Introduction to Philosophy & Logic (1999)
28. Logic of the Second Act Wrap-Up, Mr. Anti-Statement, and What Reasoning Is
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[0:02] So we've talked about the first and the logic of the first act and the logic of the second act. You notice how the logic of the first act, or rather the first act itself, is presupposed to the second act.

[0:22] If I didn't understand, for example, what a man is, 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 what 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, huh? And in understanding what a man is, I don't understand what a stone is.

[1:02] And understanding what a stone is, I don't understand what a man is. So it's two different acts, but not at the same time. But I understand what a man is and I understand what a stone is, huh? But when I form a statement, I say no man is a stone, for example, right? 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?

[1:38] I'm understanding man and stone at the same time. You make them 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.

[1:57] 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 ordered. Do you understand that those two statements at the same time, or the three statements? Well, you 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 someone else thinks of the minor premise, but no one ever puts the two together, right?

[2:34] And 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 what a man is.

[2:57] without 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. 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.

[3:21] 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 as Péguy says, what is worth saying can be said twice.

[3:40] The logic of the second act. Doesn't seem to help you to separate, right? And say which of the statements is the true one and which is the 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 the true one, which is the false one? The logic of the second act doesn't tell you that, right?

[4:07] Okay. Now we mentioned that there are three ways, at least, in which we come to know which half of a contradiction is the true side and which half is the what, false one. And if you recall, the first way is by our senses, so I know that you are sitting, right, is true, and you are not sitting is 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.

[4:49] I could have an example of an odd or an even number, but I couldn't see universally that no odd number is even just by sensation. But to understanding what an odd number is, understanding 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, if I understand what the whole is and I understand what the part is, I can see that every whole is more than one of its parts, right?

[5:23] Okay. And then the third way that you can come to know if either those two ways works is by what, Reasoning. reasoning, okay? Reasoning from statements you already know, right, or accept to this, what?

[5:46] However, there's an exception 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's

[6:01] 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 a little more colorful, I invite my good friend, Mr. Anti-Statement, in order to bring out some of these things.

[6:39] 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 see that arise.

[7:01] But students who have had the logic of the second act can usually see the difficulties that Mister Anti-Statement is in, huh? And so, let you listen to Mister Anti-Statement a little bit. You tell me what you think about what he says, okay?

[7:18] Statements don't exist. What would you say to Mister Anti-Statement? Statements don't exist. What are you talking about? That's a statement. Yeah. There's no way to say the statements don't exist without making a statement, right?

[7:48] 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 knowing what a statement is, right? Okay. And the statements don't exist. You know that doesn't say statement. And therefore, it shows that itself is false, right?

[8:25] 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 Mister Anti-Statement second? Statements. Pure admit

[8:47] Pure admit Well if That's true. You've just contradicted yourself. Yeah. Yeah. Yeah. So if the statement, no statement is true, is what? True. Then, yeah. So now you've got a statement that's true, and one statement—you know about the square of opposition. One statement is true. Then this idea that no statement is true must be what false, right? Okay. And if it's what false, that no statement is true, then by the square of opposition, some statement is true.

[9:29] It's very frustrating to see from a student these days. Okay, I have to admit that statements exist, right? And I have to admit that they're not all false, right? Some are true, some are false. Of course you notice also from the definition of true and false, right?

[9:53] Because a statement is false, since he was 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 is to say what is is, and 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?

[10:24] Okay. So he says no statements are what. No, maybe some of them are true, some of them are false, but we never know which are true, which are false ones. No statement is known to be true or false. What did you say about this? I need the other time.

[10:44] Well, that statement is either true or false. Okay. But if no statement is known to be true, then the statement that no statement is known to be true Is it known? Yeah. So how can you maintain In that?

[11:05] Plus we've already seen that what some statements are true. We know that some statements are true. We know the statement that 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.

[11:30] No. Now the last thing he says. I hate statements. What do you say about that? For him, that's true. But what would be the obvious thing to say? This is. anti statement. I hate statements.

[11:49] Well, he's just made a statement, right? He can't even say I hate statements, right? Or, well, people shouldn't make statements. Let's just take. it

[12:03] So nothing more to say, right? Mr Anti statement huh. 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? He's nothing to say, right? Even the sense to say this is so and this is not so, right? This is sweet or it's not sweet, right? so, since Mr Anti statement, he's completely what left speechless, right?

[12:31] You can't say don't make statements. You shouldn't make statements, right? Things don't exist. So there are some things that we can see through what some statements are true, some are false through the logic of the second.

