Introduction to Philosophy & Logic (1999)
Lecture 46: Logic and Syllogistic Reasoning in Geometry and Theology

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

are apt to accept an argument that is what to not delve into it too much right okay i mean i don't i don't i mean to what extent it's self-deception what he says it's just deceiving us you know i think there's an amount of self-deception there too right but kind of a voluntary thing you know the fool has said in his heart that there's no god right okay we know what it says in the bible yeah but notice he says the fool has said in his heart right as if it's not just to the outside world right but in his heart he said this right now but in the power of his will is his pride right now if you look at that preface of marks to the his doctoral thesis there um you can see the element of pride there because because he takes us his hero prometheus right well i mean the image there prometheus um is revolting against zeus right not obeying zeus and being punished by zeus but prometheus is not unaware that zeus exists he's just punishing him right so i mean it's kind of a funny image to take you think there's no god right yeah might take a man who's you know revolting against god right and being punished by god and you know it's even more clear in sartam because in sart you know he says we're not atheistic he says in the sense that we would exhaust ourselves by trying to prove he doesn't exist we're atheistic in the sense it makes a difference for us what he does it does not you know bad faith in a sense because how can i i can see a man maybe in some sense being in doubt about god's existence but saying it makes no difference what he does or does not exist we're going to go on live our same way you know seems like you know he's just uh voluntarily choosing right okay now the second kind of mistake outside of language is extremely important for the kind of distinction also that it's what we're looking at and this now is the mistake from not distinguishing between what is so simply or without qualification in the way of saying it what is so in some imperfect from not distinguishing between what is so simply or without qualification and what is so in some respect or in a qualified way qualified in division sense huh okay or you could say a mistake from mixing up right what is so simply and what is so in some what limited way right now aristotle takes a very simple example right he says are you a white man or a black man what am i looking into my eyes what color you say yeah yeah i'm black right now has he contradicted himself no because you call a man black or white simply by the color of your skin right yeah but the black man is white in his eyes right see you wouldn't say he's white period would you say he's a white man you'd say he's white and you qualify it in his eye right or he's red in his lips or tongue or we are red lips or tongue suppose there's a delicious poison huh and uh mommy is aware of this right okay and the little boy or little girl asks mommy is this good to drink what's mommy going to say no bad drink right okay but is it good tasting so in some imperfect way it's good right you can't deny it's good tasting right and someone might be deceived into what drinking it because it's good tasting in some way it's good smells good tastes good right but simply without qualifications you have to say is it good or bad to drink is it bad to make this okay is it good to rob the bank it's a bad thing to do not qualify am i saying it's a bad thing to do to rob the bank right but why do people rob the bank somewhere it's good right pieces of money in your pocket if you don't get caught in one right right okay um it's good to murder somebody who annoys you what would you say i'd say no right it's bad right not fault i mean it's a bad thing to do but it does get rid of annoyance so something that is bad simply speaking right can be in some very diminished and perfect way good right okay now is the reverse possible right well any good thing in this life prevents you from doing something else if you do it right so um i said to the students now i mean it's good to know yes well then it's good to study right but do you sometimes not study when you should study oh god see but because it might prevent you from going to the party or it might prevent you from playing a game it might prevent you from something else that's good right huh okay so in that sense anything that's good right and even necessary to do could in some way be considered but bad because it prevents you from doing something else that is good right getting up and going to mass on sunday morning prevents you from sleeping longer right right okay so i say you're making uh this kind of mistake i tell them all day long you're doing something bad because in some way it's good or you're not doing something good that you should do because in some way it's what bad right so your life is based upon this right huh okay i mean even the terrorists you know the terrorists right i think we all think they did something bad but in some way it seemed good to them right that's how they did it right so um this is a distinction now that comes up all the time in philosophy between what is so simply and what is so in some perfect way take for example in logic right now in logic our style sometimes says well there's two kinds of arguments syllogism and what induction right and so he says if the rhetorician uses the enthymeme and example uh they must be of these two kinds right well the enthymeme is a syllogism and the example is an induction right but you'll call down what in