Logic (2016)
36. Reason Knowing Itself; The Second and Third Figures of the Syllogism
Class of 2017-03-16
https://berquistcourse.com/course/philosophy/2-logic-2016/036-reason-knowing-itself-the-second-and-third-figures-of-the/

[0:00] So I have to go through the four senses of before there, you know, and I say to the students, "One sense of before is one sense of before, before another sense of before." Oh no! Why are you doing this to me? You know. But it is important to realize, huh? This is a word equivocal by reason, and that's reason looks for order, right? So there's an order among those meanings, right?

[0:24] Well, if order means before and after, it's got to be in one of those senses, right? And you got to stop and think now, right? It's the third sense.

[0:36] Another thing I like to do is I like to simply bring out to know that distinction and order, right? And I say, give me the distinction and order, distinction order. But

[0:50] what does distinction mean, right? It means this is not that, right? But order means this is before or after that, right? Okay, so that's the distinction of distinction order. What's the order, right? Well, you have to see distinction before you can see an order. And I know that by the axiom of before and after that nothing is before or after itself, right? So now you know distinction and order of what?

[1:15] Distinction and order, right? But you know this is because logic is called the the philosophy of reason, right? And what's marvelous about reason is that it can know itself, right? And so when reason thinks out the definition of reason, right, it's coming to know itself much better than it did before, right? So when Shakespeare thinks out that reason is the ability for a large discourse, between before and after, right.

[1:47] He's kind of obeying the what the seven wisemen of Greece, right? They met in the Oracle Delphi, according to the tradition, right? And they put up two things for everybody to see. You came from the oracle of Greece to go to the oracle of Delphi, right? It's like going to Rome or something, right, their capital. And they put up the thing, you know, nothing too much, and know thyself, right?

[2:14] Nice to say to students now. To whom are the words know thyself? That's an exhortation. It's not a statement. It's an exhortation. But to whom is that addressed? It's not addressed to God or the angels because they know themselves first of all, most of all, right? It's not addressed to what the trees or even to the dog because the dog can't be know what the dog is.

[2:36] It's addressed to someone that can know himself but doesn't know himself very well, and that's man, right? But more precisely, you can say it's directed to your reason, right? Because anger doesn't know what anger is, and digestion. Doesn't know what digestion is, but reason can know what reason is, right? So in a way, it's addressed to: reason know thyself, right? And this is reflected in science, in the philosophy of reason, right?

[3:09] There can be what? I mean, a definition of reason can have a definition of reason, reason can know itself, but there can be a definition of definition, right? Kind of an amazing thing, right? So the definition of definition is speech signifying what a thing is, right? And I often like to ask students and say, now is the definition of definition a definition of the definition of definition?

[3:40] Is the definition of definition a definition of the definition of definition? Who would you say? Yes or no? Let me think about it. Let me think about it. Is the definition of

[3:55] definition a definition of definition of definition? Yes or no? I started talking about this. This guy who I met who's teaching philosophy at the Western University,

[4:09] He's talking about you know what the you see the faces of the kids who are teaching philosophy, right? You know, and they start saying, why am I doing this to me? You know, that's kind of a joke.

[4:23] No, it's the definition of definition, right? Is speech signifying what a thing is, and that's true of the definition of square. It's a definition in that sense, right? So it's not a definition of what the definition of definition. It's a definition of definition in general, right? Okay. So if this is the definition of square, it's a definition of the soul. It's a you know each of them is speech signifying what a thing is.

[4:53] So the definition of definition is not a definition of the definition of definition. It's a definition of definition in general. Is that clear? Do you see it? Do I mean? No, I'm going too fast. But I mean,

[5:08] it is interesting to come back upon this, right? So you can have a definition of definition. You can have a statement about statements, right? A statement is speech signifying the true or the false. I've now made a statement about statements, right? Well, this is reflecting the fact that reason can come back upon itself and know itself, right? And reason is really the only part of me that can know itself, right?

[5:33] And therefore, reason is the only thing that can really fully obey what the great seven wise men said: know thyself, right? It's an easy thing, right? Remember how when Thomas was talking about the distinction of the Trinity, right? And he makes use of a what? Distinction of distinction, right? The distinction. You've got the formal distinction, which is by opposites, and then the material distinction, which is the what division of the continuous, right?

