Logic (2016)
38. Two Senses of Induction (God's Simplicity), the Senses of 'Body' and Touch, and the Three Figures of the Syllogism
Class of 2017-03-23
https://berquistcourse.com/course/philosophy/2-logic-2016/038-two-senses-of-induction-gods-simplicity-the-senses-of-body/

[0:00] Now, in the case of induction, does the argument from many singulars to universal? Does it follow what necessarily? It can. Well, do you in fact see all the singulars, right? So if I lived in 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 a little town of Parkas or Watertown Minnesota right?

[0:33] There's no blacks in town, right? And she tells me when this woman went down to the big city to Minneapolis, right, with her little boy, and they're walking along, a little black boy comes the other direction. He says, "Go home and wash your face." I don't know. It's kind of funny, you know. He'd

[0:53] never seen a black boy before. So if you lived in a in a place where everybody was what white, your induction you would say, you know, all men are white, yeah. If it was in darkest Africa and 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.

[1:20] 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. Yeah.

[1:29] It was kind of funny. My sister used to say, you know, if someone goes up to the to Mars or 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.

[1:48] And someone went 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.

[2:02] It's just unnecessary, right? Induction is not, you know. And sometimes it shows up as an exception, right? And a fortiori, the torque argument is not necessary, right?

[2:28] Aren't there some inductions that are necessary? Well, now you might say that there are what two kinds of induction, right? First sense induction is an argument from any singulars, universal, right? There's also induction from what the less universal to the more what more universal, right? And if your what less universals were what

[2:59] exhausted, right? You'd have a much stronger argument than you have in the singulars. You see, take for example. Did you ever read the the uh, question there in the Summa Theologiae of God is simple, God is not. simple? Now, how many articles are in that in that question?

[3:34] Probably more than one. Yeah. yeah. There's eight articles, right? Okay. Now. So the first article is that God is not a body. Okay. The second article is that God is not what. Composed of body and soul, right?

[4:25] Or matter and form. Composed of matter and form, right? What's the third argument, right? 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. So, maybe the composition of matter and form that's not the same as the composition of what the body, which is of parts of the material body?

[5:08] Okay. Back to me. I'm cheating. I have it here. Now, the third article is talking about the what, the subject, right? The singular subject and the universal what nature, right? Okay. So,

[5:31] is there a composition in me of what a man is and something peculiar to me, the flesh and blood and bones that I have and nobody else has, right? So that's of the nature you might say, right? Now, these are the number of synonyms I guess of nature, there, right? Okay. The composition God is not composed of the subject, you might say, right? One who is a man and the what, universal nature, right?

[6:08] Okay. I'm not exactly the same as what a man is, am I? Because if what a man and I were the same, I'd be the only man. Which what we say about the angels, right? They're not composed of. Gets what a man is has something to do with me, right? You find in me what a man is. Do you find something besides what a man is, right?

[6:42] Okay. So there's not that kind of composition in God, either. And there's not that kind of composition in the angels, huh? They're marvelous creatures, right? Each angel is what different in kind. Each angel is his own species, right? He has the fullness of his species, right? What wonderful creatures they are. My angel's probably laughing at me now.

[7:11] If only you understood. Yeah. But what composition is there in the angels right? Composition of the nature and of the being, right? So, show that God is not composed

[7:34] of what He is, right? In His being, right? Let's say nature, being, existence. Because all creatures receive their existence from God, so they're not the same thing as their existence, right? There's no distinction there. If God is not composed of nature

[8:00] and being, okay. Then, what is the fifth one? huh? Has God got a genus? Indifference? God does not have a genus. Doesn't have genus. Not a category of substance.

[8:50] And then God, there's no composition of what substance and accident, right? In some ways, as Boethius says, he has substance of God, right? What he is, right? God is not composed of substance and what accident.

[9:22] Now seven, right now, which is the symbol of what? Wisdom, right? Huh? What is he showing in seven? Some other way God is not composed? Some other particular kind of composition doesn't have? No. What he does in the seventh one is to conclude that God is not composed in any way. Okay. Now this is very universal, right?

