Logic (2016)
Lecture 41: Induction, Example, and Enthymeme in Reasoning

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So the strength of the example depends upon how much the two examples, singulars, are like each other. It's like induction that seems to be going from the singular. When you are taking this one singular, I'm a representative of that kind of singular that exemplifies. So when they argue from the Greek city-states, our city-states, our country, our states, they argue from one singular to another singular of the same kind. Depending on how great you thought those things were, you can see that's kind of an argument. Now it's interesting, huh? If they argue from the singulars in English now, where do you get these words, induction and example, from what language? Induction and an example. Yeah. But syllogism and entomine come from work. That's great. So it's done with that one, right? They have a word in their Latin for what? Syllogism or entomine. They just had arguments from these ones that were singular. Well, as Bwethi says, the thing is singular in one sense, right? Universal understood. Well, in the syllogism and entomine, you use something what? Universal, right? And it made syllogism there for simple statements. It's based upon what they call matine, the dici de omne, the dici de nolo. The set of all and the set of none, right? They're based upon some kind of a universal what? Knowledge, right, huh? By induction and the example are moving from what? Singulars, right? Now the entomine, huh? Entomine was defined as an argument from likelihood, or from science, right? Now likelihood is what's true for the most part in human affairs, right? Okay, boys will be boys. But are boys always acting like boys? Well, sometimes a boy is something very, what? Manly and brave and so on, right, huh? But boys will be boys after most part, right? Jews take what? Me grabbing him. I used to do that, except I told you before there. I went from a vacation. My father said he'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. He'd take a walk. I mean, it's like, you know, people say, that's what Jews are, you know. I met a Jewish boy in high school there, you know, Big Town's Military Academy here. And they said, Warren Murray goes to one of the stores with a Jewish boy, right? The owner was Jewish, right? And of course, oh, he's giving the Jewish boy a discount, right? And they thought that Warren was a Jewish boy. And of course, the Jewish boy's kind of embarrassed by this, you know, for me to see, you know, the way the Jews help each other, you know. So. Okay, so the enthymeme is from likelihood or from signs, huh? And most signs are, what? Not completely universal, right? So if you see me coming out of the bar, you know, what would you say? You can't do much. Yeah, yeah, yeah, yeah, yeah. You seem to be drunk, right? Yeah. Okay. And maybe that's true for the most part. That guy's coming out of the bar. You know, you seem to be drunk, right? But my wife, you know, worked for the Brain Injury Association, right? And you get these guys who are brain injured, right? And they, what, walk like a drunk man or someone, right? And she's actually seen for the captains, he's what? And it's false, right? So not everybody who stumbles, right? Not even an old man like that. Watch, man. You know. And you watch an older person, right? You know. I mean, you know. They're, you know. You know. It's like they're, you know. So what you take, a sign is something that strikes the senses and brings to mind something of it itself, right? But most signs are, what? Less than universal, right? They don't have quite the force of the syllogism, right? But they might be good for the most part, right? So the entropy is a little bit like a syllogism. It's kind of arguing from verisimilitude, right? But true for the most part in human affairs, right? Or from signs, right? But they lack the complete evasality of the syllogism, right? The example might be just in one singular, right? Brother Richard went to Mother Damien and his doctor, right? And his landlady was scared stiff of blacks, right? Like if some black men beat up her husband. Most black men are not that way. It's very wicked, right? Arguing from one, you know, thing in the sense, right? From one singular, right? Those guys are just afraid of wicked. So this is much bigger than induction, right? So enthomeme and example are different from syllogism and induction. But enthomeme in some way is to the example that syllogism is to induction, right? And I'm amused that the Latins had a name for these, right? But none for these because they didn't understand the higher arguments, right? I told you what the linguist up there at the ball said, you know, the Greeks were smart and they could figure out the grammar of the Greek language, right? The Latins were too dumb to figure out the grammar of the Latin language. So they imitate the Greek grammar, right? And they kind of shoved things in when they did things to the degree. And then they said the English grammarians, you know, imitate the Latin grammarians. So, you know, they said the superiority of the Greeks as far as grammar is concerned. And the same thing as the Latin, right? And that's why, you know, all they did in Latin was eventually, you know, they got Latin word out of syllogism, right? So the gizmos, you know, or something like that. The tamales were a bit there, superiority of the Greeks to the Latin. I was reading about the Vatican Museums, you know, you see the good statues there, either made by the Greeks that came to Italy, right? Or they