Logic (2016)
14. Divisions of Five, the One Convertible with Being, and the Species of Quantity
Class of 2017-01-05
https://berquistcourse.com/course/philosophy/2-logic-2016/014-divisions-of-five-the-one-convertible-with-being-and-the/

[0:00] Spirit. Amen. God, our enlightenment, guardian angels strengthen the lights of our minds, or in the images, and arouse us to consider more correctly. Saint Thomas Aquinas, angelic doctor. Pray for us. Help us to understand knowledge you have written. Father, Son, Holy Spirit. Amen.

[0:25] Was being a Thomas there in the prima pars that there were vegetarians there before the fall. Yeah, yeah. I got problems. I had a problem with our Lord about his his fish diet, you know, and now I got to have a problem with the Lord about about the vegetarians before the fall.

[0:47] Yeah, I know. One of the Lebanese told me the reason why our Lord wanted fish on Fridays and stuff was because his friends were fishermen, so he wanted good business.

[1:00] Typical Lebanese. Looking after business, anything of business. Aquinas 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.

[1:19] So what's my number? Here's this good Pythagorean question. What's my number? Well, I've always found that had attractions the number of five. I know whether it's got'cause I have five letters in my name, Duane, and maybe that's my guess and thing. Or I know it had five fingers or something like that. Maybe it's the way the way five is on your way, right? It is kind of you know that's no rather than you know that four you know or three you know and so on and so on.

[1:52] 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, yeah, yeah. Now, where is the first distinction of five that we meet in in logic?

[2:15] 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 of nature that it doesn't, but okay. So that's interesting, right? Now, where in the chapter? Quantity here, right? Where does the number five come in? Distinction.

[2:46] Does he distinguish five species? of quantity? What? Does he distinguish five species of quantity? Well, more than that, but continuous quantity distinguishes into five, right? It distinguishes you know quantity into what discrete and continuous. And the they're both distinguished by the way their parts are right. 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 number and and speech, right?

[3:22] Okay. They're kind of similar, you know, huh? And I know Hamlet, you know, when he says I'm sick at these numbers. He's talking about this kind of a poetry where he's trying to express himself, right? And so the similarity between numbers and what this meter that you have, huh? Because they don't meet the parts at a common boundary. But then the continuous quantity, huh? He divides it into five, right?

[3:52] And there's the 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 predicament you have. How many senses does he distinguish of of before? Five, right? Yeah. But it's not doesn't divide into three and two, right?

[4:26] There are four main senses there, right? In order, 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 the thumb as opposed to the other four, right? Okay. Um. Now, when you get into the study of the soul, right?

[4:54] 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 could call it a powerful hole, right? But what's the distinction of genera of powers in the soul? Do you know that? You read that before. Vegetative. That's one group, yeah.

[5:19] Sense powers, yeah. Intellect, will, and um. Oh, then the sense appetites. He he um. For the appetites, he does the sense appetites and will. Yeah. So he first divides it into the appetitive powers, right? The desiring powers, right? And he subdivides those into the sense desiring powers and the intellectual one, which is the will, right? And then you have the what?

[5:51] 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 they're a certain likeness to that, right? So baptism is like, you know, being reproduced, right? And or being produced, and and confirmation is growth, and Eucharist is is nourishment, right? Kind of interesting comparison he makes, um, it kind of does this in a sensible way for us, who are animals, right?

[6:27] Two-legged animals, Aristotle calls us in the Book of Wisdom, but you say two-legged animals with with reason, right? Yeah. So you have the vegetative powers, right? That's one group, they'll say, in the plants, and then you have the sense powers, right? Which later on they divide into the exterior senses, which again you meet what five external senses, right? Now they get the five again, right? You can divide it maybe into three and two, maybe you know, but anyway, we'll set the go for the one, and then you have the inward senses, right?

[7:04] Okay, the common sense, imagination, memory, and so on, and then you have the intellectual powers, right? And you have the appetitive powers, which are subdivided, as we said, and you have the locomotion, right?

[7:22] So Aristotle would distinguish sometimes three three souls, right? The vegetative soul, the animal soul, and the human soul, right? Then he'll distinguish four grades of life because of the animals, some have locomotion in one place, other and some don't, and they kind of resemble plants in a way, right? The oysters and that sort of stuff, right? And and then, but there are five genera of powers, right?

