Natural Hearing (Aristotle's Physics)
65. The Continuous and Its Basic Role: Beginning, End, and the Point Without a Limit
https://berquistcourse.com/course/philosophy/3-natural-hearing/065-the-continuous-and-its-basic-role-beginning-end-and-the-point/

[0:00] of rug around their cat, you know, something. But basically, you know, I'm sure she'll do one these days, and we'll be chomping up your nose. Ah.

[0:12] Interesting. Can I ask you a question? We listen to the Father, Son, Holy Spirit, Amen. Guardian Light, Amen. Guardian Angels, to open the lights of our minds, ordain luminous images, and rouse us to consider more correctly. Saint Thomas Aquinas, Angelic Doctor, and help us to understand all that you've written. Name of the Father, Son, Holy Spirit, Amen. Can't think of a work on the continuous by the modern philosophers, can you?

[1:04] I can't think of a book by Louis de Broglie, there, the great French physicist, right? The continuous and the discrete in modern science. When you stop and think about the philosophy of the continuous, how fundamental is this for philosophy and for our knowledge in general?

[1:30] Well, as you may recall, there are two chief kinds of philosophy, huh? Looking philosophy, right? And practical philosophy. And in looking philosophy, you have three particular kinds. You have mathematical philosophy. Then you have natural philosophy. And then you have wisdom or first philosophy, huh? Okay. Now, the philosophy of the continuous is altogether fundamental for natural philosophy, because motion and place or distance and time, which are the things that we saw in the beginning of book three, are about to be considered in natural philosophy.

[2:25] They're all continuous. So it's absolutely fundamental for a natural philosophy to understand the continuous. But isn't it important for mathematical philosophy? Yeah. Geometry. Because geometry is about continuous quantity, huh? Uh huh. And some of the things that are shown here are assumed in geometry, right? Uh huh. Like in geometry, we say, for example, between any two points, you can draw a what? Straight line, right? Mm hmm.

[3:08] Now, two points have come up in touch without coinciding and still remain two. Could you draw a straight line between these two points? No. But it's here that we meet, you know, in this first reading. In fact, that two points cannot what? Touch without coinciding, right? Okay.

[3:30] Of course, geometry is always assuming you can what? Get smaller and smaller and smaller a line. You can keep on bisecting a line, right? Mm hmm. You can always.

[3:45] Inscribe a square and a circle, and a circle and a square. which case, they get smaller and smaller and smaller, right? Can always bisect an angle, right? The theorem, you know, given a straight line to bisect it, that's a universal theorem, right? And then you can keep on doing that. So it's absolutely fundamental for geometry, and in a way, it's important for even arithmetic, the science of numbers.

[4:14] Not because they're continuous, but because number arises from the division of the continuous. We touched upon that when we looked at the fragment of Anaxagoras, where we talked about there being no smallest of the small, and then there'd be no greater, greatest of the great. So what is the connection between those two, right? Well, if you start off with one line, you divide it, you have the first number, which is two, right?

[4:46] And you divide again, you have three, and you can divide forever. Then the numbers can increase forever. So in a way, the infinity of numbers there, or the potential infinity of numbers, corresponds to the infinite divisibility of the what continuous, right? So the philosophy of the continuous is fundamental for mathematical philosophy as well as for what natural philosophy.

[5:16] But then, when you get into the philosophy of the soul, and a fortiori, when you get into wisdom, and you are going to be studying eventually immaterial things, right, like the angels, or God Himself. Ah, now is the philosophy of the continuous important for these things?

[5:40] Well, not if we knew these things as they are, right? If we saw God face to face, right? The philosophy of the continuous would not be necessary to consider God, right?

[5:57] Um. Although in seeing God face to face, we would understand the continuous, okay? But neither God nor the angels are continuous. But in this life, we understand more what God and the angels are. What not, right? Okay.

[6:19] Like in the Summa Contra Gentiles, when Thomas shows that there are understanding creatures, creatures that understand and have will and so on, then he shows they're not a what body, right? They're not continuous, okay. So you have to understand

[6:39] the immaterial substances in God. In part by the negation of the continuous, and that's how we also understand the immateriality, and large part of our own reason, okay, and consequently the immateriality of our soul. So, even for the study of those immaterial things, those things that are not continuous, the philosophy of the continuous is altogether what basic, right? Okay.

