Introduction to Philosophy & Logic (1999)
Lecture 32: The Square of Opposition and Contradictory Statements

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tell the truth, the whole truth, and nothing but the truth, right? The kind of truth you're interested in in the courtroom is the truth of the simple statement, right? He's guilty or not guilty, right? Everybody knows that if he murders so-and-so, then he should go to jail or something, right? The question is not so much that, but did he or did he not, right? Should he or should he not go to jail, right? You want to get back to that, to the truth of the simple statement, right? Now, the next part here, starting at the bottom of page 6, I'm going to be in there, is an expansion now on the idea of contradictory statements, because there's a little problem, right? Contradictory statements, as you recall, are regular statements, simple statements, one affirmative and one negative, right? But the problem arises when you have a universal subject rather than a singular subject, right? Now, if I say Socrates is wise, the contradictory of that is Socrates is not wise, okay? No problem, it's a contradictory, I guess, right? But now, suppose I say man is wise. What's the contradictory of that? Man is not wise, right? But now, if you think a little more carefully, you say, well, man is not a singular, right? Man is said of all men, it's universal. And so, when I'm saying man is wise, what do I mean? Do I mean that every man is wise? If I say man is not wise, do I mean no man is wise? Or do I mean some men are not? Maybe. If I say women are beautiful, what do you mean, Mr. Perkins? Well, women are beautiful. Don't get in trouble, see? You mean everyone is beautiful, Mr. Perkins? Well, you see? Now, usually they talk about this, they take a universal subject and they make a little square, okay? We call this the square of opposition, right? We allow squares in logic that there are no circles in logic, okay? That's what I tell the students. In one corner, we put the universal affirmative statement, statement in the form of, let's say, every B is A. Every woman is beautiful. And then, in the other corner over here, the universal negative in the form, no B is A. No woman is beautiful. Then down here, we put down the particular affirmative, like some B is A. Some woman. And the fourth corner of the particular negative. Some B is not A. Some woman is not beautiful. Okay? But it makes, you know, take any subject and predicate you want, right? Every man is wise, some man is wise. No man is wise, some man is not. So notice, if you go back to the definition of contradictory statements, they're statements with the same subject and predicate, right? One affirmative and one, what, negative, right? And they're opposed such that both cannot be true. Both cannot be false, right? But one must be true and the other must be false. Now, to see which affirmative and negative are such with a singular subject is no problem, right? President Bush is sitting, President Bush is not sitting. Obviously, it's a contradictory, right? But now, what is the contradictory to the statement, every B is A? Is it, no B is A? Or is it, some B is not A, right? Well, if you think, for the example here, every woman is beautiful and no woman is beautiful, they might both be what? False, right? Every man is wise, no man is wise. They could both be what? False. False, yeah. Now, it might be true in some cases that universal affirmative, universal negative is true, right? Like, every two is half of four, right? And no two is half of four. It's false, right? But, sometimes both universals are, what? False, right? Every man is sitting. It's false, right? No man is sitting. So, these two here, can both be false. So, if you know, that you have two statements in the form, every B is A, no B is A, same subject B, same predicate A, right? One true and one negative. They are not necessarily one true and then a false, right? Regardless of which you know is the true, which is the false line. For all you know, they might both be the false, right? Now, how about some B is A and some B is not A? Maybe some woman is beautiful and some woman is, what? Not beautiful, right? Maybe some man is wise and some man is not wise. Maybe some man is sitting and some man is, what? not sitting to take it. That's a controversial example, right? So, is it true that some man is sitting or some man is not sitting? They're both true. Some man is wise and some man is not wise. Some man is good, some man is not good. Okay? So, the two particulars would both be, what? Both can be true. So, as far as the form of the statement is concerned, every B is A and no B is A are not opposed as contradictories. You don't see that one of them must be true and the other must be false, regardless of which way you know is true or false, right? It's possible for both to be false. Every man is white, no man is white. Both are false. Every man is black, no man is black. Even being is male, no human being is bad, right? They're both false, right? Some man, some human being is male, some human being is not male. Both are true. Some man is white, some man is white. So, what are, what is the contradictory of every B is A? These, what they call the diagonals, right? Every B is A and some B is not A are opposed regardless of what B and A are. You know, I don't know what B or A is, right? I mean the same thing by B in both of these and by A the same thing, right? Those two statements cannot both be true. And it's kind of obvious to stop and think about it. If it's true that every B is an A, that means without an exception, right? Every B is an