Introduction to Philosophy & Logic (1999)
Lecture 27: Three Ways of Investigating Definition

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Or you could attack it from below. You start off with something less universal. Or even singular, right? Or if you attack it from the side, there would be something what? So you can... We're talking first here about where you begin to investigate definition, right? And you have three places where you might begin, right? But notice this is a division again into three. You know how most distinctions are into two or three. In fact, we'll meet them earlier in another page or so. But that seems to be all there is, right? More, less, and equal, right? What else is there, right? But in terms of something logical, right? Because the distinction between the universal and the more universal and the less universal and so on, things are universal only in the mind, only in reason, right? So this is a distinction that fits reason, right? Now, let's be more precise here. If you start off with something more universal, you're probably starting off with something like a, what, genius, right? If you start with something less universal, right? Okay? Or singular, you're starting with, what, examples of the thing, right? Now, most often in the dialogues of Plato, when Socrates asks somebody what is something, they'll begin by giving, what, examples, right? And a child will always do this, right? If you ask a child, what is a circle? They'll say, well, that's a circle, right? They'll point to the clock or something. That is a circle, right? Okay? But a lot of times in class, if you ask somebody, what is a dog? They'll say, well, dog is animal, right? They'll start with something more general, right? Something that's true, right? But obviously it's not a definition of dog, right? Ask them, what is love? They'll say, it's emotion, right? Well, maybe there's one kind of love that is an emotion, right? The emotion, even of that kind of love, is a, what? A genius, right? Okay? Those are the two very common places where people begin. I ask them, what is a sonnet? You know, if you go down in 50, I don't know, four sonnets, right? What's a sonnet? And they'll say, well, it's a poem, right? Okay? So, very often they'll start with, you know, a genius, right? But more often they'll start with the, what, examples, right? Now, if you start with something equally universal, what would you be starting from? Property. A property or a property fact, right? Okay. Property or maybe a property fact, right? So there's three places where a man might begin to investigate what something is, right? In fact, he does, we find, you know, let's say, spontaneously they will begin with one of these or the other, right? What is a comedy, huh? Well, it's a play that makes you laugh, right? Okay? Well, in a way, you're starting with something equally universal, right? What is a dog? An animal, they'll say. That's in class. I mean, animal. Right away. What's a chair? Something to sit on. Well, that's, again, like a genius, right? There are many things that we sit upon, and a chair is one particular kind of thing to sit on, right? But there are benches and solas and all kinds of things, huh? And when Socrates asks, you know, me know what virtue is, or you'd be for what ideas, or he asks details what epistabia or science is. I think I can go with examples first, right? Okay? So three places to begin, right? Now, is the road from each of those beginnings the same, or do you have a different road to get to the definition of each of those starting points, huh? Now, if you begin with examples, what is the road you take to the definition, huh? And suppose I wanted to define, like, I wanted to define what a Shakespearean sonnet is, right? And so I've got a book of Shakespearean science, and I've got 154 examples of the sonnet, right? Okay? How do you go from those examples to the definition of sonnet, huh? Yeah, you'd compare the sonnets, right? And separate out what they have in common, right? And leave aside their, what, differences, right? Okay? Now notice, huh, that way is simple enough to say, the way you perceive it, but it would take, in practice, a long time to separate out everything that the 154 sonnets have in common, right? And I might notice at first, well, they seem to have some of the same length, and if I examine carefully, this one's got actually 15 lines in it, yeah, and this one's got 14 lines, and they all have 14 lines, right? Okay? But is that all they have in common? See? As I read them, I might begin to see what it seems to be some kind of, you know, meter here, and it seems to be some kind of, what, rhyme, right? Huh? I say, well, look, look, the first line and the third line rhyme in this one, and the second and the fourth rhyme, right? I'm seeing where we are, first and the third, and the second and the fourth, right? And then the fifth and the seventh and the sixth and the eighth rhyme, right? And then they, what? They seem to alternate the rhyme, right? And then the