imitated the Greek, you know? The statues, they actually had a top of them, right? Of course, you know, the Iliad, I mean, is much superior to what? It's like talking about the Iliad, you know. It's kind of flattery in the Romans. So the poetry, grammar, logic, you know, David, you know. Even Cicero said that there was a golden river. He's a reverse, right? Mm-hmm. So sometimes we say there are these four kinds of what? Arguments, right? Sometimes they add to these, right? You could use what? Fiction, right? Poetry for a kind of what? Persuade people too, right? And so, what's that famous novel there that got a lot of Americans opposed to slavery, right? That's kind of very regarded in a sense, right? And someone says, you know, I read Romeo and Juliet and I know what young lovers are like. I mean, is that really a good argument to say that young lovers are this way because Shakespeare has represented them this way? Or should you just say, you know, that because of my knowledge of young lovers, I can say that Shakespeare has represented them well. I judge that Shakespeare represents, you know. I mean, one of the big critics you know has followed Shakespeare around the world, you know, because he's been performed in all kinds of languages he didn't even realize, you know. And then people call and say, that's us. You know, that's us. You know, that's us. You know. And hey! They need something universal, right? They insist upon that. They need something. Now, in the case of induction, does the argument from any singular to universal, does it follow what? Necessarily. Well, you know. Well, you, in fact, see all the singular, right? If I look to the darkest Africa, I might think everybody is what? Black, you know. And I always tell my mother, always tells me, you know, about, she's from the little town of Percuse, or Watertown, Minnesota, right? There's no blacks in town, right? And she tells me when this woman went down to the big cities in Minneapolis, right? With her little boy, and I walk along, and a little black boy comes the other direction. He says, go home and wash your face! That was kind of funny, you know. He'd never seen a black boy before, you know. So, if you lived in a place where everybody was, what, white? Your induction, you'd say, if it was the darkest Africa, you were black, you'd think maybe everybody is black, right? A variation on that theme is the two little children of a missionary couple who were in a Spanish-speaking country where most of the people were black, some shade of black. Yeah. When they came back to the States, the kids would only speak Spanish when they saw black people. Yeah. Because that was their experience. I'm sorry to just say, you know, if someone goes up to Mars someplace and says, hey, there's no, there's pink snow up there. I'd be surprised, wouldn't you? Would you say it's impossible? And someone up there, he said, and said, hey, the food shortage is solved, you know, because half a loaf is as much as a whole loaf up there. I said, yeah, I said, it's affected by space. This is unnecessary, right? Induction is not, you know, and sometimes it shows up as an exception, right? And a fort zuri, the Torah part is unnecessary, right? Well, now, you might say that there are, what, two kinds of induction, right? The first sense of induction is an argument from any singular, universal, right? There's also an induction from, what, the less universal, more universal, right? And if you're, what, less universal, more what? Exhausted, right? There's a much stronger argument than you have. You see, take for example, did you ever read the question there in the Summa Theologiae of God is simple, God is not simple? Now, how many articles are there in that? There's eight articles, right? Okay. Now, so the first article is that God is not a body. The second article is that God is not, what, composed of body and soul, right? What's the third? See, this is a particular kind of composition that you have in the body, right? So, if God is not a body, he's not composed in that way. He might be composed in some other way, right? Okay. It might be a composition of matter and form. That's not the same as the composition of, what, the body and parts of the material body. The third article is talking about the subject, right? The singular subject and the universal, what, nature, right? So, is there a composition in me of what a man is and something peculiar to the flesh and blood and bones that I have and nobody else has, right? So, that's of the nature, you might say, right? These are the number of symbols, I guess, of nature there, right? Okay. The composition, God is not composed, the subject, you might say, right? One who is a man and the, what, universal nature, right? I'm not exactly the same as what a man is, am I? Because if what a man and I were the same, right, as the only man. So, what can we say about the angels, right? We're composed. It's what a man is and something to do with me, right? You find in me what a man is and besides what a man is. So, there's not that kind of composition in God, either. And there's not that kind of composition in the angels, right? Each angel is a different kind, huh? Each angel is his own species, right? He has the fullness of his species, right? Only you understand. But what composition is there in the angels, right? The composition of the nature and the being, right? So, you show that God does not compose what he is, right? And his being, right? Let's say it's nature and existence. All creatures receive their existence from God, so they're not the same thing as their existence, right? He