A, it must be false that some B is not A, right? But if even one B is not an A, right? It can't be true that every B is an A, right? Those are contradictments, those diagonals. And likewise, the other diagonals, no B is A and some B is A. Can they both be true? Well, if you stop at no means and say no B is A, that's universal negative, right? A is denied of all the Bs, right? So if it's true that no B is A, it would have to be false, that even some B is A, right? And vice versa, if some B is A is true, if even one B is an A, in other words, then it must be false that no B is A, right? Now, because in reasoning we're concerned with subjects like the universal more than the singulars, right? That's why we have to consider the square of opposition, right? What statements, affirmative and negative, with the same subject and predicate, where the subject is universal, are really opposed in the way we call it contradictory? It cannot both be true, it cannot both be false. So what must be true, then it must be false. Well, it's the diagonals, right? Now, as I was pointing out earlier today, you've got to realize that when I say some B is A, it's true. I'm not denying that every B is A. I'm not asserting that some B is not A either. If I'm in my room at home, all by myself, sitting down, some man is sitting. I don't see anybody else. I don't know who you want to be. I can guess it, so, you know, see? But for all I know, everybody else might be sitting, right? So some B is A is true, whether some is not, or every is, right? Now, sometimes it's an exercise, you know, we'll take each of the four corners, right? And we'll say, if, if, and if, then, if this is true, what about the other four corners, right? And maybe you know that something is true or false because of that, or it may be unknown, right? So just do that simply there. If it's true that every B is A, then no B is A must be what? Yeah. And some B is not A must be what? But some B is A is true, right? If every student is sitting, then some student is what? Sitting too, right? Okay? If it's true that no B is A, then some B is A must be what? And every B is A obviously must be false, right? But if some B is not A, it would be what? True. Now, if it's true that some B is A, would be anything else necessarily true or false? No B is not A. Yes. False. Yeah. If some B is A is true, then it's obviously false and no B is A, right? But if some B is A, it's necessarily a B is A. So it's a unknown, right? And some B is not A is a false. No, it's both things that have to be unknown and if one is unknown, if one is known, the other would be known. But it's fair opposition, right? And if some B is not A is true, what do you know is false? But no B is A is that false? And some B is A in two diagonals. One is unknown, and the other is unknown. If one is unknown, the other is unknown. Then you go around with the opposite thing, say false. If it's false, then every B is A. What about no B is A? It's unknown. And it's unknown that if some B is A, it's going to be right. In fact, if it's false, every B is A, that can be false because some are and some are not. Or it might be false because none are. So if this is false, you know that some B is not A but the other two are unknown. The same way here. It's true that no, excuse me, if it's false, it's known B is A. You know that the A and no is like true. But the other two are unknown. It's even nowhere. If this is false, no B is A is true, and some B is not A must be true, and every B is A must be false. That's why you kind of, you know, exercise in your mind, you know, go around. With each corner, like an example, this is true, what about the other corner? True, false, or unknown, right? If this is known to be true, this is known to be true. If the universe is known to be true in particular, right? But if the particular is known to be true, the universe is not known to be true. But if the particular is false, then the universe is false. If the universe is false, the particular is not necessarily false. I mean, the most important thing to see about this is that the, what, the egg knows are what, posed as contradictories. That is to say, no matter what B and A are, they can't both be true, they can't both be false. One must be true, then it must be false, right? And when I use the letters here, I don't even know what B and A are, right? I know if they had the same B in both of those and the same A, that one of those is true and the other is, what, false, huh? And so when they get into reasoning later on, I was contrasting, let's say, demonstration and dialectic. In demonstration, you know which of the contradictories is true. You know that it must be so. And therefore, you know the other one must be, what, false. But in dialectic, you don't have the necessity, you have only probability. And so you're inclined to one of the two, right? There was some fear that the opposite might be true. Yeah. And in dialectic, you sometimes even reason, both to affirmative and to dainty, right? Because something to be said on both sides, right? And maybe one side outweighs the other, right? In the same way in rhetoric, right? Which is even more problematic, right? So in the Inchon Land, they came up there, right? A favorite example there, these, um, have the native operations and the chief of staff were both opposed to the Inchon Land. And the craft was a sport, right? The craft went out, right? It was a great, a great thing. They did. But I mean, it was a very dangerous thing to say, right? It's the second thing, right? The craft just said, yeah, I have more confidence than me, do you have? They could do this, right? If you