Introduction to Philosophy & Logic (1999)
Lecture 50: The Second Tool of Dialectic: Distinguishing Word Senses

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Einstein says, creating that in theories like writing a novel, he says. It's something, you know, much more magnitude than philosophy, right? Closer to literature, really, than philosophy. It's not a reason to acknowledge. Now, the second and the third and the fourth tools are, I suppose, this first tool, but they're very interesting, very interesting. The second tool is the ability to distinguish the senses of a word. Now, when a man makes a statement, it's always in words, right? And if you don't have the ability to distinguish the senses of a word, you could, what, misunderstand the statement, right? Or it would not be so, what, clear, right? Okay? But likewise, you could easily become, what, fall into the fallacy and equivocation, the most common mistake in thinking, according to the father of logic, right? Become a sophist in the way, right? Even knowingly or unknowingly, right? Because you'd be reasoning from words in different senses, right? The current refutation of somebody, right? At the same time, right, distinguishing the sense of a word might give you a way of multiplying in a probable opinion, right? So, the good is desirable, right? But good can mean, what, the useful, or the pleasant, or the reasonable. Now, you've got three probable statements, right? The reasonable is desirable, the pleasant is desirable, the useful is desirable, right? So, there's many reasons why it's useful to be able to distinguish the senses of a word. For clarity, what you're actually saying, right? For what? Avoiding this equivocation, right? Okay? But it's also a way, in a sense, of multiplying sometimes probable statements, right? Now, when Aristotle takes up the second tool, he distinguishes the number of ways in which one can, what? Distinguish the senses of words, right? Without going through all of them, the most basic ones are to look at the, what? Opposites, right? Or to look at the word in combination, right? So, you take the word like dry, for example, just to illustrate this thing. And the opposite of dry in cloths is wet, okay? But the opposite of dry in wines is what? Sweet, yeah? Okay? So, when I say the cloth is dry, dry is the opposite of sweet, of wet, rather. When I say the wine is dry, dry is the opposite of what? Sweet, right? So, sometimes there's even different words for the opposite, right? But then, clearly, the word dry is more than one sense, right? But if you recognize, if you had one word over here for both of these meanings, right? And you recognize one of these opposites is having two meanings, right? And the other one would have, what? Two meanings, right? Okay? What's the definition of genius, huh? What's the definition of difference? Well, it's a name said with one meaning, right? Of many things, right? Other in kind, signifying what it is. That's what genius is, right? A difference is a name said of many things, said with one meaning, of many things other in kind, signifying how they are, what they are, right? Okay? And notice, in that definition, you've got the word many, right? Okay? Now, suppose we're dealing with probable opinions here. Well, now we've got the opinion of forfri, right? Or of the genus, right? Okay? But in that definition, you use the word many, right? Now, does the word many have more than one meaning? If someone says he has many children, what would you think he means? Huh? What would you think of? Just two children? No, I think more than two, right? Because I have many children, right? Okay? We have many chairs. We have many chairs in my house. We have many chairs here, right? I think we're more than two, right? See? Well, there are many as opposed to what? A few. Right? I have a few days off. I have many days off. Right? Okay? In the other sense, many is opposed to what? Two different senses of many, right? So, when a genus or difference is defined by many, right? Which sense of many is it? So, sometimes, trying to avoid equivocation there, I'll say, more than one, right? Okay? So, a genus always has many species, meaning it always has more than what? One. Okay? But it may have only two, like numbers divided, dot, and even maybe your habit into virtue and vice, right? But all you need is more than what? Or take another one from logic. We're in logic now, right? We distinguish sometimes between a nivocal word and an equivocal word, right? A nivocal word has one meaning, right? And an equivocal word has what? Yeah. What does many mean there? More than one, yeah. A word is equivocal if it has more than one meaning, right? It doesn't have to have five, six, seven, right? Some of them do, but you have to have that, huh? So, even when somebody, you know, you quote somebody's definition, or you quote, you know, his opinion, it's in words, right? We've heard these words, right? But now we have to, what? You know, sometimes clarify exactly what those words mean, right? And the words he uses are very often critical words, right? So, what sense is he using that, right? So, you look at the opposite and if that is more than one meaning, right? Or you look at it in combination, like you have to say, dry wine and dry cloth, right? Now, if you were to define what you mean by dry wine, right, and then drop off the