the greek you'll say kiss there right it's a it's in some way it's a kundum quid that's the way you see it in latin right okay so the enthymeme is in some way a syllogism right examples in some imperfect way an induction but not simply without qualification a boy is a man in some way right a girl is a woman in some way a kitten is a cat okay okay okay but not simply without qualification okay so it's a distinction We use it. Sometimes we call it encircling a definition, other times we deny it's a definition, right? It's not a definition in the full sentence, right? If I encircle wisdom, it's the best knowledge. Do I really define wisdom when I say it's the best knowledge? No, in a way I defined it, but not simply or without qualification. So it's a distinction in the sense between the perfect and the imperfect that lies behind this, right? Which are words that, well, where do they have the perfect and imperfect, right? Would they both be as such or periscope? Also the same distinction, but sometimes you have both the distinctions involved. I take this very simple example in class here. I always sit down in a girl and I say, Do you know my brother Mark? That's my steady question. And she answers, No, right? I say, No, you all heard what she said. She doesn't know my brother Mark. I say, No, you know what a man is. You know what a brother is. And she says, Yes. That's what my brother Mark is. So you know my brother Mark, don't you? But notice, simply speaking, we'd say she doesn't know my brother Mark, right? But in knowing what a man is, in knowing what a brother is, in some way she knows every man and every brother in the whole world, right? That's a very, what, diminished sense of knowing, right? To know the universal. In that sense, I know everything. Because everything is something, and I know what something is, as opposed to nothing, don't you? I know something is not nothing, right? So some of my students would say, I'm going to go home and tell Dad that I know everything now. And I know everything now. But I mean, I'm sure you can make the distinction clearer that I have in mind there, right? In knowing the difference between something and nothing, you'd know in some way everything. Because everything is something, right? Even the guy who says, I don't, you don't know everything, he means something by the word everything, right? What does he mean by everything? Everything, right? So even to say, I don't know everything, is to admit that in some way you know what you're saying, and therefore you know what you mean by everything, and therefore you in some way know everything, right? You see? But simply speaking, I'd say, I don't know it, right? I don't know everything, right? But in some way I do know everything. See? I'm not really contradicting myself when I say that, right? Now, sometimes we say, if you're looking at our knowledge and God's knowledge, we say God is wise, and man is not wise except in some, what, very diminished and qualified way, right? Okay? But if you're looking at human knowledge, right, then metaphysics, we call that wisdom, simply, right? And we call philosophy of nature wisdom about natural things, or political philosophy, wisdom about political things, right? Okay? But metaphysics is wisdom simply about qualification. But then you're looking just at the genius of human knowledge, right? But if you compare man's wisdom with God, right? You know, the first attribute of the wise man we saw was he knows everything. But in some way, right? But God knows everything, what? About qualification, right? You know, perfectly. All things are naked, it says, open, right? To him in the scriptures, huh? So that's a very important distinction in philosophy, huh? What's good for man? What's pleasing to his senses? What's good for man? Not everything, right? What's good for man? I want the answer. With the brevity of wisdom right now. What's good for man? Okay? Even more simply, you could say, what's good for man is what is reasonable. Since man is an animal with reason, right? What's reasonable is good for man, huh? Okay? But now, what about what is pleasing to his senses? Is that good for man? Well, if you don't qualify it, you know, don't say, insofar as it's reasonable, right? You say, what is pleasing to his senses, then you're talking about what is good in some way for man, right? Yeah. What is reasonable is good in some way for man, right? Now, sometimes that might seem too weak of word, you know. You talk about the terrorist or somebody who murdered somebody, it's like that, you know. Is it reasonable to murder somebody? Is it reasonable to rob the bank, you know? To say that they're unreasonable might seem too weak of word, right? But in a very fundamental way, they are unreasonable to rob the bank, right? It is unreasonable to murder somebody, huh? You don't really see that it's bad for a man, hapless, simply, without qualification, until you see that it really is unreasonable, huh? Because man is by nature a, what? A political animal, right, huh? This is contrary to that, huh? So it's unreasonable for a reasonable animal, right? That must live in society to do what is contrary to life together, right? Now, in the Mino, you people read the Mino, huh? In the Mino, you have a beautiful example of this. Fallacy in the middle part of the dialogue, huh? In the middle part of the dialogue, Socrates has found out that Mino doesn't know what virtue is. So he proposes that they have a joint investigation into what virtue is, huh? And Mino objects, he says, how can we go investigating what we don't know? Now, he's in a sense saying, how can we, in our