Wisdom (Metaphysics 2005)
Lecture 34: Axioms, Equivocation, and the Defense of First Principles

Transcript
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If you stick with one whole, a composed whole, it's always more than one of its composing parts. If you take a universal whole, it's always said of more than one of its parts, right? So if animal is a universal whole, said of man, dog, and can, horse, it's said of more than dog is said of, right? It's said of more than man is said of, right? If you're taking animal as a composing part of the definition of man, then it is what? Put together from more than just that part, right? So I'm making the most common mistake in thinking according to the father of logic. He says the most common mistake in thinking is from mixing up different senses of the same word. I'll take another example here. We've seen the meanings of the word before, I believe. Before now, right? And you say, well, now, Chaucer, okay, now an axiom about before is that nothing is before itself. Nothing is after itself, right? Now, Chaucer came before, what? Shakespeare in English fiction. But all the critics put Shakespeare before, what? Chaucer. So Shakespeare is before Chaucer, and Chaucer is before Shakespeare, and then Shakespeare is before himself, right? I don't know. And so I seem to have contradicted the axiom that nothing is before or after itself, right? But again, I mixed up two different meanings of before, right? Because the first meaning of before is in time, and that's the sense of which Chaucer is before Shakespeare. But when you say the critics all put Shakespeare before Chaucer, that's the fourth sense of before, which is better, right? Well, better. Better. Quality. Yeah, yeah. Maybe before in the goodness, yeah, better. And so you mixed up two different senses, right? So I don't know. It's like in the other case there. In one sense, animal is a part of man, but in another sense, man is a part of animal. But you use the word part in two different senses there. Otherwise, one could be a part of the other vice versa, in the same sense. In the same way here. In one sense, Chaucer is before Shakespeare in time, right? In another sense, Shakespeare is before Chaucer in goodness, right? But if they were the same sense of before, they couldn't be before each other in the same sense of before. Did you see that? So it was Aristotle's discovery that the words in all the axioms are equivocal by reason, right? And that people who can't distinguish those senses have an indistinct knowledge, you might say, of the axiom. But also the sophists, right, can deny the axioms by a sophisticated argument. That's an argument in this case resulting from mixing up different senses of the word. But in addition to that, there are other arguments that the sophists use to deny the, what, axioms, huh? One of the famous arguments. In order to grasp something, you have to separate it from everything else, right? If I'm going to grasp this glass, I've got to separate it from everything else, huh? If everything else is there's infinity of other things, right? So you never grasp anything then, can you? See, I can't grasp the center of this table because it's connected with the rest of this table, right? I have to get a knife out here and cut it off and separate it from everything around it, huh? So for your mind to grasp something, you would have to, what, separate it from everything else, right? Everything else is infinity of other things, right? You've got to cut off from all these things, right? And obviously you can't go through an infinity of things, you can never grasp anything. Of course, when I was objecting to this objection, it's to say, I can't grasp your objection. And you can't grasp me either, but... Would the answer come down to simply the fact that when you do grasp something, you are in that grasping of it, separating it from everything else, you're seeing it on its own now? Well, in a sense, this objection proceeds from an ignorance of what? You know, of the universal. If I had to separate seven, let's say, from every even number, seven is not two, it's not four, it's not six, it's not eight. If I had to go through all the even numbers, I'd never separate seven from them, would I say? But if I know that seven is not an even number... You have made that separation? Yeah, from an infinity of things, yeah. So, our mind or reason by the universal can separate something from an infinity of other things. So there are objections against the axioms, other than simply based upon what? The falconic equivocation. And objections that most people can't answer. And de Conec, you know, Charles de Conec has a beautiful article, unfortunately it's in French, but in the whole teller, he can't philosophique, it was called Paradox de Duvenir, Parle-de-Connexion. And it's about the famous attack, which was really made by Hegel and others, but others not trying to see any way out of it, against the axiom about being an unbeak, something cannot both be and not be. And there's an apparent contradiction in all becoming, which Aristotle unties in the sixth book of an actual hearing. But most people can untied it, and Hegel revised this mistake in the 19th century. But in the article, it kind of shows the problems that it created in theology in the Middle Ages and so on. And so you say, there are objections to the axioms that are very difficult to understand, right? And objections that puzzle people all the way down through the centuries on. Now, if you have an objection against an axiom that you can't answer, right, then you might be in the position of thinking you don't know what you do know. And Aristotle pointed out in the second book of an actual