[7:50] Now you go to ethics, right? What's the famous division of five in ethics? The virtues of reason? Yeah, the virtues of reason, right? And Aristotle divides it into five, right? 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?

[8:26] So you have the two, the practical reason, huh? These are genera, right? They are, art and foresight, and then you have three he distinguishes in the what?

[8:38] In the looking reason, yeah. But natural understanding and wisdom are you know lowest species, right? In a different, in the sense, it's 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 him into the foresight of the individual man, and the foresight of the father, and the foresight of the King writer.

[9:06] 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 arguments does he give? Five. There he goes again. There he goes again, right? Seven, five. Yeah. And he takes up the substance of God. How does he divide that? Five attributes. Yeah, yeah, yeah, yeah. Now in both Sumas, you know, he will always what give together the simplicity of God and the perfection of God, right?

[9:44] But in that order, simplicity first. And then he points 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. Three days of eight hours, or two days of twelve hours. You know, that's pretty hard. Yeah, I've done, I've done both. You know, but two days at twelve is too much for me.

[10:13] Even though I was an old man, it was too much. I had a professor did it in one day. He was really strange fellow. And the

[10:33] photographic memory guy. That was a tough language. I had to look at the grammar book twice. He said. What language is that? He taught my brother Marcus Dante in Italian, right? He read the rhetoric of Aristotle in Greek with me. He did Japanese with somebody else. He's still alive? No, I think he's passed on. Passed on Wow, Good guy, good good guy. I actually, agree with Gasset's definition of a poet as a man with his brains kicked out.

[11:11] He's an unusual, unusual guy, you know. People from the some some seminaries, you know, Saint Paul Seminary is not too far away from the college, and they work to watch to hear his class. You know, this guy's great books class. You know, great books of literature.

[11:32] But my brother did did Chaucer in Middle English with them too. You know, yeah, the original. Yeah, he was very good. He wanted me to to do good in German, but I I didn't fight it. He's I was doing Japanese. Well, yeah, he was doing Arabic with some guy, you know. And Japanese haiku poetry, whatever it is, you know. and things. What language was it? that he had to look at the grammar twice.

[11:57] Do you remember? I don't know what it was. Maybe Chinese or something. Yeah, yeah, yeah. He was a good guy, in many ways, though.

[12:13] Okay. Now, at the bottom of this page, it says this distinction by measure is seen more in the species of discrete and continuous quantity than in the distinction between the discrete and the what continuous? huh? Okay, let's go on to exemplify that. huh? Can we better stop now. Okay. Perfect in that way, perfect in the simple way. So he always takes up the simplicity of God before his what perfection, to which is attached consideration of his being good, right?

[12:52] Okay. And very attached to the Summa Contra Gentiles, right? When Thomas takes up the goodness of God, how many chapters does he have? Five, right? And the first chapter shows that God is what. Second one that he's what. Goodness itself. Yeah. The third one.

[13:15] Yeah, nothing bad. Goodness itself, right? And then. Good of every good. Yeah, which is a beautiful phrase from Augustine, you know, but beautiful thing there, right? He doesn't have that in the Summa Theologiae. Sad, but yeah, yeah, yes. And then the Summum Bonum, right? The highest good, right? So beautiful, right?

[13:38] But then he takes up the infinity of God, right, and the unity of God after those two simplicity and perfection, right? But the wonder is what is God is unchanging, right? Because in the Summa Contra Gentiles, that's the first thing he takes up. It's not in Summa Theologiae till the fourth thing, right? Kind of interesting, right? You know, but the other things the order is kind of pretty similar.

[14:09] So you have five arguments for existence of God, right? And you have five what? Of goodness. You have five, yeah, but and you have five attributes of his what substance, right?

[14:25] 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. Fourth and five reason. Well, I don't know. See, if there's really a number that explains this, you know, but 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 and the, you know.

[14:55] There's five books of Moses too. Yeah, you got it. You got it. Yeah. I mean, there are a lot of divisions of four, two, and three, but but it's interesting to see this a little bit. So we left off here somewhere in the discussion of quantity, huh?

