Introduction to Philosophy & Logic (1999)
Lecture 6: The Natural Road of Knowledge: From Examples to Definition

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When Socrates asks somebody, what is something, right? They invariably give examples of the thing. If I had a little child in this room, right? And I asked this little child, what is a chair? What do you think he'd do? That's a chair, that's a chair. What is a nose? That's a nose, that's a nose, right? Okay? You wouldn't expect him to come out with a definition of what a chair is, would you? Okay? It would take some time to really, you know, define what a chair is. You might begin by saying a chair is something to sit on, but so is a bench, right? So is a saddle, right? But something to sit on for one person, you know? There's everything to sit on for one person, a chair. A saddle is for one person, too, you know? It would take you a while to think out, as we say, the definition of what? Okay? So what invariably happens is that they give examples of something, and then Socrates tells them, well, you give me too much. I want what's common to all of these, right? Okay? And then they try to frame universal definition, right? But that's something natural, you see. When my children went to kindergarten, they'd come home with a piece of paper and they'd have a circle on it and a square on it and a triangle on it, and they'd say, Daddy, this is a circle, that's a square, that's a triangle, right? But if you ask the little child, what is a circle? He wouldn't say, it's a plain figure contained by one line every point of the circle. You know, you point to the clock or something else, it's circular, right? Say, that's a circle, right? So it's natural to give examples of a thing before defining it, right? And in fact, as we'll see in logic, there is a road from examples to the definition. When I want to define, for example, what a Shakespearean sonnet is, right? I read a number of individual sonnets, right? And I compare those sonnets, right? And I try to separate out what they have in common. And the more I think about them and compare them, the more I see they have in common. They have a certain number of lines, and I look carefully and count the lines, I may see they all have in common 14 lines, right? And then I start to notice other things, there's a meter there and so on, right? And gradually thinking out the definition of a Shakespearean sonnet, by what? Comparing the examples of it, right? Okay? This is a chair, that's a chair, and so on. What does this and that have in common, right? Okay? So there's a road from examples to the definition. But it's natural to begin with examples before the definition. Now in reasoning, he has something like that. In fact, the universal statements from which the syllogism proceeds, they are usually established by some kind of what? Induction, right? Induction is an argument from many singulars to be what? Universal, right? Why the syllogism begins with something universal, and the reasons from that, right? So just as people give examples of a thing before they define it, before they give the universal definition of it, right? So induction comes for us before syllogism, right? So in the Phaedo, for example, Socrates makes an induction, and then when he gets a universal statement through induction, he reasons by syllogism to the immortality of the soul. This is one of the reasons, too, where Aristotle said wisdom is so difficult, because it's the most, what, universal science, right? So in some ways, it's the furthest away from the senses. And if you ever had a misfortune to teach philosophy, you know, you'll have students say, oh, this is so abstract, you know, right? But in a sense, they're talking about it as we're universal, right? And therefore, it's not, you know, it's kind of the most consensus, which you're thinking, right? Now, the second thing is, for the most part, you can say, we know things in and outward before inward. Now, notice, in English, outward is almost a synonym for what? Sensible, right? I remember as a child, the definition of sacrament, an outward sign instituted by Christ to give grace, right? But outward meant it was something what? You could sense, right? So, when you meet somebody else for the first time, right, you know them in a kind of, what, outward way, right? You don't know them in an inward way, do you? But as you talk to them and listen to them, right, and as you see how they act on the battlefield and other trying circumstances, right? Then you begin to know something about what they're like in an inward way, right? Now, this is especially true in ethics and in natural philosophy, right? In geometry, of course, you're dealing with things on the surface. Plane geometry, right? But the senses know things in an outward way. Reason tries to see into them, right? And so we use words like insight for a reason, right? We use words like, you know, penetrating. It's inside something. We speak of a good mind as being sharp, right? Okay? But having insight into things, can see into them, right? So, this is, again, very important in logic, because when we ask what something is, we tend to draw a line around that thing and know it in a kind of outward way before we know it what we can do with it, right? I'll give you an example of that, right? Neurostal is taking up virtue there in the end of the first book of the Nicomachean Ethics, and then around the second book, you really define it, right? But he begins by saying virtue is a praiseworthy quality, okay? Now, what kind of a notion of virtue is