Introduction to Philosophy & Logic (1999)
15. Porphyry's Five Predicables: Property, Accident, and Genus vs. Species as Relative Distinctions
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[0:00] Okay, the questions again here. Name said with one meaning of many things, signifying something. We divided into inside their nature and outside their nature.

[0:44] Okay. We subdivided inside their nature into three, right? The genus, the species, and the difference, right? Okay. Now, the outside their nature, they divide into two, and again by a complete division, either something that is connected with the nature and follows upon the nature, like an effect follows upon a cause, right? Or something that is not connected with the nature and doesn't follow upon it then. So we say either it follows upon the nature

[1:27] or it does not follow upon the nature. And the first is called in logic a property. In Greek, the Greek word is idion Okay.

[1:51] And it does not follow upon the nature. They call that an accident. In Greek symbebekos But, both in Greek and Latin, has the the word for happening, right? Now they call that an accident.

[2:17] Now, when Porphyry defines property, he'll define property in the strictest and fullest sense, right? And that's the property that belongs to only one species, right? To every member of that species and always. Okay. So it belongs to

[2:43] only one species to every member and always. Okay. But you can use the word property in a less full sense, provided stills connection with the nature.

[3:06] Now, most properties it's hard to find one name for them. Usually, you have to use a speech. The standard textbook example of one name is that man is visible,

[3:20] and that means that man is what subject to laughter, right? This is not the nature of man, but follows upon his nature because he's an animal. Can make the sounds of laughter, but because he has reason, he can see the absurdity of something that makes him laugh.

[3:38] But usually, we lack a name for most properties, and we have to fall back upon what a speech. Again, it's still a function like that. So, it's a property, for example, the number two to be what half of four, right? A half of four is expressing the relation of two to four, right? It's not what two is, but something following upon two. Now, it's because it's two, it's half of what four, and a third of six, and a fourth of eight.

[4:16] But all these things are following upon its being two, right? Now, to be half of four is a property of two in the strict sense. It belongs to only the number two. No other number is half of what four, and every two whatsoever is half of four, and a two is always half of four, right?

[4:39] Now, if you said that two is let's say less than five, that would be connected with the nature also of two, right? It belongs to every two to be less than five, and two is always less than five, but not only is two less than five; even four too, right? But still, we classify as a property because it seems to be what connected with the nature, right?

[5:07] The most common example in geometry of a property is that the triangle has its interior angles equal to what? Yeah, that belongs to every triangle and always, right? But as you learn geometry more, you realize it belongs only to the triangle. If you add another side, you're going to have more than because we have a let's say quadrilateral, you can always divide that into two triangles, and we end up with more right angles,

[5:44] than just two. So, to have the interior angles, even two right angles, belongs to only the triangle, to every triangle, and always, um. Now, if you say it's a property of man to be a logician.

[6:15] well, man is the only animal that is a logician. But it doesn't belong to what every man to be logician. and even those strange ones who are—they were not always logicians, right? Okay. Yet we classify that as a property, right? Because to be a logician is tied to nature of man as an animal with reason, right? Involved both his animal nature. That's where we have these sensible sounds.

[6:44] We're talking about words, right? Vocal sounds, but obviously tied with the fact that he has reason them. Okay. But now, if you say of the triangle or the square or the pentagon that it's green, right? Can you see any connection between the nature of triangle being green, or is that something that accidentally happens? Okay. Likewise, then, for a man to be white, is there a connection between nature of man as an animal with reason that he should be white?

[7:26] I don't think so. Okay. This seems to be something accidental, right? So this is the magician's contribution to rational harmony, right? Did we say before that rational is a property? Well, yeah. Now this is this is the question now you want to ask. Why do we go into a subdivision of names signifying something outside the nature? When you are interested in definition, right? Well, as the text explains, for two reasons, right?

[8:13] Because the property, right, has a connection with the nature, then it has a twofold relevance definition. Sometimes, if you don't know the difference, right, but you know the property, you can reason from the property back to the difference. Reasoning is a word from an effect back to its cause. So the property can be a middle term, as we see in logic, a beginning for reasoning towards the difference, right?

[8:48] But secondly, if you don't know the difference, you can use the property in place of the difference. This gives you an imperfect, right, definition, but something that might be what separate the thing you are trying to define.

[9:06] And suppose someone said to me, define dog and cat, let's say, right? Okay. I say, well, dog is an animal, so is a cat. Well, dog is a four-footed animal, so is a cat. Separates from the chicken maybe or the man, right? Okay. Now at this point, my ignorance is going to show up, right? So finally, I say, a dog is a four-footed animal that barks, and a cat is a four-footed animal that meows.

[9:36] Okay. Now, I'm not sure maybe that the dog is the only animal that barks. Even if the dog were the only animal that barks, or the cat is the only animal that meows, huh? Wouldn't barking and meowing be the species-making difference of these two animals?

[9:55] Now is he a dog because he barks, or does he bark because he's a dog? Well, if he barks because he's a dog, then barks is really like a what property following upon his nature as a dog. But because I'm too ignorant to see the essential difference between the dog and the cat, right? By the barking and the meowing, you know, strike my senses, right? Rather than be completely ignorant of the difference, you know, between the dog and the cat, I say the one is a four-footed animal that barks, and the other four-footed animal that what meows, right?

