Introduction to Philosophy & Logic (1999)
14. Defining by Names Common to Many Things: Univocal and Equivocal Names, Genus, Species and Difference
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[0:00] Now, in the next section here at the bottom of page two, we're talking about calling a thing by some name, right? And we're talking a little bit about now the name of the thing you're going to be what defining, right? But in general, we're saying that you can call something by its own name or by the name of another thing. Did you describe this at the beginning of part two?

[0:34] Did you say that? No, part one here is about names, and then part two will be about definition itself. Okay. Around page two is what I said. Okay. Um.

[0:51] So Romeo can call Juliet. He can call her by her own name, which is Juliet. Or he can call her by the name of another thing, right? Now, if he slips up and calls a Rosalind, who he's in love with, as you know before, he could be in trouble, right? He's made a mistake, right? Okay. If a child calls a cat a dog, or vice versa, sometimes you see a little child do, right?

[1:19] He's not calling it by its own name, but by the name of another thing, and he's mistaken, right? But there's another way in which you can call something by the name of another thing and not be mistaken, right? So when Romeo calls Juliet "honey" or "sweet" or something of this sort, he's not calling Juliet by her own name. But by the name of a what? Another thing.

[1:43] But he's not mistaken, as if he called her Rosalind or something, right? Okay, that's a mistake you ought to avoid. Now, this is an example of what they call a figure of speech, right? And the greatest figure of speech, perhaps, the metaphor, huh? Okay. And

[2:08] Thomas, in his commentary on one of Saint Paul's epistles, where Saint Paul uses irony, and Thomas wants to explain that Saint Paul is not saying something false; he's speaking ironically, right? Okay. He gives a good explanation of what figurative speech is, and he says that in figurative speech, the meaning of the word is not the meaning of the speaker.

[2:39] So when Romeo calls Juliet honey, he doesn't mean that she's that yellow substance produced by the bees, right? Okay. When Saint Paul, you know, uses irony, right?

[3:00] You know, if I come in and I find one of my students drunk under the table, and I say, "What a fine example of such a college student," he knows I don't mean what my words say, right? Okay. But there's a connection between the meaning of the word and the meaning of the speaker. And in the case of metaphor, the connection is one of some likeness, huh?

[3:24] As honey is sweet and pleasant, right? So Juliet is is pleasant, right? Okay. And irony, you're saying the opposite, right? Okay. That James Bond movie one time where he knocks a guy over into the bathtub, right? And he grabs a piece of wire and hits the guy. I heard somebody say it around me in the theater. You mean something like what you what the word means? In irony, you mean the opposite.

[3:56] Yeah. I can find it for you, but you know, but it might be the Galatians, you know. Okay. Um. but synecdoche is another example, right? Where you call something by the the name of the whole you give to the part, or vice versa. He's a brain, right? No, he's a human being. But he's a human being in which that part stands out for some reason or other, right?

[4:33] Okay. Or Aristotle says in the tenth book of Nicomachean Ethics that reason, more than anything else, is man, right? Okay. That's kind of synecdoche. Or the word was made flesh, right? Okay.

[4:48] Likewise, when I say somebody is a Romeo, what do I mean? This is now at in tone of masia, okay? He's a Romeo. I don't mean he's you know that citizen of Verona who ended up unfortunately, right? I mean he's a what? A lover, right? See, but everybody recognizes Romeo as a famous example of a lover, right? I say he's a Don Juan or a Casanova or something, right?

[5:13] Okay. I say my student is another Einstein, right? He's an Einstein. That'd be quite a compliment, right? You see. Um. Now there's a reason why we call thing by the name of another thing figuratively, and especially this most famous one like metaphor. It's especially to express emotion or to arouse emotion. But also appeals to the what Imagination? huh? There's a likeness there that appeals to, imagination. And Thomas, incidentally, in these commentary and the sentences there, he points out that one reason why we have metaphors in Scripture there many many reasons, huh?

[6:03] But one reason is that the imagination, like every other part of us, should be subject to God. And so, by using metaphors, we bring in the what imagination? Just like when we genuflect we bring in our knees and our legs, right? But the imagination is a is a higher and more noble faculty than the legs, right? And that's much more dangerous in a sense as far as leading us astray.

[6:27] So it's necessary to subject the imagination even to what God, right? And the metaphor brings imagination into the service of God. That's only one reason. There are many other reasons for using metaphors. So it's very common among lovers and so on that they will use metaphors to partly express their emotion, but also to arouse emotion, right? Okay. But likewise, if if I come home and I'm hoping to have another piece of pie or something, and you eat up a whole pie by yourself, and I say you pig, you know, I don't mean that you're a four-footed animal with a tail and a snout, just something like that.

