Natural Hearing (Aristotle's Physics)
Lecture 31: Contradiction as a Heuristic Tool Across Philosophy, Science, and Theology

Transcript
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Now, if you read Thomas' commentary on these reasons, apart from explaining them, he says, for these reasons, Aristotle uses dialectic in almost all his works, right? The reason that he gives here. What's unique about the third book of metaphysics is he gives kind of universal dialectic there. Well, in the other parts of philosophy, it's always a more particular dialectic. But there's a certain affinity between dialectic and wisdom. There are other reasons why he does that, too, but Thomas gives three reasons there. Okay, so that's some witnesses here to the role of contradiction from two great philosophers, right? Aristotle, the philosopher, and Heraclitus, the central thinker in human thought. And one reason why I called him the central thinker in human thought is that he sees something of this, huh? And it makes him so central. Now, let's go to science here now. And my first reading here is from Max Planck. Now, Max Planck has the title of the father of modern physics, meaning the physics of the 20th century. And it's because in December of 1900, he proposed the quantum hypothesis. And so it's kind of a nice day, right? At the dawn of the 20th century, right? And five years before Einstein proposed the special relativity, right? But in 1905, Einstein made use of Planck's theory to explain the photoelectric effect for which he got the Nobel Prize at that time, right? Now, what's interesting about Max Planck, they say he's a man now who knows something about discovery, right? But if you read the life of Planck, he went to a enrolled university in physics in the latter part of the 19th century, right? He was told that physics is complete in his principles. There are details to be filled out, right? But the basic principles are there. If you want to go into something, you know, where fundamental discoveries and so on, go into biology or something, right? Okay? Well, Planck, never less, was interested in physics, right? So here's a man who was told there's nothing really fundamentally discovered, and he's the man who starts modern physics, huh? And Heisenberg, you know, in that same chapter about the history of quantum theory there in the Gifford Lectures, he speaks of how Planck, when he discovered the quantum, he went for a walk in the park with his son, right? And said, I think I discovered something as important as Newton, right? And then five years later, Einstein showed you can't understand light without the quantum. And then 13 years later, in 1913, Bohr showed you couldn't understand the atom. So nothing in the physical world, another big world, nothing, either matter nor light, could be understood without the quantum, huh? So this is a very fundamental discovery, right? And it led eventually to the greatest change in physics from the beginning. It led to the rejection of that principle of determinism, huh? In the thinking of the physicists. It was Heisenberg who especially brought that out, huh? So Planck should know something about the way to discover it. He's a man who's told there's nothing to be discovered. He's a man who discovered something very important. But notice what Planck says then. 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 could not be fitted into the existing theory. That means it contradicts it, right? Not in harmony with it. Facts always form a central point about which the most important theories hinge. But now the key sentence here. Nothing is more interesting to the true theorist than a fact which directly contradicts the theory. Generally extended up to that time for this is his, what, particular work, huh? Now Gamow was a Russian physicist who came and stayed under Niels Bohr at Copenhagen and then eventually came to the United States, huh? And he got the Nobel Prize, huh? For explaining some very strange things the quantum physicists uncovered, right? Where things apparently do what they don't have enough energy to do. But anyway, we'll go into that. But this particular book, I suppose being a Russian, the title is suggested by the, you know, the ones of the communist books. But he's talking about the development of quantum physics. It started in 1900 with Max Planck, right? But quantum theory was not really perfected until the late 20s, so it's almost like 30 years, huh? And the Copenhagen interpretation of quantum theory was the very controversial thing, right? And the physicists were discussing it in these international meetings and the Solvay Congresses, they're called. and the final showdown came in 1927, right? When Niels Bohr refuted Einstein and finished Einstein, you know? And that kind of led to the general, you know, acceptance of the Copenhagen interpretation. But notice, Gamow reflected upon all these different developments that took place in those 30 years. And so on. And science in general, he says, staggering contradiction, you know, we saw that thing, the apparently hopeless contradiction, right? Staggering contradictions between theoretical expectation on the one side and observational facts, or even common sense on the other, are the main factors in the development of what? Science, right? Okay? Once again, another witness song. Now, the one from Niels Bohr and the ones from Einstein, of course, as I say, are the most important because these two thinkers are really most central, right? And Bohr learned a lot from Einstein, but eventually, in the interpretation of quantum theory, they, what? Broke, right? And if you get the three volumes of Bohr there, I guess he's on atomic physics and so on, he has a very interesting account of the