Introduction to Philosophy & Logic (1999)
Lecture 47: Analysis of Complex Arguments: Syllogistic Structure and Forms

Transcript
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The term I found was the natural road in our knowledge, right? But then I had to kind of manifest how the first road and the natural road would go together, right? Because the nature of the thing, or what it is, is what's first in that thing. And then I had to manifest the major premise a bit, that the natural road for man, right, is the road from the senses into reason, because, like the middle term would be, that man is an animal with reason, right? Okay? And you can see, you know, an animal with reason is the nature of man on the one hand, and an animal with reason is going to have senses, right? And his senses are going to develop before his reason, huh? So the road's going to go from the senses into the reason, okay? Well, Thomas is going to do something like this here, right? Okay? But it'll take you a while to analyze what he's doing here, right? So he says, I answer that, as has been said before, this is something we had read earlier, love pertains to the desiring ability, huh? Which is an ability that is acted upon. Whence its object is compared to it as a cause of its motion or act. It is necessary, therefore, that what is the object of love be properly the cause of love. But the proper object of love is the good. Because, as has been said, love implies a certain natural fit or agreement of the love with the love. And what naturally fits or agrees with something and is proportioned to it is good for it. Whence it remains that the good is the proper cause of love, huh? Okay? Now, this is more difficult to analyze than the one from Euclid, right? Okay? But now, I tell the students, huh? You know, the Aristotle's books are called the prior and the posterior analytics, right? Analysis. And the culmination of the books is not the generation of sojism we've been studying, but how you take apart a sojism and see how it is. Well, in an argument like this here, the way you do is, in a way, you begin from the, what? Conclusion. Yeah. The chief or main conclusion, right? And then you figure out what are the premises that are immediate to that conclusion, right? And then everything else is either superfluous or it's there to back up one or the other, or in some cases, both of those premises, right? Okay? So, the, what's the chief conclusion? That's where you begin with. Then you find the chief syllogism, and then you find what some people want to call the post-syllogism, or I call it the back-up syllogism sometimes, right? Or the back-up manifestation of these things. Okay? And you say the chief conclusion is obviously at the end there. Whence, which obviously is a sign, and he's trying to lose, right? Hence or whence. It remains that the good is the proper cause of love, right? That's the main conclusion, right? So, we've got to start with that, the main conclusion. Maybe I'll start the bottom of the page here so I can work my way back, right? So, the main conclusion is that the good is the proper cause of love, right? Now, being a trained logician, right? I say, this is an affirmative conclusion, right? Okay? So, he's not going to be using those three forms of the categorical or regular syllogism that draw a negative definition, right? It's going to be, if you're using that kind of syllogism at all, you might be using if-them syllogism too, but if you're using this regular syllogism, it's going to be in the form of every B is A, every C is B. And B is going to be a middle term, uniting C and A, right? Okay? Now, what does he use to unite those, right? By kind of, you know, if he's using that kind of syllogism, he's going to say, the good is, whatever that is, right? And whatever that is, is the, what? Cause of love, right? Does that make sense? Okay? He's got to find a middle term, huh? That unites these two, right? And often I compare the middle term and logic to the middle man economics, right? Who unites the producer and the, what? Or the matchmaker, right? Who unites the man and woman, right? Yeah. Okay? Because he knows both of them, right? So, what does Thomas use as a middle term to unite these two? Object of love. Yeah. The good is the object of love, and the object of love is the cause of love. Okay? Now, if you read through this, you see, though, there are many whences and therefore is therefore, right? And therefore there must be many arguments, right? Okay? But notice what Thomas does grammatically, right? At the end of the first paragraph, and I've mercifully separated the first and second paragraph for the students, right? I can't be honest. But at the end of the first paragraph, he must be drawing a conclusion, right? But it's not the main conclusion. It is necessary, therefore, that what is the object of love be properly the cause of love, right? The first paragraph is drawing, at the end of the conclusion, which is, in fact, the major premise of the main syllogist. This is going to be the main syllogist. Okay? But notice what Thomas does grammatically. As he begins the next paragraph, he begins giving you the, what? Yeah, yeah. Yeah, yeah. Yeah, yeah. Yeah, yeah. Now, notice, he