wine from it, which are left with, would not be the same as if you define what you mean by dry what? Cloth, right? So, these are places where, that's why the book is called About Places, right? Not Topics in Greek, right? Even here in the second tool there are places where you might look to see if a word has more than one meaning. You look at the, what? Opposite, right? Let me take another example of that. A little bit difficult here. Take this word liberal, right? Now, you find the word liberal in ethics, right? In fact, there's a virtue we take up in ethics called liberality, you know? And we speak of liberal also, we speak of liberal education, right? Liberal arts, right? And then we have liberal in the sense of, in politics, Politics is liberal, right? Okay? Now, is the word liberal difficult in these three uses, huh? if I say Senate Kennedy is liberal, We have a ... Well, liberal arts, college, what that means. Ethics, right? What is the opposite of liberal, right? Well, in ethics, the opposite of liberal is what? Meism. Yeah. Stingy, right? Okay. Stingy. What's the opposite of liberal in education? You speak of liberal education originally. Liberal arts. What's the opposite of liberal? Something like survival? Yeah. Yeah. So Aristotle speaks of the liberal education opposed to a servile, okay, slavish, huh? And so, you know, even as late as Shakespeare, I see, you know, in the editions of Shakespeare, you know, they're referring to the works of the time, right? And, you know, a survey of the liberal and servile arts, you know, a common distinction, right? Okay. Now, in politics, we contrast the liberal with what? Conservative. What? Conservative. Conservative, yeah. Yeah. Well, these three obviously are different things, right? So these have three different, what, meanings, right? Liberal, right? But the liberal might believe that the conservative is both servile and stringy. Yeah. Yeah. It might be so, you know. Erstal, in the second book of wisdom there, right, he says some people don't like, you know, precision or certitude in argument, you know, where you're very careful about everything. They think it's kind of like, what, the liberal rights, didn't you, or something, right? That's kind of, you know, almost a metaphorical likeness there between the two, right? Shakespeare, in the science, you know, he speaks of niggered truth. And niggered there is another word for stingy, right? Mm-hmm. Okay. You know, you go to somebody's house for dinner, you know, and you praise the meal, even though it may not be too good, right? You see? Or sometimes professors praise as soon as paper goes, you know, it's not very good, right? So we often tend to flatter people a bit, right, you know? Or the truth, you know, would be, like, might hurt, you know. The truth seems to be kind of what, you know, stingy, right? Stingy in your praises, you know, niggered in your praises, right? No more than you deserve, right, huh? So niggered truth is what, for Shakespeare? How does he use that? Yeah, yeah. As opposed to flattering, right? The sweet, you know, flattery speaks of as, you know, preserving sometimes peace among people, right? Oh, okay, okay, yeah. So I'm praising you beyond what you really have, right, huh? Mm-hmm. And you're saying niggered truth doesn't do that. Truth wasn't flattery? No, no. No? A flattery means you're praising only beyond what it is, right? Yeah, yeah. Who's that French professor now at Harvard there, you know, he gives two grades? Oh, he's opposed to all this grade inflation, right, that's rampant at Harvard, right? You know, maybe below a B or something, right? Mm-hmm. So he gives them the inflated grade, right, so that they can go on the record with the inflated grade, right? Mm-hmm. And then he gives them the real grade, so they know that they really deserve. Ah, ah, ah, ah, ah. He can do that, right? I mean, very funny, very so. Yeah. You know? He's, uh... I forget, this is what they deserve, and, you know, most of them are smogs. Mm-hmm. And you'd be able to do this for us in college. Your attention rates would be no good, right? So, I remember this, this is, oh, right, this, this green inflation, right, huh? When I first started out teaching in college, I was teaching at St. Mary's College in California. One of my colleagues was a very tough marker, right, you know? I get called into the dean's office, you know, you're having trouble with your teaching, you know, and, like, you know, he's not getting his material across from students, they're just giving them what they, they deserve, right? But, you know, the dean is protesting this, right? You know what I mean? So, I mean, you've got to, to some extent, copyrights there, see, you know? So people, so, you've got a job, right, you know? Proving inferiority to your teaching, but you're, so many students have functed your course. We had a professor there, and I was at the College of St. Thomas in the old days. His name was Ross, right? And he taught constitutional law. Did I tell you what his grading policy was? He announced at the beginning of the course. In this course, he said, A is for God. B is for Ross, that was his own name. C is for geniuses. And D is in us, the rest of you. Remember, you know, these colleges, they, they sound professors, you know, kind of, you know, where you are compared to other professors in your grades, right? So you