Introduction to Philosophy & Logic (1999)
Lecture 37: The Four Forms of Hypothetical Syllogism and Scientific Confirmation

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They say, if Berkowitz dropped dead last night, he would be absent from class today. He's absent from class today, therefore he dropped dead. They say, that's wishful thinking, isn't it? But it's not logical thinking. Now, in the experimental sciences, how do they confirm, or test for that matter, a hypothesis, right? Well, they say, if my hypothesis is correct, then such and such will take place, right? They make some kind of prediction of this sort, right? And if the prediction comes true, does that prove necessary that the hypothesis is correct? No. He's arguing the form I gave you, right? If Berkowitz dropped dead last night, he would be absent from class, right? Let's go and see if he's absent from class. Ah, he is absent from class! But that same conclusion could follow, that same effect could follow from his car breaking knowledge that he did the other day, and he didn't get up there, right? And so, okay. So you can't know it's necessarily that one, because it's about, right? Now, Einstein, in the, he said that, Newtonian physics, he said, predicted so many things that came true, that the scientists began to think it must, what, must be true, right? But from the very form of the confirmation, it never follows, what, necessarily that it is so, right? And Newtonian physics was kind of remarkable, the one that always sticks in my mind was, they say that when they were examining more closely the paths of the planets that they knew about, and the paths they followed weren't exactly what they should follow from Newtonian physics. Newtonian physics had been so successful, they said, there must be, what, other planets we don't know about that are interfering with the known planets, and their mathematics was so exact, they could predict where those planets would be, right? And sure enough, that's where they were. So by the time, or before Einstein, with the theory of relativity, some of the physicists said, this must be true, right? And then Einstein, with the theories of relativity, showed he could predict the same things that Newton predicted with a different theory, and in fact, predict some things that Newton could not predict, right? And then he says it became crystal clear that we never know here, right? No one's sense of being certain, right? But a scientific theory is, as he says, a system of guesses, right? But Pierre, I mean, Claude Bernard, even in the 19th century, one of the fathers of modern physiology said that doubt is always intrinsic to the experimental method, right? That a hypothesis, no matter how many times it's been tested, it can always be, what, tested again, right? Okay? It may always be, you know, the most possible thing to do at this point, right? But I mean, it might possibly, what, be contradicted, right? Now notice, the more things you predict that come true, the greater probability, you might say, to a hypothesis. Just like an induction, right? The more frogs you find with a three-chambered heart, the more probable it becomes that all frogs have a three-chambered heart, right? But it never follows, what, necessarily, right? But notice, there's more rigor in rejecting a hypothesis, right? Because there you're saying, if my hypothesis is correct, there will be an eclipse of the sun at 10 o'clock this morning. There's no eclipse at 10 o'clock. There you seem to have the form of the syllogism, right? So it seems unfair, right? But there's more rigor there in the, what, rejection of a hypothesis than there is in the, what, confirmation, right? If what you predict by the hypothesis doesn't come true, then you say, well, a hypothesis can't be true, right? But if what you predict comes true, well, maybe your hypothesis is correct. Maybe! So there's a certain weakness there in science, right? And as Einstein says, on the scientific hypothesis, he maintains it's freely imagined, right? It's not by reasoning that the scientist arrives at his hypothesis. He compares it to writing a novel, in fact, in one place. And the really crazy kinds of fiction that Einstein was reading at the time, he invented the theory of relativity, wasn't there? So the fact that it's freely imagined means that it has no justification until it's been tested, right? But when it's tested and confirmed in its predictions, right, it's still, what, not sure, right? But nevertheless, you can say this is better. But 6 is the inverse. 6 says, if the angles here, B and C, are equal, then the sides A, B, and AC are equal, right? Now, how does he prove that that is so, right, then? Well, he says, first of all, that if they are unequal, then one of these sides will be longer than the other, right? Now, it makes, as far as I'm concerned, no difference which side is longer. Let's say AB is longer. Well, then, on AB, starting at B, we cut a line off equal to the shorter one, AC, and start at the B, so let's say it's BD, right? Okay? That's the very theorem there, that you cut off a line equal to the other one. Then you draw from D to C a straight line, right? Now you have two triangles, huh? D, B, C, and A, C, B. D, and these two triangles have an equal angle contained by equal what? The sides, huh? V, C is common to both of them, right? And the other side is DB, and they'll say this is AC. So you have two triangles having an equal angle contained by equal sides. Well, the