[7:11] When Aristotle points out, and we will see it eventually when we look at the philosophy of the soul, when he takes up the human reason, he points out that the human reason' proper object is that what it is is something you can sense or imagine. So, what it is, therefore, something continuous or terribly continuous, huh? And

[7:37] so that reason never understands in this life without imagining in some way, huh? And that's why in the books on the sense and sensible, Aristotle and Thomas, explaining the commentary, say that we understand nothing without the continuous and time. Time itself is continuous, huh? Because the images are all involved in continuous and time. If you read Boethius' work in the De Trinitate there, and Thomas' commentary or his articles on it, and one of the objections, you know, is saying, "Well, we understand nothing without the continuous and time, but God is not continuous or or in time, right?

[8:22] Therefore, we don't understand God." Well, the reply to the objection is that we understand God by the negation of the continuous, huh? And we saw in eternity the negation of time, things that are found in the definition of time, okay. So, in that sense, we don't understand even God in this life, so far as we can, without the what continuous, huh? Okay. But the fact that we understand nothing without the continuous shows how basic that is

[9:00] to to all our thinking, huh? And that's found then, as we pointed out before, in the words that we use everywhere, the most basic words, huh? Now, when you study the the most basic words, like Aristotle does very fully in the fifth book of wisdom, fifth book of metaphysics, um,

[9:29] you see that these words are the words used to some extent everywhere, but especially in the axioms, huh? The statements which are known by themselves by all men, right? But they're also the words used most of all in wisdom, of course. Those words are divided into three groups, but the first group begins with the word beginning, right? And the first meaning of the word beginning is the beginning of this table.

[10:00] It's tied up with the what beginning that is in the continuous. Of course, every cause is a beginning, but not every beginning is a cause, right? So our very understanding of the word beginning starts with the what continuous, huh? Eventually, we see other meanings of the word beginning, right? They're not tied to continuous, but they're seen at first by certain likeness to the beginning that is in the continuous.

[10:30] That's an extremely basic word, beginning, huh? Every cause is a beginning, huh? Not every beginning is a cause. It's even more general than than cause, right? And its first meaning is tied to what continuous, huh? The curb is the beginning of. the. campus, they always say, to the students, right? The curb out there on Salisbury Street, right? The campus. First thing, beginning, right? Okay. And in the third part of the words, you come to the famous word end or limit, right?

[11:04] And the first meaning of end or limit is the end or limit of the continuous. So we speak sometimes the beginning of a line and the what end of a line, huh? The beginning of the table and then the end down there. But Aristotle says sometimes you use the word end for both. We can say the two ends of the table, right? The two ends of a line, the two endpoints, and so on, right?

[11:29] So end in some ways even more universal than what beginning, beginning, yeah, yeah. But the first meaning of end is again in the continuous, huh? The first meaning of end is the end of the table, and then the next meaning of end is the end of a motion, which is also something continuous, right? And then comes the sense of end, which is purpose, that for the sake of which, huh?

[12:00] And then last of all, end or limit in the sense of a definition, huh? So that's a key word in all our thinking, but the first meaning is tied to the what continuous, huh?

[12:16] You take the key words of wisdom, the most universal words like being and one, huh? Well, continuous is one of the fundamental meanings of the word one for us.

[12:30] I told you that little joke of Socrates, I think, when he asked somebody to define something and they give him what many many examples rather than a definition. And he's kind of you know playing the fact that he asked for one thing and they gave him many. And and in some of the places where Socrates does, one place at least, he seems to I think it must be kind of a standard joke the Greeks had.

[12:56] If I hand you a plate, right, and you what drop it or something, right, or I drop it in handing it to you, and you say, Well, ask for one plate, and now you've got but but no, but what happened? The thing is no longer continuous once it's been broken, right? So it's now many instead of one, right? That's kind of first meaning, it seems, almost of the word one for us, the what continuous, huh?

[13:21] And everything that is in some ways one. If it's simple, it's very much one. If it's composed, it doesn't exist unless its parts are what united, huh? So one is very important for understanding, or the continuous is very important for understanding what the meaning of one, right? And of course, it's obviously important for being in the sense of what. Quantity, right? Which is so close to substance that Descartes confused the continuous or extension with what substance, huh?

