Logic (2016)
Lecture 15: Continuous and Discrete Quantity: Definitions and Measures

Transcript
================================================================================

Sorry, I was going to do this time going up, you know. Up at the high guys, probably point. You can see the closeness here of quantity to what substance, right? That's divisible, right? Quantitatively to things that can be separated. Substances, right? Of course, you get some of the lower kinds of life. You can divide some worms and both parts seem to move around, right? That they're alive, right? And some plants can be divided, right? Maybe divide me up, you know. We'll make up a number of substances, right? That would be a lot of liquid, huh? Okay, but Aristotle does what in the chapter there, right? He divides them first by what? Continuous, right? As parts that meet a common boundary and then parts that do not meet a common boundary, right? Sometimes you point out that in natural philosophy, there's another definition of the continuous. And then, is this true about discrete quantity? Can seven be divided forever? I can divide it into two and five or three and four and divide three into two and one. Now, can you divide one? Sometimes my math gets a little mixed up in that, right? But the one that composes a number, it's simpler than, what? A point. Because a point is indivisible, like one, but it has, what? At least position. But the one in number, it's, what? Indivisible, but it has no, what? No position, yeah. Sometimes. The platonists would say a point is one with position. Because it's such a thing as two and a half points. So a number, continuous quantity, is not divisible forever, right? But why are there these two definitions of the continuance? That whose parts meet at a common boundary, which is the definition of continuous quantity in the categories, and then the definition in natural philosophy, that which is divisible, what? Forever. Yeah, yeah, yeah. That whole is to parts, something like form is to what? Matter, right, huh? Matter, what's the definition of matter as a cause, huh? What's that from which, right, something comes to be existing in it, right, huh? So the wood is the matter of the table, it seems to me, right? The wood, the table comes from wood, and the wood it comes from is in it, right? And parts seem to be in a composed hole, anyway. The composed hole comes to be from its parts, and they are what? In it, yeah. So parts seem to be like matter, right? And the whole, like what? Form, yeah. Makes sense? Now why is it more appropriate, which is being defined by whole? Well, in the logic, right, it's parts meet a common boundary, and then they form the whole, right? So it's kind of defining it more in terms of its wholeness, right? Why in natural philosophy, it's divisible, what? So forever, you're going to parts, and parts, and parts, and parts, right? So a straight line can be, what, bisected, and the two lines resulting in that can be bisected, and this can go on forever, right? Okay? How do you know that a straight line can be divided forever? Well, notice, huh? So long as you get two lines from dividing a line, right? It can be divided again, right? Because a line can always be divided, huh? The only way that a division, right, could, what, come to a halt is if you divided a line into two, what, points. The point has nodding, and you can't divide a point into something, what, smaller, right? Okay? So, the only way the division of a line could come to a stop is if a line were composed of, what, two points, right? And then Aristotle argues that if you're making a line out of points, the points would have to touch. And if they touch, does a part of one touch part of the other? Well, no, the point has no parts, right? Does the edge of one touch the edge of the other? No, then the point would be a little circle or something, right? And not a point. So, the only way the two points can touch is to coincide, in which case they have no more link, two points touching, than what? One point, which is no link. Right. Which is not a line, yeah. So, when you divide a line, mathematically, anyway, you must always get two smaller, what, lines. And therefore, so long as you have a line, you can always divide it again. Case rest, right? But natural philosophy differs in the other sciences because it brings in matter, right, in its definitions, huh? So, it's more appropriate for natural philosophy to bring out that, what, definition, huh? Natural philosophy, of course, talks about motion, right, and time. And they'll be also divisible forever, right? Aristotle is a nice way of showing that length and time are divisible forever. He shows it both together, right? All I have to admit is that one body is faster than another body. So, the faster body covers a certain distance, right, in a certain time, right? And at the same time, the slower body covers a, what? Yeah, so now that you divide the distance. Now, the faster body would cover that lesser distance in less time