Wisdom (Metaphysics 2005)
Lecture 25: The Role of Contradiction in Discovery and Knowledge

Transcript
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and other philosophers, right? And that they haven't asked the right question. And when they don't ask the right question, they don't get anywhere, right? See? So I think that's in itself a very interesting thing that Eisenberg is pointing out from his own experience as a physicist. And if you go back to this great dialogue that played with the Mino, some of you know the Mino, but in the middle part of the Mino there, Mino questions the slave boy, right? And he's trying to show Mino that the slave boy already knows geometry. And the way he tries to show this is by bringing out a theorem of geometry, the way to double a square, and the way to double a square comes out of the answers of the slave boy, answers the slave boy themselves, volunteers, right? To the questions of Socrates. So if the way to double a square comes out of the knowledge of the slave boy, as you view these answers, then the slave boy must have known already he's just fetching back something he's kind of temporarily lost contact with, right? Well, I don't think Socrates is being altogether accurate as to his assessment of what's going on here, right? Because when he first asked the slave boy, how do you double a square, the slave boy says you double the side. So not only did he not know how to double a square, he was mistaken, right? See? But Socrates is asking all the right questions. If he asks the right questions, someone seems to what? To get the answer. Yeah, yeah. But this is what we say sometimes about discovery and learning, right? From another. That learning from another should imitate discovery. Now maybe you shorten, you know, some of the dead ends that are involved in what you're trying to discover. But kind of the essential steps, right, involve going back to the way the discovery is actually made in the first place. And that's kind of the best, right? And as I tell students sometimes, we don't usually learn very well because we get knowledge secondhand, thirdhand, fourthhand, who knows how many hands. And we don't know how the actual discovery was made, right? You go back to the man who made the discovery and he'll bring this out. So what Socrates, in a sense, is showing there in the example of the slave boy is the slave boy can come to recognize his mistake out of things he doesn't know already, right? And he can come to know what he doesn't know out of things he knows already, right? But it's Socrates' questions that help the slave boy to recall and to put together for the first time in his lifetime things he knows already. And then comes this something he didn't know already. So a lot of truth to it is this marvelous observation of Heismaner, right? This marvelous statement. But now, why did I bring that at this point? Well, he said, at this point he says that physicists begin to ask the right questions and then he makes that statement. And to ask the right questions often you go lower than halfway, right? Well, what were these right questions, he says? Practically all of them, he says, had to do with the strange, apparent contradictions between experiments. That's interesting, right? Strange, apparent contradictions in their experiments. It's the contradictions they saw, right? Or at least apparent contradictions between the experiments that led them to ask the right questions and therefore to go more than halfway to the end, right? Okay? Now, compared with what Aristotle was saying there, right? Every investigation goes in the direction of the questions asked. Okay? That's why when you're on the witness stand you're on the foot. You may not like the way the investigation is going because the questions are asked of you and you see how it's going. But if every investigation takes the direction the questions asked then to ask the right question is to go in the right, what? Direction. That's the second point he makes, right? Now, if seeing these contradictions or apparent contradictions enables you to ask the right questions then it enables you to go in the right direction which is the second reason Aristotle has here, right? And then to know when you've arrived because reconciliation between the contradictions and you'll find the physicists saying the same thing, right? They knew they had arrived because the contradictions started to, what? Disappear. You see? But notice that the third reason Aristotle gives is starting to touch upon not only discovery but the judgment that I've arrived that this is the truth, right? There's the difficulties the contradictions or apparent contradictions begin to disappear this is a sign that you've arrived to the truth. And so it's not just discovery but also the judgment that what you've discovered is true, right? And the fourth reason he gives here is as the words themselves indicate in terms of judgment, right? He makes a beautiful comparison. Moreover the one who's heard all the reasons of those disagreeing like that of two parties in a lawsuit is necessarily better prepared to judge. So if you're on the jury in the courtroom and you heard one man trying to prove he's guilty and give reasons why he's guilty another man trying to prove he's not guilty right? You're in a better position to judge whether he's guilty or not if you heard just one of those disagree and it's like that except that in the courtroom you're arguing about a contingent individual affair but in philosophy you're talking about a universal thing and it's going to be necessary eventually but if you've heard the men on both sides you're better able to judge what the truth is if you heard just one side. So those are the four reasons Aristotle gives, right? for examining the reasons pro and con and the great questions of what? Philosophy, right? Okay? Now the great questions of wisdom could be divided into three parts but to begin with Aristotle divides them into two parts. Okay? And in what is the second reading here the questions are almost all about what is wisdom about? Okay? And as you go through these