Wisdom (Metaphysics 2005)
Lecture 33: Equivocation by Reason and the Unity of Being

Transcript
================================================================================

So they say, you know, kind of the theological definition of man is imago dei, the image of God, huh? Okay? You've got to see man in relation to God in theology, huh? If you consider man as an animal that has reason, you don't have to bring God into that, do you? That's what the philosopher would say. He's a two-footed aristocracy, he calls him a two-footed animal. He's a two-footed animal. He's a two-footed animal. But if you say that man is an animal that has reason, you don't have to bring God in, right? Um, but in theology, you would speak of God as, what? Made in the image and likeness of God. But you can't speak of imago dei without talking about God, right? Okay? So, you could say theology is about divine things, but the primary meaning of divine is God himself, right? Okay? Well, what about grace? Is grace God? No. But it's a partaking of the divine nature, right? Okay? So, other things are what? Yeah, related to God, right? Or we're talking theology about faith, hope, and charity, right? The so-called theological virtues, right? Well, are faith and hope and charity God? Maybe charity is in some sense. But faith, hope, and charity, the virtues, their object is, their object is God, right? Okay? So, you can't talk about something whose object is God without talking about God, right? Okay? You see that? So, divine said of God in grace, or divine said of God in faith, hope, and charity, or divine said of God in our soul, right? That's a critical. We're not divine. My soul is not divine. It says, God is divine, huh? See? But my soul is made to the image and likeness of God, right? Okay? Faith, hope, and charity are not God, but their object is God, right? Grace is not God, but it is kind of partaking of the divine nature. So, the word divine here is equivocal by reason, not by chance, huh? You see that? So, what I was pointing out here, and what we'll be putting out in the second part here, is that although the word being has many meanings, and in the fifth book of wisdom, we'll see, Aristotle's very, lay out the meanings very clearly, that is not enough to say there can't be a reason out of knowledge of being as being. If the word being is said equivocally by chance, then you wouldn't have one reason out of knowledge. But if it's said equivocally by reason, that there's a first meaning, right? And the other meanings, in some way, refer back to it, then you could, what? Have one reason out of knowledge, just like there's one reason out of knowledge of political things. Because there's a primary meaning of polis, and everything else, in some way, refers back to that, right? So, in the fourth paragraph, he begins, Being, however, is said in many ways. It's a word equivocally. But towards something one, into some one nature, and not equivocally. Now, notice what I saw as a way of speaking there, huh? Let me just indicate this again here. I mentioned this way of speaking before. Therefore, sometimes we divide something into two things. One of them keeps the common name as its own. And the other member gets a new name, right? And so, the most readily example here is this. I say to my students, How many fingers do I have? And they'll say, Five, right? And they'll say, How many fingers do I have? Four fingers and a thumb, right? So, one of the five, called a finger, gets a new name, the thumb, right? And the other four, keep the old name, right? Now, why does this finger, get its own name, a new name, right? And why do the others keep the common name? What's the reason for that? Something's added to this one. Yeah. There's something that makes one stand out, right? A sore thumb. It leaves us out being a sore thumb, that's the expression. It stands out as opposed to the other ones, right? So, when I grab my water glass, or my beer can, or something, right? You know, the imposable thumb, a biologist calls it, huh? Okay? So, one way this takes place, is when one of them adds something noteworthy, right? Mm-hmm. So, sometimes we say man is an animal, intending no insult, right? Other times, we divide man against the animal, son. Don't we? So, the beasts, the irrational animals, keep the name animal as their own, and man gets a new name, because he adds something very noteworthy to the common meaning of animal, right? Maybe the possession of reason, and so on. Why those beasts that have nothing beyond the common meaning of animal, sonates keep the name animal as their own, right? Okay? Mm-hmm. Okay? Now, when you have an equivocal word, an equivocal word is a word that has many meanings. Period. Now, sometimes, we divide that, as we say, into the word that's equivocal by chance, and the one that's equivocal by reason. And sometimes, the word that's equivocal by chance keeps the common name equivocal, although sometimes people to be, you know, avoid confusion, they'll say purely equivocal, right? And the one that's equivocal by reason adds something out. Not only are there many meanings, which is common to both, right? But in