than you divide the time. Just to alternate, right, huh? So, whatever time it took the slower body to go, the faster body would do it in less time. Whatever distance the, what, faster body went, the lesser body would do it in, what, we would do a lesser distance, right? So, it wouldn't be both divisible, but forever, right? And it's very appropriate for the natural philosopher to talk about, what, the division of continuous, right, into its parts. The kind of basic reason they give is that it's less like dividing it into its matter, right? And matter is what the natural philosopher has that the other sciences don't have, right, huh? So, Heisenberg is an actual scientist, right? But the logician is talking about what? So it's more appropriate for him to define it in terms of its wholeness, all the parts come together, right? To form the whole, right? It's very subtle. It's kind of amazing that the natural philosopher and the logician both have a definition of the continuous, right? It's not the same definition, right? It's amazing, amazing. I suppose there's some connection between the two definitions, right? Because the parts always have a common boundary. You can always divide it the boundary, right? Very subtle. Well, that's in this texture. You can read it for yourself. I'm not sure what you're saying about the difference in the two definitions, right? There's a little thing about part there, you know. When you read Euclid, huh? He'll say that two is a part of what? Six, right? But four is not a part of six. He's using part in what sense? Measure. Yeah, yeah. You measure six by three twos, right? But you can't measure six by four and see how many it is, right? Aristotle mentioned that he used the word part, right, in his time even, you know? And he'd find that in Euclid, huh? But that's not so much important for us right now. This is text in Latin, then, now, which is about the difference between those two. Notice what Thomas says there in page four there in the Latin text there, where we talked about the two definitions we've talked about here. At the top of page four there, the second paragraph there. And so, sufficiently, right? And so, sufficiently, right? Convenienter. Hec definitio ponitir here. Allia autum in what? The categories in predicamentis. Quia consideratio naturalis versater, cerca materiam, right? Consideration of the addition is about the ratio of the species, huh? We talked about species even in the Isogogi, right? This next text is the one that's very important, huh? If we see any difference between the logician and the, what, wise man, right? Remember that problem we had about substance, huh? Aristotle, in the categories here, he speaks of first substance and second substance, you know? What would the wise men say about that? That's just in your mind, Aristotle. It's a real distinction of substances in the real world. It's animal, really a different substance. That's what a dog is, an animal, right? But the logician is concerned with things as they are in our, what? Our reason, yeah, in our mind, our knowledge, right? And we have not only Socrates, but even more so in recent years, you have the universal. Teacher Albert the Great, huh, said the first thing to consider in logic is universal. Well, Aristotle will point out that it's not substance as much as, what, Socrates or Plato or you, but it signifies what Socrates is or what is and so on, dog and so on. So it's substance in some sense, right? But that's the kind of way substance is in our mind, right? There's not only Socrates in your mind, but even more so in a sense, Socrates, the species he belongs to and the genius he belongs to and so on, right? So, very subtle distinctions here, huh? Now, what does Thomas point out in this text here from the fifth book of metaphysics here that we're going to talk about? It's new here on page four. It's the beginning of it, huh? It should be known, huh? That the philosopher in the predicaments, right, lays down that time is a quantity per se, right? Right. When here he lays down that it's a quantity, what? Per accidents. Because there he distinguishes the species of quantity according to diverse, what? Measure, yeah. Another ratio of measure has time, which is an extrinsic measure, and magnitude, which is a, what? Intrinsic measure. And therefore they are laid down there as other species of quantity, right, huh? But here he considers the species of quantity as regards the very being of, what? Quantity. The wise man, right, huh? And therefore those things do not have the being of quantity except from another. He does not lay down here as species of quantity, but quantities per oxidants, right? As motion and, what? Time. For motion does not have a, what? Then time and magnitude. And therefore neither here nor there is it, what? Laid down to be a species of, what? Quantity, huh? Place over is laid down there as a species of quantity, but not here, because it has a different ratio of measure, but not another one of, what? Quantity. What