Logic (2016)
Lecture 19: Relation, Order, and the Nature of Towards-Something

Transcript
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You might measure a line by what, inches, right? Can you measure a surface by how many inches it is? Yeah, yeah. You can measure a surface, though, by square inches, right? It can be measured by something of its own kind. So an inch is a length. You use a length to measure a length. A square inch is a what? Surface, yeah. And then cube, right? Cube, can you do that? Yeah. Yeah. So I don't know. Do you measure a house properly? You say, how much? A square feet? Yeah. The kind of climate you know is going to be more or less, you know. Yeah, yeah. When you buy it, you can buy it. Now, this is an interesting thing, what he says here, in this exposition of Dionysius, right? That the ratio, the definition, or the notion of both time and the number, order follows, right? Because one species of number is naturally before, what, another. And time is also the number of motions according to the before and after, right? So is that true about, it's interesting, he's putting time and number together, right? One is a discrete quantity and one is a continuous quantity, but he's talking about they have order, right? And what did he give us an example of this order of being, post-pregnance? What's the example he gave? Because he said, my old teacher, Kisarek, said, you can tell a man is... He gave us an order there, an example there. One is before two, wasn't that the example? Opposed to my example, bricks and brick wall, bricks and brick house, right? Because one species of number is naturally before another. Three is naturally before four. Because three can be without four. Yeah, yeah, yeah. So my daughter and husband have been having these children, right? They had one child before. Of course, some of these are twins, right? They have any twins. So two is before three and three before four, right? There's a natural order there, though, right? But it seems to be like the order of the, what, of being, right? You can have three kids without having four kids, but you can't have four kids without having, what? Three. Three, yeah. Yeah. Interesting, huh? And then time, right, huh? Number two, right? Other before and after. It's interesting, huh? Very subtle things, huh? We made the same thing in the earlier text, didn't we? The next text there. And that all things partake of one, he proves through that about which it seems less. So, by number, right? Which is in some way opposed to one, right, huh? Not everything is one, right? You know? Now, when you get into wisdom, right, huh? When you get to the fourth book of wisdom, Aristotle finally decides what the subject of wisdom is. Not to the fourth book, right? And what is the subject of wisdom? Yeah. He says being in one, though. He says both, being in one, right? Well, so if number is one kind of being, it's got to have some kind of, what, unity, right? If being in one go together, right? Mm-hmm. And therefore, Thomas says, you know, things resist their being, what, divided, right? Because if they lose their unity, they lose their, what, being, right? And this is important, you know, in the military, they divide and conquer, right? Mm-hmm. Yeah. When they divide the army, right, then they, what, they dissolve the army in a sense, right? He's got a, people running on three-word escape, right? Divorce and so on kind of destroys the family, right, huh? So people, he says, they fight disunity just like they, you know, defend their being, right, huh? One go together, but numbers seems to be not one, though, right? So Shakespeare has the poem there about reason being puzzled, you know, that love made the lovers one. How could two become one? Yeah. Does the Catholic Church exist? Yeah. It's got to be one to be, right? And heresy kind of, what, divides the Church, right, huh? Kind of destructive of the Church, isn't it? Mm-hmm. It's got to be one, huh? Each, each member of the Peralta's got to be one, though, right, huh? There's got to be some kind of being there, right? I had a colleague here in the philosophy department who always maintained, you know, that France doesn't exist or, or, you know, England doesn't exist because it's just, there's a multitude of people, right? But there's no France. I mean, there's no France. I always tell you kind of a narrow view of unity, you know, because obviously a country doesn't have as much unity as the family, right, huh? And the family doesn't have as much unity as one man, right, huh? And Aristotle's criticizing, you know, the community of wives and so on and that sort of stuff in the, Socrates presents in the dialogue about the public, right, you know, that you're seeking, you know, more unity than the country should have, right, huh? Okay. But I'm not tired of my family and everybody obeys me, so, and no one can pursue their, their own interests and so on. And you might say that I'm making the family more one than it is, right? It's just me, you know, written large, right? And they taught them