Logic (2016)
3. Porphyry's Five Predicables: Difference, Species, Property and Accident
Class of 2016-10-13
https://berquistcourse.com/course/philosophy/2-logic-2016/003-porphyrys-five-predicables-difference-species-property-and/

[0:00] So the name called a genus, you could say begins to tell you what something is, right? But because it's a name said with one meaning of many things other than kind, it can't say completely what those things are. So those things other in kind of which it is said have something in addition to the genus, and this is one definition they sometimes give of the difference. The difference signifies what the species have in addition to the genus, right?

[0:36] What is a square? Well, the genus of square we saw was what quadrilateral, right? But in addition to being a quadrilateral, the square has all of its sides what equal, and in addition to being to that, it has its sides meeting at right angles, right? You see what I mean? So the difference is what the species has in addition to the genus, right? Okay. Sometimes they say the difference is what separates species under the same what genus, right?

[1:22] That's another way they they kind of define or make known the difference, right? Okay. So equilateral separates the square from the oblong, right? Right angle doesn't, right? But right angle separates it from the rhombus and the rhomboid because they have two acute angles, right? They're acute angles, right? But an obtuse angle right the square and the oblong have got all right angles, right? So the difference, right, separates it from what separates species under the same genus.

[2:02] Now I point those two things out, and Porphyry will say that. But those two descriptions of the difference, right, point to the role of difference in both defining species, right? Because you've only begun to state what the species is, the genus, right? And the difference is, like equilateral, say for square and right angled, right, will complete the definition, right? But the other description of difference is what separates the species under the same genus from each other, right?

[2:44] Points to the role of difference in dividing the genus into its what species. Okay. Now the godlike Porphyry, right, he says, "Chrysaoreus, to know what genus is, what difference is, what species is, what properties, what accident is not only useful to understand the what categories which you asked me about, right? But it's also useful to understand definition.

[3:16] And this description of difference is what the species has in addition to genus, points to its role in completing a definition which has begun with the genus, right, but not completed, right? And it's also useful, he says, for division, right? Because one of the most important divisions that are made in science is that of a genus into its what species. So quadrilaterals divided into all these species in geometry, right?

[3:47] Habits divide into virtue and vice, right? And virtue is divided into its species and so on, right? Okay. Now the word difference, right? The Greek word is dia and fora. Okay. They both have the same etymology. Carry apart.

[4:18] Carry apart. Carry apart. Pharaoh and phora very similar Greek and Latin. The word to carry and this would be a part, okay? So if you carry things apart, you separate them, right? And that agrees with what the difference does as far as what separating species under the same genus, right? It doesn't express the connection of what it's what the species has in addition to the genus that kind of follows upon that, right?

[4:58] But now the difference is also a name said with one meaning, usually of many what things other in kind, but not as many, right? Now, although it is possible, you know, they have a difference, maybe that fits only one species, right?

[5:39] Like reason, right? instead of man, right? But in the logic books, they don't use one difference for man, right? Man is defined as the mortal rational animal,

[5:53] and there are animals that are immortal that are rational too, or they thought so, right? But it's interesting the example they choose, right? Because the modern logic books they take the example of rational animal for man, and rational seems to be the only what belongs to man alone, right? But usually differences apply to more than one species, and you need a combination of differences. And so in the ancient books, right, the Platonic idea that they are immortal rational animals, right?

[6:25] You have to define man as the immortal rational animal, right? But look at the definition of square, right? An equilateral and right-angle quadrilateral, right? Equilateral is said of what square and rhombus. So it's said of many, right? Many? Means only more than one, right?

[6:49] It's said of square and rhombus, right? Right-angled is said of square and oblong. But both right-angled and equilateral is said of square alone, right? So you need a combination of differences, huh? And usually you need, huh? more than one what, difference?

[7:16] Okay. See these differences here. instead of more than one kind of thing. So it's a name said with one meaning of many things other in kind. But what does it signify?