hearing, that it's possible to think you don't know what you do know. And if that's so, that's going to really be a problem for the life of the mind. And so, it seems someone has to defend the axioms against these objections that make people think they don't know what they do know. And so long as that objection seems to stand, well then, the man thinks he doesn't know the axioms, and therefore he doesn't think he knows anything. So it's really going to be necessary to consider the axioms, isn't it? Both to have a distinct knowledge of them, because the words in the axioms are all equivocal, and to answer the common objections against the axioms, huh? So, there's at least a couple of good reasons, right, for a consideration of the axioms. And one is to have a distinct knowledge of them, because everything else is going to be built upon them. And the other is to answer the objections, right? Whether they're based upon, you know, mixing up the different senses of the words or the axioms, or based upon something else, right? Because those objections are very hard to answer, and people think they don't know what they do know. I was thinking of, you know, this heretic, as we call him that, Roger Haight there, that he's judging the articles of faith by the customary or fashionable ideas of what is called post-modernism, right? Okay? But he's putting the carpet by the horse, right? That, but our friend St. Anselm has got it right when he says that theology is faith-seeking, what? Understanding, yeah. You've got to have the faith first. And you believe what the Church teaches and so on, and then you seek to understand what you believe, right? You see, you believe that there are three persons and one God, and you seek to understand this insofar as it's possible in this life, and there are all kinds of qualifications there. But he's judging by the customary or fashionable ideas of postmodernism, the Trinity. It's all wrong, right? Well, in philosophy, you might say that philosophy is the natural understanding of the axioms, right? Seeking a reasoned out understanding of things, and ultimately seeking wisdom, right? But if a man is in doubt that he naturally understands the axioms, then you've got to clear that up before you can, what, go forward, right? Such a man is, you know, if a man is convinced by one of these sophisticated arguments against the axioms, that he doesn't know what he does know, he's in a terrible situation, right? Socrates spent his life showing the reverse problem, right? People think they know what they don't know. There's also a problem in thinking you don't know what you do know. And Socrates himself almost gets into that sometimes. But Aristotle realizes you've got to avoid both of those mistakes. So you see some of the reason why it's necessary to say the axioms, huh? But now next time, I'm going to ask the question which Aristotle will be concerned with here in the fifth reading here. Why should that consideration of the axioms belong more to the wise man than to somebody else, right? Why should it belong to the wise man to consider the axioms and to defend them against the sophisticated objections that are made against them? Why? Well, we're going to ask that next time, okay? We're not out of time here. We'll stop at 4.30, right? In trouble with the powers that be, huh? I don't know. In the name of the Father, and of the Son, and of the Holy Spirit, Amen. God, our enlightenment. Guardian angels, strengthen the lights of our minds, order the luminary images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor, and help us to understand what you have written. In the name of the Father, and of the Son, and of the Holy Spirit, Amen. So in the last reading we looked at, that the philosopher was showing that the wise man considers being as being, right? And after that, in part we've not read, he shows that being and one are convertible, and this is also about the one. Now in the fifth reading, he's going to show that wisdom considers the axioms. Now as he said last time, there's two questions you might want to answer here, and one question which we've dealt with before, is why is it necessary, right, to consider the axioms? Why not just use them, right? Since the axioms are the statements known for themselves by all men, can we just assume everybody knows these, and we don't have to talk about them, just use them and apply them? Well, the main reason was perhaps that some people, like the sophists of ancient times, and the sophists of modern times, deny sometimes an axiom, and sometimes even give a reason for denying it, a reason that most people can't untie, or can't solve. And so people begin to think they don't know what they do know. And as Aristotle says in the second book of natural hearing, the so-called physics, if it's possible, as Socrates showed, that people think they know what they don't know, then the reverse is true, huh? That it's possible that someone can think he doesn't know what he does know. And so if you think you don't know the axioms, you don't think you know anything, really. And you're kind of a universal skeptic, and so on. So someone has to reply to the objections to the, what, axioms, huh? Now, as you consider these objections to the axioms, you'll find that some of them, not all of them by any means, but some of them are based upon mixing up different senses of the words in the axioms. And Aristotle discovered that the very words in the axioms are all equivocal. That is to say they have many meanings. But that they are equivocal by reason. There's a connection among the meanings. And so to distinguish the meanings of the words in the axioms not only helps you to untie some of these objections against the axioms, but