Logic (2016)
Lecture 16: Quantity, Measure, and the Nature of Number

Transcript
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God, our enlightenment, guardian angels, to meet the lights of our minds, warm them in our images, and arouse us to consider more correctly. St. Thomas Aquinas, angelic doctor. Pray for us. Help us to understand all that you have written. I was meeting Thomas there in the Prima Pars that there were vegetarians there before the fall. Yeah, yeah. I got problems now. I had a problem with that Lord about his fish diet, you know. And now I'm going to have a problem with that Lord about the vegetarians before the fall. It's his friends for fishermen. Yeah. A little Lebanese, right? It's a hanging of business. Well, Quinn, this is what made the rule about, you know, Friday, two days a week, you know, if we have fish because we want to build up the maritime family, you know, people. So what's my number? Here's a good Pythagorean question. What's my number? Well, I've always found that I had a traction with a number of five, you see. I don't know whether it's, because I have five letters in my name, Duane, and maybe that's what I guess, and I know it's had five fingers or something like that. Maybe it's the way five is, you know, right? It is kind of, you know, that, you know, rather than, you know, that four, you know, or three, you know, and so on, and so on. Now, so I think about these distinctions of five that you have in philosophy, right? And sometimes they even break down into three and two, which is, you know. Three. So that is the first distinction of five that we need in logic. Yeah. Yeah. And you probably divide them into three and two, right? Because genus, difference, and species are essential, and then property and accident are outside the nature. And one has a connection to the nature that it doesn't, but, okay. So that's interesting, right, huh? Now, where in the chapter, quantity here, right, where does the number five come in? Well, more than that, but continuous quantity distinguishes into five, right? It distinguishes, you know, quantity into, what, discrete and continuous. And they're both distinguished by the way their parts are, right? Okay, the continuous quantities of parts meet at a common boundary or limit, huh? And the discrete, they don't, right? Then he subdivides the discrete into, what, number and speech, right, huh? Okay? They're kind of similar, you know, huh? And I know Hamlet, you know, when he says, I'm sick at these numbers. But he's talking about this kind of a poetry where he's trying to express himself, right? And so there's a similarity between numbers and, what, this meter that you have, huh? Because they don't meet the parts that are common boundary. But then the continuous quantity, huh? He divides it into five, right? And there's a line, and then the surface, and then the body, right? And then, what, place and time, right? Well, place and time are kind of extrinsic measures, and the other, the intrinsic measures. So you divide it into three and, what, two, yeah. Now, you can't divide the, in the post-predicaments you have, how many senses does he distinguish of before? Five, right? Five. Yeah. But it doesn't divide it into three and two, right? There are four main senses there, right? In order, and I call those the central senses, but then the sense of cause before effect is so important, and it's alongside the second sense that he mentions that, right, huh? So he has five senses here, right? So I use a thumb as opposed to the other four, right? Okay. Now, when you get into the study of the soul, right, huh? And you divide it into its parts, right? Which are, it's a different kind of hole here now. It's what they call a potestative hole, right, huh? Maybe you can call it a powerful hole, right? But what's the distinction of the JNRF powers and the soul? Do you know that? You read that before? That's one group, yeah. Sense powers, yeah. Oh, and the sense appetites. For the appetites, he does the sense appetites and will. Yeah. So he first divides it into the repetitive powers, right, the desiring powers, right? And he subdivises it into the sense, desiring powers, and the intellectual one, which is the will, right? And then you have the, what? You have the vegetative powers, right? Which are later on divided into three, huh? Nourishing yourself, right? Ability to grow, ability to reproduce, right? Okay. Which Thomas goes back to when he talks about the sacraments, right? That there's a certain likeness to that, right? That baptism is like, you know, being reproduced, right? And, uh, being produced, and, uh, and, uh, confirmation is growth, and Eucharist is, is nourishment, right? Kind of interesting that comparison he makes, huh? But God does this in a sensible way for us, who are animals, right? Two-legged animals, Aristotle calls this in the Book of Wisdom. But you can say two-legged animals with reason, right? So you have the vegetative powers, right? That's one group, though, see, in the plants. And then you have the sense powers, right? Which later on you divide