[7:37] Not what it is, but how it is. How it is what it is. Signifying how it is what it is. Now, Latin, the we'll say it signifies quality. Quid?

[8:01] Essential how, right? Not how are you today, you know? Because that's not essential, right? Not feeling too good today. How are you today? But this is how you are. What you are, right? A quadrilateral is four sided, right? But how are those but four sides? Are they equal or unequal? Do they meet right angles or octahedrals or acute angles.

[8:30] So the name is said with one meaning of many things other than kind. that's signified. Now, it's not as many, right? As the geniuses said, right? So quadrilateral is said of more than you know. We said quadrilateral figure or something like that. said of more than you know, or yeah, than equilateral is said of, right? An equilateral is said of square and round, right? So it's said of many.

[8:58] Okay. But the more important difference here is it signifies how, but an essential how. Now, see, in Latin, they more brief. say quale with, right? Quali signifies how. Aristotle talks about quality in the categories. Qualis in Latin, poion in Greek, right? He he defines in terms of how, right? How are you today, right? It's probably everyone today. I saw a fellow maroon down there That happens when you're right on the board.

[10:27] Yeah. Stepping back. I had done it, Lord. Okay. Now, species we get the word specific in English, right? Now, interesting thing, and you find this true in both Aristotle and Porphyry.

[10:56] When Aristotle enumerates the ten categories, right? He gives substance first, right, Then quantity, then quality, right. And then relation or towards something, right? Now he takes these up one by one, right? He takes up first substance, then quantity, and we expect quality to be next. He takes up relation or towards something next, and then,

[11:34] my goodness, What has happened to the master? He's lost. Yeah. He's got distracted. Well, you know the importance of words, right? For logic, a little bit here.

[11:48] And there's a problem there, right? Because some qualities are said to be of another. See, so I'm the father of a son. I'm the son of another man, son of a father, right? And knowledge is what knowledge of the known.

[12:12] Well, is knowledge a relation? But in words, I speak the same way, right? I am the son of Reno Victor Berquist from Parkers Prairie, Minnesota. Okay. Self-deprecation isn't it

[12:35] Named after Major Reno who was admired by one of his uncles. Her brother Marcus got the name Marcus Reno Well, Reno Major Reno's first name was Marcus. So you got to look up in the in the histories of the West, you know, and you find out who Marcus Major Marcus Reno is. Okay. Can't send on some mission he escapes Custer's last stand, right? He's greatly admired by his uncle.

[13:03] Okay. But just as I am said to be the son of Reno Victor Berquist, so knowledge is said to be the knowledge of something, right? So it seems to be relative to something, right? Right. The same way love, right? Okay. But is knowledge really a relation or is it a quality of us? You think it's a quality. Yeah, yeah. So first I have to clear up this relativa secundum dici they call it in Latin, right?

[13:34] What is said to be of another from one whose whole being, whose whole nature is to be oriented towards another, right? So take take the you know the relation like half. How much is is half? No,

[13:51] is it two or is it three? You can't say absolutely what two is, but what half is. How much is a half? I'll give you half of my money. Half of my money. half of my money. How much is that, Mr Berquist How much money do you have, Mr Berquist You have money in the pocket. You got money in the pocket. Judge says, "pay half on you."

[14:17] Yeah. You see, the whole being of half is to be towards another, right? It's nothing in itself. But the whole being of knowledge is to be towards another. Now you see, Aristotle has to clear that up, and that's why he takes up towards something before, you know. But you see how he's tied to the words, right? You know, Aristotle likes to proceed from the senses, right?

[14:49] When he first enumerates the ten categories, he does in their proper order, right? Order of being, right? Because quantity, substance underlies all the categories, and quantity is before quality because some qualities are color, presuppose, surface, and so on, right? And quantity and quality come before relation because relations are based upon quantities or upon qualities, right? Okay.