[6:05] So when Euclid divides a straight line into equal parts, right? It's it's what dividing the continuous, right? But when we divide being into substance and and what accident, we say well accident exists in another, isn't a subject, substance is not, right? It was opposites, right? So there's a there's a distinction of distinction, just like there is a what definition of definition.

[6:34] It all goes back to the fact that reason can come back upon itself, right? It knows its own act, right? Does love know what love is?

[6:48] But reason to some extent knows what understanding is and what reasoning is, right? It's kind of a marvelous thing, reason in some ways, right?

[6:58] Now the other thing the wise men said was nothing too much, right? So can you love, you know, can you avoid loving God too much? What would you say? How would you answer that? I mean, if you say the wise men are wise men, right? These are wise men right They've been profound as know thyself, right? And then they said nothing too much, right? Well, that seems to cover everything, right?

[7:23] Nothing too much, right? So you shouldn't have loved God too much, right? You uh well God's not a thing. I mean, he's nothing? You know even Boethius says that the Trinity is three things, he does, right? Or that can say he's not created. Yeah, yeah, but he's a thing. He's something, right? You got to be careful, you know, because you know they kind of it's kind of a common thing they're talking about all the time in the parishes, you know, that you got to get the guy to not regard the girl as a thing, right, to play around with, but as a person, right, okay.

[8:03] But in some sense, we might divide person against thing. Other times, you would say what person is a thing, right? Person is something, right? They're not nothing, you know. And really, to resolve it, person is something, right? And so this is one of the ways that a name becomes equivocal by reason, right? Sometimes a name is said of many things, but one of them keeps it as its own name, right?

[8:30] And a new name is given, right? An example there that they give in logic is when Aristotle talks about disposition habit, right? Sometimes he says habit is a disposition that is firm and not easily lost, right? And then there's a disposition that is easily lost, right? But sometimes he divides habit against disposition, right? As if the disposition that is easily lost keeps the name disposition as its own sometimes, and then we give a new name to this disposition as firm, which is habit, right?

[9:05] You find all kinds of examples of that, right? When Aristotle is in the in the book on physics I mean, on book of places, right, on dialectic, right, and he talks about property and definition, right? And property is what convertible with what something, right? Like half a four is convertible with two. Every two is half a four, and everything half a fourth is two, right? And but then sometimes he divides property into property and definition, you see.

[9:41] And definition, one sense of property, it's a convertible speech, right? Every square is an equilateral right angle quadrilateral. Every equilateral right angle quadrilateral is a, you know, every man is an animal that has a reason. every animal that has a reason is a man, right? You know. But definition does something more than property, right? It brings out the nature of thing what it is, right? So it's got a certain excellence.

[10:02] So it gets a new name, definition, and then the property that is not bringing out the nature that keeps the name property, right? I told you how my mother didn't like it. I said man is an animal, right? Because sometimes you keep animal for what the beasts, right? But sometimes you say man is an animal, and not insulting somebody, you know. I always say if your biology teacher says you're an animal and not a plant, it's not insulting, I don't think.

[10:28] But if your girlfriend says you're an animal, she's probably insulting you. Okay, notice here now, the two forms of universal forms here, universal premises in the first figure, two of them are syllogisms, right? And by one of them you can syllogize a universal affirmative. And this is the only way you can, by the way, in direct syllogism, right? And by one of them you can what syllogize a universal negative, right?

[11:05] We'll find out in the second figure you can syllogize sometimes universal negative, but never universal affirmative. We'll see in the second figure. And then there are two or nothing follows, right? So Aristotle brings this out, right? But notice how you know that these are valid in a different way than you know these are invalid, right? You can't prove these are valid by examples, right?

[11:34] But you can use examples to show that either of these is a syllogism, right? How can you do that, right? Well, an example doesn't show that something is always so, let alone just necessarily so, right? I'm a philosophical grandfather, okay. So every philosopher is a grandfather. No,

[11:59] but I'm not a philosophical tree or something, right? You know. So I mean, okay. Can't go over this many times, but to kind of see what we're doing, you know. Okay. Okay. Now we'll go to the second figure and take the four universal cases there. We see that. I'm going to break this little example here.

[12:39] I used to give this one to kids sometimes in the exam, you know. Every mother is a woman. Okay. No man is a mother. Now, in what figure is this?

[13:23] First, is a universal affirmative. Second, what figure the Stoicist is the middle term in? Yeah, it's in the middle, right? Yeah. So it's in the first figure, right? It's in the slanted position, you might say, right? Middle term, right? Okay. Now, if I say to my students, what follows from this? What do the students have to say, do you think? If every mother is a woman and no man is a mother, then no man is a woman, right?

