Logic (2016)
40. If-Then and Either-Or Syllogisms; the Three Figures; Prior vs. Posterior Analytics
Class of 2017-03-30
https://berquistcourse.com/course/philosophy/2-logic-2016/040-if-then-and-either-or-syllogisms-the-three-figures-prior/

[0:00] Okay. So, as far as reasoning is concerned, though, the if-then statement is very what important, right? And we spoke of the if-then syllogism, right, where one of your statements is in the form if A is so, then B is so, where A and B are standing for what simple statements, huh?

[0:30] And this something's called this formal logic, right? Because you're not looking at the matter, right? But you're saying in an if-then statement, you're saying if this simple statement is true, then this one will be what true, right? Okay. And then you go out and you look and you find out that sometimes you look at A, you might find out that A is so, in fact, or A is not so.

[0:58] And then can you say anything necessarily about B? Well, if A is so, then B is so. If A is so, then what? That B is so. Then you must say that B is so, right? Okay. That's a kind of obvious form, right? Because if you understand the if-then statement, right, you're not saying that A is so or B is so, but you're saying that if A is so, then B will be so, right?

[1:32] And if you're told that A is in fact so, then if you hold those two statements, you must admit that B is so, right?

[1:47] The students in this room are four. Then the students in this room are a what? Even number. Is that true? Depends on how many students are in the room Well, just a minute now. I'm saying if there are four students in the room, then there is an even number of students in the room. Yeah. What happened to? He's. I don't know. They're protesting. He's gonna act on.

[2:21] Yeah. What? Okay. But does a if-then statement to be true have to have its parts be true? The simple statements it's put together from.

[2:44] What's amazing is that you can make a true if-then statement out of two false simple statements. That sounds crazy, doesn't it? But does truth mean the same thing in the if-then statement and in the simple statement?

[3:06] In the statement, in the if-then statement, you're not saying that this is that or this is not that. You're saying if this is that, then that'll be that.

[3:20] Okay. Right. So if I am a giraffe, then I have a long neck. True or false? True. The truth I'm a giraffe, true. No. Do I have a long neck? No. If I am a mother, then I am a what? Woman. True or false? True. It's false that I'm a mother. It's false that I'm a woman. So truth means something different in the if-then statement, right? But we don't want to go around with those things just all by themselves, do we?

[3:59] If A is so, B is so, B is so, C is so. So if A is so, C is so. Who cares? You know, doesn't tell you anybody else, right? You want to get back to the truth of a what? Simple statement, right? So in an if-then syllogism, right? It's composed of an if-then statement, but only one if-then statement, and the other statement is a what? Simple statement.

[4:29] Simple statement. And the conclusion is what? Simple statement. Yeah. So that's amazing, right? Huh? You got from a if-then statement a simple statement, right? But you had to have a simple statement besides the if-then statement, huh? Okay. Pretty good, isn't it? Yeah. Okay.

[4:54] Now some people, when they first think of the form, they'll if A is so, then B is so. If A is not so, well, guess what? B is not so. Yeah, kinda seems right. And and you know what they say? Likeness is the cause of error.

[5:17] You know the Shakespeare's great play, The Comedy of Errors, right? And go back to as things similar with the Roman comedies, right? But the he had two sets of brothers, and they're both what? Twins. Twins, yeah. And so you know they say that even twin girls sometimes switch dates, you know, and guy guys don't know, right? I assume when they get, sometimes you know they're well enough to get married, they'll tell the part.

[5:48] They can't, right? Huh? You know, we knew a couple in the parish that twin boys, right? And and my wife couldn't keep them track. and, one day she stopped them after masses. You stand right there. I've got to stand them, you know, trying to, you know, get you know which date goes with which guy, right? But there's all kinds of comical things because the two brothers, you know, are being mixed up all the time, right?

[6:11] Huh? Okay. And myself even, I remember acting. One of the plays that showed me on there, there are two girls in the same family, and they they weren't really twins, you know, but they looked enough. I was congratulating one of them on her performance in the play, and it wasn't the the one who was formed. He just kind of smiles, you know what I mean? So, but you know, you know, that was not the the actors that played so well that night, right?

[6:43] Huh? So likeness is the cause, right? Huh? So you say if A is so, then B is so. And then you put down here A is so, and you drive to B is so right. If you put down A is not so,

[7:17] what looks like B is so over here. B is not so. Yeah, it seems it, it's kind of you know proportional, isn't it? Arithmatic. Yeah, yeah.

