Natural Hearing (Aristotle's Physics)
72. Zeno, Parmenides and the Continuous: Why Nothing Continuous Is Indivisible
https://berquistcourse.com/course/philosophy/3-natural-hearing/072-zeno-parmenides-and-the-continuous-why-nothing-continuous/

[0:00] cut into shouldn't that's right? Where name of the hole is equal to twice the rectangle, the thing by the hole in each of the lines. You know that is not obvious right?

[0:18] I guess you get to you know the average man. Son, Holy Spirit, God, our enlightenment, guardian angels, strengthen the lights of our minds. Order and illumine images and arouse us to consider more correctly. Saint Thomas Aquinas, angelic doctor,

[0:37] and help us to understand the word for today. Name of the Father, the Son, and the Holy Spirit. amen. Don't get any illumination here. From the higher powers. I was looking at Robert Louis Stevenson's novel, you know, the famous one, The Black Arrow. Do you know that one? Just the name. And you should have the illustrations of Wyeth, though He illustrated so many of these classical books, you know, and of course you're getting some of this medieval or medieval England, anyway, vocabulary and some of the words.

[1:20] So the word for bottle seems to be pottle, with a P instead of a B. Pottle. Of course, P and B you see, would change into each other because they're similar, right? In the way they're they're made, huh? P and B, huh?

[1:39] But the thing that struck me was a little bit later on. He was, so David, he's kind of watching out in the War of the Roses to see who's going to win the this particular battle, right? And then he comes in on the side that's winning all the time. See, so he's changed sides several times. You know, I can Shakespeare's plays represents the the historical events more or less.

[2:02] You know, things are changing back and forth between the House of Lancaster and the House of York, and so this guy's playing it. And of course, not to hurry to go off to the battle because he might be the wrong side. Right? Have to see who's who's winning and come in and give him a little push and get the spoils. But in talking about those who rush in, he calls them tosspot.

[2:28] It's like a hyphenated word. Toss, T O S S dot P O T. I assume that means kind of a what? Drunkard, right? Right? Huh? Maybe. I don't know. Tosspot. I don't know. It means literally toss, you know, you take a glass and you. throw it But then, then the other expression he has is a hyphenated word too. A shuttle wit, huh? Shuttle. Now, I wonder if that's uh like subtle.

[2:57] You know, I, I often use that distinction. You know, the three kinds of minds. You know, the wits, the the dim wits and the nitwits. I told you that, right? You know, that kind of the humorous name I give to the three kinds of people that Hesiod distinguishes, and that Aristotle follows in the Nicomachean Ethics, and Thomas follows, and Saint Basil the Great has the same division and so on.

[3:24] Huh? There are those who can discover these great things by themselves. That's one class. There are very few. Then there are those who can't discover these great things themselves, but they can learn from those who have discovered them. And there's a third group who can neither discover these things, nor learn them from those who have discovered them. Right. So I give them the name wit, dimwit, nitwit.

[3:51] So I classify myself as a as a dim wit. But the upper class dim wit, right? Those who know where the wits are. But the lower class dim wits don't even know where the wits are. See, okay. But this expression, so I was, I'm very fond of that word, right?

[4:12] So it's got an interesting expression, uh shuttle wit, huh? Is that someone who's always changing his opinion according to the times and circumstances. I never heard the phrase before of you. Shuttle wit, huh?

[4:33] I don't suppose Shakespeare uses that word shuttle in many other places. You might. This is not Shakespeare. No, this is this is Robert Louis Stevenson, right? You know. But the the black arrow set in the in the War of the Roses that time, huh? So.

[4:50] Speaking of dim wits. Pretty good, I thought. Right. Okay. Let's look here at the on page five here, the start of the fourth reading.

[5:09] And the first part of this reading is a continuation of the comparison of magnitude and time, right? We'd seen in the previous reading, in the third reading, was it that time and magnitude are divided in the same way, right? So if the magnitude is what not divisible into indivisibles, then time is not divisible into indivisibles, right? Or if time magnitude is divisible forever, time is also, and vice versa.

[5:54] But now he looks a little more broadly at that phrase unlimited, and he's going to say that there's two ways in which you could speak of the unlimited in regard to magnitude or regard to time, and they're going to correspond in both kinds of the unlimited, huh? Okay.