[15:17] So he enumerates them: substance, quantity, quality, relation. He takes them up in substance, quantity, relation, quality. Right. There's a reason he does that, right? Now, Porphyry's proemium right? Chrysaorius, to know what genus is, what difference is, what species is, what properties and what accident is, is not only necessary to understand Aristotle's categories, but to understand definition and division and demonstration, right? Magnificent. You know, this, oh, my gosh, how important this must be, right?

[16:00] Okay. But in what order does Porphyry take them up? He takes them up in the text itself. That was the premium. Takes up genus first, then species, and then difference, and then property Wow. Is that a big mistake or is he doing something like Aristotle? Is there a reason why he takes up genus and species first?

[16:37] Species is in the definition, you might say, of genus. They got to be known together, genus and species, right? Same knowledge of relatives, right? Same knowledge of opposites. That's where you define species, right? Simply turns around the definition, right?

[16:59] What is placed under a genus, and of which the genus is said, right? Ladies and gentlemen are, been taught by the great Shakespeare to look before and after, right? Don't descend to the level of beast, huh? Before and after. Well, in what sense does difference come before species and genus, for that matter, huh? Why does genus come before difference, and difference before species, when he, in the proemium enumerates the five, right?

[18:03] Yeah, being, yeah, yeah. Can there be a square? There cannot be a quadrilateral. No. Can there be a quadrilateral without being a square? Before and being, right? Can there be an equilateral quadrilateral without there being a square? Yeah, because the rhombus is also equilateral, right? Is equilateral can be without square, but square be without equilateral? No. So in being, genus, and even difference, are before species, right?

[18:45] And genus before difference, because you can have a what quadrilateral without the equilateral, but it can't be equilateral. Now, properties, and accident, we'll see are later on, because these are outside the nature of the thing, right? Property in accident. Oh, property is connected to nature, and the accident doesn't. That's why the properties put before the accident. But the ones that refer to nature, the thing, what it is, are put first, right?

[19:16] More fundamental, right? In being. But in the order of knowing, right? Genus and species are closer than what? Difference, yeah. Order of knowing, because species is right in definition, right? You just turn around. What is placed under a genus, and which genus is said in answer to the question what is, right? Okay.

[19:49] You see that? It's very subtle, but I really admire Porphyry that he would enumerate the five in this order, right? And when he takes them up, he does species right after genus.

[20:07] It comes after right away knowledge, right? And then comes difference. And notice when he modifies difference, he gives these other two definitions. The difference is what the species has in addition to the genus. Well then, then you're defining by species and genus, aren't you? Or the difference is what separates species under the same genus. Both of those are making known, but the difference is by what? Genus and species.

[20:36] So genus and species come before difference in our knowledge, right? Of course, in defining it's gonna be different, right? In defining, you say you've got to first find the genus and then add the differences.

[20:52] See, those things subtle, right? But you've got to look before and after to understand these things, right? It's subtle. What is he doing there? But you have to admire Porphyry. Augustine has some pity for Porphyry, you know. Why didn't he become a Christian? you know,

[21:17] He had some opposition to Christianity. We have to point out this guy we all read. Nobody has a paraphrase of him. He's not a Christian. in fact, he is probably anti-Christian. Hold on to the old. We didn't know where it was. Now, this definition here could perhaps, in some way, be understood, right? Without referring to species, like you did most descriptions, but still refer back to genus, right?

[22:01] Anyway, okay. Now, property and accident, huh? These differ from the first three because the first three refer to the nature of the thing, what it is, right? In general, what it is, or specifically what it is, and how it is, what it is, right? You all refer to what it is in some sense, right?

[22:39] But the property and accident is something outside the nature, right? That's common to both, right? So, what's the difference, huh? Well, the property in some way follows upon the nature, right? It's connected to the nature, and the accident has no connection with the nature.

[23:18] So to go back, let's say to a triangle, and you say, "Well, it's a property of the triangle to have its interior angles equal to what? Two right angles, right? Well, if you know the nature of the triangle, you know some other things. You can see that follows upon being a triangle that you will have angles inside that are equal to what? Two right angles, huh? You all know the demonstration in geometry.

