I was talking the other day, I think, about how there's something with the idea of limit, like what you showed later on about cause, that there's a cause which has a cause, right? But there's also a cause that has no cause. And the same thing that we said about the beginning, right? There's a beginning that has a beginning, right? And then there's a beginning that has, what? No beginning. God and the Father, right? Okay? The same thing is true about, what? Limit, huh? There's a limit that has a limit. So, in a square, the four sides, those four lines are the limits of that surface, right? But those four lines are limits that have a limit, namely the point, right? Okay? The same thing is true about the surface, right? The surface is the limit of a body, but the surface has limits itself, right? But then you get to a limit which has no limit. And that's the, what? Point. See, strictly speaking, you wouldn't say the point is unlimited or limited, right? You know, like a line, you know, there's a line going on forever, right? Or else it's having ends, right? Strictly speaking, the point is a limit, right? So, in limits, it's a little bit like the first cause, right? It's easy to see that, right, huh? You know? Once you realize what a limit is, then you can ask the next question, but can a limit have a limit, right? So, you know how you proceed, you know, you start with the body, then you go to the surface, and then you go to the line, then you go to the point, you're not showing the existence of these things, right? So, you see the surface is a limit before you see the line is a limit, and the line is a limit before you see the point is a limit. See? So, the limits you first see are limits that have limits, right? And notice, could the square be limited in size if the four lines containing it were not themselves limited, see? If the lines contained a square went on forever, then the square itself would be unlimited, right? So, if the square is a limit, then its limits got to have a limit. Well, careful about that, though, see? See? Or, you get to the point, Don, you see? Could you say that the point, Don? Could you say that the point lacks a limit? Is that correct to speak that way? The point lacks a limit? That's what I was going to ask you, could you speak of a point as limitless, doesn't seem so, but because also the point has no magnitude, either. Yeah, well, this is an important question, because, um, see, if I say the point has no limit, I might, you know, use the term limitless, right, or unlimited, right, what do I mean? Am I merely negating limit, or am I saying that it's lacking a limit? It's not able to have a limit, so it can't lack a limit. Yeah, yeah, in the strict sense of lack, right? Lack is not merely the non-being of something, but the non-being is something you're able to have, and should have, right? And especially when you should have it, right? So, the chair it's sitting on, right, it doesn't hear, right, but is it deaf, that chair? It doesn't see, but is it blind, right? Well, blindness and deafness are lax in the strict sense, right? The non-being of something that man or an animal is able to have, and should have, and when they should have it, right? Then you have a lack of the strict sense, right? But the chair is not the sort of thing that is by nature able to have sight, or sense of hearing, right? So it's not having something that's able to have, and should have, when it should have it, right? So strictly speaking, we can say that the chair doesn't see, but strictly speaking, we shouldn't say the chair is, what, blind? Because that would be a, what, privation, to use the Latin word, lack to use the English word, right? Okay? So in Aristotle, you know, in the categories and the fifth book of wisdom, he'll distinguish the four kinds of opposites, right? And he'll distinguish between being and non-being, that kind of opposition, and between having something and lacking it, right? So, if a straight line had no endpoints, right, then you could say it's lacking, more so, right? Because it doesn't have something it's able to have, right? Okay? But the point is not able to have a limit, right? So it's not lacking in a limit, right? So there's an equivocation there, in that word unlimited, right? Okay? That's important when they talk about God, right? Because one of the five attributes of God is that he's unlimited. You usually see the Latin word for that, infinite, right? And Thomas explains how God is said to be infinite. Amen. He's always careful to explain. It doesn't mean a lack, right? If I say the straight line is infinite, that is a what? Privation or lack, right? But when you say God's infinite, no, it doesn't mean a privation or lack. You mean that there's no what? Limit to his perfection, right? You don't mean he doesn't have something that he's able to have or should have, right? In fact, when you find out what God is, you find out that God is pure act. There's no ability in God to receive something, right? That's why you can't really give God something in the strict sense, right? When you speak of thanksgiving, right? The testament says, Deo gratias. No prayer is shorter or grander. Deo gratias, right? We should thank God, right? Are you really giving God something? Is he receiving something, right? I'll tell you about that. I'll tell you about that. I'll tell you about that. Does God