[10:01] 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? Induction based on the other Well, he does both. Right there, right? See, this is for beginners, right? And induction is easier for a beginner, right? So if you look at the seventh chapter, there be a number of arguments, but one of them will be in the form you might say of an induction, right?

[10:42] That he's gone through all the kinds of composition there seems to be in 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 universal, right? But not particulars in the sense of what singulars, but particular what kinds of composition, right?

[11:14] So this is induction. In a different sense than the argument from many singulars to universal, but it's like it, isn't it? Less universal. Yeah. So it's not. If you say you know that induction is an argument from particulars to the general, you can 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.

[11:45] 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 that God is in any way composed, right? I mean, kind of complete. This is a strong argument, as we were saying, that no matter where you're arguing from singulars, right?

[12:15] Because you can more what be complete about the particular kinds, right? Than you can about the what singulars, right? Take them into account anymore. But then he also has syllogism in chapter seven, right? Okay. He's going to syllogize, you know, that from something already learned about God that He's pure act, right? And that everything that is composed is what a mixture of act and ability, right? And he says, you know, in anything composed, either one part is to the other part as ability is to act, like for example, matter is to forms ability is to act, right?

[13:01] Subject is to nature as ability is to act, right? Nature is to existence as ability is to act, and so on, right? Even this is in a way a bit like ability to act, is an act accidental, right? And so on. And genus is a different sense ability is to act, right? So,

[13:25] but God is pure act, right? Or excuse me, let me finish that. Says either one part is to the other part as what ability to act, or all the parts are to the whole as ability is to act, right? So there is no composition without this ability of something to be actualized, right? This passive ability, as we learned in the ninth book, of wisdom right now. But God is pure act, right?

[13:51] Therefore, God cannot be what. So now you have syllogism, right? Okay. So we have an inductive argument from these six kinds of composition that you seem to enumerate, right, as being creatures, and then the what? Yeah, but you have both induction and syllogism in this, right? He's a very thorough guy, this Thomas, right? He's proportioned himself to students, right? So because they can understand an argument by induction better than an argument by syllogism, right?

[14:24] huh? And so he gives them both, right? And he leads them up. Now, you might say, why is there an eighth article right? What more can you expect from the man, right?

[14:45] Well, he's showing God is not composed in any of any things, right? Yeah, yeah. But he doesn't enter in. He's going to say in the article, he doesn't enter into what composition or something else, right? I'm just reading this morning there a little bit the starting the twentieth question there De Veritate and this is the one about Christ, right? And some people think you know that Christ didn't have human knowledge, right?

[15:14] He had divine knowledge, and they thought that the divinity of him came in was like taking the place of the soul, or he's taking part of the of the understanding, right? Huh? And then you get something that was what impossible, right? And so God cannot be a part of something else, right? And be what sharing that potency, right? Okay. So that's De Veritate doctrine, right? I mean, the article, the question is really about the simplicity of God, right?

[15:49] You might say, but he sticks that in, right? For this, God is not a composed of something else to make something else, right? Okay. So

[16:04] don't we arrive at you know, so like a principle like the whole is greater than the part? Don't we arrive at that by induction as well? And that's very sure, right? Yeah, yeah. Now, in the case of yeah, that's the point you're gonna make now. he says that even Aristotle says that the axioms, right, which are statements known through themselves by all men, right, like the whole is more than the part, we first come to these by induction, right?

[16:31] Huh? But we understand enough about what a whole is and what a part is to see that it must be true, but yeah, yeah, yeah. When I know what what a right angle is and what a triangle is, it's not obvious that the angles of a triangle become the two right angles, right? Whenever I have to syllogize to know that as people does in Proposition 32 of, Book One.

