Natural Hearing (Aristotle's Physics)
Lecture 57: Motion, Continuity, and Natural Philosophy

Transcript
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No, he's saying opposite things are all the same thing. So what we looked at, it's a text of our style, but I think this kind of helps you to see it, you know, the way that, starting with those people who later on denied the possibility of it, you know. Thank you. You got enough copies yourself? Let me say our little prayer. In the name of the Father, and the Son, and the Holy Spirit, Amen. God, our enlightenment, guardian angels, strengthen the lights of our minds, order to illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas. Thank you, Thomas. Help us to understand all that you have written. In the name of the Father, and the Son, and the Holy Spirit, Amen. I mentioned last time the passage in Shakespeare that's caught my fancy, and I've been meditating on it for weeks. The words of Romeo before he takes the poison he bought from the apothecary. It says, Come, bitter conduct, come, unsavory guide, thou desperate pilot, now at once, run on the dashing rocks, thy seasick weary bark. And he drinks the poison. Now, notice that he's got the image that Shakespeare is very fond of, and you find other poets too, that life is like a voyage in a ship. So in other plays, Shakespeare speaks of life's uncertain voyage. Of course, voyages in those days were very uncertain. They say in Elizabethan times that they had a kind of insurance policy before I go on my boat trip. I put up some money, and you people would match me, something like that. And if I come back alive, I gather it all off. If I don't, you get the money, right? So it's kind of like 50-50, right? So he's comparing, in a way, his reason, right, to a pilot, who instead of steering his ship safely into the harbor of happiness, right, suffers what? Shipwreck, huh? And in fact, the Greek word, I mean, not the Greek word, the English word for the opposite of happiness, misery, is wretchedness, huh? And etymologically, I guess it's related to the word for shipwreck, huh? Shipwreck, wreck, and wretched, huh? So this is a famous, you know, in a somewhat common metaphor, a simile that you have in Shakespeare, huh? And you see it in many plays, like in King, in Julius Caesar, where he, you know, places are tied in the affairs of men, right? Remember that particular line? You know, where if you take it at the tide, you're going to go on to fortune, but if not, you're going to be in shallow water all your life, and so on. So there's a lot of beautiful imagery associated with that, huh? What I was thinking about in particular was the first words he says, huh? What he's addressing is the word of the pilot. He's going to crash the rock here. And he says, come, bitter conduct, but conduct there means conductor. Come, bitter conduct, come, unsavory guide. When Thomas explains what wisdom is, he'll sometimes stop in the Latin word for wisdom, which is sapientia. And he'll explain it to mean sapida sciencia, savory knowledge, right? And that fits very good what wisdom is, huh? It's something that you want to savor, hmm, you know? Like a kid with an all-day suck or something, you know, hmm, so you've got good flavor, right? Or the way you savor a wine, say, why, you know, I don't savor my water or savor my soda pop or something. I mean, but wine, you've got to kind of let it roll around in your mouth and so on. And you have to do something like that with the mind, huh? A little bit like what Boethius says, too, you know, that the philosopher is a ruminating animal. And there's supposed to be some symbolism there in the Old Testament, I guess, that they could eat ruminating animals but not other ones. But the ruminating animal, he can, what, his spare stomachs, and he can bring up his food and chew it over again, huh? And, or save it, you know, and then chew it again when he has a need to do so and so on. That's what the philosopher has to do, chew these things over again, huh? I always try to get my students to chew on these things, and they don't, you know? It's in one ear and out the other ear, never stops in there to be chewed up. And so when he says, come unsavory guide, he means, what, foolish guide, huh? If wisdom is savory knowledge, then folly is unsavory, or to use another word, insipid. Reading the modern philosophers, right, this is insipid. I mean, how can a man even, you know, read this fool? Then I was thinking of the other word, huh? It says, come, bitter conduct, come unsavory guide, huh? So in a manudaxio there by opposites, right? The opposite of bitter, of course, is what? Sweet. Yeah. So elsewhere, Shakespeare speaks of sweet philosophy, right? Okay. And that reminds me of what Thomas, you know, was often quoting, some of the lines in the Book of Wisdom, say, in Chapter 8, in Summa Congentiles, in other places he quotes the first verse, I guess, in Chapter 8, where it says, wisdom reaches strongly or mightily from end to end, huh? Ordering all things, and the Latin text translates the Greek word there, sweetly, right? Could be translated gracefully, but sweetly, huh? So it kind of strikes me, right, that Shakespeare thinks of folly as being, what? Bitter, right? And unsavory, because wisdom is just the, what? The opposite. Yeah. Yeah. And later on, in that same