kind of, you know, see if you're, my teacher, Kasuri, right? He, he'd get his stuff, and he says, he says, I'm next to the lowest teacher, he says. So he looked at Ross, he said, what do you think the other guy is? So, no, these have quite different meanings. So I think, you know, conservatives are very much interested in, what, liberal education, right? I think more so than liberals and politics are, I mean, from my experience with them, right? And, so, I mean, they're quite different meanings, right? And, of course, there's a joke about the liberal in politics, right? That he's, he's liberal with other people's money. That's the joke. It's a, by the, the true liberal in the virtues, obviously, man who's generous with his own money, right? And things, right? It's kind of funny to see that professors, you know, get professors who are, who are politically very liberal, right, and they want to, you know, obviously spend up people's money in, you know, tax industry more and give it away and whatever they want to give it away. But when it comes to, you know, let's say, faculty raises and there's always different ways of calculating how the raises will be distributed, right? Then they vote exactly their one pocketbook, right? I remember one year, you know, one year where, I mean, I can, you know, cross the board thing or they can, you know, vote things and so on. And I happened to be in two different things. One, I was with, you know, advanced professors, right, who were, and they might want, like, maybe not a certain financial increment, but a percentage of equipment, which would be more for them than for the guys in the lower ranks because the percentage would be, but same percentage would be more money for them, right? And then you go to the other one where you have professors, you know, more of lower ranks, right, and they were voting to have more, like, a, you know, certain amount of money, right? And so they're all voting their, you know, like, it was their pocketbook, right? And so not really being a member with their own money, right? But their, so, let's have a pun on the two different meanings of liberal, right? I don't know, you see. And the liberal pop is the one who's liberal for the people's money. But three different meanings of the word, and so you've got to be aware of that, right? And sometimes we kind of conflate these meanings together, right? Sometimes we say liberal education in the traditional sense, and then liberal education in the sense of what befits a free man, or something like that, right? And then combining it too. That's the second tool of the Daletition, right? It shows you how closely Bajit is tied there to words, right? The opinions of all men, or most men, or all or most men in a given field, or most famous, all these opinions are expressed in words, right? And words, for better or for worse, are for the most part equivocal. And so there's a lack of clarity there if you can't distinguish the senses of these words, right? And there's a possibility of falling into equivocation. We'll get some more examples of that when we get down. We should stop and look at a little exercise. Did you have a chance to look at the exercise? Let's just go over and see. Dry set of wine and cloth. Is that univocal or equivocal? Equivocal. Yeah, okay, that's obvious. Number set of two and three. Number set of two and one. That's Marcel, right? When Euclid defines number, he says what? It's a multitude composed. It's a multitude composed. It's a multitude composed. of units, right? Aristotle says it's a multitude measured by the unit, right? Measured by one, right? And one is not a what? Or the unit is not, therefore, a number. It's not a multitude, right? Okay? Now that's the first meaning of the word number, huh? In deity speech, huh? A multitude, huh? So I would not say that I have a number of heads, right? Or that I have a number of wives, huh? Unless I want it to be misunderstood, right? But I want to get down in the unit, does it? Okay? Getting investigated now more. There's still Mormons, right? Who have, you know, throughout the plurality of wives, right? Okay? So I would not say that I have a number of wives, because I have only one wife, you see? And Shakespeare in the love poem there, Phoenix and the Turtle, he speaks of love as what? Eliminating number, right? Because love makes the lover and the loved in some way one. And of course, one is not a number. Okay? So that's the original meaning of number. You still see it in daily life, huh? So if I have one child, I wouldn't say I have a number of children, right? Now, even in Euclid, although he doesn't say explicitly, sometimes he uses number to include what? One, one, right? Okay? And the word number said of two and one is not purely, what? Equivocal, because two is composed of one, right? And there's a likeness there, because one has to two, a ratio like what? Three has to six, let's say, right? So there'd be reason to call, more reason to call one a number than to call the point a line, right? Because a point doesn't have to align the ratio of a line to a line. But one can have to a number the ratio of a number to a number. So it's something like a number, right? But now you're extending the word number, right? But there's some theorems in Euclid, you know, there's a theorem in the books on numbers, where he says that numbers prime to one