Introduction to Philosophy & Logic (1999)
Lecture 25: Definition: Nature, Kinds, and Distinctions

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So you have to stop some time and see what the words mean, right? If it's not clear. But to say that's the main, that's the only thing. It's laughable, right? But you find that thought. I remember reading one time in Heisenberg's different lectures. Now, Heisenberg is one of the greatest scientists. Some people say he's next to Einstein, right? But Heisenberg, he's a very wise man. I have tremendous admiration for Heisenberg. We're going to learn the life from him. But, you know, in alluding to Plato, you know, he speaks of the dialogues as if Plato or Socrates is mainly concerned about the meaning of names, huh? Well, you know, somehow that idea got into the modern mind somewhere and it just makes definition something relatively secondary, right? When actually the definition of a thing is what we're chiefly interested in. And the definition of a thing is very often a major accomplishment, huh? And it takes sometimes a long time to arrive at a good definition of a thing. And very few arrive. And even those who do arrive at a good definition, it takes the rest of us a long time to understand that. Descartes quotes the definition of motion, which is very important in natural philosophy, in a garbled fashion, you know? And he says, who understands that? That's it. Doesn't realize, you know, there's really a major work there to think out the definition of motion and even to understand the definition of motion when someone else has thought it out, huh? We have a good example of that in the definition of what reason, right, huh? As the ability for a large discourse looking before and after. It took a long time for us to understand what discourse means or large means and so on, huh? Okay? Now, in the second paragraph here, I give two definitions of definition, right? And one is speech signifying what a thing is, huh? Now, as we mentioned here many times, a logic is chiefly about three speeches. And we define speech as vocal sound, then signifying by custom, huh? If I do my agreement, having parts as signified by themselves, that five-part definition. And logic is mainly about three speeches, definition, statement, and then syllogism. And definition is speech signifying what a thing is, huh? Just as statement, which we'll be studying after definition and division, is speech signifying the true or the false, huh? Okay? And the syllogism, which we'll be studying after statement, is speech in which some statements lay down, another follows necessarily, because of those laid down. Now, sometimes I'm tempted to stick another word in here and say, it's speech signifying what a thing is distinctly, right? Because a name can signify what something is, too, right? But the speech signifies distinctly what it is. So, if I say, you know, what is this? You could answer, well, that's a square, right? And the word square would signify what this is. That's what this is, is a square. But not as distinctly as the speech. Well, it's a quadrilateral, right? That's equilateral and what? Right-angled, right? So, square and equilateral and right-angled quadrilateral signify the same thing. They both signify what this is, but the one signifies more distinctly than the other, huh? Okay? But then sometimes I'm drawn back and say, well, you know, nothing too much, right? If a man understands what a speech is and the difference between a speech and a name, then he should see that a speech that has parts that signify by themselves, right? The speech as a whole, being composed of those many names, right, necessarily will signify more distinctly, right, what a thing is than one name is, huh? Okay? Square is an example of a name. It's a vocal sound signifying by custom, no part of it signifies anything by itself, right? While the definition, equilateral and right-angled quadrilateral, is a speech having parts that signify by themselves, huh? And therefore it can kind of, what, blow up, you might say, expand, huh? Let you see more distinctly what the thing is, huh? Okay? So maybe it's a perforous, right, to say speech signifying what a thing is distinctly because a speech is going to do that because it is a speech, more so than a name, right? Nevertheless, you should see that that a definition is signifying distinctly what the thing is, huh? But it can do so because the speech cannot just say, what, name, huh? If the definition of speech and name are the first definitions of logica, then the first postulance would be, no speech is a name or no name is a speech. And every speech is composed of names, huh? Now, a second definition of definition. Aristotle often compares a definition with syllogism or a definition of demonstration, huh? And when you meet the definition of demonstration later on in the logic of the third act, Aristotle would define the demonstration as a syllogism, right? Making us know the cause and that of which it is a cause and that it cannot be otherwise. But he puts in the definition of demonstration, that's a syllogism, making something known, right? And so sometimes in a kind of imitation of that, I define definition. I'm talking about definition of a thing, right? I just say definition period, I'm thinking the definition of a thing, right? I'm not a modern in that sense. I'm a Greek, okay? So sometimes I define definition as speech-making known what a thing is. It's clearly we're talking about a definition of a thing here when we use the word thing definition here. Speech-making known what a thing is. So I ask my