ninth and the eleventh and the tenth and the twelfth rhyme out. And then there's two lines in the end, but they both rhyme, right? So it kind of falls into what they call three quatrains, right? With alternate rhyming, and it's completed by a rhyming cup, right? But as you also think of what Shakespeare's doing there, he's making a likeness of what? Some thought or feeling, right? So eventually I write at my definition of a Shakespearean sonnet, which is that it's a likeness of thought and feeling, right? In 14 lines of iambic pentameter, divided into three quatrains of alternate rhyming, and completed by rhyming cup. But I'm going to write that definition all at once, right? You have to read the signs and compare them, and other people maybe help you with it too, right? Do you see that? If someone asks you, what is the definition, right? Let's take some easy definitions here. You might go to Euclid, right? And you've got a bunch of definitions there at the beginning, right? Then you start to see, if you examine these definitions, that they have something like a genus, right? And then they have these, what? Differences, right? Okay? So you might arrive at the idea that definition is speech composed of the genus and differences, right? Okay? But notice you get this by comparing definitions, right? Okay? Do you see the idea? So basically, if you start off with examples of a thing, and they can be, you know, species would be examples of the genus, right? Like man and dog and cat and horse would be examples of animals, right? Or individuals, right? This man and this man and this kind of examples of man, right? Okay? But in both cases, you would compare the examples, separate out what they have in common, and leave aside their differences, right? That's basically the way you proceed, right? Now, if you start from the more universal, from the contrary place now, right? Then you start with something one. You don't have many examples. You have something one, right? The dog is an animal, right? If I started with the sonnet, right? I say, well, the sonnet's a poem, right? Okay. Now, how would you go from the more universal down to the species? How would you proceed there? By dividing, right? You divide by differences, right? And then you see under which difference the thing to be defined comes, right? Then you have that difference to the genus, and if that speech resulting is convertible, you might say, well, I've got a kind of definition of the thing, right? If it's not, I've got to have another division and add another difference, right? Okay. So, if I begin, you know, you say, what is a square? And somebody says, well, it's a quadrilateral, right? And I might say, well, now you divide quadrilateral, right? Well, parallelogram to pepsia, right? Which is the square? Well, that's opposite sides and equals equal, it seems, right? So it's a parallel there, right? And then I say, well, Q is not too single. Okay, which is this. It's right angle, right? Okay. But now is that convertible with square yet? A right angle quadrilateral, right? Well, it's not convertible yet. So notice, this doesn't substitute for thinking. You take a lot of thinking, right? You've got to do a lot of comparison down here of the examples. Here you've got to see what differences are appropriate for dividing this sort of genus, right? And you've got to think about which difference does it come under, right? And then you have to see, is the speech resulting from adding that difference to the genus, convertible or not, right? So it's a major work to define, right? I can't just go automatically from here to there like I can with adding a number of figures, right? It's like I have a little machine I want to, you know, just to do something, right? But here I can't get a little machine to go from the genus to add the difference, right? You see that, huh? So you have two distinct beginnings, huh? In a way of contrary, right? One is above and one is below. And above you start with something one, and below you start from many, right? But the way of getting from the one to the definition or from the many to the definition are quite distinct, right? The many you have to compare, right? And separate out what they have in common. And the more universal, you have to divide, right? Narastal talks about these two ways in the second book of the Posture Analytics, because he's talking about demonstration in that book, and definition is the beginning of demonstration. That's why Euclid starts with definitions. And so he talks about how you get the beginning of demonstration, right? Okay? And he talks about these two different ways. One way is more proportionate to us, right? In other ways, it's a little more rigorous, but... And he has some likeness to the distinction later on in that third act there between syllogism and induction, right? Because in induction, you go from many particular statements to a general statement, right? By the syllogism, you start off with something general, and you deduce something from it. So that's a very