fourth theorem, which has been shown already, is that triangles having equal angles contained by equal sides are, what? Equal. So that's a simple syllogism, right, then? Like the one we had there in the first theorem, right? Okay? So you say triangle D, B, C, and triangle AC, B are triangles having equal angles, the angles of C and B, contained by equal sides, DB, B, C, and AC, B, C, right? Therefore, they are equal, right? Okay? But, that's not, right? Okay? So, what that follows, if you say the sides are unequal, right? So you're going to have an if-then syllogism. If the sides are unequal, and you do all this, right, as a consequence, the part won't be equal to the whole. But that's impossible. Therefore, they can't be unequal, right? And if they're not unequal, then they must be, what? Equal. Unless you have, in a way, either-or there, right? So the basic argument is, either they're equal or they're unequal. And you're going to prove by a separate argument that they can't be unequal, therefore they must be equal. How does he prove, that's an either-or solution, right? How does he prove that they are, in fact, unequal? I mean, they can't be unequal. Well, if they are unequal, then the part could be equal to the whole. That's a way greater. But then, to show that, if they are unequal, the part could be equal to the whole, he has to use a regular kind of solution. So he's going to use all three kinds of symbolism in one, like, demonstration, right? Another example like that, but we'll come back to this after you go through this word, as I was saying, anticipation, right? Yeah. And this is kind of a very early theorem, right? Like, terribly unexpected theorem, right? You expect these sides to be equal at the innocent, right? But the proof uses all three, too, you know? We're here in geometry, you know. But those are three kinds of socials you'll be able to find. So that's the three that I teach, you know? And probably another kind of thing to hear about. Not in just junk, it's either or when it sounds common sense, right? But there's a few things to realize about this, right? Probably you can reason for an either or statement, right? Because sometimes what you do, you reason for an either or statement by eliminating all of one possibility and including to be what? Over an alien. Other times you eliminate all possibilities, right? And then you deny everything which is being divided, right? And the symbolism that Thomas gives there in the Simitansion Helix, He says, every name is said univocally of two things, it's either a place, it's a difference, it's a species, it's an arc, it's an accident. And then you know, it's all five of those, right? Therefore, there's no name said univocally of God, and it reaches out. But here, you can include two main ones, right? Now, if you had three, you know, it's a common sense if you had three, you had two, right? You can get one, right? Now, look, in one case, you know that something comes under this division, right? But you don't know which number it is. In another case, you're showing that something doesn't come under something, because all the numbers can be eliminated, right? But in this case, it must either be equal or unequal, straight lines. And so, but in the case of, is the name significantly of God and creatures, we don't know that there's anything significantly, right? And Thomas wants to show that there is a possibility, yeah. Gotta keep bringing God down. Yeah, yeah, yeah. So, um... And it's kind of common sense of either or. There's no doubt that's that analogy, right? And we tend to do that. We don't even, sometimes even stop to say we're doing that, but we are, in fact, arguing from either or statement, right? Thomas says, oh, you're doing that, I'm just assuming that I should do that, so I'm going to be doing that. But the end is a little bit more interesting, right? And there are four, and two of them are syllogisms, and two are not. And I usually put the forms up on the board, and I teach this part of logic, and I get four students and grab them up on the board, right? And ask them, you know, if something falls necessarily, right on the middle line, if it falls necessarily, if nothing falls necessarily, right, in doubt, right? And always somebody will get one of them wrong, right? And sometimes you go, oh, I think something falls when it doesn't. It doesn't fall when it does, right? So this is a sign that you need logic, right? Your mind is in serious trouble, and it thinks that something falls necessarily, and it doesn't, or it doesn't fall when it does, right? You miss out on knowing something you could know, and it doesn't think you know something you don't know, right? And all you have to do is consider those four cases, right? Which will meet them, you know? If A is so, then B is so, right? I always have to say it in this form. A is so, then B is so. Now sometimes you can't see that, the part of the is part, right? And you may find out that A is so, right? You might find out that in fact A is not so, right? Sometimes the mind looks at the negative, and you might find out that B is so, and sometimes you find out that B is not so, right? The question is, does anything fall necessarily in these cases about, what, B, right? In these cases, does anything fall necessarily about A, right? I need to put those four forms up on the board, and what do you think, of course, you would assume these in the beginning as part of logic, right? Actually, one of these