students sometimes, what in arithmetic is a perfect number? And I know they kind of know what an odd number is or what an even number is, but none of them seem to know what a perfect number is, right? Okay? How would I make known to them what a perfect number is? I can give examples. Six is the first perfect number. Twenty-eight is the second perfect number. But what is a perfect number? They don't know. But I can make known to them what a perfect number is just as what it is was made known to me by Euclid's definition. A perfect number is a number, right, equal to the sum of everything that measures it. Measures it now in a strict sense. Measures it evenly, right? So four is not a perfect number. Four is measured by one and it's measured by two. That's it. And one plus two don't have to four, do they? Five or three or two are measured only by one, which doesn't have to them. So the first perfect number is actually, what, six. It's measured by one, by two, and by, what, three, but not by four or by five. And one plus two plus three equals, what, six, right? So, when C.N. Augustine or Thomas Aquinas talked... about creation in six days, right? They see a meaning in the word six there, right? It's the first perfect number. And the things that measure are perfect in order, one, two, three. You see this in Plato's great dialogue, the symposium, right? Where there are six speakers, three rhetoricians, two poets, one philosopher, one, two, three. You go around the table from the lesser to the greater, right? But notice, I'm making known what a perfect number is, right? Through a definition, right? When I give them Shakespeare's education, I tell them it's written in blank verse. And I don't know what blank verse is. Once in a while, you have one student who knows. Most of them don't know, right? So I say, well, blank verse is unrhymed iambic metameter, right? And now I've made known what it is. If they know what unrhymed is, iambic is a metameter. If they don't know what an iambic is, I'll make that one by definition. It's two syllables with the accent on the second. Okay? So it's speech making known what a thing is. And that fits into Shakespeare's definition there of reason, right? It's the ability for discourse, right? Now remember the definition of discourse, son. It's coming to know what you don't know through what you do know, right? And the two kinds of discourse that are especially studied in logic are defining and reasoning, right? And in defining, you're making known, as Albert the Great says, a simple unknown. But something is, right? And in reasoning, you're making known the complex unknown statement, right? Where you affirm or deny one thing or another. So this fits in very much with what Shakespeare is saying there, right? Defining is a form of discourse, son. So I make known what something is through the parts, right? Now, perhaps you want to give a third definition of definition of a thing. If you go back to the words of the great Heraclitus there, the central thinker of human thought, it is a beautiful statement. It says, nature loves to hide. You can find Heraclitus saying something like that. I always think of what Aristotle says, I believe, in the politics there, where he says, we should try to say some things better than our predecessors, right? And other things as well as they said them. And sometimes, you know, a thinker says something so well that you don't try to improve upon it, right? And this is one of those examples, right? Nature loves to hide. Now, if you study the word nature, and the most full study of that is in the fifth book of wisdom, the fifth book of the so-called metaphysics, right? Where Aristotle distinguishes the basic central meanings there of the word nature. But all of them have the idea of something within, and therefore something that is hidden to us, at least in the beginning. So the first meaning of nature is birth, right? Well, birth is from within, right? And the baby, at least before some of those devices, right? The baby was what? Hidden. You didn't know it was going to be a boy or a girl. You didn't tell the baby what comes forth, right? So it's the idea that the hidden is in that first meaning. And then later on, in natural philosophy, nature takes on the sense of a beginning and cause of motion or change that's within a thing, right? And eventually the word nature takes on the sense of what a thing is. The nature of a thing, a very broad meaning. But even there, the nature of a thing, or what it is, is within it, right? And therefore it's somewhat hidden, right? So, you might define definition, then, as speech bringing out what a thing is. You know, we sometimes use that phrase on talking about the mind, right? To bring out something, right? That's a form of what? Thinking out, right? And when you've thought out, or as a result of thinking out something, right? When you've thought out something, you've brought out. So it's speech bringing out what a thing is. So Aristotle must have thought a lot about what motion is before he was able to bring out what it is. And that's true of all the great definitions, huh? Where atheists thought out the definition of eternity, right? And the consolation of philosophy. If you look in the Zoom there, Thomas has, what? A question on the eternity of God, right? And it's kind of beautiful the way he proceeds. You know, Thomas has the objections, right? He objects to every part of the greatest definition, right? Because he's got to accept, right? Then he explains the definition in the body of the article, and then he applies to each objection, right? So he concentrates