conversation, in our investigation, how can we aim at what we don't know? Well, you can't aim at something, you don't know it, right? So, why are you proposing, Socrates? And if I drive into the gasoline station, I say to the guy, how'd he get there? What's he going to say? Where? Where are you going? I can't tell you how to get there, you don't know where you're going, right? Well, how'd you get there? Okay? So, here, you know, if the teacher knows, he can direct the student to what he, the teacher, knows, right? Just like the gasoline guy can do that. But if neither one of us knows, right, how can we direct our conversation to what we don't know? Seems impossible, right? Now, this is an objection, really, that if it's good, it takes away both logic, the art of defining and reasoning, and logistique, the art of counting and calculating. Because these are the two arts that are for the sake of coming to know what you don't know. They're the two arts that direct us to a knowledge of what we don't know. Well, how can you direct yourself to what you don't know? How can you do that? You have to know what you're aiming at, right? Okay? Well, this objection is overlooking the distinction between what is known simply or without qualification and what is known in some, what, qualified and diminished way, right? Now, I take a very simple example, which I can't do in this class, but I can do it at school where you have more students. I say, how many students are in class today? I said, I don't know. Nobody knows here, do you agree? Nobody knows how many students are in class today, right? Okay? And then I, what, count? One, two, three. And I counted one class, 26, right? And I said, do you see how easily I got to the number 26? I know exactly how to get there, right? But now, how did I know how to get to 26 when I didn't know I was trying to get to 26? I mean, if we go out on the highway and say, what road should I take? Well, you've got to know where you're going, right? So, how could I have known? So, how could I have known? So, how could I have known? So, how could I have known? So, how could I have known? what road to take to get to 26 when I didn't know I was trying to get to 26. And I took the greatest of ease. I mean, I was amazed that I attracted myself to what I didn't even know I was trying to get to. How can I do that? It's amazing, right? Well, the point is, in some imperfect way, I already knew 26, right? I knew I was looking for the number of students in class, and that, in fact, is 26, right? So since 26 is the number of students in class, and I knew I was looking for the number of students in class, in some way I knew what I was looking for, right? And knowing that I was looking for the number of students in class was enough to tell me that I should count, right? That that's the road I should take, right? So by knowing, in some imperfect way, right, what I was looking for, I was able to know the road to take to know what I didn't know at all. In the 6th sense, in the full sense. Name me 26. Do you see that? Well, if the question had been, what is a student? I would not have counted them, right? I would have compared them and separated out what they have in common, right? Leaving aside the differences, right? Because I knew, without knowing the definition of student, I knew in some way I was looking for the definition of student. And that's enough to tell me that I should take one of the roads to a definition. Do you see that? It's a very subtle thing, isn't it, huh? Now, when Socrates replies to that objection, he makes the same kind of mistake in trying to reply to it. Because he tries to say, and he recalls, he says, he's heard some priests, huh? And I tell him, it's not Catholic priests, I don't know Catholic priests at most times. But he's heard some priests say that our soul existed before it was in his body, right? And maybe it had some knowledge, right? That it's forgotten and was put into the body. And if we make an effort, we can recall that, right? Okay. And Mino says, well, that's interesting, but do you have any evidence? And Socrates takes the slave boy of Mino, right? And Mino witnesses to the fact that the slave boy was born in his house and has never been given the chance to study geometry, right? Doing Mino things all his life. And Socrates asks the slave boy questions, and eventually out of the slave boy's answers comes the theorem of geometry. That the diagonal of a square is the side of a square twice as big. And Socrates says, well, it came out of his answers. So he must have been, what? Recalling this, huh? Okay. Well, now, is the slave boy, in fact, recalling the way to double a square? Or is he coming to know it for the first time in his life? See? Because Socrates is saying he's recalling it, right? But when Socrates first asked him, how do you double a square? He said, double the side. He was not only not knowing it, he was mistaken about it, right? Now, when Socrates asks him questions, the slave boy can answer the questions, but out of those answers, eventually he sees, right, the way to double a square. But maybe he's putting together for the first time in his life things that are enabling him to, what? To see this, right? So Socrates, you know what Socrates does there, honey? He says, if this is the original square, well, couldn't you put another square just like it next to it, and another one just like it next to that, and then fill up the square here? You make the square four times as big? Oh, yeah, the slave boy can see that if you put four of the original squares together, you'd have a square four times as big, right? And then