[7:05] And this, in a sense, expresses my emotion better than saying you're a glutton, right? And it also maybe arouses you, you know, you kind of press up a bit being called a pig than if you're called a glutton, say. But now, if you want to define something, should you call it by its own name or by the name of another thing?

[7:31] Yeah. Why Why that? Because you want to know the reason. You're not trying to move your emotions. Okay, and it's there for it. Not so clear. I may say, "What is a pig? " Right? What am I asking for? It's not so clear, right? And obviously, if I use the incorrect name, if I say, "What is a cat? " and I'm asking about what is a dog, that's entirely misleading, right?

[7:55] But even if I'm using the figurative thing, right? You know, what is a pig? You know, it's not as clear as the question, "What is a glutton, Right? Okay. So the logician then, when he names a thing and uses a name to ask for a definition, he wants to use the thing's own name, right, and not the name of another thing, not even the figurative naming. That's clear enough.

[8:32] Now, having seen a distinction here between calling a thing by its own name and by the name of another thing, then on page four we can raise a little question, right? Okay.

[8:51] Are we going to define a thing by its own name or by the name of another thing? It seems like you got a division there, right? And every name is either the name of the thing or it's the name of another thing, right? Okay. The purpose of my name, and all these other names are names of other persons or other things. Okay. Ah, now if you were to define a thing by its own name, then you'd be violating that rule of logic you learned in grade school and high school, right?

[9:29] Because you do not use the name of the thing being defined, right? But you can also see the reason for that rule, right? If you ask me, "What is a dog? " and I say, "Well, dog is a dog. " That's a true statement, but I don't make dog any more known than it was to begin with. A rose is a rose, and a rose is the poet is supposed to have said, right?

[9:52] But if you call it by the name of another thing, right? Well, either use an incorrect name, so far as to define dog by, let's say, cat, right? Or divide, define dog by triangle. That would be obviously more than useless, right? But can you really define a thing by metaphor?

[10:20] A wife or a lover is a honey. We tell you what they are. A glutton is a what? Pig. A pig means a four-footed animal with a tail and a snout. Is that what a glutton is? No. So it doesn't really tell you what it is, figurative name.

[10:44] And incidentally, you can't use metaphors to say what a metaphor is. You use metaphors to exemplify a metaphor, but you can't use metaphors to say what a metaphor is. And when you explain what figurative speech is, you don't use figurative speech, except a way of example, but not to say what it is. So you seem to be kind of dilemma, right? Either use the thing's own name to define it, or use the name of another thing.

[11:20] And there's an objection to both. What? Alternatives, right? Okay. So how do we get out of that little dilemma? But what distinction do we come to, which is the untying of this dilemma?

[11:43] Yeah. The expression "its own" or "my own," "your own," "his own," "her own," right? Our own, even. That expression has actually what? Two meanings, right? And the first meaning of "my own" is what belongs to me alone, right? Like my own head, right? My own nose. No one else breathes through this nose. I don't even breathe too well myself. Okay. My own. Teeth, right? Okay. And it's always something important to keeping your own teeth, right?

[12:24] Okay. What's the second sense of one's own, his own, her own, your own? That sharing common, so we can speak of our own. I can speak of my own country. Yeah. But yet it's also your country, his country. Yeah. But yet it's still mine. Yeah. So I would speak of my own mother, even though. She's not my mother alone, right? They have brothers, and sisters? I could speak of my own daughter, even though she's not my daughter alone.

[13:03] She's my wife's daughter too, okay? And you know, we say to the kids, the neighborhooders, you know, you're this, you're not. Go home to your own house, okay? Why don't you, you know, mess up your own house? You hear these things all the time, right? But that child is not only his house; it's his mother and father's house, and he's got brothers and sisters. It's their house, right?

[13:32] Okay. Now, this is a distinction that we can make not only in logic, but we can make it in what practical philosophy. It's very important. As a philosopher, what is my good?

[13:54] I might say it's truth, right? But is truth my own good, as a philosopher, and in what sense, of my own? Second sense. Yeah. It's a common good, right? Now, common good in the strictest sense is a good that can be shared by many at the same time and with no diminution, right? So if I understand the Pythagorean theorem, it doesn't prevent you from understanding it, right?