[17:01] I remember it. Take no work for that. Book One has got forty-eight theorems, right? Forty-seven, forty-eight of the Pythagorean theorem and its converse, right? I think about fifty-two is about the one I'm up to. about the right angle the triangle equal to right angles. So the axioms are not known by induction alone, right? If they're known by induction alone, you wouldn't be sure, right?

[17:42] So you you come to know them at first by induction, but then you see what is what a whole is and what a part is enough to see that the whole must be more than the part. But you have to realize, of course, that with the axioms, you know, kind of interesting thing that I was coming to in Thomas there I'm imitating Thomas there when he talks about the third book of wisdom.

[18:08] 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 dialectically before we try to determine the truth. And so Thomas, in his commentary, his exposition, this 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 dialectic, right.

[18:43] Then he points out a distinction between the dialectic of the third of the third book of Wisdom, the dialectic, let's say, of the fourth book of Natural Hearing where 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, it isn't a whole book that's just dialectic, you know.

[19:11] And he then talks about why it's appropriate for Wisdom to have a whole book. What the whole one of the fourteen books of Wisdom is dialectical. It's because of this what affinity of dialectic and what and Wisdom, huh? Their universality, right? It goes back to what Varro was about this earlier in the commentary. Well, then you get to the fifth book of Wisdom. 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 and gives their order, and links out the order, and so on.

[19:56] He says, well, Thomas doesn't make this point, but I just communicated it now. I said Aristotle and other books will talk about this word being equivocal, right? We were just looking at this. He begins to take out the senses, for example, in the second book on the soul. He distinguishes three senses of seeing, 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?

[20:35] And then the accidental sensible, right? So he's distinguishing the word sensible, right? I see your color, right? That's a 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, but I could also feel you and know your size or shape, huh?

[21:05] That's common sensibles, right? And then I'm also said to see you. But do I really see you? See, you are an individual substance, right? And what I see is your color, which is in the quality, is 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 doing. But I kind of recognize you.

[21:39] Something else only recognizes you when I see your color and you're talking and you're smiling and crying and so. 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 in, right? Says the first one is giving us the order starting the order is to be here. Thomas said, "Well, that's a clue to how order all in."

[22:13] He does so imitating him. He does, right? But why do you have a whole book devoted to distinguishing the senses of words equivocal by reason in wisdom? That's that's unique, right? And we should make the point: Why does he have a whole book devoted to this?

[22:34] Just like why does he have a whole book, as Thomas says, the third book devoted to dialectic, right? But Thomas doesn't, you know, make an explicit that thing. But what is wisdom about? Well,

[22:48] you could say wisdom is about the first causes, and in general about immaterial things, right? And they can be known and talked about only with things equivocal by reason, right? It belongs to the wise men to consider the axioms and to defend them through the foundation of everything. And the axioms, like the whole is more than the part, are expressed with words that are equivocal by reason.

[23:14] And the subject of wisdom is being in one, and they're very equivocal 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.

[23:45] I was thinking I've got a study of the soul there. About time that I don't remember a place where Aristotle explicitly, but partly he does some different places. Take the word body, right? You and I we live in this sensible world, right? In this sensible world that's filled with bodies, right? And but is body a word equivocal by reason? I think so. Yeah. Now, what are the three or four main meanings of body?

[24:24] Can be genus. Yeah. Substance, under substance. Yeah. So you divide substance. Sometimes you divide substance into material and immaterial substance, right? And they call the material substances bodies, right? And they call immaterial substances spirits, or we call them angels sometimes. The philosophers call them separated substances, right? Separated from matter, right? Okay. So that's one sense of of body, right? It's a species of substance, right? And the genus of all these things under.

[25:05] Okay. Now 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?

[25:25] And I was thinking about woman today, and I said, men shouldn't think so much about a woman's body, you know. They should think more about her soul. And she said, that's the problem, right? And

[25:41] now, when you say that I have a body and I have a soul, right? Is body the same thing as? an integral part. It's an integral part. Yeah, yeah, it's not the genus of it. That's another sense, right? 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?