[13:56] Wouldn't you kind of be tempted to say that, right? And that's why I knew Mark was wrong. you think it is no man is a woman.

[14:12] Okay. Now, the reason why he's deceived is because of the matter, right? Now, he knows that it's true that no man is a woman. At least he knows that, no man is a woman, right? And he knows that there's some connection between the fact that man, no man is a mother, and no man is a woman, right? But does this conclusion in the form follow necessarily from these two, right?

[14:38] See, well, I'll give you another one. Every dog is an animal. That's true true. And no cat is a dog. Now, nobody think it follows that no cat is a what? An animal? Because they know it's false, right? So they don't want to say that it follows. They know it's true every dog is an animal. They know it's true that no cat is a dog. They know it's not true that no cat is an animal, right?

[15:13] Okay. Well, why are they deceived by this and not by this? It's exactly the same form, right? See, if this really followed from these two premises, then would follow here that no cat is a what? Dog.

[15:35] Okay. This doesn't follow from these two, right? Even though it's true that no man is a woman, right? And given there's a reason why man is neither a woman nor a mother, right? Now, okay.

[15:58] But still doesn't follow by the form, right? See how easy this is to deceive them? You see, sometimes no man is a woman. Um, if you do the fruit turn right now, so this is A and this is B, right?

[16:20] Sometimes in this form, uh, no man is an animal, but is a woman. The universal negative is true, right? Sometimes the same form here, every B is A, right? No C is B, same form, right? Every what?

[16:48] Excuse me. Oh, right. How was it going? Cat is an animal. Sometimes every cat is an animal, right? Sometimes every C is A, and sometimes no C is A, right?

[17:08] So if the universal negative is sometimes true, no affirmative is always true. The universal negative, the universal affirmative is sometimes true, right? Then what?

[17:23] Then no universal negative is true. Yeah, then then uh the the two negatives are false ones, right? Okay, I I put this down here because it's what showed that what you're saying if this followed, right? Did you say the same thing down here? Right? That form is is invalid, right? It may be that every C is A. It may be that no C is A. There's nothing you can say affirmative or negative that is always so.

[17:49] And if nothing is always so, then nothing is necessarily so, right? Now you can put in the form of these then syllogism you wanted to, right? If something's necessarily so, then something is always so, but if nothing is always so. Therefore, nothing is necessarily so. is not so. There, A and B are standing for premises. Oh, I just give great pleasure in them. I'm curving them up.

[18:22] Yeah, yeah, yeah. What is deceived there, right? Because he knows that no man is a woman is true. He knows there's a connection between his not being a mother and his not being a woman, right?

[18:47] See how subtle it is. Is it clear? I'm going to look at the second figure right then? On the second figure, the way to remember this was that the middle term is in the second place, right? Stared out. Okay. So,

[19:19] what are the four universal cases? Every A is B, and every C is B, and we could say no A is B, and no C is B, C is B. Two affirmatives, two universal negatives, right? And then you have the two mixed ones, with in one case the universal affirmative on top, right? Like every A is B, and no C is B, and then the reverse here, no no B, and

[20:15] every C is B. Okay, those are the four universal cases, right? Every C is B. Oh, okay. See, that's it. I got this. I'm stupid. Next two mistakes. So you got to check yourself, right? Now the question is, does anything follow with C as the subject and A as a what predicate, right? In any one of these four cases, right? And if so, what follows, right? Okay.

[20:54] And take that first one: every A is B, and every C is B. You certainly can't try for the set of none, but that requires a universal negative, right? You could try for the set of all, maybe, right? Because you have universal affirmatives, right? But does anything come under the subject of this universal affirmative?

[21:22] So the set of all would require every A is a B, and whatever is an A is a B. But nothing is said to be an A, is it? Anything said to be a C? No. So the set of all doesn't apply to this. It's standard now, isn't it? You do have a universal affirmative. In fact, you have two universal affirmatives, right? But the set of all requires not only universal affirmative, but something else which is said to come under that.

[21:51] What? Subject to the universal, you got two universal affirmative inferences, but nothing is said to be an A or a C. There's no way to get the set of all, right? So, you're not going to have the set of none, right?