it also gives you a more distinct knowledge of the axioms than everyone has. And since the axioms are the beginnings of all our knowledge and statements, a distinct knowledge of them will enable you to build upon them better. So, it is necessary, for the good of the reason, to consider the axioms, right? Both to get a more distinct knowledge of them, but also to reply to the objections that some people give to them. Now, given that, the next question is, why does it belong to the wise man to make this defense of the, what, axioms? Well, that's the answer Aristotle is going to be giving here in this reading. And the basic reason is tied to what we saw before in the first reading, that the axioms pertain to being as being. And therefore, the man who considers being as being, and the one as one, and so on, and distinguishes the meanings of being in one, and so on, he appropriately considers the axioms whose parts pertain to being as being. And this is seen most clearly in the most fundamental, the axioms. The axioms about being and what? None being. And sometimes we distinguish two axioms about being and unbeing. One is that something cannot both be and not be, in the same sense of being, at the same time. And the other is that something must either be or not be, in the same sense. And so sometimes I quote Hamlet when he says, to be or not to be. That is the question. It's a question because you can't both be and not be. If someone said, you know, to eat or to drink, that is the question. Or to eat or to breathe, that is the question. No, that's not the question. You can both do both, and you better do both, right? But to be or not to be, you can't be both. And likewise, you've got to be one or the other, right? So, there you can see in the axiom which Aristotle says is the natural beginning of all the axioms. The axiom of being and non-being that pertains to being as being. So, it's appropriate then, because the science is about being as being, that it take up the axioms, huh? And that's going to be basically the reason Aristotle gives here. It should be said, huh? Whether there is one or, or should be, or many forms of reasoned out knowledge about what are called the axioms in the mathematical forms of reasoned out knowledge and about substance, huh? Of course, Euclid, you know, distinguishes some of the axioms that are particularly important in math. It is clear, Aristotle says, that the investigation about these belongs to one reasoned out knowledge and that of the philosopher. And notice now he calls the wise man the first philosopher, the philosopher, right? Kind of by Antonia Masia. For they belong to all beings and not to one kind privately apart from the others. They belong to being as being, huh? Okay? And since we found out that that is the subject of wisdom, then that's the reason why the wise man should also be the man to defend the axioms. And all the sciences, all the other forms of reasoned out knowledge, the men who practice them, use them because they are of being as being and this is said of everything. And each kind of thing is a being of some sort. And of course, they use them so far as this is enough for them. That is as far as extends the genus in which they carry out demonstrations. So the mathematician might say, you know, well, an odd number cannot be an even number, right? An even number is divisible into two equal parts. An odd number is not. They can't both be and not be divisible into two equal parts. But he's kind of taking the, what, impossibility of being and not being and taking it in his domain. So, since it is clear that they belong to all insofar as they are beings, for this is what is common to them, the consideration of the one knowing being as being will also be about them. And whose consideration is about being as being? Well, we found out in the beginning of the fourth book that it's the wise man, right? That the man who considers the cause of all considers what is said of all and what's said of all as being and the things that pertain to being as being. Since he axioms, the very parts are made up of being as being, therefore he should talk about these. Whence, he says, none of those considering by art tries to say something about these, as whether they are true or not, neither the geometry nor the arithmetician. So Euclid doesn't try to show that these are true, right? He just takes them for granted, huh? But now he says there's one exception, right? But some of the naturalists, right? Some of the natural philosophers reasonably did this, right? Why? They thought it was first philosophy what they were doing. Yeah, they thought... that natural philosophy was what? Wisdom, right? And as Aristotle was saying in the sixth book of wisdom, if only material substances exist, then natural philosophy would be what? Wisdom, right? So you could say for almost 200 years, the Greeks identified wisdom with natural philosophy. But then when they started with Anaxagoras and Plato and Aristotle, they had evidence that there exists something that could be without matter, right? Then they realized that natural philosophy is not about all things. And it's not a property of being as being to be somewhere in some place. But as Aristotle quotes there in the fourth book of natural hearing, he's talking about place. The common opinion of the Greeks before him was that whatever it is, it must be somewhere. If it isn't somewhere, it doesn't exist. If you go on Main Street today, you'd find that the common opinion too. But to be somewhere, to be contained in a place, is a property really of bodies. So you're thinking that nothing exists but bodies and what is in bodies. And if that's all that did exist, then to be somewhere would be a