[13:56] Okay. Now, I just know manifestation of the importance of the philosophy of the continuous of the continuous for all of our what thinking, huh? Okay. Now you might say, well, geometry is about continuous quantity and so on. Why is the philosophy of the continuous this basic consideration of the continuous here, which is especially in the first four readings, right? Before he goes into the division of motion in some detail, why is this philosophy of the continuous here that you have, especially the first four readings?

[14:39] Why is that belong to natural philosophy rather than to geometry, huh? See, geometry is a science of continuous quantity, right? Uh huh. You know, lines and surfaces and bodies in the sense of the three dimensional continuum, right? Why does it belong to natural philosophy to determine basically that the what the continuous is, huh? That it's divisible forever and it's not

[15:15] divisible into indivisibles, right? It's not composed of indivisibles and these things that he's been saying here. Why does it belong to natural philosophy to do that? That the geometer, in a way, depends upon him, right? He assumes, right, what he's shown here.

[15:36] One reason is that continuous is broader than just the continuous studied in geometry. For example, time is continuous. Okay. Motion. Okay. That's only when it belongs to geometry to determine what time is, right, or what motion is, right. Okay. But you could also perhaps go back to what we show in in logic, right, huh? The highest part of logic is in the prior and posterior analytics. We're talking about demonstration, huh?

[16:14] Which produces reasoned out knowledge in the strict sense, huh? And the highest kind of demonstration, of course, is a demonstration propter quid, right? Giving you the reason, right, in the sense of the cause, huh? And when Aristotle is talking about this, he he ties it up with what we know about or say about cause that you have to compare causes and effects that are what proportional, right?

[16:45] Okay. Now, that means that you have to find exactly why you know something belongs to something, right? And sometimes we're not exactly sure. See, let me give an example of this, right? You've all read the the Meno, haven't you, okay? Okay. Now, the Meno, in a way, has in Socrates' demonstration, the geometrical demonstration he gives to the slave boy.

[17:27] In a way, it's it's a particular case of the what Pythagorean theorem, right? Socrates is saying, suppose you have a square, and you want to get a square that is what twice as big, right? What will be the side of a square twice as big? And as you know, the slave boy answers twice as long, right? Okay. And Socrates will first show the slave boy that if you take a square whose side is twice as long as original one, you won't get a square twice as big, but one what four times as big, right?

[18:08] Okay. Then he wants to show the slave boy that if you take the diagonal of original square, that will be the side of a square twice as big. That's a kind of interesting theorem, right? And if you just look at a square and you say, okay, now I want to find the side of a square twice as big, and Socrates or someone tells you, well, it's going to be the square and the diagonal.

[18:34] That's very interesting, isn't it? But how would you show me that that is so, right? See. Now, if you knew, or if the slave boy knew, you knew the Pythagorean theorem, you could see this is a special case of the Pythagorean theorem, right? Because this is obviously a right angled what triangle, and the square on the side opposite the right angle, right, is equal to the squares on the sides containing it.

[19:08] Now, obviously, the squares and the sides containing it together are twice the what original square. And so, if the square and the diagonal is equal to the squares on these two sides, the square and the diagonal will be exactly twice the original square, okay? But Socrates can't assume that the slave boy knows the Pythagorean theorem. That'd be too hard to show, right? So he actually shows something more particular.

[19:40] He says, suppose this is your original square, he said, right? Now, if we put another square. Exactly equal to it right here, he says right, and then another one exactly equal to it right below it, and then a fourth one exactly equal to it to fill up the corner here right. We have kind of a bigger square composed of what four squares, and therefore four squares original size, and therefore four times as big right.

[20:15] Okay, and then he starts to draw his what diagonals right. Now it's not too hard to see that the diagonal cuts the square into exactly two parts right. Of course, we know that formally from the fourth theorem, but the fourth theorem is almost obvious. The fourth theorem says what that we have two triangles with an equal angle, and they're contained The equal angles, the equal sides. The two triangles equal, right?