has a reverse order, right, huh? But the two are really convertible things, right? So, he can turn that around and say the good is the proper object of love, huh? But notice, huh? After he says that, he says because, right? Okay? So, notice grammatically, in the first paragraph, he gave the reason and then drew the conclusion. In the second paragraph, he states a conclusion and then gives a reason. Okay? See? And he says, does that confuse you? No. It's so that the two premises, which are conclusions of earlier arguments, right, will be put together in your mind. And you can draw the conclusion right away. See? Okay? So, he ends the first paragraph with the statement of the major premise, the reason for which he's given in the earlier part of the first paragraph. And he begins the second paragraph, right, by giving the minor premise and then going on to state the reason for it. Okay? So, that the major and minor premise are right together, right? Is that what he's doing? Okay? Okay? It wouldn't have to be that. I mean, it's a little easier for the student, huh? Mm-hmm. Okay? Now, there may be, so there's some kind of manifestation of both of these premises. There must be because when he says at the end of his paragraph, it's necessary, therefore. He's obviously showing this in something, right? Okay? Now, you have to go back a little bit, you know, when you say that love pertains to the desiring ability, which is an ability that is acted upon. Well, when we study the abilities of the soul, the powers of the soul, as they call them sometimes, one very fundamental distinction we see is whether the object acts upon the power or the power acts upon the what? Object. Object, basically, right? And, of course, in Aristotle, it takes up the soul and its powers, and he'll ask the question, should we consider the powers first or the acts of the powers, right? And should we consider the acts first or the objects of the acts, right? Okay? And you eventually learn that the powers or abilities are for doing something, right? So you have to know the abilities or powers by what they do. And you don't even know you have the ability to walk if you don't walk, right? You don't have the ability to see, right? Until you do it. And sometimes you do something you didn't know you had the ability to do. You say, I didn't know I had it in me. But you didn't know you had the ability to do this, right? Okay? And, but, so if you want to distinguish the ability to see from the ability to hear, it's because you distinguish seeing and what? Hearing first, right? But seeing and hearing are both sensing, so how do you distinguish between those? Well, seeing is sensing color, and hearing is sensing what? Right? So the difference between color and sound enables you to understand the difference between seeing, which is sensing color, and hearing. which is sensing sound. And the difference between seeing and hearing, and that seeing is not a form of hearing, or hearing a form of seeing, means that the ability to see and the ability to hear are not the same what? Ability, right? Okay? But now, when they talk about the ability and its object, the fundamental difference, or one very fundamental difference is, does the object act upon the ability, or does the ability act upon the object, huh? Now, when Aristotle talks first, he talks about the ability to digest your food, right? And the ability to digest your food, the ability acts upon the, what, object, and breaks the food down, crunch, crunch, crunch, crunch, right? And all the way down my stomach there, right? I'm acting upon the food, right? Okay? But in the case of the senses, right, does my eye act upon the lamp over there? Or does the light act upon my eye? Does my ear act upon the sound? Does the sound act upon my ear? Well, these kids are going deaf because they listen to this, you know? But if you looked at the light too much, you would get blinded, too, you know? You have to look at the sun, you know, too much or something, right? During an eclipse, huh? So, the sense powers are acted upon by their object, huh? But the digestive power acts upon its object, right? Okay? Now, if you stop and think about that, you've got an either or there, right? Either the ability acts upon the object or vice versa. But if neither of those was the case, there'd be no connection between the power and the object, right? If the object in no way acted upon the power, the power, no way acted upon it, there'd be no connection between the, what, two, right? This is a fundamental distinction of abilities of the power. Now, when you come to the heart, right, the ability to desire, right, now let's call it the heart for want of a better name, is the object, does the power act upon the object or does the object act upon the power? Which kind of power is it? Yeah, yeah. And even, you know, you talk to the kids, you know, you go to the party there and you made a big impression upon her. Or she made a big impression upon you, right, huh? Okay? So the one's heart has been, what, acted upon, right, huh? Mm-hmm, okay? And that's why they speak of the heart as being, what, wounded, right, huh? And even in the highest kind of love, you know, you