[15:18] Get your law. Yeah. Okay. Page six. Okay. These are kind of subtle things here, you know. Maybe expose a first year logician to, you know, but you can see these things just go on.

[15:53] So what does he say there? Plurality, sed 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. Correct. And so when he gets into the the middle books, you might say, of wisdom, are the books on being, which are most of them, and then the book ten there, which is on what?

[16:28] One. Interesting. I'm assume I think the 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 and before it's sorry into the Trinity. He wants to emphasize it as one God. Have that in mind, you know.

[16:55] But interesting, right? Huh? That being in one there the subject of wisdom, huh? And the connection here between substance and what? Quantity, right? Okay. 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 the two, right?

[17:26] And you know, like Descartes was a whipping boy there for my doctor. He says, but but Descartes should all identify as the substance of things, but they're 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 if you grew, right? In fact, that was your substance, right? Huh? So. But every time I see these grandchildren, so I don't see them for a number of months, you know, it's no wonder that one is shooting up, you know.

[17:57] But it's been the same little boy, the same little girl, right? You know that that that your size is not your what? Substance, huh? You ever see a little kid say, "I want to grow up, you know, don't want to get don't want any bigger." Sometimes you find little kids saying, "I think I'm gonna say it one time, like something like that." And but the size, your size is not your substance, huh?

[18:23] But it shows the proximity of the two, right? Being and and quantity, right? And Plato trying to make the Pythagoreans making numbers, right? The substances of things, right? When Aristotle gets into the you know consideration of substance there in the.

[18:47] Seventh and eighth books, right? Huh? But in the in the eighth book, um, he compares the nature of things to numbers, right? As if there's some links between them, right? As if you know, a stone is one, and that plant is two, and the dog or cat is three, and you and I are four, because you got reason, right? So you you add to body life, and you get a plant, and you add that sensation, you get an animal, and you add reason, and you get a man, right?

[19:20] So it's it's a little bit like what numbers, right? And Thomas will often come back and and do that, right? And you know, he'll say, you know, if if if ten knew itself, right, it would know what you could you know partake of ten, nine, and eight, and seven, all the way down, right? And this is the way the way God knows all things by knowing Himself, right?

[19:44] You can partake this much of me, and 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 of course, one of the objections is saying, "Well, we're unequal because some of us have sinned, and some of us, you know, nature is sometimes you know makes us defective or something, you know, because something's wrong with you and your generation, so on."

[20:14] 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? How would God want to make us unequal, right? And his beautiful phrase, huh? For the pulchritudo, he says, ordinis, huh? For the beauty of what Order? order, right? It's like order seems to require inequality, huh?

[20:49] And Thomas always quoting there. It's in I guess Epistle to the Romans, chapter thirteen, the beginning of it. Quae a Deo sunt ordinata sunt. He's always quoting that, huh? And my old teacher Kasurik used to say, you know, God hates equality. Well, Aristotle emphasizes that thing about the wise man, right? That he orders things, right? That's well, God is not just wise; He's wisdom itself, right? So He really wants to order things, huh?

[21:24] So I mentioned, you know, what my teacher there, Kasurik, used to say. He was the wisest man at the College of Saint Thomas, right? Who's wiser than anybody else there? By far. He says, compared to Aristotle, he says, I got the brain of an angleworm. And Kasurik had. Great respect for Fr. Baumgartner, right? And he taught the Saint Paul Seminary, right? Which is kind of across the street, almost in the college, right?

[21:59] And sometimes I came in with a hard question and Kasurik wasn't too sure what to say to me. Can I call Baumgartner over there at the Saint Paul Seminary, see what Baumgartner thought, right? And then there's other questions that Kasurik couldn't answer. He says, when De Koninck's coming down, you ask him, right? So De Koninck stayed at his house there when he was giving all these lectures in the Twin Cities.

[22:22] There, man, six or seven lectures, I don't know, but maybe 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. Sometimes he goes to Arkansas. And so I put all these questions that Kasurik was stumped with, and De Koninck's explained them. Very clearly, and so on. You know, so here you got this order here, right?

[22:45] of Kasurik and De Koninck and Aristotle, right, and so on, and this pulchritude of order, right? I mentioned how, you know, I was reading in the thirteenth 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? Taxis huh You see, you're struck by that, huh?