property of being as being. So insofar as they thought that they were the wise men, or that this is wisdom, right? Then it's not without reason that they sometimes touched upon the axiom here about being and unbeing. There was some controversy about that. But some of the naturalists, meaning the natural philosophers, reasonably did this for they were thought to be considering about all nature and all being, all things. And so in Aristotle divides in the second reading there of the first book of natural hearing, the opinions of the natural philosophers before him, right? He said, well, it's the same way they talked about being, right? The same division of thoughts. Because you're identifying natural things with all things in some ways. But since there is someone above the naturalist, meaning the first philosopher, the wise man, for nature is only one kind of being, the consideration about these will belong to the one looking at the universal and the first substance. For natural philosophy is wisdom in some respect. It's a wisdom about natural things, right? But it's not the first wisdom, right? But now he's going to say, now, when you take up the axioms, you don't try to prove that they are true, because there's nothing before them by which they could be proven. And furthermore, they are known through themselves, through their parts. But what some speaking about truth attempt and what way it should be received, they do through lack of being brought up in the analytics. For they have to know these things before they come to them and not seek them when hearing them. So he's talking about, in the analytics, where you talk about what things can be proven, right? And what things are known without proof. And the axioms are, most of all, what is known without proof. So should you try to prove that the whole is more than limits parts? Of course. Okay. Now, the same thing is true, to a lesser extent, about the private beginnings of reason-out knowledge. So like all right angles equal, right? That's not something you really prove, right? And the so-called fifth postulate of Euclid, right? I don't know if you know the history of that postulate. But you could laze it down without giving any proof of it. And some authors down through the ages have tried to, what? Prove it. My brother Mark made a study of those attempts to prove the fifth postulate. And it shows, first of all, that the proofs are not good, that they're circular. And secondly, that it's circular because they assume the very thing they're trying to prove. And by their as, as a secondary thing there, another thing to see, the fact that they assume the very thing they're trying to prove without realizing they're assuming it, is a sign that it is really obvious, no? So, that would be true. Yeah. Okay. We have something like that with the fundamental axiom of all. down through the history of human thought, if you go down through it. Oh, the principle of non-contradiction. Yeah, yeah. You have people denying the principle of contradiction because something that they've been studying seems to involve a contradiction and they can't see any way out of it. So, they're denying the principle of contradiction because something contradicts it. So, they're accepting it in their very attempt to prove that it isn't so. They're saying it isn't so because it is so. It's a little bit like the thing I see in ethics there where one of the fundamental things you've got to know in ethics is that you should live by your reason. And someone might say, well, I think you should live by your emotions. I live by my emotions. And so, but now if a person wants to argue about this, right? Should I live by my reason or by my emotions? He's in a way admitting you should live by your reason. Because if reason has the right to decide whether you should live by reason or by your emotions, you're already saying in a way that you should live by your reason. Reason must decide how you should live. Maybe he's planning on the Lord to win from his emotions. So, Aristotle's pointing this out then, right? You've got to know how to take things. It is clear then that it belonged to the philosopher, meaning the wise man, the first philosopher, and the one considering about all substance, because substance is the main kind of being, right? To also consider about the syllogistic beginnings, the statements that are the beginnings. The beginnings of syllogisms are always statements, right? But the actions are the statements at the beginning of all statements, okay? Now we can come to the great turnaround, huh? If you understand the great turnaround, you can understand something of the order of the most of the 14 books of wisdom, not all of them, but almost all of them. It kind of reverts that, if you know. But what is this great turnaround that I'm talking about? Well, if I put down on the board here, three and then three, and you'll see what I'm talking about. In the premium, huh? We learn that wisdom is about causes, right? And at last, about the first cause, huh? So, wisdom is about the first causes. In the beginning of the fourth book of wisdom, we learn that wisdom is about being as being. And the one and the many, too, but we didn't say it explicitly. Wisdom is about being as being. And then, after this, in the fifth reading, before the book, the reading is going over, we learn that wisdom is about the axioms, okay? You might suspect that, you say what wisdom is about, that there's a little bit of what? Equivocation. Because when you say wisdom is about, the first cause is about being as being about the axioms, it doesn't mean that all three of these are the subject of wisdom. When you say that wisdom is about being as being the one, that's as a