Logic (2016)
12. The Beauty of Order: Numbers in the Treatise on the Trinity, Limit in Art, and Why the Genera of Being Are Not the First Distinction
Class of 2016-12-01
https://berquistcourse.com/course/philosophy/2-logic-2016/012-the-beauty-of-order-numbers-in-the-treatise-on-the-trinity/

[0:00] Father, Son, Holy Spirit, Amen. God, our enlightenment. Help us, God, to know and love you. Guardian angels, strengthen the lights of our minds, order and illumine our images, and arouse us to consider more correctly. Saint Thomas Aquinas, angelic doctor, and help us to understand all that you have written. Father, Son, Holy Spirit, Amen. I was playing with the numbers of Thomas there in the prima pars, and I got to the place of the Trinity, right?

[0:39] And I was remembering what Thomas was saying when he comments on the symbolism of numbers, right, in Scripture, that the square of a number and the cube of a number have the same meaning as the original number. So of course, with the Trinity, you think of three, right? But the square of three is what? And the cube of three is what? Yeah. Okay. Now, how does three and

[1:13] nine and twenty-seven come into the treatise on the Trinity. There's three at first. the first of the questions on Divine substance No. No. What question of the prima pars is the first question on the Trinity? Oh, Trinity. I'm sorry. It's twenty-seven. Yeah. Yeah, it's got to be twenty-seven. Got to be twenty-seven. Yeah. Okay. Now, what is the treatise divided into? Three or nine parts? It's got to be one of them, right?

[1:49] It's probably I'm going to guess three. Yeah. Yeah. Thomas has this beautiful statement, huh, that the persons of the Blessed Trinity are distinguished by relations of origin, relations based on procession, right? So therefore, he says, following the order of teaching, right, teaching doctrine, we consider first the processions in God, right, and then secondly the relations that arise from these processions, and then finally the what persons? So the consideration of the Trinity is divided into three parts, starting in the twenty-seventh.

[2:34] person, okay. Now, where does the square come in, which is nine? Well, gentlemen, there are two processions, huh? And therefore, how many relations? Huh? Two processions.

[3:06] Four relations. Yeah three four relations Yeah. Yeah. So the first procession is generation, right? Huh? The scripture speaks of, and the father generates the son, so you get the relation of father to son, and the relation of son to father. And then you have, you know, want of name, you know, but they call it procession. These the common word, procession of the Holy Spirit from the Father and the Son.

[3:32] And then you have the breather and breathe. You might say right then, okay. So you have four relations, right? But how many persons? Yeah. Because the relations distinguish only when they are opposed, right? Okay. So the Father and the Son are distinguished by relations of Father and Son. And then, by a common proceeding, right, of the Holy Spirit from both of them, that distinguishes them from the Holy Spirit and Him from them, right?

[4:04] So you have three what? Relations, yeah, three persons, but four relations, right? Yeah. Um. Now, two processions, four relations, three persons. Two plus four is six. Plus three is nine. Yeah. So. Now was that intentional, Thomas's part?

[4:36] Thomas discovered. Yeah. So I was kind of interested in that, huh? Beautiful. How many names does the second person have? Three. Three, yeah. And how many names does the Holy Spirit have?

[5:03] Three. Yeah, yeah. So Thomas says, you know, question each one of these. Well, he doesn't have a separate question on the son being the son because it's already seen from what you said about the father being father, right? Okay. But then you have the um, word the word, and then the image, right? But the image is given last, right? Now the Holy Spirit, the first name is.

[5:29] He takes up as the Holy Spirit, and he's got to explain that name, right? And then you have what? Gift. Love. Okay. And the last name is what? Gift, right? Now, why is gift the last name that Thomas takes up? Why is he picked it up last?

[5:51] Well, the second name is love, right? Huh. Because you have to explain how this is love personally, not. Essentially, right, creatures. But love has the aspect of what looking before and after, gentlemen. Love has got the aspect of being the first what

[6:12] gift. See, because any other good that I give to someone, right, I give to them because I love them, right. So the first thing I give them is my love, yeah. So it's good that takes up love before he takes up what Gift. gift, yeah, beautifully ordered, right? Now why does Thomas take up son and

[6:38] word, right, before he takes up imago? Which is in the piece, this is in Saint Paul, right, about imago. I think both of those first two refer to the father. Yeah, because the son is like the one from whom he proceeds, right? Same in nature and so on, right? And so he's the image, right? And the thought, right, is a likeness of the thing of which it is a father.

[7:05] It's primarily the thought of God, right? So imago is seen after you see that he's both son and word, you know, beautifully ordered, right?

[7:19] That tell you this thing. Another thing I ran across that I think was kind of interesting. Thomas talks about many places, but I ran across in the Prima Pars again. Why doesn't God, you know, make everything immediately? For example, God immediately is the cause of what Adam, right? Why didn't he make you and me and every other human being like he made Adam, right? You know. Why does he you know do all the stuff about parents and grandparents and all this sort of stuff, right?