[26:08] Now, well, that body is not the genus of what of that species, you know, of material substance, right? So that's a different sense of body, isn't it? Okay. Now what's the third sense? Body is this quantity. Yeah, yeah. So you get the species of quantity are discrete and continuous, and the species of continuous are well, line, surface, and body, right? And place and time, right now. Okay.

[26:47] Well, now people are always confusing the body in the sense of what is three dimensional. I was linked with in depth with body in the genus of what 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? And we would not be able to distinguish them, would they?

[27:14] And they get terribly mixed up because of that, right? I taught some. There's a fourth sense of body in Summa Theologiae, right? Each question divided the articles. Articles divided into what the parts. What's the middle part called? Body. Yeah. I guess that goes back. I mean, that's the definition goes back to gets to the body itself. Yes, what is the body? The corpus. Yeah, body of the article.

[27:45] What's the fourth sense? I know we actually did it for us, you know. That's kind of interesting, though, isn't it? The body of politics. Yeah. It's

[27:57] like you know, almost you'd say the substance of the article is in the body of it, right? You have his objections, you know, their answers later on, but the body of the teaching there is in the in the body of the article. You know, that's because the only thing we think of substance is body, right? I don't know. see there's another sense of body that's escaped me. you know.

[28:25] Juridical, body. Hmm Juridical, body. Yeah. Well the body politic, that's what I said Body politic, yeah, that's what. another sense. is. There's a quantitative one. in the case. It's a body of water next to the city. It's a body of water. Lake Quinsig is Yeah. body of water next to Worcester. Yeah. body politic, right? See, Paul make that comparison, yeah. Mystical body, yeah. Mystical bodies, yeah. That's another kind of political body.

[28:55] Well. But not. Supernatural in character, so. I didn't deny that. We're probably equivocating on. Well, what- what do you mean by polis? City of God, or? Oh, okay.

[29:10] What do you mean? You're equivocating on scene. And there's the Gilbert Sullivan, everybody's somebody, no one's anybody. So it's interesting how in this question, right, and in the seventh article in particular, Thomas argues both inductively, right, and syllogistically, right, but it's induction in a what second sense, right? First sense of induction is an argument from many singulars to universal. An argument from the less universal to more universal, right, would be considered induction and not a purely equivocal sense, right?

[29:59] In a sense that's proportional. When Thomas talks about manuductio right, huh In the article on teaching, right, Teacher leads you by the hand with propositions less universal, he says, right, with sensible examples and so on, right.

[30:26] We were talking last night there about how seeing seems to be more spiritual than the other senses, and therefore we carry over the word seeing from the eye, the act of the eye, to the mind's eye, as Shakespeare says, and Hamlet says, "I can see my father now." Look around. As it goes to appear again, you know, he says, "In my mind's eye," he said. It's like in his memory or his imagination, right?

[30:54] And we use the word "see" there, right? And that seems to be even more spiritual than than the outer eye seeing. And then we carry over to the understanding reason, right? I was hearing my mother saying, you know, I see said the blind man, but he couldn't see at all. She thought that was very clever. You're playing on the sense of understanding, right? That sense of the word.

[31:16] understanding. So why do you carry over the word seeing, right? You know, because it's more spiritual, right? And we 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's very, but immaterial, very spiritual. So you kind of see that, right? So I was kind of saying, even in the great Louis de Broglie, I mean it's matter and light.

[31:41] 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? You know, in naming his book that, right? Matter and light And uh But then we got thinking about uh um how we use the the act of the hand, sometimes the mind, to simple apprehension. Thomas says simple grasping.

[32:09] And as I used to use this, you know, I'd say, well, when you grasp something, it's contained in your hand. And so, when the mind grasps something, it's in the mind, right? 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.

[32:41] 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 most material, you know. And and the other is to use the idea grasp. You know, I can't grasp the center of this thing because it's connected with the rest of it, right? But I can grasp my class over there because the air gives way, right?