another are the least of all numbers that have the same ratio, and then that they measure all of the other numbers that have the same ratio. Like, for example, two and three are prime to one another, and he measures them. And all numbers that are in the same ratio as two to three, let's say four to six, ten to fifteen, they're all measured by two and three, the smaller by the smaller, and the greater by the greater, right? But he actually proves that, right? Any numbers that would be in the same ratio as two to three, they're measured by each, right? But then you say, what about this here, two to four, six to twelve, and so on. What are the least numbers in that ratio? Yeah. If you don't consider one to be a number, then that theorem would break down, right? Because, well, I took a particular example there, I'm going to say three to six, right? Well, two doesn't measure three, right? Two doesn't measure six, right? But one measures, of course, every number, and two measures four, six, and so on, right? So, the theorem would not be true unless you put his understanding by number, right? One to be a number, right? And now he's using the word number equivocally, right? But equivocal by reason. There's a reason why one might be called a number, right? It has a certain likeness to a number, right? And also because a number is composed of ones, right? So, there's a connection between one and number. And because one can have to a number the ratio the number has to a number, okay? So, most people don't realize that, right? Because we're so accustomed to the modern calling one a number, right? But you can still see in daily speech that number means what? More than one, right? I have a number of children. Do you have any children? They say, I have a number of children. Everybody's going to understand that to be more than one, right? Okay. Do you have a number of heads? You have a number of arms, right? Number of legs, right? You have a number of heads, too? Huh? You wouldn't say that daily speech, would you? I'm not sure, you know, speaking some kind of metaphorical sense, but you wouldn't say you have a number of heads, like you have a number of arms, right? Number of fingers, right? You have a number of fingers, but only one thumb on a hand, right? There's a number of fingers on a hand, but only one thumb. Not a number of thumbs on the hand, do you see what I mean? So, that's the first meaning of number, right? It's always a multitude. You see that? So, it's equivocal instead of two and one, but not equivocal by chance, right? There's a reason for it, huh? Number of set of odd and even number, equivocal, yeah. Yeah. Square of set of four and nine, square of set of a number and a quadrilateral. Equivocal. Yeah. Then there's a certain likeness there, but it's still equivocal, right? Doesn't Euclid call, you know, what we call, in modern math sometimes, the factors of a number, you know? Wouldn't you call, like, two and three, the sides of six? Huh? Think of that way of speaking? What? Yeah, but it's not the same sense of the word size when I speak of a triangle as being three-sided, right? Lines set of straight line and curved line. Yeah, because they're both linked without what? Width. Lines set of straight line and line of argument. Limits set of point and line. Continuous set of line in the proportion, four to six, six to nine. You see, when they distinguish between arithmetic and geometry, they do because of the kind of quantity they consider, right? And as we learned in the categories of Aristotle, there's two kinds of quantity, the continuous, right? And the discrete, huh? Louis de Broglie, the great French physicist, the father of wave mechanics, has a book on the continuous and the discrete in modern science, huh? Very interesting. But the continuous has two definitions, huh? Continuous is that which is divisible forever, and this is the definition Aristotle brings out in the sixth book of natural hearing, or the physics, and then the continuous is that whose parts meet at a common boundary. So the parts of a line, you might say, the left and the right side of the parts that continues at a point, and the parts of the surface meet at a line, parts of a body at a surface, right? But we can also show that the continuous is divisible forever, okay? By numbers, they're not divisible forever. They're divisible down to one, right? And that's the end. And they're not continuous because in the number six, the two and the three, or the two and four, what do you want to say? They don't meet anywhere, do they? Okay? Right, in that, see, that line, the point that's the end of the first half is the beginning of the second, right? It's continuous, right? So there's certain likeness to that, when you have a proportion like four is to six, where six is to nine, as opposed to this kind of proportion, where you have, like, two is to four, three is to six. You don't have any link there, do you? Two is to three plus four is to six, okay? But by certain likeness, we speak of a what? A what? Of a continuous proportion, right? Because you have the same number there that's the end of one, right? Six and the beginning of the next. And that same way I speak sometimes of continuous syllogisms, or continuous definitions, right? The continuous syllogisms are where the conclusion of one syllogism is the premise in the next one, right? Or you