Introduction to Philosophy & Logic (1999)
Lecture 38: The Simple Categorical Syllogism and the Three Figures

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before they reflected upon what they're doing, right? And you'll see in the dialogues later, you know, you won't see the explicit definition of syllogism, you know, but Sakhalis will say, well, now, if these things are so, then isn't this necessarily so? And someone will say, yeah, I guess so, you know? But you anticipate the definition of syllogism, right? You know, these things being so, then this must be so, then. Yeah, you're so, yeah. And we'll do that in Davy's speech, right? And the philosophy comes back. But often in Davy's speech, too, we're deceived. We have to stop and understand these things. Later on there, Socrates, you know, mind can't rest in contradiction, right? So you've got virtue can be taught, virtue cannot be taught, right? They can't both be true, can they? So now Socrates says, well, they can't both be true. There must be a defect in one of the arguments, right? And I mentioned how, in another dialogue, the behaviorist, he questions the second premise here. There are no teachers of virtue, right? Because your mother and your father were given to you, well, that's an injustice, wouldn't they, right? And the example I always give, you know, to children, you know, you'll find that you maybe did yourself, you'll find your own children, you're 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, 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 is a little lesson in what? In justice, right? Okay. And you get a box of candy for birthday for Grandma or from on so-and-so, and, well, it's tough to see. And your mother says, now, you've had enough for your day, right? We'll put it away, we'll have some more tomorrow. That's a lesson in what? Yeah, moderation, right? But Socrates doesn't, you know, point it out in this dialogue, right? I think what's marvelous about the dialogues is that we observe this aspect of our mind that we see a part of the truth before the old truth. And we see, you know, part of the truth in this dialogue, maybe another dialogue, another part of the truth, right? And we'll put it all together, or a style that was put together, we don't know. But we see the parts that are played over, you know? So 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 is now. He sees that statement is not necessarily true, right? There's another possibility for directing someone to the good, and that is what is called right opinion, correct opinion. Opinion is not knowledge, right? An opinion may be true or false, but we're talking now about a true opinion, right? And I always take a very simple example. I say, suppose you're going down the road here, and you want to get to Boston, right? Okay? You come to the fork in the road, and one of these is being to Boston, and the other will be, let's say, Collins, okay? And I'll vouch for the accuracy of this matter. Now, I've come to the fork in the road here, right? And when I get to Boston, it's as soon as 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? I would take that one, right? And I'll get to Boston, right? Now, suppose I get to that fork in the road, and I don't know which is the one, 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? So I'll get to Boston just as much as the man who, what? No. Sometimes people, you know, they bring the money to the lottery, right? Why do you play? There's never... It's kind of interesting, you know, sometimes their grandchildren's numbers are like that, right? But sometimes that number was showing up in their life somehow, right? So they had a hunch to play these numbers, right? And these numbers are the numbers that came in, and now they run a lot and sell the money, right? Now, if they had known that these numbers were going to win this Friday, then they would have played them and won it some money, right? But having a hunch that these were the numbers to play, also directed them to play those numbers, right? And they got just as wealthy as it would if they had known their numbers, right? 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 crew was the Inchon Landing, right? Okay? I read many accounts of the Inchon Landing, the planning for it, and so on. And Washington was ill-disposed to this plan, the Inchon Landing, right? And they sent the chief of staff down to convince the type of Vince McCarthy not to do it. And they sent a top advoi down to convince him not to do it, right? The Navy can't do it, right? Okay? And then McCarthy, you know, break the space of the mail, right? And I've worked confidence in the Navy, sir, that you have, you know, and so on. And now, it was a great thing what McCarthy did, right? And after success of the Inchon Landing, the troops down to the beaches and so on were pushing the sea. They saw the enemy just started to weaken the way, fade away, right? Collapsed. And you say, okay, now, did MacArthur know that the Inchon Landing was going to succeed? 