conversation with Einstein, right? But you get it from other scientists and so on. And Einstein didn't want to go along with the Copenhagen interpretation because it involved the rejection of determinism, right? And that had been the absolute principle of modern science, as he mentioned when he was studying the Sibis, right? And Einstein would invent these thought experiments to try to refute it. And then Bohr would stay up all night and come back the next day and show the defect in Einstein's rejection. And I guess the last one is that Einstein proposed in the 1927 one, quite a devastating one, and he really had Bohr worried, right? They say, they have a picture, I see the picture of the two of them leaving the thing, you know, and Einstein's rocking out, you know. You know, they're, you know, kind of, you know, smug look at his face and Bohr's coming out to be kind of worried, right? And of course, again, Bohr had a sleepless night, right? But he came back the next day and used Einstein's theory of relativity to refute Einstein. He used Einstein's own theory. Einstein overlooked at consequence of his own theory. And that was the last time that Einstein publicly ever tried to, you know, refute the thing. But anyway, both great scientists. And Bohr always speaks of the greatest respect, you know, of Einstein, you know, and how much we learn from Einstein even when we, you know, have disagreements, right? But there's really something. Now, I was talking about Bohr's early hypotheses here about the atom, right? Bohr's hypothesis. Bohr is the man who started the modern atomic theory, right, in 1913 when he applied, started to apply the quantum to the atom. And Heisenberg, you know, describes the first time he met Bohr in the early 20s there when Bohr came to Germany. And he gave a series of lectures on the atom when everybody considered Bohr to be the man who understands the atom more than anybody else. And the German physicists called this the Bohr festival, you know. It's a great thing, yeah. Okay. Anyway, Bohr's hypotheses were only of a provisional character as the first ones, inasmuch as they presented a mixture of Planck's ideas with the old mechanics, right? 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, right? In Clare's lectures, he emphasized this aspect of the problem in the following fine conclusion. Now note these very words there that are important. 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, right? With the admirably coherent group of conceptions which have been rightly termed the classical theory of thermodynamics. So, there was something I discovered that contradicted, right? Okay? Then conflict. But on the other hand, I have tried to convey to you the impression that just by emphasizing this conflict, right? By bringing this conflict out, it may be also possible in the course of time to discover a certain coherence which again means freedom of the country. and the new ideas, right? But you have to insist upon that contradiction, right? In order to discover what? A hidden harmony, as the great Heracles would say, right? A certain coherence of new ideas. This is taken from this volume there of scientists who work with Bohr, right? And they're often quoting him and making observations about him. This one here is very interesting. His turn of mind, Bohr's turn of mind, was essentially dialectical rather than reflective. A dialectic, of course, goes back to the Greeks there, right? Where you're arguing on opposite sides, right? Raising problems. 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. I read all of these physicists who sat at his feet there, you know, and it was like being with Socrates, that's what they compared it to, right? 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, right? 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 him, huh? 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. Now, this last part is the most, you know, point for our purposes. It was characteristic for these unforgettable conversations, so clearly revealing the essentially dialectical form of his thinking, that he would never try to outline any finished picture, but would patiently go through all phases of the development of a problem, right? But what are those, huh? Starting from some apparent paradox, starting from an apparent, what? Contradiction, right? And gradually leading to, what? The elucidation of that. That's the way he proceeded. And it's very clear, huh? You know, they talk about how Chesterton often writes in a paradoxical way, right? To get you to start thinking, you know? Something's worth doing, it's worth doing badly. Okay. Now, this next text is even more revealing. Logical analysis was not for him, bore a mere verification of consistency. He's not just looking to see that what he's saying, or what we're thinking, is free of contradiction, right? What you want it to be eventually. But now, this is the key thing here. But a powerful, constructive tool orienting the groping mind in the right direction. To know where you're going, as Aristotle said, right? Okay. Then he saw the heuristic power of logic and his tactical character. Now, heuristic comes from what? The Greek word, heurei, huh? And then you've got a huh, you know? And that's the Greek word to what? Discover, right? Okay. Define. So he's talking about the, what? The power of logic in his tactical character. The power of dialectic in his ability to bring out, what? Contradiction, right? Has a, what? Heuristic power. A power of discovery. Exactly what Claims and Aristotle have been saying, huh? That he saw the heuristic power of logic and his tactical character is illustrated by the striking comment he made on more than one occasion on his own early experience of