[14:28] If anything, my understanding it might be a help, you know, to your understanding, right? But if we have an apple pie in common, right? If we, you know, put our money together and buy an apple pie,

[14:44] then we can't we can't be sure that that. No one of us is going to get the whole apple pie, right? Okay. So that's not a common good in the in the fullest or most perfect sense, right? Okay. Or if we have, let's say, a a computer in common, right? But we can't both what use it at the same time, right? Huh? Or we have a chair that doesn't belong to me.

[15:09] You can sit in it too. Either one of us can sit in it, but we can't both sit in it at the same time. Okay. But truth is very much in a very perfect sense a common good because my knowing a truth in no way prevents you from knowing that truth. If anything, it can be a help to your coming to know it, right? And

[15:30] the same way with, if we're talking with God, right? Huh? The first truth, my knowing and loving God in no way prevents you from knowing and loving God. If anything, it should be a help to your knowing and loving God, huh? Okay. And it's interesting that my greatest goods, like truth or God Himself, right? My greatest good is not the good that belongs to me alone, right?

[15:58] Okay. And the same way, you know, as as as a parent, our greatest good is our children, huh? Okay. And as a citizen, you know, the common good of the country, right? As member of the basketball team or the football team, the victory, right? Huh? You know, the victory is a good that we all what everybody in the team shares in, right? Okay. So my good as a member of the team is victory in the second sense of my good, right?

[16:29] So it's very important to see that distinction, huh? Otherwise, when you defend your country, say you wouldn't be acting for your good; it'd be simply a slave or something, right? Okay.

[16:45] When I defend the truth in the way I'm defending my good, but not my private good. Well, a lot of people are stuck on that first meaning of my own. That's why I put them in form of objection because at first, you know, people don't see a way out of that, and because they're kind of stuck on the first meaning of my own.

[17:13] Okay, so that's the solution. But as I say, it's it's a important distinction for other parts of philosophy as well as for logic. huh? I have a question on page 5. I wonder if there's a problem in the text, maybe a typo or something? Trying to figure out. Page five, the second full paragraph, beginning the role of we in in. Okay, then a couple sentences down where it says induction shows.

[17:44] Induction shows that this is a we missing there or something. Induction shows. Yeah, the we. Yeah. Yeah. Lobsters is the kind of thing. That was an example of induction for him. Yeah. Yeah. Okay. I notice there at the end of that section there, the next paragraph.

[18:23] You know, when I call a dog an animal, am I calling it by its own name? In a second. Yeah. Yeah. Yeah. Because the dog is an animal, right? Yeah. Okay. But it's not its own in the sense that's the name that distinguishes a dog from everything else, like a cat and horse and so on.

[18:48] So we're going to define a thing by its own names in the second sense of its own, right? But that means then names that are common to it and something else, right? Or a name that is said of many things, right? Okay. Now we say name said of many things. The word many here has you know two meanings.

[19:22] Sometimes we oppose many to few, and sometimes many to what one, right? So when I say it's a name said of many things, I mean many is opposed to one, right? It's said of more than one, right? Okay. Now, if you think about the word definition itself,

[19:46] it comes from the Latin word finis, meaning end or limit, and the Greek words for definition, like horos and horismos, which is word horizon, they come from the Greek word for limit or end too. And this fits in a sense what a definition is supposed to do: is supposed to put as it were, draw a line around, right, the thing you're defining, and separate it from everything else.

[20:15] And just as the city limits of, let's say, Worcester, right, should contain every part of Worcester within them, right, but no part of any other surrounding town, right. So likewise, the definition of a thing should draw a line around that thing and separate it from everything else, but not include anything else within it.

[20:45] So it's a very precise idea, the idea of limit. It contains neither more nor less than that which it is a limit. And you know, if you go back to the Latin, you know, it had a concrete meaning in daily life, where a farmer would define his field when he put up what a fence around there, right?

[21:08] And that fence should fence in only my property, right, and not anybody else's property. But the question is then, how can you define a thing by names that are common to it and what other things, right?

[21:30] That seems to be contrary to what a definition is supposed to do, right? It's supposed to fit just this one thing. And if you

[21:41] form the definition by names that are common to it and something else, how are you getting something that fits just this one thing? What's the solution to that problem? Combination. Yeah. The combination has to fit just that one thing, right? Okay.

[22:03] So when somebody tries to define something, you often see, you know, Socrates will see if the definition and the thing being defined are what they call convertible, right? Okay. Now, convertible in logic has a different meaning than convertible instead of the automobile. Okay. A and B are said to be convertible if every A is a B, and what? Every B. Yeah. Yeah. And the definition should be convertible with the thing.