[10:31] You see that? So there's two reasons then why even with a view to definition, we want to see the distinction between these two names. You see, the accident, the accident is useless, right? Both for defining even imperfectly something, and for investigating the essential differences. But the property can be useful as a starting point, right, to look for the difference, right? And if you don't have a difference, or before you have the difference, it can be used to place the difference to give you a speech that's imperfect, but something like a definition.

[11:14] Sometimes Aristotle will call that a periphrase or an insert, right? It's like if I didn't know, you know, what made two to be two, and I say it's a number half of four. Well, number half of four and two are convertible, right? So it separates two from everything else. Now, if you look at the Nicomachean Ethics, Aristotle sees the need to take up human virtue. He first speaks of human virtue as a praiseworthy quality, right?

[11:49] Okay, and human vice as a blameworthy, right, quality. Well, there he's giving more the property than the difference, right? Because praiseworthy is something connected with what the virtue is. But it's not what really makes it to be virtue, right? It's praiseworthy because it is a virtue, and vice is blameworthy because it is a vice, right? What is the difference, right? And it's not until the second book of the Nicomachean Ethics that he starts to bring out the real differences.

[12:25] But the fact that he knows that virtue is a praiseworthy quality, right, is a starting point for investigating the what essential difference. What is it that is praised? Let's say in eating, let's say in drinking, right? Well, the man who eats and drinks the right amount for himself and the circumstances, right, that's praiseworthy, right? If he eats too much or drinks too much for himself and circumstances, right, or not enough, maybe, right?

[12:55] So he's passing the job and so on, right? Then this is what blameworthy, right? Well, then you are starting to reason out that virtue is a praiseworthy quality. What is praised is the middle, right? Okay, the reasonable middle, and you are starting to see more essentially what virtue is. So you start to reason your way in to the property, right? So,

[13:21] the nurse, huh? The little child who doesn't yet see the intrinsic goodness or badness of things, right? But they know certain things if they are frowned upon for doing, right? Another things that they are applauded for doing, right? Okay.

[13:40] So when we have the definition, man is a rational animal. Do we use the property because we don't know the specific? Yeah, yeah. Okay. In a sense, you know,

[13:56] in a way, we're trying to get at what's in the nature of man, whereby he has the ability called reason, right? Okay. So that's why we tend to have what just one difference there, right? But it's really a property, the property of extent. It gets us farther than a feather five days. Yeah, yeah, yeah. But interesting, even in the metaphysics, Aristotle often refers to man as simply a two-footed animal, right?

[14:26] Now, if you stop and think about these five names, right, in reference to definition, you can see there is something very complete about these five names. Species is the name of what is being defined, right? Genus is the name that begins the definition, right? Difference is the name that is used to complete the definition or a perfect definition. Property is the name that's useful for completing an imperfect definition, or for investigating, right?

[15:03] An accident is a name that is useless both for naming and defining. See how complete that is, right? We want to separate and distinguish the name of the thing being defined from the names used in the definition, right? And they are mainly the genus and the difference, right? But then the property has some usefulness for testing and reasoning, and for being used in place of them for naming a perfect definition.

[15:31] But we also separate the name that is useless, right? Green is useless for what naming triangle and useless for what defining it and investigating definition triangle. Nowhere do we see green. Nowhere in geometry would green appear, right?

[15:51] Now, as Porphyry says, these names are useful also for dividing, right? Especially for dividing a genus into species by its like. Differences, right? But if you didn't know, it's what differences, right? You might use divided by its properties, right? It's also useful, he says, for demonstration. A demonstration is you'll find out when you get into the logic of the third act. In a demonstration, you show that a property belongs to a species through an understanding of its nature, its genus and differences.

[16:34] So we demonstrate, for example, in geometry, that a triangle has its interior angles equal to right angles. We demonstrate a property of a species through an understanding of the nature of that species that involves the genus and differences. Okay, good. Thank you.

[16:58] So the the book of the five names, as they call it, the five vocal sounds, the book of the five vocal sounds, the five names, and a phonator. It's useful for definition, for division, for demonstration, and also we'll find out that Book of Aristotle is called the categories. Okay, and see if that's about later on. So it's quite a thing he did, right? And I know it's Thomas Aquinas there in the Summa Contra Gentiles in the first volume there, where he has a chapter showing that no name is said univocally of God and creatures.

[17:42] There are some names that are said of God and creatures univocally by reason, yeah, but no name is said of God and creatures univocally. And Thomas gives many arguments to show this. But one argument is an either-or argument. He says every name said univocally of things, it's either their genus or their species or their differences or their property or their accident. And then he eliminates all each one of those individually, and then he concludes that no name therefore is said univocally of God and creatures.

[18:15] So he's going all the way back to what the first book, the logic, right, the Isagoge of Porphyry, right? And you know, in terms of faith and reason, to this book, they're interesting because I can see Thomas here in the highest part of our knowledge there, reason, doubt, knowledge, and theology. He's using right this right. Albert the Great, his teacher, writes a paraphrase of this. Cajetan, the cardinal that the church sent up to talk to Martin Luther, he has a commentary on the Isagoge, right?

