Introduction to Philosophy & Logic (1999)
Lecture 21: The Ten Categories and the Five Predicables

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In the beginning of our experience are the material ones. So the distinction or division of substance into material and immaterial is something that would come, what, later, right? And then we might divide the material into the living and the non-living. And you might divide the living into the plant and the animal. You might divide the animal, following Shakespeare there, into the beast and man, huh? So in case you want to know where you are, right? In the scheme of things, huh? You're in the genus substance, or what it is, as he calls this, because these are distinguished by the way something is said of individual substances. And so when something is said of individual substances like you and me, or your dog or my cat or something, and answer the question, what is it, you can end up with something in the genus of what? Substance, right? So what is Socrates? We could say he's a man, right? More generally, we can say Socrates is a what? Animal, right? More generally, he's a living body, right? More generally, he's a material substance or a body. And most generally, huh? He's a substance, huh? So all the ones above are said of those below, signifying what they are, huh? If you, Jesus isn't it, right? Material substance, right? Living body, huh? Plank animal. Okay? So that's the first highest genus, substance, huh? Now the second one, which Aristotle also devotes a chapter to, there he actually divides the second category into its immediate species. And the second category is how much quantity is he used to use. Aristotle divides quantity, which is like the measure of substance. He divides it into two kinds. And these are called discrete continuance. Now the main kind of discrete quantity is what we call numbers, huh? The main kinds of continuous quantities are the line and the surface and body now, in the sense of three dimensions, huh? So if you use the word body for a species of continuous, and we saw before, body as a species of substance, the word is equivocal. And that equivocation deceives Descartes and others, right? Who confuse length, width, and depth with a substance that is apt to have length, width, and depth. And as I was saying, if Descartes grew up, right? The substance, the man, remained, but the size, what, changed, I mean, the quantity. Now, Aristotle distinguishes between the discrete and the continuous in one way in logic and in another way in natural philosophy. In logic, he defines the continuous as a quantity whose parts meet at a common boundary. So he says it's a quantity whose parts meet at a common boundary. Like in a straight line, for example. The left and the right side of the straight line meet at a point, huh? Which could be considered the end of one part and the beginning of the, what, next part, right? In a surface, take the diagonal, one part meets the other part at a, what, line, huh? And this line is the end of one part and the beginning of another part, huh? Or let's say it's a circle. You take the diameter. The left and the right side there, or top and below part, we're going to call, of the circle, they meet at a common boundary. This line is the end of one and the beginning of the other. And if I was to break this piece of chalk and talk about the right and the left side of the piece of chalk, they would meet at any, what, plane, huh? Time is also considered sometimes a continuous quantity, huh? In the past and the future, come up to the now, right? In the now, in the sense of the end of the past and the beginning of the future. But a discrete quantity, like number, you take the number three or the number five or the number seven. Anyway, you take the parts of seven, say three and four. Do three and four meet somewhere? So the discrete quantity is a quantity whose parts do not meet at a common boundary. And that's why it's called discrete, huh? As it were, separated, huh? What continuous implies at the end of one is the beginning of a, what, another, right? So the boundary between the United States and, say, Canada, you have an imaginary line there. It's the end of the United States and then the beginning of, what, Canada, right? Now, in actual philosophy, Aristotle would give another definition of continuous. He'll recall this one. Would he give another definition of continuous? And that is, the continuous is that which is divisible forever. He'll show in the sixth book of natural philosophy that the continuous is divisible forever. But the discrete, the number, is not divisible forever. So if I divide seven into four and three, and I divide the four into two twos, and the twos into two ones, you can't really divide the one, unless you're talking about continuous quantity. But if you're talking about the one that's the beginning of number, that is actually simpler than the, what, point in geometry. The Greeks used to speak of the point as a one or a unit having position, right? So if you can't divide the point, even more so, you can't divide the one. So the discrete is not divisible forever. And if we ever get to study the first book about the soul, where Aristotle was proceeding dialectically, but he points out something interesting about our thoughts, that our thoughts are like numbers, rather