fundamental distinction. But induction comes first for us because it starts from the singular, which is sensible. And examples are sensible or positive senses. Okay? Now, if you start from something equally universal, like it can be a property or a property effect or it could be an encircling even, right? Do you have another... What road did you take to get in there? Yeah. Reasoning, right? Okay. Now, take my example here because I could kill two birds and one stone. So, suppose someone asks me, what is wisdom? And I might say, well, my starting point is, wisdom is the best knowledge. Now, wisdom is the best knowledge, and the best knowledge is wisdom. They're like, you know, the same thing, right? It's a kind of outward knowledge here, right? And I want to reason inwardly to what wisdom is, right? So, I'm going to have to do a lot of thinking about this, right? I might say, for example, what does best mean? Well, best means better than all the rest, right? What best means, right? If I say so-and-so is my best student, what do I mean? Better than all the rest, right? This is our best model, the salesman says, right? It's supposed to be better than all the rest, right? This is the best cut of meat we have, right? Better than all the rest, huh? Then I have to stop and think and say, if this is a knowledge that's better than all the rest, why is one knowledge better than another? That's a good one of our thinking, right? In the beginning of the three books on the soul, Stahl talks about how good the knowledge is of the soul. And he begins by saying that one knowledge is better than another, if it's about a better thing, or if it's more certain, huh? So it's better to, what, smell a rose than to smell the, what, thing that I want to mention here. Okay? It's better to hear the music of Mozart than to hear noise, right? It's better to see a beautiful painting, right, than to see the ash can or something, right? Now, in the arts of animals, Stahl points out, though, that the criterion of being about a better thing is more important than being more certain, right? It's better to know a better thing, even imperfectly, than to know a lesser thing, what? Perfectly, right? It's more essential to know what it is that you're knowing. So, after a lot of thinking, I might say that knowledge of a better thing is better, what? Knowledge, right? Okay? Notice, one knowledge differs from another chiefly by what? What it's a knowledge of, right? Okay? Like we said before, when we talked about before and after, what comes before seeing a before and after? Oh, looking? Yeah. You have to see a distinction before you can see a before and after, right? Oh. Okay? So before you can see that one knowledge is before another, in the sense of being better, right, you have to see a distinction, right? And the fundamental distinction between one knowledge and another is what's a knowledge of, right? So, you figure out, then, that knowledge of a better thing is better, what? Knowledge, right? Now, if that's true, then the best knowledge must be what? Yeah. Actually, if you want to try to put this in the form of a if-then syllogism, what they call conditional hypothetical syllogism. If knowledge of a better thing is better knowledge, then knowledge of the what? Is the best knowledge. Okay? But knowledge of a better thing is better knowledge, right? In fact, I might show that by the ash can in the beautiful painting of the sunset or something, right? And the smelling of the rose and smelling things are unmentionable. So, and hearing music and hearing noise and so on, right, huh? You start to see inductively, right, that knowledge of a better thing is better knowledge, right? Okay? And then you reason from that that knowledge, the best knowledge, must be then the knowledge of what? The best thing, right? Okay? So, what's I'm doing here now? Basically, I'm constructing a syllogism here. I'm saying, wisdom is the best knowledge, and the best knowledge is a knowledge of the best thing. Now, if I know what the best thing is, I can, what? Go further, right? See? Now, I might know that the best thing is God, let's say, right, huh? Okay? I might believe this, right? Okay? So, the best thing is God, huh? Therefore, wisdom is the knowledge of what? See what I've done, right? I'm reasoning from the statements that wisdom is the best knowledge, and the best knowledge is the knowledge of the best thing, and the best thing is God, but wisdom is the knowledge of God, right? Okay? Now, you read Galileo there, but more so it would be Einstein, huh? Einstein wanted to know the universe as a whole, right? So, Einstein wanted to know the truth, right? So, Einstein wanted to know the truth, right? So, Einstein wanted to know the truth, right? So, Einstein wanted to know the truth, right? So, Einstein wanted to know the truth, right? Reasoning, right? I'll give you another example of that. Suppose I say now that moral virtue is a praiseworthy quality, right? Now how would I try to reason my way in? How would I try to get a more inward knowledge