[22:38] Being what defined right. So if equilateral and right-angled quadrilateral is the definition of square, right? Then every square should be an equilateral and right-angled quadrilateral, and every equilateral and right-angled quadrilateral should be a what square, right? So you'll see sometimes in the dialogue, Socrates turning around somebody's definition, right, to see if it is in fact what convertible, right? Sometimes in class, you know, I ask the student, "What is a chair, right?"

[23:21] And maybe they'll come out with something to sit on, right? They say, "Well, every chair is something to sit upon, right?" But is everything to sit upon a chair? Because a bench might be something to sit on, a saddle, but these are not chairs, right? So you have to add something before this speech is convertible, right? That's one thing you check, right? It's kind of the first thing you expect of a definition, is that be speech that is convertible with the thing being what defined.

[24:01] I make an interesting comparison there to pinpointing, you know, a target. Let's say you want to bomb a target or you want to go someplace, and you give the longitude and you give the what latitude, right? Now if you stop and think about the longitude is really a line, right? And there's on that longitude as many points as you want. So in a way, to give the longitude of a point is to give what it has in common with an infinity of other points, right?

[24:35] Now, how does that help you to pinpoint something, right? By telling what it has in common with an infinity of other points seems crazy, doesn't it? And likewise, the latitude gives what that point has in common with an infinity of of other points, right? But there's only one point that has both that longitude and that what latitude, right? So it shouldn't be so surprising, you know, that in a definition, right, you can what have a combination of names, right, that fit only one thing, right?

[25:14] So going back to the example there of the definition of square, quadrilateral is a name common not only to square but oblong and rhombus and rhomboid and trapezium, right? And equilateral is a name common to the square and the rhombus, like a jerk square, you know. And right-angled is common to the square and the oblong, right? But the combination of these equilateral and right-angled quadrilateral seems to fit only what the square, right?

[25:55] Aristotle's talking about tragedy and comedy, right? And the epic there in the beginning of the Poetics, and he takes the example of the great epic writer who's Homer, right? And Sophocles, the great tragic writer, Aristophanes, the comic poet, right? And he says, well,

[26:21] Homer and Sophocles have in common that they represent great men, the downfall of great men, and so on. But Sophocles and what Aristophanes have in common that they represent things as acted out rather than simply narrated, right? Okay. And then he starts to combine these things, right? So in the definition of Tragedy, there'll be something in common with epic, right? Representation of serious things of men greater than us, right?

[26:55] And something to have in common with comedy, right? That it represents things now, not simply by narrating them, but by acting them out on the stage and so on. But the combination of these differences are going to fit only what tragedy, right? Aristotle defined tragedy as a likeness of an action or course of action that is serious, complete, and of some magnitude. In sweetened language, right? Acted out rather than narrated, right?

[27:28] But acted out as a common comedy, as representation of an action that is serious, complete, and of some magnitude, with epic, right? But the combination of the two fits only what tragedy, right?

[27:46] Now notice, huh? If each name in the definition is common to the thing being defined and at least one other thing, right? No name represents a completely distinct knowledge of the thing being defined. But each name represents a somewhat confused knowledge of the thing being defined, because no name separates it from everything else. But as you put the names together, you go from a confused knowledge of what you're defining to a knowledge in which it is separated from everything else.

[28:27] And again, you know, you can see how the natural road enters in there. Right? Natural road is from the confused to the distinct, and the definition takes you from the really partial, confused thoughts about the thing being defined to a what altogether distinct, notion of what the thing is.

[28:56] So now we come to the point where we want to talk about name said of what many things Is your name common to many things. huh Well what you were just saying is, is that always true?

[29:13] Some terms like rational, which well we have to define rational, that would be composed. We see it was kind of common to give as an example of a definition in logic, the definition of man as rational animal, right? But it's not really a good example in this sense that it doesn't exemplify what you're going to find in almost all definitions, huh? That no name it really fits just the one thing, right?

[29:47] Of course, rational is actually taken from a property of man, And that's how you get something convertible with man. We'll talk about property later on. But if you go back to Porphyry, right, you always give, as an example of a definition of man something like a rational mortal animal, right? Of course, with the opinion of the Platonists, right, that there were immortal rational animals, right. But then, no part of the definition belongs only to what man, right?

[30:22] So the fact that they take rational animal as an example there in logic books is kind of a sign of their misunderstanding or ignorance, really, of logic, right? Okay. And when Porphyry defines difference, we do here. It's still something common to what many things other in kind.

[30:47] So we're down now to the need to talk about names common to many things or names said of many things. Now, Albert the Great, in his logical works, he says the first thing we need to talk about in logic is the universal. Okay, but this is more sensible, meaning more, more sensible, right? To say the first thing we really have to talk about in logic is names said of what many things, names common to many things, and even the name of the thing being defined is common to many things.