does not compose a dead tune, right? Hmm. Then, what is the fifth one, huh? It's going to cut a genius. god does not have a genus or a substance and then god composition of what substance and accident right in some ways the way he says he has a substance of god right what he is right now god is not composed of substance and what accident seven right what is he showing in seven some other way that is not performance some other particular kind of composition doesn't happen what he does in the seventh one is to conclude that god is not composed in any way and this is very universal god cannot be put together in any way okay but now how do you think he argues in the seventh chapter by syllogism or by induction well he has both for beginners right and induction is easier for a beginning right so if you look at the seventh chapter there will be a number of arguments but one of them will be in the form you might have an induction right that he's gone through all the kinds of composition there seems to be and what creatures right and he has arguments in each one of these chapters against this particular kind of composition and this kind of composition right and so you might say this is a a what a an argument from particulars right to the universal right not particulars in the sense of what singulars but particular what kinds of composition right so this is induction in a different sense than uh the argument from many singulars to universal but it's like it like it isn't it yeah so it's not if you say you know that um induction is an argument from particulars to the general you could say but particulars can mean the less universal or it can mean what singulars right and the first meaning of induction is the argument from many singulars to something universal but then the second meaning would be from what many less universals to the what more universal right or most universal and so you have an inductive argument from these six kinds of composition that you have in creatures right so well it seems like god is in anyway composed right made it kind of complete this is a strong argument you're saying no matter where you're arguing from the singular right okay because you can more what you can think about the particular kinds right then you can about the what singulars right take them into account but then he also has syllogism in chapter seven right he's going to syllogize you know that uh from some you've already heard about god that he's pure act right and that everything that's composed is what a mixture of act and ability right and he says you know and if it's composed either one part is to the other part his ability is to act like for example matter is to form's ability is to act right um subject is to nature as ability is to act right nature is to existence as ability is to act and so on even this is in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in a way in 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statements known through themselves by all men right like the whole is more than a part we first come to these by induction right then but we understand enough about what a whole is what a part is to see that it must be true but when i know what what a right angle is and what a triangle is it's not obvious that the angles of a triangle equal to two right angles right and therefore i have to syllogize to know that is what it does in proposition 32 of book one book one has got 48 theorems right and 47 48 of the pedigree theory and it's converse right i think about 32 is about the one so the axioms are not known by induction alone right if you're known by induction alone you wouldn't be sure of that right so you you come to know them at first by induction but then you see what is a lot of holes and what a part is enough to see the whole must be more than the part but you have to realize of course that with the axioms you um kind of interesting thing that's coming to thomas there by imitating thomas there when he talks about the third book of wisdom the third book of wisdom is dialectical and it's a kind of universal dialectic about what the problems of wisdom but in the beginning of the third book Aristotle gives four reasons why we should proceed to Dalek before we try to determine the truth, right? And so Thomas in his commentary, his exposition, I guess is the word for laying out the book, right? He says that for these four reasons, Aristotle not only here, but also in his other books, right, his Dalek, right? Then he points out the distinction between the dialectic of the third book of wisdom and the dialectic, let's say, of the fourth book of the natural theory, right? Aristotle has a particular dialectic about place, and he tries to determine the truth about place, right? Then he has a particular dialectic about time, and he tries to determine the truth about that, okay? He doesn't have a whole book that's just dialectical. And he then talks about what's appropriate for wisdom to have a whole book, to have a whole, one of the 14 books of wisdom is dialectical. And it's because of this, what, affinity of dialectic and, what, and wisdom, huh? The universality, right? He goes back to what it very was that said about this earlier then. Well, then you get to the fifth book of wisdom, huh? The fifth book of wisdom is a book where the whole book is taken up with names, equivocal by reason, and he distinguishes the senses of the words and gives their order, and picks out their order and so on. And he says, well, Thomas doesn't make this point, but I'm just going to imitate him now. I said, Aristotle and other books will talk