that? Is that an inward or outward knowledge of virtue? Outward. Yeah. My vice would be a, what, blameworthy, yeah? Okay? Notice praise is in the one who's praising, right? So you have a kind of outside knowledge, right? But as a child, you know, certain things, you know, you're told you don't do, and certain things you can do, right? And certain things you're praised for doing, and other things you're criticized for doing, right? So without maybe seeing inwardly why this is good or bad, you have a kind of outside knowledge, right? Okay? Now, again, you can kind of sometimes reason from this outward knowledge to an inward knowledge. So you might say become a moral virtue. It's a praiseworthy quality. But then you say, what is it that's praised, right? Well, in eating, it's the man who doesn't eat too much or too little, right? Okay? So then you start to see more inwardly what virtue is, right? It's a habit in the middle, right? Okay? So you're starting to go from an outward knowledge to a more inward knowledge. So when Aristotle's taking up human happiness, he, in the Greek he says, because he's very graphe. Graphe means, you know, draw a line around, huh? Carry it around, huh? He draws a line as we're around this, and then he begins to... Okay? Sometimes when I talk about wisdom itself, and I'll say, well, wisdom is the best knowledge. Okay? Now what kind of definition of wisdom is that? It doesn't really tell you inwardly what wisdom is, does it? Because best means what? Better than all the rest, right? Okay? But it doesn't even tell you what wisdom is a knowledge of. Right? Okay? But is there, again, like there's a road from the singulars, right, the definition, is there a road from this outward knowledge to an inward knowledge, right? Well, if I begin, they say, wisdom is the best knowledge, and best means what? Better than all the rest? And then I investigate, well, why is one knowledge better than another, right? And maybe I figure out that... Well, but they limit, right? You see? There's only one point that has that longitude and that latitude, right? But there's an infinity of points that have the longitude, an infinity of points. How do you get down to one point? You do, though, don't you? It's an amazing thing. So, this explains all kinds of things about definition, right? Why we name a thing before we define it, because you don't need as distinct a knowledge to name a thing. And why, when we define how we begin with a general thing like animal for dog, right? So, notice, these are, this is a before and after. He's knowing one and the same thing, right? Aristotle, when he gets through with all of this, stands back at these two last things we talked about, the before and after, different things are known, and the before and after the same things are known, and he sees something they have in common. And that is that what is more known to us, right, is before what is less known to us, right? So, the confused is more known to us than the distinct, right? Things are more known to us in an awkward way than an inward way. The singular, huh? Material things are more known to us than immaterial things, huh? Effects are usually more known to us than causes, right? The composed is more known to us, right? At the same time, and this is the most subtle thing he sees, that what is more known to us is less fully known. When I know something in an awkward way, it's not perfectly known, is it? And when I know something in a confused way, it's imperfectly known, right? It's more known to us. And so, we're more sure about the confused than we are about the distinct. If you give me a glass of red wine to drink, what is this? What's a dry red wine? I'll be a little more specific. And the more specific I try to get, the less, what? I'm sure I am, right? I ask the students, how old am I? Am I over 20? Oh, yeah, you're over 20, Mr. Rivers. Over 30? Yeah. But as you try to narrow it down, they get less. Is that sure what I'm in the 50s or the 60s, you know? You know? Not only when you try to find it, you're not too sure, you know? I've got to look younger than I am. Even the senior discount, the dentist this morning. Okay. Or I say, how much do I weigh? Over 100 pounds? Yeah. Over 300? No. But now as you start to get more precise, you get what? A certain, yeah. Now Descartes was all goofed up on that. Because Descartes, in his Discourse on Method, right, he identifies certitude with clarity and distinction. And do they go together? For us? You might think at first, right? Put on a mainstream and ask somebody, you know, are you more sure in your clear and distinct knowledge or in your vague and confused knowledge? You'd probably say your clear and distinct knowledge, right? See? But as I try to say more distinctly what this red wine I'm drinking is, right, I become what? So that's certain, yeah. How can I be more sure that I'm drinking Carbonet Sauvignon than that I'm drinking a dry red wine? And how can I be more sure that I'm drinking Carbonet Sauvignon from Napa Valley in particular than I'm drinking Carbonet Sauvignon, right? I can't be. You see that? So that's a little bit about the natural road there beyond Robin Ford. Could you repeat for us those two last thoughts that Aristotle would have liked on those? He says it very briefly, but expanding a little bit what he says. He says, the more known to us, before what is less known to us, right? But what is less known to us is the more known, meaning the more what? Fully or perfectly known. And what is more known to us is the what? Less known, meaning the imperfectly known. So