Introduction to Philosophy & Logic (1999)
32. Form and Matter of the Syllogism: Either-Or and If-Then Syllogisms, Right Opinion, and Proportion
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[0:00] So we all have this one here, which begins the syllogism and form and matter. of the syllogism. Now, the syllogism, as you recall, is a argument or speech, you could say, in which some statement

[0:18] another follows necessarily because of those laid down, and these are statements now that are laid down by reason and laid down implies that they are at rest in a sense in the mind in a firm way, like in laying down the law, as we were saying last time, firmness and looking forward, you might say, to a conclusion. Right? They're being ordered to a conclusion. The Greek word for premise, you know, is more explicit than the English word.

[0:50] Huh? It has the idea of stretching forward, right? Of course, the premises do stretch forward to the conclusion. Now, Albert the Great sometimes says that syllogism is the main subject of logic, because the logic of the first act is ordered to the second act, the second act is ordered to the third act, and the syllogism is the chief argument and the third act. is the chief tool there of reasoning, and it's kind of the measure of the other arguments because it's the only argument in which the conclusion follows necessarily when the premises have been laid down.

[1:33] Now, the distinction here between the form and the matter of a syllogism—sometimes we make a distinction, but mainly here on syllogism between formal logic and material logic, but they're really on science. But in the one case, you're looking at whether the conclusion does or does not follow, right? And that's what the formal logic is about. While the material logic is concerned as to whether the premises are in themselves necessarily true or only probable, right, or in some cases even false, right?

[2:12] Now, when we do the formal logic, we we use letters, and I know from experience, especially if I have female students in the class, everything was fine until we started using these letters.

[2:27] And this is actually, you know, not that difficult, but you could even, you know, back in the life of the second act, you could sort of consider the form of the statement, right? Universal affirmative, or particular affirmative, or universal negative, or what? Particular negative, right? You could consider that form apart from what B and A are, right? Whether the predicate is being said universally or denied universally, or being said of some or not of some, and so on.

[3:09] And you could see that these two statements here, regardless of what B and A are, so long as you have the same thing as B and the same thing as A, the statement "Every B is A" and "Some B is not A," we could see that those statements are opposed such that, regardless of what B and A are, one of them must be true and the other false.

[3:33] They can't both be true. They can't both be false, right? You can see that from the form, right? And the reason why it's, in a sense, useful to sort of abstract the form from the matter is that that form can be found in infinity of places. huh? And once you see how these two statements in the form are opposed. It makes no difference what you substitute for B; it's the same thing here and here, and for A here and here.

[4:03] they'll always be opposed such that one is true and the other false. They can't both be true. They can't both be false. They're always two halves of a contradiction, right? In the same way, for no B is A and some B is A, right? You're kind of abstracting from what exactly B is or what A is, right? But if B here stands for the same thing and A for the same thing, then these statements are opposed, and opposed in the way we speak of contradictions.

[4:34] They can't both be true. They can't both be false. False, One must be true. One must be false, regardless of which you, whether you know which is which, right? Okay. And so you can get somewhere just from seeing something just from the form, right? Or you might see that these two statements cannot both be true. They could both be false, or one could be true and the other false.

[5:01] It doesn't matter which one is. But they're both false. Like every man is sitting, no man is sitting, and both false. But every man is an animal and no man is an animal. Well, this is true. That's false. Where no man is a stone is true, and every man is a stone is false. But without getting into the matter itself, you can see that these two statements can't both be true.

[5:22] They might both be false, or one might be true and the other false. And with these two statements here, they can't both be what false, but they could both be true, or one could be true and the other false. Okay. So you can get somewhere on the form alone, right? Certain things. And so you've got to find in speech an infinity of statements in these forms, right?

[5:47] Anytime you have a different subject and predicate, you can have these the universal, that is to say, right? So B has. Of the universal, right? But to talk about universal statements, the universal subject. So even in the second act, you can talk a little bit about form as distinguishing or abstracting from the matter. You see that? Okay. This is

[6:18] more important when you get into the logic of the third act. Now we distinguish sometimes three syllogisms, although what we call the simple syllogism in the text here, they call sometimes the categorical syllogism. Aristotle just calls that the syllogism, and then he speaks of hypothetical syllogism. and he might speak of the disjunctive syllogism, right? Or the if-then and the either-or syllogism. We're going to start with the either-or syllogism, right?

[6:52] And I think you can multiply the forms of this by how many members there are in either-or disjunction, right? Basically, is really just two things you do. For an affirmative conclusion, you're going to eliminate all but what? One of the possibilities. And for a negative conclusion, you're going to eliminate what? All the possibilities. Let's begin with the simplest case here, just two members, right? Okay. So you might have X

[7:34] is either A or B. And notice in that case you don't know whether X is A or B, but you know that X is either A or B.

[7:53] And then you eliminate one of these two possibilities. Let's say we find out that X is not B. Then we could conclude that X must be what? A. That's kind of common sense, right? No big deal.

[8:16] Now notice that your conclusion here, I mean the subject of your conclusion, is the subject in the either-or statement. And you eliminate all but one possibility. Now if there's just two possibilities, then you need only one other statement, right? If you had three possibilities, X is either A or B or C. You know it's one of those three, but you don't know which one it is, right?