[23:11] pulchritude of order, right? And you see it in the angels, right? now, Because no two angels are what equal. And the angel just right above you is the one who enlightens you. as the things are pressed down, right?

[23:30] Monsignor Dionne sometimes compare the order of teachers there, you know, with that, huh? You know, Even a man like Thomas, so you realize, you know, he's always pulling out something from Augustine or something from, you know, Basil or Gregory or something, you know, and you know, St. Anselm, you know, he gets a lot of minds behind him, right? Huh? He does the same when he treats of.

[23:56] We just finished doing some of it. Treats of the difference of states, orders, and offices in the church. The offices are for the needs of the church. The difference of states for the perfection of the church, but orders, he says, is for the beauty of the church. Yeah, yeah. Well, don't they call that one sacrament holy orders? Isn't that the one that's when I learned at least in grade school?

[24:19] Because he's referring to different orders. Yeah, You know. Yeah, Deacon. Yeah, it says they compare it to the orders of the angels too, you know. I mean, Dionysius does, you know. He quotes from a psalm, and I forget exactly where it is, but to speak of God ordering things for beauty's sake, and I think Mhm. it's from somewhere in the Old Testament, it says something like he shall be known in the in the order, or something like there's some order by which God is known.

[24:46] That's the beauty of God, something like that. I can see Tom's getting into a lot. of trouble with the with the feminists nowadays. We actually goes to so far as to say, you know, that um, that the likeness there between Adam and God, right, huh? Because he's a source of the whole human race, huh? Even even Eve, right? He's God, he says, is the beginning, the end of all things, right?

[25:10] 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 of Eve, right? Well, you know how he's the beginning, huh? Because you know, he came from. But she was made as this kind of helper, right? Huh? So you know, but I first saw him. say the beginning, This is going too far, but even for a guy like me.

[25:40] " Yeah, man. is, uh, woman is for the sake of man. Yeah, yeah. but I hate to hit heavily some of this, you know. I say. oh, this is definitely terrible, you know. And and you're you're putting women, you know, In her place. Yeah, Yeah. It's kind of funny. on on, uh, I was watching the educational TV there the other night, and uh, they had uh, Tannhauser on by by Wagner's opera.

[26:03] Do you know that opera, though? Huh? Tannhäuser by Wagner. Yeah. I heard of it, but yeah, yeah, yeah. We didn't know it, but it was kind of interesting, you know. Kind of listened 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.

[26:25] huh? You saw Tolkien is influenced by the Teutonic 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?

[26:48] He goes around, and he was saying, you know, the three greatest opera writers are Mozart and Wagner and Verdi now. 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, "This sounds like wrong heresy, right?" That sounds like fighting words.

[27:16] Yeah, yeah, yeah, yeah. So I 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, it's kind of interesting. what he said, you know in praise of some of the Mozart operas, you know, and how he wrote all these different kinds of operas, you know, the opera buffa, you know, serious opera, and then German operas and so on, and they all excelled what they did, you know.

[27:53] And he had one piece we used talking about how Mozart done the Figaro right? and he realized it's so superior to Wagner and so on.

[28:03] I saw this quote from Wagner. He says Mozart is above all the masters in all the arts and all the ages. He recognized that's it. That's that's that's ultimate in judgment, you know.

[28:24] Okay. 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? Now. But this multitude that's absolute is, as it were, the genus of number, right?

[28:51] Quasi genus, right? Not genus in the strict, strictest sense, right? The genus is something indivisible and so on. Because the number is nothing other than a plurality or a multitude measurable by what one.

[29:14] 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 how truth and good, which is more universal.

[29:45] Truth or good. This comes up in the discussion of reason and the will, right? Because obviously the will is the good, what? Truth. Well, he says they're convertible, right? So that for 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, you know, the soul. There's truth about all kinds of things, right? Okay.

[30:17] But truth is absolutely universal, right? It's as universal as what being in that sense. But then, as far as the will is concerned, truth is a particular good, yeah, yeah. So reason can know what the will is because it can know what the good is. That comes under one part of knowing the truth. It knows the truth about the good, and the will can will that reason what learn, right?

[30:50] Can will to apply your mind to learning something, right? Because you recognize truth is a good, very great good, right? But it's because it's convertible, right? That's true about being and this one that is convertible with being, right? Okay.