the hell does that mean, huh? Well, what is a place that you studied in a natural philosophy? We haven't done that, did we? But Aristotle would define it in terms of the, what? Inner surface, right? Of the containing body, right, huh? So if you have a bottle of wine, right, huh? The wine is contained in the inner surface of the, what? Bottle, right, huh? The surface of the, what? The surface of the, what? The bottle is different from, what? The surface of the wine, right? But as to the kind of quantity it is, it's going to be really the same kind, huh? It's both, what? They're both a surface, right? Okay. But don't we, in a sense, make a separate measure of the two, huh? And they say, what do you say, Nina? Well, if you set up house, you know, sometimes, and you've got a wall there, right? And we say, well, we need a little more furniture in this house. Okay, well, let's go look at sofas, okay? And what would you measure? I want the sofa to fit the wall, right, huh? So I measure the, what? The look of the wall, right? And then I go down and measure the sofa, right? Bring my little thing with me, huh? So it's different measurements, aren't they? So there's some difference in the... measure, isn't it? To me, the same kind of what? Quantity, right? The length of the wall and the length of the, what? It's kind of a different measurement you make of each, right? Strange thing, huh? So the wise man's a little more picky about these things, right? He's interested in the being of the thing, right? When I buy a bottle of wine, sometimes I buy a one and a half liter and sometimes a three quarter liter, right? And one contains more wine than the other. They expect to pay more for the one and a half liter, right? It's like a double of what the other one is, right? You've got to know those things, right? The place is kind of like an extrinsic measurement. I don't go and measure the service of the wine. Now those things are kind of subtle, you know, beyond what he's doing in the chapter on quantities, kind of for the goodness of the doctrine. Now notice on page five there in the English now. In this text, we should also note Thomas' statement that Aristotle in the categories distinguishes the species of quantity according to diverse ratios of measure, motions of measure. Hence when Aristotle wants to show that logos, or speech, is a quantity, which is not as evidently so as number, huh? He points out that it is measured by the long and the short syllable, right? On page five there. So it's not measured by the same thing, is it? That and the number, right? The number is measured by what? By one, right? And in Greek poetry and Latin, I guess, goes by the long and the short, what? Syllable, right? So in English, though, poetry, it's the accented and the unaccented, what? Syllable, right? Thomas' prayer there, with communion there, seems to be going like what? Visus toctus gustus in te faldi tur. Visus, huh? Isn't the first syllable longer than the second one? Visus toctus gustus in te faldi tur, right? They tend to, what, not complete the last foot, right? In those ones, huh? So you, you, you, uh, use the term in clinic, they call it, they cut off the last syllable, right? Because you want to end on an accent or something or on that. Visus toctus gustus in te faldi tur. So you measure it by the long and the short syllable. That's not the way you measure a number, do you? So it's a different ratio of measure, right? But if you wanted to measure this room, would you measure it in inches? How many inches is this room? You'd measure it by what? Square inches, yeah. Yeah, yeah, yeah, yeah. If you're talking about a container, like the wine bottle, something like that, and you talk about, or a cube, you know, that kind of thing, you talk about what? Cubic inches or cubic feet or something, right? Like all these big, you know, water things, you know? How many? Gallons. Yeah, yeah. But you can't, you don't measure a line in square inches, you see? So it's not the same ratio of measure, right? How much can I take with a measure of the square feet? Yeah. This will cover about 150 square feet. Yeah, yeah, yeah. Now, notice that's here in the second paragraph. This is proper to logic because a measure is that by which the quantity or size of something is made known to reason, right? That's the definition of measure, right? That by which quantity is made known, the first sense of measure, right? Then they don't want to apply it, you know, the virtuous man is a measure of all. And logic considers things insofar as they are what? Any reason. Some Latin dictionaries give the word size as equivalent of measure. Hence, this addition considers the species or the genus of a first substance to be substance, calling it second substance. But the wise man who considers things as being does not. So likewise, he considers what have a different measure to be different species of quantity, which the wise man does not when their being is not different, huh? Well, notice how we said that the definition