win. Probably, you know, basically fail, you have a backup plan. It says, we're, it'll be lost except for my reputation. I mean, that's the nature of rhetoric, so you can argue on both sides, right? It seems to be seen on both sides. So that's kind of a contrast there between demonstration and dialectic, right? In demonstration, you argue to only one half of a contradiction. And seeing that that must be so, of course, naturally, the contradictory must not be so, right? But in dialectic, then, and in rhetoric, then, you can reason from probable opinions or from likelihood in rhetoric, right? To opposite, what, conclusions. You might be able to reason why it's wrong to one than the other. But you don't see one is necessarily so, and therefore the other is necessarily false, right? You see one is maybe more probable or more likely. So there's some probability left to the other. If there's no probability at all, that would manifest the false, and the first one would be more than just probable, it would be necessarily true. So if I see one half of a contradiction, if you speak of the two contradictory statements as has, right? If one half of the contradiction I see is only probable, then the other half I can't see as, what, necessarily false, can I? Then the first one would be more than just probable, but necessarily true, right? So once you understand the opposition of contradictories, you can see how Aristotle uses that, right? The contrast demonstration with that. In the third book of wisdom, Aristotle reasons for and against things, right? Before you turn on the truth, right? But in geometry, where the demonstrations are very clear, there's no reason on both sides of it. It's the one side. It's the one side. It's the one side. It's the one side. So do you understand this court opposition area? You've got to think about that a bit, huh? We did some kind of exercise. I gave an exercise like what you said. These two universal statements, they sometimes call those contrarys, right? So you can say the man who thinks that everyone is beautiful is contrary to thinking the man who thinks no one is beautiful. So the man who thinks that every man is good, right, is contrary to thinking the man who thinks that no man is good. But, you know, in a sense they're further apart, right? But still they're not correct. Contradictaries, right? The statement of the man upholds that one must be true, man is false. That's why we thought it should be the trepation of our opposition, because the top has to be longer than the bottom could. Well, that's something you said to that, but I mean, it's spurred me around for a long time. It's not even because of those awful circles. I don't think it's awful. One thing that kids have been in a problem with a circle, you know, they want to say, like, you know, this represents maybe everything, right? And this represents some, you know, right? The trouble is, this makes some definitely some are and some are not, right? It's misleading, right? Because if every man is an animal, if some men are animals, it's still true. If you represent it by coloring the part that is, then you're saying, you're imagining, right? That the part is not. And you get to a false understanding, but... I don't know, don't ever let me kiss you with those circles, right? There's Venn diagrams on us, that's fine. That's very bad. And you end up dissolving into the imagination, like Socrates does in the Parmenides, right? And the Parmenides, Socrates is a young man who's learning the Socratic method from Parmenides. Parmenides is a guy who emphasized contradictions, right? And avoiding it. And Socrates is trying to imagine Universal to be like one of these young diagrams, right? So it's spread over everybody, right? So man is spread over all of us. So you only have part of what man is, and you have another part of what man is. And actually, what man is, the hole that is found in you, but also in you. So you can't imagine it like a quantitative hole, like a sail over the covering of us. But the moderns often get into that problem, they want to talk about class rather than Universal. And a class is what? A collection. Universal is something, what? One, set of many. But it's not a collection of the many. The difference between, let's say, man and mankind, right? You know, the biologists talk about the animal kingdom, right? When they think of the animal kingdom, they're thinking of the collection of animals, right? Rather than something one, set of many. If you ever study Porphyry, he talks about genus, you know. He gives two meanings that are before logic, right? The genus is one man from whom a multitude of men have descended. And then another meaning of genus is the multitude of men that have descended from one man, okay? As if we were to call Adam a genus, right? And all of the Adamites, right? You know? All that descend from him, a genus, right? And both of them have something like the meaning of genus, but it's something one, like Adam, but it's not individual like Adam, right? And it has some reference to the many, because it's something one, set of many, right? But it's not a multitude either, you see? It's something one, set of many. And it's something different from the individual from whom they have descended, and the multitude that have descended from them. See, all my offspring, all my grandchildren there, right? The multitude who have descended from me, you know? This friend I saw in church, I mean, saw all these grandkids. Now, you're responsible for this. See, but I'm an individual, and I'm not set of that multitude that is sent from me, right? By man, it's set of all individual men, right? But