[7:49] You know. Why does he have these secondary causes, right? Huh? Okay. Well, one reason I've seen Thomas give many times, and he talks about this, is that God wants to share the nobility he has of being a cause, and the cause is a better thing than the effect, right? And God wants to share something of the nobility of the cause of that's right. So therefore, he has these secondary causes, huh?

[8:22] And so I thank God for creating my immortal soul, but I thank God for my body, but it came from God through my parents, right? So I have to thank them too, right? And they share in this, huh? Then Thomas gives a second reason to pick a text in the Prima Pars and struck me because I think I mentioned I had been reading the thirteenth book of Wisdom, the metaphysics, and Aristotle was discussing whether you have good or beautiful in.

[8:55] Geometry, right? And he says, "Well, the primary meaning of good is the end or purpose, right? But you don't demonstrate in geometry for the end or purpose, huh? You don't see the triangle is pointed to defend itself, you know, something has a hard time eating it or something, right? A porcupine or something, right? A porcupine, you say, these needles, have, to drive off, you know, just like the skunk gets something to drive off people, you know.

[9:20] Well, the porcupine, you know, you try to bite a porcupine, you're gonna be. There's some kind of plants too that have, you know, stuff that the animals can't really bite into. It's going to be too painful for their mouth.

[9:36] So, but Aristotle says there's beauty in geometry, huh? Okay. Now, what's the definition of beautiful? What pleases when seen? Yeah. Okay. More generally, you can say what pleases when known right? huh Okay. So the music of Mozart, Like my friend here was talking about, it pleases the ear when heard, right? Okay, and he says now the three main kinds of beauty, in the order in which he gives them is order first, right?

[10:18] And then symmetry, huh? And then what? Limit. Striking order he gives them in, in those three, right? Okay. Now, you know how Aristotle praises Homer, right? We're teaching all the Greeks how to make a good plot, and when he talks about tragedy, he says the plot is the soul of tragedy, right? That's to show it's the most important thing, right? But what did Homer do with the plot?

[10:51] What did he do? Well, it's not like a you know TV continuing series here, you know, where one thing after another happens to the hero, you know. It's a not about one man, what happens to him, right? But it's about a course of action that has a beginning, middle, and end, right? Later on, he says tying the knots and untying the knots, right? But beginning, middle, and end, you can see that's order, right?

[11:22] Okay. What's the best thing after God? The universe? Yeah, but the the order of the universe, huh? Yeah, it's like the form of the universe, huh? Okay. I mean, universe as a whole is better than just one of its parts, right? But the ultimate perfection, universe, is in the order, right? You see it most perfectly in the order of the angels, right? You know, Monsignor Dionne used to compare the order, you know, of teachers, you know, to the order of the angels, right?

[12:00] Huh? So Aristotle's like the highest angel there, and then Thomas is the one who can explain Aristotle, and then I can explain Thomas for you, and down the line, right?

[12:14] And there's some teachers who are fallen. Yeah. Yeah. So I was struck by his giving as the first kind of beauty, order, right? Huh? And you can see that in Mozart's music, right? I was listening to the 18th piano concerto and the 24th piano concerto. and I can't listen to all M Mozart's music at once. I have to go from one piece to another, right? It's I have to keep up all the time if I don't, you know.

[12:40] Haven't heard this piece for quite a long. So beautiful, I was struck, you know. I always had kind of a low opinion of the 18th piano concerto. I said this is really good. I realized just how can I have been so deaf, you know? You know? You know? And when Boss was trying to get Samuel Johnson, you know, to appreciate good music, you know, and Paul Johnson realized what he's doing for America.

[13:04] You're kidding me! Another C. S. , you know Boswell. He would he would pass up an opportunity to be with Johnson if he could go hear a concert of Handel, because he said Handel something's good, good judgment. So I was I was struck by this passage, you know. I was trying to understand what does he mean by by limits, you know? Why does he say that? And but I was remembering the things that I've read, you know, from people who are very sharp, you know.

[13:34] And one guy was a guy named Sherlock Holmes, right? And there's a famous story of his. I think it's called the the Norwood Builder, something like that. But anyway, this guy is kind of a nasty character, and he's been told to get lost by this woman, and he's trying to get with her, right? And he's trying to make it appear like she has committed her son has committed this murder, this crime, you know.

[14:01] And he's a very clever guy, right? He makes it very convincing, and even you know Sherlock Holmes is kind of you know you know taken in by it to some extent. But then he he went one step too far, right? Holmes caught him, right? And so, like there are a lot of these Sherlock Holmes stories, it's kind of a conversation between Holmes and Doctor Watson, right? His good friend.

[14:29] After the thing is you know salt and settled and so on, and he's talking to Watson. He said he was really clever. This guy, you know, he had me kind of fooled for a while, you know. Sherlock Holmes, it's really really well done, you know. But he said he lacked the supreme gift of the artist, knowing when to stop.