[22:06] Now, if I could turn this around and say every B is an A, then I'd be back in the first figure, and I have a universal conclusion that every C is A. But can you turn around necessarily a universal affirmative? It necessarily converts to the particular, but not to the universal. So conversion is not going to get me there either, right? I give up. I give up.

[22:33] But I'm a tough guy, you know, and I want to prove that when these are true, it could be that every C is an A. It could be that no C is an A, right? So I'm going to find examples. Give myself a little more room here. Um

[23:05] Just down here and we no excuse me No way it's the fake So I want to find examples for A, B, and C, right, that satisfy what two conditions?

[23:33] Well, I want to have examples for A, B, and C such that when you place them into this position, right, the premises will be what true. So there'll be no defect in matter. And I want a second condition: to have one set of examples where every C is an A,

[23:57] and one where no C is an A, and that'll knock out everything. Because there's only two possibilities: affirmative or negative. A universal affirmative knocks out universal negative and particular negative. A universal negative knocks out universal affirmative, particular affirmative. So it's all there. Did he

[24:25] get the mark? This is a man. The major premise is a minor premise. He's a major premise. Okay. So I'm going to try to find examples now for A, B, and C to prove my suspicion, right? Now, can you think of an A and a B such that every A is a B? Yeah, you're smart.

[24:54] And can you think of a C such that every C is also an animal, right? And every C is a a a dog. Well, do you know any particular kind of dog? Cocker. Yeah, that's what I was thinking. Yeah. So I'll just cocker spaniel, right? Okay.

[25:21] So cocker spaniel. Every cocker spaniel is a dog, as an animal, right? That's true. Every cocker spaniel is a dog, right? Now I need an example, another example here for a C that is always an animal but never a dog.

[25:42] Okay. Now I make stupid mistakes, right? You all make stupid mistakes. So I'm going to check my homework, right? Every A is a B. Every dog is an animal. Is that true? Yeah.

[26:06] Every C is a B. Every cocker spaniel is an animal. Yeah. Every cat is an animal. Yeah. I have satisfied condition number one, Mr. Burquist. Okay. Now you get to get up on the board, you know. They got to do all this. Now what's the second condition I asked them? You know, do you have to put that too? One statement that every C is a. Yeah. And one statement that no C.

[26:33] Yeah. Now I'll circle the every C is a cocker spaniel, right? And that knocks out any what negative statement, right? And then one example to underline where no C is an A. No cat is a dog, right? That knocks out any what affirmative statement from being always true. So this shows that when these are true, even right,

[27:07] nothing negative could always be the case because sometimes universal affirmative is the case, and no what affirmative statement could be true always, right? Because sometimes no C is A, right? All I need is one example of each, right, to show that there's nothing affirmative or negative that is always what so. That's complete disjunction. Right, it's got to be affirmative or negative, right? Universal or particular. But the universal affirmative knocks out both negatives, right?

[27:42] Kills two birds with one stone, right? Aristotle does it a lot, right? And the universal negative knocks out both affirmatives, right? Kills two birds with one stone. Okay. I could have three different examples for A, B, C, you know, but that's for those who want to do extra work, you know. We don't need that.

[28:08] So nothing follows from this case of the second figure, right? Okay. Now what about this mess down here? Can anything come from two negative parents? Huh? No, no. But I want to make sure, right? So I want to find examples for A, um, my book foot down here. A, B, and C that satisfy what two conditions?

[28:51] Well, when you substitute them into this case, both premises are true, right? And that shows that you have no difficulty with your matter, right? It's not because your your statements are false, right? It's just there's nothing false in them, right? Okay. And then what's the other condition that is satisfied? That the universe could be both. Yeah. At some time, every C could be A, which meant no negative can be always true.

[29:23] And another example where no C is A, no affirmative statement can be made, right? So there's nothing affirmative or negative that can be. I know this is a little bit like like addition, subtraction, multiplication, division, right? Now, it's one thing to have the right numbers, right, to add, subtract, multiply, or divide, right. And the other is to what? Is to multiply or to add or subtract, right?

[29:59] Okay. Now I always take the example of one's checkbook, right? And sometimes your numbers don't agree with the bank's numbers and so on. And sometimes you go back over your your checkbook and you find out you made a mistake, right? Sometimes you misread the number you wrote, you didn't make, you did it kind of sloppily, right? And you discover that, you know. But sometimes you did an add or subtract, what?