what? Yeah, yeah, yeah, yeah, yeah, yeah. I'm learning the part. Some of these texts, there's also some of these ones here. This text here at the bottom of this page, 16 here, right, is the one about the Trinity again, right? You just kind of saw that text before. Yeah. My fault? Your fault? My fault? My fault? My fault? My fault? There's that same text there again, I see on page 18, the three things. Uh-huh. That's enough to torture you with that. I don't want to torture you anymore on these things, right? I'm going to go on to the chapter towards something. What? Yeah. Yeah. Yeah. The other one I gave you. Yeah. Mm-hmm. Mm-hmm. Now, the first question you might raise here about the chapter 7 following chapter 6, right? Aristotle seems to, what, change the order, right? Because when he enumerated the 10, he gave first, what, substance, right? Then how much, right? Or size, right? And then, what, how or quality? And then relation, right? And then when he ticks them up one by one, he does substance first. And then quantity second, right, which he just kind of concluded. And now you expect a chapter on quality, and here comes a chapter on towards something. And then the chapter on quality, right? Well, you've got to read Aristotle carefully, you know. And why does he disturb, shall we say, the order that he had given before, right? And it's all because of Plato, right? Or someone defining towards something as whatever is said to be of another in one way or another, right? I'm the father of a son, or I'm the son of a father. I'm the teacher of my students. I'm the student of my teachers, right? And then knowledge is always knowledge of something. Well, then knowledge must be what? A category of towards something. Because it's of something, right? Other than itself. Is that what knowledge really is? Or is that a quality of the teacher that he has some knowledge on? What is it? Now, later on in medieval philosophy, they would call knowledge a relation, say, kundum what? Dici, right, huh? Which means that although it's said of something, right, huh? Its whole nature is not that. Its whole nature is really, what, a quality, but it's a quality that has a certain relation to the known following upon it, right, huh? Why, something like double or a half, you know? Is that something in itself, say? Well, how much is double or a half? I'll have double for dinner tonight. I have something incomplete, right? And the poor wife says, what do you mean by double, right? You know, what, double what you had last night? My father gave me some box. Some double, sir. So they've done what they call a, what? Well, it's a secundum esse, right? But its whole nature is to be towards another, right, huh? So Aristotle will proceed like he does often, right? According to what his, people are already saying, you know, Plato and the great Plato had the school act, which academic world is named, right? He's quite a guy in the Plato, right? Academic world is named from Plato's school, right? I went to high school to St. Thomas Military Academy. So I was being taught in Plato's school, right? So Plato is somebody, right? And Thomas says, you know, the philosophie pre-kipui, the chief philosopher, I guess he turns out like that, is our Plato and Aristotle, right? And my teacher, Albert the Great, said the same thing, you know, a man who wants to be a master in philosophy needs to know Plato and Aristotle, right? So Plato had this definition of, I guess, the platonic school anyway, right? And Aristotle, you know, proceeds as if this is okay until it runs into problems, right? So you can say the arm of my body is a, what, relation, right? And the heart of my body, right? And so on. And so I end up being a combination of, what, relations, and there's no substance left, right? This is a serious, serious problem, right? So we have to, you know, a part is always a part of a whole, right? So you've got to remake the definition, right? And he's going to say in terms of what? Something in his whole nature, his whole being, is to be towards another, right? That's what is in the category towards something, right? And then something which is fundamentally a quality, but has some relation falling upon it, should be treated of in what? In the category. So he does have a reason for doing this, right? But these first sites, you should be, you know, scandalized, you know, or it's in the order, yeah. Makes sense, so much. So he says the chapter on towards something is divided into three parts. The first part includes a definition of towards something, right? Then the properties of towards something are considered, right? And it seems like you're doing what you did in the other chapters, right? Up to this point, the division of this chapter would seem to be like that of substance and of quantity. But then an objection is made to the first definition. A second definition is proposed. And another, right, property is brought out, right? From the objection and second definition, we can see the distinction between what the Latins call relative secundum, okay? Let's see, take a look up. Dici, and the