Plato and Aristotle would compare our mind to going from darkness towards what? Light, right? But where it has more light is kind of blinding to us at first. So when I know I'm drinking dry red wine, I'm more sure that I'm drinking dry red wine than I'm drinking Carbonet Sauvignon, right? What I'm drinking is less known than I know that I'm drinking Carbonet Sauvignon, right? But I know the effect. I know the effect more by itself than I know it in the light of its cause, right? So we know there's all kinds of diseases they're looking for the causes of, right? Okay? So we know more the effect by itself than in the light of its cause. But you don't fully understand the effect until you know the what? Cause, right? What does Aristotle discuss that? That's not what you think about, you know? No, in the first chapter there is the so-called physics, right? We'll look at that text later on when you start to do some natural philosophy. We're going to do some logic before that. Okay? Okay? But there's something like that in every kind of education. And what comes before for us is imperfect. And what comes after for us is more perfect. And that's because in any kind of education you're developing something, right? So, if you do one of these graduated exercise things, like when I was in Canada, a lot of kids got the 5BX plan for the Royal Canadian Air Force. I still have a copy of the Royal Canadian Air Force, right? Okay? Well, these exercises are graduated, right? So, you've got to start at your level, right? How many push-ups can I do, right? How many of this or that, you know, sit-ups can I do and so on, right? And I start at this level doing so many push-ups, so many things, right? And then I gradually, what? Build up, right? Now, the first exercises I do are productive of less strength than the ones I do later on. Now, 5 push-ups produces less strength than, let's say, 20 push-ups, right? Or 100, right? But if I tried to do 100, maybe I would physically, what? Harm myself, right, huh? Okay? So, 100 push-ups would not be productive of strength more for me. But 100 push-ups are productive of greater strength than 5, you see? Okay? And the same thing is true in the education, to some extent, of the heart, right? What is more lovable to us is less lovable. See, we tend to love the sensible good, right? More than the understandable good, right? Because it's more known to us and so on, right? What's the lesser good, right? So, I love candy before I love wisdom, right? Even though wisdom is a greater good than candy. When I was a little boy, I thought my father a foolish man. He didn't fill the refrigerator with soda, soda pop. Grape, soda, and wit beer, and orange, all the wonderful things. And with his money, he could afford to fill the refrigerator with this and drink soda all day long and be a happy man, right? You see? And now that I can maybe afford to fill the refrigerator, I don't do this, right? I think there are greater things I can pursue, right? You see? But the soda pop is more lovable to me than wisdom. The private good is more lovable than what? To us, than the common good. But the common good is more lovable. It's a greater good. You know, in the discussions or conversations between Eisenhower and Zhukov, right? In Berlin after the war, right? And Zhukov was a Russian general, right? So a general, and he was in charge there in the Russian sector. And he would meet with Eisenhower because he was in charge there. And they'd talk about the American and the communist system, right? And Zhukov would say to Eisenhower, Oh, in your economic system, people work for profit, right? Well, here in Russia, we expect them to work for the economic good of the country. Isn't that much higher than working for your own profit? Eisenhower was too dumb to know how to answer this. Because the point is that the economic good of the country, the common good of the country, is a much greater good than my profit. But you begin by loving your own what? Private good more than the common good, right? What's more lovable to you is what? Less lovable. And what is more lovable, what is a greater good, in fact, is less what? To you, yeah, see? So you have to be led from the private good towards the common good, right? And of course, when you go back to the Russian system, you realize that they, you know, do in fact appeal to the private good, right? If you're highly productive, we might give you the Order of London or something, right? Or if you're stealing goods, we put you to death, right? You know? So they do, in fact, appeal to the private good to get people to work in some way for the common good, right? It's just that we do it more efficiently. You see? Profit is, you know, a better way of doing it than getting threatened to be shot or, you know. Okay? So the answer was not to try to say that the profit, the private good of this man or his company is greater or better than the common good of the country. No. You can't defend that. The good of the whole is always greater, huh? But it's more lovable to us, right? And so men have to be led from that, right? So sometimes you see a businessman who's got his own company, he's interested in making a profit and keeping the business going, and he joins, let's say, the Chamber of Commerce, or he joins some civic organization, right? And this is beneficial to his company because he becomes known, he makes all kinds of contacts, right? But as he starts to do things for the city, you find the man begins to get a certain, what? Delight in doing things that are for the good of the city, even apart from