forms is a syllogism, and we say it's obvious, right? It follows. One of them is also syllogism, but it's not as obvious what follows, right? But we can show it through the obvious form what follows. And two of them are not syllogisms at all, right? But people are very often deceived, right? And one of them is not as syllogism as Aristotle. ...says in the politics is the way Homer taught the other four times, called Good Lie. So, but you see, we use the... ...over and over again, right? It's a very common form of argument. You find it all the way through the dialogues of Plato, you find the New York style, and the time in Euclid, right? I do these two forms first, because they're very simple, right? When you get to the simple subject, it's not so simple. Because then you have to consider 48 combinations, huh? We'll see why I... Because these simple statements can be affirmative or negative, universal, or particular. There are four possibilities, and we have another variation, too, we'll see further. So, all together, if you want to do a big deal, there are 48 things you can consider. So I start with the either-or, though it's in some sense the least important, and it's always common sense, right? The end of the end, people then tend to get kind of accepted over that, right? And then the other one is, you know, there are more things to be considered, right? That's what you tend to do, the syllogism, or eczema, right? I start just calls that the syllogism, you know? And we call it syllogism from hypothesis, you know? This is used very much in dialectic, right? If you go back to the Mino, you'll see that Socrates uses the ethic and syllogism a lot. But it uses the either-or syllogism, right? It uses the syllogism, too. And you can see that, you know, I usually mean it was a magnitude of logic, and I don't get a chance to do that sometime. Yeah, so we'll see he uses these different forms in there, you know? But it's especially striking the way he uses the if-then, right? If virtue can be taught, then he teaches of it. But there are no teachers of it, therefore virtue cannot be taught. If virtue is knowledge, then virtue can be taught. If virtue is knowledge, therefore it can be taught. It's usually that syllogism, right? But then he'd go back up, then. If virtue is knowledge, then they'd say syllogism, simple syllogism, regular syllogism. So that would be that, sure. Yeah, so that first reading that I gave, right? It talks about the form of the either-or, which is kind of common sense. And then it'll talk about which of these are syllogism, right? So we'll talk about the form of the, like the pedic or if-then, as I call it, as I said, this is something you could use in a lot of prisons to come up again and again, right? Mm-hmm. This explains exactly why, once you understand what we're teaching about this, why a scientific hypothesis is never known to be true, but it remains, as Einstein says, always a guess. You can explain it from this. Because once you realize what ones are not a syllogism, and you realize that the conformation, the scientific hypothesis, uses what is not a syllogism, then you realize that it ain't necessarily so. Mm-hmm. That's interesting, yeah? Mm-hmm. Mm-hmm. I like how I told you that story about this, trying to understand something in St. Paul, and he just kind of dismissed his helpers here, just down the floor. I know, I understand it. Yeah. 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 an argument or speech, you could say, in which some statement 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. And the Greek word for premise, you know, is more explicit than the English word, huh? It has the idea of stretching forward, right? Mm-hmm. Mm-hmm. Mm-hmm. Mm-hmm. And, 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, and 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. Now, the distinction here between the form and the matter of a syllogism, sometimes we make a distinction, but mainly here, on the 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 formal logic is about. But 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? Now, when we do the formal logic, we use letters. And I know from experience, especially if I had female students in the class, everything was fine until we started using these letters. 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? Okay? Whether the predicate is being said universally or denied universally, or being said of some or not of some, and so on. 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, you have 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. 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 and fit into your place with them. And once you see how these two statements in the form are opposed, it makes no difference what you substitute for B, which is the same thing here and here, and for A here and here, 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 extracting from what exactly B is, or what A is, right? But if B, their stance is the same thing and A is the same thing, then these statements are opposed, and they're opposed in the way we speak of contradictoriness. They can't both be true, they can't both be false. False, one must be true and one must be false, regardless of which you, whether you know which is which, right? Okay? And so you get some who are just from seeing something just in 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. But that doesn't matter which one is, whether 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 and 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. 