questions I'll give you something of the dullness of them although it's fairly obvious that they may have thought differently about them. There are a couple questions in the second reading that are not about what wisdom is about, right? But they're involved in those questions, right? Okay? And we'll see when we get to those questions. But the third reading, right? Is a group of questions, right? About the things themselves that wisdom is about. It's not about what wisdom is about. It's about the things themselves, right? And mainly about what causes, right? Okay? So, we're going to go through each of these questions and see what the question is, but also indicate something of the difficulty. We're not going to go through the whole dialectic of the rest of book three because that would be a whole course in itself. But we'll stop in each question and find out some of the difficulties and why you think this and why you think that and so on, right? Okay? So we're going to stop now at 4.30 or not about that. We'll begin with the second reading, but think about this first reading, you know? Um... A little prayer, in the name of the Father, and the Son, and the Holy Spirit, amen. God, our enlightenment, guardian angels, strengthen the lights of our minds, hoard and illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor, pray for us, and help us to understand all that you've written. In the name of the Father, and the Son, and the Holy Spirit, amen. Amen. I think I mentioned last time, you know, a little bit how some others have seen something of what Aristotle talks about in the first reading, and you could summarize it under the title I've given to these little readings, The Role of Contradiction in Coming to Know. Now, what I have on the first page, as you can see here, are some texts from a couple of philosophers. Heraclitus, perhaps the first philosopher to, in some way, see a little bit of this. And the text from Aristotle that we read last time. Then, on page two, I start with some selections from the great physicist of the 20th century, starting with the father of modern physics, as he's called, Max Planck. That occupies quite a few pages here. He ends up with the text from Einstein, of course, who's the authority. And then on page five and six from theology, right? So, the purpose of this was to illustrate a little bit how, despite all the differences there are in the ways that philosophy and science and theology proceed, right, some of the greatest minds in all three see something of the role of contradiction in discovery. Now, I won't go over the text of Aristotle again, although we'll refer back to it a little bit today. But you could say, in a way, that the great Heraclitus anticipates this a bit, huh? Now, the statements that Heraclitus first gives there, war is the father of all things, the king of all things, that may be a bit of an exaggeration. And we're not concerned with the total universality. But if war is the father of all things, also in particular, it's the father of what? New knowledge, right? Okay. And the second fragment is hitting upon that same thing. Now, the third fragment from Heraclitus, the hidden harmony is better than the apparent harmony. That's well and beautifully said, huh? Now, you could apply that to a lot of things, but if you apply it to knowledge, right, harmony is the opposite of what? Contradiction. And as Socrates points out in the dialogues, to read the dialogues, most people are what? Not in harmony, there are thoughts, one with another, or with things, for that matter. But they're not aware of the contradiction. And Socrates will say, what do you think? And it's dangerous to admit three things you think. Because sometimes from two things you think, something else follows that might contradict that third thing you think. And usually Socrates finds somebody to be in a, what, contradiction, right? Like the courts we were talking about earlier, right? They contradict each other, right? So if I kick a pregnant woman and kill her baby, that's homicide, at least, right? But abortion is not. So it is and is not. That's a contradiction, huh? So most people are in a state of apparent harmony. And take the simplest example of all the dialogues in the Mino, right? Socrates asked the little slave boy, how do you square, how do you double a square? How do you get the side of a square twice as big? Well, you double the side, he says. Okay? Now, he's in a state of apparent harmony, right? But now if you take an example, let's say you have a square that's two by two, right? Well, you say that if you double that side and make it four by four, you have a square twice as big. But even the slave boy can eventually see that two by two is going to give you four, right? And four by four is going to give you sixteen. And sixteen is not double of what? Four. Of four, yeah. So he can't hold that four is double of two, and the square whose side is twice as long is twice as big, and sixteen is what? Not double four, right? Okay? So you've got to reject one of these things, right? And the thing to reject is what? Oh, sure. That the square whose side is twice as long is twice as big, huh? Well, at that moment, Socrates stops, and he turns to the slave boy's master, and he says, we've done this guy a good turn, right? Before, he would have gone out and told the whole world the way to double the square is to double the side, they asked him, right? But now he knows he doesn't know, right? So he's been, what, freed from a mistake? Or an error, right? That's good. Secondly, he knows he doesn't know now. That's good to know you don't know. And third, he'll want to know. And then Socrates has a second conversation, where he shows the slave boy that the diagonal of the square will be the side of a square twice as big. Okay? You know how Socrates does that, huh? He just says, if this is the original square, and you put another square exactly equal to it here, another one exactly equal to it here, and fill up the fourth spot, you'd have a square which is, what, four times as big, right? And then you take the diagonals of these, and after you