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 and succeed, you know, or we'll be lost except when our reputation is this. You know? And, well, anyway, they finally allowed MacArthur to go ahead, right? Elected him, right? But then on the day he's going ahead of it, they send a message that he was on his own. They denied all their responsibility for it. So there's a whole burden on MacArthur. And MacArthur, you know, they call up his, he's on the boat, they're going, and he calls up his subordinate, and he goes through the whole plan again, right? You know? That's what he knew he said, MacArthur says, right? He sits down, starts reading his Bible, and, you know, he says, I'll read the Bible, yeah. And of course, it's a great success, right? What did MacArthur know he's 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, huh? So, Socrates says, maybe the great men of Athens led Athens to good things, not by knowing, but by having, you know, the right opinion or the right hunches, right? The right instincts, as he'd say. But you can't really teach somebody, you know, maybe the right opinion or the right instincts, so that you can't teach them a hunch, right? So maybe, that's what they have, right? Now, Socrates, later on, you'll put this more formally, you know? He'll say, the great men of Athens led or directed Athens to the good, either by knowledge or by what? Right opinion, right? 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, the now, the antecedent, right? But he also has neither argued, right? Now he's concluding that they must have led the men, the city of Athens, to the good through what? Great opinion. So he's using the either or, and again, backing it up with the if, then, what? Art, and then. So you can find in that passage, all of these kinds of syllogisms, either or, and the if, then, and even that first one we had. What threats us to the good is knowledge, virtue, threats us to the good. We have regular kinds of syllogisms. So men were syllogizing before Aristotle thought out the art of the syllogism. Sometimes, like an example of Melisius there, right? Melisius argues that if being had a beginning, it has an end. If being has no beginning, it's 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, and I mean, for his book of natural hearing. But Socrates is arguing the two that are what? That are syllogism. Now, I try to, you know, when I teach students, I try to get them to be very much aware of these four forms that if-then speech and why two of them are what? 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? But the form that is not obvious, in a way you use that, in showing the two ones that are not. You can notice the way we reason. We 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? So you're using the if-then syllogism that's not so obvious, the denial of the consequence, how you have to see them, in order to see that we've really shown that those two forms are what? Invalid, right? So, it's this diagram in the middle of here. You take the obvious here, it's most known, that if A is so, then B is so, A is so, therefore B is so, right? And we 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. Now that's how we did that. We said, either A is so, or A is not so, right? And if A was 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? 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 so-gisms. 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? Now, to be a bit, you have to show an example where it is that it's 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? Okay. Now, if that were necessarily so, it would always be so. But it's not always so, for example, if I'm a dog, then I'm an animal. I am not a dog, therefore I'm not an animal. Oh, okay. So it isn't always so that B is not so, right? It might be so if I'm a man and an animal. Excuse me. If I'm a dog, I'm a goat or an animal, right? So, I'm showing, and since this is invalid, to 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. But 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? A is so, B is so, B is so, find my dog, a man, find my man, a man. It might not be so that A is so, right? So again, the examples show it's not always so, and there you deny the consequence of something being necessarily so. Herefore, you're going to be necessarily so. Now sometimes, and you see this in Euclid, but 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? A is not so. But you just run together several syllogisms. The dominant 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, B is so, C is so, C is so, D is so, right? If you eventually reach something that is not so, then everything before that gets like turned over, right? Okay. But that's just like, you know, what we call continuous syllogisms, right? It's like the dominant effect, right? You know, for the last one, all the rest go over. In the same way, if you're looking before, right? I have to start later on with the alphabet. Let's say, I want to show that D is so. 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 if B is so, then C will be so. But 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, B is so, right? Okay. Unless you're looking before and after, Shakespeare says, right? So you might keep on looking before and take it to something you know is so, right? And then you can syllogize right down the line. Or you might keep on looking afterwards if you come to something that is not so, right? Okay. And essentially, if he's doing that in that theorem we're talking about, right? If one of those two sides is a 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. And if you can do that, then you can draw a line from that end point to the other end point. And if you have that, then you have two triangles, right? Which have equal angles and equal sides. Therefore, they're equal, right? But they can't be equal, right? You might have several steps, right? So if you go on these certain nucleus, you might have several steps it