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 below, right? Certain things. And so you've got to find in speech an infinity of statements in these forms, right? Anytime you have a different subject in credit, you can have these, the universal, that is to say, right? So BS. ...something universal, right? But you're talking about a universal state as a universal subject. So even in the second act, you can talk a little bit about forms of distinguishing or abstracting from the matter. You see that? Okay. That's 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, or they call it sometimes the categorical syllogism. Aristologists call 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. Now, we're going to start with the either-or syllogism, right? And I think we can multiply the forms of this by how many members there are in the either-or disjunction, right? Basically, it's really just two things to 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 of the possibilities, right? Let's begin with the simplest case here, just two members, right? So, you might have X is either A or B. And thus, in that case, you don't know whether X is A or B, but you know that X is either A or B. 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. 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 have 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? Then you have to eliminate, what? Two. Yeah, that's just common sense, right? No big deal, right? Let's 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, huh? Depending upon how many words of the discussion you have and so on. While in regular syllogism, simple or categorical syllogism, you always have just two premises. In either-or, you just have the if-then syllogism, only two statements, the if-then statement and the other statement. So, take an example there. We're taking the sixth theorem there in Book 1 and 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. In that case, it's only two. And then, by a separate argument, which is also syllogism, but syllogism, if-then syllogism, of course, he eliminates the possibility of these two lines being, what? Unequal. And he does so because, if they're unequal, you could cut off the longer one, like, say, this is the longer one, one equal to the lesser one, and then draw a line across like that. And then you have two triangles, this triangle, and this triangle, two triangles that have an equal angle, contained by equal sides. And therefore, they have to be equal, right? And the part, therefore, to be equal to the whole, unless, as he says, to the greater end. So, he shows us that X cannot be B. Well, then it must be, what? A. Okay, you see that? Okay. If you had more than this, it'd be a bit more complicated. You'd have to have an argument about reason 39.2 there, right? Okay? Is that clear enough? Okay? Now, the negative, huh? Your conclusion, the subject of your conclusion, is not the subject of either or statement, but something else is, right? Let's say, let's call it Y. Let's say Y is either A or B. There's only two possibilities. In this case, now, what you do is eliminate all of the possibilities, right? Right here, you eliminate all but what? One. You've got to eliminate all the possibilities. So, you say, X is not A. X is not, what? B. And you conclude what? Government Y side. Well, you conclude that X is not Y. See, if X were a Y, it'd have to be either an A or a B, because every Y is either an A or a B. But X is neither an A nor a B. Therefore, X is not what? One Y. Okay? Now, notice, huh? The difference between this and this, right? One difference was that here, you eliminate all but one possibility. Here, you eliminate all, right? Here, the subject of the conclusion is also the subject of either or statement. Here, it's not, right? But the subject of the either or statement is the predicate of the, like, conclusion, huh? Why, here, the predicate is, like, the remaining alternative, right? Okay? That's kind of common sense, but, you know, you have to stop and see what you're saying, right? 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'd be some advantage of an objection because they're opposed to the truth, right? But you can still have a syllogism, right? So when he asks, for example, are faith, hope, and charity virtues? He takes the statement that every virtue is either a moral virtue or an intellectual virtue. 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. You 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 what? Virtues. Virtues, yeah. That's a form of syllogism, right? Delimiting all the possibilities. And now Thomas, when you find that, may point out that these are the natural virtues, right? Since they're required 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 Tampi Gentiles, when he shows that no name is said univocally of God and creatures, right? There he has a five-part distinction, 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? He's taking that distinction of the five names, which goes back to porphyry, right? I mean, explicitly, I said goge, 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? Okay? 