[31:10] So therefore, the one, according as it is 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.

[31:35] And likewise, plurality or multitude, according as it signifies divided beings, is not determined to some what genus, huh? I used to call these things what, like, being and one. This one that's convertible with being. They call them what? Yeah, which is kind of crazy things. I call them sort of alls. I like the term transcendental. that's a little bit too spooky for me.

[32:09] But it means, it transcends any one what genus, right? Okay. Of being and every one, right? But being is not what one genus set of substance, quantity, quality, and so on. Why not?

[32:29] Because genuses are predicated univocally. Yeah, a genus is predicated univocally, right? But these are not said univocally of these ten, right? Okay. But according as it signifies something measured, is determined to a genus of quantity, to the genus of quantity, one of whose species is what? Is number, right? Okay. And you even wanted to make another step in there and say discrete, right? And

[33:09] therefore it is said that number is a plurality measured by one, and the plurality is quasi. You got to be careful about that, right? Why? I

[33:22] don't understand why is it quasi genus and not some genus? No, because it's not said univocally of all these things, right? So when you get into trinity, right? You know 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 is more than one, you know. You see, so what kind of a multitude is this, right?

[33:49] It's not one measured by one, right? Not in the genus of quantity. 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, the Holy Spirit is more than just the Father and the Son. No, but you might be tempted to say that, right? You know,

[34:15] by 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?

[34:30] That's what I've seen and said before. It's not. We shouldn't think of the Trinity as one plus one plus one, equals three. one times one times one equals one. Yeah. Yeah. Yeah. Because then you'd be thinking they're really three gods, right? Or three parts of God or something, right?

[34:50] I was thinking about this this attribute of God. You know, the the God is what? Simple meaning not composed, right? Huh? That's almost like saying that God has no what? Parts. Yeah. Yeah. Because anything is composed is put together, and you can see it has parts in some way, right? And what Thomas does in in the Summa Theologiae, which is for beginners, right? Huh? He has eight articles, right, to show the simplicity of God.

[35:21] What does he do, right? Eliminates all kinds of composition. Yeah, in the first six articles, he distinguishes, or 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 six. He's done already. That's an inductive argument, right?

[35:49] And then he gives syllogistic arguments. You know, that nothing is what. Yeah, yeah. I mean, he argues and say that in every composition, one part is either to the other part as act is to ability, or both parts are to the whole as ability is to act. But God is pure act. There's no passive ability, right? Therefore, the can't be any, you know. So, so there can be a syllogistic argument, right?

[36:18] 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? Then he's not composed of what matter and form, and that's different than a body, right?

[36:41] 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 wood and shape, something like matter and form, right? Okay. Okay. But also you can say, well, its parts are, you know, the seat and the legs and the arms and so on, right? Okay. What's the third sense?

[37:07] Huh? He gives. Okay. Well, you see, what what am I? What am I? Well, if you want to know, I'm a two-footed animal that has reason, right? Okay.

[37:28] 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? Of two-footed animal with reason and born of a Swedish father and an Irish mother.

[38:09] You know. I told you how my friend Warren Murray says. You know, Duane says, "If you were all Swedish, wouldn't be as good a philosopher as you are. If you were all Irish, wouldn't be as good a philosopher as you are. " I don't think you'd be philosopher at all.

[38:28] So he tried he explains it. to. 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? It's an odd number. Um.

[38:47] Yeah, so there's kind of composition there, right? That's kind of 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 of the same kind, right? So there isn't a distinction between that. uh you can be distinguished from your brothers by the same mother and father Yeah, yeah, yeah.

[39:09] Yeah, as I was saying to Warren, I said, you know, I was thinking what he says there, and I said, my brother Mark was more Swedish than I am, and my brother Richard was more Irish than I am, right? See, so I'm between those two guys, right? I can kind of

[39:34] see that right now. You know, my brother Richard was was an actor and so on, right, and that sort of thing, right? Backed in many plays and so on, musicals and so on. Irishman, yeah, yeah, yeah, yeah.