subject, huh? So the subject of wisdom is. Okay? That's why wisdom is less. That's why wisdom is less. Wisdom in the sense of first philosophy here. First philosophy is less wisdom than theology. Because theology is about God as a subject. God is the chief subject of theology. But God is not the chief subject of first philosophy. It's being as being, or you could say substance, primarily as a substance. What sense then is wisdom about the first causes? Well, that's really the end or the goal of first philosophy. To know the first cause, right? To know the first causes of its, what? Subject. Do you see that? So, when you say wisdom is about the first causes, you're more talking about the end or goal of wisdom, huh? Okay? And in general, every part of philosophy is about some subject, and it seeks to know the causes of that subject, right? So, in a sense, the end or goal in any science is to know the causes of that subject. Okay? But now when you say wisdom is about the actions, this is kind of something unique to wisdom. And you don't find something like that in the other parts of philosophy. In the other parts of philosophy, you'll have some subject that that part of philosophy is about. And you'll be seeking the causes of that subject, right? Okay? But wisdom, if you go to the sixth book of the Nicomarckian Ethics, when Aristotle distinguishes the virtues of reason, and in particular, the virtues of looking reason, huh? And he'll distinguish between natural understanding and episteme, or reasoned out knowledge, and then he'll distinguish wisdom from both of them. As if wisdom is something, not just one other form of reasoned out knowledge, but it has a certain excellence that gives it a new name, and makes it stand out against all the other ones. And Aristotle will say that wisdom is the head of all understanding. It's the head of both of every other reasoned out understanding, and even of what? Natural understanding. So that the wise man in some way embraces both nous, or natural understanding, and episteme, huh? He knows the cause of the causes, right? The very first causes. But he also knows what natural understanding knows, but in a more distinct way, and in a way we're able to defend it. The natural understanding can't do that. Everybody has natural understanding, but they can't defend, and my students can't defend, by some mystical objection against the whole thing created in the park. They're convinced, rarely until I try to show them that they shouldn't be convinced. Okay? So the wisdom can be about, not only a subject, and seek the cause of that subject, which is common to every kind of reasoned out understanding, but that it also in some way embraces natural understanding, too, shows that wisdom is the unique, then, virtue of looking reason. It's the head, Aristotle says, the cot, the head of all understanding. Okay? So the wisdom is about the actions, and this is something that belongs to wisdom, insofar as it's not just another reasoned out understanding, right? It's something more. It is a kind of reasoned out understanding, but it's not just that. It embraces natural understanding, too. Because it's really a remarkable thing, reasoned out understanding. I mean, wisdom, rather. It embraces, huh? And perfects both, every form of reasoned out understanding, and, what, natural understanding, too, huh? It's really something, the highest of all of the virtues of reason, right? And the greatest of all of the virtues, the human virtues, huh? Okay? Now, what we've learned up to this point, is what wisdom is about, right? Now you've got to take these things up. Now, in the rest of book four, he defends the actions of being and unbeing, huh? Defense of the actions. Aristotle spends his time mainly defending the actions of being and unbeing, huh? Then, the way Thomas divides the things, in books five through ten, he considers being as being, and the one and the many. Okay? Consideration of being as being, one and many. In other words, in books five through ten, he's pursuing a reasoned out understanding of being as being, and of the one and the many. Then, in books, the last four books, in books seven through fourteen, he's investigating and determining the truth about the first causes. This is a quiet time, as you know, in the second book of the Summa Kami Gentiles, when he's contrasting philosophy and theology. He says, God is the last thing to be considered in philosophy. But in theology, he's the first thing to be considered, huh? So that the order of philosophy and theology, in a way, is just the reverse, huh? The contrary one together. And of course, the order of theology is much more like the order of, if you speak of an order of God's knowledge, right? It's much more like God's knowledge, because God knows all things by knowing himself. And so in theology, we imitate that in a kind of human way, right? By considering God first, and nothing else except in comparison to God as their maker or their inner, huh? Okay? Now notice the order here, right? The order in which we learn what wisdom is about, and the order in which those things that is about are taken up is just the reverse, right? I, for the fun of it, call us after great turnaround of that, okay? And to put it in kind of simple language, you could say, you learn that wisdom is about A, and then you learn that wisdom is about B, and then you learn that wisdom is about C. But then he takes up C first, and then he takes up B, right? And finally he takes up A, right? That seems kind of screwy at first sight, doesn't it? You know, somebody's saying, I'm going to talk about A, B, and C. He's telling you what he's going to talk about. You'd expect him to talk about A first, and then B, and then