[23:59] now suppose you have three green triangles, right? Does green say something about the nature of a triangle? No. Does it say something connected with the nature of a triangle? No.

[24:16] So, outside of nature, but the property is connected to nature. And so, the one is not connected with the nature, right? Accident, huh? Now, going back to the despair of Father Delac. huh.

[24:51] The accident, as opposed to substance, can be a property and not an accident, right? We have to see if it's on accident, right? Accident is something exists in another, right? Okay. Just count it. That's true. Accident in this sense too, but it can be a property.

[25:22] Now, how does you how do you how does Porphyry define the property, right? Now, he gives a definition of property in the fullest sense. A property is what belongs to one species, to every member of that species, and always. Okay. So let me put down the three things there. Give myself more room here now. Okay, you want to raise off the part here

[26:13] Belongs to only one species, every member of it, and always. Now, some properties, huh? Some properties. We don't have a name for them, right? But we have we can use the speech in place of a name, right? So,

[27:05] it's a property of two, which is a species of number, right? To be half of four, and a third of six, right? Is that connected with being two? What two is? Because it's half of four? Okay. And it belongs only to two to be half a four. Anything else half of four? You say good mathematicians? huh Aspiring. It belongs only to two. Is every two half a four, or just some twos half a four?

[27:47] Okay. And is a two, you know, as its life goes on, become suddenly half a four, or is it always? there's a little bit more of that?

[27:59] It's always, huh? Okay. So those are the three things, right? That Porphyry puts in. He's defining property in the strictest sense, right? But now sometimes we pick up the word property and apply it to something else by dropping out part of the what. Yeah. Now is a property of two to be less than ten?

[28:37] Well, every two is less than ten, right? Is two sometimes less than ten? Yeah. But is two only less than ten? But now is it by chance that we call this still a property?

[28:57] No, because it has a connection with the nature, right? Connection between what two is, right? And it's less than ten. Not sometimes, but always, right? And every two whatsoever. There's some connection what a two is. It seems to me, right?

[29:23] But now is every square green? A square is always green. What's the third thing? Only squares are green. Yeah. Oh some triangles are green. So that's clearly an accident, right? Is it?

[29:53] So you could say that half a four is a property of two, right? And in some sense, less than ten is a property too, right? But not as much so, right? Now this is another way that a name becomes what equivocal by reason, right? By dropping out part of its what meaning, yeah, um,

[30:28] by generalizing in a sense, it's it's meaning, right? Okay. Now you have a beautiful example of this in Aristotle in the three books on the soul, right? Where he says that although grammatically to see and to hear is an active grammatical sense, right? What is really seeing or hearing? Is it the eye acting upon color, or as a result of the color acting upon the eye?

[31:02] Yeah, yeah. That's why you know you have to look at the sun, sun, eclipses, you know. And if you look at the light too much; you get kind of blinded, right? These kids, they say they're going deaf because the band is too loud or something, right? Um, so Aristotle says that sensing is a undergoing, right? It's not an acting upon, right? It's a being acted upon, right? A result of being acted upon, and not acting upon another, right?

[31:40] Now, the Greek word for undergoing, of course, is suffering, right? Now, you probably don't think upon the fact that an acting upon on your ears, right? Maybe it hasn't been too painful, you know.

[31:57] But if the last half hour I'd been sticking a pin in you, you'd be very much aware of the fact that I'm acting upon you, right? And so, when you are acted upon in a way that suffers and is harmful to you, you really recognize that. That's very sensible, you know. But you walk around all day, you know, and color is acting upon you and causing you.

[32:18] You don't think about, do you? But if you bump into something, you know, oh, you know, we do sooner or later every day, not every day, but um, then you very much the fact that you've been acting upon, right?