know, we're captain of, I mean, St. Therese of Avila, right, or St. Therese of Lisieux, they receive an increase of love under the likeness of being, what? An arrow. Pierced, yeah, with a lance, right, or an arrow, yeah. So Thomas would be calling this, right, huh? That the heart, the desiring ability, and to call it an acting, is an ability that is acted upon by its object, right? And that makes clear that the object is what? Causing the love or whatever the act is, right? And you can see that in the case, if you want to proceed by example, which is a philosophical example, they call it, as much as you know, I don't say, right? You can see that in the case of the other acts of the desiring ability, like fear or anger or something, right, huh? It's the object that, what, causes it, yeah, yeah. So people had fear with this, you know, terrorist attack, right, huh, okay? So it's the object that arouses fear, right? If a man comes in here with a gun and says, I hate monks or something, right? You try to feel some fear, right? Or I hate Americans, whatever it is, right? He would be the cause of your fear, right? So he'd also be the object of your fear, right? Okay? If somebody comes and insults you, you might get angry about it, right? Okay? So the object of your anger is also the cause of your anger, right? Okay? So Thomas, in that way, is manifesting the major premise, right? You see? Now, if you wanted to put that in the form of syllogism, we'd say that the object of love acts upon the heart, right? Bringing it to love, right? And what acts upon the, what? Passibility is the cause of its activity, right? So that would be another syllogism, and the middle term would be acts upon, right? What acts upon the heart, arousing its love, is the cause of love, right? But what is that? It's the object of love that acts upon the heart, arousing its love. See? The same thing you could say, right? You can syllogize in a similar way that the object of fear is the cause of fear, right? The object of fear acts upon the heart, right? Moving it to anger. It acts upon the heart in its way as the cause of its, what? Fear, right? So you have another syllogism of the same kind, right? The middle of the United States, right? Okay? The Thomas doesn't spell it all fully, but that's what he's doing, right? Okay? So he has a syllogism to back up the major premise, right? The object of love acts upon the heart when it loves, and what acts upon the heart when it loves is the cause of love. Okay? Now, in the second premise, this kind of presupposes already what he said about love, huh? What's the middle term uniting good with the object of love, right? The agreement? Yeah. It's the idea that the good is what fits something, right? What agrees with it, right? The shoe fits where, right? And what is fitting is the object of love. How is the idea? To be manifested, right? Well, when we talk about the desiring ability, and talking in reference to the good, you have really basically three acts, right? Love, desire, and what? Pleasure or joy, right? Okay? And love is the most basic, right? But now, if you love something, but don't have it, then you, what? Want or desire, right? But if you love something and you get it, then you have pleasure or what? Joy, right? So, want or desire arises from love in the absence of what is love, and joy or pleasure arises from love in the presence of what is love, right? Okay? Um, but what is love itself, right, huh? See? Well, love is nothing other than the, what? The agreement of the heart with the, what? Object, right? Yeah? So, on the one hand, he sees that, uh, since the love is nothing other than the agreement of the heart with its object, right? And that's why you pursue it, because your heart is in agreement with the object. Then, he sees a connection between the object of love and what fits you, right? Because your heart is going to be in agreement with what fits your. And then he sees, on the other hand, a connection between the good and what fits you, right? So, it's good for you, right? The shoe that's good for you has got to fit you, right? Okay? So, fitting there is the connection between good and the object of love, right? So, notice, if you compare this with the argument of, uh, Euclid, right, huh? In Euclid's theorem there, there were three syllogisms, right? All of the same kind, right? Mm-hmm. In Thomas here, there's at least three syllogisms, all of the same kind, right? They're like that, what? Every B is A, every C is B, right? You see, in the middle term, right? Nine to two, right? But, notice, huh? In the case of Thomas, there's one main syllogism, right? And he uses that, and the other two are to back up. In the one case, the major premise, and in the case, the minor premise, right? Okay? Euclid's a little different from there, because you've got three things to prove, right? And he proves two of them by separate syllogisms that are similar, right? and the reason, but different, right? And then he takes the conclusion of the two ones he has to construct one of the premises in his third syllogism, right? Okay? But you wouldn't want to say if that's necessarily the main syllogism, right? Because he's got to show equally, you might say, that