see that the diagonal is divided into two equal parts, you end up with a square that is exactly what? Half of four, which would be twice as big, right? Okay? You can notice of the fact that we're in the theorem, but that's a little too advanced for this, for the slave boy, huh? So that's the hidden harmony, right? See? But the hidden harmony is the true harmony, right? It's really free of contradiction, huh? So, what Socrates found is that most men are in a state of apparent harmony. And then along comes somebody like Socrates and points out the contradiction in your thinking, but then hidden under that contradiction is a true harmony. Okay? That's beautifully said, right? Now, when he says nature allows to hide, huh? It's a very famous statement of Heraclitus, and I think I mentioned how it's down in the bookshop there, and I see in the science section of the book entitled Nature Loves to Hide, but no acknowledgement that the phrase comes from Heraclitus, huh? But notice the connection between that and the hidden harmony, that this is especially true about nature, right? He doesn't say the triangle or the square loves to hide, right? But he says nature loves to hide, huh? So, when we try to reach harmony in our thinking about nature, it's probably hidden in the beginning, right? Now, the next fragment, it almost seems like a contradiction, right? If you do not expect the unexpected, you will not find it. You'll never discover it, right? For it is hard to be found, he says, and difficult. Now, you might say, well, that sounds like a contradiction. How can you expect the unexpected, right? But, when your thoughts contradict each other, right, then you realize there's something hidden to you, right? And now you're expecting something, what? Which you don't know. Yeah. Yeah. And in a way, you've got to move in the direction of untying that, what? Contradiction or apparent contradiction, huh? And so, at the end, he gives us a bit of advice, huh? Dispute, right? Now, if you go to Navarre, right? Look at Thomas' works. How many of his works are called, what? Questione Disputate. Yeah. And even the great Summa Theologiae, huh? Is kind of an abbreviation of the Questio Disputata method. Okay? Because you have a disputatio, you have, what? People or reasons, right? To think it's this, reasons to think it's the opposite, right? And they say in the Middle Ages, you know, they would have... And they say in the Middle Ages, you know, they would have... And they say in the Middle Ages, you know, they would have... And they say in the Middle Ages, you know, they would have... And they say in the Middle Ages, you know, they would have... And they say in the Middle Ages, you know, they would have... Say, maybe one Monday, Wednesday, Friday, we'd have a lecture on the material, right? And there's certain things in there that are more difficult than other things, right? Certain things that historically and for other reasons men have disagreed about, huh? And maybe on Tuesday, Thursday, we'll pull those out, right? And you guys are going to all, say, try to prove the affirmative side. And you guys are all going to prove the negative side, right? And then me, the great, we're just there here, huh? I'm going to explain the thing, right? And if I thought that you guys had the truth, I'll answer all your arguments, right? And vice versa, right? If I thought these guys had the truth, I'll answer all your arguments. If I thought you both missed the boat, that the truth is somewhere between you two, then I answer all your arguments, and I answer all your arguments, right? Well, the summa does that same thing, right? Except in abbreviated form. So the following advice of what? Yeah, he's the father of the progress of the human mind. That's one of the titles I give Heraclitus, huh? He's also the central thinker of human thought. Now, between Heraclitus and Aristotle, I could take, you know, clearly like I was doing a little bit earlier here, right? In the dialogue, right? But I go down to the text of Heraclitus that we saw last time, but I'm not going to expound this text again now here. But we'll look back at it when we look at the later ones. Now, let's look at the scientists here a bit here. Now, Max Planck is sometimes given the title by the physicists themselves of being the father of modern physics, right? Of course, modern and classical is, you know, a relative thing. But the physicists of the 20th century, they call the physics of the 20th century sometimes modern physics. And the physics of Galileo, Kepler, and Newton, the physics of the 17th century and the 18th and 19th century, classical physics. So classical there doesn't mean Greek, but it means the physics of the 17th, 18th, and 19th centuries. Now, Planck is, as I say, sometimes called the father of modern physics because in December of 1900, he proposed the quantum hypothesis, which is the beginning of the physics of the 20th century. It makes it different. And Heisenberg, in his history there of quantum theory, said when Planck discovered this, he was, he knew he had discovered something very important. And he went for a walk in the park there in Berlin, I guess, with his son, and he said, I think I discovered something as great as Newton. And he was studying what they call black body radiation. And he was running into contradictions because, according to the then-existing theories, there should be infinite amounts of energy being generated here, and that's absurd. And so Planck came up with the idea that energy cannot be given or received in just any amount, but in just discrete amounts called the quantum. And five years later, right, Albert Einstein used the quantum to explain the photoelectric effect. And so it became clear five years later, it started to become clear, that all these light phenomena, electromagnetic phenomena, involved the quantum of Max Planck. In 1913, right, Niels Bohr showed that the atom involved the quantum. And he resolved some of the contradictions there. So there's Louis de Broglie says, the French physicist, nothing was made in the material world, the physical world, without