Chapter 8 there, there's another thing that Thomas quotes sometimes when he's in the beginning of the Summa Congentiles, when he's talking about how no knowledge is more sublime, more perfect, you know, more useful and so on than wisdom, huh? And he quotes another line in that same chapter where it says that there's no bitterness in wisdom. And every other knowledge might have a little bit of the bitter in it, right? Because you're tasting something besides the Lord, who, you know, taste and see how sweet is the Lord, right? You know, the famous thing. And coming back again, you know, to Shakespeare, there reminds me, too, of that prayer of Thomas where the Church has singled out after Vatican II as being of special importance in the tradition of the Church. This prayer, the Adorote Devote, huh? Well, in the, one of the quatrains there, huh, he's talking about the Eucharist and receiving it, right? O memoriale mortis domine, O memoriale of the death of the Lord. Panus vivus, right? Living bread. Vitam preistant homine, preistame mente de te vivere. And then the last line, et te ili, what? Semper dulce sapere. Sweetly, what? Savor, right? The two are right together, right? Dulce sapere. He wants to sweetly savor Christ, whose wisdom itself, truth itself, right? In the, what? Reception of the Eucharist, huh? You know? Well, as we say, you know, when you talk to perpusita, right? Shakespeare is speaking of the foolish pilot, right? The desperate pilot who's running his ship on the rocks, huh? Come, bitter conduct. Come, unsavory guy, huh? Just the opposite of dulce sapere, huh? So, it's amazing that precision of Shakespeare, I don't know where it comes from, but it's incredible, the things that you, you know? In fact, you know, I was first struck by the word unsavory, and I got thinking about the word bitter, you know, and how you couple those two, and his mind goes just like that, you know? That metaphor, you know, laser beam, you know? Yeah, yeah, yeah. You get just the right word to use, huh? It's amazing. You get this stuff. You get this stuff. You get this stuff. Well, so let's look now again at the first reading here. We'll come and look at the text of Aristotle here. And that's just to recall now since you've been all knocked for a loop here by the flu, huh? The flu changed. Yeah. Okay. The sick do want to be better. Yes, yes. You know what Aristotle says in the Nicomachean Ethics, you know, people have these different opinions about what the best thing in life is. The sick think it's health, you know, and the poor think it's money, you know. And the same person changes his opinion now. When he's healthy but poor, he thinks it's wealth, you know, that's what would make him happy. And then he has the money but he's sick, you know, if he doesn't have health. Okay, so Aristotle begins this third book, huh? He says, since nature is the beginning of motion and change, huh? That was in the very definition, right? Of nature. The full definition was it's a beginning and a cause, right? Of motion, but motion in the broad sense to include change. And rest, right? And the road we are following is about nature. Aristotle often calls philosophy in the Greek a, what? Methodos, right? It's over a road or it follows a road, huh? What motion is then ought not to be hidden, huh, from us, huh, for studying nature. For this being unknown, necessarily nature is unknown. Motion is in the very definition of nature. And in a way, the remaining six books of natural hearing are, in some sense, all about motion. In books three and four, we'll be talking about things that are very closely related to motion, like time, which is a measure of motion. But then in book five, he divides motion or change into the various kinds, huh? Change of place and change of quality and growth and so on. And then in book six, he talks about the quantitative division of motion. And then in book seven and eight, he compares motion to movers, and that's where he works out the famous argument for the unmoved mover, right? But everything, in a way, revolves around motion. But why in natural philosophy? Because nature is defined by motion. And sometimes, you know, like in the premium to Nicomachean Ethics, when he refers to natural philosophy there, he says the subject, you know, is natural things or motion, right? And kind of up front, it's motion. Because nature loves to hide, as Heraclitus said. And the natures of things are revealed to us through what they do or undergo, right? Through their changes and so on. So that's kind of up front, huh? Motion or change. So it's very much the subject here of natural philosophy. Now, that's only actually the first thing, though, he talks about in the first half of book three is motion. And what does he do in these other parts, huh? Well, he says those determining about motion ought to try to go through in the same way the things which follow upon motion, that are connected with motion. And the first thing he talks about is what's connected with motion intrinsically, huh? That motion is something, what? Continuous, right? Okay? And maybe later on, we'll look at the philosophy of the continuous, which is in book six, huh? And it's very important to understand the continuous, huh? In logic, right, when they talk about quantity, Aristotle divides quantity into two kinds, huh? And one kind, we