[33:04] So to grasp something, you have to separate it from what other things, right? That's that's so it's like in manuductio, 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. Because that's what we say to grasp it, right? And that when you grasp something, you have to to grasp something, you have to separate it from everything else.

[33:32] And you see that again with your hand to grasp something, you have to separate it from what's around it, right? So kind of beautiful thing to see that. Charles De Koninck had a famous talk there, you know, on this on the sense of sight and the sense of what touch, right? Because the sense of touch is the sense of what certitude, huh? And doubting Thomas, you know, is always an example there because he's going to trust his fingers and so on, and putting his hand on the side of our Lord and so on, rather than his eyes, right?

[34:07] He never trusts his eyes. This is really the the man again, right? So that the the sense of touch is very important for certitude, huh?

[34:20] It's interesting just because someone's being out of touch, right? Touch is reality. People are screaming, you know, all the time around that. That's what Dr. Carroll pointed out: the appropriateness of God sending Thomas to India, where they seem to deny reality. They tend to deny what they can see. It's appropriate that God's providence. That He sent this man. No, no, no. You understand, I touched it, I know."

[35:02] And that's what Saint John says to his epistle, what we've seen. and heard, what we have held with our hands. We've held with our hands Yeah. Because moderns kind of prefer the visual, you know.

[35:18] It's a famous movie there where the guy goes up in the the uh the tower. there he looks down you see little things moving around down there. you know. What about that money? You make all this much money, you know, the false medicine or whatever it is, you know, 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.

[35:40] Just can see a little moving down there, so wipe them off Cold, hard, business. They're calculating business. Yeah, yeah, yeah. You say even you know the idea of good, getting more from the sense of touch than from the sense of sight. You're mistaken. Believe me. You have to get the suffering. Oh, poor man! Otherwise, your sense of touch will be deprived. Okay. Now we talked about the if then syllogism right again today, right?

[36:27] Any question though about the regular syllogism? Because we saw, but how many ways are there of syllogizing universal affirmative? Three, two, universal affirmative. I'm sorry.

[36:53] Two. Well, here's one. This is one way of syllogizing: every C is A, right? And by the set of all, right? If every B is an A. Then whatever is a b must be an a, right? So if you're told that every c is a b, then you must conclude that every c is an a, right? Okay. If you're told only that some c is b, then you conclude that those some C's must be A Now, is there any other way to syllogize the universal affirmative besides this?

[37:41] The second figure A is B So in the second figure, your middle term is the what? Predicate in both cases, right? And okay. So what, But are they Every a is b. Every c. You couldn't conclude from that. Every c. I

[38:17] think you I think you can all conclude some set is. B 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? You don't have the set of all, do you? And if you convert every A is B, you won't convert to every B is A necessarily.

[38:43] You'll only convert to some B is A, right? So you don't have the set of all. There's no way to get the set of all, right? Even two universal affirmatives, right? The second figure you can't get the. So this is unique, right?

[39:09] But now, how many ones can you get the universal negative? How many? At least two. Maybe. No, it's three. First on the first figure, right? No. No B is A.

[39:37] Every C is B. Now here the set of none applies. Dici de omni they call it Latin. If 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. No C is A by the set of none.

[40:09] Now if you're 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?

[40:23] Now in the second figure, huh? Is there a way of syllogizing? You were here when you did the conversion. Let's go back to conversion, right?

[40:39] You say if if every every A is B is true, it isn't necessary that every B be an A, right? 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?

[41:11] Okay. You can only turn around this much, huh? Okay. If every odd number is a number, some numbers must be odd number, right? But they don't have to all be, right? Okay. So you can't turn around. They say that the universal affirmative converts partially, right? Huh? But it doesn't convert simply. Doesn't keep its. Loses power, right? Okay. But now the universal negative here, huh? Can you turn that around?

[41:42] Yeah. Now how do we 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?

[42:08] Well, 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.

[42:24] And now if some A is a B, that's possible. Let's give that A that is a B a name. Let us call the A that is a B. Let's call it X.