the, what? Quantum, right? Now, what's interesting, though, about Max Planck, also in terms of discovery, is that when he went to the university in the latter part of the 19th century, he was told that physics is now complete. The principles are all there, there's details to fill in, but the principles are all there. So here's a man who's told there's nothing really fundamental to be discovered, right? If you want to make some fundamental discoveries, go into biology or something, it's still developing, but physics is now complete. So here's a man who was told there's nothing new to be discovered, right? He makes a discovery that's the beginning of modern physics, right? And which led eventually, as Heisenberg was to show, to the greatest change there ever been in modern science. And he must know something about how discoveries are made, right? So what does he say about this? The first impulse towards a revision and reconstruction of a physical theory is nearly always given by the discovery of one or more facts which cannot be fitted into existing theory. Facts always form a central point about which the most important theories hinge. Nothing, he says, is more interesting to the true theorist than a fact which directly contradicts a theory generally except at that time. For this is his particular work. So here's the man who's told there's no discoveries to be made. They're fundamental, anyway. And he makes this extremely fundamental discovery, right? But he's attributed to what? Contradiction. Now, Gamal is the Russian physicist who came and studied under Bohr and so on and got the Nobel Prize for contributions to quantum theory. And this is a little history he gives of the 30 years it took quantum theory to develop, right? From 1900 to about 1930. And notice what he says, reflecting upon this. He says, The staggering contradictions between theoretical expectations on the one side and observational facts or even common sense on the other are the main factors in the development of what? Science, huh? That's a very strong statement, right? Now, Niels Bohr here. Now, Bohr is in some ways the most influential of the modern physicists because after he got the Nobel Prize and so on, he set up an institute for theoretical physics in Copenhagen. And men came from all over the world to study under him, like Oppenheimer came from the United States, Heisenberg came from Germany, Gamal came from Russia. They all came and studied under him. Einstein was more a loner, you know? And so Bohr himself, of course, got the Nobel Prize for applying the quantum to the explanation of the atom. And he realized that if you concede the atom as a miniature solar system, it would have no stability. It's always coming into conflict with other atoms. And he realized that the radiation being emitted by the atom was not continuous, as those theories would indicate it should be when it goes from one orbit to another. So he deduced the idea of the quantum, this jump-like thing in the atom. Now, so I say Bohr is a man who got the Nobel Prize himself, but many men who studied under him, like Wolfgang Pali, Heisenberg, and so on, went on to get the Nobel Prize. He's a very central thinker. Now, this is a collection of things by scientists who worked with Bohr and has some quotes from him. He's describing the early stages of Bohr's thinking here. Bohr's hypotheses were only of a provisional character, inasmuch as he presented a mixture of Planck's ideas with the old mechanics. Nobody was aware of the situation more than Bohr himself. Thus, in a lecture on the New Theory, which he gave to the Danish Physical Society in December 1913, in which he himself rightly considered one of his best and clearest lectures, he emphasized this aspect of the problem in the following fine conclusion. This is Bohr's words now. Before closing, I only wish to say that I hope I have expressed myself sufficiently clearly so that you have appreciated the extent to which these considerations, conflict, there is the war that Heraclitus spoke about, right? With the admirably coherent group of conceptions which have been rightly termed the classical theory of electrodynamics. On the other hand, I have tried to convey to you the impression that just by emphasizing this conflict, it may be also possible in the course of time to discover a certain coherence of the new ideas. So it's by emphasizing this conflict, by emphasizing this contradiction, right, that we may be able to, what, discover a hidden coherence, right, which is another word for what Harmon is saying. So it's by emphasizing the conflict, the contradiction, and trying to resolve it, that you might be able to make a, what, discovery. Another passage on Bohr. Bohr's turn of mind was essentially dialectical rather than reflective. Of course, dialectical with the Greeks means what? Reasoning from probable opinions to contradictory conclusions, as Aristotle says. It's like in the third part of the great dialogue to Mino, where Mino wants to know whether virtue can be taught, and Socrates says, well, we don't even know what virtue is yet. But can it be taught? Well, if he insists I say something about it, let's look, see if it can be said yes and no, right? And so Socrates gives an argument that virtue can be taught, and he gives an argument that virtue cannot be taught, right? He says, Bohr's turn of mind was essentially dialectical rather than reflective. Although he did, of course, spend long hours in solitary thought, often during sleepless nights, he needed the stimulus of some form of dialogue to start off his thinking. If the proposer of the doubt was at hand, the dialogue could be lively enough. For as soon as Bohr saw his way to the elucidation of the matter, he would make his point with unbounded eagerness and tenacity. Not at all to get the better of his opponent, but rather to get him to share his own exhilaration at solving the difficulty. So intensely did he want everyone around him to share them with them. Even after many years, he would remember every detail of the argument's progress, and he would repeatedly tell the story with the same freshness