of what virtue is, right? Well, I meant to say when a man sits down to eat or drink, what's praiseworthy? Is it eating too much, getting drunk, and so on? No, that's crazy, right? But what about these women you know that are suffering from anorexia or whatever it is? They're not eating enough, right? They're actually, what, killing themselves, right? And I don't know much about women myself, but I mean, it's a serious problem, right? You know, the kind of women are, you know? So is it praiseworthy to eat more than you need or to exist, you know? Or is it praiseworthy to eat less than you should? What is praised is in the, what? Middle, right, then? Okay. So you add to this, what is praised is not the extreme, too much or too little, but what is praised is in the middle, right? Well, now I could syllogize that moral virtue is what? In the middle, right? This is only the beginning of reasoning out what moral virtue is, right? But you see what I'm doing? I'm going in by, what? Reasoning, right? Okay. Now, as a matter of fact, you know, these three ways are proceeding. Probably nobody would use just one of them, right? You might be attacking the fortresses they do in the military. Example, right? They don't just attack one of these ways. They're attacking in three different ways at the same time, right? And he has a hard time resisting with you. Undermining him, breaking his walls down, and you see, flames are got the bombs on him, right? It's pretty hard to resist, right? And so, when I'm investing in what moral virtue is, I might be reasoning in this way, right? But I might also be looking at examples of moral virtue, right? I might look at moderation there, which is in eating and drinking. And, you know, I always quote that famous remark of Teresa of Avila, right? Someone brought partridges up to the convent, and she enjoyed them, you know, for dinner. And someone saw her enjoying them, right? And protested, and she says, penance is penance, and partridge is partridge. So you can go to, you know, a defect, right? You know, and you don't waste this wonderful food, right? And who's that woman who's always fixing the specialty for St. Francis, you know? He was a, you know, a sissy, he's a very stevious man, right? But, you know, he'd be so thankful when she brought this, you know? And you have to understand, you know, if a woman thinks you really like a particular food, and she makes it, you know, and goes out of the way to make this for you, you should receive it with, what, open arms and enjoy it, right? You know, you shouldn't not enjoy the food because, you know, it's pleasurable, right? So moderation, you might say, you know, but most people go to the opposite thing, right? Eat too much, you drink too much, and so on, huh? Okay? But then you take what they call liberality or generosity and say, well, is that also in between two extremes, huh? Well, it's in between the stingy man, right? Who doesn't spend enough, right? And then there's the man who's, what, extravagant, right? So I like to have wine with my dinner, but now if I go out and buy a $50 bottle of wine, I say, well, it's, you know, sitting at a professor's star, I should be buying $50 bottles of wine, right? Okay? That would be, like, extravagant for me, right? Okay? But now, suppose it's our anniversary, and I take her out to McDonald's. Well, if that's all I can afford, that's okay. I mean, you know, you see? So, liberality is spending either more nor less than you should for this, what, event, right? Okay? See? So, when my daughter gets married, I'm going to spend a lot more money, right? They spend a lot more money than if I'm, you know, taking my family out to dinner or something, right? Yeah? Okay? You expect to pay a lot to your father, right? On the bride, huh? Okay? But for this occasion, right? I remember one time, we just gave her, I should have cut it out years ago, some Maharaja in India, right? You know? And he's extremely wealthy, right? You know? His daughter or somebody's getting married, and he said to give a donation to the local charity, right? And he gave them, like, $20. I'm like, right, millionaire, you know, billionaire. It seems like, you know, it's an example of stinginess, right? Inapropriate for him, right? To get so small gifts, you know? He's celebrating his occasion, you know? He's just, you know, so pity, you know? So I might, what Aristotle does in the second book, huh? If you look at the second book of Nicomachian Ethics, he's investigating what moral virtue is, right? And partly, he's reasoning, you know, that what is praised is the man who, what, hits a golden knee, right? And, but then he's looking at the particular virtues and seeing what they have in common, right? And he shows that each of them is a virtue in the middle, right? Okay? But he also investigates it starting off from what quality habit is, right? And he starts to divide it, right? So he's actually attacking moral virtue in maybe all three of those ways, right? Okay? But nevertheless, you can distinguish those