[20:51] You can see that if you lay this on there at that point, right? And drop this line on that, because they're equal, they would coincide. And because the angles equal, this side would fall on this side. And because the lines equal, they would coincide. You can't draw two points, right? Excuse me, two lines, straight lines, that is, between the same two points, but only one, right? So the third line coincides.

[21:14] So now this here, okay. Now it's also not too hard to see then that these two triangles are equal, and therefore these two angles will be equal, and these two will be equal, right? And therefore each of these angles will be exactly one half of a right angle, and so two of them will be a right angle, right? Okay. So now you've got a square within a square, right?

[21:41] And it's made up of four halves of four squares, and therefore it's exactly equal to what? Twice. The half of four is two, so it's exactly twice as big, right? That square is original one. And it's on, in fact, to what? The diagonal, right? Now you've shown that, right? Now be careful. I'm going to say right now.

[22:08] That's a good argument, right? Okay. Nothing wrong with that argument at all, right? Okay. But notice what you're showing here is a particular case of the what? Right angle triangle. In fact, you want to be very precise. You could say it's a what? Isosceles right angle triangle, right? Yeah. Okay.

[22:36] Now, is it a property of the isosceles right angle right triangle, right, to have that property, or does belong to every right angle to have that property? Everyone. Yeah.

[23:00] Yeah. And if you've gone through the whole book one of Euclid, right? In the forty seventh theorem, I guess it is, right, at the end of the first book. It's appropriate takes this as a culminating point to the first book of geometry. Shows it about any what? Right angle triangle, right? Okay. So it'd be true of let's say the famous the first one in whole numbers, the one whose sides are three and four, and the diagonal is what?

[23:31] Five. I mean, diagonal, but the side opposite the right angle is five, right? Okay. Four times four is sixteen. Nine times five. Okay. But this is not an isosceles triangle, is it? See. So, is it really insofar as it's an isosceles triangle that has the angle or the square on that side opposite the right angle equal to the ones on the two sides? No, it belongs to it insofar as it's a what right angle triangle, not insofar as it's an isosceles right angle triangle.

[24:13] It's kind of subtle thing there, right? Okay. So, number forty-seven, huh? Now, it would be because a more a more perfect demonstration, really, than this one over here, in the sense that you are assigning the property to what it's proportional to, right? And something that belongs to this not as an isosceles right angle triangle, but something that has because it's a what right angle triangle. Yeah, yeah.

[24:48] You see that? Okay. But no, it would be easier to follow this thing with the slave boy than to get to understand number forty-seven in Book One, right? And so it may be even historically that men saw some of these theorems for something in particular first, right? Before they saw the more universal thing. Okay. Now,

[25:22] just give a little example, a super example in some ways, huh? To take the the fifth theorem in Book One of Euclid, huh? That's the theorem that says in isosceles triangle these two sides equal, right? Then you prove that the angles at the base are what equal, right?

[25:47] So, is it a property of the isosceles triangle to have the angles right opposite its equal sides equal to a property the isosceles triangle?

[26:04] See, the theorem I guess, is enunciated in Euclid with the name what isosceles triangle, right? Right. Yes. Yeah. But when he first defines, you know, the various particular kinds of triangle, equilateral, isosceles, and scalene, right? The isosceles is the triangle that has only two sides equal, right? As opposed to equilateral, which are all three sides, huh? Well, does this property belong to the isosceles triangle in that sense, as opposed to the equilateral triangle?

[26:41] No, no. Like this is an example of, I think. A equivocal use of the word isosceles, and it's a common kind of equivocation. At least, we're doing it right.

[27:06] It's the one I've been spoken about before already. Sometimes one of two particular kinds of the thing keep the common name as their own name, right? And the other one gets a new name, right? And there's many examples of that, right?

[27:36] So sometimes we say man is what an animal, right? And so animal can be divided into man and beast, let's say. But sometimes we let the beast keep the name animal, right?

[27:52] And so we divide animal then into animal and man. And that shows an equivocal use of the word animal, right? Because in one sense man is an animal, in other sense he is what not an animal, right? Okay. There's a reason why the beast keeps the name animal because the beast is nothing greatly noteworthy in addition to what is meant by the word animal. But man has something tremendously significant, right?

