Natural Hearing (Aristotle's Physics)
Lecture 80: Scientific Hypothesis, Contradiction, and the Road to Knowledge

Transcript
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It's totally unexpected, right? And that's kind of something that just happens, right? But the experiment itself, the reason why they chose this experiment was because they had a hypothesis that seemed interesting, right? But the hypothesis, according to Einstein, is what? Freely imagined, right? And has no justification at all from what we already know. Being freely imagined, its whole justification is what you might predict on the basis of it, right? And if you can predict not only things that you already know to be so, but if it leads to a prediction of things that nobody's ever observed, and then they are finally observed, right? The kind of amazing example in there of, in physics in the 20th century, how it sticks in my mind, is the one of Dirac, I guess. He worked out the, you know, Heisenberg, people came to him with the theories, and Dirac worked out some of these things mathematically, right? And out of mathematics came a negative electron, right? Or a positive electron, which became, but no one ever observed what, you know, something like that, something like that electron, but with the same mass, but, you know, positive charges, something like that, right? And then some months or years later, the positron showed up in the experiment, right? Here's a guy who predicted the existence of a particle that nobody knew existed, right? Came out of his theory, you know? And that's really what strikes them, you know? You see? On something that they had never observed, right? So, are these things then really known to what we naturally understand? I don't think so. Or can they be proven to what we naturally understand? I don't think so. And, of course, Einstein says that the, even after you confirm the scientific hypothesis, it remains a guess. It's a tested guess, but you still don't know it's so. So, of course, in elementary logic, we know that the confirmation is not a syllogism. You're saying, what? If A is so, B is so. B is so. It doesn't fall into saying that A is so, does it? No. And Einstein gives the example of Newtonian physics that predicted so many things. It was amazing about Newtonian physics, I guess, when they made more observations and so on about the planets, they discovered that the planets are not traveling exactly where they should, according to Newtonian physics, right? But they'd had so much success in Newtonian physics that they were not ready to jettison it, right? And so they guessed there must be other planets unknown to them. And their mathematics was so exact, they could predict where these planets would be. And they trained their telescopes and so on, right? And eventually found the last planets, see? You know, that's an amazing discovery, right? That they'd discover, you know, a planet that had not been known from, you know, over the thousands of years men have been studying the sky, right? And so that they began to think, well, Newtonian physics must be true. I mean, there's so many amazing, you know, things. And then all of a sudden in the 20th century, Einstein, with a different hypothesis, right, predicted the same things that Newton predicted, but also some things that Newton couldn't predict, right? And then he said it became crystal clear that you never really know that these things are so. But I say the basic reason is from elementary logic, right? Now, the more things you predict and the more precise those predictions are, you know, the greater probability there is. That's why, you know, when they try to use the experiment in sociology, it doesn't mean much, you know, because the predictions are so vague. But you say it's going to be a, it puts the sun starting at, you know, 504, and there it is, 504, you know? It's kind of hard, you know, to say it just happened, you know, that you're getting right in the nose, you know, 504, right? We say, you know, it's going to be trouble, you know, it's going to be a vast, you know, sociologist, very vague things, you know? So maybe through what we naturally know, you don't know these other things, right? In fact, you don't know, period. This makes sense. So if a man is accustomed to experimental method, where all ideas are hypotheses, right, then he might think, because of custom, right, that all ideas are the kind that he's accustomed to, huh? And I always, you know, to me it's kind of laughable, but, you know, one of the great scientists there, Claude Bernard, right, the biologist, right, he has a very naive view of philosophy and theology, right? For him, the scientist, you know, he has ideas, but he tests them, right? You know, his ideas, he deduces the consequences of them, and then he, what, tests the consequences, right? The philosopher, he has ideas, he deduces the consequences, he never tests the consequences of the ideas. The theologian, he just tests ideas, I said. But he's a brilliant, you know, he's one of the fathers about physiology, right, and he has a good understanding, you know, of the, you know, he says, you know, that doubt is intrinsically the formal method, right, you see? But he has these very naive views of what philosophy and theology is, because all they can be is a truncated, you know, part of what, you know, the only method is, there is, the scientific method, right? And he has no real understanding of those things. My friend Warren Murray often jokes, though, you know, they often make remarks about the ancients without reading them, right? So they're always making hypothetical statements about what the ancients did, but they never bothered to verify. So they don't use their, you know, they don't use their own method, you know? It's kind of amazing, I like to kind of kid these people a little bit, you know, you know, Plato and Aristotle Aristotle and Thomas Aquinas thought that there was a maximum speed in the universe, right? And no one thought that until, what? Einstein, right? You know? So Aristotle, in ancient times, Thomas and the ladies, in ancient times, thought there was a maximum speed in the universe, nobody else did. There's all kinds of things, you know, that are kind of interesting, you know, like that. But they make all kinds of