of the continuous in natural philosophy and the one in logic are not the same, right? And now we're talking about some things being quantities, right? In logic, but not in what? Wisdom, right? Or being substances, but not in what? For the wise man, right? There's no such thing as, you know? Man is separate from what? Socrates and Plato and Aristotle. Only your mind, Aristotle. Okay? But because your mind, what? Separates out what's common to those three, right? Each of them is a man, right? That's a substance in some way, right? So, in logic, we'll call that a substance, but a second substance, right? Wisdom, yeah. No such thing. Unless you're a Platonist, you think that man himself exists in a world of forms or something, you know? When you get through with Aristotle taking care of Plato there, then you can take care of Hegel, right? You know? Because Hegel tries to generate the whole universe from the notion of being, right? One thing produces this opposite, you know? And then you get this and this, and it's opposite, and so on. So it's kind of trying to generate the whole universe from the most, what, vague notion of human mind. Not very impressive, you know? But Hegel's better on, isn't he? When he gets down into talking about what the fine arts and so on, he's kind of interesting there, right? I used to argue with some of my colleagues there, you know. Hegel will put music before what? Painting is a greater art. And so I had some colleagues, you know, who were trying to say the painting is better, right? Because the painting's all there. You hear the music, it isn't all there, right? But, you know, Aristotle's in the politics, say, there, and he talks about what music you should listen to, right? And what paintings you should look at, right? He's very brief as to paintings, right? He's really very insistent upon what music, right? But which is more beautiful, music or the best music or the best paintings, huh? Both beautiful, right? Which is more beautiful? Give you guys an argument for you guys, huh? I get texted Thomas to show that Thomas thinks there'll be music in heaven, properly speaking. Thinks he were going with paintings? You have the vision. He said, I need a painting. What? What? Vision. So we all need paintings. Yeah, yeah, yeah. In terms, you know, in the bodies of the saints, they'll be beautiful, right, huh? You know? You need a painting for them. You got the Virgin walking around, or our Lord walking around, or the saints, right, huh? Can you imagine seeing Thomas up there, you know? The host of scribes following him. This is where he got me wrong, Wayne. Da, da, da, da, da, da. I didn't mean that. The arts that serve the liturgy, I think it puts music in the first place. Yeah, yeah. The music is the most important part. Yeah, yeah, yeah. The sight is the primary sense. It's interesting how it's the most important sense, you could say, the most useful for man. Sing joy for you to the Lord, all your lands. Sing with the Lord that has come before me. Joy for you. song with the lord is god he made us as we are his people of latin tins that's the division of the summa kind of chantillas right but it's putting it with the song right um yeah i guess the word uh songs has to have with music too right very much so the songs there's a musical instrument with right in fact even shakespeare's sonnets are taking for music right sonic when murray and i read mozart's music is even more beautiful than shakespeare's words trump's paintings the reason why it seems like there's a sort of a reverse of order all of us yeah right yes yeah i mean the eyes seem to be more important in knowing right what you see is the connection between music and the emotions and therefore between music and what the virtues right it's more relevant that way right about music and well he talks about music and education there in in the city right in the eighth book of the politics politics yeah yeah yeah not the ethics you know that i see that it takes the importance of music too right it always strikes me that historically yeah it seems to me you have the opportunity yeah yeah they don't even know once in a while so they must have had much more powerful yeah to appreciate something much less and much sooner they've heard better yeah than if we hear it we hear many many yeah yeah well you know some that can some of the performances of mozart you know where the audience you know they had to have the second movement you know the 22nd piano concerto you repeated you know they wanted to hear it again right you mean the concert itself i mean they would demand that i don't know how often that was done but yeah but uh see what i guess you most are you know at the end of the concert he'd sit down on the piano there and he'd improvise you know the melodies right huh and they'd be more than the concerts you know yeah so it's gonna mix you know you know myself was as i was a little boy there i used to like to find marches on the thing you know i still like marches you know and