[28:22] In addition to his being an animal, namely his having reason and will and so on. So man gets a new name, and the other ones keep the common name, right? Well, that happens here with isosceles, right? That in the broad sense isosceles means a triangle that has two sides equal. It says nothing about whether the third side is or is not equal to the first two sides, right?

[28:51] But the triangle that has only two sides equal, right, then keeps the name, right? And the one that has something special about that, even the third side is equal to the first two, gets a new name, right? See, you know, you know, Greek a little bit. Isosceles gets its name from what? "Skelos" means leg, "isosceles" means equal. See, so when I spread my legs and you draw a line between my feet there, right?

[29:27] I form kind of an isosceles what triangle, right? Okay. See, equal leg triangle, right? See, and notice this is equal leg, but whether I I move my feet apart this distance or I move my feet apart is If I can, as the same length as my leg, right? You know, it would still be so scalus equalae, right? Huh? See, in that case, maybe something noteworthy that the the third side is also equal to the first two sides, right?

[30:03] Okay. So when he says it's a property of the isosceles triangle, it's not a property of the scalene triangle. No two angles in a scalene triangle can be what? Equal, yeah. Um, is he taking isosceles as it said that isosceles is equilateral, or isosceles as it's divided against equilateral? Which is he doing? The general, yeah, yeah.

[30:39] That's why you know you could make explicit something. I don't remember you could make it explicit. I mean. It's so obvious to him, right? You could take that theorem and you could show from that that all the angles of a what equilateral triangle are equal, right? Okay. And you could take that in the next theorem and show that none of the angles of the what scaling triangle can be equal, right?

[31:07] You know, the next theorem is the reverse of that, it says the angles equal the sides equal, right? So since the scaling triangle has no sides equal, if any two angles are equal, by the sixth theorem, the next one after that, you have to have the opposite sides equal, but that contradicts what a scaling triangle is, right? Okay. So,

[31:32] but when you show that an equilateral triangle has all its angles equal from that theorem number five, it shows that you're not what, understanding that fifth theorem really in a way that is private to the isosceles triangle is distinguished from the what equilateral. You can apply it to it, right? Okay. Do you see that?

[32:05] So with Aristotle, or not Aristotle, with Euclid or with Pythagoras, huh? Let's take Euclid's demonstration that we have the actual reader. When he demonstrates in proposition forty-seven that it's a property, huh, of an equilateral, not equilateral, but a right angle triangle, right, to always have the square on the side opposite the right angle equal to the squares on the sides containing the right angle, right? He's showing that of what?

[32:38] He's giving a reason why any right angle triangle, right, would have this, right? Okay. Not a reason why the isosceles would have it, right? The isosceles right angle triangle. The reason is more common than that, right? Well,

[33:00] you can say that the reason why a line, or the motion over a line, or the time it takes to go that motion, the reason why all those things are divisible forever, right, and none of them is composed of indivisibles, right, or is divided into indivisibles, it's really the same reason for all three, proportionally speaking, huh, at least, huh? Okay. And therefore, like in the forty-seventh theorem there in Book One of Euclid, it's appropriate to what?

[33:38] Bring them all together, right, and show it for all of them together, right? Because there's kind of a common reason, at least proportionally, for all of them, right?

[33:49] Okay. Why, if you showed it in geometry, you'd be showing it just for for the the line, or and not for the motion or the time, right? You see, so build up like what Socrates is doing there in the other line wouldn't be bad. I think it wouldn't be the most

[34:17] universal, yeah. But even solid in that sense in which Aristotle is taking it there, right? Okay, it's a property of of whatever it is, right? As such, right? Okay. Okay.

[34:44] Is the continuous equivocal said of time and motion and magnitude? It's hard to say. There's something, perhaps, yeah, but it's something not equivocal by chance, right? Equivocal by reason, huh? Yeah.

[35:15] So it's clear in in Thomas and in Aristotle that the word beginning, right, is equivocally said of what the beginning of the magnitude and the beginning of the motion, the beginning of time, right? In in the first book of Natural Hearing, there, the first book of the Physics, Aristotle is examining the reasoning of Melissus, right? Melissus is saying, you know, that being could not have come to be, could not have been generated, right?