[32:33] And somebody bumps into you, know, and knocks your glasses off and tackles you. something, you're being acted upon, but you drop off the idea that you're being acted upon in a way that is what harmful to you, right? In fact, you're kind of if you listen to music of Mozart, your ear is being perfected by hearing the music of Mozart, because all knowledge is such as good, and knowledge of a better thing is better knowledge, right?

[33:02] So, to hear the music of Mozart rather than this rock and roll is perfection of your right. So, you've gone a long way from the first meaning of undergoing, right? Which is a connotation of something bad, right? If I say about some poor guy he's undergone a lot in life, hasn't been for the good, right? You see, but you drop off part of the idea of undergoing, right?

[33:27] That you're being acted upon in a way that is painful or harmful to you, right? And then you what? You're still being acted upon though in a somewhat bodily way because the senses are bodily, but you dropped off part of the meaning of it, right? That's being harmful, right? And then finally says that understanding is undergoing, right? And now he drops off the idea that it's even a body, right?

[33:52] But you're still being acted upon, right? By the agent, light, and the phantasms and the images. So the word is being carried over by being generalized, right, or by dropping out part of its meaning, right?

[34:10] I'm very fond of this word, "hodos," right, road. I talk about the three roads in our mind: the natural road, the common road of reason, and the private road of each reasoned-out knowledge. And you know, Thomas says, "Virtue is the road to happiness, and vice is the road to misery." But what's the first meaning of road, right? I go and ask my son Paul, the little boy.

[34:37] You know, what do you think of the basic road in human knowledge? He says, "Cars and trucks on it." I said, "Road means to him something that has cars and trucks on it, right?" And

[34:50] what do you do? You drop out the idea of what cars and trucks. Yeah, but you drop out by the idea of whatever the road is made out of—cement or asphalt or something—and you keep the idea of the before and after that's in the road, right? And now the word "road" has become what equivocal by reason. So the road in our knowledge is not, you know, cement in our knowledge.

[35:19] Warren Burr used to say, "You know, adults are like cement; they're all mixed up and set." I think that's very funny in high school. You're in the middle of the road. But in our knowledge, there's no cement or tar in our knowledge, right? It's a before and after in our knowledge, right? Sensing comes before memory, and memory before experience, and experience before a knowledge universal, right? So the before and after in our knowledge.

[35:50] So we speak analogously, he says, right, or equivocally by reason of a road in our knowledge, right? Aristotle even calls philosophy a methodos, right? It's over a road; it follows a road, right? It's a before and after.

[36:10] I was meeting with the students there on last Tuesday night. They were doing the looking at the proemium to the three books on the soul. And Thomas says that Aristotle renders the student desirous of knowing this, and then renders him teachable, right, and attentive. Well, how does Aristotle make him teachable by showing him the distinction and order that are going to precede him, right? Essentially, make him teachable by showing him the road to to follow, right?

[36:40] Whether you're following the teacher or following the the book, right, which is the teacher in a way. So the word "property" right can be carried over right to things that have only two or maybe even one of those things, as long as there's connection with the nature, right? But you're you're you're making the word equivocal by what by reason, yeah, and not by by chance. But he but he gives us the full definition, right, and the property in the strictest sense and fullest sense, right.

[37:15] What belongs to only one species to every member of that species, and always, right? Three. We need three things there to that are copied in the in fullest sense, huh?

[37:31] So, when Aristotle demonstrates that the soul is immortal, right? That's connected with the nature of what the soul is, what he's shown about the nature of the soul. But is it the only thing that's immortal? When the Greeks used to refer to us as the Homer, we're the mortals, and the gods are the immortals. Immortals was a synonym for the gods, right? Okay, there's something godlike, but our soul is, in fact, immortal.

[38:01] But and it's connected with our nature of our soul, right? But it's not a property that belongs only to man, right? You know, they're always saying this.

[38:19] litany is always talking about the immortal one. But Lithuania speaks of God as the immortal one. What I say, can you think of the child of the, divine mercy. Yeah, yeah, but God in there is called the immortal one, right? We say it every day. Yeah, yeah, yeah. So a man is not the only thing that's immortal. Or soul I mean.