scientific discovery. They want to get it from the horse's mouth, right? You know? And here's a man who made a great discovery. The decisive point about Rutherford's atom model, you know, he'd been already ignorant to study with Rutherford, right? And Rutherford's an atomic model, you know, kind of a solar system model, the atom and so on. But 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 physical laws. That means Newtonian physics, huh? They called the physics of the 17th, 18th, and 19th centuries, if you read these guys, classical physics. I don't mean the Greeks or the Latins, but they mean the 17th, 18th, and 19th. They'll call either classical physical or Newtonian physics, right? And they'll call the physics of the 20th century modern physics. Okay, that's just a common way. So it made quite clear that atomic stability could in no way be accounted for by the classical physical laws. I don't know if there was contradictions there. And thereby pointed, you see? Going in the right direction. Remember what Aristotle says, right? And thereby pointed to the quantum postulate, right? As the only possible escape from the acute dilemma, right? Well, that dilemma, of course, is a contradiction, right? And he says just the sharpness of the contradiction that he was, what, going to resolve, right? By applying the quantum to the atom made me absolutely confident of the truth of the quantum postulate because it made that sharp contradiction, what? Disappear, start to disappear, right? See? And also the two are tied there. Aristotle said in that second paragraph, right? That seeing the difficulties, the contradictions, tells you where to go and then what you've arrived, see? Because you're going in the direction of untying those contradictions and you know you've arrived where the contradictions are untied, right? The same way here, right? It pointed to the quantum postulate, right? You know? He applied the quantum postulate to the atom and that's the way he's able to explain or start to explain the stability of the atom. He could also start to explain the radioactive emissions too and their jump-like character which both of which contradicted, you know, the classical physics, huh? And it also made him confident that he'd arrived to the truth, right? See? Because the contradiction was so sharp that he had, what, resolved by doing this. Exactly the same two things Aristotle, they're kind of tied together. We'll see a text in Einstein there on where the two are tied together, right? Know where you're going and know when you're going to arrive, right? Pointed, confident in the truth now. He 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 in very high energy is that we have not so far found among these processes anyone exhibiting a sufficiently violent contradiction, right? It's like the sharpest contradiction that is itself, 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, huh? We're looking at that passage here in comparison to expecting the unexpected, right? But notice, why no progress is being made, huh? To bother the progress of the human mind. You know? Heraclitus saw that there were all conditions. Now, in the last reading from Bohr, difficulties, which involve contradictions, were for him, Bohr, merely the external appearance of good knowledge, like the outer shell of a, you know, orange or something, right, huh? You see? And in an apparently hopeless contradiction, he conceived the seed, the germ, of wider and more comprehensive order and harmony, right? That's the hidden harmony, which is better, right, than harmony he had before, right? You had some kind of order and harmony before, but now you have a more comprehensive order and harmony, right, that takes in much more, right? That's hidden, though, at first, right? See? But the seed of that is the apparently hopeless contradiction, right? It's only the great mind to maybe untie, right? Okay? You know, we looked pretty much at the text there from Heisenberg, right, huh? Okay? But there I was doing it, I could emphasize the fact of, what, going in the right direction by asking the right question, right? And how far it takes you, but that the right questions came out of the apparent contradictions between the experiments, right? And some of which, you know, might behave like a particle, other ones that didn't behave like a particle behave like a wave, right? And then Louis de Broglie showed the same thing was true about electrons, which behave like particles, but they also, if you did the right experiment, behave like a wave. So he had apparent contradictions between these pinpointed particles and these spread out waves and so on. Now, the evolution of physics is perhaps the nearest thing to a little sketch of the history of physics by Einstein. He takes some of the principal ideas down to history, right? Starting with Gialdeo and going down to his own work and the quantum physicists. But in his first reading, he's talking about his own, what, theory. Now, again, we're going to get it from the horse's mouth, right? How did this arise? It arose from necessity. Now, why does he say necessity? Because the mind cannot accept a contradiction, right? Okay? As he goes on to explain, from serious, right, and deep, he didn't say apparently hopeless, but strong words, right? From serious and deep contradictions, ...contradictions in the old theory, from which there seemed no escape. It arose from contradictions then, right? Now, the strength of the new theory lies in the consistency, which means, you know, free from contradictions, right? Eliminated it. And the simplicity with which it solves all these difficulties using only a few very convincing assumptions. So, as Aristoteles said, you know you've arrived, but you can