[12:48] In a way, the 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 what be and not be at the same time in the same way. Must either be or not be, right? We saw that in the square of opposition, right? Okay, and when you see that

[13:17] in a way that they can't both be true, right? What is is and what is is not can't both be true, right? But is not is not and what is not is can't both be true or both 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. But before we go into syllogism in detail, which will be next time, we want to take a broad view of reasoning and the four kinds of what argument.

[13:58] Okay. Now, the first question is, what is reasoning? And as Aquinas points out, reasoning is to understanding as motion is to what rest. And the English word understanding comes from the word to stand, right? So it's very well adapted to that. Now, I don't have the Latin word, but vigere still signifies something in the way of rest. But when the mind is reasoning, it's going from one thing to another, right?

[14:42] So it's a kind of movement. Okay. Now, how would you define this movement of reason called reasoning? It seems to be the most characteristic activity of reason. It's because it's named from reason itself, right? Reasoning, just adding ing. 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?

[15:11] So reasoning seems to be the activity that most of all fits what reason. Okay. And notice it's obviously a discourse, as Shakespeare spoke of reasoning, of the definition of reason. In fact, in the Middle Ages, you often see the medieval logicians using the word discursus, 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.

[15:45] The name itself is kind of the sign of that, right? So how would you define this third act of reason? How would you define reasoning? How would you define it?

[16:01] And another thing to make mention too, like Shakespeare says in Troilus and Cressida, things in motion sooner catch the eye than what not stirs, right? So reasoning, being a movement, is something that our mind 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 it's a movement, right? I'm kind of amused by I seen this bumper sticker on somebody's car in campus there, you know, and it says, "If you don't change your mind, how do you know you have one?

[16:42] Well, there's a certain you know thinking behind that I don't like, you know. You know, 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 of motion, right? It's like catching attention 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, but thinking about these things, right?

[17:17] 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 of reason called reasoning, right?

[17:41] Well, going back to to motion, you can define it either as a going or a coming to begin with. 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

[18:26] 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, whereas the coming. Yeah. Yes. You're going from let's say Assumption College through your home, right? So Assumption College is at the beginning of your trip, right?

[19:02] And your home is at the end, right? So you are at the beginning of the thing, and 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? Okay. But you're really talking about, it seems, the very same motion, okay? So sometimes to be clear about reasoning, I sometimes define it as a going, and sometimes as a what coming.

[19:36] Just a way of looking at the same movement, really. Really talking about the same thing, but okay. I tend myself to like more the coming, okay? So

[19:51] you want to say what you're going from and to what you are going, right? Okay. Now what are you going from and what are you going to with your reason, huh? Okay. Right. So. Okay. More generally, or more basically, you would say you're going from statements, right? Okay. You're going from statements,

[20:24] 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 them or something, right? You've heard them, right? So going from statements known or accepted

[20:48] to another statement, right? Okay. But is that sufficient to define reasoning, right? That you're going from statements known or accepted to another statement. That's that's true. Okay. 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, aren't they, right? And man's not a stone.

[21:22] No. Because although I've gone from statements known or accepted, a whole is larger than its parts, and no odd number is even, to another statement. Why haven't I reasoned?

[21:40] Yeah, not because of them, right? Okay. So going from statements known or accepted, and because of them, right, to another statement. Okay. Going from statements known or accepted, and because of them, to another statement.

[22:14] Now, maybe a little more precise, but a little more clumsy. Turn around now. Look at it from the point of view of the the end, right? Which is the conclusion, right then? Okay. Here I define it as coming to know

[22:40] or a statement from other statements, right? And because of them, right? Now, what's the difference between knowing and guessing? When you're guessing, you're not sure certain, right? And sometimes you 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.

[23:53] Other case, I'm not, right? Okay. Sometimes we distinguish logic between opinion and suspicion, right? But opinion and suspicion are both what? Guess, right? Okay. But the opinion is is stronger, right? And that's more an effect of dialectical reasoning, and the suspicion is weaker, right? More the effect of rhetorical reasoning. Now, Socrates in the Meno, 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?

[24:42] He says, "There's 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? So it's very, very exacting to know something, right? But in the in the Meno, he says, "I know that there's a difference between knowledge and even right opinion, right?

[25:08] 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?

[25:18] It's you got to stop and say, "Why is it so? Why is it so certain?" In other words, right? That there's a difference between knowing and guessing.