relative secundum esse, right? We can also see the surprising order, right, of considering towards something before a quality. Even though the latter is in being or causality before towards, what, something, right, huh? Why is one man a teacher, another man a student, right? Well, it's because of the character, the quality, the condition, you might say, of their mind, right? Which is the quality, right, then, that their mind has. So some relations, you know, come from quality and some from, what, quantity, right, then? And that's why quantity and quality are ordered before towards something, right? Some relations, like double and half and taller and shorter and so on, follow upon quantity, don't they? And some, like, you know, teacher and student or father and son, right, follow upon, what, qualities, right? So unless my father had the power of generating, right, father and mother, don't be this father and son, mother and son, right? So the imperfection, that definition was so famous, you know, he begins from that, right? And they say, oh, there's something wrong here. Something that needs to be corrected, huh? So you don't disagree with Plato and there's your reason for doing so, right? And a good reason for... Not me, anyway, but I wouldn't agree. Yeah, yeah. That's what I would agree. The first definition of towards something is those things which in what they are are sort of another or towards another in some way, right? There's a distinction between the first examples given by Aristotle and the second ones he gives. The first examples are purely towards something such as greater or lesser, right? Or a more distinct one such as double and half, right? But the second examples he gives are mainly equalities primarily, which have some towards something following upon what they are, right? Aristotle then considers the properties of towards something that's defined. He first considers properties that belong to some of those that are said towards something and then the stricter properties. The first property is to have a contrary. Now this fits those said towards another, which are qualities in fact, right? Such as virtue and vice. But not those which are... are purely towards something such as double or half. The second property is to admit of more or less. That's of instead of or, I guess. This also fits those said toward another, which are qualities, but only something of those purely said towards another. One thing may be more or less like another, but one thing is not more or less double than another. Hairstyle then turns to particular properties. The first is that what is said towards something will have something said reversibly towards it, right? If the master is said to be master of the slave, then reversibly the slave is the slave of the master. So if I'm the father of someone, he's the son of mine, right? No doubt. This would not seem to be true in some cases. If the correlative has not been stated correctly, it does not seem to be reversible. If the slave, for example, is said to be the slave of a man, the man is not said to be the man of the slave. But if one takes the correct correlative of master, then reversibly the master is the master of the slave, and the slave is the slave of the master. That's what I was saying about the marriage, huh? He used to say, I now pronounce you man and wife. But is man the correlative of wife? It's kind of putting away from their place, but... In Greek and Latin, it is. I mean, you see the man of a wife? Yeah. So the correlative of wife is husband, right? And then you see that they're said convertibly, right? Actually, actually, but sometimes they just say, or in Greek, they just say... Mm-hmm. Yeah. Even man and woman, are they said correlatively? You know? Am I the man of a woman? Well, maybe about my mother, but then I read the son of my mother, you know? There's a question about what she's called, because she's from a man. Yeah. Is that correct? Now, that's a joke. It says that woman comes from woe, W-O-E. Woe to man. A man's woe. Yeah. But look it up in the entomological dictionary. I guess it means, you know, that she has a veil. Yeah. So, in that case, you know, the word man becomes, what, equivocal, because in one sense of man, a woman is a man, right? She's not a dog or a cat, she's a man. And then, why does man, the male man, keep the name man, and the woman get a new name, right? Well, the one has a veil and the other one doesn't. Just like, you know, in Latin or Greek, the word name, you know, was used for noun and verb, but then the word for noun is the same as name, right? And the verb got the new name because it adds something, right? It signifies with time, and the noun signifies without time, right? And so it keeps the name, name, you know. But in English, you have a different word for name and noun. In Latin, it's nomen and verbum, right? So nomen can be common to nomen and verbum, and then it can be opposed to verbum. And that's the way woman, you know? Man can be said of man and woman, and then it can be opposed to woman, right? But a woman adds something