three ways, huh? Maybe use them, you know, separately or together, right? Then one after the other, right? Until the thing finally gives way to, okay, I surrender, right? You've got the fortress, right? You've got the, what it is, right? But none of these are the same as, is it automatic or mechanic, huh? See, with symbolic logic, or mathematical logic, as we call it in some cases, they were trying to assimilate logic to calculation, right? And as Leibniz said, you know, some of the early founders of it, Leibniz said, you know, well, in Mendes B, we'll sit down, let's calculate it. That's simple to resolve. But thinking is not that simple, right? So it never becomes automatic, like counting or adding, subtracting, multiplying. You still have to think, right? But some people, you know, logic is going to be a substitute for thinking. It's a help to thinking, right? But it's difficult to understand what something is, right? And where do you begin to investigate what something is? Well, one way of dividing it, logically, is to start with something above or universal or below. Or equally universal. And then what, are you starting from the fact? You start from one of those places. A genus or examples or a property or convertible. You know, a circling or something of that sort. And then you have a few different ways of going from each of those beginnings. So is it the error there that you mentioned that people want to try to calculate, isn't that that they don't get the distinction between reason and calculating? Yeah, defining is so much different from counting, right? Counting is something I can do just like that, you know? But defining, you've got to stop and do a lot of thinking, right? I want to count the people in here, or count the books in here, or count the chairs in here, right? You know? Going away, not one, two, three, four, five. But defining is not like that, huh? Okay. So counting is, defining is like counting. And the Greeks had two arts, and one was called logikei, where you get the word logic, right? And this is the art of defining and reasoning. And then you had logistikei, right? Where you get the word logistic, but it has a different meaning, logistic. And that was the art of counting and calculating. So as a child, you learned something in the art of counting and calculating. I learned in grade school how to count and how to add and subtract and multiply and divide, right? Well, I didn't learn logic until I was a senior in high school, and my buddy Mitchell was in college, and he started to teach me the logic course. Okay? So it's quite a different art, huh? But the mathematical logic was an attempt, in a way, to bring these two together, assembling one to the other. There's a likeness of the two. In both cases, the reason has a discourse, right? But counting is really the first step before you calculate, right? You've got to have some numbers by counting before you can add or subtract multivariate of I. and defining as a starting point for the most rigorous reasoning. Thank you. But counting people doesn't tell me what a man is, right? And telling me what a man is doesn't tell me how many men there are. We help one question the other, right? You have to be able to recognize men to count them. We have to know what man is and what reason is, like we did to the definition. But if I define man as an animal with reason, that doesn't tell me how many men are here. And then that it's going to deal with an accident instead of substance, so that it has to do with quantity, that would be... The question is, it's a different question. So what is a man and how many men are there? Well, is it the first, I mean, you're doing substance? Well, there's something accidental there, yeah. But look at the question as being a different kind of question, right? What is water and how much water is there in the world, right? The other thing I was wondering about, do we need to, it's important to, go through the different senses of reason? It seems like there's different senses of reason before, as in ratio. I came upon this because I was looking at, for instance, in St. Thomas, in the same one, the providence, the question of predestination, came up with predestination, and so predestination is part of providence, and then you get the definition of providence. It speaks about ratio ordinance, and it seems like ratio has sort of a... You know, ratio has many more meanings, you know? Yeah. I mean, if you take, let me give you an example here. Okay. It's something that's, you say, reason is the ability to give a reason. It's the word reason here. Inimical or equivocal here. Because here, reason means what? The ability that Shakespeare defined, right? You know, so you give a reason for something, you're in a way knowing one thing to another, right? So it's related to the ability for discourse, right? But this here is more like the object of this ability, right? Okay. Now, sometimes I ask students, is this a bad definition of reason, right? And sometimes I want to say it's a bad definition of