[35:51] It had no beginning, right? If it has no beginning, he says, it has no end. Therefore, it goes on forever. And Aristotle says he's going from what

[36:05] a premise that it has no beginning in time, right? And perhaps therefore no end in time, right? Which having no beginning or end in its what magnitude, its size, right? And therefore he's committing the what fallacy equivocation. He's making this mistake from mixing up two senses of the word, right?

[36:31] I mean, we we talked in here in Introduction to Philosophy the other day there, and we're talking about the disagreement between Socrates and the Athenians in the Apology. Did we talk about that? I don't know if we did one time.

[36:51] And you know, if you look at Socrates' speech in the Apology, in the first part of his speech, he explains how he got in the habit of going around examining people, right? Yeah. And often finding out they didn't know what they claimed and all, but why he started doing that. But then, the second part of the speech, he says that he's been examining the Athenians, especially about their seeming to prefer the goods of the body and exterior goods, outside goods, to the goods of the soul.

[37:25] Okay. And Socrates doesn't develop there at that point the reason why the goods of the soul are better than the goods of the body and exterior goods. But he does touch upon this in other dialogues and so on. See. So I said, you know, I stop at that point and I say, now, who's right, Socrates or the Athenians? Huh. And

[37:50] we've already shown earlier in the course that something is not good because you want it, right? So you can syllogize then that something is not better because you what. Want it more. Yeah. Yeah. See. So I say you can't say to this, you know. Well, Socrates, if you like the goods of the soul so much, go for them, right? We want these other goods, right? Huh. You can't say that the goods of the soul are better for Socrates because he wants them more.

[38:24] And the goods of the body and the outside goods are better for the Athenians because those are the goods they want more, right? Because then you'd be saying that something is better for you because you want it more. But if that was so, then it would be good because you what. Want it. But we'd already shown earlier in the course that something is not good because you want it, huh?

[38:48] See. So as I say to the students, I sometimes give them a simple example: Is something sweet because it's white? No. And so, if it's not sweet because it's white, it's not sweeter because it's whiter. While someone was saying, you know, something is sweeter the whiter it is, you'd have to say it's sweet because it is white, and if that isn't so, as everybody knows, then it can't be true, right?

[39:12] So he says. The ball, the ball game is over. That ball game is over. You can't, can't say that, right? Okay. Now you're going to have to give a reason for what you're saying, right?

[39:25] And I used to, I used to have a colleague who used to quote the Republic. Did I ever tell you this? In the Republic, I think it is Socrates says, "An opinion without a reason for it is an ugly thing." Oh yeah. And he'd say he quotes this to students. He says, "And I said, don't pawn your uglies off on me." Say.

[39:48] So, what I did was to develop, you know, the. I get them first of all to to admit that the Americans agree with the Athenians rather than Socrates. Okay, and then I develop you know all the reasons they give for Socrates being correct, right? Okay, and I say, can you give any reason the other side? You can't give the reason that they want more, right? See, well, they can't really come up with a reason, see.

[40:14] So then I try to help them a bit, see. And my favorite example you may have heard me use it, I say, which is better, philosophizing or breathing?

[40:29] And say now, think about that a little bit. Which is better? Say, look it out. How many think philosophizing is better? Raise your hands. Nobody raised their hand. How many think that breathing is better? They're all raising their hands. See, I say, okay. Okay, very good. But then I quote this thing about opinion without a reason. It's an ugly thing. what's your reason for saying that breathing is better than philosophizing?

[40:57] So finally, one student speaks up and says, "Well, if you're not breathing, you won't be doing anything else, right? Okay?" I said, "No. What are you pointing out? Aren't you pointing out that breathing is before philosophizing in the second sense of before? They've had the the text here from Aristotle, right? What he's pointing out is that you can breathe without philosophizing, but you can't philosophize without breathing, right?

[41:26] See, so you're saying that breathing is before philosophizing in the second sense of before, and I agree. But how can you conclude that therefore it's before in the fourth sense? See,

[41:40] and you know, my other stock example in class, you know, if you show that Chaucer came before Shakespeare in English literature, because Chaucer's in the 14th century, I guess, and Shakespeare at the end of the 16th, maybe the 17th century, could you conclude from that, therefore, Chaucer is a better poet than Shakespeare? No, I mean obviously they can see that that's wrong, right? Because Chaucer's before in time doesn't mean he's before in goodness, right?