what? Untie, right? So, as Bohr said, just the sharpness of the contradiction that he had in time made him confident of the quantum postulate, right? And he says, the strength of the new theory, right? The reason why one would tend to accept it, right? Lies in the consistency. It's what's freeing us from those contradictions. We know we were right in some way, right? And the contradictions disappear. We discovered something. Now, the second paragraph, as I say, Einstein was a little bit unhappy with the Copenhagen interpretation of quantum theory, right? But notice there's observation about contradiction there. One of the most fundamental questions raised by recent advances in science is how to reconcile the two contradictory views of matter, matter particles, right? And wave. It is one of those fundamental difficulties, right? There's a contradiction there, right? Which once formulated must lead in the long run to scientific progress. See? It's one of those fundamental, what? Contradictions when brought out, right? Must lead in the long run to scientific progress. Magnificent, right? Physics has tried to solve this problem. What's happening with it? You don't want to ever accept, right? You want to hold on to determinism, right? But Zierenfest said, I'm ashamed of you, Einstein. You know, you can't refute it and you won't accept it. You don't want to accept it. Yeah. Yeah. The future must decide where the solution suggested by modern physics is endearing or temporary. I was looking at the recent book there. Have you seen it? Called The Elegant Universe. You know, it's by a physicist working in string theory. It's out in the bookstores and he's got to ask him. You know, but to him it's pretty clear now that Einstein was mistaken, you know, that the struggle is over, but there's still a few people, you know. Bridgman compared, you know, to what Joe said, right? He can't quite get away from these things. These mechanical views and so on, huh? Now, the reading on page 264 of Einstein is more universal now, right? He's got his statement of his own theory, right? But now he's saying in general, science forces us to create new ideas, new theories. That can be stated more clearly. It's not science that's forcing us, it's the contradiction that's forcing us, right? Okay? It's like what he said before, that this relativity theory arose to necessity, right? From serious and deep contradictions, right? That's the mind could not accept. But now it's beautiful the way Einstein describes this. He says, their aim, think what Aristotle said, right? You can aim, you know where you're going in a sense, right? And Aristotle says, when you see the contradiction, you know where you're going because you're trying to, what, untie that contradiction, right? Einstein has a little different metaphor, but it's the same idea. Their aim is to break down the wall of contradictions, right? Which frequently blocks the way of scientific progress. So Einstein has the image there of the contradictions that make a wall that you have to knock down to go forward, right? They knock you down the walls when you go forward. And Aristotle compares the contradictions to what? You know, have your feet tied and you have to unloose the knot so you can go forward, right? But it's the same idea. But notice the choice of word there. Their aim, right? It's as if you can somehow know where you're going. You're able to aim. And now he makes what in logic we'd call a universal affirmative statement. All the essential ideas of science were born in this way, right? The dramatic conflict between reality and intents and understanding. It's interesting to use the word dramatic because as I mentioned before, when Aristotle says the good plot of a drama consists of tying the knot and then untying it, right? There's some likeness between that and philosophy and science, huh? Now let's go to theology, right? What's kind of amazing is to see despite all the many differences there are between philosophy and science and theology, how they proceed, how contradiction plays a very fundamental role in all, right? The first reading is from, I think, probably the greatest authority I could take, 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? And they said, David, they told him, right? Then how is it he said that David, moved by the Spirit, calls him Lord, where he says, the Lord said to my Lord, sit at my right hand, I'll put your enemies on your feet. If David can call him Lord, then how can he be his son? There's an apparent contradiction between two passages in Scripture. One says that Christ is the son of David, right? And the other, that Christ is the Lord of David, right? Well, the son is apparently not the Lord of his father, right? So Christ cannot be the son of David, but he is, right? Okay. Now notice, there's an enormous difference here in what Heisenberg was talking about, but Heisenberg was talking about the strange apparent contradictions between two experiments in science, right? Which lead us to ask the right question, right? Here, our Lord is pointing out a strange apparent contradiction between two passages of Scripture, okay? And now, here, it's a little bit like an examination discussion that we talked about, huh? Because Christ is showing that they don't understand what they claim to know, right? Scripture, right? Because they end up in this contradiction, huh? So He says, no one could think of anything to say in reply, and from that day, no one dared to ask Him any further questions, right? But notice, hidden under that strange apparent contradiction is this, what? Truth that Christ is both God and man, huh? And as God, He's very much the Lord, right? Of David, huh? But as man, He can be descended from David, and so