about this word being equivocal, right? We're just looking at this, and he begins to take out the senses, for example, in the second book on the soul, he distinguishes three senses a scene, or sense, sensible. What he calls the, what, private sensible, that only one sense knows, the common sensible, that more than one sense knows, right? And then the accidental sensible, right? So he's distinguishing the word sensible, right? I see your color, right? Let's say what? Private sensible, only the eye knows your color. I know your what? Size or shape, with my eyes. I see your size or shape. I can also feel you and know your size or shape, huh? Common sensible. And then I'm also sent to see you. But do I really see you? You are an individual substance, right? And what I see is your color, which is in the quality, the genus of quality. Your shape, which is in the genus of quality. And your size, which is in the genus of quantity. But I don't really see you, do I? But I kind of recognize you. Something else in me recognizes you. When I see your color, and you're talking, and you're smiling. And you're crying and so forth. You see what I mean? So he's distinguishing a word that is what? Equivocal by what? Reason, right? And in the fourth book, he gives the eight senses of the end, right? So the first one is giving us the order, the start of the order, is to be here. And Thomas says, well, that's a clue to our order, you know. But he does so imitating him when he does, right? Why do you have a whole book devoted to distinguishing the senses of words? Equivocal by reason, in wisdom, that's unique, right? And we should make the point. Why does he have a whole book devoted to this, huh? Just like why does he have a whole book, as Thomas said in the third book, devoted to dialectic, right? Well, Thomas doesn't, you know, make an explicit fact of the thing. But what is wisdom about? Like I say, wisdom is about the first causes, and in general, about immaterial things, right? And they can be known to talk about only with beings of critical by reason, right? It belongs to the wise men to consider the axioms and to defend them. They're the foundation of everything. And the axioms, like the whole is more than a part, are expressed with words that are critical by reason. And the subject of wisdom is being in one, and they're very critical by reason, right? You know? So it's appropriate that the wise men have a whole book where he distinguishes the words that are used most of all in wisdom, right? But used in the axioms, right? And to some extent, everywhere, right? And they're all equivocal by reason. I was thinking, I've got to understand the soul there. About time that, I don't remember a place where Aristotle looks missily, but partly he does some different places. Take the word body, right? You and I, we live in this sensible world, right? And this sensible world is filled with bodies, right? And, but is body a word equivocal by reason? Now, what are the three or four main meanings of body? Yeah? Under substance. Yeah. So you divide substance, some days you divide substance into material and immaterial substance, right? And they call the material substances bodies, right? And they call the material substances spirits. So we call them angels sometimes. The philosophers call them separated substances, right? Separated from matter, right? So that's one sense of body, right? It's a species of substance, right? And the genus of... And what's... But now, what about when you say, you know, I, Dwayne Berquist, or you, I have a body, and I have a soul. And my body is not my soul, right? I was thinking about a woman today, and I said, men shouldn't think so much about a woman's body, you know? They should think more about a soul. And she said, that's the problem, right? And, uh... Now, when you say that I have a body, and I have a soul, right? Is body the same thing as... What? It's an integral part, right? Yeah, yeah. It's not the genus of it. Yeah. That's another sense, right? Yeah. And Aristotle says, you know, that the soul is the first act of a natural body having life and ability. It's the first act of a natural body composed of tools, right? Well, that body is not the genus of what? That species, you know, a material substance, right? So that's a different sense of body, isn't it, right? And what's the third sense? Yeah. So you get the species of quantity are discrete and continuous. And the species of continuous are, well, vine, surface, and body, right? And place and time, right? Well, now, people are always confusing the body in the sense of what? It's three-dimensional. It's linked within depth with body and the genus of what? The substance. Quantity is the genus closest to substance in some way, right? So they confuse those two senses of what? Body, right? So you have those three meanings of body, right? You would not be able to distinguish them. I toss in. There's a fourth sense of body, you know? In Summa Theologiae, right? Each question is divided into articles. The article is divided into what the parts. What's the middle part called? Body. Yeah. I guess that goes back. I mean, not to get to that goes back. Then it gets to that, right? It's self-focus, yeah. What? The body of the purpose. The purpose. Yeah, the body of the purpose. Is it? Yeah. That's a different, that's a fourth sense of body. I mean, why don't you take it in for us, you know? It's kind of interesting though, isn't it? The body of the logic. Yeah. It's like, you know, almost you'd say that the substance of the article is in the body of it, right? Yeah, these objections, you