Socrates takes the, what, diagonals, right? And the slave boy can see the diagonal divides into equal parts. And eventually he can see that this square inside the square is made up of four halves of the four squares, and therefore he knows that half of four is two, so it's, what, equivalent to two of the original squares, right? Original square. So he now knows that the diagonal is the side of the square, twenty-six, what? It's big, right, huh? See? But maybe he's putting together these things for the first time in his life, huh? And then he's coming to know something he never knew before. Take a simple example of that, right? See? If one day I measure this oblong, and let's say the length is ten, and another day I measure the width, and it's four, do I know the area? Well, if I don't, if I had to multiply these two numbers, I wouldn't know it yet, right? But if I know the length, and I know the width, I know how to multiply, I'm able to know the area, right? But it's able to know the same as actually knowing. But after I multiply them, then I would know the area is forty, right? So there's a distinction between knowing something and able to know it, right? Now if I ask you, about something that you're able to know but don't know yet, right? Do you know it? What would you say? I don't know it. Right? See? Okay? Even though you know it in ability. But that's a qualification that is in a perfect way, right? So in a sense, what Socrates is saying, that because the slave boy was able to know this through what he knew already, right? That therefore he actually knew it, right? So he's confusing his knowing ability with knowing actually. He's confusing these two, right? Knowing in act is knowing simply or without qualification. This is knowing only in a qualified sense, right? And I think a more difficult example of this because here, a built in act that's so close together, you might not see that they're different, right? If I take the example, you know, the man who's been putting items in his grocery basket and he examines the price of each item he puts in his grocery basket and he's got a big basket full. But now as he approaches the checkout counter, if someone asks him, do you know what that's going to cost? Does he know? See, I don't know until they bring it up, right? See? But I'm able to know it, right? If I know the price of each thing I put in there and I know how to add, right? I don't actually know it until I add up those or they add it up for me. Right? Do you see? So if he asked me as I approach the checkout counter, I've been adding up myself whether I have any type of data. You know? I don't know a little penny. I don't know. Right? Even though I'm able to know, right? I have to qualify that. I have no inability. See? I don't know how to get there. I don't know yet. So Socrates is claiming that the slave boy already knew how to double a square, right? And he gives the appearance of that because it comes out of what he does know, right? But it comes out of it in the same way that the area comes out of these two numbers, right? Or it's like that, right? But to know those two numbers is not to know the area. But it's to be able to know the area, right? But to know something in ability is not to know it simply without qualification. So Socrates in replying to the objection of Mino and trying to see a way out of it, right? Makes the same kind of mistake that Mino makes. The mistake that comes from mixing up what is so simply and what is so and so what? Respect It's unqualified, right? You wonder who the Plato did that on purpose, huh? That's a beautiful example here, right? Of a tremendous example of this, right? Because it's something so basic, right? The very existence of logic depends upon answering that objection, right? And that objection if it's good means there's no logic that's the end of logic and there's no logistique either no art of counting and counting it's all art. There's no art at all to direct us to what we don't know, right? You see, understanding what logic really is about logic involves on the one hand, right? Directing you to what you don't know because in some limited or qualified way you do know it and logic involves what you don't know Using what you do know, right, to come to know what you don't know, right? But in the beginning, you don't know what you don't know. But you're able to know it through the things you know already, right? So you know it in ability, right? That's what you have to see to understand the logic it's all about. It's one of the discourse of reason is, right? The discourse of reason is coming to know what you don't know through what you do know, right? It's one thing to know what you already know, another thing to come to know something through it, right? So when Socrates says that learning is recalling, it's not recalling what you learn, but it involves recalling what that through which or by which or from which you learn, huh? Learning by reason, right? Involves that, and all advanced learnings of that sort. That's kind of a marvelous thing to see what was done there, right? But he's teaching us in a way, he's giving us what was going on there, right? That's kind of a marvelous thing to see what was going on there, right? That's kind of a marvelous thing to see what was going on there. That's kind of a marvelous thing to see what was going on there, right? And in both of those, there were four arrangements that are, in fact, in the form of a syllogism, right? The 12 that are not, right? And there's one for universal affirmative conclusions, an only one, right? Yeah. They call it mood or case, right? And three, one