translate in English as discrete quantity, C-R there, and the other kind of quantity as the continuous, okay? C-R-E. And the main kind of discrete quantity is number, huh? And the main kinds of continuous quantity are the line, which is continuous in one dimension, and the surface in, what, two, and the body in, what, three, right? Okay? Mm-hmm. Okay? Now, time and place are also in some way continuous, but the basic ones are those. And this distinction is important in mathematical philosophy, huh? If you look at Euclid's Elves, for example, the first six books are mainly about, what, continuous quantity, huh? Lines and angles and figures, right? Later on, the last books, you'll be talking about solid figures, spheres, and cubes, and so on, right? But books seven, eight, and nine are about, what, number, right? Arithmetical philosophy, huh? So this distinction here is important, first of all, for understanding the difference between geometry and what the Greeks called arithmetic, right? Not arithmetic in the sense of simply the art of calculating, but the science of numbers and their properties, huh? So that's one reason why this distinction is important, huh? Now, another place that's going to be very important is when we look at the three books about the soul. Even in the first book, when he's critiquing Plato there, huh? He says that thoughts are like, what, numbers, huh? Thoughts are like the discrete. Thoughts are not really, what, continuous, right? That's going to be very important for understanding the immateriality, the non-bodily nature of reason, huh? You see that reason's thoughts are not continuous, huh? And that reason understands continuous things in a non-continuous way. Right. And this is obviously not due to the thing being understood if it's a continuous thing to understand it, right? So the fact that we eventually discover that reason knows even continuous things in a non-continuous way is a sign that the reason is not something continuous. But a body is something continuous. Therefore, reason is not a what? Body, right, huh? Okay. So this is going to be very important for understanding the soul. And as Thomas says, I study the body in order to study the soul. And I study the soul and I study the angels. And I study the angels and I study God. And that's it. That's the end of my thinking. So, what is this distinction between the discrete and the continuous, huh? And it's important to know here because he's saying that motion inwardly is something continuous, huh? Rather than discrete, huh? And he's going to say the same thing about time in book six, huh? You know, the magnitude or the line or the rotor which you might go forward or roll forward. So this distinction between the discrete and continuous is very important, huh? For many, many reasons. I'm just giving you some of the main reasons, huh? Now, in logic, there's one way of distinguishing that, which will be recalled here later on in book six in natural philosophy. But in natural philosophy, he works out a second definition of the continuous. And what is the difference between those two definitions of the continuous? And why is one definition appropriate to logic and the other to what? Natural philosophy, huh? Well, let me just recall here the distinction in logic between the discrete and the continuous, huh? What's common to any kind? What's common to any kind? quantity is that you have a multiplication of parts and so the way our style distinguishes them in the logic is from the fact that in a continuous quantity the parts meet at a common boundary or a common limit so if I take for example something continuous in one dimension you could say this part and this part meet at a what? point, okay? they're continuous at that point if I had a surface, right? you could say this part and this part meet at a what? line, right? you had a circle and you had the diameter, right? the diameter in a way is the end of this part but the beginning of that part, right? so they're continuous at a what? limit, right? the two parts of the chakra you could say are continuous at a what? surface, right? like a circle there, imagine that so a continuous quantity is a quantity whose parts meet at a common boundary, right? understand the genes there whose parts meet at a common boundary let's say they're continuous at that common boundary, yeah? and the discrete we can define by negation of that, right? whose parts do not meet at any boundary, yeah? so if you had the number seven and you thought of the parts of seven you could take three and four you could take two and five whatever you want to but the three and the four the two and the five they don't meet in anything, do they? and as I mentioned in the first book of about the soul Aristotle will point out that thoughts are like numbers thoughts don't have a common boundary, okay? but we're not going to try to manifest that fully now but that's going to be the starting point for seeing that the mind of the reason is not something continuous and therefore not a body it's very important to see that now, in the text there and more explicitly unfolded in the sixth book although he recalls this definition he works out another definition of the continuous and that is a definition that is the one of the natural philosopher as opposed to the logician and the second definition is