outrageous statements, you know, about what the ancients were doing without ever, what, testing their hypotheses. But, of course, we can't always be consistent, you know, to errs, human, huh? Okay? So next time we'll start on the fourth reading, right? Over below the other, then that's contrary to all the radii being equal. Okay? And therefore the definition is separate, right? So therefore they affect one side, right? But Euclid doesn't get there as a theorem, does he? Inclusions and not axioms, right? But in some way the axioms... There is a tendency, right? Yeah. Yeah, yeah. See? And so there's some kind of a movement of the mind there, but more so, say, in the fourth theorem of Euclid, right? Or more so in that movement from the definitions of circle and diameter, right? To the equality of the two parts of the circle, gotten by the diameter, huh? It's not so much steeper, but I mean, I think there's some kind of a manifestation of that, right? See? But the same way, when you take the pops so that the... the... all radii angles are, what? Equal, right? Okay? And Euclid doesn't try to prove that, does he, right? Okay? Now, we know by the definition that these two angles are equal. And by definition that these two are equal. But how do you know that this is equal to that, right? Well, I think you go through a little process there, right? You imagine this line laid at this line at that point, right? Okay? Now, if this line coincides with this line, then obviously they're equal, right? Mm-hmm. Straight lines are cut into instruments, right? Where in the name of the hole is equal to twice the rectangle taken by the hole in each of the lines. You know, it's kind of unstopped, right? I guess you can get to, you know, the average man. Son, Holy Spirit, and man. God, our enlightenment, guardian angels, strengthen the lights of our minds. God bless you. God bless you. God bless you. God bless you. God bless you. God bless you. Order and illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor. Amen. And help us to understand the word for today. In the 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 now, you know, the famous one, the Black Arrow. Do you know that one? Yeah, just the name. And you should have the illustrations of Wyeth, though. He illustrated some 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. 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 made, huh? P and B, huh? The thing that struck me was, a little bit later on, he was, so David, I was kind of watching out in the War of the Roses to see who was going to win 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, after Shakespeare's plays, it represents the historical events, more or less, you know, things are changing back and forth between the House of Lancaster and the House of York, huh? And so this guy's playing it. And, of course, not to hurry to go off to the battle, because he might be on the wrong side, right? See who's winning, then come in and give him a little push and get the spoils, see? But in talking about those who rush in, huh, he calls them tosspot, it's like a hyphenated word, toss, T-O-S-S, dot, P-L-T, and 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 class and you're, so. But then the other expression he has is a hyphenated word, too. A shuttle wit, huh? Now, I wonder if that's a, you know, I often use that distinction, you know, the three kinds of minds, you know, the wits, the dimwits and the nitwits, I've told you that, huh? Right? You know? That's kind of the humorous name I give to the three kinds of people that Hesiod distinguishes and that Aristotle follows in the Nicomachian Ethics and Thomas follows and St. Basil the Great has the same division and so on, 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. Then 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. So I classify myself as a dimwit. But the upper class dimwit, right? Those who know where the wits are. But the lower class dimwits don't even know where the wits are, see? But this expression, I'm very fond of that word, right? Bravities of soul, wit, and all these things. So it's kind of an interesting expression, a shuttle wit, huh? That someone's always changing his opinion according to the times or circumstances. I've never heard the phrase before, have you? Shuttle wit, huh? Does Shakespeare use that word shuttle in many other places? This is not Shakespeare now, this is Barbara Bill Stevenson, right? But the black arrow set in the War of the Roses at that time, huh? Speaking of dimwits, it's pretty good. I thought I'd into it. Okay, let's look here at page five, the start of the fourth reading. 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 and magnitude is divisible forever, time is also, and vice versa. 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 in regard to time. And they're going to correspond, huh? In both kinds of the unlimited, huh? Okay? 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, you're traveling a line that has no beginning and no end, how long are you going to be traveling, right? For a time that has no beginning, no end, on infinite time, 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? Why, 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, way, right? These two, huh? Now, since he's already manifested that if one is divisible forever, the other is divisible forever, we saw that they could be done together, he touches upon a, what, problem that Zeno raised, right? Okay? Now, do you know who Zeno is? Zeno is, yeah, he's a student of Parmenides, right? And Parmenides is not really a natural philosopher, although I still just talk about him a bit, sometimes he's a 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 of natural science. 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 of practical philosophy, you could say, huh? Now, Parmenides' pupil, Zeno, is trying to defend his, what, master, right? And, of course, they were attacking Parmenides, saying, what's ridiculous, denying that motion or change exists, right? And, as you know, would try to point out that you're in a ridiculous position, maintaining that it is. Okay? And, apparently, one argument, as you know, would be based upon assuming that going some distance involves, what, touching upon an infinity of, what, points, right? Okay? 