goes through. This is so. That'll be so. This is so. But you're just repeating the same argument. The same kind of argument, I should say, right? We might not 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 all for argument. But it's basically the same syllogism repeated several times. The same kind of syllogism. I call these syllogisms continuous, right? But the conclusion of one is a premise in the 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, with the previous argument, therefore C is so, right? Sometimes your data seems so obvious you don't even bother to spell it out, right? Just have A is so, B is so, B is so, C is so. Today A is so, therefore C is so. But in fact, you're showing from A is so that B is in fact so, and from B, B in fact so, A is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B is so, B I see that there's a consequence of the furniture, and they can stay down to multiply these unnecessarily complications. In dialectic, when you study the tools of dialectic, the fourth tool of dialectic is the tool of likeness. And Aristotle says the mind is exercised more in seeing a likeness between things that are further apart, and seeing the likeness of ratios. I was doing the first chapter in the class of Nietzsche 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 cell dressing, or hear a symphony, or see a painting, we don't distinguish the parts clearly at the first time. Then he makes a direct comparison between whole and part, in general in particular, right? And he's seeing a proportion there. He wants to show that the general is known before the particular, the more universal before the much universal. And he's showing that the whole is known before the parts. 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 general, the universal whole, instead of its parts, rather than opposite, right? But the English word particular there obviously comes with the word part, right? So the particulars are like parts, right? And in Greek there, the word for general is kapalou, that's the word capital, right? But kapalou in Greek comes with the Greek word for whole, kata, hola, according to the whole. It 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? 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? Yeah, makes sense, right? 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 clarinet and the violin and the viola and so on, right? When we study the regular syllogism, you'll see that you have pre-turned regular syllogism, like in the one we had there from the meaning there, and it agrees what? What directs us to the good is knowledge, right? Okay, virtue directs us to the good, therefore virtue is knowledge. You have one term used twice there, right? They call it middle term, right? But in proportion, you have four terms, right? So you want to reason from a proportion, you put it in the form of a what? You have a dense statement, right? You have four terms. And notice how 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 the education, you use reason, right? What kind of if then syllogism is Shakespeare implicitly giving that? What is a man, if his chief good and market of his time be but to seek good feed? A beast no more, right? What is he saying? And he was saying 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 unbeast. Then, like in math, we alternate the proportion. As the chief good of man is the chief good of the beast, so man is the beast. 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. He'll rave and rant, he's more than the beast, right? You see? Okay? So notice the way he's reasoning around, from the now to constantly, right? If the chief good of man is no more than the chief good of the beast, then man is no more than the beast. But man is more than the beast, right? He denies the... In the second part of the situation, he points out what man has, the beast doesn't matter. And he builds it up before and after. He builds it up before and after. He builds it up before and after and stuff, 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? Okay? But Shakespeare seems to be using there more of 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, then man is no more than the beast. But you know that isn't true. Therefore, therefore the chief good of man must be something more than the chief good of the beast. So, that's a logic, right? That means it's very well. In the argument, to the purpose of man, we use some time in this then argument, to be an example therein, I'll say, what is to man as seeing is to the eye? What is to man as seeing is to the eye? Yeah, see. If I ask, what is to the ear as seeing is to the eye, what would you say? You take the act that characterizes you, right? That's peculiarly, right? What is to man as seeing is to the eye? What's the act that involves reason in some way? Then you syllogize for the more known. If seeing is the, what, 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. 