his own, what? Yeah. And now he's been morally educated, right? See? In the same way in the Christian life there, you know, where you might first be concerned about, what? You know, fires of hell, right? Your own private laws, right? And then you have to be graduated from that to, what? The love of God, right? The love of the common good, huh? So in the beginning, the sensible good is more lovable to us than the reasonable good, right? And the private good than the common good, because the senses know only the sensible good, that's where our knowledge begins. You know only the private good. You have to be gradually let on. The same way in the education of your taste, right? It might be taste in food or taste in the fine arts, right? As a little boy, I was known for always trying to find a march on the radio. And I still love marches, right? But I know now that there's not as much to hear in these marches as there is in a Mozart, what? Something or a Mozart opera, right? I remember my brother Richard brought home the magic flute the first time I heard it, you know. I listened to everything attentively. I didn't hear anything. But I continued to hear these things from mind, you know. So Mozart's music is more hearable than the march, but the march is more hearable by me as a child. Everybody loves a parade, as they say, right? They're stirring, huh? I noticed the child is going to, his imagination is going to be struck more by Little Red Riding Hood than by King Lear. But as you continue to read Little Red Riding Hood, you kind of exhaust the story after a while, right? I have been. But King Lear, I can still come back to King Lear. It was more for the imagination. I used to notice at Christmas time, my mother would put the Christmas cards up over the mantel or the fireplace. And you tend to go down those cards and just stop in the ones that have reproduction of a famous painting. And you keep on seeing more and more in that painting. But the child will see his own childlike drawing quickly first, right? He won't appreciate the painting, maybe, the famous painting, right? But there's really more to be seen there. There's less seen by us in the beginning. But it's because in all of these, huh, education, you're going from the imperfect towards the perfect, right? You're developing something. So what comes first for us is always, objectively speaking, imperfect. So Plato compares us to men who are born in a cave, huh? There's hardly any light in the cave. And someone gets out of the cave, out into the sunlight, where things are more noble, right? But he's blinded at first when he gets out there, right? What I can say is in the Bible, God dwells in light, inaccessible. He's too understandable, right? Okay? So, as far as the axioms are concerned, no one has ever tried to enumerate all the axioms, right? You can enumerate some that are especially important in geometry, right? And Aristotle talks about the most basic ones, that something cannot both be and not be, right? It must either be or not be, right? But there are many other axioms, like the whole is more than a part. You talked about the word before, didn't we, here, a little bit? Mm-hmm. Huh? The word before? Yeah. Oh, we did, though. Okay. But nothing is, what, before itself. That's an axiom. Nothing is before or after itself. Today is before tomorrow and after yesterday, but can today be before today or after today? So there's many axioms, huh? Nothing is the beginning of itself. As I say, no one has ever tried to enumerate all of them. Aristotle says, by nature, the most fundamental ones are, you can't both be and not be, right? You must either be or not be. To be or not to be, that is the question, right? It's a question because you can't both be and not be, right? You must either be or not be. So as you read the demonstrations in Euclid, you'll see it using these axioms, huh? Even the postulates, in a sense, presuppose the axioms, huh? Take a simple example here. You take the postulate that all right angles are equal, right? Okay. Now, when a straight line makes a straight line and makes equal angles, we call them, what, right angles. That's the definition. And this straight line makes equal angles. Now, how do you know that these angles are, what, the definition doesn't tell you, it tells you these two are equal, it tells you these two are equal, right? It doesn't tell you this is equal to that one, and so on. It's a big pair, right? Mm-hmm. How do you know this is like a straight line? You know, you see, divide a line into two equal parts. I've done that, but this is not equal to that, is it? So how do you know that this angle is equal to that angle? Well, you can imagine this line laid on that line, right? At that point, right? Now, if this line here coincides with this line, obviously they're equal, right? If it doesn't, it falls to one side, right? Now, this angle and this angle here are equal, right? But now, if you take this angle here, this whole angle here is greater than this part right down here, isn't it? Why? Because the whole is more than a, what, a part. That's an axiom, right? Okay. So, if this is equal to this, and this is greater than this, and this is greater than that, right? Okay? Therefore, this, if you add to the greater one, right? This here is greater than this. If you add this, then this is much greater than that, right? But since that is the one that's over there, right? This is also equal to that. So, what is much greater is also equal. So, it's both is and it's not. That's impossible, right? So, you're using the axiom that the