it's that which is divisible forever that which is divisible forever while the discrete quantity is not divisible forever so I could divide seven to three and four and I could divide four into what? two and two and I can divide two into one and one can you divide further? now sometimes the bottom of the with its fractions and so on gets you all mixed up on this, right? because he's thinking really of what? numbers on a continuum, right? okay? so one line, yeah, is divisible, right? okay? but is the one in the pure science of number divisible? the one in the pure science of number is simpler than the point in geometry the point in geometry has no parts, right? it's indivisible but it does have position while the arithmetical one, it's indivisible but doesn't have any position it's neither here nor there so that's why in the second book or the end of the first book rather the Poster Analytics Aristotle says that arithmetic is more certain and sure than geometry and the reason he's giving there is that there's more things to be considered in geometry and he points to the point and to the one they're both indivisible but the point has an addition position it's here or there, right? and in practice if you do geometry, you know like we have Heath's addition, let's say, of Euclid, you know you'll find in some of the geometrical theorems there is a number of cases to be distinguished right, yeah and what Euclid does is to give you the most difficult case usually and Lee's the less difficult cases for us to figure out in our own way but Heath will maybe refer to Proclus or some other commentator on him who distinguishes the other cases and sometimes they distinguish more cases than you need to distinguish but I know myself in learning about those cases because they've kind of, you know, they've got all the essential cases now right, they've covered all the angles, right? and so there's a lesser certitude there, right? then in arithmetic we'd have to consider where the point might be to take some examples of the points you take three as opposed to three points so three points could all be on a straight line, right? or you could draw a straight line through them or they could be such you could draw a straight line through all three of them, right? because of their position but you don't have that variety there with the three ones and three they're neither in a straight line nor in a triangular arrangement, right? so sometimes the students think you can divide one into two halves or three into, you know, five into two and a half or something, right? so it's hard to tell you, well, you've got about five points now, huh? if you could always divide five into two and a half then you could divide by the point, right? because there's five points there if you've got four, I don't care whether it's four legs of a chair or four legs of a dog, you take away two, you've got two left, right? okay? so you could take away two and a half from five then you could have two and a half points but the modern mathematician kind of, you know, mixes up the mind there now, that again, you're trying to understand how thoughts are like numbers they're also like numbers in the sense that they're not divisible forever for example, in a definition, right? sometimes part of a definition is what? in need of being defined, right? so Euclid defines, let's say, a square as an equilateral and right angled quadrilateral but you can divide that into the definition of quadrilateral rectilineal plane figure contained by four straight lines, right? you can divide that into the definition of rectilineal plane figure and that into the definition of plane figure and that into the definition of figure but does that go on forever? well, if it did, there'd be an infinity of definitions before what? any definition, right? there'd be an infinity of things you have to understand before you can understand anything and we never understand anything by definition in that case so there must eventually be something which is known not by definition, right? that's the beginning of all definitions so definitions are not divisible forever in the same way with reasoning, right? we can break down the statement back into the statements in which you've reasoned it out and sometimes they have to be reasoned out, right? but does that go on forever? that's a story, huh? that's a story, huh? But then there'd be an infinity of what? Proofs before the proof of any statement. So eventually you've come to a statement that are known without having to be proven, huh? Like the statement, the statements exist, right? Can't really avoid that, can you? When I say statements exist, that's a statement, right? And if you want to say statements do not exist, you're making a statement too. There's no way to get around that, huh? The ball game's over, right? There are statements that are known that are known without what? Having to be proven. And so when you divide thoughts, you get back eventually to those statements. Or when you divide definitions, eventually you get back to something that is known without definition. Descartes thought it was motion. Aristotle gives us a true answer in Book Nine of the Wisdom. It's an act that is known without definition. But he points out in the Ninth Book. But, you know, you see that little comparison I make two to words, huh? You