[8:50] They're going to have to eliminate what two? Yeah, that's just common sense, right? No big deal, right? They say. So you might say X is not B. X is not C. So you might have more than two statements in an either-or syllogism, depending upon how many terms of disjunction you have, and so on.

[9:19] Whereas in regular syllogisms, simple or categorical syllogisms, we always have just two premises. In either-or, you just have the if-then, excuse me, the if-then syllogism, only two statements: the if-then statement and

[9:34] another statement. So, take an example there. We're taking the sixth theorem there in Book 1 of Euclid, and Euclid is talking about in a triangle, if the angles at the base are equal, he wants to prove that these two straight lines are what equal. Well, he can see that those two straight lines, like any two straight lines, must be either equal or what unequal, right? There's no other possibility.

[10:01] In that case, it's only two. And then, by a separate argument, which is also syllogism, but syllogism and if-then syllogism, we'll see, he eliminates the possibility of these two lines being what unequal. He does so because if they're unequal, he could cut off the longer one. Let's say this is the longer one, one equal to the lesser one, and then draw a line across like that. Then you have two triangles: this triangle and this triangle.

[10:33] Two triangles that have an equal angle contained by equal sides, and therefore they have to be equal, right? And the part therefore is equal to the whole. That makes it equal, a lesser, as he says, to the greater. So he shows that X cannot be B. Well, then it must be what A? Okay. You see that? If you had more than this, it'd be a little more complicated.

[10:57] You'd have to have an argument or reason for denying two of them, right? Okay. Is that clear enough? Okay. Now, the negative, your conclusion, the subject of your conclusion, is not the subject of neither-or statement, but something else, right? Let's say that's called Y. We'll say Y is either A or B. There's only two possibilities.

[11:36] In this case, now what you do is eliminate all of the possibilities, right? Right here, you eliminate all but what? One. Because you eliminate all the possibilities, so you say X is not A. X is not what? B. And you conclude what? Y.

[12:09] Well, X is not Y. See, if X were a Y, it'd have to be either an A or B, because every Y is either an A or B. But X is neither an A nor a B, therefore X is not what? Y. Okay.

[12:28] Now notice, huh? The difference between this and this, right? One difference was that here you eliminate all but one possibility. Here, eliminate all, right? Here, the subject of conclusion is also the subject of the either-or statement. Here, it's not, right? But the subject of the either-or statement is the predicate of the conclusion, huh? Why here the predicate is like, the remaining alternative, right? Okay. That's kind of common sense, but you know, instead of stopping, see what you're saying, right?

[13:07] Okay. You give an example of this syllogism, right? I'll take a theological example, huh? You know how Thomas, when he takes up an article in the Summa, there he gives objections against, okay? And there'll be some advancing objection because they're opposed to the truth, right? But you can still have a syllogism, right? So when he asks, example, our faith, hope, and charity virtues, he takes the statement that every virtue is either a moral virtue or an intellectual virtue.

[13:41] Aristotle divides the virtues of man into the moral virtues and the intellectual virtues. And then he points out that faith, hope, and charity is not among the moral virtues. They go through the moral virtues, right? And you come back and I think, it's not among the intellectual virtues. Therefore, faith, hope, and, charity are not virtues. Virtues, yeah. That's the form of syllogism, right? Eliminating all the possibilities.

[14:10] And now Thomas is defining that and point out that these are the natural virtues, right? Since they're acquired by natural powers, but these other ones are built on grace and so on, right? Okay. But notice the form of the argument is in this one we have right here. Now I mentioned how in the Summa Contra Gentiles when he shows that no name is said univocally of God and creatures, right?

[14:41] There he has a five-part disjunction, right? He's saying every name said univocally of many things is either their genus, or their difference, or their species, or their property, or their accident, right? Okay. He's taking that distinction of the five names goes back to Porphyry, right? Made explicit in the Isagoge as being a complete, right, division of name said univocally of many things. If you follow that part of the course, you'd see yes, that is complete, right?

[15:18] Okay. Now he then goes on and shows that no name can be a genus said of God and creatures, and then he shows that no name can be a difference, and no name can be a species, no name can be a property, an accident. Separate arguments for each of those, right? But the main argument is saying they can't have a genus, they can't have a difference, they can't have a species in common, they can't have a property, they can't have an accident.

[15:43] Therefore, what? No name, right? Said univocally of many things. No name is said of God and creatures who said what univocally. Said univocally of many things, no name is said of God, univocally of many things, no name is said of God, univocally of many things, no name is said of Right. Okay. So in that case, you eliminate all possibilities, right? Okay. You see that?

[16:07] So one thing that's curious too, in the second and the negative form, you have to introduce a second. Yeah, another term. Yeah. Yeah. Yeah. You see, we do this. As I say, it's almost common sense, and when you stop and try to express it, you have to stop and think, you know. But we do it almost automatically, right? I mean, you know, maybe at school, you know, and what night can we get together say, well, I can't be here on Sunday, you know.