and animation. It was characteristic, now, for these unforgettable conversations. So clearly revealing the essentially dialectical form of this thinking. That he would never try to outline any finished picture. Now these are the key words here. But would patiently go through all phases of the development of a problem, starting from some apparent paradox, which means a contradiction, right? And gradually leading to its, what? Elucidation, the untying of that. Now those who were partaking in these conversations with Bohr, they said they were reminded of Socrates, right? They thought they'd been talking to Socrates, you know? But there's a certain likeness there, huh? Okay. They always start with an apparent paradox, something of a contradiction, and then gradually unravel that, huh? Break down that contradiction. Now this next passage is maybe even more precise about this. Logical analysis was not, for him, Bohr, a mere verification of consistency. He wasn't just looking to see if what you said was free of contradiction. That's important, but that's not all he was interested, right? But rather it was a powerful, constructive tool, orienting the groping mind in the right direction. I noticed that, right? To know where you're going, right? Orienting the mind in the right direction. That he saw the heuristic power of logic in his dialetal character. Now what does the word heuristic mean? Yeah. It comes from the Greek word hurain, which means to find or discover, right? So he says, that he, Bohr, saw the heuristic power, the power of what? Discovery, right? The power of finding something you don't know. In its dialetical character, in its ability to bring out what? Contradictions. Well, no. Oh, okay. That in its dialetical character, that insofar as logic teaches us to bring out these contradictions, right? Yeah. It has a heuristic power. A power of discovery, right? He's illustrating by the striking comment he made on more than one occasion on his own early experience of scientific discovery. The decisive point, this is quoting Bohr now, the decisive point about Rutherford's atom model. Rutherford was a British physicist there, and Bohr went over to England to study under him, right? Cambridge, right? The decisive point about Rutherford's atom model was that it made quite clear that atomic stability could in no way be accounted for by the classical, meaning the Newtonian, physical laws. Okay? And thereby, what? Pointed, huh? The quantum facet, right? See? Orienting the groping mind in the right direction. As the only possible escape from the acute dilemma, the acute contradiction. Just the sharpest contradiction that was there, right? Between the classical laws and the atom there. Made me, Bohr, absolutely confident of the truth, the quantum postulate. So it not only oriented his mind towards the quantum postulate, huh? It pointed to it, that's the only way, right? But it also convinced him, right, of the truth of it, right? It's just the two things that Aristotle has there in the second paragraph. It shows you where you're going and helps you to know that you've arrived. You're going in the direction of resolving this contradiction, and when the contradiction disappears, it's a sign you've made some progress, right? You've arrived in some sense. Bohr was still remembering this lesson when in one of his last conversations he observed that the reason why no progress was being made in the theory of the transformations of matter occurring at very high energy is that we have not so far found among these processes anyone exhibiting a sufficiently violent contradiction. With what could be expected now. In other words, expect the unexpected, right? With what could be expected from current ideas to give us a clear and unambiguous indication of how we have to modify these ideas. So until you find a strong enough contradiction, you're not going to, what, make any progress, right? That's why I call Heraclitus the father of the progress of the human mind. If he first saw something of this, right? And the last reading here from Bohr, or about Bohr. Difficulties, which are these contradictions, were for him, Bohr, merely the external appearance of new knowledge. Like the outer thing of an orange or some food like that, right? And in an apparently hopeless contradiction, these staggering contradictions that come out, talked about, right? He conceived the germ, right? The seed of wider and more comprehensive word and harmony. That's the better harmony, right? That Heraclitus spoke about. So it's beautiful, right? To see in different words, right? The same thought coming out again, huh? Now, Heisenberg is probably the most illustrious of the pupils of what? Of Bohr, huh? And if you read Heisenberg's books, he always comes back to his first encounter with Bohr and his conversations with him, you know? Bohr, you know, at that time was regarded as a man who, in the 1920s, knew more about the atom than he was in the world. And he came from Copenhagen to Germany to give a series of lectures on the atom. And the German physicists called it the Bohr Festival. You know, it's a great thing. Well, anyway, and one of the lectures there, Heisenberg was present, he was still a student at the time, right? In the question period, Heisenberg posed an objection to something, right? And Bohr gave some kind of an answer to the objection, right? But kept on looking back at the guy, you know, as he went on. And so at the end of the period, he came over, Bohr came over to Heisenberg, he says, let's go for a walk. And he went for a walk, and he talked about atomic theory for, I don't know, a couple hours. And Heisenberg said it influenced all his subsequent, what, thinking, huh? Now, Heisenberg, you know, is responsible for a lot of things. I mean, he was the first guy to propose that the nucleus of the atom was composed of protons and neutrons. They knew there were protons, they didn't know about neutrons, but he was the first guy to propose that. But he's the man who formulated the, what, principle of indeterminism in quantum theory, which was the greatest change in physics