look up a word in the dictionary, they explain it by other words, right? And sometimes one of those words is not known, so you look that up, right? Does that go on forever? Do you know all words by other words? No. Eventually, you have to know a word by associating it with something you can sense. So the first words are not known to other words. The first thing is, the first thing is, This would be very important, as they say, in understanding that reason is not a body, because every body is continuous, right? Now, if you look at these two definitions, are they continuous? You see they're both, in a way, in terms of the parts, right? Because quantity seems to consist in multiplicity of parts and so on. But, in the one definition, the one in logic, you seem to be looking at how the parts come together to form the whole, right? They meet at a common, what? Boundary, right? Well, here you're looking at the parts as simply what? From the direction, from the whole down to the parts, huh? Well, the parts of a thing alike matter. Whole is not formed. Well, logic is an immaterial science, huh? So it defines it in terms of its wholeness, its form, you might say, huh? And the natural philosopher defines it in terms of its, what? Matter, huh? We talked about the four kinds of causes, remember that? And Aristotle will find out how, in a way, all parts are like matter, why the wholeness is like the, what, form, right? So the whole is to the parts, something like form is to matter, huh? Matter is that of which something is made, and the whole would seem to be made out of its parts, right? So, in the second definition, you're thinking of the parts going in the direction of division, right? When you divide, you're going from the whole towards the parts. So, it's more like, what, defining by matter, which is appropriate to natural philosophy. Here, you're thinking of the parts coming together to form the whole. They come together and meet, right? Okay? Just like in a triangle, right? The three lines meet at their end point, right? And that's how you get the wholeness there, huh? So to define by form and define by matter. The difference between logic, right? Natural philosophy. Natural philosophy, as we saw in the distinction there between natural philosophy and mathematics, right? That natural philosophy defines with matter or motion. In mathematics, you don't have that. Well, logic is even more a formal one than mathematics. It doesn't even have that imaginative extension that you have in math, which sometimes we call kind of intelligent matter. So, it's remarkable that the character which Aristotle defines it in logic, as opposed to the way he eventually defines it in natural philosophy. How appropriate, right? It is for that science, huh? That shows how artful Aristotle, what, is, huh? Adapts himself perfectly to the instrument. I would have, I guess, I would have thought, it's also true, that the visible forever is less manifest, and even maybe needs to be proved in a way. The definition from logic, that seems kind of evident, but if someone said, well, it's the visible forever... That could be true, too, yeah. He does, in fact, recall the one from logic, right? Because logic, in a way, directs us into all the sciences, right? So, he does recall that from logic, huh? But it's an interesting observation, yeah. When you get to book six there, we'll see how he proves that, right? And there's a number of ways of proving it, huh? There's one way where he proves it by taking distance and time together. Did I mention that before when we talked about Enix Egress, huh? We all know that some bodies move faster than others. So, the faster body moves the same distance as the slower body in less time. But in that lesser time, the slower body would move a lesser distance. But the faster body would cover that lesser distance in a lesser time. So, just belting that, you can see that time and distance are divisible, what? But, forever, huh? But, we'll see, you know, many things about that when we go to book six. Now, Aristotle mentions the word unlimited because he's thinking of the fact that motion is something continuous. That's going to be shown more explicitly in book six. Of course, but there's something unlimited about the divisibility of the continuous, huh? So, he says, those determining about motion ought to try to go through in the same way the things which follow upon motion. For motion seems to be among the continuous things. He says seems to be because he hasn't yet, what? Proven that, right? And it's really proven in the, what? Sixth book, huh? And the unlimited, he says, first appears in the, what? Continuous, huh? It's divisible forever. Now, another thing about the continuous, huh? All these things that we'll be talking about here, like motion and place itself and time, they're going to all be continuous. And he'll be showing that, you know, in the philosophy of the continuous in book six. But the continuous is also very important in all of our, what? Knowledge, huh? In all of our naming, huh? When you study our reason there in the third book about the soul, you'll find out that our reason in this life, it never thinks without, at the same time, our imagining something, huh? And when we imagine something, we always involve the, what? Continuous, huh? And when you examine the way we name