in the first figure and two in the second figure for universal negative. So now I have to look at the third figure, okay? The third figure comes third because it's third in power, right? As we'll see, it has no universal conclusions, right? So we'll look first at the four cases where you have two universal statements, okay? Now the third figure, your middle term is the subject in both cases. And then you have the universal affirmative, major premise, and the universal negative, minor premise. Every B is A and no C is B. And then you have the reverse, the universal negative is the major, no B is A, and every C is your minor premise. And then you have the two universal negatives, no B is A, and no B is C. So notice the middle term, oh, see? I wasn't thinking less of it, huh? Yeah. Oh my goodness. Now the first figure, right? Mm-hmm. Okay. So, B is the, what, subject in both premises, huh? Okay? Now we're asking really, is there anything that falls necessarily with C as a subject and A as a, what, predicate, huh? That's all we're asking. On the basis of the statements laid down, huh? If anything, you can say affirmatively or negatively about C as a subject and A as a predicate, right? Now, as we mentioned before, in the second and in the third figure, the set of all or the set of none never apply to it exactly as it stands, huh? But sometimes by conversion you can get the, what, set of all or the set of none, huh? And so you have to know how to convert statements, right? And if you recall, universal negative converts simply and stays universal negative. The universal affirmative converts partially, right? And you get a particular affirmative, right? The particular affirmative converts to a particular affirmative. But the particular negative doesn't convert that at all, okay? So conversion is a necessary tool for making clear that a syllogism, the second and third figure is, in fact, a syllogism, right? Okay? Now, look at the first case here. Every B is A, every B is C. So these forms will be used again and again, right? Okay? And they use it very much in theology, because in theology you're proceeding by the via negativa, right? Via negationis, huh? You're showing that God is not something, right, huh? Now, I might mention there, just as a particular thing there, that God, who's not universal, right? I'll give you an example of what I mean, huh? If Socrates is not a woman, then no woman is Socrates. If God is not a body, no body is God, right? But vice versa, if no woman is Socrates, Socrates is not a woman, okay? If no body is God, God is not a body. You see that? Okay? So all the time, you know, when you're syllogizing there in theology, you're finding something which is said of God and denied of other things, or vice versa, right? Okay? Everything corruptible has parts. God has no parts. Therefore, God is not corruptible. Okay? Whatever has what? Parts is a composition of act and ability. God is not a composition of act and ability. Therefore, he has no parts. Okay? If you're going to find these used again and again, you have a negative thing, huh? Have you people read the Theta, or I don't know? Yeah. Oh, and Socrates is reasoning against the soul being the harmony of the body, right? He wants to find something that is affirmed of the soul that is denied of the harmony of the body, or vice versa, right? So one argument he has is that the soul resists the body, right? But the harmony of the body does not resist the body. Therefore, the soul is not the harmony of the body, right? Or the soul has a harmony, right? But a harmony doesn't have a harmony. Therefore, the harmony is not the soul, right? So he's using these forms here, if they're offering the second figure, right? That's very common, huh? So these four forms are used again and again. And notice that it's easier in a way, this is more ways you can draw a negative conclusion than a universal affirmative, right? When do we do that? And notice, in a way, you're trying to find the reason why we're there at that middle term, huh? The first road in our knowledge is what? But I want to show you guys that the first road in our knowledge is the road from the senses into reason, right? Okay? So, the first road in our knowledge is C, and the road from the senses into reason is A, right? What I want to do is define the middle term, right? That brings together first with the road from the senses into reason. And the middle term is natural, right? The first road is the natural road in our knowledge, and the natural road in our knowledge is the road from the senses into what? Reason, huh? Okay? Now, you may want to come back and back up to my major premise, right? Why is the first road the natural road, right? Well, if you know that nature means what a thing is, and a thing must be what it is before there be anything else, obviously what is natural is first in a thing, right? So, obviously, the first road is the natural road. And vice versa, for that matter. And then, why is the natural road the road from the senses into reason? Well, the nature of man is to be an animal with reason, right? An animal is defined by senses, huh? But man is not just an animal, he's an animal with reason, huh? But what is genuine a thing develops before what is what? Particular. So, the natural road, then, is from the senses into reason, right? And the senses he has an animal to reason, which is particular. So, we're finding a middle term there to unite those two, right? Okay? Can you explain that final line statement? Ah, wisely and slow? Yeah. Well, when I started thinking about it, I began to realize that he's coupled wisely and slow