than like the continuous. And we saw that, huh? When you divide, say, the species into the genus and the difference, right? And sometimes the genus is a species, right? So it can be divided into another, higher genus and difference. But it doesn't go on forever, does it? We show that there are highest genu, of which quantity is one, right? So a discrete quantity is not divisible forever, and that's the way our thoughts are not divisible forever. But the continuism is divisible forever. That's a kind of sign, huh? That thoughts are not continuous is a sign that our reason, the universal reason, is not material. Because everything material is what? Continuous. And even our thoughts about continuous things are not continuous. And that's not explained by the fact that they're about the continuous. It's explained by the nature of our reason, huh? It's one of the first places in the Dhyanism, in the first book, where you get a reason for thinking that our universal reason, that understands what things are, is not, in fact, what? A body, right? That the brain, in fact, is not the organ of thought. I don't know, it's related in some other way, we'll say, to thought when we study the three books about the soul. So, motion, especially local motion, is something continuous. So, if I walk down the garden path, and that path is something continuous. So, if I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I walk down the garden path, I and you can divide forever, so likewise my motion could be divided into infinity of parts. And even the time it takes me to walk down, that is divisible forever. But the discrete is not divisible forever. Now of course, this distinction between the discrete and continuous is even more basic to mathematics than to natural philosophy, because mathematics is about quantity. But arithmetic is about the main discrete quantity, which is number, and geometry is about continuous quantities, the line and the angle and the plane, the surface, the body, and so on. So the distinction between arithmetic and geometry, both of which are found, by the way, in Euclid's elements, is based on this distinction here between the discrete and the continuous. So sometimes they say, how much, or how many, right? There's a little difference there, the way we speak. So this is the second category. And notice, the most basic division of the continuous is that which is continuous in one dimension, a line, and in two dimensions, a surface, and then in three, the body, right? Of course, we show later on in geometry that there can only be three dimensions, only three lines that are each at right angles together, too. Well, it's kind of interesting if I contrast a little bit with logic here. In the beginning of logic, we distinguish three acts, right? And there are three parts of logic corresponding to those three acts. Here we have three species that are continuous, the line, the surface, and the body, with only, what, two parts to geometry, plane geometry and, what, solid geometry, right? Kind of interesting, huh? Plane geometry is both about, what, the line and the, what, two massive figures, right? The very first theorems, if you recall, in Euclid there, the very first theorem, right, is ordered to the second theorem, right, and so on, and eventually to cutting off a line equal to another line, right? But you have to use circles and figures, so you're already in a plane, right? So if you have some experience of beginning of geometry there, you can kind of see why there's no geometry of the line distinct from the geometry of plane surfaces. But there is a distinction between plane geometry and solid geometry, huh? Books 1 through 6 are really plane geometry, and books 11 through 13 are solid geometry, huh? And he interrupts it with 7, 8, and 9 with the mathematical books. And there's a reason for that. So you said our thoughts are discrete quantities in that it is a sign that... Yeah, they're not quantities at all, but they're like numbers, he said, right? Okay, but you said it was a sign that it's immaterial. Yeah. And so I'm trying to understand, why is that? Okay, well, if you see the connection between the continuous and the body, right, every body is continuous, huh? Yes. So what is received in the body is received as continuous. But even when we receive the, you know, the continuous into our mind, our reason, in the form of thoughts now, right? The thoughts are not continuous. So we receive the continuous in a non-continuous way. Why is that, then? It's not because of what is received, because that's continuous. Therefore, it must be due to the nature of the receiver. Whatever is received is received according to the nature, the condition of the receiver. So it's a sign that the reason is not a body, that it knows bodies, the continuous, in a non-bodily way, a non-continuous way. Okay? And if you go back, say, to the definition, which we've been talking about, but mentioned a little bit already, the genus being one part, and the difference being another part. Do the genus and the difference in a definition meet at a point, a line, a surface? I don't know. If they met at a point, the definition would be a line. It's not a line. If they met at a line, they'd be a surface, but not a surface. So we're getting ahead of ourselves by just mentioning, you know, how the distinction here in