into the exterior senses, which, again, you meet, what, five external senses, right? No, you get the five again, right? You can divide maybe into three and two, maybe, you know? But anyway, we'll set the girlfriend one. And then you have the inward senses, right? The common sense, imagination, memory, and so on. And then you have, um, the intellectual powers, right? And you have the appetitive powers, which are subdivide, as we said. And you have the locomotion, right? So Aristotle will distinguish, sometimes, three souls, right? The vegetative soul, the animal soul, and the human soul, right, then? But then you'll distinguish four grades of life, because of the animals. Some have locomotion in one place to another, and some don't. And they kind of resemble plants in a way, right? The oysters and that sort of stuff, right? And then, but there are five again or powers, right, then? Now you go to ethics, right? What's the famous division of five in ethics? Okay, the virtues of reason, right? And Aristotle divides it into five, right, then? So you have nous, or understanding, or I call it natural understanding. Then you have episteme, or scientia, or reasoned out, knowledge, right? And then you have wisdom, right? And then you have art, and you have foresight, or prudence, right? So you have the two, the practical reason, huh? These are jama, right, huh? They are art and foresight. And then you have three, he distinguishes in the, what? In the looking reason, yeah. But natural understanding and wisdom are, you know, lowest species, right? In a different, in the sense that they're not divided into species, right? But the episteme is divided into species, right? Okay? And then the art and the foresight are, right? So, when Thomas takes up foresight, he divides them into the foresight of the individual man, and the foresight of the father, and the foresight of the king, right? That way, huh? So that's another division of, what? Five, right, huh? Now, for some reason, when Thomas takes up the existence of God, how many arbustes does he give? And there he goes again, there he goes again, right? He takes up the substance of God, how does he divide that? Yeah, yeah. Now, in both summas, you know, he will always, what, give together the simplicity of God and the perfection of God, right? But in that order, simplicity first, and then you point out, but because in stone and plant and cat and man, right, the more perfect is composed of a lot of different things, right? But God is not perfect. three days of eight hours, or two days of twelve hours, you know. That's pretty hard to go. Yeah, I've done it. I've done both, you know, but two days of twelve is too much for me, even though I was an old man was doing it. I had a professor who did it one day. He was really a strange fellow. That's a tough language. I looked at the grammar book twice, he said. What language was that? He taught my brother Mark as Dante in Italian, right? He read the rhetoric of Aristotle in Greek with me. He did Japanese as somebody else. He's passed on. I actually agree with the search definition of a poet as a man as his brains kicked out. He was an unusual guy, you know. People from the, some seminaries, you know, the St. Paul seminary is not too far away from the college. They worked to watch, to hear his class, you know, this guy's great books class, you know, great books of literature. But he and my brother did Chaucer and Middle English with him too, you know. Wow. He wanted me to do good in German, but I didn't find him. I was doing Japanese, yeah, he was doing Arabic with some guy, you know. And Japanese haiku poetry, whatever it is, you know. What language was it that he had to lift the grams? Do you remember? I don't know what it was. Yeah, yeah, yeah. He was a good guy in many ways though. Now at the bottom of this page it says, this distinction by measure is seen more in the species of discrete and continuous quantity. And the distinction between the discrete and the, what, continuous, huh? So I'll take something like that, huh? Can we better stop now, huh? Okay. Okay. He's perfect in that way, he's perfect in a simple way. So he always takes up the simplicity of God before his what? Perfection, to which is attached to consideration of his being good, right? And very attached to the summa condu gentiles, right? When Thomas takes up the goodness of God, how many chapters does he have? Right? And the first chapter shows that God is what? Second one that he's what? The goodness itself. Yeah, the third one. Yeah, the kind of thing bad of goodness itself, right? And then, yeah, which is a beautiful phrase from Augustine, you know, but a beautiful thing there, right? He doesn't have that in the summa theologiae. Sad, but he's rough. Yeah, yeah, yes. And then the summa bonum, right? That's good, right? So beautiful, right? But then he takes up the infinity of God, right? And the unity of God after those two, simplicity and perfection, right? But the wanderer is what? Is God is unchanging, right? Because in the summa condu gentiles, that's the first thing he takes up. And