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 with reason done well, right? But everybody knows the purpose of the eye is to see well, right? Because of the purpose of man must be the act with reason done well. So he can syllogize, right? So, this is, you can use the if-then syllogism with four terms. You can't use the various syllogism. And notice, you can always put, you know, the other form into the if-then. And instead of saying, let's say, if, let's say, three is odd, and what is odd is not even, and what is odd 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. It's a very common form, so it's good to know this, right? Next time we're going to go into the next group of readings, right? It's called the form of the simple syllogism, but it's not so simple, right? Okay? And there, instead of four cases, we want to be complete, we have to consider 48. So, most of which I consider in this thing, and all of them, you can go through all of them, right? Okay? So, we say, you know, the worst, the last. Okay? That's probably why I do it this way, right? That's kind of obvious form, either or, and yet then there's a little more receptive in some cases. And then we go through, yeah. Does your schedule change, do you still manage every week, or do you have? I'm going to go, yeah, this stuff here, I'm second age to me now, you know. Brother Richard taught me logic when I was in high school, so. I went to college, I took the exam, and they gave me credit for the courts, you know. Oh. So. So. I've done magic. I'm doing it in my sleep, you know. Our scripture there, you know, you have to do it in the morning. So, I didn't school, you know, I needed two weeks of that, you know, to that, I'm reading, you're reading, I'm second age to me now, you know. I thought it was your schedule or something. Just to bring it home. Right. Right here. Right here. Okay. In the name of the Father, and the Son, and the Holy Spirit, Amen. God our enlightenment. Guardian angels, strengthen the lights of our minds. Order and illumine our images, and arouse us to consider more quickly. St. Thomas Aquinas, angelic doctor, and help us to understand all the truth. Amen. In the name of the Father, and the Son, and the Holy Spirit, Amen. So, today we're going to look at the form of the syllogism, which Aristotle simply calls the syllogism, right? And in a way, if you look at the definition of syllogism, it's speech in which some statements lay down, another follows necessarily because of those laid down. Now, in the regular syllogism here, the conclusion is in no way, really, in the premises, actually, right? It's in the power of the premises, right? In the case of the either-or, it's already there, but not yet asserted, right? In the case of the if-then statement, it's already there, but not yet said in fact to be so. Right. But here, when you have this simple syllogism, like an example that every animal is alive, every man is an animal, well, the conclusion that every man is alive is not actually found in the premises. So, the idea that the conclusion is another statement, right, from what's on the premises is more true in the syllogism than in the if-then syllogism or the either-or syllogism, right? Just seeing a nice either-or syllogism this morning in Thomas Aquinas, he's reasoning that the relation of God to creatures is not a real relation, but a relation of reason. And he says, well, if it's a real relation in God, it'd either have to be an accident in God, or it'd have to be the very substance of God, right? Well, in the first book, the previous part, he showed there are no accidents in God, right? So, if it isn't an accident, it'd have to be the very substance of God, and then his very substance would be towards a creature, and there'd be some dependence of God upon the creature there to be. And we'd shown in the first book that he's what's necessary to be through himself, right? So, it's a beautiful way, you know. There are two possibilities, right? Either it's something existing in God, but not what he is, or it is what he is. And then he excludes both possibilities, therefore it can't really be in God. So, now, we recall the definition of syllogism, though. Now, in the regular syllogism, we take it apart, and Aristotle wrote two books, which in English are called the prior and the posterior analytics, two books about demonstration, depending on the syllogism you have in geometry and elsewhere to some extent, too. And, um, in the prior analytics, which means, you know, before, analytics means take apart in a sense. And, um, in the prior analytics, which means, you know, when you're in geometry, you know, you know, when you're in geometry, you know, when you're in geometry, you know, when you're in geometry, you know, when you're in geometry, you know, when you're in geometry, you know, when you're in geometry, you know, He takes apart these arguments to see if the conclusion follows necessarily the premises. And then the posterior analogy, he takes them apart again to see if the premises are necessarily what? True. And that's, as we said, is proportional to a man checking his calculation to see if he added or subtracted correctly or multiplied correctly, and then checking to see that he had, in fact, the correct number. To add or subtract. So, when you take apart the syllogism, we'll call it the syllogism period analysis, you always find that it has two premises. If you take the premises apart into their subject and predicate, you find not four different terms, but what? Two in Greek, right? There's one term that is found in both premises. And then two that are found just in one, right? Okay. And that term that is found in both is going to what is, if it's really syllogism, it's going to enable you to put together the other two, right? In a permanent statement. Or separate them in a, like, negative statement, you know? And so we sometimes compare the middle term to the middle man economics, right? That's inconvenient for, let's say, the consumer to get together in the cases of the producer, right? So there's a man, then, who