[6:20] And if either is unlimited, either time or magnitude, right? So will be the other, and as the one, so the other. As if time is unlimited in its extremities, so will length in its what extremities. So if you're going along a line, and traveling a line that has no beginning and no end, how long you going to be traveling that? For a time that has no beginning, no end, an infinite time.

[6:55] See, okay. And if that's saying like it has no extremities, right? The distance or the time. If one has no extremities, the other one doesn't, right? Well, if one is limited, the other will be what? Limited, right? Okay. And another one that we've seen already before, that if the magnitude is divisible forever, then the time is divisible forever, and vice versa, right? Okay. So they'll be limited or unlimited in the same what?

[7:27] Way, right? These two. Now, since he's already manifested that if one is divisible forever, the other is divisible forever, we saw that they can be done together. He touches upon a what? Problem that Zeno raised, right? Okay.

[7:49] Now, do you know who Zeno is? He's a student of Parmenides? Yeah, he's a student of Parmenides, right? And Parmenides is not really a natural philosopher. Although Aristotle does talk about him a bit. not his natural philosophy, because he denied that motion existed. He denied that there's any change. Well, nature is defined as the beginning and cause of motion and rest, etc. So to take away motion or change, right, is to take away the whole natural science.

[8:32] Just like Thomas says when he's in ethics, there, you know, someone denies free will, he's taking away the whole of what? Ethics, huh? And the whole practical philosophy, you could say, huh?

[8:50] Now, Parmenides' pupil Zeno is trying to defend his what? Master, right? And of course, they were attacking Parmenides and was ridiculous denying that motion or change exists, right? And

[9:08] Zeno would try to point out that you're in a ridiculous position, maintaining that it is. Okay. And apparently, what argument Zeno would be based upon? Assuming that going some distance involves what? Touching upon an infinity of what? Points, right? Okay.

[9:34] Because the continuous is divisible forever, right? I've got to go to this point before I can go to another point. There's going to be infinity of points going to have to touch upon. Well, how much time is it going to take me to go any distance? If I have to go through an infinity of points to get out of this door, right? Then it seems they're going to take what infinity of time to get out of this place, right?

[10:00] Okay. Okay. So I can never go any, you know, it's going to take me forever to get out of this room. I'll be here for for for eternity, right? Trying to get out of this room. Okay. Aristotle says, well, we can kind of answer Zeno, right? By what we saw before, that and what he said again here in general, even more generally, that time and magnitude are equally what. Yeah, or un Or limited, in the same way, right?

[10:32] So that if the magnitude is divisible forever, then time would be divisible forever, right? And if the magnitude involved what, infinity of points that you went through, you'd have an infinity of nows in a finite amount of time, nevertheless, right?

[10:50] One point or one instant for each what, point of the what, magnitude, right? See, and as if Zeno is thinking what, that to go to each point along that line, being an infinity of points on that line, is going to take an infinite amount of time. He's talking about infinity there in the sense of what, a time that doesn't have any end point, right? Okay.

[11:22] But if time is divisible in the same way that the continuous is, if the continuous line was composed of infinity of points, then time would be composed of what, infinity of instances, right? You'd have enough instances to go through all the points, right? So just like in a finite line, right, there's an infinity of points according to that false thinking, right? So in a finite period of time, there's an infinity of nows or instances.

[11:53] Once you have enough nows, right, to cover all the points in the magnitude, it only takes you a finite time. Do you see that? See. Well, no, no, no. What the guy, guy saying? He's falsely imagining, right, that in a finite distance, let's say from here A to B, there's an infinity of points along that line, right? He's thinking like the modern mathematician says a line is composed of infinity of points.

[12:26] So I've got to go to one point and then another point and then another point and another point and then another point, right? Yeah. It's going to take me some time to go from one point to the next point. We just assume it is. Right? Okay.

[12:41] And therefore, it's going to take me infinity of time to go through all these what, infinity of points. Yeah. Okay. See, therefore, it's going to take infinity of time, right, to go a finite distance. So one will never be able to leave a room, will he? No. One will never be able to get home. I've got to go through an infinity of points to get home. Yeah.

[13:06] And always takes me some time to go from one point to a later point. Since there's infinity of points, it's going to take me infinity of time to get home. Huh? Yeah. Yeah. Gotta call home. Yeah. Are you home? You see the point? See. Yeah. Aristotle's saying, well, no. It won't take an infinity of time, a time that goes on forever and ever and ever, right? You can go through an infinity of points in a finite time, let's say x y, because these are divisible in exactly the same way.