addition to the many meanings, there's an order among those meanings, right? There's a connection among those meanings, huh? Maybe there's a fundamental meaning, and the other ones relate back to it. Okay? So, and sometimes, they'll call the word equivocal by reason, they'll use the word analogous, right? And then they'll call the one here, just equivocal. That's what Aristotle's doing here, right? Okay? Do you see that? And the sooner you get that into your head, that way of speaking, that way of, of, in which the word equivocal here can become equivocal, the better off you'll be, right? Because it comes up again, and again, and again, as you go through philosophy, and you find it in daily speech, too, it's not just, it's just equivolous to contradict yourself. And not equivocally, right? But he's using equivocal, right? Purely equivocal. Not equivocal by what? Chance, right? Okay? Now, Thomas, you'll find Thomas often calling the word equivocal by reason analogous. To some extent, I mean, I really didn't know this, I wasn't spelled very well on the board there. You know how to spell it, right? Analogous or proportional, to use a Latin word, huh? But I think you've got to be kind of careful about that way of naming, because not every analogous word, or proportional word, is by proportion, right? Because there's different forms, I think I've talked about some of them before, but this is not, this one before us is not an example of proportion, like there's a ratio's. So he says in the fourth paragraph, being always set in many ways, but towards something one and to some one nature. There's a fundamental first meaning, and not equivocally, meaning purely equivocal, or equivocal by chance. Do you see that? And Aristotle makes a comparison here. But it's everything healthy towards health, right? The one in preserving, another in making, right? Another in being a sign of health, another in being receptive of the same, right? So the body is called healthy because it sees health. The complexion of something, because it's a sign of health, right? The diet, because it produces it or something, right? Okay? And then he says, again, the word medical is said towards one thing in medical art. For one is said to be medical in having the medical art. He's a medical man. Another in being naturally fit towards the same, a natural inclination of those things. Another in being the work of the medical art, right? Okay? So there's a clear example. Aristotle, you know, is the son of a medical doctor, right? Yeah. You know, a very illustrious doctor, right? He was the court physician there. That's how Aristotle became known there in the court of Macedon, right? Because his father was the court physician. So that's how Aristotle got to be chosen as the teacher of Alexander the Great. So Aristotle often takes examples from that. You see that in the ethics, right? Where he says, you know, a man who listens to the philosopher in ethics but doesn't act upon what he says is like the man who goes and gets medical advice but doesn't do what the doctor told him to do, huh? One of my friends back home there, his lung collapsed, you know, and they can inflate it again. But the doctor told him to stop smoking. Well, he refused to, right? So he's a useless hearer of medical advice, right? There's some men who tell him that this is wrong to do, right? Morally. And, you know, they're going to do what they want to do anyway. So they're useless hearer. And so he often takes things from the medical art. Okay? And we can take other words said in like ways to these, right? So I was taking the word political there on the board a few minutes ago, right? Okay. And so he's saying, now being is like the word healthy or like the word medical or, my example, like the word political, right? Thus also being is said in many ways but all towards one beginning or first meaning. For these are called beings because they are substances. These because they are the undergoings of substance. Others because the way to substance or corruptions or lacks or qualities or productive or genitive substance. But always in reference to substance in some way, right? Now when Thomas comments on this, he says in this plethora of meanings that Aristotle is giving, you can perhaps distinguish four meanings in direct order. And let's give those four. I think it helps to clarify things a bit to see these four as kind of simple. You can say that the first meaning is substance, right? And the second meaning is what we call accident. An accident in the, not in the sense of actions opposed to property, but accident in the sense of the categories. A thing that exists, right? But not by itself exists in another as in a subject, right? And can't exist apart from it. So an example of substance would be, let's say, a man, or a dog, or maybe a tree or something. An accident would be a thing like what? The health of a man, right? Or the health of a dog, right? But health is not something by itself, it's something of a man, right? Or the shape of a man, or the shape of a dog, right? Okay, so the second meaning of being, which is that of accident, refers back to substance, huh? Okay, it's