[42:53] Now X is both. 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? But and that contradicts this.

[43:17] And why did we get into that terrible situation contradicting what we started off with? Because we didn't admit. But I say it had to be so, right? If you admit even one single A could be a B when no B is 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.

[43:44] And therefore, there's some B, even by name X, that is an A. And that contradicts no B is A, right? So the universal negative converts and keeps its universality It converts simply, right? So as far as conversion is concerned, the universal negative is more useful, right? Than the universal affirmative, right? That's why you get more what universal negative conclusions. Yeah. Yeah. Yeah. Now, in the second figure,

[44:25] there is Aristotle calls the syllogisms in the second figure he calls them imperfect, Tom, because you have to convert to see that it does follow necessarily, right? And he calls the syllogisms in the first figure perfect, right? Because the set of all or the set of none applies to it just as it stands, right? It's very clear, right? But when you convert in the second figure, you end up in the first figure again.

[44:53] Lo and behold, by magic, it has its hinges. Okay. So, on the second figure, the middle term is the predicate caseus. So you have no A is B and every C is B. Now, the set of none doesn't apply to us now, stands, right? You do have universal negative, but you have to have something coming under the subject of that. Nothing is said to be an A.

[45:30] Oh, I give up. But you forgot it. We learned about conversion. Yeah. You can convert universal negative, and it doesn't lose power. It remains universal. Wow. So you make this conversion,

[45:47] bring this over, and lo and behold, you are in the first what figure? That second figure. And since no B is an A, whatever is a B is not an A. Whatever C is a B, therefore no C is an A.

[46:15] Now, you wouldn't expect you to get a universal negative from two universal affirmatives in the second figure, would you? No. You can't even get the universal affirmative, right, to that. Yeah. Don't you expect anything but two universal negatives?

[46:38] Two universal negatives. Yeah. Could you get could give you a negative? Well, stop and think here now. If no A is B and no C is

[46:57] B, what? You can convert the first one. Now, the way we were showing, the way you showed that this is invalid, right, is that just to find examples for A, B, and C, right? It satisfies 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,

[47:30] and one example where no C is A. Now the example where every C is an A, that's true once. Can any negative be true then? So then, no negative conclusion is true always, right?

[47:52] And therefore, is any one necessary? Can something be necessarily so if it isn't always so? I say two is necessarily half of four, right? It's got to be always so, right?

[48:10] But a man is black. Is that that's a man? I'm a racist. so I say a man is white, right? But is man always white? Is man necessarily white? Okay. Well, he's necessarily black, right? Well, no. Not every man is white. So if man is necessarily white, every man would be white. If man is necessarily black, every man would be black.

[48:42] But every three is half of six, right? It isn't necessarily half of six, right? Okay. So we're taking last class examples for A, B, and C. Can you think of an A and a B such that no A is a B? Well, it's not too hard to think, right? You can take what?

[49:11] Dog. Let's take an example. Animal, right? And we'll take for a tree, we'll say what? Tree. So no animal is a tree, right? Now I got to find two examples for C, where neither one is a tree, but one is always an animal and one is never a what? Animal. Can you think of something that is never a tree, but is always an animal? Oh, gee, very good, very good.

[49:53] Now can you think of an example of something that is never a tree, but never an animal either? Stone. Stone, okay. Now to make sure I make no stupid mistakes, you just check your your work, right? Have I satisfied the two conditions? Are these examples, when they're substituted in to that form, do you have true statements? Because you want to make sure that you have good matter.

[50:24] There's no problem matter. Just nothing follows. That's all. Okay. So no animal is a tree. No A is B. No animal is a tree. Yeah. Okay. No C is a B. No dog is a tree. No stone is a tree. I have satisfied condition number one. These statements are true when you put these examples in, right? Now, do I have the second condition? Do I have one example where every C is an A?