on, right? But if you don't expect the unexpected, you'll never find it. For it's hard to be found, right? But that apparent contradiction would make you expect something unexpected about Christ, there's something about Christ that's rather unique, whatever that is, right? You know? And you can find that, you know, in other passages of Scripture, right? You know, the Father is greater than I, and the Father and I are one, right? I mean, was He equal to Him or not, you know? Well, some is, I mean, as man, the Father is greater than Him, right? But as God, He is the Father and one, equal. And so on. Now, incidentally, this particular passage here is like Socrates, too, because if you go back to the division of the Gospel of Matthew, chapter 22 is a number of about three chapters, if I remember rightly, where Thomas says Matthew is presenting why they wanted to put Him to death, right? And here, the reason is something similar to the way they wanted to put what? Or why they wanted to put Socrates to death, right? Because he was showing men who claimed to know something that they didn't know what they claimed to know, right? So, that's only one of the reasons the way I put Christ to death, but that's one of the reasons. So notice what Christ is showing there, right? You see, we can proceed from sacred Scripture, divinely revealed as it is, right? Divinely written, right? And bring out what seem to be contradictions, huh? And the untying of that will be a great, what? Discovery, right? The hidden army, right? Okay? Now, I go from our Lord there to St. Augustine, right? And St. Augustine is perhaps the greatest mind among the, what? Church fathers, right? Right, huh? Okay? And as we'll see in this decree from the Second Vatican Council, you know, if you look at that just for a second before I look at Augustine, and this is the decree on priestly training where the order of dogmatic theology is given, he says, dogmatic theology should be so arranged that these biblical themes are proposed first of all, right? And so I start with the example from the Gospel of Matthew, right? Next, there should be opened up to the students what the fathers of the Eastern and Western Church have contributed to the faithful transmission development of the individual to the Revelation. And so Augustine is one of the greatest, what, fathers, right? Perhaps the greatest mind among them is any of the Western Church. So look at this one particular passage from Augustine. But even the heretics yield an advantage to those who make proficiency, right? According to the Apostles, St. Paul saying, there must also be heresies that they would which are approved may be made manifest among you. Whence too it is elsewhere said that the son who receives instruction will be wise, and he uses the foolish as his servant, right? Now what sense is the heretic a servant of Augustine, say, huh? See? Well, he goes on to explain why that. For while the hot restlessness of heretics, right, stirs up questions about many articles of the Catholic faith, the necessity, that's the word that we saw in Einstein, right? The necessity of defending them forces us, right? The same two words we saw in Einstein. In other words, when the heretic, right, takes something from Scripture to contradict an article of the faith, or something from philosophy, right, the church fathers were forced to defend that article of faith, right, against that misuse of Scripture or philosophy, right? Okay? And in refuting that error, that's the way they themselves came to a deeper, what, understanding, right? You know? And Thomas, you know, when he's talking about Augustine, Augustine is authoritative in many things, but, you know, one thing that the church has singled out is Augustine teaching on grace, right? You know, one of the popes say, you know, that the mind of Augustine on grace is the mind of the church on grace, right? But Thomas, you know, in discussing what Augustine says, says that, you know, after the Pelagian, at least the heresies arose, Augustine spoke much more carefully, you know, and exactly about these things, right? And you have to be aware of the fact that Augustine's understanding is developing as he refutes these heretics on them. Okay? So for a while, the hot restlessness of heretics stir up questions about many articles of the Catholic faith, the necessity of defending them forces us both to investigate them more accurately, to understand them more clearly, and to proclaim them more earnestly. And the question mooted by an adversary becomes the occasion of instruction. If you look at the works of Augustine, even the titles of the works, you'll find a predominance of titles like Contra-Celsum, Contra, Contra, Contra, Contra, right, you know? In other words, there is an individual article of faith, it may be the Incarnation, it may be grace, it may be predestination, or it might be, but a heretic has denied this particular article, and so we have to defend this particular article, right? Okay? And so there is to some extent in the Fathers of the Church a kind of ad hoc, you might say, right, character, because of replying to this particular, you know, heresy that has risen at this time, right? And therefore, if you look at the third reading here now, which is going to lead us up to Thomas, but if you look at the second paragraph again, next there should be opened up to the students what the Fathers of the Eastern and Western Church have contributed to the faithful transmission development of the individual truths of Revelation, that's touching upon the ad hoc character, right? In other words, Augustine accepts the whole of faith, right? But he takes up and defends those articles of faith that are being denied by this or that heretic in his