there's a one-to-many relation there. So, corphing leads you from those earlier meanings of genius, which Aristotle gives in the book of wisdom, too, right, to the one that we're interested in, in logic. But you have to kind of transcend your imagination, which wants to imagine a collection rather than universal, which cannot be imagined, and understand universal. Now, the logic of the second act is easier than the logic of the first act, and much easier than the logic of the third act. Now, when I was going through the things, I found that I had some of the things I have copies of, but the first one, I don't have copies, let me give you a copy of it, and you can reproduce it for the general, okay? The ones on syllogism in particular, I have those, I think, I have copies, I think, yeah, I haven't talked about it for a while, so these things get reproduced. But the first thing I do is a kind of general thing on the four kinds of arguments, syllogism, induction, and to be an example. So this one that I'm going to give to you, you can use it, you have that, right, you can use it. Reasoning and the four kinds of arguments, right? So this is what we'll do for the next time. This is all together, what, eight, seven, eight pages here, okay? And kind of imitating Monsi and Dian, one time we gave a course to four kinds of arguments, but beginning from the ones that are closer to the senses, right, and then moving up right to the four profound ones. The main thing we studied in the logic of the third act is the syllogism, but these other forms are important, too. Okay? So next Tuesday, we'll read on that record. Okay? I noticed that in the particular statements, you would say some man is wise. Yeah, you should really say some man is wise rather than some men are wise, right? I was wondering, what's wise? Well, because they might both be false, right? Every man is God. False, right? Some men are God. Some man is God. Yeah, that's true. Some, every man is my father. Some men are my father, but some man is my father. So, if it's false that every B is A, there must be at least one B that is an A, right? Or not an A. It doesn't have to be a, three or four of them. I think a lot of times, I see myself in the former years, I might have, you know, said some, every man is wise, some men are wise, but then it's a mistake, you know? It says some man is wise, because those are the ones that cannot both be true or both be false. Every man here is the avid, right? Every man here is the avid, right? Some men here are the avid. It's just one man, right? So, this is so they can't both. They can both be false in that some men are the avid, and every man is the avid. Yeah. But some man is the avid. It must be true if it's false that every man is the avid, but not that some men are the avid. Every bishop is the pope, right? We didn't see that. We were just arguing, oh, we need to talk about something, we need to be exhausted. We thought about exhaustion if it was an actual singer. Every bishop is the pope, right? False, right? Therefore, some bishop must be the pope. Well, yeah, we need to just one bishop, the bishop of Rome is the pope, right? You see the pope's remarks there on the Transfiguration there? All right. All right. So we've talked about the first and the logic of the first act and the logic of the second act. And notice how the logic of the first act, or rather the first act itself, is presupposed to the second act. If I didn't understand, for example, what a man is, which is the first act, right? And I didn't understand what a stone is, let's say, right? I couldn't understand the statement that no man is a stone, right? Notice another thing interesting about that. The act of understanding what a man is and the act of understanding what a stone is, two different acts. And in understanding what a man is, I don't understand what a stone is. And in understanding what a stone is, I don't understand what a man is. So it's at the same time that I understand what a man is and I understand what a stone is. But when I form a statement, and I say, no man is a stone, for example, then I'm understanding man and stone at the same time. Even though it takes me, you know, brief time to say, no man, before I say, it's a stone, right? I'm understanding man and stone at the same time. So there's a kind of unity there, right? In the second act, the things that are known by separate acts in the first act, huh? Okay. Of course, in the third act, you'll be combining, what? Two statements. And you have to think about these two statements together. And they form a kind of unity there. It's an order. Do you understand that there's two statements at the same time, or the three statements? Well, you have to understand the two statements together that are used as premises, yeah. Eventually, otherwise you can't draw a conclusion, right? I always say to the students, you know, if one person thinks of the major premise and somebody else thinks of the minor premise, but no one ever puts the two together, right? If he thinks about the two together, they're not going to draw any, what? Conclusion, yeah. So you can see how these acts are, as Thomas says, ordered, right? The first is ordered to the second, and it couldn't be the second without the first, right? And the second is ordered to the third, and it couldn't be the third without the, what? Second. I couldn't understand understanding that a man is not a stone. But I couldn't understand what a man, that a man is not a stone without understanding what a man is. And likewise, I could understand a statement without putting it together with another statement and drawing conclusions. But