[39:48] But Mark had these strange interests, like in Sibelius and so on. You know, the Swedish, that's Finnish, I mean. It's like the Swedes, you know, Scandinavians. So a little more, and Richard was outgoing, and then Mark was, you know, Mark was. So I'm getting kind of, you know, okay. And then you have what? What other kind of thing comes after that?

[40:19] Well, that of substance and being, right? Because even the angel, you had that, right? See, in in you and I, we've got the composition of matter and form, but also the composition of our substance with our being or existence, right? In the angel, you've got the composition of substance and being, right? But not of matter and form, right? So I'm really put together, right? I'm the same in a nice way, much more composition than in that angel.

[40:48] Somebody might see your piece of work. Yeah, yeah, yeah, yeah. But but also it's composition between you know my common nature, you know, that I share with other men, and what's odd about me or peculiar about me, right? You know, okay. And then comes what the composition of genus and difference. He brings in that, right? So God's not in any genus, right? And he when he calls them, he takes up God being infinite later on, right?

[41:18] Because he's not limited to any genus, right? I told you how deconic, like the English word predicament, right, which comes from the word for predicament, right? But when you're in a predicament, you know, and your life is hard to get out of it, right? No way to go, get out of it, right? Well, that's where categories are, right? Or predicament is, you know, a quantity can't be a quality, and the quality can't be a relation, you know, and none of these can be a substance, you know.

[41:49] If you're stuck in one genus, you're you're gonna stay there. You can't get a. It's like a prison, right? I mean, in a sense. But God is not in any what genus, right?

[42:03] And He has the perfection of all genera, right now, but in a simple way. He's remarkable. He's He's very unusual, you know. Very unusual. And then the fifth kind of composition is what? I mean, this. Yeah, the sixth one, I mean. Yeah.

[42:26] I'm a white man, right? I'm a philosophical man. right? Accidental. Yeah, you yeah, substance and accident, right? Yeah. See, we don't have that composition of God either. Okay. So you want to say, "geous did, Thomas?" Exhaust all the kinds of composition and creatures, right? How could he be so 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.

[43:14] You know, these these animals that don't have locomotion one place to another, right? And they're kind of kind of sick thing, you know. So it's significant that he says "quasi," right?

[43:38] Thomas doesn't multiply words unnecessarily, right? And he does not say that it be simpliciter a genus, right? Because just as being is not a genus, right, properly speaking, so neither is the one that is convertible with being,

[44:07] 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? But now if you inflict that upon a beginner in logic, right? But make you stop and think, right?

[44:40] Thus, therefore, taking the one that is the beginning of number and has the notion of a what measure, right? And the number which is a species of quantity and is a multitude measured by one, right, are opposed to one and 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?

[45:15] Which the one is said relatively because the other is referred to it, and thus they oppose the one number in so far 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. Okay.

[45:37] So put that in your head and shoot huh Father Bodai used to always talk about mental indigestion. He had some very concrete when he talked about mental constipations.

[45:59] But I mean, he's very concrete. Now the second division of quantity is into those having parts that have a position, right, or placing toward each other, and those which do not have such a placing or position. In some quantities, the parts are laid out toward each other, and in other quantities, they are what? Not Aristotle gave this division, right? First gave the the main one is discrete and continuous, right?

[46:35] Whether the parts meet a common boundary or do not, right? But then he talked about another division, right? Into one whose parts have a position with respect to each other, right, and one that but does not. Okay.

[46:58] 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?

[47:10] 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?

[47:29] 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?

[47:47] Well, it's called the what? A number of the before and after in motion, right? See, so you take the motion of the sun around the earth is a most regular one we kind of know, right, and daylight. And every time it comes over the border, it will You know I'm, I'm probably saying Crusoe or whatever it is, and and I'll mark down you know a day, right?

[48:13] So I'm numbering the before and after in the motion of the sun, yeah. Or even do hours, right? In the position of the sun, before and after. But that's kind of strange. It's the number of the before and after. In what motion, right? So is it a discrete quantity because it's a number? I mean, number is is the first species of what discrete quantity, isn't it? See, so time is a number.

[48:46] Number is a discrete quantity. Therefore, time, right? You're numbering something continuous. Yeah, yeah, yeah. See, so I mean, is 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.