something of another, right? Okay. Now the third meaning would be the coming to be of a substance or an accident, huh? Okay. Coming to be of a substance, an accident. And also that's more remote, huh? Coming to be, you say, well, coming to be is not being at all, is it? But in some sense, isn't there such a thing as coming to be? Right? But certainly not is in the way in which some sense there actually is. So becoming a man, or becoming healthy, isn't the same thing like being healthy or being a man, is it? We get an existence in some way, doesn't it? Yeah, okay. Coming to know, right? Existence somewhere, right? Not as much as knowing does. And then, fourth sense would be the lack of release, right? Okay. Substance or accident, huh? Such a thing as blindness, right? And notice, when you get to blindness, you say, Oh, is blindness, is that being, or is that not being? Yeah, yeah. Yet, you say that somebody is blind, don't we, right? Okay. This is almost like what you call being a reason, right? Okay. I have blindness, huh? You have something, you don't have something. But we'll say that you have it, right? Okay. Now, notice how you're moving away from substance, right? But accident is something of substance, right? Something exists in substance, huh? Coming to be, is it coming to be of a substance or an accident? And this here is a non-being of some accident, right? Or substance, huh? Death, right? Okay. Blindness, huh? But in some sense they are, aren't they? See? Now, the Greeks had an interesting common statement. You can't get something from nothing, right? In a way, this is kind of a common thought. And King Lear says at the beginning of the play there, right? Nothing will get you nothing. Nothing comes from nothing. And Julianne was thinking about that in my, in Sound of Music, right? Nothing comes from nothing, right? I think you're a quit. Without saying, I'd say to you, When you say you can't get something out of nothing, Does the word nothing have some meaning? Does it mean something? Now you're saying nothing means what? Something. Something. Yeah. So now you've carried the word something all the way over it to... And that's about as far as you stretch the word, right? Mm-hmm. Yeah. You know, teacher, the circuit is a joke. You know, philosophy is the only subject where you can get paid for talking about nothing, he says. Ha, ha, ha, ha, ha, ha. That's what apologies, don't get paid for it. Yeah, yeah, yeah. Yeah. You see, the point of the dialogue is we're wondering about this, right? You know, because the Greeks would often say, and we find it in Shakespeare sometimes, too, to tell falseness to say what is not. Well, how can you say what is not? Because what is not is nothing, right? So how can you say nothing? That's not to say anything at all. But yet we do say that you said nothing, right? What did you say? You said nothing. In some sense, that's what you said. You know nothing. So you see how far you move there, right? Towards the end, huh? So the fundamental meaning of being is substance, just as the fundamental meaning of political is the, what, polis, the city, the nation. But the other meanings of being, like accident, or the coming to be of substance or accident, or the lack of one of these things, has some conviction with substance, right? Okay? Because the health is something of the man or the dog or whatever it is healthy, right? And the shape is the shape of something, right? Other than itself, huh? You see that? So he starts saying the word being. Okay. then, is not equivocal by chance, it's not purely equivocal, but there is an order in the meanings. It's equivocal by reason, you use that phrase, equivocal by reason in some places. But the fundamental meaning is substance. And so this science of being as being is going to be chiefly about what? Substance, yeah. So the seventh and the eighth book of wisdom are devoted to substance. So in the next to last paragraph he says then, just as there is one reasoned out knowledge of all healthy things, because the word is not equivocal by chance, right? But they all refer back to one thing. So likewise the same in other things. For it belongs to one reasoned out knowledge, not only to look at those said by one, by having one meaning, like you might say, well, arithmetic is about number and numbers said uniquely of all these things, but also those said towards one nature. For these are also said in some way by something one, right? It is clear then that to look at being as being belongs to one reasoned out knowledge, and we saw before that that was the same as the one that aims at the first cause, right? Okay. So is that clear? I want to take a little break from here to go on the next page. See if you didn't do this reading. So the top of the second page here now, Aristotle is going to point out that the chief subject of this is what? Substance, right? But the chief subject of revealed theology is what? God. Yeah, yeah. But that's not the chief subject of wisdom in this thing, although it's the end or goal, you might say, to know God. So Aristotle used the word theology later on, describing wisdom, but you've got to realize