[30:24] Corrected, right? Sometimes you might have made both mistakes, right? Okay. So your number you get by adding, subtracting, multiplying, or dividing can be the wrong number, right? Either because you have the wrong numbers or one wrong number at least, right? To add, subtract, multiply, or divide, or because you didn't add, subtract, multiply, or divide. If you're really stupid, you could make both mistakes, right? I had no.

[30:52] And you know, in Aristotle, if you remember in the first book of Natural Hearing, he takes a what? Listens, right? He says, well, his premises are false, right? And his conclusion doesn't follow. So that already finishes the guy off, right? I mean, he strikes you as if they're true, it would follow, right? But but so you know what they say is the bad happens in many ways, the good in one way, right?

[31:20] So in order for your your syllogism to be good, the premises have to be good, that is to say true, right? And the conclusion has to follow, right? See, just like in order for my addition, you know, we're out in the the ocean there and going to buy ice cream cones for the grandchildren. So I'm going to have to, you know. So I got to know how many grandchildren I have, which is 19, and what an ice cream cone costs, right?

[31:49] And then I have to multiply correctly, right? Yes. Yeah. So if I have the wrong price for the ice cream, right, or the wrong number of grandchildren, I can be mistaken what's going to cost me. Or if I don't multiply correctly, right? Yeah. So there's a link there between the two, right? The Greeks called the art of calculating, you know, logistike right? Forget about it We're going to have logistics, right?

[32:15] And but the one for reasoning is logic, I think. But they're both taken from reason, right? Because reason does both of those things, right? Okay. So

[32:29] can you think of an A and a B such that no A is a B? Nothing wrong with the same examples more often. Yeah. What? No stone is an animal.

[32:46] Okay. It's easy to think of that, right? I got a little more thought, you know. I got to find two examples for C. One such that no C is an animal, right?

[33:03] What is it? Tree. Tree. Now, tree is not an animal, and it's not a what? Stone. Yeah, it'd be kind of hard to follow, right? I have all kinds of stones.

[33:20] So that's maybe not an example for me because I'm kind of stupid about knowing the names of particular kinds of stone, right? But you could if you had no particular kind of stone, right? Okay. So

[33:36] I take stone for our middle term here, right? A lot of things are not a stone, right? Can you think of a C and A that is not a stone? Well, you could say animal, right? No animal is a stone. Can you think of a C that is not a stone, but it's always an animal?

[34:01] Well, dog, right? I got to think of another example where instead of every C being an A, no C is an A, but it's still not a what? Stone either. Tree. Tree, yeah.

[34:19] If you can use the same stones, you know, to kill two birds, do so, right? Okay. Now I'm stupid and I make stupid mistakes sometimes, right? I think I showed something here. So I just check my my work here. With these examples, are these statements when you substitute them in, are they true? Well, no A is B. No animal is a stone. That seems to be quite true, right?

[34:47] No C is a B. No dog is a stone. That seems to be true. And no tree is a stone, right? Okay. I have satisfied condition one, but that's not enough. Now do I have one example for the second condition, right? Of every C is A, and one example where no C is A. Yeah. And I'll circle the one where every C is A. Every dog is an animal, right?

[35:16] And I'll draw a line under the one where no C is an A, right? I have satisfied both conditions, right? So dog and animal show that when these premises are true, no negative statement is true always, right? And these examples, animal and tree, show that when these statements are true, no what affirmative statement is always true. So nothing affirmative, nothing negative is always the case, right? And if nothing is always the case, then nothing is what necessarily so.

[35:59] And if nothing is necessarily so, you've got a syllogism. What's the definition of syllogism? Well, speech, right, in which some statements laid down, another follows necessarily because of those laid down, right? Okay. When Shakespeare says it must follows the night the day, if you're true to yourself, you canst not be false to any man, right? But is that a syllogism, right? That night follows the day, right?

[36:37] Not because, not because of day it does night, right? It's something else, right? It's the sun going around the earth. I don't believe the earth turns on its axis.

[36:52] Okay. What? Can you go through any other second condition? Yes, sir. Okay. The two conditions, huh? When these premises are true, I want to show it could be that every C is A, or it could be that no C is A. And if it could be that every C is A, then no negative could be always true when these two are true. And if sometimes no C is A, who is it?

[37:25] No affirmative could always be the case. So there's nothing affirmative or negative. That's all there is. That's a complete division, right? Of simple statements, right? Are either affirmative or negative.