C, right? So why this complete contrary order, right? In which we learn what wisdom is about, and the order in which we take up and determine the truth about those things that it is about. What's the reason for this, huh? Axioms are the causes of our knowing about these other things. Yeah. So you would begin there, and then those are the things that would be most common for all to begin. Well, what is the thing underlying both of these orders? Because once you understand the reason why for each of these orders, and it's actually the same reason, basically, once you see that reason, you realize that why is this order to be right there, that this order is the only order to which it would be wise to go. Finally, isn't it, because just given the mode of human understanding, because I'm having, I guess, with the axioms, I agree with them. Well, notice down here, it's perhaps easier to understand the order in the second part, right? Since the axioms are the statements known themselves be all men, these statements are the most known of all statements, right? Why the first causes, you might say, would be what are least known to us, right? So the basic principle that we're following there in the second half, right, is starting from what is more known to us, right, and proceeding towards what is less known to us. And that's the inborn road in our knowledge, right, from what is more known to us towards what is less known to us, right? Being is being is in between, right? It's less known to us than the axioms, but more known to us than the first causes, just as effects are usually more known than causes, right? But now, the paradox, right, you want to pause the paradox a bit, the paradox is that what is most known to us is least known that wisdom is about it. And that what is least known to us is most known that wisdom is about it. Why should that be just the reverse? I mean, at first sight you say, well, if the axioms are most known to us, right, would it also be most known to us that wisdom is about them? What is there? What principle is he following up here? Is he still following up here in the first three, when he says that wisdom is about the first causes, and then showing it's about being as being, and then it's about the axioms, is he still following up there the rule of going from what is more known to us towards what is less known to us? What would you say? Yeah. It would be most known to us that wisdom is about the first causes, than that wisdom is about the axioms. Yeah, yeah. Now, if you stand and think about it, what seems at first to be a paradox is not too paradoxical. The fact that the axioms are so well known to us, that everybody seems to know them, right? Mm-hmm. And if there's even a question that he's solved, why consider the axioms at all? Just use them, you know? Mm-hmm. The fact that they're so well known is iniquity with the fact that that's the least thing, or the last thing you think wisdom is about. Mm-hmm. You see? Because you look to the wise man as being, what? More knowing than the rest of us, huh? Above all the rest of us in his knowledge, right? Huh? That's what's, you know? I mean, when I start sometimes in a text of philosophy, I ask, you know, a classroom of freshmen, do you think wisdom comes at the beginning of our knowledge? Well, none of them think that. Does it come in the middle, or do you think it comes at the end? And they'll usually say it comes towards the end. Almost everybody in this class, right? So having the haziest notion of what wisdom is, they think it is something ultimate, something highest, something last in our knowledge. So the last thing you think that wisdom is about is what everybody knows. Right? So it's least known to us that wisdom is about what is most known to us. Right? Why, if you take the first clauses, huh? Somebody might be skeptical as to the possibility of ignoring the first clauses, right? But no one would be in doubt if someone did know the first clauses that he should be considered wise. You see? So everybody thinks that wisdom is about something most difficult to know, something most worthwhile to know, and so on. And to say, therefore, that wisdom is about the first clauses, that's very well known, huh? But to say that wisdom is about being as being, you know, that sounds kind of general, doesn't it? It doesn't seem at first sight to be anything like wisdom, does it, huh? You know? You gave me something to drink here, you know? What is it? Well, it's something. It's not nothing. Well, that's very general, right? If I say, give me a glass of water to drink, my knowledge is more advanced, right? Give me a glass of dry red wine to drink, and they say, this is dry red wine. And you say, what is it? Carbonet Sauvignon, Pinot Noir? I say, well, it's Carbonet Sauvignon, Napa Valley, and I think. Ah! See? So a man can tell you it's Napa Valley, Carbonet Sauvignon. His knowledge goes beyond the man. He can just tell you it's a dry red wine, right? So that the wise man should be about what is said of all, these very general things, right? Like being, you know, it is. Call that wisdom? You know? We think of the man whose knowledge is more advanced as having a more particular knowledge, normally. See? So it's less known to us that wisdom is about being as being than that it's about the, what? First causes, huh? Okay? So what seems a paradox at first sight, right, is actually makes a lot of sense when you stop and think about it. The fact that the axioms are what is most known to us, that they are, in at least a confused way, evident to everybody, makes it, at least likely, the axioms would be about what everybody knows. Now, sometimes I compare this to a tree, right? And you say, well, of all plants, the