[14:52] That's an amazing thing, right? And I have a beautiful book at home there on Italian paintings, you know. And the the very very perspicacious, you might say, this this guy writing about the Italian paintings. And I know I'm talking about Titian's painting of the Assumption of Mary. You know, it's beautiful. It's one of the church's church and so on church, and so on. And but in the course of praising Titian as as being the supreme master of this kind of thing, he always knew where to stop, you know.

[15:26] These guys are very sharp, you know. It's the same thing that my friend Sherlock Holmes was saying, you know. The admirable stories that Sherlock Holmes is, as Albert Einstein said, right? Admirable, you know.

[15:40] And then I've read many books on Mozart, you know, and I've seen the same say the same thing by these great critics, you know. Mozart always arrives at his goal, but never goes beyond. He always knows when to stop, right? Huh? And you know, just I just think the thing to I was struck by the way he ends the the greatest opera of all, the opera of operas, on Don Giovanni, right?

[16:06] huh? As Kierkegaard says Don Giovanni is the opera, but the Iliad is the epic, right? It's never going to be anything better than the Iliad among as epics. It's never going to be anything, you know. My good friend Washington Irving, right, Don Giovanni is the opera of operas, right? Oh, yeah, We appreciate it, huh? I just the way Mozart did such a, you know, I would go on, Beethoven would go on from bar to bar, you know, I'd be like, I've done such a great thing, you know.

[16:40] So Mozart knows just when to stop, right? You know, you know. I used to talk to my my girl students there at Assumption, and I explained that the Greek word cosmos, right, which is the Greek word for universe, but it means a beautiful ordered whole, right? Now, do you see the connection between that and the Greek word cosmetics, right? Father Harden calls the art of reducing cosmetics as role playing.

[17:10] Yeah, he says everybody's trying to look different than they are. But cosmetics can help a woman look more beautiful, right? But you have to know when to stop. If somebody's going to slather it on, and just, just, yeah, yeah, yeah, yeah. So, so that's what that Horace means means, right? The idea of limit, I can see it in these things, right? The beautiful woman's face, the the great music of Mozart, the paintings of Titian, right?

[17:44] Huh? Sherlock Holmes saying the same thing, right? Huh? But the first thing Aristotle gives is that of what order, right? Huh? Well, what I was struck by was had that in my mind. I mean, I go around for a week, you know, with the same sentence in my mind. He said, "I'm going to see Diann all the time. " You know, lay down and still laying down yourself.

[18:07] Think it was one sentence, you know. Montaigne was. I told you that time, and I was trying to solve a problem I had as an undergraduate, you know, and it became relevant to my doctoral thesis, right? And I was I was writing on Monsignor Dionne, and I put together something Thomas said, something Monsignor Dionne said, "and BAM Like that, you know like that? " He said, "I'm going to check this out.

[18:30] This has been four or five years since I first found this problem. " And I said, I ran down to see Monsignor Dionne you know. and I started off on a nice roadway He said, "I know where you're going to, " he says. He said, "Damn it! " I said, "Can I go there anyway? " My music, marvelous man. Okay, so, but the first thing Aristotle says is order, right?

[18:52] Now, I was struck by Thomas. He gave us two reasons, huh? Why God doesn't cause everything immediately Himself, right? He wants to work through what. Secondary causes and so on, right? And one reason I said I already gave was that give us a share in the excellence of what Causality. Uh causality, right? You know, if we were just just effects, all immediate effects of God, then the creatures would have no share in the causality of God, right?

[19:22] And that would be a great defect, right? And the other reason he gives is so that there could be the beauty of the order of causes. That's something, right? I was struck by using the word what? beauty there, right? But in terms of what order, order, yeah, yeah. That order is something very beautiful to the mind, right? He says about the Church right? He talks about the Contemplative Life, Act of Life.

[19:50] He talks about orders, duties in the church, the states. Yeah. And he says part of the reason for these distinctions in the church is the beauty of the church. one of the Yeah. beauty. of the church Yeah, yeah, yeah. That's why we have a hierarchy, which is comes I guess from the angels, right? But you know, they have kind of imitation of the hierarchy of the angels, you know, in the church, yeah.

[20:13] And so you realize what a beautiful thing order is, right? I was talking earlier about how Thomas. When he picks up the names of the of the Holy Spirit and the names of the Son, right? Why does he have Imago, image last, and and

[20:31] gift last, right? Love comes before gift, right? He's looking before and after Thomas. He does that, right? That's a question of order, right? He's seeing two orders, right? He's seeing that love has a notion of the first gift, right? Everything else you give somebody you give because you love them. So the first gift has to be love. But that's why, what? Love is given as a name to the Holy Spirit before he takes up the the name what?