[18:49] On this thing, and and the Mohammedans of course use this, and the Greek philosophers. But Porphyry was violently anti-Christian. And Augustine, you know, talks about this, right? The Christian emperor burned his anti-Christian books. We don't have them, right? But Augustine, I think in the City of God, if I remember right, there he speculates as to why Porphyry was, whether it was pride or something, right? But despite the disagreement between, you know, Porphyry about religion and the Christians, obviously, right, and even the Mohammedans, right, they all took this book the eisogogy, right, and it's common what teaching, right?

[19:32] Of course, it really grows out of what you can see people doing naturally. When I go into class and I say to students, "What is a dog?" they'll say an animal. They'll naturally get the genus, right? I go into love and friendship and I say, "What is love?" and they say, "Well, it's emotion." Well, one kind of love is an emotion. I say, "So is anger. So is fear."

[19:51] So they naturally get the genus, and they've got to add what differences, right? So this is something really common to us and it's natural whether you're. A pagan, like maybe Porphyry was, right, or a Christian, like Thomas Aquinas, or Albert the Great, right, or Kajetan. or even a Mohammedan or Islamic, you know, or even you know one of the native Greek philosophers who might not be a Christian, right?

[20:14] But they all take this as the fundamental word, and it's called as they say in Greek. You know, the Isagoge carries out Aristotle's categories, but for short it's called Isagoge. The introduction, and eventually it started to be used by by Ammonius as the introduction not only to logic but to the whole of philosophy, in a way, because you are defining and dividing and demonstrating. That's the pure philosophy: define, divide, and demonstrate.

[20:39] but that's the three Ds right? In English, define, divide, and demonstrate. And these are important for that. Understand definition. So think about those five names then in comparison to definition. How complete that is, right? You are separating and distinguishing and defining the name of the thing being defined, as opposed to the names used in the definition. You are distinguishing between the name that begins the definition and the names that complete the definition, and between the names that complete it perfectly and imperfectly, and all these being distinguished from the names that are useless for naming a thing or for what?

[21:24] Defining it, or for investigating a definition, right? So, you'd be surprised that many philosophers don't know the Isagoge, right? Some, you know, some of you haven't even heard the name of the Isagoge. Others have heard the name but they've never read the book. And

[21:46] you know the Isagoge, out of it, didn't you So, Porphyry would define all these, and then he'll you know compare them, you know, what they have in common and so on. So many

[22:06] questions up to where we are now. Notice that the definition of genus has a genus, right? What's the genus of genus? Name. Name, yeah. Name.

[22:31] You have these differences, right? Said with one meaning, right? Of many things, other in kind, signifying what it is. Those are all differences, right? The genus of all five of these is name, right? Name said with one meaning It's common to them. We need break. We need... Say the genus is that which is said of many other species, signifying, you know what it is. And so it kind of left up in the air whether you are talking about the name, genus, right, or the general kind of thing signified by it, right?

[23:13] And I think that the word genus and say species are equivocal by reason, right? Because sometimes you use the word genus to mean the name of a general kind of thing, and species the name of a particular kind of thing. And sometimes you use the word genus to mean the general kind of thing, and species to mean the particular kind of thing. So when you are dividing a genus into species, I think you are dividing a general kind of thing into particular kinds of that thing.

[23:44] You are not dividing a name into names, right? Okay. But because the definition is composed of names, and when we ask for a definition, we use a name. That's why we distinguish the names here.

[23:59] Now, sometimes we use the word genus and difference even when you have a name is equivocal by reason, right? But that's a little bit different, right? A little different meaning of the word, a looser use of the word genus, huh? So when he first distinguishes five names, we're taking them in the strict sense, huh? Where there each of them is a name, said with one meaning of many things.

[24:26] Now I might make a little footnote here about the difference between logic and what grammar, okay? Now take this example: green triangle and equilateral. triangle.

[25:00] Now the grammatical analysis of the phrase "green triangle" and "equilateral triangle" would be exactly the same. The grammarian would say, "Triangle here is a noun, right? And green or equilateral is an adjective modifying triangle, as far as it goes. " There is no difference between those two from a grammatical point of view, is there? Okay. Now the logician comes on the scene, right? He says, "There is an enormous difference, right?

[25:35] " Triangle here can be taken as a genus or a species, right? Green is a what? Accident, right? But equilateral is a species making what difference? Oh, difference. Oh, yes. Okay. Now the logician would ask, you know, what is a triangle? Triangle is a plane figure contained by three straight lines. Now, is green one way of being three sided? No, nothing to do with three sided at all, right?

[26:06] But equilateral is one way the three sides can be, right? Isosceles is another way, right? Where just two of them are equal, and scalene where none of them are equal, right? Okay. So, scalene, isosceles, and, equilateral—they determine three different ways of being what? Three sided. Green or red, white, and blue might sound patriotic, but has nothing to do with being three sided. Genus or species, for that matter, more by a noun, right?