[51:01] Yeah. Dog. And I just told you a simple one that is every C is A, right? And you have one example where no C is A. Okay. Yeah, it's underlined that word stone, right? Okay. And what does that prove? Well, if even once the universal affirmative is true, then once any negative is false, right? It's false that no dog is an animal. It's false that some dog is not an animal, right?

[51:39] So no negative conclusion is what always true, and none is always true. No negative conclusion is necessarily true, right? Now I have one example where no stone is an animal,

[51:56] and can any affirmative be true in that case? Going to be true always, any? No, because if no stone is an animal, you have one example where universal affirmative is false. Every stone is an animal, and particular affirmative is false. Some stone is not. an animal. So this knocks out any affirmative statement as being true always. This knocks out any negative statement as being what true always.

[52:27] Together, they knock out any conclusion. It's got to be affirmative or negative, right? Because none that's always so. Because there's nothing that's necessarily so, right? So,

[52:42] okay, it's gone right now. Okay. So we don't have a syllogism here. We don't have one here. What about the other one that has universal negative and a universal affirmative but reversed here, right? You know, universal negative below and the universal affirmative above, right? Okay.

[53:11] You have every A is B. No C is B, right? Okay. Now, is any conclusion necessarily the C is a subject and the A is a predicate?

[53:31] Well, I'm not going to fiddle around with this thing because I know you can't convert these and keep the result. You're just going to lose power right now. But let's move this one over, and we get no B is C, right?

[53:46] And move this down here, and you get every A is B. Now, if no B is C and every A is B, right? Then no A is what? Yeah.

[54:07] But I didn't ask any conclusion with A as a subject and C is a predicate. Is anyone who C is a subject and A is a predicate. But I can convert again. See, why? Because that converts to no C is A.

[54:26] So I've got another way. I'd be right. I have to convert twice to see the necessity, right? So now I got what? Two ways in the second figure of concluding, right? That no C is A, right? This form here and this form here. But here I have to convert once to see that something does follow, right? Here I got to convert twice, right?

[55:02] But now, so there's one way of concluding universal affirmative, but three ways of concluding a universal what? Negative. Okay, but let's look at the third figure.

[55:17] My math teacher in freshman college, right? Had blackboards all around the room, and he worked all the way around. Probably falling around the room. So you're just looking at being a blackboard, you see. Okay.

[55:41] Now in the third figure, you have two universal affirmatives. The what? Middle term is the what? Subject Subject in bold, right? Every B is A, and every B is C.

[56:09] I got a universal affirmative here. Every B is A. But is anything said to be a B? Not yet. Okay. Um. How could I get something to be said to be a B? Yeah, I could convert this, but it what? Loses power, right? It drops to some C is B.

[56:43] Now if every B is an A, then whatever is a B must be an A, by the set of all. You're told only that some C is B. So all you can conclude from two universal affirmatives in the third figure is what? Some C is Some C is A.

[57:05] If you can't get a universal affirmative conclusion from two universal premises, how the hell are you going to get it from the other ones, right? We could go through all sixteen of them, but I mean. Okay, so I can get a good We could go through all sixteen of them So all you can get in the third figure. You'll find out it's what particular. Particulars, yeah. Now let's take another example here.

[57:29] No b is a, and every c, excuse me, every b is what c, right? Okay. Well, you're going to try from the sudden done. If no b is an a, whatever is a b is not an a. But you're not told here that anything is a b, are you? But you can convert the inverse affirmative, right? But it what loses power, right? So you get some c is b.

[58:15] No b is a. Now no b is an a, whatever is a A, but you're told only that some C is B, right? So the conclusion is that some C is what? Is not A.

[58:36] You can't get a universal conclusion there, right? You can get a what? Particular, right? So Aristotle called these three figures the first, second, and third, right? Because the first figure is more powerful than the second, because it can do both universal affirmative and universal negative, right? The second figure can do only universal negatives, right? Among universal conclusions. The third figure can't even do any universals, just particulars, right?