things, we tend to name things as we know them, right? And our knowing starts with our senses and with our imagination and so on, and these things are all continuous. And so we tend to name the continuous before anything else. So like when you study the word beginning in the fifth book of wisdom, the first meaning of beginning is the beginning of the desk right here. And the first meaning of end, that's the end of the desk down there. But it's the limit of the continuous, that you're first calling a beginning, right? Now when God says, I am the Alpha and the Omega, the beginning and the end, that's a much later sense of the word beginning, right? But we start with this sense here. And then Aristotle gradually, what, moves forward to the less known senses, right? And eventually it comes to the sense in which God is the beginning of things. You may recall the chapter that we had from the categories there on before and after. And the first meaning of before was the before in what? Time, right? And to that sense of before, you would lead back the before in the motion, right? As time is, as we'll see, is tied up with the before and after in motion. And the magnet over which you go. So again, the first meaning of before is tied up with what? Something continuous. Motion, time, right? Okay? In the fourth book of natural hearing, Aristotle takes up place, huh? And things are said to be in place, huh? And one place, he distinguishes the central meanings of the word in. And he gives eight different meanings, huh? Whole and part, whole in the parts, the part in the whole, genus in the species, species in the genus. I got you in my power. I left my heart in San Francisco. Form in matter, right? and I'm in this room. And he doesn't order the eight meanings, in that text, anyway. So Thomas, when he comes to common eight meanings, he says, now, and Sarastyle doesn't order these meanings, we're going to have to order them ourselves, but following the way he taught us in the fifth book of wisdom. So Thomas says, what does Sarastyle do there with the word beginning, right? He starts with the meaning that is most, what? Obvious to our senses, huh? And then he goes forward, ordering the meanings from that, huh? So the first meaning of in is what? We're in this room. It's much more obvious than the way that a genus is in a species, our species is in a genus, right? Even a part and a whole. And then he orders perfectly, Thomas, the other seven meanings, exactly where each one comes, always to the last meaning. And we can study that sometime if you want to. And it's a very important thing, huh? But notice, the first meaning, again, is in place, it's tied up with something continuous, huh? The first meaning of before was tied up with time, something continuous, huh? First meaning of beginning, the limit here of, right, something continuous like this desk, huh? So you find that the continuous dominates, huh? All of our naming, huh? And, you know, of course, you go back to the senses, but what you're using there is what you'll find is called the common sensible, huh? Because the continuous is something that more than one sense knows, as opposed to color or sound which just one sense knows. And those proper sensibles, like color and sound, they aren't that important as far as carrying the word over to mean other things. Sometimes we do, but it's not so important, huh? But the continuous, the names of the continuous, they're all carried over, right? And all of our thinking expressed in words goes back to those. In fact, even when we talk about discrete things, like numbers, right, sometimes we borrow the word continuous, huh? And one important example of that is when you're talking about proportions in arithmetic, and, you know, you say two is to three as four is to six. And then you have something like this, four is to six as six is to what? Nine, huh? And sometimes they call this, say, what? Continuous proportion, right? Okay? That's a different meaning of continuous, right? Because numbers are not continuous in the way we define them. But it's because you have the same number here, right? The number that ends this ratio is the number that begins that one, right? Okay? And sometimes, you know, I borrow the same word and I apply it to logic, right? And I speak of continuous syllogisms. What does that mean? The conclusion of one is the premise. Yeah. The conclusion of one syllogism is the premise in the next one, right? Or you can speak of continuous definitions, huh? So the definition of motion is continuous in the definition of nature. Okay? So when you define nature, you put motion in the definition and then you define that, right? So there's a certain link there. You can see that in Euclid, right? When he is defining it. He defines, I think, figure and then plane figure and then rectilineal plane figure and then quadrilateral and then square, right? They're all continuous, those definitions, huh? But notice, we're borrowing a word from the continuous, huh? And of course, you're all aware of the fact that, you know, even today we still speak of square numbers, right? And cube numbers, right? And Euclid speaks of the size of a number, right? What we call factors. But he's speaking the same way you do when he speaks of a square number, right? So maybe the, instead of saying the factors of 6 are 2 and 3, he'd