[49:20] Doesn't have parts, right? That exist to each other, like the parts of a line do, right? Or the parts of a place do, right? Okay. We take the inner wall of this room. There, this containing us here, right? Let's say this part and this part. They're laid out in relation to each other, right? See, but they all exist together, right? And the parts of a line, the parts of a spot, surface of a body, and so on, right?

[49:49] But parts of time and speech and number, right? Don't have. You know, they distinguish between a point even and a one, right? Because the point is much closer to the one than anything else. But the point has what? Position. Yeah, yeah. And the one has no what? Position.

[50:20] 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 can't always do this, but sometimes, right? But can an even number measure an odd number?

[50:43] Oh yes, we can. Thanks, easy. You see, if an even numbered, 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?

[51:07] So no, no even number, right? Huh? Can measure a what odd number? But an odd number can measure sometimes, not always, but sometimes an even number, right?

[51:25] So no even number except two could be prime, right? The first number, two. But every other even number is measured at least by two, right? And some are measured by odd numbers too. But odd number can measure odd numbers sometimes, like three measures nine, right? But sometimes you have an odd number that no other number can measure, like five, which I'm attached to, or seven. So, I'm going to attach it to seven too, right?

[51:57] It's a lover of wisdom, right? There's what seven kinds of philosophy. Seven kinds of philosophy. Yeah, three kinds of looking philosophy: natural philosophy, mathematics, and wisdom. Three kinds of doing philosophy: practical philosophy, ethics, domestics, political, 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 than parts, right? Because parts is too much. Makes them too. Too much one,

[52:46] three different kinds of philosophy, okay. Seven kinds, huh? Seven gifts of the Holy Spirit, huh? Seven sacraments, seven teachings of our Father, yeah. So I feel

[53:09] like numbers that you keep on looking for, you know, all the distinctions of five or seven, like we're doing here, you know. So time, although a continuous quantity, because time is divisible, what? Forever, right? Okay. That goes back because it's a number of motion, which is divisible, what? Forever, right? Okay. And you know how Aristotle does it sometimes, you know, he'll combine, you know, showing that the motion is divisible forever with what?

[53:46] Distance is divisible forever, right? By the fact that one of you guys runs faster than another guy, right? So the distance that the faster guy runs, right?

[54:01] 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 in less time, that guy would have covered even a lesser distance. So they're divisible forever, right? Just by using those two things, right?

[54:27] So because time is a number of of the before and after in motion, it's divisible, what? Forever, right? That's where you get these paradoxes of Zeno, right? You know, how can you how can you get out the room? You know, you got to go half of the way before you can go the whole way, and you got to go half of the half of the way, and so on, right?

[54:47] You know, you're never going to 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. 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?

[55:28] This is connected with the reason Thomas gives in his commentary on the Posterior Analytics why no difference is what convertible. You know, when I was first starting out in logic, huh, you're always giving as an example of difference rational, right? And man is a rational animal. That was you know, animal is a genus and rational. But how does Porphyry define difference?

[55:55] See, it's a name said 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?

[56:18] 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, a definition is composed of a genus and differences, or genus and difference.

[56:39] Well, for the most part, right? When they give the definition, they'll say, you know, that man is a what? Animal with reason. Yeah, but immortal. Mortal. Animal reason, and then these, you know, species. These what they call these, Socrates goes there, you know.

[57:03] It's it's a a rational immortal animal, right? So neither rational nor immortal in that example, right, is convertible. See, you know, it's better to give a definition. I mean, example of differences. You see the definition of square, right? My master Euclid defined square as a equilateral and right-angled quadrilateral. Well, is equilateral convertible with square? No, because the square and the rhombus are both what? Equilateral. Is it convertible with right-angled?

[57:52] No, because both square and oblong, right, are right-angled. But is any quadrilateral besides a square that is both equilateral and right-angled? Is it? So you need a combination of what? Differences, right? Is that more appropriate to this? See, that's the way differences really go, for the most part, anyway, right?

[58:21] Now. That means it takes you longer to go from the distinct, confused rather, to the distinct. 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, like a joker, huh?

[58:45] You know? Do you see what I mean? That's why we have now three calendars in sacristy. More distinct. We had some confusion before. No, but as I say to students, you know, I mean, suppose you want to pinpoint some target, right? Huh? We got to have the longitude, latitude, right? Huh? Can you get one point that has both this and this? It's on both lines, right? But with one line, can you really pinpoint something?