[16:36] Oh, I get a class on Monday. You know, Tuesday I, you know, play poker or something. Yeah. Now, if you eliminate every day, but let's say Wednesday, you might conclude, well, I get back to our meeting on what Wednesday, right? Now, this is common thing all the time, and people are saying, you know, well, you know, but that means can we meet for a departmental meeting or something like that, right?

[16:56] Sure. And I can't come on Tuesday because I'm up here, say. Okay. And someone else can't come on Monday or whatever, you know. So you might, you know, eliminate all the possibilities, but what? Um. I happen to quote that statement of Sherlock Holmes right now. Ah. When all the possibilities but one have been eliminated. Ah. The one that remains, he says, no matter how strange, must be it, right?

[17:22] Yeah. You might have, for example, three people who could have murdered so and so, right, in the detective thing. And we have a reason why this person couldn't have done it. It's an alibi, you know, some reason. And the reason why that person couldn't, then the third person, strange as it may seem, is highly respectable person or something, right? Must be the what? The murder. Strange as it may what?

[17:46] Be right. Yeah. We've all the other possibilities, but this one has been what eliminated, right? Mm. But notice again how the difference between formal logic, material logic. If I say either Joe or Tom or Paul committed the murder, and Joe and Tom have alibis that can't shade, right? Then must have been Paul, right? But if I don't have all the possibilities, right? Yeah. And you know, someone else could have murdered him.

[18:13] They don't know about it. Yeah. And only Powell was one of these three. Yeah. Well, then you can go to prison, right, or worse, because of what? The either-or argument, right? Ah. That's a common thing, right? Mm. Okay.

[18:32] So you can see how the either-or argument. The problem is not so much in the form, but the problem isn't having a what? Complete division, right? Now it's easy to see that every straight line. Let's say any two straight lines are either equal or unequal, and that's the impossibility, right? Or it might be easy to see that every triangle is either. You know, equilateral, or isosceles or scalene, right?

[18:55] But that every name said univocally of many things is either a genus, a difference, a species, a proper accident. Someone who does not, you know, learn the doctrine of Isagoge, right? Wouldn't know that, right? Okay.

[19:12] So, when Thomas is is showing that that in theology the Father is not before the Son, eliminates all the senses and this one thing can be said to be before another, right? Basically, what we see in the categories, right? And therefore, in no way is the Father before the Son, right? I guess it's in the Athanasian Creed. The Athanasian Creed, you can find that in the official collection there, the Creed at the end of the Creed and so on.

[19:46] But there, it's explicit that there's no before and after in the Trinity. But it's hard to see that I've eliminated every, you know, kind of before and after, right? So the problem, you know, is more one of material logic, right, the difficulty, right, than a formal logic, right? But these same forms you can repeat them again and again, right? Okay. You could maybe argue in one place that every number is either odd or even.

[20:17] And he gives a reason why this number can't be even. Therefore, it must be what odd. So you can use that same form is infinite possible places where you might use that, right? Okay. Any question on the on the negative conclusion there? When I said Y is not X. Now, I guess because of the formal logic, you say, well, it follows this particular form. Is there a case if if you were to say, well, Y is not X, where

[20:52] I don't know if there'd ever be a distortion? in the logic there? I mean, because I just think of it as mathematically... We'll come to that question when you can turn a statement around, right? And you have to do that when you take up the second and third figure of the regular syllogism. You have to talk about when, or to what extent, a statement is convertible, right? We'll go through that, right?

[21:12] But we'll go through it again using letters, right? That's kind of interesting, right? It's so interesting. For example, that Aristotle will show that if no B is A is true,

[21:27] no A is B is also true. He's going to show that when this is true, this is always true. That's kind of amazing the way he does this. And we'll see because there's an infinity, right, of possible statements, right, in the form "No B is A" that are true, right. You can't possibly look at an infinity of statements and see in every case the reverse is true, right?

[21:54] So how does he show that every time "No B is A" is true, whatever B and A are, so long as it's true that "No B is A," it's going to be true that "No A is B." How does he show that? He's going to use letters, right? He's going to show that it must be so. It's an amazing thing, right? He's showing for infinity of possible statements, right, an infinity of universal negative statements that are true.

[22:21] Their converse, right, are also necessarily true. He's going to show, you know, this is not true for every B is A. The reverse is true for A is B necessarily, right? We'll take up that conversion, right?

[22:39] Here you can just see the difference between, you know, the way you reason to an affirmative and to a negative statement from an either-or statement, right? You see the differences between the two now? Would you say that you'd have a form to a negative, or why wouldn't you say "X is either A or B"? X is A, therefore X is not B. Yeah, but the same thing.

[23:04] I don't just. Just. Yeah, it is. No difference. Yeah. But the main point is that you eliminate all but one and conclude affirmatively to many, right? But then you have to know in your first statement that X is going to be one of those possibilities, right?

[23:32] So no question about that, right? Easy enough, huh? Now the it's then is is is far more important. People are very easily deceived with this one. I'm going to speak of four forms of if-then speech, but as you'll see, only two of these forms are syllogism, and only two of them does something follow necessarily. In the other two cases, nothing follows necessarily. So,

[24:19] here we're going to use the letters to represent what the simple statements that are put together. So we'll say if A is so, then B is so. Where A represents a simple statement, right? And B another simple statement that follows from that first one.