[31:19] You don't define Socrates; you define man. You don't define Lassie; you define dog, right? You don't define champion; you're not Bucephalus, but horse, right? So even the name of the thing being defined is a name said of what many things, and even more so the name set inside the definition. So now we have to talk about name set of many things.

[31:46] Now, the fundamental distinction of name set of many things is the. We use Latin words here. Names said of many things, with. Yeah, he'll tell us exactly when he needs this because it might take a little bit. Okay. The fundamental distinction now of name set of many things

[32:25] is whether you have one meaning in mind, right? Whether you have the same meaning in mind when you say this one word of many things, right? Or whether you have what many meanings in mind, right? Okay.

[32:50] Okay. Sorry for that. Okay. Now notice, huh? Most names probably have many meanings, and but even if a name has many meanings, you can say it of many things with one meaning in mind. Take the word bat, for example. The word bat is equivocal in the sense that it has many meanings, right? And could mean the piece of wood used in baseball, right? Or could mean the flying mouse that's in the Belfry, right?

[33:35] Okay. And if it were said of those two, it'd be said of them equivocally, right? Because you wouldn't be calling this piece of wood a bat, for the same reason you call this. Flying mouse a bat, right? You don't have the same thought in mind, the same meaning in mind. But if you said the word "bat just of, let's say, three baseball bats, then that word would be said what univocally, right, or with one meaning.

[34:03] Okay. And we use the Latin word Univocal or univocally, the adverb, for with one meaning, right? Okay. So we can say that a name said univocally of many things is a name said with one meaning in mind of many things, right? You have the same meaning or the same reason, you might say, right? Calling each of these the same, right? So the word "man" is said of each of us, right?

[34:36] Is being said univocally, right? Each of us is being called a man because we're a animal with reason, right? Okay. Likewise, if "animal" is being said of man and of dog, it's being said univocally because you have the same meaning in mind. It's a living body with sensation. Okay. If quadrilateral is said of square and oblong and rhombus and rhomboid, it's said univocally because you have the same meaning in mind.

[35:07] It's a plane figure, a rectilinear plane figure contained by four straight lines. Okay. Now maybe it's not in this text here, but maybe sometime we can talk about equivocal names. Okay.

[35:31] Let's maybe make a little footnote here, a little addition. Name equivocal by chance, and name equivocal by reason. Okay. That word "bat" instead of the baseball bat and the flying mouse, it's by chance that they both are called a bat. Some of them look at the baseball bat and the flying mouse, the feeder mouse, and say, "I see they have something in common, or I see some connection between these two," right?

[36:23] Um. But now, sometimes a name is said of many things equivocally by what reason? There's reason why they have the same name. So if I say, for example, I see you, right? Then I say, now I can see my son now, meaning I what? Picturing my son in my imagination, is that by chance that I call both of those seeing?

[36:56] Here I can see a certain likeness of my picturing my son, right? To my seeing, right? When I dream, my imagining, I think, is like seeing, and deceived by the likeness. So there's a reason why we both call seeing, right? And so we speak of such a name as being equivocal by reason, as opposed to something equivocal by chance. Now these words that are equivocal by reason are very important in philosophy, especially they're important in wisdom.

[37:35] In fact, all the key words in wisdom are equivocal by reason. But you could say the words in the axioms are all equivocal by reason. It was Aristotle who discovered this. Discovered that the most common words are all equivocal by reason. These are the words used also in the axioms, and that these are the words that are used especially in wisdom. In fact, as one of the 14 books of wisdom, there, 14 books of metaphysics, is devoted to distinguishing the meanings of the key words in wisdom and in the axioms and everywhere, right?

[38:16] Words are equivocal by reason. And we had a couple examples here earlier. We talked about the word to see, and to do this now again, right? But we had a little text of Aristotle where he talked about the word before, right? The word before is a word that is equivocal by reason. And as you know, reason looks before and after. There's order among those four meanings of the word before, before in time, before

[38:46] the discourse of reason, before the sense of better. So in a word that's equivocal by chance, there's no order among the meanings. But in a word that's equivocal by reason, there's going to be a certain order and connection among the meanings.

[39:07] So some people say that logic is not philosophy in the same sense that geometry or natural philosophy are philosophy. But it's a tool for acquiring geometry. You can see Euclid is starting with definitions and statements, and then he has syllogisms, right? So it's not purely by chance. It's not purely equivocal or by chance that we call logic philosophy. If it's not philosophy in the same sense as geometry, natural philosophy, and wisdom, it's a tool for acquiring logic.