logic, which Aristotle points out in the chapter on quantity and how much, this distinction between the discrete and the continuous. Every quantity has parts, right? Either the parts have a common boundary or they don't. That's the basis for the distinction between geometry and arithmetic, then. But it's also important later on in coming to understand that the reason, the universal reason, the ability for a large discourse, right, looking before and after, is not a body. As Anaxagius, who we'll meet, when we do some natural philosophy, will first begin to suspect that the mind is not something material. But Plato, and especially Aristotle, brought this out more fully. Aristotle gets to the chapter on quality, the chapter on how, or to use the more abstract word, quality. Here we have an example now of a division into four, by the master himself. And this is one of the prime examples I give, why I don't think that one should always divide into two or three. Okay? I'm not a fanatic about that. I think it's a good rule, because it's true for the most part. Now, the first species of quality that Aristotle speaks of is called disposition, or habit. Now, habit is, in a way, a disposition, but it's a disposition that is firm, right? And therefore, it's got its own name, habit. Later on, we divide habit into virtue, vice. Now, the second species of quality is natural ability, or inability. And there we put the ability to digest, ability to see, ability for a large discourse, looking before an actor. It's like a quality of man, right? Natural ability. The third one is the sense qualities. And the fourth one is figure or shape. So, Aristotle distinguishes, then, or divides the genus quality, which is one of the ten highest genera, into these four. And if you ever look at the Summa Theologiae of Thomas, in the Prima Secundae, we started to take up what we call oral theology. He wants to talk about virtues and vices and so on, right? But he recalls what Aristotle says about quality, and he sees that the virtues and the vices come under quality. But then he will recall this distinction of the four, right? And then show that virtue and vice come under this one. So you can see how the different highest genera are starting points for the different sciences, right? For the distinction between geometry and arithmetic, we sometimes go back to what Aristotle says about quantity. When Thomas wants to talk about virtues and vices, he comes back to this, right? As Aristotle himself does in the second book of the Nicomachean Ethics, when he wants to define virtue, right? Passions come under this thing, too. What we call feelings, right? Similarity there. Aristotle will ask, you know, are the virtues a natural ability? Or are they a passion, a feeling, right? Or are they a happy disposition, right? He's pretty sure they're not this thing over here. But which one of these is a virtue, right? Is anger a virtue or a vice? Or is the ability to feel anger a virtue or a vice? Or is it some kind of what? A habit of disposition, right? Where I'm disposed to feel anger when I should, or when I shouldn't. Depending on whether it's a virtue or a vice, right? The vice is going to conclude that the genus of moral virtue, moral vice, is disposition or habit, right? Habit in particular. The same way for temperance and all these virtues. It's not the ability to be hungry that makes you temper or intemper, right? It's not hunger as such, right? The fact that you're disposed, right? To desire these things moderately, reasonably that you are virtuous, or because you're disposed to desire these things more than you should, that you may be very intemper, right? Okay. So Aristotle, in the chapter on quantity and quality, he gives the first division of the genus into its species, huh? And that helps us to understand the highest genus are better because we can't define them in a strict sense, huh? Because the genus, the highest genus doesn't have any genus above it, right? And so there's no genus in differences whereby you can define it. So the way you have to know it, by the issues of that which is divided, yeah, makes it more clear to us, huh? But it's also a starting point for investigating the things, huh? Forgetting the genus, eventually of virtue or vice, or the genus of reason, right? Now, like substance, the basic division of towards something, huh? Aristotle doesn't make it explicit there in the physics he does. Towards something. Sometimes we use the more abstract word there, relation. But we might mention a little bit about this, huh? Relations are based upon something more fundamental, and some relations are based upon quantity, and others are based more upon acting upon and undergoing them. And quantity, they sometimes distinguish there between quantity in the strict sense, and then the one which is the beginning of quantity. So I'm taller than you, or I'm shorter than you, right? Or I'm equal. These are relations based upon what? Quantity, right? Okay? But I could be taller than one of you and shorter than somebody else, right? Being towards another, right? But it presupposes my quantity, my size, right? In years too, for that matter. Okay? In one, huh? Actually, equal should go over here. Because that's kind of unity, right? Or we're alike, huh? Same, huh? Same, like, equal. But here we have double, third, greater, less