[13:51] And so, for every point on this line, there's another what? There's a corresponding instant or now, right? So I have enough nows here to go through this infinity of points, and it'll still be a finite time, right? Here to here. Do you see that? Okay. So Aristotle, as Thomas says, that's what they call in an argument ad hominem, right? To the man, right? Because the man is assuming what?

[14:24] That the line is composed of an infinity of points, right? And therefore, you have to go through an infinity of points, right? And then the argument is going to take an infinity of time, right? Okay. Why? Because you have to take some time to go from one point to a later point, huh?

[14:47] But if time is divisible as much in the same way as the magnitude, right? Then there will be for every point on the finite line, right, an instant of time, right, to be there, right? Okay. So the time will be finite, even though composed of an infinity of what? Nows. Just as the distance is finite, although composed of an infinity of points, huh? Aristotle doesn't think that a line or time is composed, actually, right?

[15:25] He showed that before, right? But he's just showing here that one could answer the man's, Zeno right? With that assumption still. With his assumption, right? Yeah. See. Okay. This kind of like just kind of like a corollary that falls out of seeing that they're infinite and infinite in the same way, right? If there, if one is infinitely divisible, then the other is able to be divided forever.

[15:55] See? Okay. The use of ad hominem. I always thought that kind of argument was sort of like what you do is instead of talking about the argument, you attack the person like his character. No, it's not really attacking a person, but it's kind of answering his what objection, right? Not in reference to the truth, but in reference to what he thinks, right? Oh, okay, okay, okay.

[16:27] So. But kind of almost like an aside in the sense of Aristotle, right? Yeah. That's a good question: Maybe there is something I missed before, but so then what? What did people like Parmenides, for example, in the school of Zeno and the school? On the one hand, it almost seems like a primitive form of kind of skepticism. Or what did they do with the data of the senses that they perceived every day?

[17:00] They saw things moving, coming and going, and they knew that they were happening. They basically denied the data of sense. They said it was an illusion, right?

[17:12] Actually, let's make a little reference to this. If you read the text that we have of Parmenides, he thinks of two roads, right? And one road you might say is the road from the senses.

[17:43] But as Heraclitus showed, and many other thinkers have, reasserted: when you proceed from the senses, you often get into what seems to be a contradiction, right? Okay.

[18:07] Now we saw a little bit of the fragments there of our friend Heraclitus, because he said the healthy become sick, right? And sick become healthy, and day becomes night, and night becomes day, right? And we all say that, don't we? Okay. But the word "becomes" means what?

[18:35] Comes to be, right? Now, can the healthy be sick? No, then the healthy would both be healthy and not be healthy, right? They'd both be sick because they're sick, and not be sick because they're healthy. So it involves a contradiction, right? And so you may remember the fragment of the great Heraclitus, where he says, "You know, men admire Hesiod, the great poet, along with Homer, and he didn't even know day and night.

[19:15] They are one," he says Heraclitus, because day becomes night, and night becomes day. And maybe Hesiod said, "You know, he does a work called 'Works and Days, ' and so maybe he said, 'You know, get up in the day and do your work, right? Get your work done. '" And you go to bed at night and get your rest, right? Just day is one thing and night something else.

[19:36] One is more appropriate to labor and the other to get your rest, huh? As if they're two different things, but they're one and the same. And he says the same thing about the waking and the sleeping, right?

[19:51] Now it may be that Heraclitus did not really think that day is night and night is day, right? That the waking are the sleeping and the sleeping are the waking, right? And I point to another fragment we have of Heraclitus where he says, "We should not act and speak like those asleep." He goes on to show how profound this thought is, right? But should indicate that he obviously thinks there's a difference between being awake and being asleep, right?

[20:26] Okay. But nevertheless, he's pointing out what seems to be a contradiction in what what we sense, right? See, now if you go down through the history of philosophy and history of science, that matter, following your senses often leads the mind into at least apparent contradictions like that. We'll see ones later on here in book six on the one that that got our friend Hegel right into, the twentieth century, huh?