special, you know? So a woman likes that explanation better. See, the other way I explain it is that man means, in general, an animal has reason, right? Well, man only has reason fully. So he keeps the name man, and the woman gets to do that. You want to know how a woman thinks you marry one? Well, that could be in trouble if I speak. So the rest of your life is going to figure it out. Yeah, so I'd be there like, oh, yeah, something of a man doesn't have. Oh, yeah, yeah. That sounds definitely nice. I would like to say it was made from the dust of the earth. A woman was made of it. Yeah. It's more noble than that. Yeah, oh, yeah, yeah. Yeah, so. So this is the stricter property, right, then? And the second stricter property is that the qualities are together by nature, right, then? But here Aristotle says that this is true of the purely relatives, such as double and half. But it is not true of relatives that are qualities such as knowledge and sense. What knowledge and sense are of can be before them and without them, right? So the moon can be before some other planet to sail, before we have knowledge of it. At this point, Aristotle raises an objection or difficulty, which leads him to reject or modify the first definition of towards something, right? Each part of a substance can be said to be of another. For example, the hand of a man or the head of a man, right? If the first definition of towards something is correct, then substance would be a collection of relations, huh? Hence, there is need to look again at the definition of towards something to avoid this absurd consequence of it, huh? Aristotle then modifies the original definition to that whose whole being or nature is to be towards something, right? And not just to be, just said to be of another, huh? He then gives another property of towards something, which is that if one of the correlatives is known, so is the other. They are known together, right? And this is a part of another, more universal truth, that there's the same knowledge of, what? Opposites, right? Aristotle ends the chapter on towards something by noting the difficulty of the, what? Matter, huh? Now, having given an outline of the chapter, we can come back on a number of things, right? First, we should concentrate on the name of this genus, right? It is correctly translated towards something, or in Latin, to what? Ad aliquid, right? That's what you have in the great song. In Latin, for the pros, T of the Greek, right? Rather than by the word, what? Relation. Thomas Aquinas points out how the more abstract word is not said towards something, right? It's like a more substantial word, right? You know, something in itself, right? Now, this text of the metaphysic is a little bit about that, right? He lays down three ways by which some things are said ad aliquid, not by themselves, but according to something else, right? The second mode is when some abstract things are said ad aliquid, because the concrete things having those abstract things are said to another, as equality, right? And likeness, right? Are said to be ad aliquid, right? Why? Because simulae and equale are ad aliquid sutta. So, my cousin Donald says, Duane, that's just like your father. You couldn't say it was like this, could you? Kind of abstract, right? So, there's something important about the concrete word, right? Ad aliquid, right? Towards something, right? Would you say these tables have equality? You can say that, right? But, is have equality, you know? Like the word equal to each other? Yeah. And abstract, right? Yeah, yeah. So, he says equality in simili tudo, secundum nomen. are not said towards something, right? Nevertheless, we probably see it in the relatives, right? Now, you always make fun of this term that you're, even priests, I think, talking about your relationships. It's like an abstraction of an abstraction, right? Because relationships are already more abstracted towards something, right? And relationship is the essence of... Some other thing. Yeah, yeah. They're having a relationship. Yeah, yeah, yeah. And we say, what's our relation, right, you know? It's kind of abstract right now. What are you towards me? Or am I towards you, right? That means it gets down, you know? If you're nothing towards me, then we don't have any relation. That's interesting. And that's the way it's to the Father in the Gospel. What to me and to thee. That's the way it's strictly being. That's the Greek. Yeah. And the canon feasting. Yeah. What to me and to thee. What's this to me? Yeah, yeah, yeah. More of it to speak, I say there. More of it to speak of a relation between two things than to speak as if there's one accident between them, right? Now, Thomas says in this text here from the Sentences, some say, as Avicenna, in his head of physics. What? Okay. He says that the same in number is relation in both extremes, huh? Which cannot be, he says, Thomas says, right, huh? Why? Because one accident cannot be in two, what? Subjects, right? And therefore, it should be said that in both of the extremes, right, there is one relation differing from