[26:40] And the accident, or even the difference, by an adjective, right? Because the difference does signify how it is what it is, right? Okay. And we're more apt to signify how by an adjective, than by a what? Noun, right? Okay. Now, another thing that we've touched upon that come back to here.

[27:09] In a definition, can there be more than one genus? No. If there was more than one genus in a definition, you wouldn't be talking about one thing, one thing, right? Okay. But there is usually, if not always, more than one what? Difference, right? Okay.

[27:37] Now, if you read the dialogue called the Meno, right? When Mino tries to eventually define virtue, and then Socrates examines the definition, right? And Socrates makes you know one critique of the definition. But when I first hear the definition, he defines virtue something like this: the desire for good things and the ability to achieve them. Sounds pretty impressive, right?

[28:09] But when I examine that, it seems to me that he has two what? Genus, right? That's a plural of genus, huh? The desire for good things and the ability to what? Achieve them, right? Is the desire for good things and the ability to achieve them are those the same? No. And couldn't a man have the desire for good things without the ability to achieve them? Right. Or vice versa, he could have maybe the ability to achieve good things, but not what?

[28:45] Desire them, right? So really, talking about two different things, right? The desire, right? And the ability, right? If I desire money, right? I may not have the ability to get money.

[29:02] Or someone else might have the ability to get money, but not desire it. The famous anecdote about babies right? One year decided to show he can make money. Just to show this is so that a philosopher could make money if he wanted to, right? At least there's an interest in that, right? Okay. So if I got a gun, I got the ability to get money, right? But maybe not the desire to get money that way, anyway.

[29:27] Someone else doesn't have has the desire to get money, doesn't have the gun, so they don't have the ability to get the money, right? It's two different things, see. So really. That's kind of the first criticism I make of Meno's definition, right? So there should be only one genus and what many differences, right? That's an interesting difference there, right?

[29:58] When Aristotle defines tragedy, right, the genus is imitation or likeness, right? The likeness of an action that is serious, et cetera, right? And then it's acted out, right? So there are many differences, right? That say like this is something serious, it has in common with epic. That it's acted out, it has in common with comedy, right? But the two differences there are separated from both epic and comedy.

[30:29] But there's just one genus. Now a second difference here you might want to point out between logic here and grammar, right? In English, we tend to put the what adjective before the noun, right? Okay. So if the genus is signified by a noun and the difference by an adjective, the difference will be given before the genus, right? So when we say that the genus is the first word in the definition, what does that mean?

[31:09] Should that be understood grammatically? Sense of first being speaking Yeah, first in our understanding of the thing, right? Okay. And unless you understood the genus first, you wouldn't really see why these are differences, right? Unless I understood, let's say, what a quadrilateral is, right? I wouldn't see how equilateral or right angle there are differences of quadrilateral. Unless I understood what a triangle is, I wouldn't see how equilateral and isosceles and scalene are differences of triangle.

[31:52] Why red, white, and blue are not. Red, white, and blue are not three ways of being three sided, but equilateral, isosceles, and scalene are. So unless you really understand the genus, right, you don't understand the differences. Aristotle talks about tragedy and comedy, epic. He points out that each of these are likeness, right, imitation, and therefore they can differ by that in which they imitate or what they imitate, and so on, right?

[32:28] But you wouldn't see those as being the sources of differences unless you saw in general that it is a what. Like this imitation. So,

[32:42] the genus. Let me see. That's the first word in a definition. We don't mean that the first word is necessary in a language like English, for example, when you write it out grammatically, right?

[32:58] So, if I say in English that a triangle, excuse me, a square is an equilateral and right-angled quadrilateral, right? Quadrilateral is the last word in the sentence, right? In the speech, right? I say the definition of square is equilateral and right-angled quadrilateral, but nevertheless, quadrilateral was the first in our what understanding as the logic is concerned with, right? Okay.

[33:24] But maybe in Latin or in Greek, you could put the what adjective after the noun, right? And you can, you know, play around with this in English. You could, you know, do with the phrase, right? Okay. I say, man is an animal. What with reason? There, I give the genus first, right? But if I use the adjective instead of with reason, I said man is a rational animal.

[33:54] I'd have to put, as an English grammar, rational before animal. It would sound right in English to say man is an animal rational. I think I'd just say man is a rational animal. Right? Even in my grammar to say animal rationalis or something like that, right? Okay. So the grammatical order is not the logical order, right? And it doesn't mean you have to, you know, go against the grammatical order by using phrases, you know, but understand to act, right?

[34:23] It's like when I was explaining the definition of name. There, I begin with it's a sound, right? And then I added some vocal sound, vocal sound that signifies a custom, and then, you know, no part of which signifies by itself, right? But I start with the word that, logically speaking, is before the rest, right? Okay. As I say, when you ask the child there, you know, when you ask a, class of students, say, "What is it?"

[34:54] They call a question out of the blue. Say, "What's a dog?" They'll begin by saying animal. They won't begin with four-footed. You see, they'll say animal first, right? Okay. So even though later on they might say four-footed animal, they didn't what? Think first of four-footed, right? They thought of it being an animal. Okay.

[35:21] Or if they were, you know, thinking of tragedy and comedy, you see, it's a play, right? You know, well, they wouldn't use four-footed or two-footed to separate one play from another, as I thought it would say. Okay. Um.