[21:04] Gift, yeah, beautiful, huh? Now then, I was thinking about my yeah. I wanted to ask you with regard to essentially this gift of participation in God's causality. Yeah. Are there different levels of it? For example, for material creatures procreation and but, were there the other senses in addition to the procreation, such as the higher angels teaching the lower angels? Yeah, yeah, yeah, yeah. So it's ordered all the way down, right, from the highest angels, right?

[21:38] And the angel illumines the angel right below him, right? Because he's more proportioned to him, right? You know, brevity is the soul of wit. So the wiser the angel is, the more he knows and fewer thoughts. But you have to divide them for the dummies below you, right?

[22:00] It's marvelous things, huh? But then I was thinking of of what my friend William Shakespeare was saying, right? The culmination of this definition of reason is that it looks before and after, right? Now, if you're looking before and after, you're looking for order, right? And if you find order, then your mind is going to be what? Pleased, right? That you're looking for order. You see some kind of an order, right?

[22:27] It pleases the mind when seen. See how the all things tied up, right? You know, this. I was reading the text of Aristotle, the 13th book of Metaphysics, where he gives order as the first form of beautiful. And then Thomas, where he's talking about something else, but he talked about God wanting there to be this the beauty of the order of causes, right? Which it couldn't be unless you shared causality with them, right?

[22:57] And then, I mean Shakespeare's definition of reason, right? They all fit together, right? That's a culmination of the definition that reason looks before and after, right? That's what it wants, right?

[23:13] I mean, you can you know divide it up for you, you know, and say, doesn't reason want to know why? It is looking for the order of cause and effect, right?

[23:31] Who really is better, Corelli or Vivaldi right? I'll finally admit that Corelli's concertos are better than Vivaldi's. So, in a qualified sense, at least. Yeah, yeah, yeah. But they had a reason for Corelli, right? That the you know, you know, even Corelli's Gloria and so many of the masses and beautiful things, you know.

[23:58] But you tend to look and see which is the best, right? People always asking me, "What is Shakespeare's best play?" You know. I don't mean presumptuous, right? I used to kid Warren Murray, you know, He was saying that Shakespeare is greater than Homer, you know. I said that's awful, Presumptuous. isn't it, right? So he qualified it in a way, you know. Okay. So we're going to look at quantity today.

[24:32] huh Okay, Size. I was, I was Tuesday night there. I was looking with my students at the beginning of the second book on the soul, right? And Aristotle has the brevity of wisdom, right? Now, starting to approach the definition of soul, he says, "Substance is one genus of being." He goes on. Now Thomas, he says, Aristotle is going to define the soul. He makes a beautiful comparison between the definition of the soul and the definition of an accident.

[25:24] So what is he doing? You know, why is he making this comparison? Well, an accident has to be defined in reference to something other than itself. It's something of another, right? So sometimes they kind of define quantity as the size of substance, right? Okay. Well, quantity is not the same thing as substance, is it? But it's something of substance, right? It's the size, huh? The measure of substance, right?

[26:06] Sometimes they say quality is what the disposition of substance, right? So you have to define an accident by what it is of, right? If you were to define what is health, right? Daddy, what's health? You know. Well, it's a good condition of the body. Okay, kind of a attempt to define it. But you're defining it as something of the body, right? And it's not a body.

[26:44] Well, now, why is the definition of soul going to be like the definition of an accident? Because the soul is not in the genus of what quantity or quality, or any other accident. Why is that? The form of something. Yeah, yeah. And Aristotle will say, you know, that the soul seems to be in the genus of substance, right? Now, but then he has a second division. He divides material substance into what matter and form, and then the what composition of the two, right?

[27:20] So the soul is going to be the form of a body, right? So Aristotle has three divisions. On the side of the soul itself, and then some divisions on the side of the what body, which it is the form, right? So beautiful comparison, right? But the first division, he says, Aristotle is talking about the what distinction of what? What is being distinguished in the main, huh? In the book called Categories, what are you distinguishing?

[27:55] Genus. Yeah, I usually call it the highest genera, right? But Thomas says, like following Aristotle there in the text, where he says substance is one genus of being, right? So what are you distinguishing here in these ten?

[28:14] What? See, being is not a genus, right? Because a genus is said with one meaning of any things other than kind, signifying what it is. But being is not said of these things with one one meaning, right? But you are distinguishing the what genera of being, right? The way Thomas describes it, huh? Distinctions. My friends come he's excited to hear about substance.

[28:50] He didn't know he was a substance. Well, this is a a very you want to talk about order, right? This distinction is where where is it belonging in the order of distinctions?

[29:13] Very high, the highest. Seems almost doesn't. It's very high, right? Right. And if you're interested in going into what's under these genera, you can go to all the different parts of what philosophy, right? Like for example, under quantity, you're going to see the distinction between what discrete quantity, right, and what continuous quantity, right. And then under discrete quantity, you'll get what number and speech, right.

[29:50] And then where do you study number? Well, in mathematical philosophy, but in particular in arithmetic, right? Arithmetic, huh? The reasoned out knowledge of numbers, huh? But continuous quantity, you'll get that over in what geometry, right? But you put place and time with line and angle and surface and solid, right? And where you take up place and time.