that God is not the subject of the science, but he's the end or the goal. But in revealed theology, God is the subject of the science as well as the end or the goal. So it has more right to the name of theology, right? But before that, somebody might call this theology, as Aristotle will in the sixth book, right? Call this that. I don't know the name he gives it. When I was in college, I used to have a course in philosophy that's called natural theology, and what you could know about God by reason. And there would be more appropriate to say that that's a part of metaphysics rather than that. Yeah, yeah, yeah, right. Culmination of it. But some people, you know, say, you know, is Aristotle really interested in God because he doesn't spend the way Thomas does? But that's not the subject of the science. It's the end of the goal. If you want a more expensive knowledge of God, you've got to go to Thomas and reveal theology. That's right. To me, it doesn't make any sense for a Catholic who's a philosopher not to be, you know, ordering his studying to theology eventually. It doesn't make any sense to not do that. Something disordered, right? My old teacher Kassirik had a beautiful passage from Albert the Great, you know, where he says, if you're not studying everything you're studying for the sake of knowing God, you have a perverse attitude towards knowledge. You know, unless you've been forced to, based on necessity, you're a plumber, you've got to do something else. But I mean, you know, if you're pursuing knowledge in itself or by itself, it should be all ordered to eventually knowing God. It shows that modern philosophy is not too good, right? It seems like almost the purpose of modern philosophy is to show that it's impossible to talk about God or to know Him or something. So at the top of the second page here, but everywhere reasoned out knowledge is chiefly about what is first, right? And that upon which other things depend and through which they are named. So what's first under being is substance and the others depend upon that, huh? Like the accidents or something else, substance, and so on. And to which they are named, or called beings, right? If then this is substance for being, it would be necessary for the philosopher to especially have the beginnings and causes of what substance is. And notice here he calls the wise man the philosopher, right? Now, what kind of a use of that, or the word is that? Because sometimes you'll call wisdom philosophy, period. And the man who's engaged in this, the philosopher. You might say, isn't the political philosopher a philosopher? Yeah. Isn't the geometry a philosopher? Yes. Isn't the natural philosopher a philosopher? Yeah. Isn't the magician a philosopher? Yeah. So how could he call the man pursuing wisdom here, the philosopher? Because he's pursuing the highest part of wisdom. So isn't it most appropriately predicated of him? Yeah. And of course, philosophy, although etymologically philosophy means a love of wisdom, right? The meaning of the word philosophy is not the love of wisdom, but the knowledge one would pursue because of the love of wisdom. Well, that's like Grant's, who's buried in Grant's tomb. And it's wisdom, obviously, is the knowledge that the love of wisdom is going to be pursuing. So there's a reason to call wisdom and the man pursuing it philosophy and the philosopher. So Aristotle will slip into calling him that. Okay? But this is the other reason why we call, why the common name is kept, right? By one of them, right? This is not because he alone has it, but because he alone has it. What? Most of all. Or most of all they have. Yeah. It's like this other example we give here where we use the word understanding, the name, not the act of understanding, but the ability to understand, right? In which they call it intellectualism. Well, sometimes we'll divide the understanding into understanding or intellectus and reason or ratio, right? Okay? And so the understanding of an angel is called understanding intellectus. The understanding of a man is called reason or ratio. Now this is the other way of naming, right? Why does man get the new name and the angels' understanding keep the name understanding? Why? Because everything they know is under that aspect, whereas we only know first principles as intellectus. Everything else we know as reason. Yeah. It's because reason is a kind of, what, overshadowed, as Thomas said, Overt. Overt. As he says. Overt. Understanding, right? Very weak understanding, right? Because we have the ability to understand in an imperfect way and not fully and we have to reason out things to get a little bit of understanding, to get very far, so we get the, what, new name. This is for the, because you don't have fully what it's meant but a common one. Yeah. Okay? It's a little bit like, you know, if you say, you know, if your little child asks you, you know, what's the difference between a kitten and a puppy? You say, well, a kitten is a cat and a puppy is a dog, right? But then you might sometimes divide dog against puppy, right? Mm-hmm. Cat against kitten, right? Um, so when you divide dog into dog and puppy, cat into