uh you know people would uh go down to west point you know sometimes there's a game down there you know but they'd go you know they could watch them the march but you're representing in the march there what the virtue of what courage and can in a painting can you represent courage as well as the march does they get the essence of courage yeah i used to play marches for my my son marcus he's a little boy you know and uh it's for heroes right and one day he said i want to be a hero too maybe being inspired by by these marches right you see in a way um you can you have a bad scene and a thing that's going to inspire courage in the way that the march does yeah yeah and i was always talking about the music that's going to move the emotions in a way that's in harmony with reason right now i know when i was getting very interested in classical music there and the suric asked me you know do you find it helps you to to control your emotions more you know that's he wanted to see what the effect is this rock and roll stuff is really crazy you know when it's first coming out and there's some place there down the east there where they're picking up these you know these chairs that uh you know they're closing them up right from those you know those chairs that fall flying through the air you know but there's the effectiveness of this crazy but music you know you go these mixtures used to have a song you know that i remember the words of the song song about i'm going to make a monkey out of you you know you know that's what music does it makes you you know it makes you kind of you know best you you know it's the wrong kind of music right but the good kind of music you know elevates the soul right now in a way that a painting can't quite do you know like i mentioned how mozart's last uh symphonies there you know he's representing magnanimity right in the 36th symphony and in the jupiter symphony right they're both in c major right that's the key of magnet but then in in the in the 40th symphony in the 38th symphonies he's uh imitating what courage right but uh there's two acts of courage one is to approach the the difficulty the threatening thing and the other is to is is that a patience right that in the 40th is more that and the 38th is more tell people it's feeble compared to what mozart does in the 38th symphony you know that's what einstein said about mozart and beethoven didn't he he says he said beethoven made his music right mozart founded him mozart's music always seems to have been a part of the universe it's kind of a very good couple right and i always compare it to my brother mark you know saying can you imagine fiction without roman juliet just had to be a part of it right you couldn't have fiction you know you just seem like to be a natural part of the world of fiction right you know that's the way einstein was saying right mozart's music you describe einstein you know and he'd hear somebody playing a little bit of mozart you know drop whatever he's doing you know you give a public lecture you know you get these stupid questions afterwards you know well what do you feel about all this and you know even already took out his lab then heisenberg was a great pianist you know that's how he got his wife she admired his piano playing you know don't think physically we have the same effect of our woman okay what time do you have to stop now um always talk about order don't we huh about the middle of page five there and the reason why aristotle puts number in discrete quantity before continuous quantity it's connected with this that we distinguish these by the species of what or the ratio of measure right for measure is found first or more perfectly in number since the one is simpler and absolute and indivisible, right? What do you use to measure length? You know, a foot? Oh, the king's foot? Or there's no king now. What do you do? But I mean, it's not as exact, right? They say that the meter there, which was used, you know, for centuries, is really, what, a bar in Paris, right? That's measure. Well, a metal meter is what can contract or expand under heat and so on. Not very exact, what? Temperature control, so it's comfortable. Oh, yeah, yeah, they've got to do a lot of things to prop it up, right? We don't have to worry about the one in number, right? You know, contracting or, you know? Yeah. That's very, very accurate, right? I was going to say, even the king's foot, you know, when he got older, it got bigger. Yeah, yeah. That's interesting that Aristotle has that order, right? He puts the discrete before the continuous, even though in the definition, you might say it's in the definition. The continuous has got a definition that's affirmative, you might say, right? And the other one that is, what? Yeah. Strange, isn't it? Most of the care that Aristotle writes in it, why does he do that, huh? I mean, it's because he's distinguishing these by the ratio of measure, right, that's being used. And the measure's more accurate here than there. Curious, huh? Okay, I