[35:38] Okay. Now we come to a nice subtlety here. Now, the bottom of page twelve. Can the same name be both a genus and a species?

[35:53] And the answer to that question is going to be yes. Okay. Species as we define it. But in order to understand that answer, I distinguish between two kinds of distinction that you find in sciences. And one we could call an absolute distinction, and the other a what? Relative distinction, right? Because absolute means in itself or by itself, right? And relative means what? Towards another, right? Okay. So I give a number of examples of this distinction, right?

[36:30] Between two distinctions. Um. The distinction in human beings between a man and a woman is a what? Absolute distinction. A man cannot be a woman. A woman cannot be a man. Okay. But what about distinction between a father and a son?

[36:49] Well, the same man can be a father and a son, but in relation to different what? People, right? Okay. But you can't be a man in reference to one and a woman if it's somebody else. Okay. You're either a man or a woman. Okay. Or take numbers, right? The distinction between an odd number and even number is what? Yeah, you're either an odd number or an even number.

[37:15] Number. One of the two. But double and half is what? Yeah. It's possible for a number like four to be both what? Double and half, but in comparison to different things, right?

[37:33] So is the distinction between genus and species as we define them, right? Is that an absolute distinction of names, or is it a relative distinction of names?

[37:47] It's relative, huh? So that the same name could be a genus in comparison to these, and a species in comparison to those. Take our stock example, quadrilateral, right?

[38:03] Well, if you compare quadrilateral to rectilineal plane figure, plane figure contained by straight lines, quadrilateral is a what? Species, right? Along with trilateral or triangle, right? Okay.

[38:32] Pentagon and so on, right? Okay. But quadrilateral, in comparison to square and rhombus and oblong and so on, is a what? Genus, right? Do you see that? You know, it's relative here. It doesn't mean that this thing is subjective or not precise or not certain, right? The two is half of four is very certain, right? And the quadrilateral is a genus, and square is very certain, very precise, right?

[39:06] It's a species of rectilineal figure. But it's a different distinction, right? Than an absolute distinction. I am really the son of Reno Victor Berkowitz right? But I'm really the father of Paul Berkowitz. So I'm both the father and the son, but not towards the same man.

[39:32] Now, this is a similar thing. Once you see this, then arises kind of the kind of ultimate questions, and this happens in other areas too, right? If you realize that the same man can be both a father and a son, you might go on and ask: Now, is every son also a father? And is every father a son? Right?

[40:06] And there are some sons who are not fathers, as we know, right? Okay. Is there a father who's not a son? What we're told about Adam, right? Right. Okay. And so, Adam is a father, but not a what? Son. Okay. Son of God Yeah but not you know, he doesn't have a father like you and I have a father, right? Yeah, yeah, yeah. But notice that that may be hard to know.

[40:39] Is there a father, right, who's not a son, right? Okay. We might know that there is a son who's not a father, right? We're not always sure. But you have two questions, right? Looking at either end, right? Okay. Now, take another example of this sort of thing. Can something be both a cause and an effect? Of course, it's an absolute distinction between cause and effect. The same thing can be a cause and an effect.

[41:14] Yeah. Okay. Now you ask the question, though, but is every cause a what? An effect, right? And the answer that's eventually going to be no. There is a cause that is not an effect, right? Maybe there is an effect that's not a cause. at the other end. Okay.

[41:35] Now, take whole and part, right? Is that an absolute distinction, whole and part, or relative? Okay. Yeah. So, Massachusetts can be what? A part of New England, right? Okay. So New England is a whole, which Massachusetts is a part. But New England is a part of the United States, right? But again, Massachusetts has parts. You know, I live in Worcester County, right? So Worcester County is a part of Massachusetts, which is a part of New England, right?

[42:18] So now you ask the ultimate question, right? Is there a part that's not a whole? And vice versa, is there a whole that's not a part. Okay. Now, in modern science, in the twentieth century. Um. The physics of the twentieth century is distinguished from that of the sixteenth, seventeenth, eighteenth, and nineteenth. In the first part of the century, there are two great things, right? One was the discovery of the quantum, right?

[42:48] And Max Planck in December of 1900, right, dawn of the century, he proposed the quantum hypothesis, right. It took about 30 years for quantum theory to be, which is full development, right? And then 1905, Einstein proposed special theory of relativity, right, which he followed later on with the general theory of relativity in 1915, right. After special relativity and quantum theory were somewhat perfected, these physicists went in opposite directions, and the quantum physicists went in the direction of looking to see if there's a part that is not a what, whole, and so they're going from what atomic physics, which quantum theory in a way completed, right, down to the study of the elementary particles, right, and they were what accelerating elementary particles and shooting them, right,

[43:37] and trying to split them, right, but they're trying to see if you come to a part that is what, Yeah, that's no longer a whole It's a part that is not a whole, right? Okay. And. Which means it doesn't have parts. Oh, it's indivisible. Yeah, yeah, yeah. And actually, for a while, they were promoting the idea that there's a minimum length in the universe. Minimum what? Minimum length in the universe.