[37:38] So neither any affirmative, dog an animal shows what? No negative statement is always the case. This shows that no affirmative statement is always the case. Therefore, the ball game is over, right? This is not a syllogism, right? Okay.

[38:01] So this was what? Same thing, wasn't it? Yeah. So these neither one of these is a syllogism, right? Yeah. Okay. Now, how about down here now?

[38:20] Well, thank God you can what? Convert universal negative, and it remains universal. There you go. That's why you can get universal negative in the second figure. So I convert to no B is A, right? We showed you could do that always. And then just bring this over, right? You get every C is B. Okay. To abbreviate everything, every. And lo and behold, back in the first figure.

[38:53] See why we call that the first figure? All you can do in the second figure is show the universal negative, right? But to do so, you got to convert and you run back in the first figure. It's more powerful figure, and it's more clear. It's all kinds of easy to put it first. Okay.

[39:13] So by conversion, I see then that it follows that no C is A. So this is another way I can prove the universal negative, right? Propositions in that form.

[39:28] What about up here? What? Got a universal negative. Yeah, yeah. The bottom. So I could, you know, I could have, but could I have any conclusion with C as the subject and as a predicate? That's the question I'm asking, right? Because no B is C would put that here. No B is C, and every A is B. Well, then no A is what? Is C, right? No A is C,

[40:08] right? Which converts. I can convert that around to no C is A. So I left this to last because you had to convert twice, right? Again, a universal negative, right? Now you might suspect you can't get universal affirmative conclusion even out of two universal affirmative statements. How you gonna get so with you know a negative statement or you have particular statements, right? So it's falling off. The power is going down, right?

[40:39] You know, you can get universal conclusion, but only universal negative in the second figure. The first figure could have universal affirmative and universal negative, right? So that's a more powerful figure, right? And if it's still just in the first figure, you can see it right away from the set of words, doesn't it? Here you've got to convert, right? Here you've got to convert twice. Oh my goodness!

[41:07] So see, here you just have to convert the major premise to you. All set. Back in the first figure. Here you've got it. A and C are reversed, and you can turn that around. Two conversions.

[41:32] Well, that was fun, wasn't it? Good. Good. I like lots. Lengths and exercises. Did you switch the? What? You put the minor premise to the major. Yeah, I can know AC and I turn around to know CSA. I wanted to see what the conclusion is. Suddenly, it's predicate, right? And you're kidding by two conversions, right? Yeah.

[42:01] Kind of missing there. To take me back to painful memories of my freshman year. God. Well, you take you take. I took logic, but I wasn't very. One, I wasn't entirely awake, and it wasn't very. It wasn't a good presentation. Yeah. My favorite class. In high school. You

[42:30] never get anything in any figure but two negatives, huh? Well, the affirmative and negative because it always has a what? Negative conclusion. To affirmatives together, affirmative conclusion. Now in the third figure, your

[43:02] middle term is the subject in both cases, right? Okay. So you've got every B is A and every B is C, C, right now. Okay.

[43:26] So the middle term, the common term, is the subject in both premises, right? In the second figure, it was the predicate in both, right? In the first, it was that slant, right? It was the subject in the first major premise and the predicate in the second. Or middle term should be in between, right? Okay. And then you have down here these two negatives, right? No B is A and no B is C.

[44:05] And then you have the two ones where you have a mixed one, universal affirmative. Like every B is A and no B is C, and then it's the reverse. No, no B is A and every C. Yes, not the other one, right? Every B is A.

[44:41] Okay. Now the question is, with premises that are true in this arrangement, does anything follow necessarily, right? Now every B is an A. Ah. Now if I could find out that something was a B, I could say it's an A, right? Mhm. But I'm not saying anything is a B over here, am I? But could I turn this around? Mhm. Yeah. You can convert a what? Universal affirmative partially, right?

[45:21] So I can convert this to some C is B and keep on top here every B is A. And lo and behold, by magic, what figure are we now? First figure. Yeah. Well, by conversion, I get back to first figure, and I can see right away that the set of all, right, applies. If every B is an A, then whatever is a B is an A. Now you only know that some C is a B, right?

[45:53] So some C is a B Yeah. So this is going to see in the third figure you only you only have particular conclusion, right? So even out of two universal affirmatives, that's the most from from affirmation you can get, right? Can only get some C is A, right? Oh, he's trying. He's squeezing as hard. Yeah, he can't even get that particular. See, but I can reason out that some C is A, right?