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, a separate argument 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, therefore, but 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 God. Right? Okay? So, in that case, you eliminate all possibilities, right? Okay? You see that? So, one thing that's curious, too many seconds in the negative form, you have to introduce a second. Yeah, another turn to that, right? Yeah, yeah, yeah. You see, we do this, as I say, it's almost common sense, and we 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 and say, well, I can't be here on Sunday, you know. I get a class on Monday, you know. Tuesday, I, you know, take hope or something. Yeah. Now, if you eliminate every day, but let's say Wednesday, you might conclude, well, I'll get back to our meeting on, what? Wednesday, right? You know, this is a common thing all the time. People are saying, you know, what afternoon can we meet for a departmental meeting or something like that, right? 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 we might, you know, eliminate all the possibilities, but what, right? I haven't put that statement at Sherlock Holmes right now. And all the possibilities, but one, have been eliminated. The one that remains, he says, no matter how strange, must be it, right? You might have, for example, three people who could have murdered so-and-so, right? In the detective thing, yeah? And we have a reason why this person couldn't have done it, some alibi, you know, some reason. And the reason why this other person couldn't, then the third person, strange as it may seem, this highly respectable person or something, right? Must be the what? The murder, strange as it may, what? Be, right, yeah? And all the other possibilities that this would have been, what? Eliminated, right? But notice again how the difference between formal logic and material logic. If I say either Joe or Tom or Paul committed a murder, and Joe and Tom have albis that I can't shake, right? Then it must have been Paul, right? But if I don't have all the possibilities, right? And, you know, someone else who could have murdered him that I don't know about, right? And it's only probable that it's one of these three. Well, then you can go to prison, right, or worse, because of what? That either-or argument, right? That's a common thing, right? Okay? So you can see how the either-or argument, the problem is not so much in the form, but the problem is in having any, what? Complete division, right? Now, it's easy to see that every straight line, let's say, any two straight lines would be equal or unequal. And that's the only possibility, right? Or it might be easy to see that every triangle was either, you know, equilateral or isosceles or scavene, right? But that every name said univocally of many things is either a genus, a difference, a species, a proper accent. Someone does not, you know, learn the doctrine of Geisogogia, right? Wouldn't know that, right? Okay? So, when Thomas is showing that, in theology, that the father is not before the son, it eliminates all the senses, and there's one thing that he 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, now. It's in the Athanasian Creed, you'll find that in the official collection there. The Creed at the end of the Creed and so on. But there it's explicit that there's no before and after there in the Trinity. So, 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 of a material logic, right? The difficulty, right? Than a formal logic, right? But these same forms, you can repeat them again and again, right? You could maybe argue in one place that every number is either odd or even. And he gives you a reason why this number can't be even. Therefore, it must be, what? Odd, right? So, if you can use that same form, it's infinity, if possible, in places where you might use that, right? Okay? I had a question on the negative conclusion there. When I had 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 you were to say, well, y is not x, where, I don't know if you're going to get the story. 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? Uh-huh. 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? Uh-huh. And we'll go through that, right? All right. But we'll go through it, again, using letters, right? Uh-huh. That's kind of interesting, right? It's interesting, for example, that Aristotle will show that, you know, no B as A is true, no A as 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, I'm going to see, because there's an infinity, right, of possible statements, right, in the form no B as A that are true, right? You can't possibly look at infinity statements and see, in every case, the reverse is true, right? So how does he show that every time no B as A is true, whatever B and A are, as 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 that are on verse, right, are also necessarily true. He's going to show, you know, how this is not true for every B as A. It would be racist to every A as B necessarily, right? Take up that conversion, right? 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 what statement, right? Okay? Do 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, I thought it was just, yeah, no difference, yeah. But the main point is that you eliminate all but, what, one and include affirmatively humane, right? But then you have to know in your first statement that X is going to be one of those possibilities, right? Now, the if-then is far more important. People are very easily deceived with this. 