cat and kitten, that's like dividing understanding into understanding and piece of devalty. Mm-hmm. That's a different thing than what we had before where we're dividing, um, uh, disposition to disposition and habit, right? Or we're dividing equivocal into equivocal and analogous, right? Do you see that? So when you divide animal, into animal and man, uh, man has what is meant by animal just as much as the beasts have it, right? He's an animal, he's a living body with sensation. But he has something noteworthy in addition to the common meaning, huh? Mm-hmm. But when you divide understanding into understanding and reason, it's because, uh, the ability to understand is so imperfect in man. And, and, and it's perfect in the angel, and therefore he keeps the name understanding and man gets the new name because he's not fully possessing the ability to understand. Okay? Do you see that? So, there are two different ways in which one of two things in which something is said keeps the name, right? One, because it alone fully has what is meant by the common name. And another, because, what? That's all it has, nothing more. Do you see? So, those, those two ways of naming come up again and again and again, right? Okay. What do you think? Say, um, do you think, do you think the next election will be won by the Republicans? Hmm? I say, yeah, I think so. Do you know that, Mr. Berkwist? No. Say, um, do you think the two is half of four? Yeah, I think that. Right? You know it? Yeah, I know it. So, sometimes you divide knowing against thinking, right? Mm-hmm. And then thinking, you're just thinking. By knowing you have, what, the certain two that you have, right? Okay? So, I think, um, I'll live to be 80. Ha, ha, ha. Yeah, I know it. Yeah, I know it. Yeah, I know it. Yeah, I know it. Yeah, I know it. Do I know I'm going to be 80? No, no. You say, wait, do you think I'm going to be 80 per person? I think so, yeah. I think I'm going to be 80. Do you know that? No, I don't know. Do you think that two is half or four? Yep. But I know that, right? Yeah, yeah. Okay. So it's people signing to say to you, do you know that? Or do you just think that's all right? And then they're using thinking as opposed to knowing, right? Mm-hmm. Or distinguished from it. But the man who knows something thinks something too, doesn't he, right? Which of those two ways is that? It could almost be either. You could say that knowing adds certitude, or you could say that thinking is sort of an imperfect knowing. Yeah, yeah. But you see, thinking doesn't, in its very meaning, right, imply certitude or something, right? So you can say a thinking that is just a thinking keeps the name thinking, and the thing that adds the certitude of being sure gets the new name knowing, right? You see? And so, but like Socrates, you know, when he's distinguishing between opinion and knowledge, right? You don't see it as the word opinion because that's already more particular, right? That's like, you know, contrast man and beast, right? You've got two different names. Each has got its own name, right? Mm-hmm. But sometimes instead of saying man and the beast, you say man and the animals. Mm-hmm. And then animal has been taken by beast as its own name because it adds nothing beyond what an animal is. That's greatly noteworthy, huh? So thinking is sometimes divided into thinking and knowing. And knowing gets in the name because it adds something, the idea of the certitude, okay? So it's like the fingers, huh? Five fingers and four fingers and a thumb. The animals can be divided into the animals of man. And once you kind of understand those two ways, you'll find examples, you know, over and over again of these things. I want to buy a plant, see? But you don't think you want, you know, a tree? No, you can't exclude a tree if we can come into that thing, you know? But in some sense, a tree is a plant, right? Mm-hmm. So the little plants keep the name plant and the tree gets its own name. I want to buy a tree. See that? But there is one sense and one reasoned-out knowledge of every one genus as one grammar looks at all speech. Hence, to look at the species of being as being, you shouldn't have been species now loosely, right, huh? The more particular things. Belongs to one reasoned-out knowledge in general, but the species to special ones. So the ways of being that are a division of being as being pertain to what? The science, huh? But a division is not a division of being as being, but not pertain to the science. So, we know now that wisdom is about causes and ultimately about the first causes, right? And now we know secondly that wisdom is about being as being, right? Now the part that I'm skipping here, going up to the fifth reading, he shows that being and one are kind of convertible, right? So he'll speak of wisdom as being about being and the one, okay? But now in the fifth reading, he's going to show that wisdom is about the, what? Axioms, huh? Okay? And this will be a third thing now that wisdom is about, huh? Now, let's recall what an axiom is, huh? What is an axiom? In the sense that you're a sound, it's easy to put it in, huh? Not the sense that there's