tree is above all the rest of them, right? Okay? But also, the tree is what? Yeah. Which is more known to us, that the tree is above all the plants? Yeah, we give the tree a special place among the plants, because it's above all the rest of them, right? But is there a connection between the fact that the tree is above all the other plants, and its roots go down below all the other plants? Yeah. Right? Because it's got to have that foundation, right? So, in a sense, the wise man is like that, right? He's above everybody else, especially knowing the first causes, huh? He rises above everybody else, his knowledge. But he also goes back to the beginning of our knowledge, and goes much more deeper into it than anybody else, huh? Mm-hmm. Okay? I guess biologists, or botanists, would say, you know, that the height of the plant, or the size of the plant, above ground, and the root system down below are kind of proportional, right? Mm-hmm. So, I compare the wise man to a tree in that sense, huh? The way his mind grows, huh? And it shouldn't really be paradoxical that what is higher than all the rest of the tree should be lower than all the rest, too. There's kind of a reason for that, huh? The exact same reason is here. There's a reason why, huh? The man who's above everybody else in knowing causes, and reaching the end and goal of our knowledge, should also go down in the beginning and know that better than anybody else. And you find that, you know, the further you want to go, even in other sciences, the forms of reason of our knowledge, you've got to go back to the beginnings and know them better, right? Mm-hmm. Have to return to those beginnings and know them better. The defense of the axioms, then, would be an expression I've heard of wisdom is that it's glorified common sense. In that way, the defense of the axioms, at least, would be that. I mean, some of these arguments are very difficult. I think I referred to this beautiful article by Charles de Connick there in the Naval Theologique and Philosophique. It's in French. But the paradox, the devenir, part of contradiction, the paradox, right, the parent contradiction of becoming, what? Parcadiction means from being, then, being, right? Well, Hegel, you know, in the 19th century there, he gives an argument that in becoming, there is a contradiction, the same thing both is and is not. And that thing has been solved by Aristotle in the sixth book of natural gift. But it's a very difficult thing to solve, huh? But the iconic in the article shows the difficulty it caused all the Middle Ages in trying to understand the Eucharist and so on. And Thomas could solve those difficulties because he knew Aristotle that he could solve. So, it's difficult, right? It's not just common sense in that sense. It's difficult to solve some of these apparent contradictions. But you should begin, like, see, a natural philosopher with the first book of natural hearing where Aristotle unties the apparent contradiction and change that Heraclitus was pointing out, right? You know, Heraclitus is dead. Night is the same thing because day becomes night. You know, becomes means comes to be, right? And the hard becomes soft and soft becomes hard, right? Becomes means comes to be. So if one contrary comes to be the other one, then what is the other, right? And so on. That one is easier to solve, huh? than solved in the first book that you're hearing in the 11th reading. Okay? But this other one is much more difficult, the one that's solved in the sixth book. And of course, if you heard Zeno's paradoxes, right, about motion, most people can't solve those, right? So it's possible to give an objection to something we all know is true. Zeno's saying, you know, you can't walk out that door, right? You've got to walk half the way before you can walk the whole way, right? Before you can walk half the way, you've got to walk half of the half. And before you can walk half of the half, you've got to walk half of the half. And this goes on forever because it continues to be divisible forever. It's different to get out that door, aren't you? And again, you know, Achilles, the fastest runner, is not going to ever catch up with the little turtle or something, right? If you give the turtle a little head start, right? Because if you give him a little head start, before Achilles can surpass him, he's got to catch up to where the turtle is. And that's going to take some time, however little. And that time, the turtle is a little further. And he's got to catch up to that part before he can catch up with him and the turtle is a little further. First off, unties those in the Eighth Books of Natural Hearing, but most people cannot, what, untie them. And so, first off, in the rest of Book 4, he would show where these doubts arise, and a lot of them arise from motion and from change, right? In other ways, they arise too, but those are some of the most important ones. And he'd show how they're solved, right? So, if you understand the great turnaround, and you see that it's the same reason in both, right? Why they go in that order, right? And the reason is in more. We should go from what is more known to us to what is less known. You can see the order cannot be otherwise. And this explains the order of most of the 14 books. It doesn't explain why the rest of Book 1 is there, or Book 2 or 3, right? But it does explain the premium and Books 4 to the end. So you can see, kind of as a whole, that Aristotle is perfectly, what, ordered this. Now, not only is the order perfect, but to some extent, you could say, these things are continuous. Not continuous here, not in the original sense of continuous, but imitating the great Euclid, right? Euclid says sometimes, in