your mind in every single word, right? See, wise and slow, right? It's an innocent definition. Breathe is. We also have the definition of person, right? That breathe is thought out. Thomas does the same thing with that, right? It takes a while. So it's speech bringing out what a thing is. That's another way you could define the definition of a what? Thing. Yeah. Now give it a little tongue twister, right? Notice how logic here, in a way, in definition here, it reflects the nature of reason that Thomas spoke of in the premium there to logic, the major premium, that reason can think not only about other things, about how to use your hands or your feet to do things, but reason can also think about its own act, huh? Reason can reflect, we say. It means to come back, in a way, upon itself, huh? But there's something like that when you have a definition now, not of other things, but a definition of definition, right? And you can make statements about cats and dogs and all kinds of things, but you can also make statements about statements, right? You can reason about all kinds of things, but you can also reason about reasoning, right? Okay? Now my tongue twister. Is the definition, right, of the definition of a thing, right? Is the definition of a definition, right? Is the definition of that definition? I would say no. No, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no It's a definition of any definition Now, so I define definition as speech signifying what a thing is Well, the definition square, right, is speech signifying what a thing is, right This is in a way common, isn't it, to all definitions, huh One thing is something more general there You can have a thought about a thing, right And you can have a thought about your thought, right But can you have a thought that's about itself? Can you? Yeah, you can have a thought about what's common to all thoughts, right But can you have a thought that's just about itself in particular? Are you talking about a particular instance of a thought? Because if you reflect on a thought that you've had, you're bringing that one thought back again So, you're reflecting on that thought If you're talking about a thought at that very instant, no. Okay. You have a thought about a thought. Is it the same thought as the first thought? It isn't. Is it even the same in kind? Suppose I have a thought of a triangle, right? And then I have a thought about the thought of a triangle, right? Well, the thought of a triangle is about what? A triangle, right? And the thought about the thought of a triangle is a thought about a thought. That's never really exactly the same, is it? God gets closer to this, but he doesn't have any thoughts. So that's a little aside there, huh? Just to make you think a little more. It's the definition of a definition. We define definition of a thing, right? And I gave three definitions of it in a sense. But this is not said only the definition of a thing. It's said the definition of square and the definition of circle and the definition of motion and so on, right? Each of them is a definition in a sense, huh? Yeah. Then I define the definition of a name. And that's speech making clear the meaning of a name, huh? It's a much less rigorous thing. Now, what is the order of these two kinds of definition, huh? The definition of a thing and the definition of a name, huh? It seems to be a four in the third sense of a four. Okay. I don't know if that's the same. Let me see. Okay. Now, in the posterior analytics, Aristotle has a famous discussion there, the second book of the Posterytics, which is the, in fact, the greatest book in logic, where he speaks of four questions, right? And the questions are, does it exist? And then the question, what is it? And then, whether this is that, I want to say, is this that? And then the question, why is this that? So, I might ask the question, does the atom exist, right? And if I answer yes to that question, right, then I'll say, what is the atom, right? I might ask, does man laugh? And if the answer is yes, then I ask, why does man laugh, right? Is the light of the sun cut off during the day? Yes. And then I say, why is it cut off, right? Was the government of Saudi Arabia overthrown? The answer is yes. Yes, why was it overthrown, right? He sees an order in one of these questions, right? The question, does it exist, comes with the question, what is it? And the question, is this that, before, why is this that, right? Now, when you ask, does something exist, you can't just use the word it, or the pronoun it, you've got to use, what, the name of the thing, right? And so, you have to have some meaning in mind, before, the name, right? And there may be something out there corresponding to it, right? There may not be, right, huh? Okay. Do vitamins exist? It's not obvious that vitamins exist, right? Well, what do you mean by vitamin? Do atoms exist, right? What do you mean by an atom, right? Now, in that sense, the definition of the name would come before even the question, does it exist, right? Do unicorns exist, right? Do the sandclaws exist? And so on, right, huh? Do mermaids exist, right? In the account of Columbus's first voyage there, there's a sighting of mermaids, huh? If you may know exactly what they have in mind, what did you mean that you saw, right? Well, the mystery's a mystery, right? In theology, when you ask, does God exist, right? You've got to have some meaning to the word, what? God, right? So that's one way that the definition of the name comes, what, before, right, huh? You don't really have a definition of a thing in the strict sense as such until you