[46:26] This is what's called reasoning out, right? Or thinking out a conclusion, right? The ultimate thing, right? So I mean, episteme you know, reasoned out knowledge sometimes, right? Geometry is a reasoned out knowledge of lines and angles and figures, right? And arithmetic is a reasoned out knowledge of numbers and so on. Okay. Now,

[46:53] how about no B is A and every B is C? Can I get the set of none there? Well, you got a universal negative, no B is A. Was it even said to be a B? No. But I can convert every B is C to every what? All. Oh,

[47:17] yeah. Some C is B and no B is A. Ah. Lo and behold, by magic, I am back in my figure. First figure, particular figure, right? Okay. You have the set of none, right? If no B is an A, then whatever is a B is not an A. But you know only that some C is a B. So. C is not an A. So again, it's a particular conclusion, right?

[47:53] See the defect of the third figure, right? The weakness of it. So those ones are kind of obvious, but you make them for fun, right? Okay. Now no B is A and no B is C. Well, two negative parents, you're all not gonna have any offspring, right? Okay. And you can't get a set of all. You only have an universal affirmative, right? Can't even get the set of none because that requires something affirmative, doesn't it?

[48:29] If no B is A, whatever is a B is not an A. So you got to have an affirmative part there. So two negatives, you just expect nothing. So we're going to find examples for A, B, and C that satisfy the two what conditions, right?

[48:50] And. So can you think of a B and A such that no B is an A? No stone is an animal, right? Okay, now I got to find two examples for C. Um, one where no stone is it, right? I mean, or both where no stone is it, but one is a what? Always an A. Do you think of something that is never a stone but always an animal?

[49:28] Dog. Oh, yes. Okay. So no stone is an animal, and no stone is a dog. Is it true, right? Can you think of something else that no stone is it and is not ever an animal? A tree, right? Okay. Now just so to avoid a stupid mistake, right? Have I satisfied both conditions? Condition number one: when I substitute what I have for A, B, and C as examples, these premises will be true.

[50:07] So I have perfect matter. Okay. The numbers I'm multiplying are cracked without any doubt. So no B is A. No stone is an animal. True. Looks true to me, right? No B is C. No stone is a dog. No stone is a tree. I have satisfied condition number one. With those examples, the premises are both true. There's no defect whatsoever in matter, right? I'm just concerned with the form.

[50:39] Okay. Now to have one example where every C is A. Yeah. So let's circle the example of the universal affirmative, right? Example. Now I've knocked out two birds, right? Two universal negative and particular negative. They're not always true, are they? And I have one example where no C is A.

[51:07] Yeah. Underline that example, right? Okay. So sometimes universal negative is the case, right? Knocked out the two affirmatives. So two stones, I've killed four birds. The game is over. Cheeto is not a soldier, right? Okay. Now how about every B is A and no B is C, right? Can I get a conclusion with C as the subject and A as the predicate, right? If you convert the second.

[51:39] Well, I'm going to have to try for the set of none, right? Huh? Now if I convert every B is A, this would be some A is B, right?

[51:56] Some A is B, and no B is C, right? I could conclude that some A is not C, right? But does that give any conclusion to C as a subject? No, because you can't convert a particular negative, can you? If some A is not C, then you can't turn around and say sum C is not A. So there's no conclusion with C as a subject and A as a predicate, right?

[52:29] This is the question we're asking, right? So let's see now if I can get examples to prove this. A, B, and C. Can you think of a B and A such that every B is an A? Well, animal dog, right? Okay, that's the easy part, right? Every dog is an animal. Now, can you think of a C such that no dog is a C, but every C is an animal?

[53:07] Cat, yeah. Can you think of an example of a C such that no dog is it, and it's never an animal either? Stone, yeah. Okay. Now, if I satisfied the two conditions, are the premises in fact true? As a matter of perfect, every B is an A, every dog is an animal, true. No B is a C. No dog is a cat. No dog is a stone.

[53:46] I have satisfied condition number one, Mr. Burgess, Dr. Ferguson. Okay. Now, second condition, right? I have one example where the universal affirmative is false, so I can knock out the two negatives. Yeah. Every cat is an animal, right? So I got one example. Yeah. Where every C is A, which means that no C is A, and some C is not A, can't be true always. Therefore, not true necessarily, right?