[30:23] We take it up in the fourth book of Natural Hearing, fourth book of the Physics, right? Now, at Laval there, De Koninck would give a course on the first or the second book of Natural Hearing, the Physics, as we call it. That's not really still so clear, you know. We used to call it the Physics, but the actual title is Natural Hearing, right?

[30:49] He gave a course on the first or the second book for the first year students, right? So if you were there for more than one year, you'd you'd sit in on get the first two books, right? But then he gave a more advanced course for the older students, one of the later books. And when he got to the fourth book, there he would give one course, whole semester in place, and then another, you know, course, another year, another semester, whole course on what?

[31:18] Time, yeah. The one at the end of time, there is definition eternity, right? And so you have to go to arithmetic and geometry, right? And Natural Philosophy to take up those particular what? Species of discrete quantity or continuous quantity. Maybe you can go to the book on the poetic art to hear about meter and so on, right, in poetry, huh? I told you my mnemonic device, right?

[31:53] Added, added, the most common forms. But if you want to know about substance, right? Where would you go? Well, if you want to know about material substances, you go to what? Natural Philosophy, right?

[32:19] Well, if you want to know substances in general, right? Even immaterial substances, you've got to go to what? First Philosophy, right? To wisdom. Well, these are all different sciences, different parts of philosophy, right? And you can't you can realize how universal this is, right? Now later on we'll get into what qualities, right? And one kind of quality will be habit or disposition, right? The place where I meet habits the most is in ethics.

[32:54] I was asking my students last night, you know, about the book. And but where do you find the abilities or powers? Well, the animal, yeah, the powers of the soul, right? Okay. And where do you get shape? Those things, though, go back to geometry, right? So you see how how this is higher, right? You know. So I was saying to myself, is this the first division or not?

[33:22] The first distinction, I mean, the distinction of the the genera of being, the genera of what is. Being means what is there, right? He says this is something very universal, right? It's funny, you know, Aristotle is going to define the soul. He says we're going to first define the koinotatas, the most common definition, right? That covers the plant soul and the animal soul and the human soul, right?

[33:56] And then you take up each kinds of powers, and you'll realize what's peculiar to the plant soul where it stops, so to say, and then what the animal soul has in addition to that, and then what the human soul has. All right, goes through in that order, right?

[34:25] So you're going to see is this the most universal? Is this the first distinction? What do you think? Our mind starts off with a confused being confused, as Aristotle brings out in the *Premium to the Eight Books of Natural Hearing*, and those things in a confused way, right?

[34:53] I know I had this painting of Canaletto, painting of the canal there in Venice, right? And put up on my wall there, and I was a bachelor, you know, blank wall, so I have a little bit of, you know. And one day I'd gone from one side of the room to the other room, and I said, "Hey, just notice something, you know. You're over here looking over there, and you're looking straight down the canal, and you get over to that side, and you're looking that way towards the painting, and you're still looking straight down the canal.

[35:33] My gosh, that's interesting, you know. What kind of knowledge do I have of the painting before I saw that? Geometry or something. I had a confused knowledge, right? You sting the parts, right? Huh? Okay. Sometimes you see somebody in the art museum there, you know, you walk through there and you get these kind of chairs or benches or what they call them, and see somebody standing there, sitting there, you know, looking you know at the painting, you know, but you start to see more as you go on, right?

[36:03] Okay. I told you that thing about Mozart's Jupiter Symphony. My friend Warren Murray says, "What do you? " I said, "How much I like the Jupiter Symphony. " He says, "You know what he does there in the last movement? " And I said, "Kinda. " He combines all five melodies together. He does? What kind of knowledge do I have of the Jupiter Symphony? Yeah. Aristotle gives that kind of example, right?

[36:28] Huh? I like your salad dressing. huh? What do you use in your salad dressing? You know? I told you that story of my brother Mark going into the wine place there in California, and they had these used to be Paulsiette. They have these names like Burgundy, you know, not to mean Burgundy wine, but just combination of red wines, right? And everybody had their own what ratios and so on, their own combination of what they had and what they thought tasted good together.

[36:58] And my brother Mark was tasting one of them, says, "What do you use in this? " Yeah, I guess you know. Think I'm stupid? I'm telling you what we're using, you know. So my brother was tasting one of them, and. He started telling the guy one after another what he had in there. The guy says, "Come on to the back room here and taste these combinations. Which one do you think is the best?

[37:14] " That this guy knows what he's doing, you know. But my brother Mark couldn't do it. He first went out to California, right? Huh? And I couldn't do it now. You know, I did wine quite regularly. And what kind of knowledge do you have of the the wine then? You know, Confused. Yeah, yeah, And uh they're putting out a lot of these wines here in Italy now that are, you know, the famous Chiantis, but they're, but Sangiovese maybe ninety percent and there's ten percent Cabernet Sauvignon thrown in.