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 an infinity of points that I'm 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 it's going to take, what, an infinity of time to get out of this place, right? Okay? Okay? So, it could never go any, you know, it could take me forever to get out of this room. I'll be here for eternity, right? Trying to get out of this room. Okay? And Aristotle says, well, we can kind of answer, you know, 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 limited in the same way, right? So that if the magnitude is divisible forever, then time would be divisible forever, right? And if the magnitude involved, what, an infinity of points that you went through, you'd have an infinity of nows in a finite amount of time, nevertheless, right? 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 along that line, is going to take an infinite amount of time. But he's talking about infinity there in the sense of what? A time that doesn't have any end point, right? Okay? But if time is divisible in the same way that the continuous is, if the continuous line was composed of an infinity of points, then time would be composed of what? An infinity of instances, right? And 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. 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? I'm sorry. See? Well, no, no, no, what the guy's saying, he's falsely imagining, right, that in a finite distance, let's say from here A to B, there's incentive points along that line, right? He's thinking like the modern mathematician, who says lines are composed of infinity of points. So I've got to go to one point, and then another point, and then another point, and then another point, and then another point, right? And it's going to take me some time to go from one point to the next point. Let me just assume it is. Right? Okay. And therefore, it's going to take me an infinity of time to go through all these, what, infinity of points. Yeah. Okay. See? Therefore, it's going to take an infinity of time, right, to go a finite distance. So one will never be able to leave a room, will they? Okay? One will never be able to get home. I've got to go through an infinity of points to get home. Yeah. Yeah. And it always takes me some time to go from one point to a later point. Right. Since it's infinity of points, it's going to take me an infinity of time to get home. Better call home, right? Yeah. It's going to take me an infinity of time, a time that goes on forever and ever and ever, right? You can go through infinity of points in a finite time, let's say xy, because these are divisible in exactly the same way. 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 will still be a finite time, right? Year to year. Do you see that? Okay. So he... There's now, as Thomas says, that's what they call, in an argument, a hominem, right? To the man, right? Because the man is assuming, what? 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 he argues it's 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? 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? Now. Just as the distance is finite, although composed of an infinity of points, huh? I don't think so. Aristotle doesn't think that a line or time is composed, actually, right? He's shown that before, right? Yeah. But he's just showing here that one could answer the man's, you know, right? Yes. With his assumption, still. With his assumption, right? Yeah. See? Okay. It's kind of like, it's kind of like a corollary that falls out of seeing that they're infinite and infinite in the same way, right? If one is infinitely divisible, then the other is able to be divided forever. 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 a person like he's character. No, it's not really attacking a person, but it's kind of answering his, what? Objection, right? Not with reference to the truth, but in reference to what he thinks, right? Oh, okay. Okay. Okay. So, but kind of almost like an aside in the sense of Aristotle, right? Yeah. Maybe there's something I missed before. So then what did people like Harmonies, for example, in his school, in his school, 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? They saw things and they were coming and going. and they knew that they were happening. Yeah. Did they simply deny the data of the sense? They say it was an illusion, right? Actually, just to 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, 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? Now, we saw a little bit of the fragments there of our friend Heraclitus, because he said, that the healthy becomes sick, right? And the 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? 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. And for there one, he says, Heraclitus, because day becomes night and night becomes day. And, maybe Hesiodo said, you know, he doesn't work, call it works in days, and so on. Maybe he said, you know, you 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 is something else. What 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? 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 profound what this thought is, right? Which would indicate that he obviously thinks there's a difference between being awake and being asleep, right? Mm-hmm. Okay. Okay. But nevertheless, he's pointing out what seems to be a contradiction in what? What we sense, right? Now, if you go down through the history of philosophy and the history of science, for that matter, following your senses often leads the mind into at least apparent contradictions like that. We'll see ones that are on here in Book 6, the one that got our friend Adler, right? Again, the 20th century, huh? The same thing happens in experimental science, huh? Heisenberg, if you look at his Gifford Lectures there, was giving the history of quantum theory, and he talked about the strange apparent contradictions between the experiments. And you may know a little bit about the history of science that back in the time of Sir Isaac Newton, I guess. Sir Isaac Newton proposed a hypothesis about light, which consisted of what? A shower of particles, right? Pinpointed little particles. And Hugh Jens, right? Proposed a theory of light that was a wave-like phenomenon. Spread out like a wave, huh? And