it's not in summa theologiae until the fourth thing, right? Kind of interesting, right? But the other things, the order is kind of pretty similar. So you have five arguments for the existence of God, right? And you have five, what? You have five, yeah, and you have five attributes of his, what, substance, right? So you can see I'm attached to the number five. For some reason, I'm drawn to that number for some reason, you know? For five reasons. Well, I don't know, you see. I don't know if there's really a number that explains this, you know, but if there is, mine might be explained by five, because I'm drawn to these examples of five, right? I always talk about the five senses of before, you know? Yeah, you got it, you got it, yeah? And there are a lot of divisions of four, two, and three, you know, but it's interesting to see this a little bit, huh? So we left off here somewhere in the discussion of quantity, huh? Yeah, okay, page six, okay. These are kind of subtle things here, you know, you might be exposed a first-year logician to, you know, but you can see these things just go on there. So what does he say there? Plurality, sidi, multitudo, absoluta, which is opposed to the one that is convertible with what? Being, yeah. So Aristotle, in Wisdom, he says that the subject of Wisdom is being and what? One. Strange thing, right, huh? Most people won't tell you, but that's what Aristotle says. Right. And so when he gets into the meatiest books, you might say, of Wisdom, or the books on being, which are most of them, and then the book 10, which is on what? On the Summa, I think, God being one, is, I think, the last of the five attributes he takes up, right? And that's before he gets into the operations of God in 8.4, sorry, into the Trinity, he wants to emphasize that there's one God. He had that in mind, you know? But interesting, right, huh? Yeah, being and one there are the subject of Wisdom, and the connection here between substance and what? Quantity, right? And people often confuse body in the genus of substance, which is one kind of substance body, and body is one of the species of what? Quantity. And they can't distinguish between those two, right? And, you know, like Descartes, who's my whipping boy there from my doctor, he says, but Descartes, you know, identifies the substance of things with their, what, extension, right? That's why I used to say, you know, Descartes never grew up. Because you wouldn't have the same substance, right, if you grew, right? And that was your substance, right, huh? But every time I see these grandchildren, I don't see them for a number of months, you know, it's no wonder that one is shooting up, you know? But it's been the same little boy and the same little girl, right? That your size is not your, what, substance, huh? You ever see a little kid say, I want to grow up, you know, they don't want to get going any bigger? Sometimes you'll probably be a little kid saying, yeah, I think I'm going to say it one time, I like to say it or something like that. And, but the size, your size is not your substance, huh? But it shows the proximity of the two, right? Being and quantity, right? And Plato trying to make that, in Pythagorean, making numbers, right? The substances of things, right? When Aristotle gets into the, you know, consideration of substance there in the seventh and eighth books, right, huh, but in the eighth book, he compares the natures of things to numbers, right? As if there's some of the mites between them, right? As if, you know, a stone is one and the plant is two and the dog or cat is three and you and I are four because you've got reason, right? So you add to body life and you get a plant and you add to that sensation, you get an animal and you add reason and you get a man, right? So it's a little bit like, what, numbers, right? And Thomas will often come back and do that, right? And he'll say, you know, if 10 knew itself, right, it would know what? You could, you know, partake of 10, 9 and 8 and 7 all the way down, right? And this is the way, the way God knows all things by knowing himself, right? You can partake this much of me, you can partake more of me and this more and so on, right? I was reading Thomas there in the Prima part just this morning by chance and he's asking, well, the men are all equal, right? And because one of the objections is saying, well, we're unequal because some of us is sin and some of us, you know, and nature is sometimes, you know, makes us defective or something, you know, because something's wrong with you and your generation and so on. And Thomas says, no, God could make us unequal without there being any sin and without there being any, what, defect in nature, right? But why would he want to do this, huh? I would have got to make us unequal, right? And it's a beautiful phrase, huh? For the pocuitudo, he says, ordinis, huh? For the beauty of, what? Order, right? It's like order seems to require inequality, huh? And Thomas is always quoting there. It's in, I guess, Epistle to the Romans on chapter 13, in the beginning of it. Qu'e adeo sult, ordinati