[24:46] Now it's going to have that same form in all of these. Now the simple statement in the if part they call that in logic the antecedent. It's a name they give to it, and I guess ante means what? Before. The ante room, the house, right? And the simple statement in the B part they call that the consequent, which at least for the second part there is the one that follows, right?

[25:44] Now one thing you notice in the if-then syllogism and in the either-or syllogism, it's only a or syllogism it's only a First premise that is a compound statement, either or statement, or an if-then statement. The second statement, or in some cases there might be more either or. The second statement or statements will always be simple statements, right? And the conclusion will also be a simple statement, right?

[26:14] And the reason for that goes back to what truth means in these. We want to know the way things are, right? What is so and what is not so in reality? And it's only in a simple statement that you have the truth about things. And you know, if I go to the courtroom, I say, "Now, if

[26:35] John murdered so and so, then John should be punished." Okay. But you want to know whether John did murder so and so, right? Whether John should be punished, right? Of course, if John murdered so and so, then he should be what punished, right? But did he in fact murder so and so, right? And therefore, should he in fact be punished, right? Okay. So you want to get back to that fundamental meaning of truth, right?

[27:01] Okay. So there's four possibilities. Sometimes we look at the antecedent to find out whether it is or is not so, right? And sometimes we look at the consequence to see if it is or is not so, right?

[27:23] Now, when we look at the antecedent to see if it is or is not so, we might find out that in fact it is so,

[27:33] okay? Or we might find out that A is what, That's right. Yeah? Either A is so or A is not so, Back in the door, right? Okay.

[27:47] And now, from the form of the speech you have now, the question is: Does anything follow necessarily from having laid down these two statements, or having laid down these two statements? Does anything follow necessarily about B, right? Okay. When I do this in logic, I'll, in the class, I'll put these four forms, you know, separately across the board. I'll get four students. especially when they'll look too bright.

[28:16] I get the form from the department and I'll say, "Now, if anything follows necessarily, right under the line but follows necessarily. If nothing follows necessarily, right invalid under the line, right? And I know from experience, I'm from teaching logic for years, that I can hardly ever get four students up at the board without some of them thinking that something follows necessarily when it doesn't, or thinking it doesn't follow when it does, right?

[28:50] And sometimes they got all four wrong. That would be wonderful, right? I mean, the point you want to make is you're in serious. Difficulty, right? If you think something follows necessarily when it doesn't, because now you're going to be thinking something is true, right? When it isn't. Or if you think something doesn't follow when it does, you're going to miss out on knowing something you couldn't know, right?

[29:14] So you are in deep, deep trouble, right? You are, you are, you are, you are really need logic, right? Then I go through the forms, explain which ones are syllogisms and which ones are not, and why, and so on. And then when they say they all see it, then I say, now something's gonna get wrong in the final exam. And experience is played with that, right? Teach your logic.

[29:39] Somebody, and numbers, will get some of these wrong, right? Even though we've gone through them, right? It shows you how apt human mind is to make a mistake. In the second book about the soul, there Aristotle talks about the early Greeks and they tried to explain how it is that men and the other animals know, but they did not explain how men and the other animals are deceived.

[30:06] And Aristotle says their consideration was not complete, right? In fact, animals and men seem to be more deceived than knowing the truth. So that to want to explain what takes place in men, they should be explaining why make these mistakes. Okay. Now, likewise, this other way of arguing over here.

[30:28] Sometimes they look at the consequent, and we might find out that it is so, right? Or the other possibility, we might find out that B is not so.

[30:42] Now the question is, must you say anything necessarily about A from having laid down these two? A is so, B is so, B is so. or. From having laid down these, if A is so, then B is so, B is not so, right?

[31:06] Well, one of these forms is really obvious, and that is which form? To think that accurately, right? In sociology, you might actually have very vague predictions, right?

[31:28] Of course, the scientists will say that a theory is more interesting when it predicts things that we didn't even know existed, and they find out later on that they do exist, right? Heisenberg went to England there and conferred with Dirac, who was a super mathematician and so on. And Dirac worked out some kind of mathematical theory and ended up with a negative electron coming out of his theory, right?

[31:56] These equations, talking about negative electron, ain't no such animal. And then some time later, they discovered in experiments the positron, right, which had the same mass, I guess, as electron, but the opposite charge, right? Here's a kind of particle that nobody knew existed, right? But it came out of the mathematics of Dirac.

[32:18] So it's strange, right? But in terms of the form of speech in which you confirm the hypothesis, right? If A is so, if hypothesis H is so, then P is so, right? P is so, it doesn't follow necessarily that H is so. It's not a syllogism. Some weakness there.

[32:54] Kind of syllogism I used earlier when we're showing that not every genus has a genus above it, but that there are highest genera. Do you use the hypothetical syllogism? Yeah. Or not?

[33:23] If every genus has a genus above it, there would never be most universal names, right? Okay. But there are most universal names, right? Like being and something, right?

[33:38] Therefore, you could have either or if you wanted to. First, you could say either every genus is a species, that's one way of stating it. or there's a genus that's not a species, right? Or another way of stating it: either every genus has a genus above it, or not. There's genus or genera that don't have anything above them, right? Have you one or the other, right? Now, we're limiting one of the possibilities: that every genus has a genus above it, right?