another in some differing according to species, right, huh? Just as in those things which are, what, named by diverse names as maternity and filia, see, all right? So, if I'm the father of you, you are my son or my daughter, right, huh? But in some, you know, if I'm like you, you are like me, right, huh? But in some things, they do not differ in species, but in number, what, only. Just as when both, there's one name as in similitude and equality, right? So if I'm equal to you, then you're equal to me, right? And then the relation which is in one, as in a subject, as in the other, as in a term, in a conversa. So it's really two different things, right? Now, the question also arises why towards something is considered before how or equality. And Aristotle would distinguish the first four genera in the order of nature. But in the order of teaching, he places towards something before equality. And then I have a brilliant comparison here, right? That Porphyry has imitated that in the, what, premium. Yeah, in the premium to the Isegogi, he says, O Chrysorius, to know what genus is, what difference is, what species is, what property is, what accent is, is necessary not only to understand the categories, but also to divide, he says, and to define and to demonstrate, right? But then when he takes them up, he takes up what? Genus, and then species, and then difference, and then private accident. So there's one difference in the order there, right? When he enumerates them in the beginning, it's the difference. And that's the order of nature, right? Now, you can say, you can see that in the definition of square, right? It's an equilateral and right-angled quadrilateral, right? Well, can quadrilateral be without square? But can square be without quadrilateral? No. So quadrilateral is before square in nature, right? Now, how about equilateral? Can equilateral be without square? Yeah. So what they call the rhombosis, I guess, squares in a jerk. That's equilateral, but it's not a square. So equilateral can be without square, but there cannot be a, what, square without an equilateral. And then the other difference is, what, right-angled, and can right-angled be in quadrilateral without square? Oh, I mean, can right-angled, rather, be in quadrilateral without square? Yeah. Hence, in what they call the oblong, right? Incidentally, a lot of students will call that a rectangle, right? But that's because a square is something special, right? So it gets a new name, and the other ones, yeah. But if you want to give it its own name, it's oblong, right, huh? So a quadrilateral can be right-angled without being a square, but it can't be a square without being there. So differences, well, as the genus, right, are before, right, huh? But quadrilateral is before the differences, right? You can't have a quadrilateral without equilateral, but you can't have equilateral without, you know? But anyway, but the order has changed for a different reason than Aristotle's, right, in the categories, right? And that is that the, what, genus and species are kind of defined together, right? So the genus is a name said with one meaning of many things other in species signifying what it is, right? And a species is what is placed under a genus, and of which the genus is said and answered the question of what it is, right? So they're defined by each other, right? They're like, almost like relatives, right, huh? And so you compare them to father and son, right, in Aristotle, you know, the word genus goes back to generation after all, right, huh? And a father can have many sons, right, huh? Can a son have many fathers? Not in the same sense exactly anyway, right? So it's a different reason than the categories, right? But you have the same thing, right, huh? That these two great men, right, huh? Poor free. He's taking this from Aristotle's remarks about genus and difference and so on. But it's interesting that both of them do the same thing, right, huh? It's the precision these guys vote with, you know? But we in democratic times, you know, it's all sloppy, sloppy, sloppy, and sloppy thinkers, you know? It's just a mess, you know? I remember, you know, they had these big fights, you know, they had fights in the colleges all the time, right? You know, when the other faction was in power there at the College of St. Thomas, right, they divide philosophy according to being and good and true and so on. So logic is about true and ethics is about the good and metaphysics is about being or something, you know? These are all transcendentals, right, huh? And that means that they're, what, convertible, right, the transcendentals, right? And so they all belong to the same science. They talk about the transcendentals, right? And that's sloppy thinking, though, you know? Sloppy thinking, you know? The, I know enough, you know, to make fun of that. So Thomas, in the beginning of the day, Trini taught, right, this question of Trini, he's got to get the true and then you see these things are really, what, convertible, right? And so the mind knows the truth about the good and the will