whole is more than the part, and something cannot both be and not be, right? Or take another example here from geometry, how it adds to the agenda. Euclid defines, what, circle, right? You've seen the definition, I guess, huh? And then he defines diameter, right? And then he states what Reed is a postulate, that the diameter bisects the circle, that is to say, dividing two equal parts, right? I asked the students, how do you know that the diameter bisects it? They said, well, just by definition. He said, no, no, that's not a definition. You see, you define a circle, right? A plane figure became the one line, every point which is to keep you distant from a point in the interior called the center, okay? And then you say, if you take any point on the circumference, right, and you draw a straight line to the center and through to the opposite, that's what we call a diameter, right? Now how do you know that diameter divides the circle into two equal parts? Because it says, and it divides into two equal parts. Well, again, you can imagine this is the word flipped over in the top of the other side, right? Okay? Now, the base is the same, of course. Now, when we flip it over, if this coincides with that, then it's obvious that they're equal, right? If it doesn't coincide, it's going to fall either above or what? Below the other. In which case, all the radii are not what? Equal. Yeah. That's already the definition of the circle, right? So, they're both equal and not equal. Impossible, right? To go back to the fundamental axiom, something in that will be enough, right? Or if I say in the arithmetic, something kind of obvious here, no odd number is even, right? This is the statement known to itself, we say. It's known to knowing what an odd number is not even numbers, right? When we define an even number, we say it's a number divisible into two equal parts, right? An odd number is a number not divisible into two equal parts. So, if an odd number were to become an even number, right? Or to be an even number. That number, that number would both be and not be divisible into two equal parts, right? And that's impossible, right? So, everything rests upon those axioms of being and non-being, right? Now, sometimes you have someone who denies these because of science and the fun of it, but sometimes because of some difficulty he can't solve. But, notice, when they deny, for a reason, the axiom of contradiction there, something in that, they do so because something seems to contradict it. So, they're saying it isn't so because it is so. They're holding on to it when they say something contradicts it, something contradicts it, you get on to it. So, they accept the principle of contradiction, right? They do that. But some just denies it for fun. They say, well, do you want to go to the cliff? And they say, it's the same thing, it's just boring, and that's still boring. The same thing with a bullet figure, not a bullet figure, right? And it appears to be that they're not the same. So, that's the first of the four questions here under the fourth question. What are the natural beginnings of philosophy, right? With two desires, the natural desire to know the cause, what's in the sake, right? And the natural desire to live well, right? And two, in our knowledge, the natural road, the road from the senses into reason, and we unfolded a bit the before and after along that road, huh? And then the, what, natural understanding of the, what, axioms, right? Okay. Now, the next question was, why do you want to come into philosophy from the natural beginnings, right? And let's give some of these reasons here, huh? Now, the first four reasons I'm going to give are based on the fact that the natural beginnings are beginnings, and in fact, the very first beginnings. That's right. That's right. So, first reason. We've talked about this, I think, in the day already a little bit. The man who considers something from its beginning will understand it the best. Okay? Who considers something from its beginning. Now, I took this simple example there. If I want to understand a man, I'm writing the biography of Winston Churchill, let's say, of some other famous man, I'm going to go back to his, what, beginning, right? His origin, right? I'm going to follow him up from his origin, right? And that will understand him the best, won't I? Okay? If I'm writing the history of a country, I'm going to go back to its, what? And I mentioned how de Tocqueville said that, what, you're in a better position to understand America than France because you can see its beginning, right, how it began, huh? When de Tocqueville began the famous profound research, I guess, reading into the French Revolution, right, you know, that first volume he completed, right, leads right up to the French Revolution, right, and the French Revolution seems like a foregone conclusion, you know, very thing he brings out in that volume, right, but he's seeing it from its, what, beginning, right, huh, okay? So you're going to understand philosophy best if you follow it up from its, what, beginning, and the natural beginnings here are the very, what, first beginnings of it. Makes sense? Okay. You read that famous book of C.S. Lewis, The Allegory of Love. It's been a kind of masterpiece in fiction, right, huh? And he says, you know, compared to this, the Renaissance was a ripple on the literary history, certainly. It goes back to the origin, right, huh, eventually to Shakespeare and Spencer, right, going back to the Middle Ages, right? And you see this thing from its beginning, you have much better understanding