since, what, Galileo, Kepler, and Newton. But in the Gifford lectures that he gave there in Scotland there, which they put out in the title, Physics and Philosophy, but it's the Gifford lectures. He's talking about the history of quantum theory here. He says, Bohr's theory had opened up a new line of research. The great amount of experimental material collected by spectroscopy through several decades was now available for information about the strange quantum laws governing the motions of electrons in the atom. The many experiments of chemistry could be used for the same purpose. And now, he makes a very interesting observation. It was from this time on that the physicists learned to ask the right questions. And then he makes a very interesting observation. And asking the right question is frequently more than halfway to the solution of the problem. Well, I told you that I had drawn my line on the board there, but it's good to think about this, right? You represent by a straight line the time and the what? Difficulty, right? It takes to go from ignorance to knowledge. The average Joe would think that asking the question comes somewhere at the beginning, right? And all the rest of that time and effort in answering it. Let's see. Let's see. Put this here as a midpoint, let's say, huh? Heisenberg says, asking the right question is often to go more than halfway, right? In other words, you spend more time, maybe, and more effort before you ask the right question than after you ask the right question getting the answer. Now, I found that myself to be true in philosophy, right? That I spend more time and effort in trying to get your ignorance to knowledge before I ask the right question, but once I ask the right question, boom, you know? And I always tell you, that example always sticks in my mind when I was, like I mentioned it last time, when I was doing my doctoral thesis, you know, and I had a problem that I'd been thinking about on and off, not only, but for 10 years, right? I had an undergraduate and so on, in my years of teaching at St. Mary's in California and so on, and then all of a sudden I put together something Thomas said and something and Dion said, dang, I had to answer it like that, you know, and ask the right question. And so I went down to check it out with Monsignor Dion there, the best of mine I've ever known, and I came in and I asked the question. He says, I know where you're going, do I? You see? But they asked the right question, you know, and I said, damn it, can I go there, you know? But, but, now, you can see that also illustrated in a way in the great dialogue of the Mino, right? Because Socrates merely asked the slave boy's questions, right? And out of the slave boy's answers, the slave boy recognizes his mistake first, and then later on he recognizes the true way of doubling the square. And Socrates says, well, I didn't teach him, you know? Well, he did, right? But what Socrates was doing is asking all the right questions. And then the slave boy seemed to, what, teach himself or to draw it out of himself, right? But it shows you the greatest work is maybe, what, asking the right question. Now, Heisenberg goes on. What were these questions, huh? They were the right questions. Practically all of them had to do with the strange apparent contradiction between the results of different experiments, huh? So it's not until they saw those strange apparent contradictions that they asked the right questions. And once they asked the right questions, they were more than what? Yeah. I think I mentioned last time how in one of Heisenberg's other books there on his conversations that he said he had with scientists in his lifetime, right? And he tells this conversation he had with Einstein, and Einstein pointed something out about the way he had come to the theory of relativity and so on. And then later on, when Heisenberg and Niels Bohr are trying to figure out quantum theory, and they're giving each other's nerves and so on, and finally Bohr says, I'm going skiing, and Heisenberg stays in Copenhagen there, and he asked the right question one night. And all of a sudden, bang, he's there like that, right? And he's so excited and nervous, he goes back and he's calculating, making all kinds of mistakes. Finally, he calms down and starts calculating correctly, and everything is out perfectly, all the numbers, you know. But once he asked the right question, right? He was there in no time. But notice, it's these contradictions that enable you to ask the right question, right? And we had an example of that in discussing the great fragment of Anaxagoras on the mind, right? On the one hand, we saw that, what? The mind is self-ruling, and we point to logic as a sign that the mind can rule itself, right? And then on the other hand, Anaxagoras says the ruler must be separated from the ruled, but the mind is not separated from itself. So you've got a contradiction here, right? But that led us to ask the right questions. How is it that the mind can direct itself, right? When the ruler must be separated from the ruled. It's not that we have two minds. It's not that the mind has two parts, one of which rules the other part, right? But that there are some things known to the mind and some things not known to the mind. And so the mind is ruled in what it doesn't know, but what it does know. And ruled in what is less known to it by what is more known to it. But, until we see that contradiction, we didn't really understand how the mind, what? Goes forward, huh? How the mind does, in fact, direct itself. And then we see how Socrates is at the beginning of this when he was trying to get people to separate what they know from what they don't know, right? And most people would mix those up. Now, Einstein is perhaps the most famous of all the physicists, scientists of the 20th century. You know, Time magazine, they made him a man of the, what, century, right? Okay. But as I tell the students, I'm always quoting this proverb, and they don't seem to know it, you know. Get it from the horse's mouth. Hmm? You ever heard that? Mm-hmm. Yeah, I don't know. They don't seem to know