mentioned in parentheses there, we'll see that when you get to quality. This is also the reason why habit or disposition is given as the first species of quality. Well, habit or disposition seems to be less fundamental than natural ability, right? But, no, it's the reason they give here, right? For by habit, one is well or ill-disposed towards one's nature. That comes first. There's a special reason why it's given that first. A number can be measured by the indivisible one, but a line cannot be measured by the indivisible point. So you've got to get some screwy length there, right, to make that. And what would be the length to measure by? It's kind of arbitrary, isn't it? By number, it's quite clear, the one, huh? You're going to measure every number. Now, prime numbers can measure other numbers too, but not all numbers can be measured by a prime number, right? But they can all be measured by one, and that's very exact, huh? That's striking because the difference is, you know. Why is continuous quantity defined affirmatively and the other negatively? Because affirmation comes before negation, right? You have to know what you're negating before you can understand negation, right? Yet he puts, you know, because of his recent affirmation, maybe we're sorted. But why is it continuous more known, it seems. Yeah. The number is a kind of an immaterial thing, right? I was talking to these students here about the soul there, and I was attacking McInerney, as I mentioned earlier, because he was confusing the etymology with the meaning, right, of the word philosophy. So I was saying, what is the origin of the word soul, right? I mean, the word psuche in Greek, right? Breath, yeah, yeah. You can have the idea of breath, wind. And why should they name breath? That's not the meaning of the word soul. But why was, that's the etymology, right? But why was, what is the connection between breath and the soul? Yeah, that's part of it, yeah. But, you know, we even call the angels the spirit, right? The same, you know, idea of breath or wind, right? Well, it's because air seems to be, it's a substance that's invisible. That's one reason they give. And the other is it's a substance that doesn't seem to have much matter. Yeah, yeah. I make ice cubes out of water every day. Well, not every day, but quite often. But you make things out of wood and so on, right? What do you make out of air? It doesn't seem to be really a material thing almost, right? So it seems to be, it's invisible. It seems to have less of matter than water does and water less than wood, you know, something like that. So we took, we borrowed that word, right? Even though it's not a material substance, it's not really air, the soul, you're curious, huh? So, but is continuous quantity more known in some way to us? Seems to me, if you use the affirmative before the negative, right? Now, the subject definition, even in actual philosophy, you'd say that a discrete quantity is a divisible for everything. And Aristotle, when he talks about thought, he says thoughts are like, what, numbers more, right? Because is a, is a definition, you know, we need to find reason with, with, with following Shakespeare. We had to define what discourse is, right? And, uh, we had to, you know, define the sense of what before and after is, or what the words and mentions on. But, is every part of every definition in need of being defined? Because in that case, definitions would be divisible, what, forever, right? And, uh, and likewise, you know, the conclusion of the syllogism, we get it from two other statements, right? So, you can kind of divide it into these statements that I'm reliant, you know? But is every statement in need of proof by other statements? In that case, you wouldn't be able to know any statement, would you? So, um, definitions and statements are divisible, not forever. Yeah, so Aristotle compares thoughts more to numbers, right, huh? He compares, in the, uh, Eighth Book of Wisdom, he compares forms to numbers, right, huh? Continuous things, right? As opposed to evolution, he doesn't want to compare it to some continuous, right? Yeah, yeah. Because, you know, these things are infinitely divisible, right? They're continuous quantity. But is, is the natures of things more like numbers than like lines? Ha, ha, ha, ha, ha, numbers, huh? Moreover, the property peculiar to quantity, to be equal or unequal, that we'll meet with and get to the properties. Suppose there's something that has been measured, right? And by quantities that have a common measure. Hence, a line and a surface cannot be, what? Could you speak of a line and a surface being equal or unequal? And can, uh, can, uh, time and, uh, be, uh, equal or unequal? Well, I used to say Quebec is eight hours away, and my home town of St. Paul is 24 hours away from where I am now. 24 hours is a lot more, longer length, right? It's kind of playing around a little bit, huh? It's how long it takes me to get there, right? We're not the St. Paul, we're going to do it in...