[21:01] The same thing happens in experimental science. Uh, Heisenberg, if you look at his Gifford Lectures there, was, giving the history of quantum theory, he talked about the strange apparent contradiction between the experiments. And you may know a little bit about the history of science that back in the

[21:24] time of Sir Isaac Newton, I guess, Sir Isaac Newton proposed an hypothesis about light that consisted of what a shower of particles, right? Pinpointed little particles. And Huygens, right, proposed a theory of light that was a wave-like phenomenon, spread out like a wave, huh? And they could use either hypothesis to explain what they had seen about light, huh? And so no one knew who was correct, although some of them, you know, were not trying to follow Newton because he was a great authority, right?

[22:05] But then the nineteenth century, they performed an experiment that indicated that light had to be a wave, right? Spread out like waves, and so it seems to have been resolved in favor of what Hugh Jens, right? But then, in, 1905, Einstein got the Nobel Prize for explaining the photoelectric effect. That's a theme this year. We had three papers, you know, all worthy of the Nobel Prize. But the photoelectric effect, he could explain that effect only by assuming that light was not in waves but in pinpointed particles.

[22:43] So now you have these pinpointed particles indicated that in one experiment And a spread out wave in the other. Okay, so you have this strange apparent contradiction. And quantum theory arose and developed trying to what overcome that contradiction, huh? Okay.

[23:06] And finally, did okay. But then Einstein developed the special theory of relativity and the general theory of relativity, and apparently, if you really let them confront each other, they start to contradict each other. So the situation now in science is you either do general relativity. And forget about quantum theory, or you do quantum theory, forget about general relativity, because you can't combine the two, right? And this what they call string theories is

[23:42] what they're trying to develop in order to resolve the two, right? Okay. So I mean, it's not an unusual thing down through the history of of natural science, whether you are using you know experiments or just using your senses alone, which you run into what seems to be contradictions, right? Okay. Now,

[24:12] Parmenides sees the contradiction, but he sees no way out. Okay. And then he talks about another road, the road from the impossibility of a contradiction

[24:35] in things in reality. Okay. The impossibility of something both being and what not being, right? And he says you can't even even think that something can both be and not be, yeah. And these men who say day and night the same thing, he calls them what two-headed mortals, right?

[25:00] You need one head to think it is so, and another head to think it's not so. But one the same head couldn't think that both is and is not, huh? That's kind of a beautiful way. Because obviously, two-headed mortal would be a monster, right? And so monsters mean something what, a pose to nature, right? So it's against the very nature of our mind to think that something can both be and not be, right?

[25:27] And Plato's dialogue called the Parmenides, where Parmenides is examining Socrates as a young man, and Socrates is contradicting himself in the same way that the men that Socrates examines elsewhere, right? But he comes to Athens with his pupil Zeno, right? And they talk to Socrates, so Plato represents Socrates as in a way learning what we might call the Socratic method, right, of examination from Parmenides and Zeno.

[25:58] But Socrates' method is in fact based upon this here, right? He examines you to see if the different things you think fit together, whether they contradict each other, okay? Um.

[26:17] So he says this is the true road, and that's the what false road, right? The road of illusion, right? Okay. Now, we talked before, I think, didn't we? I gave those papers on the rule of contradiction in our knowledge, didn't I? Yeah, yeah. Now, Aristotle coming on the scene, and perhaps Plato too, but very clear, Aristotle especially. Aristotle coming upon the scene says, "Well, Parmenides is perfectly correct in saying it's impossible to both be and not be right."

[26:54] Okay. And Aristotle spends a good deal of Book Four of Wisdom refuting attempts to deny this, right? Okay. That's something really obvious to us. But at the same time, he says it's absurd to what? Deny that there is change, right? But that's clear in our experience that there is change, huh? Okay.

[27:20] Now, how do you avoid the contradiction? Well, by realizing that what seems to be a contradiction in change is not in fact a contradiction. Okay. That's an apparent contradiction in things, right? Could be a real contradiction, in our thinking, but an apparent contradiction in things,

[27:49] under which is hidden something that we haven't seen yet, right? Like Heraclitus said, the hidden harmony is better than the apparent harmony. Okay. Now we saw a little bit of how Aristotle unties that, right? See. Because you've got a problem. You see, if you don't admit in some way that the healthy become sick, right? You say the healthy can't be sick. Therefore, they can't come to be sick, right?

[28:20] Then the healthy will always be healthy. Hope you're healthy today. Okay. But likewise, if the sick cannot what? Be healthy, the sick cannot come to be healthy. So if you're sick, you're always going to be sick. Tough luck.