I couldn't put it together with another statement and draw conclusions unless I understood the, what? Statements, huh? Okay. A lot of times I conclude my consideration of statements by a couple of things I think are kind of interesting to think about. One we've touched upon before, but it's competitively says, what is worth saying can be said twice. The logic of the second act... doesn't seem to help you to separate, right? You can say which of the statements is a true one and which is a false one, right? It tells you what statements are contradictory. And from the logic of the second act, you know that one of them is true, the other is false. But which is a true one, which is a false one, the logic of the second act doesn't tell you that, right? Okay. Now, we mentioned that there are three ways, at least, in which we come to know which half of the contradiction is the true side and which half is the what? False one. And if you recall, the first way is by our senses, huh? So I know that you are sitting, right, is true, and you are not sitting as false through my sensing you're sitting, right? But when you have a universal statement like no odd number is even, I couldn't know that simply by my senses. I could have an example of an odd or even number, but I couldn't see universally that no odd number is even just by sensation. But to understand what an odd number is, and understand what an even number is, and this might require defining, right? The logic of the first act. I can see that no odd number can be, what? Even, right? And more generally, now the part is, I can see that every whole is more than one of its parts, right? Okay? And then the third way that you can come to know that either of those two ways works is by what? Reasoning. Reasoning. Okay? Reasoning from statements you already know, right? Or accept to this. However, there's an exception, huh? To the rule that the logic of the second act doesn't tell you which statement or which half is true, which is false, right? And it's kind of interesting because it reflects the fact that logic arises because reason can think about itself, right? And this is reflected in the fact that we can have a definition of definition as well as of other things. And we can have statements about statements as well as statements about man and stone and so on, right? And sometimes to make it a little more colorful, I invite my good friend, huh? Mr. Anti-Statement in order to bring out some of these things, huh? Now, before I introduce Mr. Anti-Statement, I want you to know that he has an irrational, right, an unreasonable hatred of statements. But when he talks about them, he gets even more angry because of the problems you'll see that arise. But students who have had the logic of the second act can usually see the difficulties that Mr. Anti-Statement is in, huh? And so I'll give you that you listen to Mr. Anti-Statement and you tell me what you think about what he says, okay? Statements don't exist. What would you say to Mr. Anti-Statement? Statements don't exist. What are you talking about? That's a statement. Yeah, see? There's no way to say that statements don't exist without making a statement, right? And therefore, statements exist is kind of obvious, right? Okay? If I make the statement, statements exist, the statement itself, in a way, confirms itself, right? Okay? So here's a statement you know is true, just from what a statement is, right? And if statements don't exist, you know, that bad is a statement. And therefore, it shows that itself is false, right? Okay? Well, all statements are false. No statement is true. They exist, but they're all false. No one is true. What would you say to Mr. Anti-Statement second? What would you say to Mr. Anti-Statement second? statements that's true you've just contradicted yourself yeah yeah so if the statement no statement is true is what true then yeah so you've got a statement that's true and once statement you know if it's fair opposition one statement is true then this idea that no statement is true it must be but false okay and if it's what false that no statement is true then by the square of opposition some statement is true it's very frustrating to see from a stand-by statement okay I have to admit that statements exist right and I have to admit that they're all false right some are true some are false the definition of true and false right is saying what is is not right or it's saying what is not is right and then the opposite statement right would have to be true right the opposite of saying what is is not to say what is is that's what true means and the opposite of what is not is is what is not is not and that's what true right so he says no statements are what no maybe some of them are true some of them are false but we never know which have to which involves once no statement is known to be true or false what do you know so how do you maintain that plus we've already seen that what some statements are true we know that some statements are true we know the statement the statements exist is true and we know that the statement statements do not exist is false right so some statements are known right okay see how he's caught right he wants to understand what these things are now the last thing he says I hate statements what do you say about that for him that's true yeah but what would be the obvious thing to say this is anti-statement I hate statements well he's just made a statement right he can't even say I hate statements right or people shouldn't make statements that's just it right so he doesn't want to say right Mr. Antti's statement it's like Aristotle says in the fourth book of the