a model that's using the word axiom. The first principle, a self-evident principle? Well, that's true, but the genus of axiom is statement, huh? Okay. Every axiom is a statement, but then every statement is an axiom. Okay? So the first thing you want to say about an axiom is it's a statement. Now, in logic, we define a statement as speech signifying the true or the false, right? Okay? And speech is vocal sound, huh? Signifying by human agreement, you know, part of which, having parts that signify by themselves, huh? Okay. But now an axiom is a statement known through itself rather than through other statements. So it's a statement known through itself not through other statements, huh? Now, are there statements known through themselves or only statements known through other statements? There have to be some that are known through themselves or you have an infinite regression. Yeah. Yeah. Because if you use statement A through B and that had to be known through another statement and that through another statement and so on, you'd have to go through an infinity, right? Of statements an infinity of reasonings in order to know any statement, right? So, if every statement was in need of being known through other statements then no statement would be what? Known. Including the statement I just made. and sometimes you know someone denies that there's some statements known through themselves what about the statement that statements exist? Did you try to prove the statements exist? And if someone says the statements do not exist he's showing that they do exist, right? You can't deny the statements exist without making the statement, right? So there are statements that are known through themselves, right? Now, Boethius in the Book of the Trinity makes a further distinction or points out of the distinction. There are statements known through themselves by all men and there are statements known through themselves by those who are wise in some sense. Now, which are the axiots? Are they a statement known through itself by the wise only or by all men in some way? By all men, yeah. A statement known through itself by all men. Now, an example of a statement known through itself by all men would be that a whole is more than one of its parts. Because everybody knows what a whole is and what a part is and if you know what a whole and what a part is, if you know that a whole always has parts, right, then it should be obvious to you, right, that a whole is more than one of its parts. And can you live without experiencing whole and part and what a whole and part are? Unless you take your steak in one gulp and your water or beer or whatever it is in one gulp, you're going to experience whole and part and know what a whole and part is. So, as an example of my statement known to itself by all men, but now if I say that a perfect number is always a composite number, right, is that known to itself by all men? No, probably not. Because most men don't even know what a perfect number is, and some men don't even know what a composite number is, right? But to a man who knows what a composite number is, which is a number measured by some other number, right? One not being considered a number, right? And a perfect number is a number which is equal to the what? Sum of everything that measures it, right? Well, obviously, if you measure you're not you're not If you're not measured by some other number, but only measured by one, you're not going to add up the number in hand. So the first perfect number is, what, six, right? Which is measured by one, and by two, and by three, but not by four and five. And one plus two plus three adds up to what? Six. And so Eston and Thomas refer back to six being the perfect number, the first perfect number, and the things that measure one, two, three are in perfect order, one, two, three. And this is one reason why Scripture speaks of God making the universe in six days, right? It doesn't mean six in the sense of days in the ordinary sense of day, right? But these six, they're symbolizing the perfection of what God has made, right? They use this perfect number, they think. But as I say, most people don't know what a perfect number is, and even some people don't know what a composite number is. So that every perfect number is a composite number, is a state that is known to itself by the wise. Not wise in the sense of fully wise, but someone who has a little education in geometry, or in the arithmetic in this case, huh? Okay? For every rhombus is a quadrilateral. Well, some of you know what a rhombus is, right? But the man who knows a rhombus is a little training in geometry, right? Of course, a rhombus is a quadrilateral, right? Okay? And so that's the statement known to itself by those who are wise in some art or science, huh? Now, Aristotle, in the posterior analytics, he will speak of these two kinds of statements. I'll put the other one down in this, so he can make this comparison. Statement known to itself by the wise. Aristotle will point out that these two kinds of statements are the beginnings of reasoned-out knowledge. But the first kind you'll call the common beginnings of reasoned-out