these two sides are equal, these two sides equal, and these two sides equal. But there's a certain order among them, right? He has to show that these two are equal and these two are equal before he can show that these two are equal, right? You see that? But here, it's constructed a little bit differently, right? Here, there's clearly one main syllogism, one main conclusion, right? Not three things you've got to prove. You want to prove one thing, that the good is a proper object of love, right? And your middle term is object of love, right? And then the other two are one to prove the major premise, one to prove the what? Minor premise, right? But the proof of the major premise he gives before he what? Stakes the major premise. The minor premise he states and then proves it. So you can see these two together, right? Put them together in your mind, right? Okay? But notice there's only one kind of argument being used in these, right? In one case, the matter is very easy, relatively speaking. And the other one is very difficult to compare it, right? Okay? But nevertheless, there's a structure, there's a difference in the way the three syllogisms are, what? Worded, right? Okay? Do you see that? Now, Proposition 6 here is perhaps the first one in Euclid, that I remember anyway, that uses all three kinds of syllogisms. It uses what Aristotle calls the syllogism period, but some people call this some more categorical syllogism. And it uses the if-then syllogism, maybe a couple of them if you want to make it spot out anymore. And it uses the what? Either-or syllogism, right? Okay? Now, notice he wants to prove that in the triangle ABC, that when the angles at B and at C, the angles ABC and ACB are equal, that the two sides, AB and AC, will be equal, right? Okay? Now, how does he go about showing that, right? See? What is the main syllogism? See? What kind of a syllogism is the main syllogism? When I say main, the one that has the main conclusion, right? See? Yeah, yeah. In other words, he proves that AB and AC must be equal because they can't be unequal. Right? Okay? Now, you say, how's that proving it? Well, you have to realize that they're either equal or unequal. That two straight lines are either equal or unequal. There is no other possibility, right? So, if you exclude unequal, then you must include the equal, right? So, he doesn't prove, we say, directly that you're equal, right? But he shows that the other possibility is impossible, right? Okay? So, notice here you have an either-or syllogism where you know that the two lines, right, must be one or the other, right? So, it's the form of the either-or syllogism where you eliminate all but one possibility, right? Because you know that one of them must be the case. The two lines are either equal or unequal. They're two straight lines. You can see that, right? There's no other possibility. So, if you eliminate, you know, them being unequal, then they must be equal. Now, you don't always spell this out, because it's so kind of obvious, this form, as they say, right? You say, these two straight lines are either equal or unequal, but they cannot be unequal, therefore they must be equal, right? It sounds almost childish, but in a sense, that's what he's arguing, right? Okay? So, the main syllogism, then, is an either-or syllogism. Okay? Now, how does he eliminate the alternative or the possibility that they are unequal? Well, basically, it's by the if-then argument. Yeah. Now, he's saying, if they are unequal, right, then the lesser will be equal to the greater. But you can go through several steps to see this, right? You might have, you know, okay? What he's saying is that if they are unequal, and it makes no difference which one is longer, right? Let's say AC is longer, right? If they are unequal, then you can cut off the lesser one, or the greater one, a line equal to the what? Lesser one, right? Okay? So, he says, let AB be longer than AC, right? Okay? If one of them was unequal, right? One would be longer. Then I could cut off on AB, starting from B, a line BD equal to AC, the shorter one, right? Okay? That's a consequence of the fact that they're of unequal, right? And as you know, it's an earlier theorem, where you cut off a greater line, and that line equal to a given line, right? Okay? And if you did that, then you could draw a line from what? D to C, right? And then you'd have two triangles, DBC, ACB, one of which is clearly a part of the other, and therefore lesser than the other, right? Okay? Now, where's the difficulty, right? Well, because of proposition number four, you could say, or you'd have to say, that DBC and ACB have to be equal, though. Why? Because DBC and ACB, the two triangles, have equal angles. DBC, we said, was equal to ACB, right? They have equal angles contained with equal sides. BC is common to both, right? Common to both, right? And DB was constructed equal to AC. So, though they turn around, there are two triangles with equal angles contained with equal sides. So, by proposition four, it follows necessarily that they're equal. But that's absurd! Because the lesser can't be equal to the greater, right? Okay? Therefore, they've overthrown the idea that they're unequal, right? Okay? Now, you