[25:31] You could never come to the right conclusion. I mean, if everything was just guessing, you'd really never know anything. Everything would be uncertain. Well, now you're trying to give reasons why there's got to be knowledge as well as guess, right? But I'm saying that there's a difference between knowing and guessing. Why is Socrates so sure that he will, contrary to his usual remark? I don't know what virtue it is.

[25:50] He says, you know, to get the dialogue, if you've read many of those, he'll say, "I know, I know." It's one of the very few times in the dialogues 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; other case, you're not certain. The same thing cannot both be and what?

[26:16] Not be, right? It can't both be certain and not be certain, right? So that's what. Sure, there's a difference between knowing and what? Guessing. And that doesn't mean that you're always aware of the fact of whether what you think is 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? Can't both be and not be, right?

[26:48] 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? " He's objecting to Socrates. He's our himself making the distinction, right? If you deny that Socrates knows the difference, right, you say he just guesses that there's a difference.

[27:27] See, then you're saying, "All right, there's a distinction between the two, right? " Yeah. So you see how certain Socrates is of that, right?

[27:39] I notice here when you guess that something is so from other statements and because of them, 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?

[28:11] Okay. The great philosopher, the central thinker of human thought here. Let us not guess, he says, at random about the greatest things. Beautiful little fragment. I say to students, and look at that fragment. Let us not guess. Put it on the board here. let us not guess at random. So what he's saying here is, in a way, if you must guess, right, have a reason for your guess, right?

[29:14] Don't just guess wildly, right? Okay. I know that sounds If I try to imagine your parents' home or something, right? I have no reason to say your parents' home is two stories or a ranch or whatever, right? You know. So it'd be kind of purely imaginative in my part, right? I wouldn't have any reason for guessing one rather than another, right? That would be a wild guess, just a pure guess, right?

[29:44] Okay. But in the sense he's saying here, let's have a reason for our guesses, right? Now we see if we can get more than a guess knowledge. That's even better obviously. But let us at least begin with a reasonable guess, right? Okay. Now if we do some philosophy of nature sometime in another course, we looked at the fragments, you know, of the natural philosophers that come down to us.

[30:13] And when I teach those, I say now we're looking for at least reasonable guesses that these men are making, right? And the reason why what they say, they might have for saying what they say, right? And notice in most cases, son, a man guesses the truth before he what knows it, right? Even in the easiest sciences for us, like geometry, the geometry would tell you that he guesses that something is true before he finds the reason why it must be so.

[30:52] And you know, in these simple theorems of geometry, like you, you have an isosceles triangle. You would probably guess that the angles at the base of the isosceles triangle are what equal, right? Or an equilateral triangle, I would guess that the what angles would be all equal, even before the rigorous proof is found, right? I wouldn't look for the reason why those angles must be equal if I had not already what guessed that it was true, right?

[31:25] So in man's thinking, apart from those things that we kind of naturally come to know, like the axioms and their parts, we tend to guess the truth before we know it, right? And sometimes a reasonable guess is as far as we go right? Okay.

[31:48] I might mention there that in the Greeks, son, the Greeks found two common arts of guessing. And one is called dialectic, and the other is called what rhetoric, right? We found two arts of guessing, and dialectic is an art of guessing about general questions, and rhetoric is in part, although there's other parts to it, but part of rhetoric is about guessing about the singular contingent, who done it, what should as a country do, and so on.

[32:31] So there are two arts of guessing, not of making wild guesses, but of making what reasonable guesses, huh? And then in modern times, you're all familiar with the number of arts of guessing that are more particular than dialectic or rhetoric. And so the weatherman, for example, right, he has an art of what guessing the weather, right? You might say there's a seventy percent chance of rain tomorrow.

[33:03] Okay, he's guessing there's going to rain tomorrow, but he's obviously what doesn't know, okay? And then the economist has an art of guessing what the economy's going to do, right? Okay, and you read the interviews where he said top-notch economist, the U. S. News and World Report, and he'll say what the economy's going to do over the next few months, right? But there'll always be in there some phrase barring unforeseen circumstances, the economy, da da da da,

[33:39] and you see Merrill Lynch, you know, talking about you can get their paper now and what the effect of the Bush tax refund upon the economy, how the effect, you know, in guessing what the effect is going to be, right? But no, see, people are paid to guess. The weatherman is paid to guess. The economist is paid to guess. By industry or by government, right? And people are not paid for making wild guesses.

[34:06] They're paid for making reasonable guesses. Now, of course, you might have a low opinion of the weatherman's art, but he has some basis for saying it's going to rain tomorrow or likely. You know, expect some showers or something, right? You'll say. I know back home, you know, they used to have a contest in the newspaper, you know, where you'd out guess the weatherman.