sult, he's always quoting that, huh? And my old teacher, Castric, used to say, you know, God hates equality. Well, Aristotle emphasizes that thing about the wise man, right? That he orders things, right, huh? That's, well, God is not just wise, he's a wisdom itself, right, huh? So he really wants to order things, huh? So I mentioned, you know, what my teacher there, Castric, used to say. He was the wisest man at the College of St. Thomas, right? He's wise to anybody else there. By far. He says, compared to Aristotle, he says, I've got the brain of an angler. And Castric had great respect for Fr. Baumgartner, right? He taught at the St. Paul Seminary, right, which is kind of across the street almost in the college, right? And sometimes I come in with a hard question. Castric wasn't too sure what to say to me. Can I call Baumgartner over there at the St. Paul Seminary? See how Baumgartner fought, right? And then there's other questions that Castric couldn't answer. He says, when Deconic's coming down, you ask him, right? So Deconic stayed at his house there where he's going, and all these lectures in the Twin Cities there. Not six or seven lectures, I don't know, but they gave one lecture at the college, and one at the, you know, seminary, and one at the seminary, and one at the, even the high school, so he's going to talk and so on. So I put all these questions that Castric was stumped with, and Deconic's explaining. very clearly, and so on, you know? So, here you've got this order here, right? Assyric, and deconic, and Aristotle, right, and so on. And this pulchritude of order, right? I mentioned how, you know, I was reading in the 13th Book of Wisdom there, and Aristotle was talking about order, right? And the first species of order, he says, I mean, he's talking about beauty, rather. And the first species of beauty is what? Order, he says, right? Taxi, he says. You see, he's struck by that, no? A pulchritude of order, right? And you see it in the angels, right, no? Because no two angels are, what? Equal. And the angels just right above you is the one who led into you, and the things are pressed down, right? Monsignor Dianna starts to compare the order of teachers there, you know, with that, huh? Even a man like Thomas, you realize, you know, he's always pulling out something like Gaston or something from, you know, Basil or Gregory or something, you know, St. Anselm, you know. He's got a lot of minds behind him, right, huh? He does the same when he treats the difference of states, orders in the church. The offices are for the needs of the church, and the states and the effect of the church, but orders, he says, is what he says. Well, don't they call that one sacrament, holy orders, isn't it? Well, that's what I learned in the Eastern Great School. Yeah, it says they compare it to the orders, the angels, too, you know. I mean, Pinesis does, you know. Quotes from a psalm, and I forget, but I think of God ordering things for beauty's sake, and I think it's from somewhere in the Old Testament, it says something like, I can see Tom's getting into a lot of trouble with the feminist nowadays. It actually goes so far as to say, you know, that the likeness there between Adam and God, right, huh? Because he's a source of the whole human race, even Eve, right? He's God, he says, is the beginning, the end of all things, right? And the Alpha and Omega, the first and the last, the beginning and the end. And he says that Adam is the beginning and the end of Eve, right? Well, you know how he's the beginning, because, you know, but she was made as this kind of helper, right? And so, you know, when I first saw him say the beginning, this is going too far, I'm not sure, you know, for a guy like me. You know, I hate to hate having this, you know, this is definitely terrible, you know, and you're a pretty woman, you know. You know, you know. In your place. Yeah. Yeah. It was kind of funny, I was watching the educational TV there the night, and they had Tenhauser on by Wagner's Opera, you know that opera at all? I think Tenhauser by Wagner? Yeah. I heard of it. Yeah, yeah, yeah. Well, we didn't know it, but it was kind of interesting, you know, kind of listening to it and so on. And so then I, at least I went on the internet and I went up to Wagner's Operas and I was seeing some more things about it and the ring and so on. I saw Tolkien as influenced by that kind of mythology and so on. And I was talking to Warren Murray, he used to have a lot of the Wagner operas, you know, and so on. I guess my brother Mark got Warren interested in the Wagner operas, right? And so on. So anyway, one thing led to another thing there, and there's some guy up there who, very interesting character who's an expert in operas, right? He goes around and he was saying, you know, the three greatest operas are Mozart and Wagner and Verdi. So, anyway, so I was kind of seeing his, you know, his, some of his papers and talks, you know, and so on. And I saw one of his papers was entitled Putting Mozart in His Place. I said, sounds like wrong heresy, right? That sounds like fighting