wills the what? Yeah, well, it's just no truth, right? It's an interesting mistake there, if I have a son in there, right, no? But you kind of, you know, what that, right? So if we have a relationship right now, that's something one, you know? You know, you'd be thinking of it as something one, right? Relationship. And they used the expression, I'm in a relationship. Yeah. Very bad ways of speaking, huh? Yeah, yeah. The circle won't let me speak in those ways, not today, I was inclined to do so anyway. Instead of saying, you know, what's our relationship, you know, what are you towards me? That's the right direction, isn't it? How are you towards me? It's interesting, the word lover, right? What genus did you put the word lover in? Yeah, but is it a relative secundum esse or relative secundum dicci, right? Is it like... Maybe only the second, it seems. Yeah, yeah, I mean, is it fundamentally a quality, right? It's like the one about knowing, yeah, yeah. He's a surgeon. So, I mean, is love a... Fundamentally, is that a quality of the heart or a relation of the heart? Yeah. But the father is a relation upon him, right? So it's relative in some way, right? That's why Plato, instance, was mixing them up a little bit, huh? But is it fundamentally a quality that is in relation, falling upon it, right? So I say, what are you towards me? And you say, a lover, right? You know? Which is relative in some way, right? You could say that, you know. It's like saying, what am I towards numbers? The seventh, eighth, ninth books again. You click. It's the books on numbers, right? So what am I towards numbers? I'm a knower, right? I'd probably say, you know, I'm towards my children more a lover of my children, right? Than a knower of my children. I would know of my children, too. But you'd probably say, you know, I'm more a lover of my wife or a lover of my children than a knower of them, right? Though I know them pretty well now. For their sake. Yeah. Because the college could be a knower, right? But without being a lover of you. So at the bottom of this page, then, you have Aristotle's reason for changing the order, right? So, but notice, these are different senses of order, aren't they, right? So if I say to you, is Porphyry speaking orderly when he enumerates the subject of his book, right? And is he proceeding orderly when he takes these up, right? Well, it's not the same order, you know? Well, in the premium, Porphyry's got a medicine premium, right? He shows the importance of knowing these five, you know? He says, oh, Chrysaurus, you know, who asked him, you know, I'm trying to understand the categories, and Aristotle uses these words, I don't know what they mean, very much. And he says, it's not only to understand the categories, but to understand what? A division, right, huh? Because one of the most important kinds of division is that of a genus into species, right? And to understand definition, because it's composed of genus and difference. And to understand demonstration, because he's demonstrated a property of a, what, species through its genus and difference, right? And he says, oh, this is, oh, my gosh, I want to know this, right? I mean, this is, you know? But in there, he says, to know what genus is, what difference is, what species is, what property is, what accident is, right? But then he takes up, that's the order of what? Of being, right, huh? Okay? But then when he takes them up, he gives them in the order of what? Learning, yeah, yeah. Here he shows Aristotle's great respect for Plato, right, that he, you know, thinks, well, we've got to, this is the accepted definition of relation, maybe, you know, recedes as if it's okay, you know? You know, Thomas points out that Aristotle will often give examples, you know, in logic, you know, that they commonly accept at the time, right? And before he takes up those things, you know, and maybe corrects them, you know, in other books, right? So you've got to be careful, you know, huh? Because sometimes you have an objection, you know, and taken from the categories, even, you know, and when he talks about opposites and so on, and Thomas says, well, maybe he's doing this according to the customary positions of Pythagoras or somebody, you know? Now we've got a nice text, we've got to stop right now, okay? Start with page three there with a nice text from my master by this written word, Albert the Great, huh? From logic, huh? When I first went to, uh, to, uh, the Walder, we had a, the logic, of course, they gave us was, was the one with porphyry, right? But now with porphyry, you're using actually, um, Albert the Great's paraphrase, you know? Paraphrase, isn't it? Albert kind of, you know, paraphrases the man, he's kind of, he's a little different, he worked in Thomas's, well, if Thomas was teaching, we'd advise the text, you know, but, uh, quite helpful, you know, magician, there's some, there's some teachers by the written word, Carol Staddle, and Thomas, and Albert, and Boethius, and so on, Augustin, somebody spoke of it, right? Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you.