[28:43] So it seems you've got to admit somehow that the healthy become sick and the sick become healthy, and the light becomes dark and the dark becomes light, and the hard becomes soft and the soft becomes hard. There's going to be any change at all. But then you seem to be admitting what? Something impossible. That something both is and is not hard, both is and is not light, huh?

[29:10] Okay. Of course, we all speak that way. It's not like some some madman saying this, right? We all say that, right? Okay. Sometimes the good become bad, right? Sometimes the bad become good, right? See. Otherwise, we'd be we'd be Calvinists.

[29:31] If you're good, you'll always be good. You don't have to worry about, working your salvation. once you're in trouble, if you're bad, you're also, you know, give up. You know, you're never going to become good.

[29:44] You see what I mean? Okay. Now, if that's impossible, why do we speak that way? Well, suppose the cook is a pianist, right? Well, then you could say that a pianist cooked dinner, right? And if the cook sits down and plays the piano after dinner, you can say the cook played the piano, right? You can say that because to be a pianist happens to the cook, right?

[30:24] And to be a cook happens to the pianist. But does the pianist, as such, through the art of playing the piano, make a nice dinner? And does the cook, as such, through possessing the art of cooking, know how to play the piano?

[30:49] It's the cook, as such, that cooks, and the pianist, as such, that plays the piano, right? See. So it's not really the healthy, as such, that becomes sick, right? But that to which healthy happens, namely the body, right? And it's the body, as such, that becomes sick, right? And it's not the sick, as such, that become healthy, but that to which sickness happens, the body that becomes healthy, right?

[31:23] So in a way, you're being deceived here by the first kind of mistake outside of words, right? Mistake from things. The mistake of the accidental. What happens, right? Okay.

[31:41] And the reason why this apt to deceive us is because necessarily before you become healthy, you're sick. And before you become soft, you're necessarily hard, right? And before you're light, you're necessarily dark, right? See. And so here's something that happens necessarily, right, to what becomes something, but it itself cannot become that, right, and as such.

[32:14] But if you can't untie or break down that apparent contradiction, you see no way out of it, right? Then you'd have to choose, as it were, between the road from the senses which leads you into contradictions, right, and the road from the impossibility of a contradiction, right. But Aristotle, seeing the truth, seeing the impossibility of contradiction in things, right, and yet realizing that change what exists and that's clearer than a thing, he can understand, right, the road from the senses into reason, huh?

[33:05] Okay. And that the what seems to be a contradiction to our senses cannot immediately be a contradiction, right? But the appearance of a contradiction there is very important in the development of our knowing. Because we get into these apparent contradictions, because there's something hidden there we don't see. Okay,

[33:39] so when the Greeks, you know, spoke of change as being between contraries, they didn't see clearly that there was a third thing involved in change, It is really the subject as such of this change.

[33:54] So in a way, it points out where there's something hidden to our mind under that apparent contradiction. But down through history, you'll find men like in modern times to take Hegel, let's say, or or Karl Marx, who seem to speak, you know, as if there really was a contradiction in things, huh? Comrade Lenin, right? Let me just use some quotes from Lenin there, because Lenin makes concise statements, and he says, "Talk about what dialectics means in the Marxist sense.

[34:35] You know, the official name for Marxist philosophy is dialectical materialism, and dialectics, the Marxist means, as Lenin tells us, it's a study of the contradiction within the very essence of things.

[34:52] So Hegel and Marx and following them and so on, they admit what contradictions, right? And sometimes you find the modern mathematicians saying, "Well, you can't do some of this higher math without accepting contradictions, right? " I heard that. Oh, said by men who are in the mathematical world, yeah. And Weizsäcker, you know, the people, Heisenberg, you know, he was trying to what? Have another logic, another logic, right?

[35:25] For subatomic events, right? They didn't observe the what impossibility of contradiction and the impossibility of something being between the two, right? I mean, really, there's two axioms here of being and non-being, and one is it's impossible to both be and not be, right? And the other is it's necessary to be or not be.

[35:53] Shakespeare, when he says, "To be or not to be, that is the question," in a way, touches upon both, right? Because the question, because you can't both be and what not be, right? And you must be either one or the other, right? Okay. So he wanted to

[36:13] have a logic, right, where you could avoid those things, right? You know, or admit them in a sense, right? Admit what they deny, and Heisenberg, I think, is a little wiser there because he says. He's got Aristotle more, and he understands more potency or ability than than Weizsäcker does, right? Okay. And

[36:51] there's nothing in between being an act and not being an act, but in a way, potency is in between the two, right? Okay. So to understand that, he he he wants to kind of have new logic. So you find it's down to the history of human thought. You know, I run into philosophers, the Heideggerians, you know, or talking to one Heideggerian, you know, real Heideggerian, right?