words. Yeah, yeah, yeah, yeah. So I looked it up to see what he says, right? And of course, he's putting Mozart in first place. That's what he's doing. Yeah, yeah, yeah. He is the best, right? So, oh, boy! That's putting in order, right? You know, we use the word place there, you know, put things in place, right? And, well, he's kind of interested when he said, you know, he praises some of the Mozart operas, you know, and how he wrote all the different kinds of operas, you know, the opera Bufa, the series opera, and the German operas, and so on. And they all excelled what they did, you know? And one piece of news talking about how once they've done that, you figure it right, they didn't realize it's so superior to Wagner, and so on. I saw this quote from Wagner, he says, Mozart is above all the masters, and all the arts, and all the ages. You recognize that? That's it. That's the ultimate judgment, you know? So he says, plurality, or multitude, absolute, which is opposed to the one that's convertible with being. Well, Plato got these kind of mixed up, the one that's convertible with being, and the one that is the beginning of what? Number, right? But this multitude that's absolute is, as it were, the genus of number, right? Quasi-genus, right? Not genus in the strictest sense, right? The genus is something indivisible and so on. Because the number is nothing other than a, what? Plurality or a multitude measurable by, what? One. Thus, therefore, one, according as it is simply said to be an indivisible being, right? Is convertible with, what? With being, right? That's interesting. Thomas is always talking about truth and good, which is more universal. This comes up in the discussion of reason and the will, right? Because obviously the will is the good, what? Well, he says they're convertible, right? So that for a reason, huh? The truth about the good is one part of truth, right? Well, there's truth about the bad, there's truth about, you know, the soul, and truth about all kinds of things, right? Okay? The truth is actually the universal, right? It's as universal as what? Being in that sense, right? But then, as far as the will is concerned, truth is a particular good, yeah. So, reason can know what the will is, because it can know what the good is, that comes under one part of knowing truth, it knows the truth about the good. And the will can will the reason what? Learn, right? It can will to apply your mind to learning something, right? Because you recognize truth is a good, very great good, But it's because it's convertible, right? That's true about being in this one that is convertible with being, right? So, therefore, the one, according to it, simply said to be indivisible being, is convertible with being, right? But according as it takes on the notion, the ratio of a measure, this is determined to some genus of quantity, in which there is found properly the ratio of what? Measure. And likewise, plurality or multitude, according as it signifies divided beings, is not determined to some, what? Genus, huh? They used to call these things what, like, being in one, this one that's going to root with being, they call them what? Yeah, which is kind of a crazy thing. I call them syllables. I like the transcendentalist that's a little bit too spooky for me. But it means it transcends any one, what? Genus, right? Okay? Of being and everyone, right? But being is not, what? One genus set of substance, quantity, quality, and so on. Why not? Yeah, a genus is predicated univocally, right? But these are not said univocally of these ten, right? But according as it signifies something measured, it's determined to a genus of quantity, to the genus of quantity, one of whose species is what? It's number, right? And you even want to make another step in there and say discrete, right? And therefore it is said that number is a plurality measured by one, and the plurality is quasi. You've got to be careful about that, right? I don't understand why is it a quadruple? Because it's not said, you didn't give all these things, right? So when you get into the Trinity, right, they'll say, what kind of a, what do you mean you say are three persons, right? Is the Father and the Son more than the Holy Spirit? Well, two is more than one, you know, you see? So what kind of a multitude is this, right? It's not one measured by one, right? Yeah. It's not that two persons is more than one, and the Father and the Son is more than the Father, and the Father and the Son and the Holy Spirit is more than just the Father and the Son. No. See? You might be tempted to say that, right? You know? Right? Three grandchildren is more than two, and two grandchildren is more than one, right? That's not true about God, huh? Strange. Very strange, God, right? I've seen it said before, it's not, we shouldn't think of the Trinity as one plus one plus one plus one. One times one times one. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. In the first six articles, he distinguishes, you know, six different kinds of composition, right? And shows each one of them is not belonging to God, right? And then in the seventh one, right, he's saying universally now. In no way is God composed, right? And he refers to the six he's done already. That's an inductive argument, right? And then he gives syllogistic arguments, you know, that nothing is what? Yeah. Yeah. I mean, he argued and said that in every composition, one part is either to the other part is act as to ability, or both parts are to the whole as ability as to act. But God is pure act. There's no ass of ability, right? They're for the capini, you know? So there could be a syllogistic argument, right? There's also the inductive argument based on the first six, right? If you go through that, you can find in other texts of Thomas where he's talking about a certain kind of whole that you have here, right? Okay. So the body, first thing is to show that God is not a body, right? And he's not composed of what? He's talking about matter and form, and that's different than a body, right? Okay. And you can see a little bit even in accidental things, I mean like artificial things, you know, that in a way you can say the chair is, you know, is wooden and shape. Something like matter and form, right? But also you can say, well, it's parts are, you know, the seat and the legs and the arms and so on, right? Okay. What's the third sense, I think is? Well, you see, what am I? What am I? If you want to know, I'm a two-footed animal that has reason, right? Okay. But you are too, a two-footed animal that has reason, right? And you are too. See? But I'm a two-footed animal that has reason that was born of a Swedish father and an Irish mother. How about you? See? Yeah. Yeah. So, you know, what I am, right? And my individual man that I am, right, huh? You know? There's a composition there, right? A two-footed animal with reason and born of a Swedish father and an Irish mother. I told you how my friend Warren Roy says, you know, Duane says, if you were all Swedish, you wouldn't be as good a philosopher as you are. If you were all Irish, you wouldn't be as good a philosopher as you are. I think you'd be a philosopher at all. Yeah. Yeah. Yeah. So, he explains it, you know? You see? So, you know, this unique person I am, huh? Or this odd person I am. Five is an odd number, right? So, I'm an odd number. Yeah. So, there's kind of a composition there, right? That's kind of a strange thing, you know? But you don't have that composition in God or in the angels, right? Either of matter and form, but even each individual, you know, there's no two angels at the same time, right? So, there's a distinction between that. Oh. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. So you wouldn't say, gee whiz, did Thomas exhaust all the kinds of composition and creatures, right? How could he be fiendishly clever? It's kind of amazing, you know, compared to Aristotle, I've got the mind of an oyster or something. It's hard to distinguish from a plant, as Aristotle says, you know. These animals that don't have locomotion one place to another, right? Sick thing, you know. So it's significant that he says quasi, right? Thomas doesn't multiply words unnecessarily, right? And he does not say that it'd be simplicitare a genus, right? Because just as being is not a genus, right? Properly speaking. So neither is the one that is convertible with being, nor the plurality or the multitude, right? Opposed to it, right? But it is quasi-genus, right? Because it has something of the notion of genus, insofar as it's something, what? Common, right? But it's not common in a univocal sense, huh? That's how subtle it is, right, huh? But I don't know if you didn't flick that upon a beginner in logic, right? But it makes you stop and think, right, huh? Thus, therefore, taking the one that is the beginning of number and has the notion of a, what? Measure, right, huh? And the number which is a species of quantity and is a multitude measured by one, right? Are opposed to one in the many, not as contraries, as has been said above, about the one that is convertible with being and the plurality opposed to it. But they're opposed as some of those things which are, what? Towards something, right, huh? Which the one is said relatively because the other is referred to it, huh? And thus, they're opposed to one number insofar as one is a measure and number is, what? Yeah. Those aren't contraries, are they? No. No. So, you know, subtle as guy is, huh? Yeah. So put that in your head and shoot, huh? In the old days, they always talk about mental indigestion. He had some pretty concrete when he talked about mental constipations. By the way, he's very concrete, huh? Now, the second division of quantity is into those having parts that have a position, right? Or placing toward each other, huh? And those which do not have such a placing or position. In some quantities, the parts are laid out toward each other. In other quantities, they are, what? Not, huh? Aristotle gave this division, right? He first gave the, the main one is discrete and continuous, right? But the parts made a common boundary or do not, right? But then he talked about another