[39:46] I mean. Geometry, natural philosophy, and wisdom. So there is a connection between the two, right? But that word convertible, right? That seems to be almost purely equivocal there. Kind of an equivocal feel, right?

[40:06] Definition. Okay, now we can come back sometime and talk more about name equivocal by reason, how that takes place. This is the fundamental distinction: name equivocal by chance and by reason. Now, sometimes a name is equivocal by reason. They'll want to call analogous, right?

[40:33] And sometimes the one that's equivocal by chance, they'll call just equivocal or purely equivocal. I think it's better to call them by chance and by reason. You have more people to talk to about that. An analogous there is actually taken from one kind of name equivocal by reason, so you tend to get too narrow an understanding of all the various ways names are equivocal by reason.

[41:15] The most common mistake in thinking Aristotle says in the book called On Sophistical Refutations is for mixing up the senses of a word, and you do so mainly with the ones that are equivocal by reason because the meanings that are said in similarity or close connection you mix them up.

[41:37] What's an idea in English? What's an idea? Read John Locke. He's always talking about ideas. What? Yeah. But sometimes an idea is a what? Image. Yeah. Yeah. Yeah. So if the girl says the guy don't get ideas, yeah, she probably is using ideas in the sense of what? Image, right? Yeah. Okay. He's not doing too much thinking now, right? Right. But he's imagining. But when we say the philosopher's ideas, it should be thoughts and not just images.

[42:17] So Locke is often confusing idea in the sense of image with idea in the sense of what? Thought, right? Okay. But that's probably what equivocal by reason, huh? And that's why Thomas, you know, spoke of how the Arab philosophers actually make reference to that. They speak of the first act of reason as kind of an imagination through the understanding, right? Okay. There is sort of likeness there, right?

[42:43] When I imagine something, I form an image of it. You may think about something from a thought. Image and thought are not the same thing. If you study John Locke, you'll see that he really confuses the two. months.

[43:07] Okay. And when you define something, you want, to first know what mean you have in mind, like it down to one meaning, right? So, what we're going to talk about next is name said univocally of many things, right? Okay. And the first book really that in the Greek philosophical tradition has come down to us as a part of logic was a book written by Porphyry. right And Porphyry was one of the Neoplatonic philosophers later Platonic philosophers.

[44:14] These are ours. there, ours, these. Porphyry wrote a Isagoge, which is the Greek word for introduction. He wrote an Isagoge introduction to Aristotle's Categories, book that Thomas referred to. The only book that's come down to us from Aristotle for the logic of the first act is this book called The Categories. We'll see what it's about. huh? But Porphyry wrote this for a student who was having a hard time understanding the Categories of Aristotle.

[44:46] So Porphyry wrote a book which was called the Introduction to the Categories. And what he actually does in that book is to distinguish the names said to denote things. But as he says in the proemium to his Isagoge, usually see this having English form Isagoge meaning introduction. You'll point out that the Isagoge is useful not only for understanding the categories, but for definition, he says, and for division, and for demonstration, which is the most perfect kind of syllogism.

[45:30] And so we'll see that when we get, we go through this how it's useful. But especially at this point, we're interested in the view to definition, right? Okay.

[45:45] Now, Porphyry divides these names said to denote things eventually into five, but we can arrive at those five by division. Either the name which is said of many things signifies something like inside their nature, right? Meaning by nature, not what they are, or it signifies something outside their nature, right?

[46:28] So names said to denote many things signifying something inside their nature. Mean by nature what they are, or it signifies something outside their nature.

[47:02] So, if you had three triangles and you said triangle of them, or you said, or generally plane figure of them, or figure, you'd be saying something that signifies something inside their nature. But if you said green of the three triangles, you'd be signifying something what outside their nature, outside of what they are.

[47:30] This division is obviously exhaustive, right? Then, either signifies something inside the nature of the many of which it is said, or it signifies something outside the nature. There is no other but alternative, right?

[47:48] This number can be divided by either, right? Now he's going to subdivide. We're going to subdivide both of these. And the first here, we're going to subdivide into three, and the second we're going to subdivide into what two? Almost

[48:19] great rule, two or three. Now, the first word that, or first name that he talks about, is called in Greek the genus, and Latin you have almost the same word genus, right? And in English, we take over the word genus from the Latin, right?

[48:50] Now, the genus, the name said of many things. Of many things, other in kind. It's a name signifying what it is. Now, I ask in class, "What is a dog?"