[59:11] And because when you convert, you get back into the first figure, right? So let's let's manifest, right? Now if you have the reverse of this here, you have

[59:29] every B is A and no B is C. Well, you can't try it for the set of all, because the set of all requires two affirmatives, right? How about the no B is C? Nothing's said to be a B, right? So you can what? Convert. You can turn this around and say some A is B at all. You only get part there. You lose power, right? Some A is B.

[1:00:12] No B is what? C. So you get some A is not C. But you can't get a conclusion. that. C is a subject, A is a predicate, because you can't convert the particular what? Negative, right? So all you get is particular conclusions there. What about

[1:00:34] no B is A and no B is C? Okay, well, two negatives. I say to the kids, you know, if your parents are both negative, you won't have any children. Yeah, no problem. Yeah.

[1:00:55] Well, you can't get the set of none out of these two because set of none requires one affirmative, right? Set of none is that if no B is A, then whatever is a B is not an A, right? So you got to have something affirmative. But we showed it's invalid by finding examples for A, B, and C. It satisfies the two conditions, and when you substitute them into this form, the premises are true, so there's no difficulty in the matter, right?

[1:01:29] Well, in one case, you have one example where every C is A, which knocks out any negative as being true always, and therefore any negative as being true necessarily. And then one example where no C is A, which knocks out any affirmative. So can you think of an example for A and B such that no B is A? Well, take animal and stone, say. No stone is an animal.

[1:02:00] Can you think of something that is that a stone is not, but that is always an animal? Dog, yeah, that's not too hard. We'll circle that, right? You think of something that is not a what?

[1:02:19] It's not a stone nor an animal. Tree. Okay. Now I'm kind of stupid sometimes. I make stupid mistakes. So let's check and see if we satisfy both conditions. No B is A. No stone is an animal. That's true. No B is C. No stone is a dog. True. No stone is a tree. I have satisfied condition number one, but the second condition I gotta satisfy. I have one example of C and A where every C is an A.

[1:02:59] Yeah, one circled here. That knocks out any negative as being always the case, and therefore none of them are necessarily the case, right? I have one example where no C is A. Yeah. And that knocks out any affirmative as being always so.

[1:03:20] Now, so I'm using kind of the if then syllogism, right, and saying if something follows necessarily, then it's always so, right? But nothing is always so, therefore nothing follows necessarily. So I love that if then syllogism, right? I'm so happy when I see that. I think of Augustine's word out of those words. you know God made us for Himself, and our hearts are restless until they rest in thee But you can make an if then statement out of it He made us for Himself our hearts are restless until they rest in Him.

[1:03:57] Okay. So you find out there's a reason why Aristotle calls him the first, the second, and the third figure, right? If it's valid in the first figure, the set of all and the set of none will apply to just as it stands. The second figure and the third figure, you can see something following necessarily by what Conversion. conversion? Yeah, and so it's not just obvious, right? And when you convert, you get back to the first figure, right?

[1:04:33] So the first figure, rightly is placed first. But then you also find out in the first figure you can have universal affirmative and universal negative conclusions. But in the second figure, you can have only what negative conclusions, and the third figure, it can only have particular conclusions, right? It was a falling off, right? So you, you know, Aristotle before and after you have to say that, right?

[1:05:00] And like Shakespeare, Shakespeare said, right? He's somebody who could look before and after, could see the before and after, you know. See this, huh? And notice, huh, You couldn't prove by examples that a form is valid, right?

[1:05:27] Because that'd be like trying to prove by induction, right? Something isn't so just enough. Okay. Because examples wouldn't even show that it's always so, right? No, not necessarily so, right? One black man can disprove this racist who says that all men are white. You know, man is necessarily white. What a little boy he met on the sidewalk. that little boy from from uh, Watertown, Minnesota, right? You know.

[1:06:03] They had one priest in town, right? That's all they had. of course. You know. Mother would tell me, they bring Father Reed over to uh, a house there on Christmas Eve, you know, and so on.