[37:49] And that's as if I can. I think I'm confused still, right? I'm not sure if I hear everything. Buy another bottle to. try it. Yeah, Yeah. So, he gives the example of the child calling all men father and all women mother, And then later on they distinguish, right? And I told you I was watching my children one day. They were watching some woman go into a house across the street.

[38:21] They say, "Well, look at that mother." Well, may or may not have been a mother, right? But they don't have a distinct knowledge of what a mother is yet, right? Kind of confused knowledge. Sometimes you find a child calling a cat a dog or something. You know, a little, little, little man piece.

[38:42] So we go from the confused to the distinct, right? What's the first distinction we meet? Is is it the distinction of the, genera of being? I mean, being is is pretty universal, isn't it? Everything that is in any way whatsoever. Is a being, right? You know. So here you're distinguishing the genera of being. It's a very universal distinction. It's just, is it the first one? I mean, all these things can either be actual or potential, which would be.

[39:19] Yeah. Now you see, when Aristotle takes up being, as such, right? In, wisdom, he distinguishes between accidental being, right, in a different sense now than accident here. Um. If you if you say that I am a what, Christian geometer, right? That's an example of what. Yeah. And. Aristotle would say, Is there, "Any way of becoming a Christian geometer."

[39:53] I don't think he asked that question. Well, he wouldn't have been here, right? It was a way of there's a way of becoming a geometer, right? Which is to buy Euclid's Elements and read them carefully, right? Think about them. There's a way of becoming a Christian, which is to get baptized and so on, right? Believe and so on. Is there any way to become a Christian geometer?

[40:21] Is that anything? Yeah. You could see in some way that you know I really am a Christian geometer, aren't I? Or I am a philosophical grandfather. Is there any way to become a philosophical grandfather. Is there any way to become a philosopher, right? Is there any way to become a grandfather, right? Is there any way to become a philosophical grandfather?

[41:00] So here seems to be a distinction before what this distinction, right? Distinction between being per se and being what per accidens, huh? And then he gives two distinctions of being what per se. One is according to the figures of predication, is the way we distinguish these things. But you could also say it's a distinction of the what the genera of being, right?

[41:28] And then the other distinction he gives is into being an ability and being an act, right? Now is that a distinction of the genera of being, or what is that distinction of? What would you say it's a distinction of? To distinction of you brought it up, Father.

[41:50] That's good that you did, but what is the distinction of? What senses of being? Different senses of being. Well, that's but these are different senses of being too. Okay. Can't see anywhere that you have confused knowledge of

[42:14] senses of being. Senses mean like meanings, right? They probably say in Latin terms modes of being, right? But I think in English we'd say

[42:34] two ways of being, right? Being an act and being in what ability. In some way, this seems to be more universal even than this, because in any genus you can speak of ability and what act, yeah. I'm kind of struck Aristotle in the fourteen books of wisdom there, the metaphysics, so called. He takes up the distinction of being according to the figures of predication and mainly a consideration of substance because that's being in the fullest sense.

[43:14] Before he takes up the what distinction of being by being an ability and an act, right? So in in books seven and eight, right of the fourteen books of wisdom, he singles out what consideration of substance, right? But in this in the Seventh book, he leads you from what logic right into it, right? And then the ninth, eighth book, he leads you in from what natural philosophy.

[43:42] So you talk about matter and form and that sort of thing, right? And and then the ninth book, which comes after the seventh and eighth, of course, he talks about ability and act, right? Well, that seems to be more what universal and even God, right? Who's a being? Huh? He said, "I am who I am," right? I think he he qualifies to be. He's more real than we are, right?

[44:15] Sometimes does the scripture speak as if we're nothing compared to God? But when you take the simplicity of God, one thing we show is that God is not in any. What genus? huh Okay.

[44:35] But yet he comes under act, huh? I was talking about my great excitement in following this middle term of God being pure act, right? You can show from him as being pure act that he's infinite, that he's altogether perfect, right? That he's altogether simple, right? You know, bang, bang, bang, you know, with this one middle term. But you can speak of act, right? Huh? You can speak of ability if you take act of ability, right?

[45:02] In? God, huh? Father is said to be almighty, right? God is almighty, all powerful. So I mean, this seems to be even taking God in some way, right? Taking God, you know. We can't put God in one of these genera, genera. Yeah.

[45:25] So is that the first distinction? Why does Aristotle take up this one here before that? huh? We should leave that question until I study the first philosophy.

[45:56] And even the consideration of substance in seven and eight, he takes it out from logic first, and then from what? From philosophy. Of course, this distinction here is by the figures of predication, right? From something logical, right? Nice subtle guy that Aristotle, right? Huh? You know. My teacher De Koninck said he'd been teaching the books of natural hearing for the nineteen thirties, right? He never went through them again to lecture on them that he didn't see something he didn't see before, right?