division, right? Into one whose parts have a position of respect to each other, right? And one that, what? Does not, huh? Okay. Now, the same species are, to some extent, do you say, separated by this difference as by the previous difference, which was discrete and continuous, right? With one important, what? Difference, huh? Time, although a continuous quantity, does not have parts that are laid out toward each other for the past and future, do not exist together, right? This also seems to bring in another formal consideration of parts, that is, by how united in the whole, right? Now, see, number is, time is a strange thing, because what's the definition of time? It's called the, what? Yeah, number of the before and after in motion, right? See? So you take the motion of the sun around the earth as a, with regular one, we kind of know, right? And every time it comes over the border, it will, you know, I'm, I'm probably saying cruiser or whatever it is, and, and, and I'll mark down, you know, a day, right? So I'm numbering the before and after in the motion of the, what, or even the two hours, right? The position of the sun, before and after. But, um, that's kind of strange, huh? It's a number of the before and after in, what, motion, right? So is it a discrete quantity because it's a number? I mean, a number is, is the first species of what? Discrete quantity, isn't it? So time is a number. Number is a discrete quantity. Therefore, time, right? Yeah, yeah, yeah. So I mean, it's three feet, a continuous quantity or a discrete quantity? Well, three is discrete. Therefore, it's a discrete quantity, right? No, but you're numbering a, what? Yeah, yeah, yeah. It's interesting, huh? But time is not, what? It doesn't have parts, right, that exist to each other. Like the parts of the line do, right? Or the parts of the place do, right? Okay? We take the inner wall of this room there that's containing us here, right? And say this part and this part they're laid out in relation to each other, right, huh? See? Because they all exist together, right? And the parts of a line, the parts of a surface of a body and so on, right? But parts of time and speech. You know, they distinguish between a point even and a one. The point is much closer to the one than anything else. But the point has, what? Yeah, yeah. And the one has no, what, position. Can an odd number measure an even number? Yeah. Like, for example, three measures six, which is an even number. Five measures ten, which is an even number. You don't always, you can't always do this, but sometimes, right? But can an even number measure an odd number? You see, if an even number measured an odd number, right, an even number can always be measured by two, right? Then two would measure an odd number, and then the odd number would be divisible into two equal parts, right? So, no even number, right, can measure a, what, odd number, but an odd number can measure sometimes, not always, but sometimes, an even number, right? So, no even number except two could be prime, right, the first number of two. But every other even number is measured at least by two, right? And some are measured by odd numbers, too. But an odd number can measure an odd number sometimes, like three measures nine, right? But sometimes you have an odd number that no other number can measure, like five attached to, or seven. So, I'm going to attach it to seven, too, right? It's a lover of wisdom, right? There's, what, seven kinds of philosophy? Yeah, three kinds of looking philosophy, natural philosophy, mathematics, and wisdom. Three kinds of doing philosophy, practical philosophy, ethics, domestics, and then the tool of philosophy, so-called logic, right? So, there's seven kinds of philosophy, right? I prefer calling them kinds of philosophy than parts, right? Because parts is too much. Makes it too much. much one, three different kinds of philosophy, seven kinds, seven gifts of the Holy Spirit, seven sacraments. So if I like numbers that you keep on looking for, you know, all the distinctions of five or seven like we do here, you know. So time, although a continuous quantity, because time is divisible what? Forever, right? That goes back because it's the number of motion which is divisible. And you know how Aristotle does it sometimes and he'll combine, you know, showing that the motion is divisible forever with what distance is divisible forever, right? By the fact that one of you guys runs faster than the other guy, right? So the distance of the faster guy runs, right? And the distance he covers, the slower guy is going to cover that same time. a lesser distance, right? But the lesser distance that the slower guy covers in the whole time, that lesser distance, the faster guy would have to cover in less time. And that lesser time would have covered even a lesser distance. So they're divisible forever, right? Just by using those two things, right? So because time is a number of the before and after in motion, it's divisible what? Forever, right? Let's make these paradoxes of Xeno, right? You know, how can you, how can you get out the room, you