they could use either hypothesis and 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? But then in the 19th 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 thing 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. So now you have these pinpointed particles indicated that in one experiment, in 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? And finally it did, huh? Okay? But then Einstein developed the special theory of relativity, the general theory of relativity, relativity, and apparently if you really let them confront each other, they start to convict each other. So the situation now in science is you either do general relativity and forget about quantum theory, or you do quantum theory and forget about general relativity, because you can't combine the two, right? And this, what they call string theory is what they're trying to develop in order to, what, resolve the two, right? Okay? So, I mean, it's not an unusual thing, down through the history of natural science, whether you're using, you know, experiments or just using your senses alone, which you run into what seems to be contradictions, right? Okay? Now, Permanides sees a contradiction, but he sees no way out of it. Okay? And then he talks about another road, the road from the impossibility of a contradiction in things, in reality. Okay? The impossibility of something both being and, what, not being, right? And he says you can't even think that something can both be and not be, yeah? And these men who say day and day the same thing, he calls them, what, two-headed mortals, right? You need one head to think it is so, and another head to think it is not so. But one in the same head couldn't think that both is and is not, huh? That's kind of a beautiful way, because obviously a 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, huh, to think that something can both be and not be, right? And Plato's a 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 you to see if the different things you think fit together, whether they contradict each other, there, okay? 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 think it was papers on the role of contradiction in our knowledge, didn't I? Yeah, yeah. Now, Aristotle, coming on the scene, and perhaps Plato too, but it's very clear in 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, okay? And Aristotle spends a good deal of book four, of wisdom, refuting attempts to unite us, right? 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? 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 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? Because you've got a problem, you see? If you don't admit in some way that the healthy becomes sick, right? If you say the healthy can't be sick, therefore they can't come to be sick, right? Then the healthy will always be healthy. Hope you're healthy today. 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. So it seems you've got to admit somehow that the healthy becomes 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? Of course, we all speak that way. It's not like some madman is saying this, right? We all say that, right? Sometimes the good become bad, right? Sometimes the bad become good, right? Otherwise, we'd be Calvinists. 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'll also give up. You know, you're never going to become good. You see what I mean? Now, if that's impossible, why do we speak that way? Well, suppose the cook is a pianist, right? Well, then you can 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? And to be a cook happens to the pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a pianist. Well, then you can say the cook is a 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? It's the cook as such that cooks, and the pianist as such that plays the piano, right? 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? So, in a way, you're being deceived here by the first kind of mistake outside of words, right? The mistake from things. The mistake of the accidental. What happens, right? Okay? And the reason why it's 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 could not become that, right? And that's such, yeah? See? 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 a contradiction of 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? Okay? And that the, what seems to be a contradiction to our senses cannot mean to 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. And some of 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. 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 the modern times, to take Hegel, let's say, or Karl Marx, who seem to speak, you know, as if there really was a contradiction in things, huh? A comrade Lenin, right? I used to use some quotes from Lenin there, because Lenin makes concise statements. And he says, talk about dialectics means in a Marxist sense, you know, the official name for Marxist philosophy is dialectical materialism. And dialectics of Marxist means, as Lenin tells us, it's a study of the contradiction within the very essence of things. So Hegel and Marx, and following them, and so on, they admit, what, contradictions, right? And sometimes you find the amount of mathematicians saying, well, you can't do some of this higher math out except in contradictions, right? I heard that all said by men who were in the mathematical world, yeah. And Weitzacher, you know, the people of Heisenberg, you know, he was trying to, what, have another logic, another logic, right? For subatomic events, right? They didn't observe the, what, impossibility of contradiction and the impossibility of something being between, huh? The two, right? I mean, there's two axioms here of being and unbeing, 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. Shakespeare, when he says, to be or not to be, that is the question in the way it touches upon both, right? It's a question because you can't both be and what? Not be, right? And you must be the one or the other, right? Okay? So he wanted to have a logic, right? Where you could avoid those things, right? You know? Or admit them, admit what they're denied. 