these things. Stitching nine, says nine. They don't seem to know these things that my grandmother told me. But the meaning of the get it from the horse's mouth is you're going to win the race, right? Oh. The horse is down there. They're close enough. They know who's going to win, right? And so somebody says to you, how is the theory of relativity discovered, right? This theory that made Einstein world famous. Well, get it from the horse's mouth. You know, don't take somebody else's word for it, right? Now, the evolution of physics is probably the nearest thing to a kind of a history of the main ideas of physics, the development of physics. And this is what Einstein says in that book. He says the relativity theory arose from necessity. Now, why does he say necessity? Is it determinist? No. Because of a pair of contradictions that it's pushed in that direction. Yeah, because the mind can't accept a contradiction, right? Yeah. Okay? From serious and deep contradictions, right? These staggering contradictions, huh? Apparently hopeless contradictions, huh? Yeah. From serious and deep contradictions in the old theory from which there seemed no escape, right? So Einstein is saying the same thing that Bohr said, right? That it rose from a contradiction. Now, the strength of the new theory lies in the, what? Consistency, right? The freedom from contradiction. Contradiction and simplicity with which it solves all these difficulties, right? So, it arose from a contradiction and that you've arrived at something, right? Shown by the contradictions disappearing. Okay? Now, those two things are what Aristotle is talking about, right? In the second paragraph. Where he said that seeing these difficulties, these contradictions beforehand, tells you where to go, points you in the right direction, as Bohr says, huh? It orients your mind in the right direction. But it also tells you when you've arrived, huh? Because that the contradictions disappear is a sign that you've, what, made some progress, right? Now, the second paragraph from Einstein is talking about quantum theory. I think I mentioned before, Einstein didn't want to go along with the indeterminism, right? That Bohr and Heisenberg, right? And, of course, the great showdown was what? The Soviet Congress, you know, physicists in 1930, or 27 or earlier, there were several of them. But the last one, Einstein was posing objections to the so-called Copenhagen interpretation of quantum theory that Bohr was defending and Heisenberg and so on. And Bohr would stay up the night and come back the next day and refute Einstein. And Einstein would think of another objection, right? And Einstein's final objection was sounding pretty good, you know, and Bohr was pretty worried. And one of the books they have is a picture of Einstein and Bohr coming out of that session where Einstein proposed his last injection. and Einstein's looking pretty, you know, kind of cocky a little bit, you know, I mean, not overdone, but a little bit, you know, like I put the nail on that thing and Bohr's coming afterwards, you know, like let's talk about more in his luvian words, you know. Well, he was up again, the other night again, and he discovered a flaw in Einstein's objection, a flaw which, of all things, was based upon Einstein not applying his own theory to the question. And that shut Einstein up, right? Einstein never publicly again tried to, he wouldn't accept it, you see, okay? But notice what Einstein says about this, though, nevertheless. One of the most fundamental questions raised by recent advances in science is how to reconcile the two contradictory views of matter and way. is one of those fundamental difficulties, right, which once formulated must lead in the long run to scientific progress, right? Okay. As I say, Einstein didn't like to. It's a solution. That's pretty much his problem, you know. Now, the last reading from Einstein is more general now, right? And he perhaps could express himself a little bit better in that first sentence. It's not science that forces us to create new ideas, new theories, but it's the contradictions, right? I guess he has a mind, huh? But notice now his words, I think they're kind of interesting. He says, their aim is to break down the wall of contradictions which frequently blocks the way of scientific, what, progress, right? Now, notice, Christel used the metaphor of your feet being tied together, right? By contradiction, huh? The mind being tied together like the feet. I used another metaphor, but the wall of contradictions. It's the same idea that these two guys have in mind, right? Whether you run into a wall that blocks your way going forward or whether your feet are tied by the contradiction. In both cases, you're expressing the idea that contradiction stops the mind, at least temporarily, right? Okay. And Aristotle says, if you consider that contradiction, it'll tell you where to go. And where are you going? You're going in the direction of untying that contradiction. And Aristotle compares it to looking at the, you know, if your feet are tied by rope, you look for the loose end, right? And then you start to unravel it, right? Well, notice Einstein's word here. Their aim, right, is to break down the wall of contradictions, which frequently blocks the scientific progress. So in a sense, you're taking aim, right, at the unknown there, right? The untying of that contradiction will be this discovery, huh? And now Einstein gives what in logic we call a universal affirmative statement. No exception, right? He says all of the essential ideas in science. All of them. Well, it's a very strong statement. We're born, right, in a dramatic conflict, huh? War is the father of all. In a dramatic conflict between reality and our attempts at understanding, right? I like the choice of the word dramatic, too, right? Because as Aristotle pointed out in the book on drama there, the Poetics, a plot consists of, what, tying the knots and untying them, right? And that's why the philomuthos, the lover of plots, is in a way a philosopher, right? And the plot, in a way, is like philosophy, huh? Because philosophy