[34:35] But what we call experimental science is also involves guessing, right? But when Einstein speaks of the guess of the scientist, which is an hypothesis, he says it's not a reasonable guess. He says that the guess of the scientist is freely imagined, so it's a wild guess.

[35:05] Is that again? Einstein. Einstein. He says that the guess of the experimental scientist, of the physicist, of himself, right, is not a reasonable guess, right? It's a freely imagined guess,

[35:25] and therefore his guess has to be what tested, right? As it is by its consequences and so on, right? So you have something even weaker there than a reasonable guess, right?

[35:52] But a reasonable guess is something less than knowledge. So reasoning then is coming to know or guess a statement from other statements, and because of them, you have to see that in there, right? Not just going from these statements to those statements, but the statements you're coming to is because of the ones you first who are accepted, huh? Now sometimes a man will make a bunch of statements and say, and therefore, and then the conclusion emerges, but it's really that, right?

[36:34] It doesn't really come out of his premises, right? Okay. Now perhaps you could define this or change the language a little bit differently here and say that reasoning is coming to know or guess a statement through other statements, huh?

[36:58] Okay. And we could add a phrase that's known or accepted, right? Okay. Period. Two from other statements known or accepted. Huh? Is that same phrase there? Okay. So reasoning is coming to know or guess a statement from other statements already known or accepted, right? And because of that, right? Okay. Or reasoning is coming to know or guess a statement through other statements, right? Okay.

[37:38] Already known or accepted. Okay. Sometimes you don't add an old phrase, but that's kind of understood there, right? Okay. That's what reasoning is. Now, calculating is something like that. But calculating is what? Coming to know or guess a number. A number from other numbers, right? Okay. Or from other numbers. Okay. Now, someone might say, "Why do you use the word 'guess' when you talk about calculating? Is it adding, subtracting, multiplying, or dividing?

[38:23] Isn't that a rather rigorous thing, right? Well, that's true. But even if you add, subtract, or multiply or divide correctly, the number you get, you may still be only a guess. Why? Either you started with numbers that were a guess. Yeah. So when we sit down and say to calculate how much that's going to cost us or something, right? Or how much you know it's going to cost us for this dinner, right?

[38:57] Huh? Okay. And so maybe we had the. Number of guests are going to be coming to dinner, right? And then we have to multiply that by the number of of beers per guests, let's say, right? Okay. So I can multiply the number of guests that I have—I think are going to come, right—and the number of beers on average that each guest will drink, right? And multiply those numbers very correctly, and yet am I sure the number I get?

[39:25] No, because some guests might not show up, right? Or there might be some uninvited guests, right? Someone might get sick, whatever, right? So we get some of them coming, and they might be particularly thirsty that night because it's a hot night, or you know, or they might be a stevious right? They might have taken the pledge or something, who knows. And so the numbers I multiplied I wasn't sure about, right?

[39:53] So in calculating, we'll see is a bit like the syllogism. In syllogism, the conclusion follows necessarily from the premises. But if you're not sure about the premises, the conclusion is not what something to be sure about, even though it follows necessarily from that, right?

[40:18] So in order to be sure of the conclusion, you'd have to both be sure of the statements on which you reason, and the conclusion would also have to follow

[40:32] necessarily. And it's possible to have one of those without the other. Now, sometimes I guess those due to the fact that even though your statements might be true, you might not be sure about them. The conclusion doesn't follow, but necessarily from that, right? Because it's not really a syllogism, there. So you have no idea what reasoning is now. I sometimes say to my colleagues, even in philosophy, I say, "Now, do you try to get students to reason in their class?"

[41:11] And they say, "Yeah." And I say, "What is reasoning?" And even people, you know, teaching philosophy, they don't have any definition of reasoning. You know, they've really not thought out distinctly what reasoning is. And notice

[41:26] this here does say more clearly and distinctly what reasoning is than the word reasoning does, right? I kind of like to use the word coming more, you know, because you can use the word going, right? So it's coming to know our guess at a statement, right? From and because of right other statements already known, or accepted

[41:55] So. now we know a little bit what reasoning is Now, an argument the same thing as reasoning. An argument. What's the genus of argument? then? Tool, Tool, okay. But these tools that we're studying in logic are speeches, right? Okay. So, argument is speech

[42:43] bringing together the statements from which we're going to reason, right? So, a speech bringing together the statements from which we reason. Now, the statements from which we reason, as we maybe said in the text I mentioned last year, the statements which we reason are called the what premises. And I'm kind of stubborn. I prefer to spell my premise that way, but a lot of people want to spell it the P-R-M-I-S-C, right?