[7:31] Don't break the down your notes. As in purposes teaching, right? But so easily you you know you get me in trouble, right? The fireman, the teacher doesn't know his logic, right?

[7:49] Now it's possible, you see, for both of these to be true, and yet this is not true, right? And you can take infinity of examples. You can have B where it. Follows from many particular things, right? Something more universal. If I am a dog, then I am a what? Animal. If I am a cat, I am an animal, right? If I am a horse, I am an animal.

[8:17] So if I am not a dog, I am not an animal. If I am not a cat, I am not an animal. It could still be true, right? That B is so, right? Even though, right? Okay. It might be that B is not so. And if you had the matter that was convertible, right? If the number is two, then the number is half of four. The number is not two, therefore it's not half of four.

[8:45] But you know that because of what? The matter, not because of the what? Form. So this ain't necessarily so that B is not so, right? It might be that B is not so, but it might be that B is so, right? Now, you can prove that a form is not a syllogism by examples, but you can't prove that it is a syllogism by what? Examples. Now, why is that?

[9:16] You need to go to all the examples possible, and that's, that's too many. Well, I would probably put in the form of an if-then statement now we're doing statements, right? You know.

[9:32] If something is necessarily so, right? Then it is what? Always So. that's kind of a uh, obvious if you stop and think about, it, right? Okay. So if man is necessarily white, then is man just sometimes white? No, then he's always white. That's a true statement. If Man is necessarily white, then he's always white.

[10:14] The book is always blue covered, right? Necessarily so. It's necessarily blue covered, and it's always blue covered, right? Okay. Okay. So if you have one example of a man who's not what? White. It shows that he's not necessarily white. You can find a book whose cover is not blue. Is a book necessarily a blue cover? Many people books have blue

[10:44] covers, but actually, it comes in red and green covers. But here you can't prove this by examples, can you? So one one black man is enough to show that man is not always white, and therefore enough to show that man is not necessarily white. But how many white men do you need to prove that man is always white?

[11:24] Endless numbers. Yeah. Well, even that's enough. No. See, keep going. See, I maintain that all numbers are odd, right? Now, how many even numbers do you need to disprove? Just one. How many odd numbers do you need to prove that numbers are always odd? I can give you as many as you want. Ten one, three, five, seven, nine, eleven, thirteen, one. There's no way to prove them.

[11:53] You know, how can you deny that? It seems unfair that you can just take one example to disprove my statement, and I've got you know zillions of examples to prove that it's always. He's spent so much time working up all those examples. Yeah, yeah, yeah, yeah. Sure. You kind of suspected the weakness of induction, right? In some sense, right?

[12:24] Okay. So you really have to kind of see in this first case here. You couldn't show it by examples that B is so right now. But if this is true, and this is true,

[12:43] then this will have to be true, right now. Because here you're admitting that if A is so, then B is so. Now you're admitting in fact A is so. Therefore, B is so right now. Okay.

[12:57] But here you're not saying that A is so. Are you saying it's not so? It seems kind of you know, it's kind of something to me, you know. The yeah.

[13:13] There's a Shelley there. There's a thing on poetry. No, the first. He says reason always you know, tell us the differences of things, but poetry sees the likenesses of things, right?

[13:26] It's certainly poetry higher than than than reason, right? You know, you know, the imagination is higher, It's more likable. Yeah, yeah, yeah. Differences divide. Yeah. And, uh, the. uh...

[13:43] You know, say they say that uh, to some scientists that most uh, discoveries are made in science by seeing proportion, right? So by seeing the likeness, the ratio, seeing the likeness. of things.

[13:58] But likeness is a what? Yeah, yeah. It's a slippery thing. Yeah. The, uh, in rhetoric they use the term likelihood, right? It's likely. Okay. So this is is

[14:21] not following necessarily, right? So it doesn't follow that B is so, right? So if I'm not a mother, I'm not a woman. Okay. But if you look at the Bs instead of the As, when does something follow necessarily?

[14:56] You say if A is so, then B is so. If you look at the Bs and you find that B is so, does by reason of the form follow then that A is so?

[15:29] It seems like it should, doesn't it? You know, and it seems that the scientists, the sciences are the model of rigor, rigorous thinking, right?

[15:43] So Louis de Broglie, great, the greatest French physicist of the 20th century, you know, Louis de Broglie proposed the idea of wave mechanics. You know, the French have this, the Comedie Francaise, you know, the great festival, you know, of comedy, and that they applied it to his theory, It's ridiculous, La Comédie Française right? What's it? called They're making fun of him And Einstein said, I think there might be something.