could make that in the cerebral ifs if you want to, but basically you're saying, if the lines are unequal, then the part would be equal to the whole, the less to the greater, right? But that's impossible. Therefore, they can't be unequal, right? Okay? So, you have an if-then argument, at least one, if not. And then you say, but how do you show that it would follow from these admissions that they're equal? Well, you'd say that the triangle DBC and the triangle ACB are triangles having equal angles contained with equal sides, and triangles having equal angles contained with equal sides are equal. That's the regular syllogism, right? That's the one he used back in number one. So, all three kinds of syllogisms are used in what is a very simple and very elementary geometrical demonstration, but it shows you you can't really analyze it without knowing all three kinds of what? Syllogisms, right? You see that? Where's the simple one at then? The simple one is you're giving a syllogism that triangle DBC, which is a part of ABC, right, is nevertheless equal to it because DBC has an angle DBC which is equal to the angle ACB in the greater triangle, right? And that angle is contained with equal sides because DB is equal to AC and BC, of course, is common to both, right? So sides DBBC surrounding the angle at B are equal to ACCB surrounding the angle at C, ACB. So you have two triangles then, right? Having, what, equal angles contained with equal sides and all such triangles we go by 0, 4 are equal, right? Therefore. So there's a middle term proposition 4. Well, proposition 4 gives you the middle term, yeah. Proposition 4 gives you the premise, one of the premises really, right? It says, triangles having equal angles contained by equal sides are equal. And then we can show from the constructions a man has made that these triangles fulfill those two conditions, right? And therefore, they must be equal, but they can't be equal because one is clearly a part of the other, right? Euclid says, you know, lesser to the greater, but it goes back to really the axiom that the whole is greater than the part, right? So he's resolving all the way back to the axioms, which are the statements known to themselves by all men, huh? You see that? Okay. I mean, the triangles are turned around, you know, I mean, you know, but you can turn around and see if they're the same. Now, this is not a particularly interesting or profound proposition, number 29. But, again, to show you how a very elementary theorem can sometimes involve... all three kinds of syllogisms. So the second page is different from the first page, they're all just one kind of syllogism, right? But here you have all three kinds. And he says any prime number is prime to any number which it does not measure. It's almost obvious, right? Okay? So he says let A be a prime number. You know what a prime number is, right? A prime number is a number which is measured only by one and not by any other number. So one and two and, not one, but two and three and five and seven and eleven and so on are prime numbers, but four is composite, right? Measured by two. Six is composite. Eight is composite. Nine is composite. Ten is composite. Twelve is, right? You know the difference, right? Okay? Now a number is said to be primed to another number when there's no number that what? Measured them, right? Okay? Now sometimes Euclid will, you know, if you have three and nine, are they primed to one another? Well Euclid will say no because three and nine are both measured by what? Three. Okay? You've got to understand that way of speaking, huh? Okay? So he says let A be a prime number and let it not measure B. I say that B and A are primed to one another, right? Derimation by no number, right? Now, for if B and A are not primed to one another, what kind of syllogism is he going to be using here as his main one? Well, it's going to be either or because, yeah, you see. Now when you say the main syllogism, we don't mean it's the one that is the most interesting or the one that really is the great discovery, right? But we mean the one whose conclusion is the main conclusion, right? Okay? Okay? Okay? And either these two numbers are primed to one another or they're not, right? He wants to prove they're primed to one another, but he shows that if they're not primed to one another, some difficulty follows, right? Okay? So he's going to be using the either or syllogism, eliminating one of the possibilities and concluding to the rest, right? Okay? So he says, for if B and A are not primed to one another, some number will measure them, okay? That's obvious, right? Okay? Let C then measure them, right? Now, what kind of syllogism is this? Since C measures B, right? According to this hypothesis, right? And A we're given does not measure B, that's one of the things we're given at the beginning, right? Therefore C is not the same with A. Since C measures B, and A does not measure B, therefore C is not the same with A. Even though the others were using and talking about the syllogism. Just a simple syllogism. Yeah, yeah. And what figure is it in? And what figure is it in? First, second, or third? C is second. Yeah, see, now there you have a syllogism