[46:45] We heard that when he and Monsignor Dionne went to Rome, their parity for the Vatican Council, that Monsignor Dionne pointed something out in the physics, and De Koninck said, "oh boy, how could I miss that all these years teaching it for thirty years?" You know. I'm reading, re-reading the the prima pars now, and I said, gee whiz! Did I really see that the last time? Am I just reviewing what I already know, or am I seeing something I didn't see?

[47:23] But you know, as my teacher Kasurik said, you know, compared Aristotle got the brain of an angleworm, right? And these guys, wise men, they say more in a what few words, huh? We dummies, there we say not very much in a lot of words, huh? Amazing things, huh?

[47:45] So what's the first distinction? Is it being an act and being an ability? I mean, if you if you get that by dividing, let's say, substance into matter and form, things like that, right? I mean, know things in a confused way before we know them distinctly, maybe, You know? puzzling, right? Huh? But then there's another thing that comes up, you know. I'm kind of amazed with these guys, Plato and Aristotle.

[48:26] One of my teachers was Albert the Great, and he said, "To be a complete philosopher, you gotta know Plato and Aristotle." And Thomas says Plato and Aristotle are the chief philosophers, the philosophi principales you know, the chief ones.

[48:43] And both Plato and Aristotle said that there's the same knowledge of what? Yeah. What's the opposite of being? Yeah. Yeah. Yeah. And that's one main way of distinguishing things, right? Is by opposites, right? He's going to distinguish discrete and continuous quantity by what kind of opposition. And did we share a common boundary or anything Yeah You're going to say that in a continuous quantity, the parts meet at a common boundary.

[49:18] Parts of a line meet at a what? Point. And like in a circle, if you divide into two semicircles, right? They meet at a what? Line. The parts of a body at a surface, right? And the past and the future meet at the now, and so on.

[49:37] Why discrete quantity is one that what? They don't share a common boundary Yeah. Yeah, it's opposition of contradiction, right? Yeah, yeah. Parts have a common boundary. Parts do not have a common boundary. So the number seven does the two and the five meet, or the three and the four meet? No. He did that the beginning of the category. What's set up or not set up? Yeah. Yeah.

[50:07] So being what's the contradiction of being non-being, right? That is the word. Yeah. Yeah. That's why why Shakespeare says it right, huh? To be or not to be, right? But when Aristotle takes up, what is the first statement, right? Something cannot both be and not be at the same time in the same way, right? It's in terms of being and non-being, right? Huh? Does that distinction come before the distinction of, of being?

[50:34] You know, isn't the distinction between being and non-being before the distinction of, the genera of being? Seems like yes, so. That's why the principle contradiction, right? Even God can't.

[50:52] He can't make something that's contradictory, can he? Can God make the? When I was a little boy, you know, used to be the, the, you know, Catholics would say God is all powerful, right, and then the, the.

[51:07] Enemies would say, you know, well, can God make a stone so big He couldn't lift it? You know, and then you seem to be caught, right? Huh? He said yes or no, right? Huh? You say yes, then something can't do. He can't. That's no. You say no, then something can't do. He can't. Just no.

[51:26] You know how to answer that, I assume? It's contradiction. Can God make a square circle? No, there's no such thing. He wouldn't be making anything.

[51:43] Can God make? Can God make nothing? Nothing is impossible for God. Or the distinction between something and what? Nothing, right? And since corresponds almost to the distinction of being, being and non-being, right? Huh. And you can see that these are the ten genera of what. The most general kinds of things, right? That can be, right? Yeah.

[52:13] So, no wonder Boethius, you know, he's really impressed with Aristotle, right? Now, see these ten things there. This chapter is divided into two parts. In the first part, Aristotle distinguishes the species of quantity, and then separates quantities by happening or per accidens, right? From those that are quantities as such, right?

[52:50] Or quantities per se, which are in fact the species of quantity. In the second part, he gives three what? Properties of what? Quantity, right?

[53:05] Aristotle distinguishes the species of quantity in two ways. He does so in both by looking at their parts, right? And seeing something they have or do not have, right? Either parts have a common boundary. Or they do not have a common boundary, right? Either parts have a what position with respect, right, to each other, or not.

[53:34] He then unfolds each of these ways. Okay. Now I raise a little question here. The understanding of quantity in its species is properly done by looking at its parts. Why is that so?

[53:51] For every quantity consists in some multiplication of what parts. Now you don't want to take my word for that, right? So let's see what Thomas says here, right? And this is from my favorite book, the Summa Contra Gentiles. Every quantity consists in some multiplication of what parts. And an account of this number is the first of quantities. It doesn't unfold that fully yet, does he huh

[54:29] Where plurality Right, works no difference. Neither is there anything right that follows some difference, huh? Makes sense right there doesn't? it There's just something that follows quantity. That makes a difference. Does that make sense to you that every quantity consists in a certain multiplication of parts? Seems every quantity would be composed of parts. Yeah, yeah, yeah, made up of parts.