of that, right? Okay? Relations based more upon quantity. And then the other ones are based more upon qualities in the acting upon and undergoing the result of that. So, father and son, right, huh? Mother and son, right? Teacher and student, right, huh? Teacher's acting upon you. You're undergoing it, right? One friend of mine, Brother Riches, who teaches, you know, describing, you know, his classes there, where is he at the University of Colorado somewhere? Looks down upon the students looking up at him. Kind of expression in their face, why are you doing this to me? But the mover and the moved, right, huh? Okay? So, you have one group of relations that are based more on quantity, and the other is on acting upon and undergoing in some way, huh? That goes back to qualities, right? Okay? But notice, if I know something, that's a quality of me, right, huh? But I have to in some way act upon you, right, before I can be said to be your teacher, or you can be said to be my, what, student, right, huh? Okay? I can have muscles, right, huh? But I have to actually move something before we have this relation of the mover and the, what, moved, huh? Now, the last six categories, Aristotle just kind of enumerates them, huh? Question? The relation based upon, did you say that, I was writing something else here about, based upon quantity and quality? Well, in a sense, they usually say acting upon and undergoing, but those kind of presuppose are qualities, right? I think I've seen St. Thomas divide relations into acting upon and undergoing, or based upon that, and based upon measure. It's the same things. Equal to quantity, yeah. Now, the remaining categories, we're not going to do that so much, but you kind of wonder, you know, you have the category of where, and the category of when, right, category of position or positioned, and then you have what I take the liberty of calling outfitted, but to have in the Greek or Latin, and then you have acting upon and undergoing. But I often wonder about where, I mean, we are said to be in this room, right? We are said to be in, what's the genus of that? To be in fellowship? And the genus of that is to be in Massachusetts? Is that the genus? What would be the genus, huh? It seems to be more like, whole and part, obviously. Yeah. At least not just the species in the same way you have in the first four there, right? Or to be, you know, here today, right, huh? To be here this week, huh? To be here this month. It's kind of strange. If that's the genus, it's kind of strange. Our different sense almost is to genus, huh? To have a suit on, to have a tuxedo on, right? But this is Aristotle doesn't even devote a chapter to those, he just enumerates them, exemplifies them, that's it. But he has a whole chapter devoted to substance and one to quality and one to quality and one to relation. He takes us up again with the words of the metaphysics. Mike Benchton, though, when he takes up the word how there in the metaphysics he distinguishes four senses, but he eventually introduces them to two, you know? You know, two and three, right? Occasionally. So, up to this point now, we've been introduced Thank you, sir. Thank you, sir. I'm introducing you a bit to the two fundamental works in logic, in the logic of names, you might say, which is the first part of the logic of the first act. One book called the Aisagoge, right, which is by Porphyry, and I mentioned before how the word Aisagoge is the Greek word logically the same as our word introduction, right? Aisagoge is like duxio, leading in, leading in, okay? In Greek it would be E-I-S, I guess, E-I-N. Aisagoge, so it means the introduction. Now, originally, the occasion for Porphyry writing this work was somebody who was having a hard time understanding the book called the, what, Categories of Aristotle, right? And in the book called the Categories of Aristotle, we'll use words like genus, species, difference, as if everybody knows what these mean, right? And there are places elsewhere in Aristotle where he talks about the word genus and difference and gives some information about them. So it was originally written as introduction to the categories, but then it got kind of contracted to, what, introduction, right? This happens down through history, right? If you look at Sir Isaac Newton's major work, it's called in Latin the, what, you know, Principia Mathematica, the Mathematical Principles Naturalis Philosophiae, the Mathematical Principles of Natural Philosophy. But it got referred to for centuries as the, what? Principia. Principia, yeah. But as time went on, they began to see, calling this just the introduction, as a kind of example of what? That figure of speech, yeah? Antonia Messia, right? This is the introduction to logic, which in a way is a tool of the whole philosophy, and therefore in a way it's an introduction to the whole philosophy. So it is by Antonia Messia, the introduction, right? And they often refer to this as the book of the five names, genus, difference, species, property. Accident to use the Latin derived words, right? Genus, diophora, idas, propria, gidias, and it's biblic lots, right? So they call it the book of the five names, huh? Actually, the Greek, they often say the book of the five opus sounds, okay, genus, species, difference, property, accident. But Porphyry says in the premium, that