in the second figure, right? Yeah. You're affirming and denying the same thing, right? You're affirming measures B of C and denying measures B of A, right? Okay? You were given above that, you know, any prime number is primed to any number which doesn't measure, right? So you're given that A does not measure B, right? So if A and B were not primed to one another, something would measure both of them, namely C. And C couldn't be A, because C measures B in this hypothesis, and A doesn't measure B, right? Okay? Therefore C is not the same with A. Now since C measures B and A, then it follows that it measures A, which is prime, right? But no prime number can be measured by any other number only by itself, right? Which is impossible. Okay? Therefore no number of measure B in A. Therefore the other two must be true that they're primed to another. Okay? So you have actually, in that, you have all, what, three kinds of syllogisms, huh? And major, I mean the, what do you call it, the chief syllogism, the main syllogism, is that A and B are either primed to one another or not primed to another. But they can't not be, they cannot be what? Not be primed to one another. Cannot have something measuring them, right? Therefore they must be primed to one another, right? Now the either or statement is obvious, right? Either they're prime or, you might say either they're prime or composite to one another, right? Okay? And therefore they can't be composite, they must be primed to one another. How do you know they can't be composite? Well, if you say that they're composite, right? Then it would follow that some number of C measures both of them, right? Okay? And this number of C that measures both of them couldn't be A because we're given that A doesn't measure B, right? Therefore there must be some number of C that measures both A and B, but A is a prime number. And no number can measure their prime number. Except itself perhaps, right? You can speak that way, right? Three by saying three, right? So therefore, that's impossible, right? Therefore the antecedent, that they're composite to another, right? That they're measured by some number, is impossible. Therefore, the other alternative must be the true one, that they're primed to another, right? What do you see at that? Well, he's saying if, if they are what? Composite, right? Then there's some number that measures them, right? And if there's some number that measures it, then that number measures A, right? But no prime number can be measured by any number except perhaps by itself. But he excludes that possibility, right? Because A doesn't measure B, right? And C is the number that measures both A and B. So A can't be C, or C can't be A. Because A doesn't measure B, C doesn't measure B. So you have a syllogism in the second figure. Here we get the second figure syllogism, unlike the first page where they're all in the first figure, the affirmative. And you get the, basically the either or, and you get the if then, huh? You know, I was mentioning that, wasn't it the last time I was here, I happened to be reading the, my favorite book there, the Summa Contra Gentiles, and Thomas was arguing that the relation of God to creature is not really in God, okay? And he says that, um, a relation, um, if it was really in God, either have to be the substance of God, right? Or an accident, right? Or an accident of God, right? Okay? But in a previous chapter he's shown there's no accidents in God, therefore he eliminates that possibility, right? Okay? And then he eliminates the possibility of being the substance of God, because if it was the substance of God, then God would be, what, his very substance towards creatures, and therefore he'd depend upon creatures, huh? But God in no way depends upon creatures, therefore he can't be that, huh? So he, he, he, he's got, what, all the kinds of syllogisms there, right? So these things always drive students crazy, but that's the, that's the reason, but no, the reason why I give it here is not so much that I'm crazy, although that's, that's laudable too, no, I mean, it's to show that even in a very elementary theorem, like these two, it might require as many as all three kinds of syllogisms, right? Now, when the conclusion of one syllogism is the premise of another syllogism, I call those, what, continuous syllogisms, huh? Just like the mathematician, you know, sometimes, you know, he calls, um, a proportion like this, four is to six, and six is to nine, you call that proportional because you put the end to one and it's the beginning of the next one, right? But if you have to say two is to three and four is to six, it's not proportional because it's not the same thing that the end of one and the beginning of the other, despite kind of a metaphorical likeness there to, to put the continuous symbols. In the continuous, the end of one is the beginning of the next, right? The end of America is the beginning of Canada, or the end of America is the beginning of Mexico, and vice versa. So when syllogisms, when the conclusion of one syllogism is the premise of the next one, I call those two syllogisms, what, continuous, or when what is defined, you know, and what is defined, you know, and what is defined,