know that the thing in some way exists, right? And then you seek to know what that thing is, huh? But you can have a definition of a name even if there's no thing corresponding to the reality. So as I mentioned, the word unicorn there, or mermaid, and so on, even if there's no such thing in the world, right, as a unicorn with a, you know, a horse with a lance coming out of its forehead, it doesn't work, and a mermaid, a half, you know, a woman, half a fish, even if there's no such thing, you still have a meaning for the word, right? Do you see that? But there'd be no definition of a thing, there's no thing corresponding to that, huh? It's a figment of the imagination I have, to the best of my knowledge, right? Mermaid, and centaur, and unicorn, and so on, right? Now, another reason why you might have to define a name before you define a thing is that the definition itself, like every speech, is composed of names, right? So if you didn't know the meaning of a name, I might have to, what, explain what that word means, huh? So you can see something of the order there, right? Now, when Aristotle gets to the post-analytics and he's talking about epistame, like geometry, and so on, then you come back to the definitions of, say, Euclid there, in book one, right? And when he first defines these things, are those definitions of things, or are some of them just definitions of names, huh? How should you understand those, huh? Well, if you've looked at the first theorem of Euclid, it's the construction of a, what? Yeah. So, in a way, the existence of the equilateral triangle is not presupposed to proposition one, right? Okay? So in that sense, when you first define right angle, I mean, equilateral triangle, right? You're not yet, what, talking about a thing, huh? Yeah, okay? And then you show up there's such a thing by, what? Constructing an imagination. The same way with right angle, right? Is it possible to draw a straight line in a straight line, such as to make equal angles, huh? Well, later on, Euclid's going to have a theorem there for the construction of a right angle. So maybe some of the definitions there, when they're first given, they're definitions of names, right? Later on, it might become the definition of a thing, right? But there has to be something that you start off with that's existing, like the point or the line or something of this sort, right? Okay? So, that's some subtle things there, right? So in order to understand, even Euclid, fully and perfectly, you have to know some logic, right? Although it's such an easy science, you know, as Thomas says, even the boy can learn it, right? You can learn it in high school, to some extent. So we're going to be concerned now, principally with the definition of a thing, from now on, in our discussion here. And we're going to give here, actually, three fundamental distinctions among definitions of things. And the first two are very similar. All right, but they're stated a little bit differently, and it's good to... Outward knowledge of a thing, right? Okay. And notice how that order reflects the natural world, right? We know things in an outward way before inwardly. That was one of the, it was the second before and after there, and the order in which we know the same thing. And the reason why we do that is because our knowledge starts with our senses, and the senses have a kind of outward knowledge of things. So outward in English is almost a synonym for sensible, right? The outward appearance is something. And so, and secondly, the third thing we said about the order which we know the same thing, we know it in a confused way, right? Before distinctly. And the encircling gives you a very confused knowledge, right? When I say that wisdom is the best knowledge, it gives you a very confused and indistinct knowledge of what wisdom really is. So because we know things in a confused way before distinctly, we tend to encircle things before we define them fully, right? And, you know, someone asks me, you know, what is a dog, right? I say, well, it's an animal. I say, well, so is a man. Well, it's a four-footed animal, not a two-footed animal. In fact, so is a cat, right? And then my mind breaks down. And I say, well, the dog is a four-footed animal that barks, right? And the cat is a four-footed animal that meows. And that's as far as my mind able to penetrate. See? Well, it's kind of an outward knowledge of the dog, right? Somewhat, huh? And the cat, but do something that is, what? Sensible, or the barky, or the meowah, I think. So that's what we tend to know things. And when I define virtues of praise with equality, notice as a child, you know, certain things, you know, your parents frown upon your doing, right? And you learn about that. You don't do that, right? But you see not what is intuitively bad about it at first, right? But just that it's, what, something you're going to be blamed for, criticized for doing, right? And other things you're praised for, right? You know, if you're generous and you share your candy with your brother or sister or something, you know, you're praised, you know, huh? Okay? One of my little grandchildren there, she's got, it was her birthday, and she's got some presents, right? And one little package had two things in it, right? And she's, oh, one for me and one for Sarah. She gave one to her sister right away. And everybody's so pleased with that, you know, that kind of generosity, right? And it's just, America's good, right? So you're praised for some things and other things, you know, you're spanked or people frowning at what you're doing, right? And that praise or that