knowledge. And by common, I mean common to more than one or to all forms of reasoned-out knowledge. They're the common beginnings of reasoned-out knowledge. The common beginnings of every statement. And the ones that require you to have a certain foundation in the science, like the man knows what a rhombus is and knows what a perfect number is and so on, right? Those beginnings are beginnings private to one form or reasoned-out knowledge. So that a perfect number is a common number, is a beginning private to, with many, science of numbers. And that a rhombus is a quadrilateral, is private to what? That jump, right? So those are the private beginnings, huh? Private beginnings of reasoned-out. So Waste distinguishes between a statement known to itself by all men and a statement known to itself by the wise. In the Book of the Trinity, and Aristotle distinguishes in the posturalytics between the common beginnings of reasoned-out knowledge and the private beginnings. But the common beginnings are the same as the axioms, right? And the private beginnings are the same as the statements known to themselves by the wise in some art or science. So this is an important, a very important distinction. And you can see in the case of the statements known to themselves by the wise, that you need some consideration, some teaching, right, to know those, right? So it's not until I was taught, let's say, the definition of perfect number and taught the definition of composite number, that it just became obvious to me, right? I know of great advance in my knowledge, but it's something I have to have in mind, right? Like the first one, you don't seem to have to be taught, right? Everybody knows that, right? So, I learned what a perfect number was when I started reading Euclid. Euclid taught me this, right? Well, who taught me that a whole is more than a part? That experience. Yeah. I mean, I wasn't really taught this by somebody writing that to sit down, right? Now, as we asked before, and this was one of the problems there in the third book of wisdom, is it necessary that we stop and consider these axioms, right? And say some things about them, and so on? Or, can we say that because everybody knows them, we can just use them and proceed from them, right? We don't have to prove them, obviously, because they can't be proven, right? They're before all proof. And everybody knows them, so why don't just use them, right? Is there some reason that we have to stop and talk about what everybody knows? Instead of just using it and proceeding from it, that might seem to be sufficient, right? And what was the reason we gave before why it seems you've got to stop and consider these to some extent? Some of them indistinctly or... Okay. Yes. Yeah, one thing that you discover when you examine the axioms is that the words in the axioms are all equivocal. Oh. Equivocal, not by chance, but by reason, right? And even the axiom that the whole is more than a part. The words whole and part are equivocal. And from the equivocation of the words, men called sophists, right, will sometimes tie people up. And I give a very simple example of that with the whole and the part. And I tell my students, I repeat this, you've heard this before, I say, man's an animal, isn't he? Yeah, yeah. But he's not just an animal, right? He's an animal that has reason. Yeah, okay, okay. So animal is only a part of what man is. Yeah, okay. But animal includes besides man, what, dog, cat, horse, elephant? Yeah, yeah. So it's only a part of man, includes much more than man. So sometimes the part is actually, what, not only not less than the whole, but includes more than the whole. Oh my God, yes. And the students say, yeah. Yeah, Jimmy. Oh, oh, yeah. So now I've apparently refuted the axiom that the whole is always more than one of its parts, right? And my students, you know, they're convinced, yeah. Now, Thomas calls that, if I left them in that situation, Thomas calls that leaving the cistern open, right? Somebody falls down and they're responsible for that, right? Well, this argument against the axiom, most people couldn't answer. At least not right away. But what's wrong with the argument, huh? I don't know. It's a different type of whole. And in a way, animal is only potentially these things. Yeah. Not actually. In the fifth book of wisdom, Aristotle would distinguish between what is called the composed whole, which is a Latin word meaning put together, right? The whole is put together from its parts. And then what is called the universal whole, right, which in Greek is katalu, gets its name from kata, according to the holos, the whole. And the less universal, or the particular, gets its name from part, right? And this is the whole which is set of its parts, but not put together from them, right? And so what you're doing in this argument is confusing animal as a composing part of the definition of man, as an animal that has reason. And obviously that whole, the definition, has something besides animal as a part of it, namely has reason, or two-footed, as Aristotle says. Two-footed animal. And then animal as a universal whole, set of man, dog, cat, and horse, right?