[38:49] Well once once he resurrected, we'll be immortal, in the body. Athanasius. means immortal. Athanasius. Yeah, Alathanasius. Without Darth. That's good. And we'll get me and all Dantonasius so they can tell him. I said you know Greek. It is. I said, you know what I mean? I said, the immortals. Alleluia. Alleluia. Well, the accident is not connected to nature, right? Okay. So green, instead of square or triangle, right?

[39:28] Well, notice how useful it would be to know what these five things are, right? Not connected with the nature, right? But still, green, like we said, a triangle and a circle, and so on, right? Instead of many things, huh? Notice what the great Porphyry says now, huh? Just come back to his proemium right, right?

[40:09] He says to Porphyry, to Chrysaorius to understand what a genus is, what a difference is, what a species is, what a property is what an accident. It is useful not only, Chrysaorius, to know the categories of Aristotle, which is what his request was, right? What led to his request, right? And if he met. it's useful for understanding definition and division and demonstration. Now we talked a bit about how definition is involved here.

[40:41] What you define is a species, right? You begin the definition by the genus, right? And you complete the definition by the differences. That's useful, to know, right? Okay. It's also useful, he says, for division, right? Because one of the most important kinds of division is the division of a genus into its species by differences, right? So every science divides some genus into what?

[41:21] Animals are divided into four-footed and two-footed, and so on, right? Feathered and a two-footed. Feathered and non-feathered. Yeah, yeah. But it's also useful, he says, for demonstration. On a demonstration, you prove a property, right, of a species by an understanding of the nature of that. So in the case of the triangle here, right, you've got to know what a triangle is, and then you extend one side and draw a line parallel, and that's why you're going to prove the property of the triangle that these three triangles will be equal to what?

[42:01] Two angles. You know this angle and what? And equal. What do you know? Those two. I don't know the demonstration, so I'm going to guess. It stands here. Okay. So in demonstration, you're actually proving a property of the what? Species, right now. Okay. Through an understanding of the what? The nature of the thing, right, which involves the genus and difference, right. So that helps you to understand what a demonstration is in a broad sense, right?

[42:48] You're going to prove a property of a species by the genus and difference of the species, right? And that makes sense because the property is connected with the what? Nature, right now. And this brings out the nature fully, right? So it enables you to see why that property belongs to species. huh

[43:29] So that's in a nutshell what Porphyry's doing in the what? Isagoge," right? Makes sense. So the Greek commentators later on would call this the Book of the Five Names. Very concrete, huh? Modern logicians

[43:47] never do that. Never be so concrete. To the point, you know. Okay. And the categories in the Book of the Ten Names, right? Okay. Now let me raise a little question here. in your mind Maybe we got to start now with ten. minutes

[44:02] Yeah. Okay. Just to ask a little question here, right? Notice the definition of genus and the definition of difference, right? We both define them by what they're said of, right?

[44:18] And what they say, of what they're said of, right? And then we saw the difference: the one is said of them as regards what it is, the other how they are, what they are, right? That's why grammatically we tend to use a noun for the genus and, you know, adjective for the difference, right? Okay. And what about the species? He didn't define that by what's below it, what it's said of.

[44:45] What's above? Yeah. Now, is it great inconsistency, isn't it? Or did the great Porphyry know what he was doing? What do you think? I mean, can we save the teaching of Porphyry here? After all these centuries, it's been basic introduction to logic, Among those, you know what logic is.

[45:12] Even, even, you know, take the symbolic logic course you want, you want, you want, but these what's the little thing say, "Twinkle, twinkle, little star, how I wonder what you are. " What and why are the what things that wonder makes you ask, right? So wonder whether these guys are philosophers in the original sense, because both Plato and Aristotle were the chief philosophers, as Thomas said in the Middle Ages.