know? You gotta go half of the way before you can go the whole way and you gotta go half of the half of the way and so on, right? You know, you never get out, right? Don't even try. Yeah, yeah. It's possible to divide the same genus into species in more than what? One way, huh? Number is sometimes divided into odd and even and sometimes into what? Prime and composite, huh? And perhaps it could also be divided into perfect and what? Imperfect, huh? This is connected with the reason Thomas gives in his commentary on the Posteroanalytics, why no difference is, what? Convertible. You know, when I was first starting out in logic, huh? You're always giving us the example of difference, rational, right? And man is a rational animal that was, you know, animal's a genus and rational. But how does Porphyry define difference, huh? It's a name set with one meaning of many things, right? Other in kind, huh? Signifying how they are, what they are. So he speaks of it as if difference is said of more than one, what? Species. And rational seems to be said just of the species man, right? Wait, Porphyry seems to be saying no differences are what? Not convertible, right? You need a combination of differences he seems to be saying, right? You know, the definition is composed of a genus and differences or genus and difference, huh? Well, for the most part, right? When they give the definition, you'll say, you know, that man is a what? Yeah, but immortal. And what reason? And then these, you know, species, these, what do you call them? These, you know, sucker, these ghosts there, you know. It's a rational, immortal animal, right? So neither rational nor immortal, in that example, right, is convertible. You know, it should be better to give a definition, I mean, an example of differences into the definition of square, right? My master Euclid defined square as a equilateral and right-angled quadrilateral. So is equilateral convertible with square? Because the square and the rhombus are both, what, equilateral. Is it convertible with right-angled? Because both square and oblong, right, are right-angled. But is there any quadrilateral besides the square that is both equilateral and right-angled? You see? So you need a combination of what differences, right? Is that more appropriate to do this? See, that's the way the differences really go, for the most part anyway, right? Now, that means it takes you longer to go from the distinct, confused rather, to the distinct. And you've got to have a, what, combination of differences, yeah. But it kind of fits our mind better, right, than having one difference that is, boom, boom, boom, like you're a joke, you know, huh? You know? Do you see what I mean? No, I say to students, you know, I mean, suppose you want to pinpoint some target, right, where you've got to have the longitude, latitude, right? And then you've got one point that has this, both this and this, it's on both lines, right? But with one line, can you really pinpoint something? Well, you could have at least two, right? The mind's to require that, right? That's so it's very exact, you know, distinctive point, you know? And, but you've got to have two lines, which, for you to locate this, yeah, yeah. My son sent me, you know, Riley's book on Killing the Rising Sun, you've heard that book? It's the best song. He's a whole bunch of killing, you know, killing Kennedy, killing this, killing Christ, even. And this is Killing the Rising Sun, right? I guess the Japanese, the Chinese called Japan the Rising Sun, because it gets the sun before, yeah, yeah. And so they took it over. But when they're trying to drop the bomb, you know, in these places, right, and you had to get the target real, really, really, uh, things that they can't have one line, anyway. I was reading about the time when they're knocking out Saddam Hussein's, you know, uh, country there, the army, and they had a pretty good defense system there, you know, and they wanted to knock out that before they sent their airplanes in, right? But they had two sets of airplanes, you know, one coming in, you know, they were targeting the target that was going to, you know, drop the thing, yeah. And one was marking out the place for the other one to do it, right? That's how complicated these things are, you know, huh? Interesting. So I'm finding all kinds of little odd facts, you know, huh? MacArthur was opposed to dropping the bomb in the Japs, because he thought I was killing too many, you know, soldiers, yeah. And David Lawrence there, who started the National, I mean, started the News News Report, you know, he was opposed to it too. And, uh, at least the old great critic there was his name, you know, New York Times in the old days, military critic. He was opposed to it too, you know? Don't come back to haunt us. Okay. So number is sometimes divided into odd and even, and sometimes into prime and composite, right? So I like to say, what is two, huh? Two is the even prime number. Well, it's not the only even number. It's not the only prime number, but it's the only number that is both even and prime, you know?