frown or that blame is something outside, right? But more known to you than the inward goodness or badness of the thing, right? And later on, you try to bring out the inward goodness or badness of the thing, right? So this is a very important distinction. But notice also, as they say, what the use of the word, right? See, somebody might say, you know, you say, what is wisdom? I say, it's the best knowledge. And somebody might come back and say, you really haven't told me what it is, right? It's only in a very perfect way that I've told you what wisdom is. And so you might, in one sense, say, that's not really a definition. Oh, no, we'll call it. Let's call it drawing the line around. But a very important distinction. And it's a mistake, you know, except perhaps in geometry or arithmetic maybe, where things are very, you know, superficial, meaning on the surface of things, right? To try to begin with the definition in the full sense, to have certain things first, and then gradually, as we're filled in, there's something more inward, right? To penetrate, huh? Now, in the next section there, come back here upon these. As you mentioned before, if the first definitions of logic, so they're very close to the first thing, are the definition of speech, right? Because logic is about to be speeches, and the definition of name. Then perhaps the first statements that are kind of obvious from these definitions are that no speech is a name, or vice versa, right? No name is a speech. And then the other one, a little more subtle, that every speech is composed of names, huh? Okay? Now, some speeches are composed of other speeches, but eventually you get down to names, huh? So in the next section, we talk about the names that you have in these two, right? And in the definition, in the full sense, you have the genus, and what they call the differences, or to use the full phrase, the species making differences, huh? Okay? But in certain, instead of the, what, species making difference, you have something in the way of a property, right? Or some combination of common attributes, right? It separates them. So, really, to be the best knowledge, say, to be better than other forms of knowledge is not really the very nature of wisdom, but it's a, what, a property of wisdom, or a result of what wisdom is, huh? And likewise, to bark is not what makes a dog to be a dog, huh? That's something that follows upon what a dog is. Okay? So, we tend to use the genus here and differences, as we learned them in Euclid, or in that porphyry. And here you have, maybe the genus, but not the difference, right? And you have a property or something common, like best, or something of that sort, right? Okay? I mentioned somewhere in the text there, you know, if you don't have to do that in math, but if someone was to define a triangle as a rectilineal thing, a rectilineal plane figure with the least sides, he hasn't told you what a triangle is. But to have the least sides is a result of the fact that you can't contain a space with less than, what, three lines, right? But it'd be stupid to do that in geometry, right? It's so clear that a triangle has three sides, right? Okay? So it's superficial philosophy without wanting to pun too much in the word, but everything's on the surface, right? And other things, things are not on the surface. Your courage, your temperance, or your vices are, what, on the surface of you, right? It's kind of hidden deep down in you, right? Especially pride. This word stubborn, you know, which is titled pride, comes from the idea of what? The stub, the root of a tree, you know? If you ever take a tree or something out, you realize that it's a pretty easy to chop the top part down, but then to get the roots out is really resist, right? Even the checkbook, you know, you have something that's what they call stub, you know, that part would, it's hard to come out. The other part, you know, we're going to pay, you know, that comes out easily because the stub stays in there, right? So deep down within you, there's these bridges or vices, right? That were hidden to us. Okay? So now we have the distinction of those two and we've gone a little bit into the names that composed it, right? Okay? And that's necessary because you have to take some of your parts and know it fully, right? Now in the second half of page three we come to another way of distinguishing definitions of the things that's almost the same as this but it's a little bit different. And we might call it definition by cause and definition by effect. And the definition by cause is a more perfect definition because the causes are what makes the thing to be what it is. The effect is really a result of what the thing is. So the definition by cause is something like the definition in the full sentence, right? And the definition by effect is something like the definition that we call it. instead of speaking of genus and difference or genus and property or something like the property we speak of definition by cause or definition by effect. Okay? And sometimes this distinction is a more natural one to use in certain contexts. A clear example there would be taught us by Socrates in the Euthyphro, right? Where Euthyphro is trying to define what piety is, right? What the pious is. And the definition he comes up with finally is the pious is what the gods approve of, right? Or the pious is what pleases the gods. And then Socrates asks the famous question, well, is it pious because it pleases the gods or does it please the gods because it is pious? In a sense he's asking are you defining piety by its cause or by its effect, right?