[16:11] to what Louis say? So they ran an experiment, right, and built Bell Telephone laboratories in New York, I guess, and exactly what he predicted was so. They repeated the experiment in Europe? again, same results, right?

[16:30] So if my hypothesis is so, then there will be an eclipse of the sun at such and such a time. But there is an eclipse of the sun at such and such a time. Have I now proven that my hypothesis is correct? That A is so, have I?

[16:47] Seems like it would appear to be seen. I took an example I was using in class. I said, if Perkis dropped dead last night, then he'll be absent from class today. Okay? And my hypothesis is that he dropped dead last night. Now we waited to see if he shows up. He didn't show up, right? Therefore, he dropped dead last night. That's wishful thinking. It's not logical thinking.

[17:22] Because there's more than one reason why he might be absent from class, right? His car broke down, right? Huh? I missed the class at the monastery on Monday because Rosie had done so much. We had two cars, but Rosie had one of them. I went in the garage and we left the door open a little bit. You know, it hadn't closed all the way the door, and we hadn't driven the car for a couple days.

[17:43] You know. And the battery was dead. Yeah, yeah. Oh boy. And so I couldn't make that class up there. You know, I had to call Triple A. You know, and come out there and so on. I was disgusted with life, you know.

[17:57] So it wasn't because I dropped dead? you know, it's because the battery. right Battery's dead, no Or I could be sick. I guess if I get fed up with life. and. I'm tired of teaching and so Go to Florida Yeah yeah Okay

[18:15] So it doesn't follow that A is necessarily so, right? We have many possible causes of the same effect. We could have something less universal from which something more universal would follow, right? But that more universal is so, we can't see which one of the other ones is so, right?

[18:38] If I am a woman, then I am a human being. I am a human being. Therefore, I am a woman, right? If you are an odd number, then you are a number.

[18:53] You are a number. If you are not a number, no. So this is no good, right? The form, right? Okay. They sometimes divide logic, you know, into the formal logic, right? Or use A, B, and C, which drives my wife crazy. It's not about those A's and C's.

[19:14] But you can kind of abstract, right? Consider the form apart from the matter. So Aristotle wrote these two famous books, the Analytics, right? The Prior Analytics, which is what formal logic, A's and C's and C's, and then what material logic, which is Book B, Posterior Analytics, right? Okay.

[19:40] But if B is not so, does something follow about A? I think so. Yeah. Now it's not as obvious though as the case that we saw before, right? So we use a more obvious case to show that it must be when B is not so that A is not so, because by the first case that was obvious, when A is so, then B is so. But you're given that B is not so, right?

[20:15] So A can't possibly be so when B is not so, right? And therefore it must be not so. Makes sense. So in these four arrangements of the if-then

[20:35] statements, the other one, if you say that A is so, you must say that B is so. But if A is not so, you don't have to say that B is not so. Or B is so, you don't say anything. But if B is not so, then A is not so, right? So use those forms over and over again, right?

[20:57] And so I go into the regular syllogism. I use this form here to show why. I've disproven it, right? If something follows necessarily, then it's always so. But it's not always so, as my examples show, right? Therefore, it ain't necessarily so. Therefore, it ain't a syllogism, right? syllogism is an argument. What does syllogism mean? Funny, creative, weird, weird. It's two statements, or is it a? It's the conclusion.

[21:29] Here, here you got the formal syllogism, right? But it's an argument, right? Or you can say speech, you know. It's speech in which some statements laid down, right? Another follows necessarily because of those laid down, right? Okay. I like to know the word they say in Latin. but in English you would put it down as laid down, right? And I sometimes know speak of how we speak of the law being laid down.

[22:12] And you say laid down is kind of a what? At rest is what's been laid down, right? It's firm, right? And I've laid down the law. I expect what you to follow the law, right? Okay. But when I've laid down these two things, I expect something to follow necessarily, right? So it's beautifully defined, right? It's speech in which some statements laid down. I mean, those are in the mind at rest, huh?

[22:44] In a firm way. They're not going to just. If I lay this, if I lay this down, if I just you know think of this and then I forget about it, then I think about this and then I can't syllogize at all, right? I've got to lay them down together, right? Okay, I

[23:02] lay down. They're at rest and firm in my mind, and then I say, ah, those are laid down. Then this follows, right? When I laid down the law, I expect you to follow the law, right? I'm going to be punished, right? You'll be in here, or you'll be home here at ten o'clock, you know, or wherever the law is, right? Now,

[23:28] my father used to have down in the cellar a little bit of whiskey or something, you know, huh? Of course, we as kids, you know, we'd go down there with with with our root beer, you know, a bottle of root beer and some little you know glass, you know, pretend we're drinking, you know. And of course, one time we we dropped one of the glasses, right? Reno, I think you drank your stuff down there.