[44:07] Oh, I know it. Yeah, yeah. So notice, without you know trying to say what the conclusion will be, they're moving in the direction of looking for what other part, right? And that would go on until you came to a part that was not a whole, right? Okay. I'm not saying there is such a thing, but okay. Now Einstein, with the general theory of relativity, went in the opposite direction.

[44:33] Use this as a starting point for kind of an explosion in the study of the cosmos as a whole, right? The general theory of relativity led to a great what interest in cosmology, the study of the universe as a whole, right? Okay. And you know what came out of the attempts to understand the universe at first from the general theory of relativity? It appeared that the universe was what finite, contrary to what the moderns had thought since the Renaissance.

[45:01] Aristotle thought the universe was limited, right? Although the first Greek philosophers thought it was infinite, or the first modern scientists thought the universe was infinite, and now with the general theory of relativity, it seemed that the universe was finite, limited. This was quite a shock to them, and Einstein himself just didn't fully realize the consequences of its own theory, It was leading this way, huh? Okay. But notice if the universe is not finite, if it's limited, not infinite.

[45:31] Then there is a whole, that is not a what, part. See, notice the ultimate questions you might say, right? Are what, Following out once you recognize that a whole can be a part and part as a whole. The ultimate question is: Is there a whole that's not a part? And that takes you in the direction to study the cosmos, the universe as a whole, and the other one down into what, the atom down towards what, elementary particles, and then there are quarks, you know, down that direction, right?

[46:05] And you're looking to see: Is there a part that is not a whole? Kind of the ultimate question, right? But the most ultimate question is: Is there a cause that is not a what, effect, right? Um, which is similar question with the father and the son, right? The same way with the mother, right? Same woman can be a mother and a daughter. Was there a daughter who's not a mother?

[46:29] I think there are daughters who are not mothers. Is there a mother who's not a daughter? What about Eve Okay But notice now, we're not assuming that any of these series, you know, are closed at either end, right? They might be open at both ends, for all we know. Give an example in geometry, right? Is there a? You could have one straight line be, let's say, half of another straight line, right?

[47:06] But is there a straight line that is half of some other straight line, but not double of some other line? When you get to study the continuous in Book Six of Aristotle's book, The Physics or Natural Hearing, as it's called in Greek, you'll find out that the continuous is divisible forever. So you can always bisect the straight line. So you never come to a straight line that is double and not what?

[47:37] I mean, this half and not double, right? Okay. But again, if you can always geometrically extend the straight line. Is there a line that's double of something, but there's no line that it's half of?

[47:53] Goes on forever, right? But now with numbers, right? Unless you're a. Crazy modern who thinks he can divide the one, right? You know. But the one is actually simpler than the point. It's indivisible. There's a number that is double, like two, right? Huh? Okay. Or the number that's half, like three, right? Three is half of six, but it's a double of it. So three is a half that is not what?

[48:25] Double. By four is a half that is double, right? But now is there a number that's double but not half? So in the case of number, a case of double and half in numbers, right? There is a half that is not double, but there's no double that's not half. It's closed at one end, so to speak, not the other end. But in in straight lines, there's no line that is it's open at either end, right?

[48:59] Okay. Or father and son without, you know, faith, right? You might say, "What he was was there a man who was not, was a father but not a son, right? You know. But when you hear about Adam, he seems to be a father, right? Okay. So we're going to ask a similar question here now, logical questions, right? Okay. Well, we ask it also when we reason. See, when we reason, we find out that the conclusion of one argument can be a premise in the next argument, right?

[49:29] So to be a conclusion or a premise is a relative distinction, right? So in Euclid, the conclusion of one theorem, right, is a premise for the next one, right? But is every premise a conclusion? No. In that case, you'd never know anything, right? Okay. So we ask then, now quadrilateral is both a genus and a what species, right? Now we go in both directions. Does is every genus a species?

[50:05] Another way of putting it: does every genus have another genus above it, right? Well, see, above rectilinear plane figure is what plane figure, right? Above plane figure is figure, right? Does that go on forever, right? See, that you always have a thought above every thought, yeah. And then vice versa, you know. Does every what species have species below it, right? Or do you come eventually to what we call a lowest species, a species that has no species below it?

[50:41] In other words, a species that is not a what genus, right? And then the other question, the other other end, right? Do you come to a genus that is not a species? A genus that has no genus above it. You come to what we might call the highest genus, right?

[51:02] This is where Aristotle comes on the scene with the categories. right the Isagoge maybe Aristotle's that for lesser minds, right? But he always takes the most difficult thing, right? Just like you know, he points out about Euclid, right? He takes the most difficult case and makes an easier case for us, secondary minds, okay? So are there species that are not genera?

[51:37] square. Square. Yeah, yeah. Are there different kinds of square? No. But how about oblong? Is oblong a lowest species? Are there different kinds of oblong?

[51:58] Different shapes of the rose. Yeah, they are. Yeah, yeah. So this oblong here and this one here have exactly the same shape, do they? Right. But if you had an oblong, let's say, where the longest side is to the shorter side is two to one, maybe that's the lowest what species, right? Okay. How about triangle, right? Is triangle a lowest species?