[59:25] I could have at least two, right? Minds to require that, right? That's so it's very exact, you know, distinctive point, you know, and but you got to have two lines which help you to locate this. How you find the center of a circle? Yeah, yeah. My son sent me, you know, Riley's book on killing the rising sun. You heard that book? It's a bestseller. Oh, this is I know.

[59:53] He's he's a whole bunch of bunch of killing, you know, killing Kennedy, killing this, killing Christ, even. And this is killing the rising sun, right? I guess the Japan, 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 they had the targeted real.

[1:00:17] Really, really, uh, and the things that they, well, can't have one line anyway. I was reading about the the time when they're knocking out Saddam Hussein's, you know,

[1:00:47] country there, the army, and they they had a pretty good defense system there, you know, huh? And they wanted to knock out that before they sent their regular airplanes in, right? But they had to have two sets of airplanes, you know, one coming in, you know, they were targeting the the target that was going to, you know, drop the the thing, yeah, and one was marking out the place for the other one to do it, right?

[1:01:09] You know how complicated these things are, you know. Interesting. So I'm finding all kinds of little odd facts, you know, huh? MacArthur was opposed to dropping the bomb on the Japs because he thought it was killing too many, you know, soldiers. Yeah. And David Lawrence there, who started the National, I mean, started U. S. News and World Report, you know, he was opposed to it too. And that

[1:01:42] used the old great critic. There, what is his name? The New York Times in the old days, military critic. He was opposed to it too, you know. Don't come back to haunt us, you know.

[1:01:59] Okay. So numbers sometimes divided into odd and even, and sometimes into prime and composite, right? So I like to say, what is two? Two is the even prime number. Unique distinction. You know, 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.

[1:02:40] Okay. Perhaps could also be divided into perfect and imperfect, right? What's a perfect number? No, well, it's it's no, number is equal to the sum of its parts, the numbers that measure it, right? So six is the first perfect number, right? And it's measured by what one and by two and by three, but not by four or five. And one plus two plus three equals six, right? Then the second perfect number is what twenty-eight, right?

[1:03:18] And that's measured by what one, two, four, seven, yeah, yeah. What's the third one? I forget. But it gets good. It gets pretty high math after a while, you know. Got some math chart, yeah, yeah, yeah. But they would do

[1:03:43] prime numbers. I think they were prime numbers. There were some two brothers. I think they were twins or something, yeah, right. And they were autistic, and that's how they had pleasure with each other. They proposed the next prime number. Yeah. That's all they would do all day, just thinking the next prime. I don't know how they figured it out. Yeah, yeah.

[1:04:04] I was talking this interesting thing that I was kind of just thinking about by the students there. I was talking about proportion, right? Huh? And if four numbers are proportional, then the first is to the second as the third is to the fourth. But if the first number is to the second as the third is to the fourth, the product of the first and the fourth will always equal the product of the second and the third, right?

[1:04:29] Huh? Consider even twenty-eight there, right? Huh? So if two and fourteen, right? Huh? Well, let's see. One and seven. One and seven. Well, I can't have four numbers, right? See, so if you say two and fourteen, right, make twenty-eight, right? And four and seven make twenty-eight. So they must be proportional in those numbers.

[1:05:08] So two is to four as seven is to what? Two. Yeah. Interesting. It's going to work out that way, you know. So if you take a big thing like here, you take a hundred, and say, what two numbers can equal any pair of numbers, right, that equal hundred, right, multiplied together, laid out with the lowest to the highest, we give you four numbers that are proportional. Kind of beautiful to see that, you know.

[1:05:35] But it's good for people to see that, right? Huh? Because when I was a student, I mean, a teacher, an assumption, I'd say, you know, I'd say two is to three. As four is two, and somebody say five, you know. And so, if you don't know what a proportion is with numbers, you're not going to know what a proportion is with these other things, you know. Which, you know, proportions in math should be the clearest in some sense, right?

[1:06:01] But I mean, you got to see that two is the same parts of. I mean, four is the same parts of six. The two is of three. So if you think of six as being three twos, then four is two of the three parts, right? So it's practically proportional.

[1:06:20] Okay.