[34:14] That every genus is a species of a higher genus, right? I say now, what follows from that? That would what? recognize it's false, right? What would follow from it is that there would be no most universal name, because the genus is always said of more than a species. So, if every genus has a genus above it, there's always a name said of more than any name. But how can there be something said of more than being or something?

[34:45] Could there be something that isn't something. Could there be something that isn't a being? Well, there it is, has to be. So the fact that you've come to most universal names means that you're denying the consequent, right? of every genus having a genus above it, right?

[35:05] You might also argue, you know, that if every genus has a genus before it, then every definition has a definition before it, right? And therefore, we know nothing by definition, right?

[35:23] So we use these forms without maybe recognizing that we're using them, right? And you know, you wonder when when they call Aristotle the father of logic, right? He's the first man to think out the basic parts of logic. And but now when you see Socrates, you know reasoning that way, right? Say, well, he uses the two forms of if-then speech that are syllogisms, right? He avoids the other forms.

[35:55] Does he know that explicitly, or did he just? Doesn't go the other way, right? There seems to be, you know, men must have reasoned to some extent. Before they reflected upon what they're doing, right? And you'll see in the dialogues, Plato, you know, you won't see the explicit definition of syllogism, you know, but Socrates will say, "Well, now if these things are so, then isn't this necessarily so?"

[36:26] And someone will say, "Yeah, I guess so," you know. But you anticipate in the definition of syllogism, right? You know, these things being so, then this must be so. Then, yeah, I guess so. Yeah. And we'll do that in daily speech, right? And the philosopher comes back, but often in daily speech too, we're deceived. We have to stop and understand these things, right?

[37:01] Later on, there, Socrates, you know, mind can't rest in contradiction, right? So you've got virtue can be taught, which cannot be taught, right? It can't both be true, can it? Okay. So now Socrates says, "Well, it can't both be true. There must be a defect in one of the arguments, right?" Okay. Now I mentioned how in another dialogue with Protagoras he questions this second premise here. There are no teachers of virtue, right?

[37:41] Because your mother and your father were giving you little lessons in justice, weren't they? Right. And the example I always give you know, children, you'll find that you maybe did yourself or you find your own children who are in the store and they'll take a piece of candy, right, from the count, from the sting without paying for it, right? And the mother and father you must put the kid back to the store.

[38:03] You have to give it back to the clerk, right? And it makes a great impression upon the kid, right? You know, you know, he doesn't think that's eating it yet, right? So that's a little lesson in what? In justice, right? Yeah. Okay. And you get a box of candy for birthday for grandma or for mom, so and so, and well, stuff is. And the mother says, "Now you've had enough for today, right?

[38:27] Put away. We'll have some more tomorrow." That's a lesson in what? Temperance. Yeah. Moderation, right? Okay. But Socrates doesn't, you know, point it out in this dialogue, right? Okay. And what's marvelous about the dialogues is that they observe this aspect of our mind that we see a part of the truth before the whole truth. You see, you know, part of the truth in this dialogue, maybe another dialogue, another part of the truth, right?

[38:55] And we'll put it all together, or Aristotle put together, we don't know, but we see the parts there, Plato, you know, and Aristotle. So

[39:08] Socrates comes back and. He thinks he sees a weakness here, in what, his second premise, right? But going back to the argument, that what directs us to the good

[39:28] is knowledge. He sees that statement is not necessarily true. Now, there's another possibility for directing someone to the good, and that is what is called right opinion. Right opinion. Opinion is not knowledge, right? An opinion may be true or false, but we're talking now about a true opinion, right? Now I always take a very simple example. I say, suppose you're going down the road here, you want to get to Boston, right?

[40:07] Okay, you come to the fork in the road. Okay, and one of these is being to Boston, the other one being to let's say Providence okay. You know, I'll vouch for the accuracy of this map here. Okay. Now I come to the fork in the road here, right? And I want to get to Boston. I assume it's good to go to Boston, right? Okay. Now, if I know that the right road here, I suppose the left one here, I know that's the right road, the correct one, right?

[40:38] I would take that one, right? And I get to Boston, right? Now suppose I get to that fork in the road and I don't know which is the one to take, but I think that this is the road to Boston. I don't know. I think it is. I'm going to take that road, right? In this case, I'm thinking correctly. I have the right opinion, right? But I don't know, right?

[41:01] Okay. So I'll get to Boston just as much as the man who what? No, right? Okay. Sometimes people, you know, they win the money in the lottery, right? Huh? And why do you play those numbers? It's kind of interesting, you know. Sometimes their their grandchildren's numbers are like that, right? But sometimes that number was showing up in their life somehow, right? Okay. So they had a hunch to play these numbers, right?

[41:27] And these numbers are the numbers that came in and now they want to buy some money, right? Okay. Now, if they had known that these numbers were going to win this Friday, then they would have played them and won some money, right? But having a hunch that these are the numbers to play also directed them to play those numbers, right? And they got just as wealthy as they would if they had known their numbers, right?