proportion, it's continuous. What does that mean? No, you can keep on going up. So, like, if I've got 2 is to 4, is 4 is to 8, as 8 is, etc. Yeah, if you've got the end of 1, it's the beginning of the next. Yeah. So 4 is to 6, as 6 is to 9, right? So, the end of 1 is the beginning of the next ratio, right? As opposed to, if I say, 2 is to 3, as 4 is to 6. These are not continuous, because 3 is not 4, right? Now, they're proportional, but it's not continuous proportionality. Now, sometimes I speak of syllogisms, in imitating what Euclid's doing there, as being continuous, when the conclusion of one syllogism is a, what? Premise in the next one, right? Okay. And I was remarking, you know, I was taking this great delight in the 14th theorem of the 2nd book of Euclid, where, in part of that theorem, he's showing how to make a square, or to find the side of the square, equal to a given, what? Ablo, right? And he uses the Pythagorean theorem, right? Which is proven at the end of book 1. And he uses that wonderful theorem 5, about cutting a line into equal and unequal segments, and so on. Okay. So the conclusion of those arguments, right, are starting points for seeing this. Okay. So I call syllogisms continuous when the conclusion of one is the beginning of another, right? Okay. And if you want, you can call definitions continuous, right? Like to say the definition of quadrilateral and what? Square, right? Okay. And what's defined in the definition of quadrilateral, then quadrilateralism is actually the square. Okay? Well, if you look at the reasoning we've seen so far, Aristotle reasoned from wisdom being about first causes, reasoning from wisdom being about the cause of all things, to wisdom being about what is said of all. Remember that? We were pointing out that if you consider a more universal cause, you talk about what is said of more, right? So the science about the king is going to talk about what is said of more than the science about the general. The science about the general is going to talk about the soldier, and the science about the king is going to talk about the citizen. The citizen is said of more, right? So the cause of all things, the most universal cause, the first causes, right, will have a subject which is said of all, right? So he reasons from wisdom being about the first causes to wisdom being about being as being. So you can see these are continuous, right? Which is shown in the premium, he reasoned out that wisdom is about the first causes. So your conclusion there is the beginning for showing this next thing, the beginning of book four. And once you've concluded that wisdom is about being as being, now you have the beginning for showing that it's about the what? About the axioms. Yeah. Because he reasoned that the axioms are about being as being, right? And so the science that is about being as being is the one that should pick up the axioms. So he reasons from the conclusion that wisdom is about being as being, he uses that conclusion as the premise, huh? For reasoning that wisdom is about the axioms. Okay? And that shows you how tight-knit these things are, right? Because if the end of one is the beginning of the other, then there's nothing you can put in between. Right? You know? If the end of the United States is the beginning of Canada, that line up there, right? Is there some country between the United States and Canada? It's very big. Not a big one. You see? So if you go from Mexico, let's say, to the United States to Canada, right? Well, the end of Mexico in the northern direction, right, is what? The beginning of the United States. And then the end of the United States in the northern direction is the beginning of Canada. You see? So it's a very... So nothing between Mexico and the United States. Nothing between the United States and Canada, right? So it's very well ordered, right? Just like we met with Augustine and Thomas, you know, I try to understand creation there being in six days. Of course, Euclidus taught Augustine and Thomas that six is the first perfect number, right? Mm-hmm. And so it doesn't necessarily mean six days in the ordinary sense of days, but the six there symbolizes the perfection of what God has made, right? What's remarkable about number six is not only that everything that measures it adds up to six, because it's measured by one and two and three, but it's not measured by four or five, and one, two, and three together add up to six, but there's nothing between them. One, two, three. It's perfectly, what? You know? In that way, without perfect numbers you wouldn't have that, right? You know, I mean, 28 is the next perfect number, right? You'd have to be four and each other's seven, you know, and so on. To one, two, three, it's just very, very tight. So it's really a number to symbolize the perfection of what God has made. That's why it's every six days he rests. It's easy. So if the conclusion shown in the premium is the premise for showing what is shown being in the fourth book, and the conclusion there is the premise for showing the reasons about the axioms, it's very tight fit, huh? Okay? Now, the same thing is true down here, because the axioms want reasons from the axioms from those statements to all the statements that you ever know. Not only from those statements, right? Like Euclid doesn't reason to say only from the axioms, reasons from things that are private, right, to that. But you do reason from the axioms. So the axioms although they're not conclusions, they have premises for reasoning out and understanding of being as being. And the reason out understanding of being as being will be the premises, will give you the premises for reasoning out what the first clause is. and the reason out