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 Weizsacher does, right? Okay. And 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 that I understand that, he wants to kind of have a new logic. So you find it's down through 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? And, you know. And of course, this principle of Prometides is mentioned, that's taken quite a beating, actually, hasn't it? Like, you know? Now there's lots of it, right? Take quite a beating. I remember saying that to me. So, I mean, it's not that this is, you know, something unique to the Greeks, right? That they would run into these things. I told you the time I would teach at Kasurik that undergraduate he was down at some philosophical meeting in Chicago there, and Kasurik has a tough carmography, you know? Oh. And he'd, so you've got this guy in a contradiction, right? Like, soccer company. And Kasurik says, now what are you going to do about it? Oh, that's a contradiction I've learned to live with. Oh, wait. So, you have to go around like this, you know? It's kind of funny now, you know, in the political situation now, because the United States is kind of forced 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? On that. And, uh, 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, since they built their stockpiles. And, uh, but of course everybody knows Arafat is kind of a terrorist himself. He's been supporting the terrorism over there, and so on, 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, uh, you know, say we're going to go after the terrorists and those who support the terrorists. Well, then we should be going after Arafat. But, in this case, there are other things that make it, you know, not maybe prudent to be after him right now, see? And he's going after other people who do that, right? See? So, isn't this contradictory? Well, 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 we're going after some terrorists, but not after this one, or after these people who support the terrorists, the Taliban, 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 fourth book of wisdom, right? And he says, you know, some people might deny it just... you know, out of perverse stubbornness, right? But more reasonable people deny it because something seems to what? It may not be, it seems like running in the day. Yeah, yeah. Now what they don't realize is that they're denying in words the axiom contradiction because something contradicts it. So they're denying it because they what? Accept it. It's actually all good. 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? Now, they assume is one of their premises, you might say, right? What they're trying to deny in their conclusion. 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? 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. What Shakespeare calls a woman's reason. Yes, right. In Two Gentlemen of Rona, you know, when they're talking about the various suitors for the hand there, and she asks her maid, you know, who she thinks is the best, right? And she thinks Prodeus 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. Okay, well, it's instinct, right? 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. 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? And it's 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, it can't be so. It's not a contradiction, can it? 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? I mean, excuse me, these two here 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 Frist understands is what Hermetides was pointing to, right? And, but you can reconcile the two because the apparent conviction that arises here, right, is not a real conviction. But the apparent convictions that arise, they puzzle the reason because it knows that can't be so. And then he 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 a discovery that you didn't think. A discovery that you didn't think will be an untying of it. And so those reasons that Aristotle gave to the rule of contradiction in the development of reality are very important. But it took some time to get there, huh? Yeah. I mean, he speaks, you know, explicitly there about, about these two roads, right? But there really ain't one road. Okay? And 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, 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. It's kind of interesting that he singles out the sense of sight and the sense of touch, right? Because those are, in terms of knowing, the most important. And a sense of sight is a sense of clarity and a sense of distance. And a sense of touch is a sense of, what, certitude, huh? But they're the only senses that know the shape of a thing. And you know how important shape is in knowing everything from a chair to a cat, right? And I recognize the cat, not really 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? But by its color, but by its shape. But the sense of touch and the sense of sight are the only senses of no shape, no form, right? And there's other fragments where he talks about sight and hearing, too, huh? Like the other guy, Hercules, does, right? So, he emphasized that road from senses into reason, huh? Prometheus 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? So, that's kind of just an aside, in a way, of 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, huh? What he's shown, mainly up to this point, is that nothing continuous is composed of indivisibles, right? Nothing continuous is composed of indivisibles, or you could add or divide it into indivisibles, right? And they kind of go together, right? Or if I'm going to put it affirmative, they could say, every continuous is divisible forever, right? Or every continuous is divisible to things that are always divisible, okay? Second definition, that we do, continuous, huh? But now he wants to say, in the Psalms, it's necessary 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 these active paragraphs, it's just going to make that explicit, huh? Now, in a way, you say it's almost unnecessary, because if by continuous, you mean that whose parts meet a common what? Boundary, right? Well, then you have parts of the very definition of the continuous, right? You know, if you go back to logic there, where the chapter on the quantity, and you divide it into discrete and continuous, right? And as Thomas says elsewhere, every quantity seems to consist in a kind of multiplication of parts. Okay? Okay. And, uh...