reason because you're using the thing you're defining in the definition, right? But if you're not using the word in the same meaning, right, and you know the other meaning of the word reason, then this is not really defining something by itself. And you'll notice in some things, like you take the word taste, for example. Sometimes the word taste is the name of a sense, right? Okay? But we speak of the taste of the food, right? Well, taste in the sense of one of the five senses is the ability to sense the taste of things, right, huh? Okay? And to some extent the word smell is like that, right, huh? It would smell something, okay? But we also use smell maybe for one of the five, what, senses, right, huh? And this is something like that, right, huh? So you want to distinguish between those two senses, right, huh? Okay. Now when you speak of to reason, apart from the grammatical difference here, you've got to balance the verb, but I'm going to finish it. But notice here you're talking about the ability, here you're talking about the, what, act, and here you're talking more about the, what, object, right? So you want to distinguish those three, right? And reason gives a reason for a, what, statement, right? And, but there are more than one kind of reason that it gives. So sometimes I ask the students, what's the best reason you can give for a statement? And you give an example like this, and I say, here's an example of geometry. Straight lines intersect, right? Are these angles here equal? What would you say? Now one reason for saying they're equal is they look like they're equal. Is that the best reason you can give for saying those angles will be always equal? Another reason might be some amygdala, you measure these two, right, huh? Okay. That might tell you that these two are equal, but will they always be equal? No. If you measure hundreds of them, you'll find it to be true. It's kind of induction, right? Is that the best reason you can give for saying they're equal? Or to say, well, you could say they're equal. Are you from authority, right? That's the reason to say that they're equal. So, is that the best reason you can give? No. The best reason you can give for a statement, like the straight lines intersect, these angles are equal or that by these ones, the best reason you can give is the reason why it must be so. And this is what a demonstration is, huh? The reason why it must be so, huh? When Aristotle defines demonstration, he defines it as a syllogism, making us know the cause, right? And that of which it is a cause, and that it cannot be otherwise, huh? That's really a demonstration that involves the reason why it must be so, right? Now, the reason why it must be so is basically because the lines are, what? Straight. And so, because the lines are straight, angle A and angle X must be, what? Two right angles, huh? Or equal to right angles, huh? Okay? So, A plus X must equal two right angles, huh? And because this is a straight line being a straight line, B plus X must equal two right angles, huh? And the rest is simply the obvious axiom. So, the quantity is equal to the same, equal to each other, therefore A plus X must equal to A plus X, and then equal subtracting to equals results equal, right? But all of this follows because the lines intersecting are straight, right? Because they intersect their angles, but because the lines intersecting are straight, A plus X must equal two right angles, B plus X is equal to two right angles. Now, there's an early theorem in geometry, then, when a straight line meets a straight line and makes two right angles, or angles equal to two right angles. That's pretty easy to see. Once you've seen that, then you see the reason why A and B must be equal, right? You know? And that's the best reason you can possibly give, right? And Plato had seen that before Aristotle, right? And he talks about that in Reno, right? He talks about the difference between knowledge in a strict sense and right opinion, huh? Because when you have the right opinion, the right to, and he's saying something true, see? Everybody says, in the case of knowledge, what you think is not only true, but it's tied down by the knowledge of the cause, right? So, the cause of these lines, these angles being equal is the straightness of the lines. And the demonstrator, in that demonstration, Euclid shows that the reason why A and B must be equal, right? He's given the reason why it must be so. That's the most perfect reason you can give. You can't always give that reason, you know? That's the best reason you can give. It's the perfection of it. So, if you define reason, right, as the ability to give the reason why it must be so, you're defining reason by the most perfect reason you can give, right? Of course, that's already involved in looking before and after. That's a chronic sense of before, right? That the cause is before the effect, right? That leads to the same thing, right? Kind of marvelous the way it does. Looking at Tom's today, he's talking about the sacrament of orders.