[37:18] You know, and of course, with this principle of Parmenides is mentioned. That's taken quite a beating lately, hasn't it? Like, you know, no, it's not the matter, right? Take quite a beating. They were saying that to me. So I mean, it's not this is you know something unique to the Greeks, right? That they would run into these things. And

[37:44] I told you the time my old teacher, Kasurik did undergraduate was down at some philosophical meeting in Chicago. There, Kasurik was a tough guy when he graduated, you know. Oh man. Did so you got this guy in contradiction, right? Exactly. And Kasurik says, "Now what are they going to do about it? "

[38:05] The guy says, "Oh, well, that's a contradiction I've learned to live with. " So I mean, you have people go around like this, you know. It's kind of funny now, you know, in the political situation now, because

[38:29] the United States is kind of forced to to deal with what, Arafat, right? Because to some extent, he represents the what Palestinian people, right? Okay, so they have to somewhat deal with Arafat, right? Yeah. And for that reason, and also because he has some support among the Arab nations, and if they don't deal with Arafat, they might what lose the support of the Arab nations when they go after Hussein, as they're going to have to do before too long, okay?

[38:59] Since they built their stockpiles. And but of course, everybody knows Arafat is kind of a terrorist himself. He's been supporting the terrorism over there, and so on, and and they actually have documents to show this, and so on. So we have to kind of have a contradictory policy, right? You see, and we can't, you know, say we're going after terrorists and those support the terrorists. Well, then we should be going after Arafat.

[39:26] But in this case, there are other things that make it, you know, not maybe prudent to go after him. Right now, see? And he's

[39:36] glad other people could do that, right? See, so isn't this contradictory? I suppose it is, but but I mean the course of action. I mean the thinking that they know he's a terrorist. not thinking that he is, that he's not a terrorist, right? But there are other reasons why they're going after some terrorists, but not after this one or after these people who support the terrorists, the Taliban.

[39:58] We did right, but not these ones, right? So, do you have any sense of sort of what's this infatuation or whatever with this denying the principle of non-contradiction? It's just all over the place. Well, I know. I mean, it's Aristotle, as I say, takes this up in the in the fourth book of wisdom, right? And he says, you know, some people might deny it just. You know, out of perverse stubbornness, right?

[40:31] Okay. But more reasonable people deny it because something seems to what. It may not be, it seems. night turning into day. Yeah, yeah. Now, what they don't realize

[40:49] is that they're denying in words the axiom of contradiction because something contradicts it. So they're denying it because they what? Accept it. Actually, hold your own. Accept it. Yeah. You see. And that, of course, shows that their what objections are invalid, right? Yeah. Because they're based on assuming the truth of what they're trying to deny, right? Yeah. Now they assume it's one of their premises, you might say, right?

[41:23] What they're trying to deny their conclusion. Yeah. And so, but like you know, I think I mentioned before how my brother Mark, when he worked on the so-called attempts to prove the fifth postulate, right? And there have been doubts since ancient times, even in Proclus, right, that where the fifth postulate is known by itself or something in proof, right? And my brother Mark defends it as something known by itself, not as obvious as some other things, right?

[41:55] But something nevertheless really obvious. But he's examined the attempts of various people down to the ages to try to prove it, and apparently every proof assumes the very thing he's trying to prove as one of his premises. And so my brother Mark points out that that obviously makes the argument invalid, right? Yeah. Um.

[42:20] So Shakespeare calls a woman's reason. In the two gentlemen of Verona, you know, when they're talking about the various suitors for the hand there, and she asks her her maid, you know, who she thinks is the best, right? And and she thinks Proteus is right. And she asks her for a reason, and she says, "I have no reason, but a woman's reason. It is so because it is so."

[42:48] Okay. Well, it did stick back. This is the right man for you, you know. But she can't really give a reason. Okay. So you're saying it is so because it is so, isn't it? You know, it's not a reason really. But the second point my brother Mark makes is that this is a sign that they really know it, right? That without realizing it, they're always assuming it for granted, isn't it?