could say the definition of quadrilateral and the definition of square are continuous, right? Because what is defined by the definition of quadrilateral, namely quadrilateral, is in the definition now of what? So reason now of knowledge is really an effect of continuous, what is what, syllogisms, so Euclid, you know, prove one thing and use that to prove something else and so on, right? You know, define this and what is defined here, you define something else, right? So body set of a stone and a geometrical sphere. Equivocal, yeah. Even in different genera. One is in the genus of substance and the other in the genus of quality. Healthy set of body and soul. Equivocal, yeah. Sick set of body and soul. So they shouldn't say that somebody has a psychological problem, right? You know, naming the thing from the science that studies it, right? You see, he's sick and a soul, right? He's got a sick soul. Okay, healthy set of body and diet. And diet. But it's equivocal, these examples of healthy and so on, equivocal by reason, right? Because the diet is a connection with the health of the body, right? So it's not purely equivocal, huh? Convertible set of automobile and statement. That's obviously equivocal, right? Good set of pleasing and reasonable. That one day is equivocal. Equivocal, yeah. Yeah. So premarital sex is good in the sense of pleasing, but not good in the sense of reasonable, right? Yeah. So what is good, simply speaking, for a man? That's what is reasonable, right? Good set of beautiful and useful. Equivocal. Equivocal, yeah. Equivocal. Equivocal, yeah. See, good set of the end of the means, the same thing, right? Science set of geometry and logic. Equivocal. Science set of geometry and experimental science. Equivocal. See, geometry and logic are both a reasoned-out knowledge. That's what science means there. They're an effective demonstration, but experimental science is not a reasoned-out knowledge, huh? It's not an effective demonstration. Because Einstein says, right, the hypothesis is free to imagine, right? Okay? And then you test it, you know, but even if it's confirmed, it's not by syllogism. You're saying, if my hypothesis is correct, there will be an eclipse of the sun at 9 o'clock this morning. There is an eclipse of the sun at 9 o'clock. You're fine. It's not syllogism, right? If A is so, B is so, B is so, therefore, mm-hmm. But the more predictions you make that come true, and the more precise those predictions are that come true, the greater probability, you might say, right? Or possibility, right? But it's not really reasoned-out. It's not reasoned-out knowledge as logic and geometry are. So it's being used equipically, huh? Seeing, instead of the act of the eye, and understanding. And likewise, seeing, instead of the act of the eye, and imagining, right? You know how Hamlet says there, I can see my father now, and I'll come off of the ghost, right? And he says, in my mind's eye, he means reading his imagination or memory, right? But Gregory the Great, you know, he says, what? Anger disturbs the eye of the soul. What does he mean by the eye of the soul? Kind of a metaphor for a reason, right? You know? Dog said of what? Living dog and a dead dog. Equivocal. Yeah. Dead dog is not really an animal anymore, right? An animal. It's a destroyed house. Isn't it a house? It's a destroyed house. No, it's not really a house anymore. Anymore than a melted ice cube is an ice cube anymore, right? It's a melted ice cube. That's the kind of an ice cube it is. If you insist upon calling it an ice cube, you know, you're really being equivocal there, right? So a dead dog is no more a dog than a melted ice cube than an ice cube. Okay. So you can see, it's important to separate different meanings of a word, right? Again, Aristotle has done a lot of that for us. So this is the second tool of the daletition here. The ability to distinguish the senses of a word. Who's a different example of that? Another way you said about seeing the genera of which the word is said. We have an example of it there. We're talking about body, right? In the genus of quantity, right? We have line, surface, body. And then body in the genus of what? Substance, right? Okay. That was an example right there. So knowing the categories of Aristotle is a big help, right? Aristotle is distinguishing the meanings of the word disposition, right? And sometimes disposition is the name of a, what? Quality, right? But sometimes it's almost the name of a genus by itself. Disposition or position, right? But then sometimes they speak of continuous quantity. It's a quantity whose parts have position. And sometimes they'll speak of quantity as a disposition of matter, okay? So disposition, in one sense, is its own category or position. In another sense, it's a species of quality. Another thing it pertains to the category of quantity, right? So obviously the word disposition is being used in three different words, right? In Greek and in Latin, the category for man, in particular, being clothed and so on, right? That's called habit. Hexis in Greek, habit in Latin. Habitus, right? So habitus can be its own category, right? If you have a monk's habit, right? It goes back to that sense of habit. But then habitus can be the sense of what? A virtue or a vice that you have. A quality that you have, right? So it's a different one of the sense, right? Yeah. And