there, right? And so, he's not recommending slowness, period. Because there's a slowness of stupidity and et cetera, right? Okay? But there's a slowness that... is wise, right? So, it's applied now to his thinking. When does the wise man proceed slowly, right? Well, the most obvious time he proceeds slowly is when there are many things to be considered before you can decide a judge. And obviously you have to proceed slowly, right? But secondly, he proceeds slowly when something is difficult to understand. And there the text comes from the second book of Wisdom when Aristotle shows that there can be a difficulty in things either due to the thing itself or due to the weakness of our mind, right? And in natural philosophy, the difficulty is due to the weakness of the thing. But in theology, it's due to the weakness of our mind. And so he proceeds slowly in those matters, unlike Descartes, right, who, you know, skips over the definition of motion, right? Never understand this because it's too hard to understand. What do you think that he says? You know, that's it, you know? No real attempt there to understand something as difficult as a definition of motion. And then when Descartes talks about God, you know, well, it's kind of obvious what God is and so on, you know? It's obvious what thought is, maybe. Okay? But then the most subtle thing, and this is the very important thing, the greatest minds are very slow in the beginning, huh? And DeConnick, you know, pointed out that even Edgar Allan Poe sees that, right? He says the law of inertia applies to minds as well as to bodies, Edgar Allan Poe says in the Purloin letter, huh? You know how a ping-pong ball is easily set in motion but easily stopped? By a heavier body, it's hard to get moving but once it starts to move, it's hard to stop? He compares the great mind, the little mind, to that, right? Okay? Then you start to think, hey, why did they call Thomas the greatest mind in the Middle Ages, maybe the greatest mind of all time, the dumb ox? You know, Chizartin took that whole thing, the dumb ox, and it's entitled to this little biography, huh? Why would it be the greatest mind for the period to his fellow students to be the dumb ox? Well, Thomas was proceeding slowly in these fundamental things, right? Because they are so important that everything else you want to know depends upon them. And if you make a mistake in those fundamental things, all the rest of your thinking is going to be affected by that. Aristotle and Thomas give the comparison to a man who comes with a fork in the road, right? And makes a little mistake, turn this way, run that way, and the further he goes, the further he is. So the wise man is especially slow in the fundamental beginnings, huh? And that's why Thomas was called the dumb ox, right? And I compare him, you know, I tell you that little anecdote there about Gamal, one of the Nobel laureates, in fact, who studied under Bohr, the way he described Bohr. Well, you see, in Copenhagen, Bohr set up an institute for the study of theoretical physics. And this is actually became famous for his understanding of the atom, quantum theory of the atom. And this became a very famous place. People came over the world to study under him, like Oppenheimer came to the United States, and Heisenberg came from Germany, and Gamal came from Russia. And many of these guys who studied under Bohr got the Nobel Prize themselves later on, right? So he was a tremendous influence upon the other generation. We flew him out of Denmark in the Second World War, right, to help with the E-bomb and so on, huh? But anyway, Gamal says that because this place was so famous, there was always some physicists coming through, right, with a new theory or hypothesis, right? And they would get, like, a seminar room, like we're here, and sit around the table, and the visiting, you know, physicist would explain the new idea. And he said, he saw this happen over and over again. Everybody seemed to get the idea except Bohr. He says, and then we'd turn to Bohr, and we'd, what, try to explain it to Neal's Bohr, right? This would go on for some time. And finally, Bohr says, ah, now I see it. Isn't it this way? And he explained the way he saw it. He said, they get all wrong. And then they ended up a long conversation, at the end of which they went to, what, end up agreeing with Bohr. Now, the point of that, you see, so it's happened again and again and again. The last man to get the idea was the first man to get the idea right. Yeah. See? Wisely and slow, right? They stumble and run fast. So, there's a certain likeness there of Bohr, right? You see, there's a dumb ox there, right? And there's Thomas Aquinas, huh? Okay. Do you see that? So there's a slowness of stupidity. That's not what Fr. Lawrence is talking about, huh? But there's a slowness that the wise man has in those three or four places, right? And there's many things to be considered, right? When they're difficult, for the two reasons, different reasons that our style is, well, it can be difficult in the second book of wisdom. And then he's slow in the fundamentals, right? That everything else, what, depends upon, huh? Okay? I remember my mother, you know, telling me that about my father. My father's kind of a self-made businessman and so on, but when he was a young guy coming up, you know, and the boss was somebody who's called my father in, and the other young executive, to kind of, you know, I asked her advice or, you know, to toss that ear around, and the other guy would, you know, come out with his answer. My father says, I'll tell you tomorrow, but I think. He always followed my