[45:45] Quite a long time after these two guys, right? Kick the bucket. He says, "What? Wonder is the beginning of philosophy, right? There is no other beginning. " Socrates is very strong. It's the arche he says the beginning. There is no other beginning of philosophy than wonder. What do you wonder about? What something is, or why it is so, right? And this is key to both definition and demonstration, which answers the questions what and why.

[46:16] So why don't you begin there? I mean, you just think from the way where you're coming from, right? You're not coming from wonder, right? They say, "If it

[46:30] calls God wonderful, talk to my my niece there, Lady Wisdom. " Say, niece, I say, Sophia, what is wisdom? She says, "The knowledge of God. " And it's the knowledge of God in both senses. It's the knowledge in which you know God, and it's the knowledge which God most of all has, right? It's a beautiful amphiboly of knowledge of God. Beautiful answer, right? To the question. So I go back refreshed from Sophia's wisdom, right?

[47:03] Lady Wisdom's wisdom. Now, why doesn't he define species? By what it's said of, how could he fail to do that? He defines it in reference to genius, right?

[47:29] And always has that relation to a what A genus above, right? It's always under every species is under a what genus, right? And that genus is set of it and answered the question, what is it, right?

[47:46] But what's under a species? Just individuals, yes. Ah. Or could be another species. Yeah, yeah, yeah. A species could be a genus in comparison to what is below it. Take an example here. Habit is a genus, right? Said of virtue and vice, right? What's below virtue? All kinds of things But courage and temperance and justice, right? And they are what species? So it's a what? Species under genus that has species under it.

[48:28] Yeah, yeah. And now you get down to what they call the lowest species, right? Then what's below the lowest species? Yeah. So does every species have individuals under it immediately? No, some have what species? Yeah. So you see why you might not want to define species by its gradation to what is below it. We need that to be developed later on, right? Because you wouldn't be able to get the same definition.

[49:02] That which is said of many other in kind. Well, yes or no? Circle might be said only of one of individuals, right? Yes. Maybe circle is the lowest species, right? A shape, right?

[49:24] So different circles might be one might be bigger or smaller than another circle, right? But a different kind of figure. So circle is said only of individual circles, huh?

[49:39] But quadrilateral, right, is a species of rectilineal plane figure. That is to say, a plane figure contained by straight lines, right? And then under that is triangle and and quadrilateral and and pentagon and hexagon and so on. And but then under quadrilateral was the ones that my master Euclid of Alexandria did, right?

[50:11] Square, oblong, rhombus, rhomboid, trapezium, right? Okay. So, what? Yeah, maybe smarter than we thought. This guy, right? He's a step ahead. Yeah, yeah, yeah, yeah. And then we'd bring this out, right? That's an important thing to see, right? Now, when Aristotle talks about the figures of predication,

[50:37] you know, that's how we distinguish being according to the figures of predication. This is the categories, right? But why does he say figures, right? What name is borrowed from mathematics, right? And a figure is something that is contained by what limits, right? Some sort. Well, maybe there's a limit, huh? Yeah, and that comes from the word limit, too. Yeah. But maybe the same thing can be a genus and a species.

[51:08] That's the great stepping stone. From this treatise to the what categories, right? That the same thing, same name can be both a genus and a species, but a genus with respect to what is below it, and a species with respect to what is above it. Like virtue, is virtue a genus or a species? See, it's like it's like asking, am I a father or a son? Well, I'm I'm both, but not with reference to the same man, right?

[51:39] You know, Victor Berquist is from Parkers Prairie, Minnesota is my father, not my son, and Paul Berquist or Marcus Berquist is my son, right? Sons, You know. So you can be both a father and a son, but not towards the same man, I don't think.

[52:00] Not even God, would be that, right? But does that go on forever? Is every genus a species, and is every species a genus? Aristotle's use of the word figure of predication, right? As if there is a what limit, both in the direction up and the direction down, right? Now, trying to get students a little interested in this, idea. say you know that it's sometimes the greatest question, right?