sometimes Aristotle uses the word habit in the Greek word for anything it's had. That you're having in positive, as opposed to a lack. Okay? So Aristotle is always careful when it's necessary to distinguish the senses of a word, right? And Thomas Aquinas is the same, you know. But the modern philosopher is, they never do that. You know what they're saying. And they're always using words in any sense without ever bothering to distinguish them. Warren Murray, I thought it was a good example. He was trying to show that value isn't the same as good. So he said, well, what's the opposite of good? What's the opposite of value? It's not the same. Okay. Now, number three here. The third true aristocracy is the ability to see the difference between things, right? To see a difference. And this is something almost natural, right? So he's not going to give you rules for seeing a difference, right? Okay. But the thing he's going to point out, I think it's kind of interesting, in his ability to see a difference, is that when you want to exercise the ability to see a difference, that the mind is exercised more in seeing the difference between things that are close together than seeing the difference between things that are what? Far apart, right? Okay. And you might start with things that are further apart because it's easier to see, right? But if you exercise the mind, you want to get things that are very good. clothes, right? Okay. So you take, for example, the amino, let's say, where the question comes up in that solution to the arguments to contrary sides, right? Contradictory sides. Well, can't a man be directed to the good by right opinion, right? And not just by knowledge, right? Okay. And so, you know, to go back to my simple example there, the fork in the road, right? Won't I get to Boston just as well thinking that this is the road to Boston as knowing that this is the road to Boston? But notice, you're contrasting now, and then Miriam comes in and says, well, there's any difference between knowing and having right opinion, right? They both seem to be, as far as action is concerned, just as good, right? See? Why there's an enormous difference between false opinion, right, and incorrect opinion, and knowledge, right? But right opinion and knowledge, in both cases, you're thinking what is true, right? Okay? So they're much closer. So what is the difference between those two, right? The difference between knowing and false opinion, that's obvious, one is true and one is false, right? But what's the difference between right opinion and knowledge, right? Well, knowledge is certain, as Socrates he says, right? The right opinion and answer to you. What you think in knowledge is tied down, he says, right? And what you think in your right opinion is not really firmly tied down in your mind. And he goes on to explain what demonstration is, right? Because he says it's tied down by knowledge of the, what? Cause, right? And so the kind of reason you give in a demonstration is the reason why something must be so. If you see why this must be so, then your mind is, like, tied down. What your mind thinks is tied down to mine, right? If you don't see why it must be so, something might change your mind, as Socrates says, right? See? So if I start down that road that, in fact, is going to Boston, because I think it's the road, but I don't know it is, right? I don't know it is, right? And some jokes just says, that's not the road to Boston, that's the road to Boston over there. Oh, I might believe him, right? See? Or someone has put up, you know, a different sign, right? If I'm driving from New York and those buildings are longer there, right? Well, it can't be New York, right? Something changed my mind, right? I never even heard about this, you know, world trade business, right? Okay? And my example in classes, you know, your mother and father tell you what's right and what's wrong, and you go to college and some smart professor convinces you that these bad things that your parents told you are bad, that they're okay, right? And now you change your opinion, right? So, yeah, go to college where they'll help you know what you believe, right? So, this is very important, obviously, when you're asking if the two things are the same or different, right? They're really different knowledge, right? But it's also very important for, what? Defining, right? Those two things, huh? Now the fourth tool, and kind of it goes with the third tool, because that's inside, is the ability to what? See a likeness between things. Now, Aristotle says in exercising the mind with these last tools, you do so in a different way, because the mind is exercised in seeing differences when it considers things that are close together, where it's hard to see their difference, huh? But the mind is exercised in seeing likeness when it sees likeness between things that are further apart, right? So, in seeing the likeness, say, of a dog and a cat that have the same genus, that's not too hard, because it exercises the mind too much, right? Okay? But the kind of likeness that re-exercises the mind is the ability to see a, what? Proportional, right? Proportional likeness, huh? So, like when you're talking there, to take an example from logic, then, you go back to the mino there, you're talking about the art of defining and the art of reasoning, right? And introduced to the