[43:14] And something like that, I think, you know, people deny the axioms about being and unbeing, the axioms about contradiction, because something seems to contradict it, right? And so they're really assuming it in order to make an objection at all. But they don't realize they're assuming the very thing they're denying. It's a sign that they really know it, right? Well, can't be so. Something contradicts it, can it?

[43:40] Okay. So, you know, this kind of prepared the way for Aristotle then to see more fully that these are not really two different roads, right? Right. I mean, excuse me. These two are not two different roads, right? But the road from the senses into reason, right? It starts with the senses, and then when reason starts to understand some things and to understand some statements, what first, understands is what Hermenides was pointing to, right?

[44:23] And but you can reconcile the two because the apparent contradiction that arises here, right, is not a real contradiction. But those apparent contradictions that arise, they puzzle the reason because it knows that can't be so. Okay. And then realizes after a while that hey, this can be useful, right, in discovering something you don't know because hidden underneath this there must be something you don't see, and that the untying of that contradiction will be the discovery of that hidden thing.

[45:14] And so those reasons that Aristotle gave to the rule of contradiction in the development of reality very important. It took some time to get there. Yeah.

[45:27] I mean, he speaks explicitly there about about these two roads, right? But they're really one road. Okay. He kind of breaks the road. See, Heraclitus, you know, says the things that can be seen, heard, and learned are what I prize the most. Going from the senses there, right? Sense of discovery, sense of learning, right? Things that can be seen, heard, are what I prize the most. And Empedocles says, right?

[45:59] You know, he says you can't see God, right? And you can't touch him. And this is the broadest road leading into the mind of man, he says. Kind of interesting that that he singles out the sense of sight and the sense of what touch, right? Because those are, in terms of knowing, the most important. Sense of sight is a sense of clarity, the sense of distance, and sense of touch is a sense of what Certitude, huh?

[46:30] But they're the only senses that know the shape of a thing. And you know how important shape is, and knowing everything from a chair to a cat, right? And I recognize the cat not through by its color, but by its what shape, right? And I recognize the chair not by its color, but by its shape, right? I recognize a man not by white, he might be black or something else, right?

[46:54] But by its color, but by its shape. But the sense of touch and the sense of sight are the only senses of shape, no form, right? Now, there's other fragments where he talks about sight and hearing too, huh? Like the other guy, Heraclitus does, right?

[47:19] So, emphasize that road from the senses into reason, huh? Parmenides wants to follow this road from the impossibility of contradiction, but they're really different stages, you might say, along the same but road, right?

[47:42] Okay. So that's kind of just a an aside in a way or for this reading. They are, if you've seen the text of Thomas, they're divided now against everything almost as gone before, okay? And it's almost unnecessary for a number of reasons to do what he does, but he's doing it in a kind of a formal way.

[48:11] What is shown mainly up to this point is that that nothing continuous is composed of indivisibles, right? That the continuous is composed of indivisibles,

[48:41] or you could add or divide it into indivisibles, right? They kind of go together, right? Okay. Or I want to put it affirmatively and say every continuous is divisible forever, right? Or every continuous is divisible into things that are always divisible, okay?

[49:17] Okay. The second definition of continuous, huh? Okay. But now he wants to say, and it's almost unnecessary to say if he wants to say it, like he's supposed to? say, that nothing continuous is indivisible either, so it's neither composed of indivisibles. Nor is it what is it indivisible? Okay, okay. So in these last two paragraphs, he's just going to make that explicit. Now, in a way, he says it's almost unnecessary because if by continuous you mean that whose parts meet a common what boundary, right?

[50:04] Well, then you have parts in the very definition of the continuous, right? You know, if you go back to logic, there where the chapter on quantity, you divide into discrete and continuous, right? And as Thomas says elsewhere, every quantity seems to consist in a kind of multiplication of parts, okay, and. So that the difference between the discrete and the continuous is in the continuous quantity, the parts meet at a common boundary or limit.

[50:38] But in the case of the discrete, like the number seven, the parts like three and four don't meet anywhere. Don't meet at a point or a line or anything else. Okay. So if the continuous is that whose parts meet at a common boundary, then parts is the very understanding of the continuous. So how could the indivisible be what? Continuous. Yeah. How could the continuous be something indivisible?