time, right? Okay? But eventually the heretics got around to deny everything, right? So you're building up, right? You know, this, huh? But there still is a kind of ad hoc character in any one church father, right? Okay? And something like that in the third paragraph, the further history of dogma should also be presented account being taken of its relation to the general history of the church. So you go to the Council of Trent where they're dealing with heresies of Luther or somebody else, maybe about the sacraments, you know, and about justification and so on. And so those mysteries of the faith are, what, defended and illuminated, right? And got into more, but they're forced to because of the prevalent ones at that time, right? So, again, it has something of the ad hoc character, right? Okay? But in the earlier councils, maybe there is about the Mother of God, right? I mean, somebody gets up and says, you shouldn't call her the Mother of God, you're called the Mother of Christ. And they started throwing things at them. But you also have to, you know, refute this, right? And show why she should be called the Mother of God, right? You know? In a sense, he's denying that she was the Mother of God was, in a way, a divided Christ into two persons. Rather than one person who is both God and man. Now, finally, it comes down to Thomas, huh? And notice the way the scripture speaks. It's very strong. Not scripture, but the Second Vatican Council. Next, in order that they may illumine the mysteries of salvation as completely as possible. That's an awfully strong phrase, right? Okay? The student should learn to penetrate them more deeply with the help of speculation under the guidance of Thomas, huh? They go to Thomas, say, in the Summa Theologiae, and even more fully in the question of Disputate, and he's always, what? Every article starts in a way of the contradiction, right? And he's untying it. And it's saying you should follow Thomas there in order to illumine the mysteries of salvation as complete as possible. What does Thomas do? Well, he's always raising these, what? Difficulties, right? And then resolving them. See? One after another, huh? So that's a very clear text on that, right? And the last thing it says there that you learn from Thomas, too, is to perceive their interconnections, because in Thomas you have kind of in the Summa Theologiae, you're looking at all the areas of faith, in a sense, huh? Okay? And so you kind of bring them all together in an orderly way, right? What you don't have in the Church Fathers in most cases, because it's that ad hoc character, right? So there's two things that they see that one should be guided by Thomas, and one is to illumine the mysteries of salvation as complete as possible and to perceive their interconnections, right? But both of those are what? As seen in the Summa Theologiae, it's always starting with what? Contradiction, right? So go on to, you know, the role of contradiction there is to illumine the mysteries of faith as much as possible, right? It leads to that, huh? It's interesting, you know, when you read Thomas, too, and I always think of Thomas and Augustine when Thomas is giving the reasons of the Incarnation, right? And he's quoting Augustine, right? You know, like Cajetan said in his famous commentary in the Summa Theologiae, Thomas seems to have inherited the mind of all the Church Fathers because he's so reverence there, right? Well, in the Incarnation, you know, Augustine has his beautiful kind of dialectic a little bit. He says, he's talking about the suitability of the Incarnation, right? It's not the only way God could have redeemed us but it's the most appropriate way. And the best don't say, you know, God should be followed but he can't be seen. Man can be seen but he's not a perfect model to follow. Well, you've got a problem. What are you going to do? Well, God became man, right? So you've got a perfect model to follow, right? Or he'll say, man sinned in a way committing an infinite crime, right? Because he rejected God, right? Who's an infinite good, right? So man can't, what? Do an infinite preparation, right? God can do that but God didn't sin, right? You know? So how do you make the one who sinned do something in a way infinite? Well, God became man, right? You know? But the very way of Augustine speaking and then Thomas is, you know, just quoting Augustine really is starting with a kind of, what? Paradox or a kind of contradiction, right? Man sinned in a infinite situation but man can't really do it. You see? God could do it but he's not the one who should do it. You know? So God became man so that what? Man in a way could what? You know, make a preparation for man. But being both God and man he could do this, right? To a sufficient one. So that's a little introduction there to the role of contradiction development of our knowledge, right? But we saw it in two very clear examples in the course there. One was in a time the contradiction the apparent contradiction between a statement of what? An exegres that reason is or mind is self-ruling, right? In a statement that the ruler must be separated from the world, right? And then the other one here about what? Change, right? Okay. But there are many other contradictions. Those are two striking ones, right? Okay. Let's at least go on and stop. It's about a quarter to five. Do you think you could finish we could finish by five or? No, I wouldn't want to go that fast. Yeah, then let's wait. Yeah, yeah, yeah. I have a problem next week because this is exam week now. Like I'm giving an exam next Tuesday and one on Thursday and one on Friday and so on and one Saturday. So I'll be, you know, getting an exam and enjoy. I'll be right back to it. I'll be right back to it.