[49:46] Students will usually answer, "it's an Animal," right? Okay. Now, animal there is an example of a genus, right? It's a name said with one meaning of many things, other in kind, like dog, cat, horse, dolphin, right? It signifies what it is, right?

[50:08] It signifies it in a very what general way. We'd say in English, right? Very general, not to the logical degree, to the genus, right? Okay. Again, why do we tend to start with the genus?

[50:26] Because we know first confused. Yeah. Because the genus represents a confused understanding of what the thing is, right? Confused because it's understanding what it is in common with many other things, and therefore it's not distinguishing one of those kinds from another.

[50:49] I ask students, "What is a sonnet?" And they'll say it's a poem, right? But the sonnet is only one what kind of poem? There are many other kinds of poems. I said the sonnet.

[51:09] I ask somebody, "What is a tragedy or a comedy?" What are they going to say? Yeah, it's a play or a drama, right? Okay. But play or drama, as an example, can be genus, right?

[51:25] Um. When I say reason is an ability, right? Well, no, the only ability. There are many different kinds of abilities we have, right? Reason may be very important, but it's still one of many abilities we have. It's a name said with one meaning of many things, other in kind, signifying what it is. I think I'm giving myself room here, I think I'm going to release this temporarily.

[52:16] Now the second name we talk about is the name of one of these particular things that are in the genus, right? Okay. Now the Greek word they use for that is eidos, right? And the Latin word they use is what species.

[52:41] And both eidos in Greek and species in Latin, they have the sense of a form, but of a form you can what see. Eidos is related to the Greek word eidēnai, meaning to see, right? Species is related to the Greek word speculatin, speculation, speculor, to look, right? So it's the form or shape you see, huh? In English, we tend to borrow either the Latin word species, right, or sometimes we simply use the word what form in English, right?

[53:21] Okay. So species is the one we usually use in logic. So species is the name of a particular kind of thing under a genus.

[53:52] Okay. So if the the genus is animal, then cat and dog and horse and elephant would be what species, right? Species is one of those funny words that is spelled the same way, I guess, in the singular and the plural. Okay. Um,

[54:14] if the genus is what government, right? Then maybe monarchy and oligarchy and democracy and so on would be different species of what government, right? Then. But then, she might speak of them as to be forms of government, right? Okay. If play or drama is the genus, maybe tragedy and comedy are the species, right? Maybe there's a another species in between tragedy and comedy.

[54:53] If quadrilateral is the genus, then square and oblong and rhombus and rhomboid, right? And trapezium are the species under that genus, right? The names of the species, or the forms. of quadrilateral Sometimes we don't have a name, like square, but you could say. In that case, use a speech in place of the name. You might say that equilateral triangle and isosceles triangle and scalene triangle are the species of what triangle, right?

[55:32] We don't have a name for equilateral triangle. Virtue and vice are names of species under the genus what? habit habit, okay, good habit and bad habit, and so on.

[56:01] Now, very often, you find that two is not enough, right? And Aristotle points this out in the first book of Natural Philosophy. And our language is a sign of that. Three is the first number about which we say all. Now, if you think about these two names, can you see the need for a third name?

[56:37] Yes, because the species is is more particular than a genus, but doesn't say. The genus doesn't tell you distinctly what the species is, right? So, if I ask you what is democracy, and you say it's a form of government, right? Well, so is you know, oligarchy. So is monarchy, right? Okay. They ask you what is, you know, a tragedy? What's a play, right? Or a drama? So, so is comedy, right?

[57:08] Then. So there is something in species in addition to the what genus, right? And you need a name to bring out what the species has in addition to the what genus, right? Okay.

[57:25] Or since these species are things other in kind, you need a name that would signify what distinguishes one from the other, what separates one from the other, right?

[57:40] And so this is the third name, which is appropriately called difference. Sometimes they call more explicitly species making difference, right? But usually just call for short the difference species making difference.

[58:07] Now, Porphyry gives when he gets to the species making difference, he gives actually three. In a way, definitions of difference, right? But two of them are in terms of the role of difference, right? The role of difference in defining a species, and the role of difference in separating one species from another. So, as you can see in the text, there,

[58:42] you know, say the difference is the name of what the species has in addition to the genus, right? Okay. A species is the name of what separates one species from another species under the same genus. But those two definitions are of difference in terms of its function in defining something, right? And its function or use in dividing a genus into species, separating species.

[59:23] So, but if you stop and think about it, it's going to be the same name that separates one species from another that is also used to what define the species, huh? Take again the simple example there. Take the genus quadrilateral, right, huh? Okay.