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, right? So, now here we're going to use the letters to represent what? The simple statements, huh? They're put together, right? So we'll say if A is so, then B is so. Where A represents a simple statement, right? And B is another simple statement that follows from that first one, right? Now, it's going to have that same form in all of these. The simple statement in the if-part, they call that, in logic, the antecedent, meaning they get to it. And I guess ante means, what, before, the ante-rume of the house, right? And the simple statement in the B part, they call that the consequent. So the second part there is the one that follows, right? One thing you notice, huh, in the if-then syllogism and in the either-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it's only a-or syllogism, it The first premise that is a compound statement, an either-or statement, or an if-then statement. The second statement, or in some cases, the record more, the either-or, the second statement, or statements, will always be simple statements, right? And the conclusion will also be a simple statement, right? And the reason for that goes back to what truth means in the example. We want to know the way things are, right? What is so and what is not so in our own statement. 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 John murdered so-and-so, then John should be punished. Which is what I 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? 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? Now, when you look at the antecedent to see if it is or is not so, you might find out that, in fact, A is so, okay? Or you 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. Okay. 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. I get the far from the department, and I'll say, no. If anything follows necessarily, write under the line, but follow necessarily. If nothing follows necessarily, write in the valid under the line, right? And I know from experience, and I've been 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? And sometimes I got all four wrong. That'd 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? So you are in deep, deep trouble, right? You are, you are, you are, you are really need logic, right? Now I go through the forms and 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 somebody's going to get it wrong in the final exam. And, experience is clear to that, right? It's a teacher of logic. And somebody, a number of people, will get some of these wrong, right? Even though we've gone through them, right? It shows you how after 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. And Aristotle says their consideration was not complete, right? In fact, animals and men seem to be more deceived in knowing the truth, so that, if they want to explain what takes place in men, they should be explaining why they make these mistakes. Okay. Now likewise, there's another way of arguing over here. Here, sometimes they look at the consequence, and you might find out that it is so, right? Or, there's a possibility you might find out that B is not so. 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, A is so, then B is so, B is not so, right? 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, what, vague predictions, right? Of course, the scientists will say that theory is more interesting when it predicts things that we didn't even know existed. And you find out that they do exist, right? Heisenberg went to England there and conferred with Dirac, who was a super mathematician and so on, and Dirac put out some kind of mathematical theory, and ended up with a negative electron coming out of his theory, right? These equations, huh? Talking about negative electron, ain't no such animal. And then sometime later, they discovered and experienced the positron, right? Which had the same mass, I guess, as an electron, but the opposite charge, right? Here's the kind of particle that nobody knew existed, right? But it came out of the mathematics of Dirac, 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 is so, if H is so, then P is so, right? P is so, it doesn't follow necessarily. That's right. H is so, it's not a syllogism. It's some weakness there. The kind of syllogism that I used earlier when you were showing that not every genus has a genus above it, but that they're our highest genus, right? I have a better possibility. Yeah. If every genus had 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? Now, you could have an 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 a genus or genera. I 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? That every genus is a species of a higher genus, right? I say, now, what follows from that and that would, what, recognize what 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, right? But how can there be something said of more than being or something? Maybe something isn't something? Could there be something that isn't a being? Well, there he 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? 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? So we use these forms without maybe recognizing that we're using them, right? And, you know, you wonder when they call Aristotle the father of logic, right? Because he's the first man to think out the basic parts of logic. And, but now you see Socrates, you know, reasoning that way, right? You say, well, he uses the two forms of if-then speech that are syllogisms, right? He avoids the other forms. Does he know that explicitly or he just, it doesn't go the other way, right? There seems to be, you know, men must have reasoned to some extent