[41:53] Okay. So the right opinion, right, right thinking can get you to the good just as well as knowledge. So maybe the great men of Athens directed Athens to the good not by knowing what was good for Athens, but by having the right opinion as to. you see that comment there, right? They say that MacArthur's, you know, greatest military coup was the Inchon landing, right? Okay. I read many accounts of the Inchon landing, the planning for it, and so on.

[42:31] And uh, the Washington was ill disposed to this plan, Inchon landing, right? And they sent the chief of staff down to convince MacArthur not to do it. And they sent a top admiral down to convince him not to do it, right? The Navy can't do it, right? Okay. And then MacArthur you know, you're a very persuasive man, right? Yeah, I have more confidence in the Navy, sir.

[42:55] than You have, you know, he went on, he went on. And now it was a great thing what MacArthur did, right? And after the success of the Inchon landing, the troops down the beaches and so on, are being pushed to the sea, they saw the enemy just starting to weaken away, fade away, right, collapse. And you say, okay, now did MacArthur know that the Inchon Landing was going to succeed?

[43:22] Or did he think it was going to succeed, right? And thought correctly, You know, Because apparently the Inchon Landing is a very risky thing, right? And the tide, I mean, you read the description of the tides, and it's a very short amount of time you can come in, you know, and all kinds of things, right? And MacArthur had maybe, you know, they set a plan to withdraw, if they didn't succeed, you know, or little will be lost except my reputation he says, you know.

[43:50] And well, anyway, they finally allowed MacArthur to go ahead, right? Reluctantly, right? But then on the day he was going ahead with it, they sent a message he was on his own. They denied all their responsibility for it So the whole burden was on MacArthur And MacArthur you know, they call up his he's on the boat they're going, and he calls up his his subordinate. And he goes through the whole plan again, right?

[44:15] You know, that's something to do with Socrates, says right? And he sits down starts reading his Bible after that. And of course, it's a great success, right? What did MacArthur know he was going to succeed. Or he just had the hunch, the right? instinct, right? In any case. He led us to the good, right? Okay, you see that? So Socrates says maybe the great men of Athens led Athens to good things not by knowing, but by having the right opinion or right hunches, right?

[44:53] The right instincts, as they say. But you can't really teach somebody, you know, maybe the right opinion or the right instincts. So you can't teach them a hunch, right? See, so maybe that's what they had, right? Now Socrates, later on, he'll put this more formally. He'll say the great men of Athens led or directed Athens to the good either by knowledge or by what? Right opinion, right.

[45:23] And then he eliminates that they led them to it by knowledge because if they know, then they could have taught, right? But they couldn't teach. Therefore, they didn't know. That's the now the consequence and now the antecedent, right? But they also need to argue, right? Now he's concluding that they must have led the men, the city of Athens, to the good through what? Right opinion. So he's using the either or and again backing it up with the if then argument.

[45:59] So you can find in that passage all these kinds of syllogisms: either or, and if then, and even that first one they had. What contributes to the good is knowledge, virtue. What contributes to the good? The other great kind of syllogism. So men were syllogizing before Aristotle put out the art of syllogism. But sometimes, like an example, Melissus there, right? Melissus argues that if being had a beginning, it has an end.

[46:31] If being has no beginning, his reason for saying that, therefore, it has no end, right? So he's arguing from the form of if-then speech that is not a syllogism, and Aristotle points this out in the first book of Natural Hearing. But Melissus is arguing from the two that are what? That are syllogisms, son.

[46:52] Now, I try to, you know, when I teach students, I try to get them to be very much aware of these four forms of if-then speech, and and why two of them are what,

[47:05] and two are not, and two are valid. And the fact that one of these valid forms is what obvious, and through the obvious one, you show the form that is not obvious, right?

[47:19] But the form that is not obvious, in a way, you use that in showing the two ones that are not, right? Because that's the way we reason. The reason that if something is necessarily so, then it's always so, but it's not always so, as the examples show. Therefore, it's not necessarily so. You see that?

[47:48] So you're using the if-then syllogism that's not so obvious, the denial of the consequent, in order to see that we've really shown that those two forms are what invalid, right?

[48:04] So just just diagram it a little bit here. You take the obvious here, which is most known, that if A is so, then B is so. A is so, therefore B is so, right?

[48:31] I use that to show the not obvious form. If A is so, then B is so. B is not so, therefore A is not so. That's how we did that. We said either A is so or A is not so, right? And if A is so, then by the first case, B would have to be so, right? So if A is so, B is not so, and A is so, those three statements are not what compatible, are they?

[49:12] Because if A is so, then B is so, and A is so together contradict B is not so by the first case. So by the first case, we see that it's impossible that A is so and B is not so, and therefore it must be that A is not so and B is not so. Right. Then we come down to those other forms that are not syllogisms.

[49:38] If A is so, then B is so, and A is not so. And the other form, if A is so, B is so, B is so, right?

[50:00] Now to be complete, you have to show an example where it is not so, but just take the one where people are more actively deceived. They're apt to think that if A is not so, that B is not so, right? Now, if that is necessarily so, it would always be so. But it's not always so. For example, if I am a dog, then I am an animal.

[50:25] I am a not a dog, therefore I'm not an animal. So it isn't always so that B is not so, right? It might be so if I am a man and an animal.