father's advice. You know, things got interesting, though. A little example of that, right? You know? The other guy was quick to state his mind, and my father said, I mean, think about it, you know? But the next day, right? You get out of a much better idea, huh? There's something like that, right? You know, there's a slowness, which is stupidity, right? You know, but there's a slowness that the mind realizes, huh? Because of the difficulty of the thing, or the complexity of it, or because it's so fundamental that you've got to be so careful about this, huh? That's what I used to say about what's in Dhyana, there's predominant passion is fear, you know, the fear of being mistaken, right? Especially the fear of being mistaken about something that's so fundamental, right? Okay? There was one of the desert fathers who was known to do that. They would ask for advice, and he would say, wait, he would wait a month or something before I say something, but they would always want to hear what he said. Yeah, yeah, yeah, yeah, yeah. Now, If quoting him is wisely and slow, I'd run fast, yeah. Yeah. There's another remark about stumbling that fragrance makes, too, that's very interesting, huh? They said it for, We're not on the earth so vile, but to the earth and special good doth give. And are aught so good that's drained from that fair use, revolts from true birth, stumbling on abuse. What's that phrase? Revolts from true birth, stumbling on abuse. On abuse. On abuse. Abuse? Yeah. Very nice to talk about that, too, right? There's nature there. The word nature comes from birth, right? So he's using the word birth there. He's extending the word in English like it's extended in Greek and Latin, right? So you revolt from true birth, from your, what? Your very nature. Then you stumble on abuse, right? Or as Heraclitus says, wisdom is to speak the truth and to act in accord with nature. You've been here and there, too, huh? I was looking at the beginning of Macbeth there, you know, and the weird sisters of the witches, huh? You know, they kind of say they have a companion animal or they assume the form of an animal, right? And one of the witches says, she'll be a rat without a tail. And the old, you know, Hudson Edition has a very nice remark upon that that there's always some defect in the animal that they assume. Like the cloven foot of the devil and so on, right? Isn't that subtle, huh? That the, what? The body that they assume, you know, has a, what, actual defect, right? It shows that they are, what, twisted out of what their nature can be, right? Ah, right. They're actually contrary to nature, right? Mm-hmm. Why, if the good angels, you know, assume a body, I mean, that doesn't mean incarnation, I mean, just in the parents of it, you know, like when they come to Abraham or something, right? You know, it's not a deformed body, right? You see? But a body that has what it should have naturally, right? Ah, no. Ah, no. You see that? They're depraved from nature. Uh-huh. Terrible thing. Ah, no. Now, I'm going to just take a few little examples here. Now, as I've been saying, there are four forms here of the syllogism that are used the most, these are the four to remember. But then in addition to these, there's the two forms of the if-then syllogism, right? One where you deny the consequent and then deny the antecedent, and the other where you affirm the antecedent and then affirm the consequent, right? We mentioned how Socrates in the Mino, he uses the two forms, right? If virtue is knowledge, then virtue can be taught. If virtue is knowledge, therefore virtue can be taught, right? You affirm in the antecedent that virtue is knowledge, right? In the second premise, right? And then the other form is when you deny the consequent. If virtue can be taught, then there are teachers of it, right? If there are no teachers of it, therefore it cannot be taught, okay? Now, and then there's the two forms of the what? Either or syllogism, right, huh? Okay? And the difference is then one, you deny, right? All but one of the alternatives, because you know what you're talking about comes under one of these, right? You're trying to find out which one it is. The other is where you deny all the possibilities, because you're wondering whether what's being divided into something that the thing you're thinking about comes under or not, right? I was explaining in class today in Classity of Nature, you know, the reason why Empedocles gave up the attempt to find one first matter, right? And I said, well, if there's one first matter, either it has definite qualities, or it has no definite quality, right? Now, if it has definite qualities, like sugar is definite, everything would have to be sweet in the world, right? If water was the beginning of all things, everything would be wet. If fire was the beginning of all things, everything would be hot. But we live in a world of contraries, so it seems you can't have one matter with definite qualities, right? Now, if you take the other alternative, which the legions are trying to do, and they go take water, which seems kind of quality-less, and then they take air, right? If you say that the one matter has no qualities, how do you get any qualities in the world, right? In the world, right? You know, when you were a kid, you had a Kuwait to water, and you got some taste and some color and so on. But if you had water to water, you'd never get any taste, any color, right? You see? So it has maybe a greater problem. How do you get something out of nothing, right? See? So those are two alternatives, right? If there's one matter out of which all things are made, either it