[43:43] But I got attached to premise, so okay. Premise, you mean you mean the premises of property, right? But I always spell premise P-R-E-M-I-S-S. You see, some people spelling. P R E M I S, right? I'm probably a minority. I know one, but some of the minority, right?

[44:12] And the statement to which you reason is called the what? Conclusion, right? What is the sense of the word premise? Well, the Latin word premise

[44:29] is used to translate the Greek word from protasis. Protasis, protena, protena. Greek has a sense of stretching forward, right? The Latin word has a sense of what? Sent before, right? But the Greek word in the sense is more accurate. Protasis, Greek word, or premise, protasis. But it comes, I think, from the word proteino, which means to what? Stretch forward, right? So the premises not only come before the conclusion, right?

[45:04] But they stretch forward, producing the what? Conclusion, right? Notice in in reasoning and in calculating, for that matter, which pertain to two different arts, which the Greeks called logiké and logistiké. They have a similarity, right? They're both arts for coming to know something you don't know, right? But we imitate

[45:39] the premium, the, logic, the nature premium, right? It reasons so far as possible, it imitates nature, right? Now, notice in nature, two dogs come together, male and female, and produce another what? Yeah, two dogs don't come together and produce a. an elephant. That's that'll be unnatural, right? And two. elephants, other than male and female, and they produce not a dog or a cat, but a what? Elephant, right?

[46:10] So when two statements come together, they produce what? Another statement, okay? So like the parents of that, right? And likewise in calculating, when two numbers are added together or multiplied, or whatever, you get another what? Number, right? Okay. As the British astrophysicist there, Sir Arthur Eddington, right, the head of the scientific team, they confirmed the general relativity, right? And he says, you know, put in numbers, what do you grind out?

[46:46] More numbers, right? Well, that's natural, right? Imitating nature, right? The the offspring resemble the parents, right? And you'll see another likeness there too that. Just as in sexual reproduction, it's two parents are enough to produce a third one, right? So, in the most exact reasoning, all you need is two statements to produce, say, what third statement? Then the syllogism you see that, right? Right. So you have just two premises, and they produce a third one, right?

[47:27] And notice you need at least two numbers before you can add or multiply or divide and so on, right? The idea of two producing one is like this. There.

[47:42] So, argument then is speech bringing together the statements from which we reason. So, what we're going to do now is to look at the main arguments, right? And this is the four kinds that we start talking about here on the second page.

[48:01] Now we're going to kind of enumerate these four kinds of arguments first, but towards the end of the the paper or this these pages, we're going to divide the arguments, right? How do you get the four? Right. A couple ways you can divide to get the four, right? Okay. But it's I think useful to first meet each one of the arguments by itself along the road, which is natural to us, right?

[48:35] And that's the road from the senses into reason. So sometimes I draw that road on the board for you. Okay. The road from the senses into reason, right?

[48:55] Now you notice that I draw the road. Pure, right? And sensing is easy, right? But the further you go along the road, more difficult it is. It's an uphill

[49:12] journey, right? Okay. And that kind of fits also the fact that we put the more universal above the less universal, right? And so a thing, when sensed, is singular, as Aquinas says, and when understood, it's universal, right? So the chair that I see with my eyes, an individual chair, a singular chair, right? The chair that I can grasp and feel, a singular, right? But when I understand what this is in front of me, this is a chair, right?

[49:47] I'm understanding something what universal? Because what a chair is it's common to this chair, and to other chairs, right? So a thing is singular when sensed and universal when understood. We talked about that a bit when we talked about the natural road, right? And therefore, those arguments that begin with something singular are more known to us, right? And they're easier for us, and they're closer to our senses, right?

[50:19] Okay. So the argument which the logician calls example, and the argument which the logician calls induction, these two kinds of argument begin from something singular. An example can be just one singular, right? While the induction begins from what many singulars, right? Okay. So these two arguments, first, you might say, along the natural road.

[50:56] Now the last two arguments that we meet along the road, the enthymeme and at the very top here, the syllogism. The enthymeme begins more from something universal rather than singular. Usually not something quite universal, but something maybe true for the most part, you know. But it's not so much starting from singular, but more starting from the the general. But the syllogism starts from something completely what universal.

[51:36] So in that sense, the syllogism is most into what reason, right? Okay. So we're going to talk about example, and then about induction, and then about enthymeme, and then about the syllogism, right? Which are these four kinds of arguments?