consists of seeing knots and then untying them, right? And the plot has those two things, right? And I was quoting, you know, the great Shakespeare there in Twelfth Night, huh? Where all the knots have been created there, and the character says, O time, thou must untangle this, not I. It is too hard a knot for me to untie, right? And Aristotle says time is a good helper for the philosopher in untying some of these knots. It takes time sometimes to, or it does take time most of the time, or all the time, to take these down, huh? Um, but Aristotle makes an interesting observation in the Poetics. He says that the younger poets or the lesser poets are better at tying the knots than untying them. You can see it's a fourth story about the philosopher, huh? Most philosophers can tie themselves and even others into knots, but they can't untie them. And, you know, sometimes you see a movie or something, or you read a story, and you get kind of engrossed in the story, but then the way it turns out is, you know? You see that defect to the artist, huh? And, um, but somebody like Aristotle or Thomas, they can untie these knots, huh? Okay? But you do kind of, you read the summa, you know, you read the objections and the contour, then you kind of, you know, let that knot settle into your mind, then you try to untie it yourself, and sometimes you can make a little progress, sometimes you don't need progress at all, and then you go turn to Thomas. How does he untie this? That's kind of the way to do it, you know? You know, sometimes I give students an article in the class, and I'd rather give them the whole article, I'd just give them the objections and the contra, and then the rest of it, the body of the article and the objection, they put on a separate piece of paper, which I'll pass out after they, you know, thought a bit about the thing, you know? So those are some wonderful things from some of the greatest physicists of the 20th century seeing the role of contradiction, right? Now, the last selections here are from, what, theology, right? And like in the text from the decree on priestly training here, which starts with the scripture and then the history of the church, and then the fighting comes to Thomas, I do the same thing here, right? Now, chapter 22, in the logical division there, the understandable division there of the Gospel of St. Matthew, chapter 22 is one of three chapters, right, in the third part of Matthew, which are giving the reasons why they wanted to put him to death, the Pharisees and so on, right? And, you know, one chapter is because he's correcting their faults, right? And so there's different reasons for it. But this chapter is where he's, what, refuting them, right? Now, while the Pharisees were gathered around, Jesus put to them this question, What is your opinion about the Christ? Whose son is he? David, they told him. Then how is it, he said, that David, moved by the Spirit, calls him Lord, where he says, and he quotes a song, The Lord said to my Lord, sit in my right hand, and I will put your enemies under your feet. If David can call him Lord, then how can he be his son? So notice what our Lord is doing. He's pointing out an apparent contradiction between two passages of Scripture, right? Okay? And the Pharisees, who would claim to know the Scriptures, right, they can't answer that, right? So he's doing a little bit what Socrates does with the slave boy, right? He's showing the man to be, what, ignorant of what he claims to know, right? But now, the hidden harmony is better than the apparent harmony, right? Hidden under this apparent contradiction is the truth, right? The unexpected truth that Christ, that Jesus, is both man and what? God, right? And so as man, he can be descended from David, right? But as God, he is the, what, Lord of David, right? Okay? Or sometimes they take one to the New Testament, they'll say, you know, Christ will say, the Father is greater than I. One of the times they're talking about him as being equal to the Father. Well, how can he be less than the Father and equal to the Father? That's a contradiction, right? Well, he's both God and man. As God, he's equal to the Father. But as man, he's less than the Father. In fact, as man, he's less than himself as God. You see? So hidden under these apparent, what, contradictions, right, is a profound truth, right? And notice, you know, despite all the difference, say, between, let's say, quantum theory and this, because quantum theory is proceeding from these experiments, right? This is proceeding, Christ is proceeding here from the books of the Old Testament, right? But the quantum physicist is seeing a strange apparent contradiction between different experiments. And the untying of that apparent contradiction will be the discovery of something, huh? Christ is pointing out an apparent contradiction between this part of Scripture and that part, but hidden under that is a profound truth. That Christ is both God and what? Man, right? Okay? So there you have our Lord, in a sense. It's a little bit like Socrates, because the reason why they put Socrates to death was because he was going around doing this, right? He was showing men who claimed to know something that they didn't know what they claimed to know. He was showing men who had a reputation for knowing something that they didn't know this. Now, this is only one of the reasons why they put Christ to death, but it's interesting, huh, that Socrates and Christ share that particular reason, right? Now, after Scripture there, you have the Church Fathers, and I take perhaps the greatest mind there among the Church Fathers, St. Augustine, right? And Augustine says in the city of God, but even the heretics yielded an advantage to those who make proficiency, according to the Apostle saying, meaning St. Paul. There must also be heresies, right? That they which are approved may be made manifest among you. Now, Augustine is starting to talk here about how heresy... Socrates is starting to talk here about how heresy... Socrates is starting to talk here about how heresy... Socrates is starting to talk here about how heresy...