[51:07] Right. Okay. Likewise, if we've shown that the continuous is divisible forever, how could be something what? Indivisible. Right. Okay. But nevertheless, Aristotle wants to make this kind of explicit, right? Because he's shown before that what the continuous is not composed of indivisibles, right? And you might want to add, nor is it an indivisible. Does that read the same statement? Right. Exactly. Say. Okay. So having shown that it's not composed of indivisibles, now Aristotle wants to show that it's not indivisible.

[51:53] Right. Okay. And and and it says you have to have kind of suspension there. I mean, kind of keep you wonder up, right? Kind of suspension of what you learned before in a way, right? And you're asking now, can time be something what? Indivisible, let's say, right? Huh? Okay. Or a magnitude be something indivisible, right? Okay. Can the distance you travel be something indivisible? Can the time you travel be indivisible, right?

[52:25] Okay. Like here and even with the first, I was wondering: Is does he have some other kind of common notion of continuous? Because what he's trying to prove is a definition, or is he just like just thinking of examples without like magnitudes, time, and. Well, it's like it's like he's not thinking explicitly of the definitions there, right? Huh? Okay. So he says it is clear from the aforesaid, as if it almost comes out of what you've seen before, right?

[52:57] This is next. This is the last paragraph now on page five. It is clear from the aforesaid that neither line nor surface nor body nor time, right, nor generally any continuous thing will be what indivisible, right?

[53:16] Not only through what has now been said, but also because it will happen that the indivisible be what divided. Okay. Now, here's a way of showing this, which is similar to what we've seen before. and

[53:32] starts out with certain reasonable assumptions here. Since at all time there's the faster and the slower, right? And the faster, of course, it seems goes through more in equal time.

[53:47] There can be somewhat ratio between the faster and the slower, right? And it's kind of indifferent which ratio take, but let's take three to two, right? Okay. It may happen to go through double and one and a half the length. This may be the ratio of speed. Let then the faster be brought one and a half the distance in the same time, and let the magnitudes of the faster be divided into three indivisibles, A, B, B, C, B, D.

[54:18] So the faster body in this amount of time is going from what through A, B, B, C, B, D, which indivisibles? And the slower, which is only what two thirds as fast, right? Is going through E, F, and what F, G, right?

[54:38] Accordingly, the time will be divided into three indivisibles. It goes through an equal distance in equal time. Let then the time be divided into K, L, L, M, N, N. Okay. So the faster body has gone through the indivisible magnitudes A, B, B, C, B, D in the indivisible units of time K, L, L, M, M, N, right? Now the slower has been brought the distance what?

[55:07] Has only gone through two of those indivisibles, E, F, and F, G, the distance E, F, G. So it's going to what? The time K, M, in half. Yeah. In which case, how do you divide three units, three points, and three indivisibles? You've got to take one and a half, right? So you got to divide the indivisible, It's of course, as contrary to what the indivisible is.

[55:37] The indivisible therefore will be what divided, and it will go through the partless not in indivisible but in more. And of course, you could turn around and divide the other if you want to.

[55:51] Instead of that, you could say what? You could divide the magnitude E, G into three parts. Yeah. Yeah. The same argument basically, huh? But then you could do that simpler in a sense. You could say that what in one unit of time, which is indivisible, right? Let's say the what slower body goes a certain distance, right? That same distance, then the faster body goes in in less than one unit of time.

[56:29] You can't go In one unit of time, because it would be just no faster? What what is our less than one indivisible of time, right? Well, see, not be that different from what's gone before. I mean, it's basically the same, right? But it's a little difference to say that something is what not composed of indivisibles, and it's not what indivisible. Yeah, yeah, yeah. Okay. Because something could be what

[57:04] what not composed of indivisibles, but indivisible. Yeah, yeah. Like a point is right. Okay, point is not composed of indivisibles, but it is indivisible, right? The one that's the beginning of number, right, is indivisible too, right? But not composed of indivisibles.

[57:31] See how modern math follows? you up, right. Because they'll think that they're always comparing the what you know number to the continuous, right? And they're really dividing the continuous as if they were dividing the what number number. Yeah, so they divide the one into two halves, right? But actually, the one that's the beginning of number is simpler than the than the point. Infinitely. Yeah. I mean, I mean.

[57:58] So sometimes, you know, the the Greek geometers would say that a a point is a one having position. It adds to one an idea of position, right? So if the point is indivisible, then even more so is the one.

[58:18] Okay.