[55:25] You can have parts in every quantity. Now, in the Greek, here Aristotle uses what—not the abstract word "quantity," right—but the word what? How much or how many Yeah, posos, right? How much? How many, right? And that seems to tie up with parts, doesn't it? How much? Yeah, yeah. But what else besides parts does it touch upon? The words "how much," "how many." They're more concrete, more proportioned to us than the word "quantity," right?

[55:59] What is it? How much? Well, we'll meet this later on. in some texts here that Aristotle is distinguishing these species of quantities by their measure, right? What measures them, right? Doesn't "how much" and "how many" imply not just a multiplicity of parts, but what? Some kind of measure. Yeah, Yeah, Yeah. I mean, if I said to you, "How many chairs are in this room?" There's a

[56:36] plurality of chairs. Would I consider my question been answered, right? Got to measure it in some ways, right? Yeah, you got to count these chairs, right? Okay, count them by one. How many times one is repeated, right? Okay. Got my little ruler and measure this. How big this this table is, right? Huh? How big is this table, right?

[57:09] My wife asked me, "How big is the table you sit at?" I can't. I can't stretch my arms till the end of it. I mentioned how my my first grade teacher there, Roman Caserik, there, you know, kind of beat into my mind the idea that. Aristotle is using the concrete terms, right? He doesn't use the word relation. He uses the words towards something, right? huh Pros ti right?

[57:42] Uh Albert in his commentary on this calls it, or paraphrase of this calls it ad aliquid right? huh The Gospels say what? Pros ton theon yeah, pros towards, huh? And for quantity and quality, he uses things like how it is, right? Either how much it is or how many.

[58:08] Now I point out here, moreover, the first sense of whole and part is is in what? Quantity, huh? First sense of composed whole. So it is natural to distinguish the kinds of quantity by their parts, huh?

[58:28] In the fifth book of wisdom, Aristotle distinguishes quantity in general from other wholes by the parts into which it can be divided. It is divided into parts that are in it, somewhat in act, not fully in act, because they're not? divided, huh? And each of which is apt to be something one and this something, right?

[58:55] Now if compare that to the other kind of whole, like a universal whole, right? When I divide animal into dog and cat and horse and elephant, are they all actually inside animal? No That's your antecedent or whatever Yeah, yeah. They're an animal in what ability, as you would say? Yeah. An animal can be a dog or a cat or a horse, we could say, right? But is it any of these actually?

[59:35] The genus? Color can be red or white or blue or yellow or green, but are these all in color in general? Are the pieces of a pie, right? Are they already in some way actually in the pie?

[1:00:05] Who gets to it first? See one thing they do to a poor guy in his first year at West Point, right? He's sitting at the table with upper classmen, right, and he's got a you know there's a pie there for dessert, and he's got to cut the pie into even pieces, right? Well, if it's dividing into four pieces, it's not too hard to do it, right? Well, if you got to divide into five pieces evenly, we're going to eat the whole pie.

[1:00:29] We don't need it. Need for the health. And how do you divide a pie into five pieces? And the other guy just, you know, cut the pie. Yeah, I mean, you don't do right you know, they're looking for anything they can do to you, you know. I told you my my son followed his first inspection of course he knew he had his hair cut short and he had the the the barber do it, you know.

[1:00:53] But the guy looked at the hair and he said, "What are you, a hippie or something?" He wasn't close enough for them, you know. Plus, I never suffered in my life, you know. you get some guys at west point you know, were kind of amused by this uh this uh you know way of finding something wrong with you, no matter what. when I was in the military academy, it wasn't like West Point, but, but you know, shined my shoes right before inspection, right?

[1:01:28] and he looks down, he says, "didn't like my shoes right. How many times you sh- you shined them? I said, three times, sir? Try a dozen." if you really know you could find funny, you know. but most of the time you're kind of you know so scared, you know.

[1:02:06] but you know, is the universal whole defined by its parts? So what was the definition of genus? Yeah, differing in species, right? Simplifying what it is, you know what it is. in potency, right? Yeah. But in the case of the mathematical one, it's they're actually in there, right? In seven, aren't there 7 1s and actually 7 1s in 7? And 5, there's five ones, and so on.

[1:02:51] Remember the orders of of the word in right. The first meaning of in was in place, huh? And the second one was part and whole, right? And then the third was genus in what? In species, right? Huh? And those were all where the thing was actually in it, right? And then the fourth sense was what species in genus. That's ability, and then the fifth one was what

[1:03:25] form in matter, right? Okay, originally it's in matter and ability, right? And it's like species in genus, right? So genus is like matter. So sometimes you get into natural philosophy. They'll say, "Well, the genus in natural philosophy has got to be the same matter, right?"

[1:03:48] So if the heavenly bodies, don't have the same matter as bodies down here, they wouldn't be in the same genus. It's based upon it, right? Species is kind of named from form in in in uh Greek. huh? Okay.