[59:48] Well, equilateral, say, or right-angled, then these are names of what some of the species of quadrilateral have in addition to being four-sided, right? Some of them, in addition to being four-sided, have those four sides what equal, right? Some don't, right? Okay. Some of them, in addition to being four-sided, they have those sides being at right angles, and some do not, right? Then. So right-angled is both the name of something that, let's say, the square and the oblong have in addition to being quadrilateral, but right-angled also separates square and oblong from rhombus and rhomboid and even trapezium, huh?

[1:00:42] Okay. Likewise, equilateral, right, are something that square and rhombus have in common, right? The rhombus is like a square that's been jerked, right? So it's not right-angled, but it's still equilateral. They're just square. And

[1:01:08] why the rhomboid is is what an oblong has been what jerked, right? The way I remember that mnemonically is the rhombus ends in S, S is the first letter in square, so the rhombus is like the square, and that's how I remember. But the rhombus equilateral separates the square and the rhombus

[1:01:38] from the oblong and the rhomboid, and from the trapezium too, say. Okay. So the same name that is a name of what the square and the rhombus have in common, or in addition to being quadrilateral, right, is also a name that separates the square and the rhombus. From the other what?

[1:02:06] Yeah, the other species of quadrilateral, right? So he looks at both the use of the difference in defining, right? Because in order to complete the definition of square, you've got to add to the genus what square has in addition to being quadrilateral, right? And that's both equilateral and right angle, right? But he also speaks of its use in dividing a genus into species. Okay. And actually, the word "difference" is using the Latin word, right?

[1:02:43] The Greek word is etymologically the same. The Greek word is "diaphora," but they come from "phero or "phora," which means to carry, and "dia," which means apart. So when you say quadrilateral, all these things seem to be what together, right? And then the difference what carries them apart and separates them, right? Equilateral separates square and rhombus from the other three, right? And then you know, right angle separates you know, oblong and square from the rest, right?

[1:03:19] And the combination, as we saw, of equilateral and right angle separates the square from all the rest, right? Okay. So it's in fact the same name that separates species under the same genus, right? And that is also the name of what those species have in addition to the genus, right? So it's both the name is going to be used to complete the definition, right? And the name is going to be used to divide a genus into species.

[1:03:55] Okay. You can see that Euclid uses the difference both to complete the definition of things like square, right? But also to divide quadrilateral into the various kinds of quadrilateral.

[1:04:14] But then Porphyry gives a definition of difference, going back to what we're dividing, right? Okay. And he says that it's a name said with one meaning of many things other in kind, but signifying instead of what it is, signifying how they are, but they are.

[1:04:43] It's important to see that it signifies how rather than what, right? But you have to add signifies how they are, but they are, because it's an essential difference, okay? In the very nature of the things, what they are. As opposed to just a how by itself, it might be something accidental, like "How are you today?" "I'm well today," or "I'm sick today," or something like that, right?

[1:05:08] But this is how they are, what they are. So it'd be the same, have the same definition as genus, except for the last part. Instead of signifying what it is, signifies how.

[1:05:32] It is what it is. That's for species and genus. That's the difference now in the definition of difference. Now Porphyry is not yet here in the following chapter, but not yet given the definition of species, as a name said of many things, right? And we'll see if we can point that later on.

[1:06:07] After we discuss how the same thing can be both the genus and the species, it's really only what we call the lowest species, but that it's another thing before we see that. So you have the definition there of difference and of genus as names said identically of many things, right? Signifying something in the nature, but the one signifies in a general way what they are, and the other signifies how they are.

[1:06:37] Now, as we go on here, right, you can see how those three names are very important for talking about definition, because the species is the name of what is being defined, and the genus and the differences are names, right?

[1:06:59] Used to define it, but the first and most basic name is the genus, right? Then you have to add usually two or more differences, right, to complete the definition. So we've we've separated here, right? The name of the thing being defined, which is called the species. You're always defining a species, a particular kind of thing, right? And the name that begins the definition, and the name that completes the definition.

[1:07:31] This we've said before. Back then, I went to find what a name is, right? We have to distinguish between the name of the thing being defined and the names used in the definition, right? And even among the names used in the definition, between what genus and the difference and the order among them, that the genus is being the fundamental name, right? And the difference is determined how it is what it is.

[1:08:07] Any question about that? Those three names. Now, since the other names signify anything, signify something outside the nature, right? Outside, but the thing is, it might seem superfluous to subdivide those names, right? Because the definition is to say what the thing is, right? But there is a reason for subdividing those other names, even as regards definition, but also as regards later on demonstration. And you see that once we subdivide those names, which they're Just gonna erase that.