art of defining in the first part of the mino, and the art of reasoning in the third part, right? What's the middle part about, right? About what's common to defining and reasoning, right? And in both, you, what? Come to know what you don't know, do what you do know, right? Now, if you see in the case of either defining or reasoning, that you can't have continuous definitions or continuous arguments going back forever, but then you have to go through an infinity of definitions to get to anything, right? If you realize that there must be some statements that are known not to other statements, right, then you must realize, you realize analogously, right, or yes, you do it together, that there must be parts of some definition that are known without definition. So, when Euclid defines, say, square, he puts quadrilateral in the definition of square, right? But quadrilateral was defined before that, right? And before quadrilateral was defined, rectilineal plane figure is defined. And before that, plane figure is defined. And before that, figure is defined, right? But does that go on forever? That every part of every definition needs to be defined, huh? If that was so, you could never come to know anything by definition. There'd be an infinity of definitions before you can define anything. Now, notice, that's analogous to what? If every statement, if every premise, and every syllogism was in need of proof, you'd have to go on, what, forever, right? Because every statement of every syllogism would have been proven by syllogism before, right? And statements of that, proven before, right? And you couldn't begin to even syllogize, because any statement you try to begin with to syllogize, people would say, well, prove that before you use it. And then the premises I would use to prove it, prove will before you use that. So you couldn't really start, right? In the same way, you know, you know, someone could say, you know, before you define square, define quadrilateral. Okay, makes sense, right? But if every part of every definition had to be defined before it could be used, you couldn't begin to define anything, right? Because anything you use to define anything, someone would say, no, you can't start there, you can't define that first. So you see the analogy there, right? The likeness, huh? Okay? So that, you know, the, what we call the highest genre, right? The ten categories are in a way to defining what the axioms are, right? And the statements known to themselves are to, what, reasoning, huh? You see a certain likeness there, huh? So the mind is exercised in seeing a likeness between things that are, what, further they're apart, right? You have a likeness that this is to that as that is to that, right? Or sometimes I compare what we just said about defining reasoning to words, right, huh? If every word had to be explained by other words, you could never explain any word. If you knew no words without other words, right, you wouldn't know any words. I couldn't begin, right? So, you know, I, you know, start the dictionary and I say, well, in the dictionary, you know, you look up a word and it explains that word by other words, right? Well, now maybe some of those words you don't know, so you look them up. But if every word was of that sort, then what? You couldn't begin to use the dictionary because you come into this world knowing no words, right? When a baby comes into this world, the speculation is he's going to say mama or dada first, right? And my brother Richard said daddy first. My brother Marcus said mama first. I said to my mother, what did I say first? She said, you seem to say both of them at the same time. So I was the diplomat of the family, right? But the point is, you're waiting to see what they're going to say first, right? But the point is they come into the world knowing no name. Not even mama did that, right? And, uh, so the first words we don't learn from what? Other words, right? And the first statements we reason from, we, I think we had a reason to. So the mind is kind of stretched, you might say, right? By seeing the lightness between things that are further apart. Or in the case of the tool of difference, the mind is stretched by seeing the difference between things that are closer together, right? Now, the fourth tool is useful for definitions too, right? Right? Because seeing the lightness of things enables you to what? Find the genus, right? Okay. Aristotle says it's also useful for what? Induction. Because you have to have light things to induce. And induction, as we mentioned before, is the other tool. The tool, the other argument of the dialectician. And he says, and this is the most interesting in some ways, it's useful for if then are hypothetical syllogisms. Because we often reason from one ratio that's more known to us to a what? Another one, right? When you have four terms that are different, how can you have the regular syllogism? Because that has three terms. So I might reason from saying, right, something known without defining is to defining, right? But something that is known without reasoning is to reason it. And if I saw this in one of these, I could reason to the other from it, right? If reasoning begins with something not reasoned to, then defining begins with something not what? Defined, right? Okay. And more specifically, if reasoning begins with statements not reasoned to, but