[52:32] But now, what about scalene, isosceles, and equilateral, any of those lowest? And you could still have the length difference. Yeah. What about equilateral triangles? That would be. They still have. You know, bigger or smaller. Yeah. But that's not really a difference in. In the figure, right. So all equilateral triangles have the same shape, right? Oh, yeah. Okay. But not all isosceles triangles, right? Okay. So that's kind of interesting to see that in the species you get from dividing a genus, one of them might be already a lowest species, like square, but not oblong, right?

[53:15] Yeah. Okay. Um, a circle would seem to be a lowest species, right? Yeah. Okay. You happen to have different shapes of circle, right? Okay. Um. Is man a lowest species?

[53:33] What did you say? Yes. See, if you think of man as an animal of reason, if there are species of man, they have to have different kinds of reason, right? Now the white man and the black man and the yellow man and the red man had a different kind of reason, right? Then you might argue that what man is a genus and not a what lowest species, right?

[53:59] But if red and black and so on are not different kind of reason, but they're really accidental differences, right? Then maybe man is a what lowest species, right? Okay. Now it's not as easy to see that as it is that a circle is a lowest species, right? Some men and women don't have the same. Don't think the same way. But now I'm not sure that that you know these can say that the media have a different kind of reason, right?

[54:27] Now. Okay. You know. It seems more more obscure. It is in math, right? With that, male and female, it doesn't seem like it seems more than an accident, though. Hmm. That wouldn't

[54:38] be like a cross. Well, that's that's a very difficult subject, right? Oh. I'm saying the logician will explain what a lowest species is, right? Okay. It's a species that is. You give definition of it now. See. And it's a name, right? We take the lowest species now as a name. It's a name set of many things, right? Not other in kind, right? It's a set of many individuals, right?

[55:08] Signifying what it is. Like circle, for example, is a set of many individual circles, right? Okay. So, um, I get the definition of lowest species here now.

[55:22] I remember the the definition of species we gave before was in comparison to genus, right? Okay. If you look at what's below species, if that species is also genus, so there's a genus we respect what's below. But if you come down to the lowest species, then it has a unique relation of what's below. it. So, it's a name set with one meaning

[56:03] of many individuals, not other kind. That's understood as individuals, signifying what it is. So you take a circle here, said of this circle, this circle, this circle, right? It's a name set with one meaning, right? The reason why I call this a circle is the same reason why I call This a circle. and This a circle. Of many what individuals right, okay. Many that differ only as individuals, not differing in kind, signifying what it is.

[56:45] What is this a circle? What is that a circle? What is that a circle? Right. Now, if you compare the definition of difference and the definition of what genus, right, with the definition of lowest species, the definition of genus shares this with lowest species definition, right? But it differs here, right? Okay. Because the genus is said of many other in kind, the difference shares many other in kind with what the definition of difference, but a difference can signify how they are what they are, right?

[57:25] Then you see the idea that you need one one difference, right, to define these things, right? Even to define genus, difference, and lowest species. Genus, difference, and lowest species have in common that they're a name said with one meaning of many what things, huh? Okay. But the genus and species differ from difference because they signify what those many things are. Why difference signifies how they are what they are.

[57:58] But genus differs from lowest species because it's said of many other in kind, and the lowest species is said only of many other individuals, right? Okay. And it has in common with difference that it's said of many other in kind,

[58:20] but difference by that. So you need, in a sense, both this and that, right? Okay. Just like you need the definition of genus, this and other in kind, and the definition of difference, other in kind, but how it is what it is, right?

[58:39] So the logician explains what lowest species is, but he leads to the geometry to determine what is a lowest species in geometry. And Euclid maybe would tell you that the circle is a lowest species, and equilateral triangle is lowest species, and square is right. But maybe oblong is not, and I suppose triangle is not. Maybe if you specify the oblong what the ratio is, the longer to the shorter side, right?

[59:07] Like two to one or three to one or something, then you have maybe a lowest species, right? Okay. The mathematician would say that what even number and odd number is not a lowest species, but seven is, right? Okay. But prime and composite are both genera and species, right? Okay. You leave now to the what biologist to say, you know, natural philosopher, whether man is a lowest species, right?

[59:38] Okay. Who the dog is, or there are different kinds of dogs, right? Okay. And you lead to the the poetic science, right? Is comedy a lower species, right?

[59:57] Or I would say myself from my study of comedy that what I call the good natured comedy and the satire are different forms of comedy. The good natured comedy I think is much superior to the satire, right? Because the the good natured comedy expels what melancholy, right? But the satire kind of makes you what misanthrope. What they say about about Swift, right? You know, kind of melancholy, really.

[1:00:29] No, but even Shakespeare he has the three good natured comedies and they're much more enjoyable than the two satires, right? You know, but satire sometimes gets a little bit, you know, crusty. Yeah.

[1:00:43] Shakespeare has a black satire, you know, towards the Crasyd. This is a shock, you know, because go bare heroes and that's all right. That's heroic. Okay.