say the size of 6 are 2 and 3. Interesting way we name that, right? Okay? And we've talked here about how I was using the word road and all the Greek philosophers like Pedocles and Heraclitus and Parmenides and Plato himself, they speak of a road in our knowledge, right? But the road is originally something, what? Continuous, right? Okay? And thoughts are not continuous as we define the continuous, right? But what you'll see is how, what? One thing is linked with another thing in the science, right? We define nature and then we see the connection between nature and what? Motion, right? Motion, entity, but continuous and so on, huh? So, we're kind of linked these sort of things, right? Yeah. So, you'll find that it's very common that most of these common words, in fact, an awful lot of them, seem to name, first of all, something continuous or it's tied up with the continuous and then either on they're carried over and applied to other things. But it's very clear at the word beginning, the word before, the word, what? In, right? And how about the word under and above and below and those sort of words, right? I'd put Shakespeare above Chaucer, wouldn't you? I'd put Aristotle above Plato. That word, origini, is taken from what? Place, isn't it? From the continuous, huh? Understanding, to stand under, right? Yeah. So, Aristotle distinguishes, let's say, the eight senses of in when he talks about place, huh? But he distinguishes the senses of before in logic because reason, as you know from Shakespeare, looks before and after. So, the science of reason, right? Has a special connection with before and after. Hence, it takes place that those defining the continuous use many times the notion of the limited as the continuous is what is divisible without limit, huh? Now, when Thomas comments on this, Aristotle, in the third book, he takes up motion and then the infinite, huh? And then, the next thing he talks about here, place and time, he takes it up in book four. And Thomas speaks of the unlimited or the continuous, which is defined by the limited, as following motion intrinsically, right? It's a continuous thing, right? Why place is something kind of outside of things, right? And time, if you measure, let's say, every motion down here by the motion of the sun around the earth or the apparent motion, some people think, of the sun around the earth, right? It is a kind of extrinsic measure there, huh? So they follow upon motion extrinsically, he says, Thomas. So that's part of the distinction between the third and the fourth book, between the unlimited here and the other. In addition to these, motion is impossible without place and the empty and, what? Time. Now, Aristotle doesn't think that motion is impossible without the, what? Empty. Who thought, what famous philosopher did he read said that atoms and the empty exist? Aren't they real? Yes. Yeah, yeah. And he thought that motion was impossible without the empty. And, although Empedocles had denied that there's anything empty, huh? Mm-hmm. As if it kind of involves a contradiction, huh? Of course, we're accustomed in modern times to speak of empty space, right? But I suppose Empedocles would say, what do you mean empty space, huh? Does it have length and width and depth? Oh, yeah. It's vast. And you'd say, well, now, is there something there that has length and width and depth? Or is it nothing that has length and width and depth there? Well, how can nothing have anything, including length, width, and depth? That's absurd. And if it, what? There's nothing, there is something there that has length and width and depth, well, then it's not really, what? Empty, right? Now, Einstein, some of the things I've read there, he seems to be denying the empty too. Because for Einstein, there are, what? Fields everywhere, right? Gravitational fields and things of this sort. And the field is a very subtle medium, but since Faraday, they began to think that the field is not just a mathematical device, right? But it's a reality, huh? So, Einstein is perhaps coming back to Aristotle's idea that there's nothing empty, right? But the early modern scientists, until Einstein, perhaps, were fouling Demarchatists, right? Dalton and people like that were, you know, talking about atoms, right? Under the influence of Demarchatists and his followers. You might say, oh, is Aristotle lying here when he says that, right? When he's saying what he doesn't think? Just taking the common notion, which is what you begin with, or what's commonly held. Yeah, yeah. And Thomas mentions in more than one place that Aristotle often, you know, in illustrating something and so on, will speak according to the opinion of his contemporaries until he comes to the point where it's now time to determine the truth about this matter. And then he'll say what he thinks and give reasons for it, huh? And then the other part that, one particular text that I remember, I think I mentioned last time, is that in the beginning of the Nicomachean Ethics, right, Aristotle begins by pointing out how every action, every choice, and every art, and so on, seems to aim at some good, right? Hence, they, you know, define the good well, say the good is what all want, huh? And then he goes on, but as there are many arts or sciences, there are many different goods, right, corresponding to these arts and