[42:06] Okay, so how can they reason that because breathing is before philosophizing in the second sense, therefore it's before in the fourth sense? Obviously, doesn't follow, right? So Chaucer doesn't know what to do then." I said, "Well, I'll help you make your argument a little bit stronger, right? See,

[42:30] which is worse for me to stop philosophizing for the next hour, or to stop breathing the next hour? Well, obviously, to stop breathing will be worse, right? To stop philosophizing for the next hour. See, that's that's quite true, quite true. See, and isn't it, you know, probable that the opposite of the worse is what better, right? So if it's worse to stop breathing than to stop philosophizing.

[43:03] Then the opposite of stopping breathing, which is breathing, right, must be better than the opposite of what stopping philosophizing, which is philosophizing. Oh, yeah, yeah. Now they get the argument. See, come on. Help them. See, I said just like you know, I said if if you say

[43:21] it's worse to kill a man than to kill a mosquito, well then a man must be better than a what mosquito, right? I said, or if it's worse to kill a man than to rob him, right? Well then the man's life must be something better than his his money, right? Okay, yeah, yeah, yeah, yeah, okay. But there's an exception to the rule. There's an exception to the rule.

[43:48] That the opposite of the worse is better, and that is when the lesser good is before the greater good in the second sense of before, when the lesser good can be without the greater good, but the greater good cannot be without the what lesser good, right? Then the loss of the lesser good is worse than the loss of the greater good because it entails also the loss of the greater good, why the loss of the greater good can leave you still with the lesser good.

[44:28] And sometimes I, you know, go into the famous theological example where Thomas, you know, following you know Saint Paul and everybody like that, sees that charity is greater than faith, right? It's a greater good than faith, but yet he'll speak as if the loss of faith is worse than the loss of what charity, right? Because if you lose faith, you lose hope and charity, huh? Because faith can be without hope or charity, but they can't be without faith.

[45:01] So the loss of the lesser good is worse. Okay, so that's what the exception is, right? So since breathing and philosophizing in this life only are the lesser good, their breathing is what before in being, right? Then the loss of it can be worse without it being, in fact, the greater good. I usually take a simple example, and I, you know, I'll say, and which is better, just to live or to live well?

[45:37] And they all say to live well, right? But obviously, to live is before living well in the second sense, right? So that argument breaks down, see. So I say it's pretty clear that that the word beginning, right, is equivocal, and that

[45:56] this fallacy of equivocation is being made by Melissus, right? When he argues that because being always was, right, and always will be, that therefore it must be what, you know, go on forever, right? Okay. But these are nevertheless what much closer to being what the same, right? Because one kind of follows upon the other, right? Okay. It doesn't mean to fall upon, you know, something having a beginning in time that has a beginning in size or vice versa.

[46:36] So Aristotle for example example thought that the universe was what, you know, had limits in size, but not limits in time. It always was, right? Okay.

[46:57] Okay, so let's come back here again to the first reading a bit. Here I looked at it again a little bit. Another kind of another logical point here too.

[47:17] Another thing we learned in the Meno, huh, you know, in the Meno, if you recall, Meno wants to know whether virtue can be taught. Remember that? And Socrates says, "I don't know. " Furthermore, I don't know what virtue is. Furthermore, I never met a man who knows what virtue is, huh? And Meno says, "Well, I know what virtue is." And Socrates says, "Oh, okay, tell me." And it turns out, of course, in the conversation, like usually happens in the dialogues, Meno doesn't know what virtue is either, right?

[47:49] And so then Socrates is proposing that the two of them put their heads together and try to figure out what virtue is, but Meno is not willing to do this. But later in the dialogue, he still wants to know whether virtue can be taught. And Socrates says, "Well, I can't really think too well about this without knowing what virtue is exactly, but I'll I'll look on both sides and see what seems to be said on both sides, right?

[48:13] Reasonable on both sides. But he's pointing out that you can't really know perfectly or reason perfectly that virtue can or cannot be taught before you really know by definition what virtue is, right? So Aristotle here, you know, he's beginning with the definition of the what? Continuous, right? Okay.