[54:24] And now, do I have one example where no C is what? A. Yeah, under underline that example. No stone is an animal, right? So I have one example where the universal negative is the case, no C is A, which means no affirmative statement is true always. So nothing affirmative or negative is true always, and therefore, huh?

[54:51] Nothing is true necessarily. Therefore, you don't have a syllogism, right? A syllogism is featuring some statements laid down, another follows necessarily because of those laid down. So nothing follows here necessarily. So notice you have two cases here. You have a conclusion, but they're both particular, right? But you have to convert, right, to see that, right? That's where the first figure comes first, but also because it's more powerful, right?

[55:23] You have both the universal affirmative and the universal negative in the first figure. Second figure used to have universal negative. Here you've got no universality, right? This is really, you know, feeble, feeble. So we put that third, right? Now, now I was

[55:48] thinking about God, right? You use these forms, right? But of course, God is not universal, right? Not strictly speaking. Of course, in philosophy, we don't know about the Trinity, but even there, you got to be careful. Because the universal, in the strict sense, is said of many that have quite a separate existence, right? The existence of the Father, the Son, the Holy Spirit is the same. I am who I am, God.

[56:17] But I noticed that with the universal, with a negative, with the singular, you can convert it. Let me show you what I mean here. Socrates is not a woman.

[56:36] Can you convert and say no woman is Socrates? Yeah. Some woman could be Socrates. We'll call that person X, and X is both Socrates and a woman, and therefore some Socrates is some woman. But we said Socrates is not a woman, right? So you can convert that, right? That's important to know, right? Because if you syllogizing with God as one of the terms, right, you can treat a Socrates as not a woman the same way as no man is a woman, right?

[57:18] You can convert it, right? Say no, no woman is Socrates. Tabitha is not a dog. That's my daughter's cat. Tabitha, If you don't know, my cat. Tabitha comes into my often example. Tabitha is not a dog. Well, then, no dog is Tabitha, right? Kind of obvious, right? So you can syllogize, you know, and convert with that, just like you do with universal negative. That's where

[58:10] we syllogize all these things about God in the Summa. God is pure act, and no, nothing composed is pure act. We can go into this maybe next time a little bit, you know, but but it's logic is not studied for its own sake, right? Thomas says it's reduced to looking philosophy as a tool, but not as a chief part, right?

[58:51] Kind of amazing though, you know, Aristotle takes up being. You know, he speaks of the two main distinctions of being as act and ability, which goes back to what we do natural philosophy, and then being according to the figures of what predication, right? Substance and quantity and so on, right? So you borrow one. It comes out natural philosophy that you you understand act and ability, which is one of the main divisions of being, and then the other main division is being into the according to the figures of predication, the figures of being said of, right?

[59:30] Being said of individual substances like you and me. But it's interesting when Thomas is talking about Aristotle's leading us by the hand, you know, from sometimes from this science and this other lower science. Sometimes he uses by the hand from logic, like in the eighth book on substance, right? He leads us by the hand from logic, and then the ninth book he leads us by the hand from natural philosophy, right?

[59:56] And Thomas says with the brevity of wisdom that natural philosophy proceeds per modum motus, by way of motion. That's how you first learn act and ability, right? You know, when you're in grade school and you get the lump of clay and you can mold it into a sphere and mold it into a cube, you just have to get the idea of ability and act, right? But then in logic, it proceeds by way of of predication.

[1:00:20] Thomas says, by the way that something is said of something, right? So the Isagoge is about the five predicables, right, and the the categories about the ten predicaments, right, and you've got the said of all and the said of none, right? So I mean, logic is about the way something is said of something, right? Because something is said of something in reason, you know. That's the only place where something is really said of something.

[1:00:46] We use language too, by means of signifying that something the mind is said of something. So it's kind of interesting the two main distinctions of being. One is gotten by the way something can be said of individual substances,

[1:01:00] and that gives you substance, quantity, and so on, right? What are you? How big are you? How are you? Towards what are you? You know, and so on, right? Where are you? And the other is from act and ability. My two greatest teachers, you know, in graduate school were Charles De Koninck and Monsignor Dionne right? Monsignor Dionne would be leading us in from logic, and De Koninck from natural philosophy, right?

[1:01:34] And they could both do both, but I mean, it was kind of. But I mean, you know, they wouldn't teach metaphysics, son, because you got to get through natural philosophy first and logic, right? And and it's kind of interesting. Get the second grade guys to teach metaphysics. Yeah.