wisdom there the man who denies a statement about contradiction he eventually goes back to the state of vegetable right there's nothing to say right even the sense to say this is so and this is not so right or this is sweet or it's not sweet right so since Mr. Antti's statement he's completely what left speechless right you can't say don't make statements you shouldn't make statements right things don't exist so there's some things that we can see through what some statements are true some are false through the logic of the second in a way this logic of the second act is very close to what Aristotle calls the first axiom the natural beginning of all the axioms it's impossible to be and not be at the same time in the same way you must either be or not be right you saw that in the square of opposition right and when you see that in a way that they can't both be true what is is and what is is not can't both be true right and what is not is not and what is not is can't verbal be false okay so let's turn now to the logic of the third act the third act and this is going to be mainly about the tool called the syllogism and this is going to be mainly about the tool called the syllogism and this is going to be mainly about the tool called the syllogism and this is going to be mainly about the tool called the syllogism and this is going to be mainly about the tool called the syllogism But before we go into the syllogism in detail, which will be next time, we want to take a broad view of reasoning and the four kinds of what? Argument. Now, the first question is, what is reasoning? And as the way he points out, reasoning is to understanding as motion is to what? Rest, huh? And of course, the English word understanding comes from the word to stand, right? So it's very well adapted to that, huh? You don't have the Latin word, but to vigere still signifies something in the way of rest, huh? But when the mind is reasoning, it's going from one thing to another, right? So it's a kind of movement, huh? Now, how would you define this movement of reason called reasoning? It seems to be the most characteristic activity of reason, because it's named from reason itself, right? Reasoning, just adding I-N-G. So just as tasting would seem to be the act that characterizes the sense of taste, the name itself would seem to reveal that, right? Or smelling is the act of the sense of smell, right? So reasoning seems to be the activity that most of all fits what? Reason, huh? Okay? And notice, it's obviously a discourse, as Shakespeare spoke of reasoning, huh? Of the definition of reason. In fact, in the Middle Ages, you often see the medieval logicians using the word discourses, you know, for reasoning in particular, although it can be taken in a broader sense than just reasoning, right? But that's the kind of discourse that's most characteristic of reason. The name itself is kind of a sign of that, right? So, how would you define this third act of reason? How would you define reasoning, huh? How would you define it, huh? And another thing I might mention, too, like Shakespeare says in Troia Sincresida, things in motion sooner catch the eye than what not stirs, right? So reasoning catches more than the understanding, right? The understanding is more, what, the beginning and the end of reasoning, but the reasoning kind of stands out because there's a movement, right? I'm kind of amused by it. I've seen this bumper sticker on somebody's car on campus there, you know? And it says, if you don't change your mind, how do you know you have one? Well, there's a certain, you know, thinking behind that I don't like, you know? You know, they used to accuse Socrates, you know, you always say the same thing about the same things, right? And Socrates says, well, that's better than always saying opposite things about the same thing. But no, nevertheless, right? It's the idea that motion, right, is like catching the tension of our mind, right? So if a person does change his opinion, right, hopefully for the better, but not always, if he does change his opinion, we're aware of the fact that he is about thinking about these things, right? And a lot of times we make mistakes or we don't, you know, think out something too clearly, right? And so that change kind of reveals the fact that you are using your mind, right? And it's more known to us, motion, than anything else. So how would we define this act of reason called reasoning, right? Well, going back to motion, you can define it either as a going or a coming to begin with, huh? Now, the words going and coming are interesting enough. I say to the students sometimes around, let's say, Thanksgiving vacation, you might say to your classmate, I'm going home for Thanksgiving, right? Meanwhile, your mother, back home, is saying that you are what? Coming. Coming home, right? Now, are you and your mother referring to a different trip, a different movement? No. Was it that you and your mother have a slightly different speech or slightly different way of vocabulary, shall we say, for the same thing? Are these simply synonyms, going home and coming home? one refers to the going is from the point of the beginning where it's coming. You're going from, let's say, Assumption College through your home, right? So Assumption College is at the beginning of your trip, right? And your home is at the end, right? So you're at the beginning of it. So you call this going home, right? Your mother is back home here, right? At the end point of your trip. And so she says you're what? Coming home, right? But you're really talking about, it seems, the very same motion. So sometimes, to be clear about reasoning, I