[1:00:55] But as they say, the logician then leaves. He explains what a lowest species is, and he might exemplify it, but he really leaves together science to determine what that is. But in the other direction, then the logician is the master here, right? Okay. Is there a genus that is not a what species, right? Or does every genus have a genus above it, right? Well, if every genus had a genus above it, you have to know the genus before you can know the species.

[1:01:32] You could know what a quadrilateral is without knowing what a square is. but You can't know what a square is without knowing a quadrilateral. So if every genus had a genus above it, how many genera would you have to know to know anything? Yeah, in which case you'd know what. Thank you. That's obviously not true, right? Okay. You couldn't even say you don't know anything. You know what?

[1:01:53] What is to know? Okay. And how many definitions would be presupposed to the definition? Infinite definitions, right? So you wouldn't be able to do anything, right? Okay. And you couldn't begin even to define, right? Because you have to define the genus before you can use the genus, right? You have to define the genus that

[1:02:18] I'm using that to even begin, right? Okay. Another way I don't think mentioned in the text here, why not? That should be. If every genus had a genus above it, right? Then there'd always be a more universal name or universal word than any word you have, right? But there are most universal words. Like take the word something or the word thing or the word being, right? Can there be something that is not a being?

[1:02:53] No. Can there be something that isn't something? Boy, no man. Yeah, but but I mean, if it's a name, it's something, right? Okay, so there can't really be something that isn't something, right? There can't really be something that's not a being, right? Okay, there can't be a thing that's not a thing. So there are most universal names, right? Like being and something and so on.

[1:03:25] Thing. Well, if every genus had a genus above it, right? You'd never come to most universal name, right? Okay. So this is one way, another way, rather I should say, that we show that what not every genus has a genus above it. The consequence of that is that there's no most universal name, but there are most universal words and names, right? Therefore, not every genus has a genus above, right?

[1:03:56] Okay. And the other way we show it is by the fact that you have to know the genus before you can know the species, right? And therefore, you have to know infinity of things before you can know anything. In which case, you never know anything, right? And there'd be an infinity of definitions before any definition. So you never know anything by definition, right? Okay. So we know anything, right?

[1:04:18] So there's nothing to say. Can't even say I don't know anything because you just know what it is to know. I know anything. He really doesn't know. What does he say?

[1:04:34] But now the next step is key here. Now, once you realize that there are most universal names, right? There's a name that's said of everything, like the word thing or something, right? Does that mean that there's one genus of everything, right?

[1:04:56] Well, if you go back to the definition of genus, now it's a name said with one meaning of many things of a kind, signifying what it is, right? Well, the question is, are those most universal names like being or thing or something, right? Are they names said with one meaning of everything? Are they said with more than one meaning? Are they said univocally or equivocally? If they're said equivocally, then there isn't one highest genus, right?

[1:05:29] There's going to be more than one highest genus. If they are said univocally, then you do have one highest genus, right? Now Aristotle showed, I'm going to follow him this way, is that those most universal names are not said univocally with the same meaning. That is, not said equally, right, of everything. Therefore, there can't be one highest genus.

[1:05:59] But then you have to say, well, how do we distinguish then the many highest genera? That's Aristotle's famous book, The Categories, about. Now I'm not going to go further today because ten degrees stop right there. Okay. And so we'll start with that question, you know. It's a follow-up here of the realization that the same name can be a genus and a species, right? And that gives rise to two questions: Is there a species that is not a genus, right? Or is? every species, and then the question concerns now is there a genus that is not a species?

[1:06:41] Right? We show that there is, but is it one or more than one? Right? We'll take up with that. Last issue, of L'Osservatore Romano where the Pope speaks, you know. And this is the July-August issue. And it was kind of interesting for a thing here, a little interesting quote, I

[1:07:10] thought. Apostolic zeal, fraternal friendship, and supportive charity will enable them to turn daily social relationships into opportunities for awakening, awakening in others that thirst for truth,

[1:07:28] which is the first condition for the saving encounter with Christ. That's interesting, right? He's saying that the thirst for truth, there is a thirst for truth, which is the first condition for the saving encounter with Christ. Huh? Kind of interesting thing to think about, huh? All right. Yet a thirst for truth, right? And eventually, that led him to Christ, huh? These other things we think about, you know, where a man realizes his sinfulness,

[1:08:05] and so on, or this humility that you need, right? They have a connection with with truth, I think. Also, there's a famous saying of Saint Teresa of Avila that

[1:08:19] humility is the truth, and that's what we call in philosophy a predicatio per causam. Humility is not truth, but its cause is truth, right? And so, a person realizes his dependence upon God and how the good that he does, God is chiefly responsible for, right? But that he is chiefly responsible for the evil he does. That truth, in a sense, is the foundation of what true humility, right?

[1:08:50] You know. And likewise, I think you know, in terms of recognizing one's sinfulness. I mean, nowadays, you know, it's commonly said, you know, people don't even know what sin is, or is such a thing called sin, or you know, but they have no desire to know the truth about the moral law, or to know the truth about their own moral condition, right? But then there's also you know this thirst for truth in this broader sense that leads a man, you know, to wonder about the afterlife and universe and so on, and that, in a sense, leads him to Christ, huh?

[1:09:23] And it relates to that truth. Oh, the one that the. Yeah.