of what it is. In the deeper world, that's what it was. That's an example of the same thing, right? A man who considers something from its beginning, you understand it's the best, huh? And you read that masterpiece there, really, very long. Now, the second, the second, huh? The Shakespeare's, the ones that call romances, they're the last place. They go back to the haletic romance, huh? Oh. But the romantic comedies, the romances in that sense, they go back to the medieval romance. So you follow it up and make it, you know, better understanding what these two different forms and plays are. They're different from tragedy and comedy, right? One has its origin in the Hellenic period and the other has its origin in the medieval. Now, the second thing, huh? There's a connection between beginning and order, okay? And the connection is that order is based on some beginning. Order events historically, we take some event to begin with, don't we? We take, for example, the birth of Christ, right? And we order all events by what? Distance from that event, right? Okay. So this is 2001, right? Okay, but the French Revolution began in 1789. The American Revolution began in 1776, maybe, right? Yeah? Okay. England was conquered by the Normans in 1066, right? We're ordering all these events, but by some what? Beginning, right? Now, if you want to understand the order of an army, or, in fact, the order of the federal government, if there is any order there, you go back to the one who's at the beginning of things, right? You go back to the general, let's say, right? And instead of the general, there are maybe, let's say, the colonels. Now, the colonels are captains, right? Or you go to the president, and now the president, the different department heads, and then all the way down the line, right? So you order things from the what? You know, often times you kind of remember something, if you go back to the beginning, then you can... Right, yeah. Yeah. Remember things in order, right? Okay. So since order is based on some beginning, an ordered, as opposed to a disordered, approach to philosophy must be from its beginning. Therefore, an ordered approach to philosophy must start from its beginnings. And these being the first beginnings, and the natural beginnings, and the first beginnings, if you don't come into philosophy from these natural beginnings, you're going to have a disordered approach to philosophy. And, of course, that's inappropriate if philosophy is what? Now it's over a road, right? That you approach it in a disordered way, right? And if the end of philosophy is wisdom, and the wise men, especially in those order, right? It's obviously most inappropriate to approach philosophy in a disordered way. Now, the third way, suggested by the famous Greek proverb, the beginning is half of all. And it's a proverb that Plato and Aristotle and the other great Greek philosophers often quote, the beginning is half of all. And Plato says, you know, he quotes the proverb, the beginning is half of all, but he says, it seems to me to be more than half, okay? And that's because the beginning is like a, what, a seed, right? It contains everything else as in a seed. So, although it's small in size, it's great and all that it, what, he arrives to, huh? So, the beginning is like a, what, a seed, huh? Small in size, but great in power. So, you can say everything else is contained in the beginning as in a seed, right? In the power of the beginning. And that's why the philosophers say that even a little mistake in the beginning is a great one in the end. You know, he's compared to a fork in the road, right? Take the wrong turn there, the fork in the road, you're not far from where you should be, but the further you go, the further you'll be from where you should be. So, if you begin well in philosophy, you're going to be helpful of the whole philosophy by itself. If you begin badly, you're going to be impeded all the way through philosophy by itself. Now, a fourth reason, huh? When you study knowledge, you'll find out that knowledge involves two things, huh? Knowledge involves grasping and judging. So, even when you read, say, a philosopher, you have to grasp what the man is saying. You have to understand what he's saying, right? But that's only the beginning. And the culmination is to be able to judge whether what he says is true or false, right? To separate the true from the what false, right? Now, that's one of my complaints about some of the modern philosophers, right? They write so obscurely that it takes you a long time to figure out what they are saying, and you have a little time left over to judge, right? When the bulk of your time and effort should be taken up, you're finding out whether what they say is true or false, right? And what does that mean? And I was teaching at St. Mary's College there. I taught there three years. When I came out there, Joe there in the department was trying to figure out what Heidegger meant by being, right? Three years later, when I left, he was still trying to figure out what Heidegger meant by being, right? So, the proportions all work. Now, what is judging, huh? Well, judging is separating the true from the false. And we're in a space here. We just did it. Judging is separating the true from the false by some beginning. Okay? So Euclid will be separating the true from the false by going back to the beginnings of geometry, to the definitions and to the axioms and the parts. That's right. But ultimately, Euclid is going all the way back to the natural beginnings, because those are the very first beginnings.