sciences. So the end of the medical art is health, and the end of the household art is wealth, and he goes on, right? But then when you get to the first book of the politics, he argues that the end of the household art is not wealth. Wealth is only an instrument of the household. So he's speaking there, when Thomas comments on the beginning there of the Nicomachean Ethics, he said Aristotle is speaking according to a, what, prevalent opinion, right? And when it comes time to take up the household, as he does formally there in the first book of the politics, then he says, this is what the truth is, and this is why it's this way, not that way. Well, it's kind of interesting that he speaks that way, huh? You might, you know, want to examine why he does that, but, I mean, as a matter of fact, he does do it, right? And this is a good example here in natural philosophy, like the one I gave you in Ethics, huh? But not to give his contemporaries unnecessary impediments until the time comes, right? Right? Yeah. Because it's not essential yet, right? So he does take up place first, and then the empty, in book four, place the empty in time. But in taking up the empty, he refutes the arguments for the existence of the empty, and so on. So, what kind of motion or change is change of what? Place, huh? And as we saw in the great thinkers there, Empedocles and Anaxagoras explicitly, they seem to say that's the only kind of change in the world, huh? And we mentioned how in the modern natural scientists in the 17th, 18th, and 19th century, they began their study with the study of change of place, and there was that same tendency in modern science to think of this as being the only real, what, change of place, right? I mean, the only kind of change in the world. Of course, Aristotle was to challenge that and reject that, but also to show, Aristotle was able to show how these other kinds of change are possible, right? But in modern science, the turning point seems to have come in quantum theory, huh? And, at least in the theories there of Bohr and Bohr is what? The electron have different energy levels, right? And when they go from one energy level to another, they have to compensate, huh? You know, by maybe emitting energy, right? And this can be studied, and it had been studied for, you know, for many years before Bohr came to this work. What they noticed was that the emission of energy is, what, jump-like, right? And so they could no longer imagine the electron as going, right, by a change of place from one orbit to another one, right? Because then there'd be, what, a continuous motion, and a continuous emission of energy. And that contradicts the study of the spectrum, the study of the emissions. So, it can't be understood as a change of place. Strange, huh? Yeah. So, I mention that, again, because if there's any kind of change in the world, it's a change of place, huh? Yeah, yeah. And the other kinds of change that our style talks about, they presuppose change of place, because in order to have a change of quality, I have to, in order to melt the butter, so I have to take it out of the refrigerator and, you know, put it someplace where it's warmer than the refrigerator, right? And to freeze it, I've got to put it inside the refrigerator, huh? And to get a chemical change of some sort, you've got to bring the chemicals together in the same place, right? So you can bring things together, maybe, in the same place without having a chemical change, but you can't have a chemical change without bringing, what, things together, right? Mm-hmm. And then change of quality and even a substance is presupposed to, what, growth, right? You've got to be able to change carrots into something more like human flesh or blood or bones, otherwise. We'd be a mini-patched fool, right? Mm-hmm. In our appearance. What a carrot here. Wow, I see I brought you last night. I see I see I had carrot last night. And so on. And so on. And that's why Aristotle, when he studies change in particular, he studies change of place first in the four books on the universe. But in some ways, he's still going from the general particular. So you can have, what, you know, change of place without chemical change, but not vice versa. And you can have chemical change in the non-living world as well as the living world, right? But growth, in the strict sense, you have only in the living world. So you're still, in a way, going from the general to the particular. Now, can you have change of place without place? If there's any kind of motion, obviously, there's change of place, right? Mm-hmm. And you can see, if you go back to his predecessors, right? I mean, Aristotle agrees with change of place, but disagrees with that being the only kind. But it doesn't be supposed to other kinds. But can you have change of place without place? But would you distinguish, would you distinguish between a body and its place if one is a larger place? It's because the place where one body is, later on, there's another body there, right? Mm-hmm. That's a good reason to say that the place is not the same as the what? Body. Body, yeah. See? Yeah. Is the president and his position the same? Well, it's always the same man occupying the office. He might have a difficulty to distinguish between the two, right? But if one man has his position, then another man has his body,