[52:34] Can something be both, for example, a cause and an effect? Yeah, but is every cause an effect? Will eventually come to the first cause?

[52:47] And is every effect a cause? Can the same man be a father and a son? Yeah, but is every father a son? Well, not Adam, but there's a first man, right? And there are sons who are not fathers, right? So there's an end to things, right? Then I go to you know be modern, I go to to the two developments in the physics of the 20th century, right?

[53:14] Quantum theory and what relativity theory, right? And I said, well, when Heisenberg and Bohr and so on, got through with the quantum theory. You know what they did? They started looking at elementary particles, right? And see, you know, near the end or something, Heisenberg said, never thought this will go on forever. so theody said water is the beginning of all things, and we said, well, there's something before water.

[53:43] We discovered it, called hydrogen, right? It generates water, right? And then we discovered something before hydrogen, with a proton-electron. Heisenberg said, this goes on forever, right? So they were looking for a part that is not a what? Whole.

[54:02] Einstein was doing the reverse. He was going from special relativity to the general theory of relativity, and that led to kind of explosion in cosmology, right? Einstein came to the conclusion the universe doesn't go on forever, not like Newton said or something, you know, that the universe what comes to an end, right? So then the universe would be a whole that is not a what part, right?

[54:29] But notice after you realize what a whole and what a part is, you make the marvelous discovery that it's possible for the same thing to be a whole and a part, but not of the same thing, right? So New England is a part of the United States, but compared to Massachusetts, it's a whole, right? Made up of you know the six states or six. And and then you say, well, but does that go on forever?

[54:55] See, is there a well? There's two questions: is there a part that is not a whole, and is there a whole that is not a part? And Einstein concluded that there was a whole that is not a part, but the universe was in fact, like Aristotle said, finite, right? And Heisenberg said I was convinced that there was going to be a part that is not a what whole.

[55:19] He's looking that direction, right? Even before you you you conclude or you know they're not, maybe they haven't come to the end yet, right? You see? And but more generally, the idea of cause and effect, right? Because something can be both a cause and effect. Does it go on forever? You know? But there's a first cause.

[55:41] Well, I say this is logic, right? No? Is every genus a species? Because a genus something can be both a genus and a species, like virtue is a genus and a species, right? But not in comparison to what is above and one below. it but the species of what's above it does this go on forever, right? Well, Aristotle's book, The Categories, says the discovery that there were what highest genus as well as lowest what species, huh?

[56:11] But you know, you get into this thing, you know. Have I come to the lowest species, right? Like when I was studying, you know, comedy, right? Is comedy a lowest species, right? Or there are two kinds of comedy, right? You know, I'm kind of inclined to think that there's what I call the good-natured comedy, and then the satire, right? And I don't like satire as much as a good-natured comedy, right?

[56:43] And and I was talking to one of my colleagues there who taught Shakespeare, you know, and I was talking about Troilus and Cressida, which is sometimes put the tragedies, you know, but it's really a comedy, right? And I was saying to him, he says, yeah, but a rather dark one, he said. You know, because Shakespeare really tears us apart there, you know. I mean, and it's like Swift, you know, the satire is really kind of vicious, you know, huh?

[57:09] It's a woman, really beautiful. You have a look close to it. I mean, take a microscope and her skin is very nice, and so on. You're facing the the the awful part of things, you know, and so on. So maybe maybe there's two. Maybe comedy's not the lowest. Maybe there is satire and good-natured comedy. The merry wives of Windsor, you know,

[57:34] or even at the end by Falstaff himself, you know, to join the cheer and so on. Okay. So should we start to look at the categories next time? or what Why not? Yeah. Okay. I will pass out that other one as a review You want to take this here? Is it down here Yeah it's on this one Yeah And it's called. First distinctions and definitions and logic.

[58:03] Yeah. Yeah. Those those aren't numbered by me. See, maybe you had numbered things. Yeah, I couldn't figure out number these ones out, so I wrote them in there. So.