to know genus, difference, species, property, and accident is useful, my friend, not only to know the category, right? But it's useful for understanding definition. And we saw that because among those five names, you have the name that begins a definition, the genus, right? And the name that completes a perfect definition, difference, right? And the name of what is being defined, namely species. And then the name of what is useful to investigate, the what? Difference if you don't know it, namely property, right? And which can be substituted for a kind of imperfect definition, if you don't know the difference, right? And then the name that is useless, for naming a thing, or for defining it, right? So green is useless to name triangle, and useless for defining triangle, okay? So he says it's useful not only for the categories, but also for definition. And he says it's useful for division. And you can see that because one of the main kinds of division in philosophy is the division of a genus into its, what, species. Like in Euclid, you have the division of quadrilateral, like the square, oblong, round, round, wide. You divide a genus into a species by differences, right? So it's useful not only for definition, but for division, right? And the fourth thing he says it's useful for, it's useful for demonstration. Understand demonstration. Now in a demonstration, you tend to prove a property of a species. You show, for example, that it's a property of the triangle, to have its interior angles, you go to two right angles, proposition, what, 32, of the book one of the elements, right? You prove a property of the species, and you show why that property belongs to that species. Now as you know from your understanding of property, it's something that follows upon the nature of the species. So if you define the species and know its genus and difference, you would maybe be able to see why this property belongs to the species. The old example of the logic books is that risible is a property of man. Risible means this, what? Yeah, we're ridiculous, we dare, I don't know. Now to define man, as we do as an animal with reason, right? You can see why he's the animal that laughs, right? Because as an animal, he can make the sounds of laughter, right? But because he has reason, he can see something laughable, something absurd, something ridiculous, right? Something preposterous, right? And so, in a way, the conclusion of a demonstration is stating the property of the species, right? Man is risible, right? And the middle term, uniting those two, is the definition of man, which includes the genus and the difference of man. So species and property and genus and difference are necessary for understanding what? Demonstration, right? And this will be the highest kind of reasoning, huh? Apoditesis in Greek, right? Demonstration is called in Latin. That's why you can just see at the end of the demonstration, those have the Latin initials there. Q-E-D, right? What was to be demonstrated? Done it. I'm from Missouri, you better show it to me. The word Apoditesis in Greek, and Demonstration, Stare, and Latin, from the word to show, right? I'm going to show it to you now, right? It's clear. Well, that's really a magnificent, absolutely magnificent framing he has to his own work. He says to the friend who asked him to write a book, explaining what these words that Aristotle was using in the categories, genus, species, difference, and so on, property. He says it's useful not only for what you asked me for, right? But it's useful for understanding definition, for understanding division, for understanding demonstration, right? And there's a text from Thomas, I can't get to where it is, but kind of a summary of the scientific method. He says in three words, definiendo, dividendo, demonstrando. Three Ds, they're on a nice alliteration. Defining, dividing, demonstrating. Just like Euclid, right? He defines these things like triangle, he divides them into their species like equilaterals, scaling, isosceles, and then he starts demonstrating properties, right? Defining, dividing, demonstrating, right? So this is what this is useful for, defining, dividing, demonstrating, and for understanding categories. Now, in Latin, those five were sometimes called the predicabilia, so in English we call them sometimes the five predicables, able to be said of, right? In Latin, they used a similar word to describe the ten categories, they called them predicamenta, to use the plural, predicamentu. And you see, that's where you get a word predicament, huh? And they kind of used to enjoy the fact that when someone says, I'm in a predicament, right? In a situation, it's hard to get out of. I'm in a real predicament, you know, I'm in a real predicament, you know, can you help me out? And that's kind of a reflection of the ten categories, right? Because you can't get out of there, right? If you're a quality, you know, like your habit, you can never be a substance or quantity, right? If you're a number, you're always going to be a quantity, you're stuck there, the rest of your being, right? And so, it's kind of funny here, here's the, it seems like the abstract word has come into daily speaks, though, huh? And so you see this in literature and so on, as it's predicament, huh? Actually, the Greek word, though, categorias, comes from the courthouse.