[50:41] If I am a dog, I am a different animal. So I'm showing that since this is invalid, two examples. Why are examples enough? The examples show it isn't always so, and if it isn't always so, that shows it isn't necessarily so. In a way, I'm using this second form, right? If it's necessarily so, it's always so. But it isn't always so. Therefore, it isn't necessarily so. Now the same way over here, right?

[51:16] If A is so, T is so, B is so. If I am a dog, I am an animal. If I am a man, I am an animal. Might and not be so that D is so, right? So again, the examples show it's not always so, and there you deny the consequence of something being necessarily so. Therefore, you won't be necessarily so.

[51:39] Now sometimes, and you see this in Euclid. Sometimes you might have several of these syllogisms run together, right? You might say if A is so, B is so. If B is so, C is so. C is not so. Therefore, B is not so. Therefore, what? B is not so. But you just run together several syllogisms, That domino effect we used to talk about, right? Okay. But no matter how far you go down the line, if A is so, B is so, if B is so, C is so, if C is so, D is so, right?

[52:14] If you eventually reach something that is not so, then everything before that gets turned over, right? Okay. But that's just what you know what we call continuous syllogisms, right? then? It's like the domino theory, right? You knock over the last one, all the rest go over. The same way, if you're looking before, right? I have to start later on the alphabet. Let's say I want to show that D is so.

[52:44] I find out if C is so, then D is so. But I don't know that C is in fact so. But then I see that B is so, then C will be so. I don't know in fact B is so. But then if A is so, then B is so, and I do know that A is so. Therefore, B is so. Therefore, C is so. Therefore, D is so, right?

[53:02] Okay. I know you're looking before and after Shakespeare says, right? So you might keep on looking before until you get to something you know is so, right? And then you can syllogize right down the line. You might keep on looking afterwards until you come to something that is not so, right? In a sense, you've been doing that in that theorem you're talking about, right? If one of those two sides of the triangle, remember, where the angles were equal, if one of the sides is longer, then from the longer side you can cut off a what line equal to lesser.

[53:36] And if you can do that, then you can draw a line from that endpoint to the other, side. And if you have that, then you have two triangles, right? Which have equal angles, contained by equal sides. Therefore, they're equal, right? But they can't be equal, right? You might have several steps, right? Okay So as you go on, these theories you might have several steps you go through.

[53:58] you know This is so, that'll be so, this so this so. But if you're just repeating the same argument, the same kind of argument, I should say, right?

[54:09] We might not, you know, bother to make explicit the whole syllogism, right? If I say If A is so, B is so, if B is so, C is so. But A is so, therefore C is so. But I don't bother to say but B is so. It's an awful argument, but it's basically the same syllogism repeated several times. the same kind of syllogism. I call these syllogisms continuous, but the conclusion of one is a premise and the what?

[54:39] next one, right? If A is so, B is so. A is so, therefore B is so. If B is so, C is so. If B is so, by the previous argument, therefore C is so.

[54:52] Sometimes you get things so obvious you don't bother to spell it out, right? Just if A is so, B is so, B is so, C is so. but A is so, therefore C is so.

[55:02] But in fact, you're showing from A is so that B is in fact so, and from B is in fact so, and C is in fact so.

[55:32] Two declares clear So. Aristotle doesn't explicitly do this, does he? Well, he just sort of does. He talks about it very explicitly yeah There's not a book on the. a book on the a book on the hypothetical syllogism. right? He complicates it more than is necessary, right? Uh-huh. I think it's simple enough to consider four possibilities, right? And two of which are, two are not, right? But he'll maybe multiply it depending on the statements are what, affirmative or negative, right?

[56:09] Okay. But I say if you deny the consequent, you have to deny the. Excuse me. consequent is a term ator They can stay out there. Multiply these unnecessary complications. In dialectic, when you study the tools of dialectic, the fourth tool of dialectic is the tool of likeness, huh? And Aristotle says the mind is exercised more in seeing a

[56:53] likeness between things that are further apart, and seeing the likeness of ratios. Okay. Now, doing the first chapter in the first chapter in the Natural Hearing this morning, Aristotle is talking about how the confused is more known than the distinct, right? And he's talking about how when we taste a salad dressing or hear a symphony or see a painting, we don't distinguish the parts clearly at first.

[57:25] Then he makes a direct comparison between whole and part, in general and particular, right? Okay. And he's seeing a proportion there. He wants to show that the general is known before the particular, the more universal before the less universal. And he's showing that the whole is known before the parts.

[57:52] Well, he's saying that in a way, the general is the particular as the whole is to the what parts. And sometimes they call the the general the universal whole

[58:06] instead of its parts, rather than opposite, right? But the English word particular there obviously comes from the word part, right? So the particulars are like parts, right? And in Greek, there the word for general is katholou in Greek comes from the word kata. The katholou in Greek comes with the Greek word for whole kath' holou, according to the whole. They went together two words. So the Greek word for general is taken from the Greek word for whole, and the word particular here in English is taken from the word part, right?

[58:39] So the general, in a way, is the particular, like the whole is to the what parts, right? So you might reason then that if the whole is known before the parts, then the general is known before the what particular. Yeah, makes sense, right? Yeah.