know, they're answering later on, but the body of the teaching there is in the body of the article. You know? That's because we think of substance in the body, right? Yeah. Yeah. Yeah. It's a body of water next to the city or something, a body of water, a body of water, a body of water, a body of water next to Worcester. So it's interesting how this question, right, and in the seventh article in particular, that Thomas argues both inductively, right, but it's induction in a, what, second sense, right? The first sense of induction is an argument from many singular to universal. An argument from the lesser universal to more universal, right, would be considered induction in not a purely critical sense, right? In a sense that it's proportional. When Thomas talks about minodexio, right, teaching, right, teaching religion by the hand, with propositions less universal, he says, right, with sensible examples and so on, right? We were talking last night there about how seeing seems to be more spiritual than the other senses, and therefore we carried over the word seeing from the eye, the act of the eye, to the mind's eye, as Shakespeare says, when Hamlet says, I can see my father now. Look around, look around, look around, look, you know, as it goes to period again, you know, he says, in my mind's eye, he says, but it's like in his memory or his imagination, right? And we use the word see there, right, and that seems to be even more spiritual than the outer eye see. And then we carry over to the understanding of reason, right? I always heard my mother saying, you know, I see through the blind man, I don't see at all. She thought that was very clever, you know. You're playing on the sense of understanding, right, that sense of the word understanding. So why do you carry over the word seeing, right? Because it's more spiritual, right? And we speak of seeing God face to face, or seeing God as he is, that's the way you describe it, right? But they're talking about an act that is very, what, immaterial, very spiritual, right? So you kind of see that, right? So I was kind of saying, even in the great Dewey DeBroy, I mean, it's matter and light, is it? Light is not something material, right? It's not kind of matter. Although he might think it is in some way, but he's just kind of beside himself, right? In naming his book there. But then we got to think he had to take something to the mind, too. Simple apprehension, Thomas says, simple grasping. And as I used to use this, you know, he'd say, well, when you grasp something, it's contained in your hand. And so when the mind grasps something, you're kind of contrasting the mind and knowing with what? Love, right? It's in love. Love is in the thing loved, right? But in knowing, the thing known is in the knower. And grasp gives that idea better. And take from the hand, right? The sense of touch, right? Rather than from the sense of sight, right? It's kind of, in some sense, the moment material, you know? And the other idea is to use the idea of grasping. I can't grasp the center of this thing that's connected with the rest of it, right? But I can grasp my class over there because the air gives way, right? So to grasp something, you have to separate it from other things, right? And that's, that's, it's like in mind, it's actually lead you by the hand, right? To understand something about the mind. The thing known is in the, what? The mind, when it knows it. That's why we say to grasp it, right? When you grasp something, you have to, to grasp something, you have to separate it from everything else. And you see that again, with your hand, to grasp something, you have to separate it from, you know, what's around it, right? You need to see that now. Charles DeConnick had a famous talk there, you know, on this, on the sense of sight and the sense of, what? Touch, right? Mm-hmm. Because the sense of touch, you need the sense of, what? Certitude, you know? W. Thomas, you know, is always exemplary because he's going to trust his fingers and so on. He put his hand on the side of the board and so on, rather than his eyes, right? You don't trust his eyes. So, this is really the, the man again, right? So that the, the sense of touch is very important for certitude, huh? It's interesting because some of the big others are in India. But they seem to deny reality. They don't have the tendency to deny what they can see. That's good, that's good, that's good. It's appropriate. You know, they said, this man. No, no, no, you haven't seen it. I touched this. I know. Well, we have held with our hands. Yeah. Because moderns kind of prefer the visual, you know. It's a famous movie when it stands, you know, things moving around down, you know. What about that money? You make all this much money, you know. The false medicine or whatever it is, you know. And you don't really, but the sense of touch is really the sense of sympathy, you know, rather than the sense of sight right now. And we talked about the U.S. then soldiers are right again today, right? Any questions? And we talked about the regular syllogism. Because we saw, but how many ways are there of syllogizing universal affirmative? Universal affirmative? Well, here's one. One way of syllogizing is that every C is A, right? And it's by the set of all, right? If every B is an A, then whatever is a B must be an A, right? So if we're told that every C is a B, then you must conclude that every C is an A, right? Okay? If we're told only that some C is B, then you conclude that some Cs must be A. Now, is there any other way to syllogizing universal affirmative besides this? So in