[48:39] Now, I think this is a little bit puzzling here, and I'll explain to you in a moment what I think is puzzling here about this. But there seems to be, first of all, two definitions of the continuous. Okay, I think you mentioned that before, right? And the first definition of the continuous is the one that is given originally in logic, right?

[49:10] And then back in the earlier books here of the book three, I think it was, he gives the second definition of the continuous. But both definitions are in terms of the what? Parts, right? Okay.

[49:31] Just like the definition of of number, that Euclid gives is a what? You know, multitude composed of ones, right? Composed of units, right? He's defining it in a way by its what? Parts, right? Okay. So the definition of a continuous in logic

[49:55] is that whose parts meet at a common boundary. Remember that? Okay. That whose parts meet at a common boundary. Or we could say that whose parts have a common what? Boundary, a common limit, right? Okay.

[50:41] That whose parts have a common limit. Aristotle uses this to separate line and surface and body and so on, these continuous quantities in the category quantity from a number, right? Things of that sort. Because the parts of a line, like the parts the left, let's say, and the right side of this line, they have a common limit, which would be a point, right? Okay. Which could be considered the end of one as the beginning of the other.

[51:19] That's a common point. In a circle, right? The diameter could be considered the end of one part and the beginning of the other, right? And so on. In the boundary between us and Canada, right? But in a number like seven, the three and the four, do they meet at a point or a line or something else? No. So he calls that, you know, discrete quantity.

[51:46] Okay. All right. But now in the the third book here of the physics of the natural hearing, he gives another definition of the continuous, and it's that

[52:08] which is divisible forever. Yeah. So this is the one given in logic, but it's taken over here because logic is common to all sciences in some ways. And this is a definition that seems to be appropriate to natural science or natural philosophy. I think we mentioned before how Thomas gives a reason why the first definition here is more appropriate to logic than the second one to natural philosophy.

[52:48] And it's because of something we saw before when we were studying the four kinds of causes. Remember that? And Aristotle pointed out how all parts that compose something are something like matter, okay, and so you have a nice proportion there that the whole is to the parts something like form

[53:15] is to matter. Remember that proportion? Now, what part of philosophy is about matter? Natural philosophy. Yeah. Okay. While logic is more like what geometry, it's about form.

[53:36] Some people go so far as to make all logic formal logic. Okay. So the form is like the whole more, and the matter is more like the parts, right? Well, when you define the continuous, that which is divisible forever, you're going in the direction of what? Parts and parts of parts, so right? So it's like going in the direction of matter, right? Which is the way natural philosophy goes towards what?

[54:03] Matter, right? Usque ad elementa, as the Latin says in the first reading. But here you're looking at the what? The way the parts are united to form the whole. They needed a common boundary, right? Okay. Because if you what in that circle there you brought these two semi circles together, right? Then to form this whole what circle, right? So it's more appropriate for logic to define it this way, and natural philosophy what?

[54:37] That way, right? Okay. But now going back to what we learned in the Meno there, but you know it's taught more explicitly in logic in the prior and posterior analytics. Reason out of knowledge is based ultimately upon definition, right? Okay. So in a way, it's going to reason from these two definitions, huh? Okay. And which does he reason from first?

[55:11] The first one. Okay. So let's go back to the first paragraph and just look at this again a bit. He says, "If the continuous and the touching and the next are has has been determined before, continuous whose edges are one touching whose edges are together, next of which there is nothing of the same kind between, it is impossible for anything continuous to be from indivisibles, huh? As a line from points, huh?

[55:47] If the line is something continuous, that's what we mean by line, and the point is something what? Indivisible, right? Okay. Now, what's he going to try to prove here? Okay. That you

[56:08] can't put together something continuous from indivisibles. Okay. And also in a way, you can't put together by having them touch either. Okay. And he's even going to touch upon the fact that in a way you can't

[56:27] put together points that next to each other. Say. Um, like when you have a row of houses, right? And each house has a house that's next to it, right? And maybe one next on this side and one next on that side, but there's a house next to it, right? But two points cannot be continuous. He's going to argue they can't what touch and remain distinct, right? And they can't even be what next to each other.

[57:02] Okay. So in no way do they seem to come from something indivisible. It's kind of very thorough way Might be that it can't be continuous, right? Okay.