[59:19] But we know that in fact the whole is known before the parts, right? When I taste the salad dressing the first time, I don't pick out the different ingredients, the herbs and so on. When I hear it simply the first time, I don't pick out the oboes and the clarinets and the violin and the viola and so on, right?

[59:55] When you study the regular syllogism, you'll see that you have three terms in a regular syllogism, like in the one we had there from the medieval era. And agree with what? What directs us to the good is knowledge, right? Virtue directs us to the good, therefore virtue is knowledge. Have one term used twice there, right? They call it middle term, right? But in a proportion, you have four terms, right?

[1:00:19] So you want to reason from a proportion. You put it in the form of a what? If then statement, right? You get four terms. I

[1:00:30] notice how the the mathematician will argue. Sometimes you'll see that x is to y as a is to b, okay? And they can form propositions that x is equal to y, then a is equal to b. If x is more than y, then a is more than b, right? We saw Shakespeare reason that way, right? In in the invitation to use reason, right? What kind of if then syllogism does Shakespeare present to the reader?

[1:01:02] What is a man if his chief good and market of his time be but to sleep and feed? A beast, no more, right? What is he saying? And then then you say he's not a beast. Yeah, but the original proportion is that the chief good of man is to man as the chief good of the beast is to the beast. Then, like in math, we alternate proportion. As the chief good of man is the chief good of the beast, so man is the beast.

[1:01:32] Then you say, if the chief good of man is no more than the chief good of the beast, meaning to sleep and feed, then man is no more than the beast. Well, we all know that man is more than the beast. If the man says he doesn't know that, we'll treat him like a beast and put him in a cage and so on. You know, he'll rave and rant and he's more than a beast, right?

[1:01:51] I think I am, You see, Okay. So notice what the way he's reasoning there, from the now to consequent, right? If the chief good of man is no more than chief good of the beast, then man is no more than the beast. But man is more than the beast, right? He denies the thing. In the second part of education, he points out that man has what he doesn't have, namely the ability to look before and after, ability to have discourse and so on.

[1:02:20] right? But notice, you could take some of these things and you could argue the other way around and say, if man is more than the beast, then the chief good of man is more than the chief good of the beast. But man is more than the beast, therefore the chief good of man is more than the chief good of the beast, right? Then you'd be using the first and the obvious form, right?

[1:02:46] Okay. But Shakespeare seems to be using there more the what the not obvious form, right? He's saying if the chief good of man is no more than the chief good of the beast, and man is no more than the beast, but you know that isn't true. Therefore, the chief good of man must be something more than sleep and feed. Shakespeare understands these things naturally. After he studied logic, he reasons very well.

[1:03:30] They argue to the purpose of man, we do this. huh? We use some time in this then argument. huh? We can use that for there.

[1:03:49] I'll say, what is to man as seeing is to the eye? What is to man as seeing is to the eye? Act. Yeah. See, if I ask you, what is to the ear? As seeing is to the eye, what would you say? Yeah. You take the act that characterizes the ear right? The peculiar, right? What is to man as seeing is to the eye? What's the act that involves reason in some way?

[1:04:29] Okay. Then you syllogize. For the more known, if seeing is the purpose of the eye, then the act of reason is the purpose of man. But everybody knows that, in fact, seeing is the purpose of the eye. Therefore, the act of reason must be the purpose of man.

[1:04:51] Or you come back and you say, "What is to man as seeing well is to the eye? What's the act with reason done well, right? So, if the purpose of the eye is not just to see but to see well, then the purpose of man must be the act of reason done well. And everybody knows the purpose of the eye is to see well, right? Because we wear glasses.

[1:05:17] Therefore, the purpose of man must be the act of reason done well. So we can syllogize. Then, so this is you can use the if then syllogism with four terms. You can't use the regular syllogism.

[1:05:35] And notice, you can always put you know the other form into the if then instead of saying. What do you say? If let's say three is odd, and what is odd is not even. Therefore, three is not even. You might say, if three is odd, then it's not even. If three is odd, then it's not even. You can put the thing with three terms into the if then syllogism, but four terms you can't put it in. The other form.

[1:06:15] But you couldn't be in the form. So it's a very common form, so it's good to know this, right? Now, next time we're going to go, I gotta run off here. Next time we're going to go into the, what, next group of reading? You have the next group of readings, right? Yes, sir. Yeah. It's called the form of the simple syllogism, but it's not so simple, right?

[1:06:36] Okay. And there, instead of four cases, if we want to be complete, we have to consider 48. Okay. Most of which I consider in this thing. All of them, you go through all of them, right? Okay. So we save, you know, the worst to last.

[1:06:57] Okay. That's part of the reason why I do it this way, right? So that the kind of obvious form, either or, and yet then there's a little more receptiveness on the cases, and then we go to the, the, uh... Does your schedule change, you still manage every week, or do you have... I can go, yeah, this stuff here, that's second nature to me now, you know. Yeah, okay.

[1:07:21] Brother Richard taught me logic when I was in high school, so I went to college, took the exam, and they gave me credit for the course, you know? Oh. So, done logic.

[1:07:34] Do it in my sleep. You know, our scripture there, you know, have to do it more, you know. I see. You know, that's why basically I needed 2 weeks