[23:53] I know she really thought, or she just you know. Scary here. They're playing. Okay, so there's two ways of reasoning from an if-then statement with necessity, right?

[24:12] But notice, son, an if-then argument is not put together from two if-then statements, son, but from an if-then statement and a simple statement, right? I mean, if you wanted to, you could, you know, combine these and say, okay, if A is so, then B is so. If B is so, then C is so, right? And then argue that A is so, therefore what? C is so, right?

[24:42] But you're kind of giving two arguments there, right? So one simple argument, one compound argument has got a simple statement. No, no. Why do you have that, right? Well, truth doesn't mean the same thing an if-then statement as in a simple statement, and which is primary meaning of truth? Yeah. And the kind of meaning of truth or falsity in the statement, you're saying that what is is and what is not is not, huh?

[25:18] That's true, right? But if you're saying that what is is not or what is not is, then you're being false, right? So you want to get back to a simple statement, right? Makes sense.

[25:34] Now you could have a either-or syllogism too, right? And either-or is not as deceptive as sometimes if-then is, right? How do you argue from an either-or statement?

[25:54] Well, if you argue affirmatively, you're going to what? Eliminate all but one of the what? Alternatives, right? This straight line is greater than, less than, or equal to that straight line. But it's not greater than for this reason. It's not less than for this reason. Therefore, it is what equal, right? But Thomas says, you know, if the father is before the son, he's either before in time or duration, or in being, or in what?

[26:26] Excellence. In knowledge, right? Okay. Or in goodness, right? But he's not before in time. He's not before in what? Being. He's not before in what? Knowledge and same knowledge of relatives, opposites, and he's not better, right? Therefore, he's not what? Then you eliminate all the possibilities, right? We can be crushed out, right? That doesn't Jesus is there?

[27:04] That's kind of kind of common sense, you know. Common sense, but sometimes it's downright hard to argue, you know, even from the either or thing. Now, when you get into the syllogism with all simple statements, right? That's the thing Aristotle just calls a syllogism, right? He usually calls that syllogism. period. And he calls, you know, the other kind ex hypothesi or something you know or something, you know, Hypotheses.

[27:35] Now, Aristotle, there in the syllogism from two simple statements, he divides them into how many figures? Two or three. Three, three, yeah, yeah. Now,

[27:59] what do you need in a what? In the two simple statements, right? In order to syllogize, well, you've got to have what? One of the

[28:15] each of them's got an ability. I mean, excuse me, a subject and a predicate, right? Huh? You got to have some, you know, connection, right? Okay. So either you have them

[28:30] like this, or you have them like this, or you have them like what? B. Yeah. Now they tend to call B the middle term, right? Huh? But it's really in the middle in the first figure over here. They call this the first figure, right?

[29:08] We call this the second figure, and this the third figure. Now, we see that Aristotle did not arbitrarily, just by custom, call this the first and second and third. There's a reason why he put them first, second, and third, right? So he says the predicate can be above both of the subjects, or below them, right? Or in the middle. There's three possibilities, right? Huh? Okay. Any other combination?

[29:47] Some of you might say, "Well, what about C B? How about that? How about that? " Monsignor Dionne used to call that playing checkers. You can arrange, you know, you get, you know, the by checkers, you get the black checkers and the red ones, and you can arrange them one more way, right? Okay. But this is not act to be, right? It's really what?

[30:38] This is set up for the set of all, right? It's going to have to put it like this, right? And then this is really the same as that, except you're you're playing about the things, right? Okay. So forget about the fourth figure. You'll find people thinking it's a fourth figure, right? Not knowing that two is the first number. You say all, right? It's all really, okay. Now,

[31:12] in the first figure, right? The second figure, the third figure. The premises can be affirmative or negative, right? And they can be universal or what? Singular, right? So how many possibilities is there for each figure?

[31:37] Four. If there's four, if this can be universal affirmative, or particular affirmative, or universal negative, or particular negative, there's four possibilities for this, right? And if this can be what? The same four possibilities, right? Sixteen. Sixteen, right? So there's sixteen cases in the first figure, and then there's sixteen the same cases in the second figure, and then sixteen in the what? Third.

[32:09] So forty-eight, yeah. Like the number of states we have, right now? Used to. We still got 48 billion. You can't do logic. Yeah. So Aristotle in a book called The Prior Analytics, right, the before analytics, right?