known, right? Then defining, right, begins with things not defined, but known. And if nothing is known without defining, then nothing is known. You don't know what anything is. And we don't even understand our statement, you know, about defining, right? We're going to say what to say, right? We don't like to say. But anything. And if no statement were known without reasoning, then no statement would be known. Including the term I just made. You ain't got nothing to say, you know? You ain't got nothing to say, right? John Duffy, one of my brother's friends, said to me about some professor, he don't know nothing. John would get himself in trouble, you know. One exam, you know, final exam, I guess it was, that was a stupid exam. So he walked up to the professor, he says, this is the stupidest exam I've ever seen. He ripped it off. I walked out. I don't know what the best he did, but. I got him played a great interview. It doesn't, doesn't Moldier, you know, comedy about the man who's perfectly honest all the time. Nothing gets you in more trouble than to be perfectly honest, you know. Now, why does he give the tool to see differences before the tool to see a likeness, huh? Do you see a difference, huh? Perhaps. Perhaps. Not sure about that, though, huh? Because people often see the likeness among things without seeing their difference, right? And that's why they're often deceived, huh? You know, Plato speaks of how likeness is the cause of, what? Deception, right? And he warns you about likeness. But, you know, if the good didn't resemble the bad sometimes, or vice versa, or the true resembled the false, or the false, the true, people wouldn't mix up the two, would they? And likeness seems to be, in general, the cause of deception. So, if you see the likeness between things but not their difference, then you will be, what? Deceived, yeah. Just like we were saying in proportion, right? Now, someone says, you know, well, two is to three, and four is to six, right? Okay. And two is, what? An even number. Three is an odd number. So, this is an odd number. This is an even number, right? No, no. No. The likeness is not in that, right? Okay. If you don't see the difference between these things, you might overextend the likeness, right? And so, perhaps he gives the tool of difference before the tool of likeness, because it is what? Why is it so? Because of the danger of seeing a likeness without seeing the difference, huh? Oh. It's interesting, you know, how when they, you know, like in modern science, even when they go from waterways to soundways to lightways, right? You know, there's sort of an analogy between these things that there are differences, right? And there's different ways that the ladies are propagated, huh? And so, you might carry over and assume there's more likeness than there really is, right? So, if you see the likeness without the difference, you're active to being, what? Deceived, right? It's homosexual. These are almost called in marriages now, you know? That's the reason. There's something like this. There's two people, right? There's a lot of difference between this and the legitimate thing, right? You see? I mean, that's a gross example, but people, you know, they see the likeness without seeing the difference, right? Without seeing the difference, right? And so, there's a danger there. But also, the ability to see a difference is more like distinguishing the sense of a word. Then, of course, the ability to see the sense of a word is very close to the probable statements because they're all expressed in words, right? So, there may be a reason why the third tool comes before the fourth because it's closer to the second, right? Which is immediate to the first tool, but also in terms of avoiding deception, huh? One time in the senior seminar, you know, I did it on the fourth tool, right? And on the ability to see a proportion, right? And how important this is, huh? And, you know, each student did one part of philosophy. One looked for proportions in logic and one looked for proportions in ethics and other looked for proportions in natural philosophy and other looked for proportions in the book on the soul. So, it's amazing how many proportions run through those books, right? How many things you can't understand without seeing a proportion? It's amazing how important that is. And incidentally, it's very important in experimental science, right? Pierre Douaume, who was a famous physicist around the turn of the century, and he worked in thermodynamics, but he also was a famous historian of science, huh? Very famous historian of science. And then he finally wrote books on the nature of science, which is still, you know, republished 50 years later, right? And he speaks that the ability to see a proportion, that this is the most important thing in the discovery of a physical theory, that most physical theories are discovered by seeing proportion. And Albert Einstein, in his book, The Evolution of Physics, talks about the importance of that, especially when he's discussing wave mechanics, right, in the 20th century. How Louie Dubreuil saw these proportions, right? And how he developed the theory out of that. And this often happens, he says, in physics, right? It's a very strong thing. You know how the first inverse square law And this is a very strong thing, right? And this is a very strong thing, right?