has some definite qualities, like red wine is red, or sugar is sweet, or something, right? Or it has no definite qualities, right? And either one is a problem, right? Therefore, it seems it can't be just one matter, right? There's a way out of that, but that's what you have to proceed, right? So there are really eight things you have to know in the sense that they'll come up again and again, right? The four ones we have on the board here, right? And then the two ways of arguing from an if-then statement, right? And the two ways of reasoning from an either-or statement. And these will come up again and again, right? Now, sometimes, of course, you'll use the induction also, or the enthymeme, or the what example, but as far as the syllogism is concerned, those eight are the ones that come up again and again. Now, in this first example here from Euclid's Elements, right away, Book 1, Proposition 1, I start with that one because he uses exactly the same kind of syllogism throughout there, right? Now, this is a construction theorem. On a given finite straight line to construct an equilateral triangle, you've met this theorem before. Let AB be the given finite straight line. Thus, it is required to construct an equilateral triangle in the straight line AB. So, a center AB, with center, what, A in distance AB, let the circle, what, BCD, right, be constructed, right? Okay. And then, again, with center now in this case, the other end, B in distance VA, let the circle ACE, right, be described. And from the point C in which the circles cut one another to the points A and B, let the straight line C, A, C, B be joined, right? Okay. Now, that's the way he's going to construct an equilateral triangle. But he has to prove that he has, in fact, constructed an equilateral triangle by doing that, right? So, he has to prove that AC and AB and BC, that each of those lines is equal to the other two, right? Okay. Now, how many sojisms does he need to prove that, right? Well, he has one sojism to prove that AC and AB are equal, right? One sojism to prove that BC and BA are equal, right? And then he has to have a third one to prove that AC and CB are equal to each other. Okay. Now, what's the sojism to prove that AC is equal to CB, huh? What you're looking for there is a middle term for connecting now, right, those two lines with what? Equal, right? Okay. And what's the middle term? It enables our mind to see that those two lines must be equal. What's the middle term? Well, right, yeah, I have the same term. Yeah, yeah. So, if you want to put it in a formal term, you could say these two lines, right, are radii of the same circle, right? Radii of the same circle are, therefore, these two lines are equal. Simple enough, right? Do you see that? Okay. In the same way, you would prove that BC and AB are equal, right? Because they also are radii of the circle ACE, right? And radii of the same circle are equal, therefore. So, there's two syllogisms there, right? Now, he wants to prove that the remaining two lines are equal, that AC is equal to what? CB. But he can't prove that in the same way, can he? Because they're not radii of the same circle, are they? Okay. So, what's the middle term to unite the lines AC, CB, and equal? What's the middle term for uniting those two? Things which are equal to the same thing. Yeah. AC has been proven equal to AB, right, already. And CB has also been proven equal to AB, right? By separate arguments, right? So, you can take as a premise, then, AC and CB are equal to AB. And your major premise would simply be the axioms, quantities equal to the same, or what? Equal to each other. To each other, right? So, you have three syllogisms in this first theorem, right? But they're all of exactly the same form, right? They're all basically in this form here, right? You could say, all angle, I mean, all radii of the same circle are equal, right? These two lines are radii of the same circle, therefore, they're equal, right? Or, all quantities equal to the same are equal to each other. But these two are equal to the same, therefore, they're equal to the same, therefore, they're equal to each other. You see? Okay? Now, in the second one here, this is more subtle here, more difficult, much difficult matter, right? This is the first article in the Summa, in the treatise on love, in the question on the causes of love, right? Thomas' treatise on love there, he has a question on the nature of love, and it has several articles, and then a question on the causes of love, and then a question on the effects of love. And there's four articles on the causes of love, and six articles on the effects of love, right? And I use that in the Love and Friendship course, right? We could do it sometime if we wanted to, you know? Consider those things, you know? What I do is, for each article of Thomas, I begin with a page from Shakespeare, to leave them from their own experience of love to something more universal, and then you see it in Thomas. Okay? But this is the, he wants to syllogize that the good is the cause of love, okay? And sometimes in an article, you not only syllogize a conclusion, but one of the premises, or in some cases both the premises, are in need of being manifested, right? Okay? Now, take the example I was giving you there, from my own thinking there. I wanted to syllogize that the first road in our knowledge must be the road from the senses into reason, right? So I had to find the middle term uniting first road with the road from the senses into reason, right? And the middle term uniting first road with the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses of the senses