[32:33] Why does why does he put the you know formal logic, prior analytics, and material logic, the posterior analytics? Why does the para analytics come before, you know, before Analytics?

[32:52] And the after comes the after Analytics. But but the one is dealing with form, right? That's why he talks about the form. The other about the matter, right? why does he put form before matter? Well, maybe taking you know the application of form and matter, right?

[33:17] But Aristotle, you know, is aware of the fact that man goes from a what? Confused knowledge to a distinct knowledge, right? And which is more universal? Which comes first, then the more universal, or the less universal. More universal Yeah, more universal is more confused, right? Okay. That's why at the beginning of the of the books of natural hearing, right, he says that we should consider things in general before particular, right?

[33:51] Okay. Because it's more known to us to go from being confused to distinct, right? So I go from name said of many things, right?

[34:06] To equivocal and equivocal, right? And then I go to from equivocal to equivocal by chance, equivocal, right? So equivocal means that you have one name said of many things with different meanings in mind, right? But now you find out that sometimes there's no connection between those meanings, and sometimes there is an order among those meanings. Well, order starts to Aristotle's definition of reason that must be. We'll call that equivocal by reason, right?

[34:36] There's no order, no connection. We'll call that by chance, right? Equivocal by chance, right? So I'm going from the general to the what particular, right? Well, sometimes these premises, when you go to the matter, find out that they are necessarily so, right? Sometimes we find out that they're only what probable, right? But they have the same form, right? So in dialectic and and

[35:09] demonstration, right, in science, I'd be stating, in one case they're necessarily true, right? Other case they're what probable, right? But the form is the same, right? So the form is more what general, yeah, than the matter, right? Okay, so we should take up the form before. So prior analytics, you know. I call it the before analysis. Okay.

[35:44] What do you do in your checkbook though? You don't have a checkbook. Some of us don't. Sometimes you know. Sometimes you or most of the time your checkbook doesn't agree with the bank, right? Sure. Because I made some mistake or something, you know. We check we check first. Did I add the track correctly, right? And then did I have the right numbers right The right number in some slot and I misread the number, you know.

[36:14] Yeah. I do that sort of stuff, you know. My father gave my mother her own bank account, right? So we have two bank accounts there. My mother's bank account didn't work out of the bank, but she figured she'd spend the way. up, trying to find a thing, you know. People were very virtuous in those days. I say they thought that was supposed to work, you know. My brother Mark used to be that the the radios and the cars were always very imperfect, right?

[36:48] Didn't work very well. I know if you're old enough to remember that, you know. Now they're a little bit a little bit better now, you know. But they didn't seem to ever work very well, you know, in those days. My brother Mark said, you know, turn the money on. If it works well. you can take it in and get it fixed. It doesn't work. It's just supposed to work.

[37:09] It was a problem. It didn't work very well. Okay. Now we can we can give you the extreme pleasure of going through all sixteen. You know, but we should at least go through the what four universal cases right now. Okay.

[37:33] And we'll find out that in the four universal cases of the first figure, there's a case where you can syllogize a universal affirmative conclusion, right? And there's a case where you can syllogize a universal what? Negative. Okay. On the second figure, you'll find out there's cases where you can syllogize a universal negative, but there's no way of syllogizing a universal affirmative. So it's a little. Falling off, in what you can do, right?

[38:08] And in the third figure, the universal cases, all you can do is get particular what conclusions. And it will be very clear in the first figure by the set of all and by the set of none, which are obvious. Let me actually state them in the form of a what if Ben stated, right? It will be very clear that the if the set of all and the set of none apply when it is a syllogism, right?

[38:36] Here you can't simply apply the set of all and set of none the way they stand. You've got to what convert. Yeah, and so Aristotle calls these imperfect syllogisms. This is a perfect one. Okay. Doesn't need any help. Yeah, yeah, yeah.

[38:58] So let's just take the universal cases again in the first figure here. Every B is A, and every C is B. That's with two universal affirmatives, right? And you have the two universal negatives, right?

[39:26] Okay. Then you have the mixed ones, where one is affirmative and one is negative, right? So you have, let's say, no B is A, and every C is what D.

[39:49] And then you have the reverse, right? We have every B is A, and no C is B. Any other case? We have both premises universal besides these four in the first figure.

[40:11] But it's four, not three, right? Berquist? Right. So pay attention. Okay. But if you're trying to understand this, it's because you know you have what two is there, right? It can be universal or particular, it can be affirmative or negative, right? So if you take them both, you crisscross, you get four, right? So you can't escape that two or three.