sometimes define it as a going and sometimes as a coming. Just a way of looking at the same movement, really. I'm really talking about the same thing. I tend myself to like more of the coming. So, you want to say what you're going from and to what you're going, right? Okay. Now, what are you going from and what are you going to with your reason, huh? Okay. More generally, or more basic, you could say you're going from statements, right? Okay. You're going from statements and from statements either that you know, right? Or maybe statements that don't really know in the full sense but that you accept, right? Because they're probable or likely or you believe in or something, right? You frame them, right? So you're going from statements known or accepted to another statement, right? Okay. But is that sufficient to define reasoning, right? Which is going from statements known or accepted to another statement. That's true. And if I go from the statement a whole is larger than its part and no odd numbers even those statements are both known and accepted by me, right? And man's not a stone. Any reason? Because although I've gone from statements known or accepted the whole is larger than its parts and no odd numbers even to another statement. It's not because of them, right? So you're going from statements known or accepted and because of them, right? To another statement. Going from statements known or accepted and because of them to another statement. Now, more precise but maybe even more clumsy. Turn around and I'll look at it from the point of view of the what? The end, right? Which is the conclusion, right? And here I define it as coming to know or a statement from other statements, right? And because of them, right? And guessing. Now you're certain and sure. Yeah. When you're guessing you're not sure or certain, right? And sometimes I guess, of course, you guess something false, right? But even... Correct, yes, right? Differs from knowing, not that the statement in one case is true, in that case it isn't. They're both true, right? In one case I'm sure about it, in the other case I'm not, right? Sometimes we distinguish the logic between opinion and suspicion, right? But opinion and suspicion are both, what, a guess, right? Right, but opinion is stronger, right? That's more the effect of dialectical reasoning, huh? And the suspicion is weaker, right? More the effect of rhetorical reasoning, huh? Now, you know, right? He says, I know there's a difference between knowing and right opinion. And you might have said, I know there's a difference between knowing and guessing, right? He says, there is a difference between knowing and guessing, right? When I say this, I know it, I'm not guessing. Now, it's kind of unusual, I point out to students, if you read the apology of Socrates, how he's always claiming not to know, right? But in the Amino, he says, I know that there's a difference between knowledge and even right opinion, right? Even correct opinion. And when I say this, it's not just an opinion I have. I know that, right? Why does he know that, right? You've got to stop and say, well, why is it so certain, in other words, right? That there's a difference between knowing and guessing. You could never come there, right? I mean, if everything was just guessing, you'd really never know anything. Or anything would be uncertain. Well, now you're trying to give a reason why there's got to be knowledge as well as guess, right? But I'm saying, if there's a difference, why is Socrates so sure that he will, contrary to his usual remark, I don't know what virtue is, as he says, you know, to get the dialogue, you've never been a matter of rules, you'll say, I know, I know. It's one of the very few times the dialogue, when Socrates ever says he knows it then. So he would have to know that in order to know that he doesn't know something. Yeah. But the difference, in one case you're certain, in another case you're not certain. The same thing could not both be and what? Not be, right? You can't both be certain and not be certain, right? So that's what you're guessing on. And that doesn't mean that you're always aware of the fact of whether what you think is a guess or knowledge, right? But you do what you are sure. There's a difference between being certain and not being certain, right? It can't both be and not be, right? Just like you're sure that no odd number is even, because it can't both be divisible by two and not be divisible by two, right? Okay. And notice, if someone said to Socrates, oh, Socrates, you don't know that difference, right? You're just guessing that there's a difference, right? You're checking to Socrates, he's himself making the, what, distinction, right? If you deny that Socrates knows the difference, right? You say, just guess that there's a difference. See? Then you're saying, all right, there's a distinction between two, right? Yeah. So, you see how certain Socrates is of that, right? Now, notice here, when you guess that something is so, from other statements and because of that, your guess is not a wild guess, right? It's not freely imagined, right? You have a reason for your guess, right? But the reason is not sufficient to say it must be so and cannot be otherwise, right? Okay? And so the reason may be stronger or weaker, but it's not strong enough to say it must be so, right? Socrates, the great philosopher, the central thinker of human thought here, let us not guess, he says, at random about the greatest thing. It's a beautiful little fragment. And I say to students, when you look at that fragment, let us not guess, let me put it on the board here, let us not guess at random.