has a shop, and he has contact with the producer, and he has contact with the, what, consumer comes into the shop, so he kind of, what, brings them together, right? Okay. Or like a matchmaker, right, huh? Maybe someone who thought this man and woman would just cry for each other. And so he arranged to have a party at which everybody there was a married couple, except for these two. So they, as far as necessity there, they started talking, and they were very suitable for each other, and in a week or so they knew they were going to get married, you know? They did eventually get married, and they had children, so. So he's, what? He knew the guy, his work, and he knew the woman, and he just said, yes, you just, you know? Okay? So that's what the middle term is a little bit like, actually, okay? But then sometimes, too, you have two guys fighting, and somebody comes in and, what, separates them, right? Separates them, you know, and separates them, right? And that's like the negative statement, right? You know, you separate. This is not that, right? Okay? Now, that middle man, or that middle term, as they call him in logic, he can have three relationship terms, huh? He can be, as it were, in between the two, right? The subject of one of them, and the predicate set of the other. Or he can be, what? The predicate in both cases, set or denied of the other two. Or he can be, what? Subject. Subject, right? Okay? Now, when Aristotle does this, he actually uses, in the Greek, if you look at it, he uses different letters for these three arrangements, huh? And, to example, that in English, you know, he said, well, in this first figure, as he calls it, the middle term is in the middle position, right? And then, in the second figure, that middle term is the, what? Predicate in both cases, huh? Okay? The predicate seems to be more universal than the subject usually. It's more apt to say man is an animal than an animal is man, right? In the third figure, the middle term is what? Subject. Subject, right? Okay. But now, we're sometimes accustomed, and when we do it like in here, to use A, B, and C for all three arrangements, right? But then you have to realize that the order of the letters doesn't necessarily correspond to the order of the terms, right? It does in the first, right? But not in the second and the third. So, using the same letters, then, to say, he had this arrangement, he called that arrangement with the first figure, and then you have this arrangement with the middle term. In each of these arrangements, we're going to be asking, are these statements such that you can say something about C and A, with C as a subject and A as a what? Predicate, right? There's any conclusion. C as a subject and A as a predicate. Can you see necessarily that every C is A, or can you see necessarily that no C is A? Or can you see necessarily that some C is A, or see necessarily that some C is not A, right? Is there some statement, in other words, universal or particular or affirmative or negative, right? Being those four possibilities we have in this preposition. Is anything that is necessarily so because of these statements, okay? Now, the complication arises because you've got those same four possibilities for each of these statements in this arrangement. You have every B is A, no B is A, some B is A, some B is not A, right? And like if you have four, what? They're down here. Every C is B, no C is B, some C is B, some C is not B. You've got four possibilities here and four there. How many possible combinations do you have in that arrangement? Sixteen. Yeah, not four plus four, it's four times four, right? Okay. You've got four men and four women, how many possible marriages? Sixteen possible. Yeah. Each one of the four men could possibly be married to one of these four women, right? So there's sixteen possibilities, right? I mean, it's tough here, right? Yeah. So in each figure, there are sixteen cases, or sixteen moves, they call them sometimes, and I like to wear modes, to be considered and asked the question, does anything with C as a subject and A as a predicate follow necessarily, right? And you'll find out in all three figures that in most cases, nothing does solve, okay? Bad for most part. The good is rarely, huh? Okay? And sometimes when they speak of these sixteen, they'll speak of four cases where you have two universal statements, right? And four cases where you have two particular statements, and then eight mixed cases where you have the first premise, the universal, and the second particular, or vice versa, right? Okay? So we're going to be considering those. And of course, the most important ones to think about are the ones that have two universal statements, and they're not the only ones where you have a soldier. Now, you might suspect, when you reason out things, you have to start with something that is obvious, then, okay? And there is a couple of obvious things that will be found in the arrangements that are, in fact, the syllogism. Sometimes we call these two obvious things the set of all and the set of none, which fits more Aristotle's grammatical way of saying these things, huh? So let's take these two principles, huh, and ask yourself, is this something that needs to be proven, or something that's kind of obvious, if you understand it, then? This is the set of all. If A is set of all B, then A will be set of whatever B is set of. If animal, for example, is set of all dogs, right? Then whatever dog is set of, animal will also be set of, right?