the second figure, your middle term is the, what, predicate in both cases, right? And so what? I like it. You don't have the set of all as it now stands, right? Because every A is B but nothing is said to be an A, right? And every C is B but nothing is said to be a C, right? So you don't have the set of all, do you? And if you convert every A as B, you won't convert to every B as A, necessarily. You won't only convert to some B as A, right? So you don't have the set of all, so there's no way to get the set of all, right? Even two universal fermetives, right? In the second figure you can't get the... So this is unique, right? But now, how many ones can you get the universal negative from? First of all, the first figure, right? No B is A, every C is B. Now, here the set of none applies. It's each and only, they call it my taboo. If no B is an A, that means no B is an A. Then whatever is a B must not be an A. So if you're told that every C is a B, then it must be that no C by the set of none. Now, if you were told only that some of the C's are B's, you could say that those some C's being B's cannot be an A, right? But you wouldn't know it about all of them, right? Now, in the second figure, huh? Is there a way of syllogizing? Now, you weren't here when you did these conversion. Okay, let's go back to this conversion, right? You could say if every A is B is true, and this is necessary that every B be an A, right? And you can see many examples of that, right? If every dog is an animal, must every animal be a dog? If every odd number is a number, then every number must be an odd number? No. So it doesn't turn around necessarily. So you can't use that to get a syllogism, right? You can only turn around this much, huh? If every odd number is a number, some numbers must be odd numbered, right? But they won't have to all be, right? So you can't turn around. They say that the universal affirmative converts partially, right? But it doesn't convert simply. It doesn't keep its thing. It loses power, right? But now, the universal negative here, huh? Can you turn that around? Yeah. Now how do we know that, right? How do we know that, let's take a second figure here. If no B is A is true, then it must be true also that no A is B. How do we know that, right? If this isn't necessary, as I say it is, right, then you're saying it's possible there could be at least one A that is a B, right? Okay? And now, if some A is a B, that's possible. Let's give that A that is a B an A. Let us call, let's call it x. Now, x in both factors. If x is the A that is a B, x is an A, and x is a B. Therefore, there's some what? B that is an A, namely x, right? And that contradicts this. Why do we get into that terrible situation, contradicting what we started off with? Because we didn't admit what I say would be so, right? If you admit even one single A would be a B, with no B as A, we can give a name to that one lonesome A that is a B, and we'll call it x, right? And then you're forced to say that x is both an A and a B. And therefore, there's some B, even by name, x, that is an A. And that contradicts no B as A, right? So, the universal negative converts and keeps its inner self. It converts simply, right? So, as far as conversion is concerned, the universal negative is more useful, right? Than the universal affirmative, right? And that's where you get more, what? Universal negative conclusions. Yeah. Yeah. Yeah. Yeah. Now, in the second figure, there is, Aristotle calls the soldiers in the second figure, he calls them imperfect now because you have to convert to see that it does follow necessarily, right? And he calls the soldiers in the first figure, perfect, because the said of all, or the said of none, applies to it just as it stands, right? Pretty clear, right? But when you convert in the second figure, you end up in the first figure again. Lo and behold, the magic is as it is. Okay. So, now the second figure, the middle term is the predicate for the cases, huh? So, you have no A is B and every C is B. Now, the said of none doesn't apply to it as an outstanding, right? You do have the universal negative, but you have to have something coming under the subject of that. And nothing is said to be an A. Oh, I give up. But you forgot it. You learned about the conversion. You convert the universal negative and it doesn't lose power. You mean universal. Wow. So, you make this conversion, bringing this over, and lo and behold, you are in the first what? The figure. That's not it. And since no B is an A, and every is a B is not an A. Every C is a B. Therefore, C, you wouldn't expect you to get a universal negative from two universal negatives in the second figure, would you? And you can't even get the universal affirmative, right? Now, would you expect anything with two universal negatives? Well, stop your think here now. No A is B, and no C is UB. Now, the way we are showing, the way you show that this is invalid, right? Is that, is to find examples for A, B, and C, right? That satisfy two conditions. One is that when you put them into this form, the statements are true, right? But you have one example where every C is A, in fact. And one example where no C is A, right? Now, the example where every C is an A, that's true once. Can E negatively be true then? So then no negative conclusion is true always, right? And therefore, is anyone necessary? Can something be necessarily so if it isn't always so? I say two is necessarily half of four, right? It's gotta be always so, right? But a man is black? Is that, or a man, I'm racist, so I say a man is white, right? All right. All right.