rejoice in our thanking Him? Does He enjoy our thanking Him? It doesn't give Him more joy. It doesn't give Him more joy. But does He rejoice in our thanking Him and our loving Him and so on? Does He rejoice in that? I would say, even in His divine nature, right? Because it's clear that God loves us, right? And if you love someone, then you rejoice in their good, right? Now, it's our good, not adding to His good, right? But it's our good. It's good for us to thank Him, right? It's good for us to love Him, right? It's good for us to honor Him, right? Since He loves us, He rejoices in our good. It doesn't increase His joy, does it? No. Because God's love and His joy, they follow upon His, what? Knowledge, right? And His knowledge is, what? Eternal, right? So, He's not, what? Learning, but all of a sudden, when breakfast is starting to honor Him, right? You know, when it says there's more joy in heaven, doesn't it say that somewhere? You know, where one sin repents, right? Okay. But the joy that God has over my repentance, or my starting, God says to love Him, or to honor Him, or to thank Him, right? That joy cannot be new, right? Because He always knew my repentance. It's always present to Him in His eternal knowledge, right? And He always loved me, you know. It says in Jeremiah, it says in the book, you know. It's literally a perpetual love, right? An eternal love, right? His love is eternal, like His knowing. And therefore, He always rejoices in my repentance. That kind of is an interesting thing, though, you know, He's distinguishing God's pleasure and God's joy, right? And the pleasure is really in Himself, right? The joy is both in Himself and in what? Preacher, yeah. Yeah, very interesting. So could you say it belongs to love, to sorrow, right? If someone loves someone, they will be sad over their evil. See, strictly speaking, though, you see, just as joy arises from love, right, so sadness arises from what? Hate. When what I hate is forced upon me, or those I love, right, huh? Then I have sadness, right? But there's no hate in God. So there can't be any sadness in God, see? But it takes the course of our friendship sometime, okay? But, you know, in us, you know, you have to start with, huh? When we distinguish between love or liking, which is a weaker word for love, but we distinguish between love or liking and wanting or desire, right? And then joy or pleasure, right? What's the difference between those three, right? Well, in us, wanting or desire or joy or pleasure arise from love or liking, right? And how is that, right? Well, if I love or like something, but I don't have it, right, then I want or desire it, right? So wanting or desire arises from love or liking in us when what we love or desire, or love or want, or like, rather, we don't have it, right? Okay? But if I get what I love or like, then I have joy or what? Pleasure, right? Okay? Well, God's not liking anything, right? So there can't be any desire in God, except metaphorically speaking, but properly. But he always has his good, right, huh? So there's always love in God, and there's always, what, joy in God, right? You know, the Psalms talk about that, right? Okay? And they have the same similarity in the other three, right? In the hate, right? Or dislike, right? This is a weaker word, right? Now, the things I hate or dislike if they're threatening in some way, I turn away from them, right? Okay? But if they're forced upon me, I can't avoid them, then I have, what, pain or sadness, right? Okay? I hate trekkie exams, most professors do. You see? So I want to avoid trekkie exams. But since I can't avoid, you've got to get an exam. Okay? So then I have sadness, right? I wouldn't have sadness unless I hated doing that, right? Okay? Or as a child, you know, or even growing up, I guess, certain foods I hate or dislike, anyway. Asking sir for dinner, right? Or go to somebody's house and they're serving that, right? So I'm sad and relieved, but because something that I hate is being forced upon me. So there's no hating God, right? There can't be sadness in God. There is love in God. Why isn't there a hate? There's no hate? Well, we won't get into that too much, but that's the first thing you have to see, right? But God is love itself, right? Love itself, it can't be any hate, right? Like you saw back in the first book, when you're actually hearing there, right? Right? Can hardness itself be soft? Can health itself be sick? So can love itself be hating? That's not. God's only good and simple, right? Okay? God is whatever he has. Okay? So if he has love, and you know he does, then he's love itself, right? Love itself can't have any hate. Okay? So, the sense in which the point is said to be, what? Unlimited. It's a little bit like the sense in which God is said to be unlimited, in that it's not a, what? A lack, but simply a, what? Negation, right? Okay? So if two points have no end or edge or limit, right? Or boundary, right? How can they have a common edge or limit or boundary? They can't. Nor can their, what? Limits be together. They have no end or limit, huh? Now, the way Thomas speaks in the third paragraph, he's kind of adding this in a way because of the fact that you want to show that the line cannot be made at other points touching in any way, right? Now, what I usually do, you probably remember when I was talking about the fragment there of Annexagrius,