De Anima (On the Soul)
Lecture 144: Logic, Argument Structure, and Syllogistic Form

Transcript
================================================================================

I told the students, I put you all in jail today, right? If you're the man who robbed the bank today, then you are a man. True or false? True. But you are a man. True, right? Therefore, you're the man who robbed the bank, right? You see the idea? You see? You can't reason from the affirmation of the consequent to the affirmation of the antecedent. You can reason from the affirmation of the antecedent to the affirmation of the consequent. Okay? You see the idea? So, if he reasons this way, his matter is good, his premises are true, but the conclusion doesn't follow. If he reasons this way, the conclusion follows, but the premises are, what? Not both true, one of his thoughts. Now, there are four key people here, I'm going to buy you all a $20 book. Now, four times 20 is, what, $100, so it's going to cost $100, right? Okay. What's wrong with that? There are four people here, right? Yeah. The book does cost $20, but I multiply them correctly, right? Okay? Now, let's put it another way, right? I'm going to buy a book for all the students here, right? Put another book. And there's three students here, and there's three students here, and a book is $20, so three times 20 is 60. That's four students. Yeah. There, I multiply correctly, three times 20 is 60, but one of the numbers was incorrect, right? Yes. So, there's two ways my checkbook or something like that can get off. Yeah. Either I didn't add or multiply or subtract correctly, right? Or I didn't have the right number to add, subtract, or correct, right? Mm-hmm. So, as soon as you have both things, they're all wrong. And Aristotle refutes Melisius there, right, in the first book of Natural Philosophy. He both has false premises, and his conclusion doesn't follow either. So, he has both defects. But all you need is one defect to say the argument is bad, huh? Mm-hmm. Okay? But for an argument to be good, both the premises have to be true, and the conclusion has to follow necessarily. And that's why Aristotle, when he talks about demonstration and logic, he does so in two books, the prior and the posterior analytics, we call them in English, huh? But the prior analytics is looking at whether something follows necessarily or not, right? The posterior analytics is looking at whether the premises are necessarily true or not. And both are required, right? Yeah. Before you're sure of the, what, conclusion, right? So, you can have one of those without the other, right? But both of those are necessary before you can be sure about the, what, conclusion, huh? So, a demonstration is a syllogism whose premises are necessarily true. And therefore, it's a syllogism whose conclusion is necessarily, what, true, right? While a dialectical syllogism is a syllogism whose premises are only probable opinions. And so, they may or may, the conclusion is only, what, probable, right? Right. Okay? But in arguments like induction or entameme or example, there the conclusion doesn't follow necessarily, right? The last Honda I bought lasted me ten years. The next Honda will last me ten years. Right? It doesn't follow necessarily, right? No. See? But we use that kind of an argument all the time, right? But to be necessarily true, both the conclusion has to follow necessarily for the premises, and the premises have to be necessarily true, right? In this case here, in the first one, the conclusion doesn't follow necessarily for the premises, even though the premises are true. It's like when I say, you know, I'm going to buy you four guys each a $20 book. Yeah. It's going to cost me $100. See? Well, I know, I might know correctly how many people are here, if there's four of you here now, anyway. I might know correctly the price of the book, $20, right? If I multiply it correctly, right? That's one kind of mistake. Another mistake is not to, what? To multiply the wrong numbers. But to multiply the wrong numbers correctly. Okay? I have to make both mistakes. If I multiply it incorrectly and I have the wrong numbers, I can't have any trust in the final result, can I? That might happen to be correct. Okay, so Dr. Perkwis, in the logic game, what's the shorthand for these? The first one is an error of... Well, they call that, the form is bad, right? Speak of the form. Bad form. But the matter is good, right? The matter is good. So, I guess I'm trying to resolve it into like, if A, then B is your... Yeah, yeah, yeah. You see what they do? Imagine. They will extract the form of this argument, right? Yeah. In this case, the form of this argument is, if A is so, then B is so, B is so, and then you're trying to say that A is so, right? Then A, okay. Well, it doesn't follow necessarily from the form here, because it's possible that B might be a result of many things, right? For example, if A is something less universal than B, right? If I am a dog, then I'm an animal. If I am a cat, then I'm an animal, right? Yeah. See? What's this dog's name? Rosie. Rosie? Rosie. Okay. If Rosie is a cat, then Rosie is an animal. If Rosie is a horse, then Rosie is an animal. That's true, isn't it? Yes. Rosie is an animal. She sure is, yeah. If Rosie is a horse. She's a beast, actually. Yeah, Rosie is an animal. You see? Okay. Or if A is one of many possible causes of an effect, right? Okay. If Burkwist is visiting his grandchildren, then he'll be absent from class, right? Yeah. If Burkwist is sick, then he'll be absent from class, right? Mm-hmm. Right? Mm-hmm. So, if you see that Burkwist does not come... Then you know that... Any one of those in particular is sick? No. You might have forgot. You see what I mean? Okay. That's clear, yeah. Forget things, yeah? Yeah. So, I mean, there are many things from which my absence could follow. Yeah. If I dropped dead, then I'd be absent, right? Yeah. Only I'd come through as... So, therefore, if I'm absent, I must have dropped dead. So, I tell the students that's wishful thinking. Mm-hmm. It's not logical thinking, right? So, if A... Those are two large classes, right? If A is something, what? Is one of many possible causes of B, right? Then you can't include A from the existence of B, can you? Take an astronomical example here, right? The ancients thought that the, what, sun went around the Earth, right? Yeah. And we think that the Earth turned on its axis, right? Now, if I say, if the sun goes around the Earth, then there will be day and night. But there is day and night, isn't there? Therefore, the sun goes around the Earth. Is that foul, necessarily? No. If the only way there could be day and night is by the sun going around the Earth, then you could argue that way, right? Right. But if it's possible, say, that the Earth is turning on its axis, right? Then, there's more than one possible cause, right? Of day and night. From which day and night would follow, right? Okay? If the Earth turns on its axis, then there will be day and night. Right. If the sun goes around the Earth, right? Then there will be day and night. So, the fact that day and night doesn't tell you which one of those is necessarily the case, does it? So, the sun goes around the Earth, right? So, the sun goes around the Earth. So, the sun goes around the Earth. If I'm opposed to Wesley Clark on abortion, then I'll vote against Wesley Clark, right? But is that the only reason why I might be opposed to him? For other reasons too, right? Someone else might be voting against him for some other reason, right? So I say either way you reason, one case you're reasoning from two premises, but your conclusion doesn't follow. Other case your conclusion followed, but one of the premises isn't true. So in any case you've shown that the brain is in fact the organ of thought. Read my writing here, right? I'm getting it to see, so in the second version... The form is good, but the matter is bad, huh? One of the premises is false, huh? The first one, the premises are true, but the form is not good, the conclusion doesn't follow. Which was, I think, that's pretty much what I was having a hard time seeing was, I mean, I knew the conclusion didn't follow, but I couldn't see it until you did the A&D thing. So I would make an comparison to your checkbook, you know, where the number that you got is wrong, right? Yeah. It's because either you didn't add or subtract correctly, or because you had the wrong number, right? Okay. And sometimes you go back checking over your book, you discover that you had or subtracted incorrectly. Sometimes you discovered, you know, you wrote it in, you know, in a kind of illegible way, or put the decimal point in the wrong place of what it was, you know? That could be thousands of dollars. Yeah. But, okay, or you can make both mistakes, obviously. I think I've got it now. How many forms are there where the conclusion necessarily follows? Would the if-then arguments be? Yeah. Well, there's two. If A is so, then B is so, A is so. Then it's obvious that B is so, right? Yeah. If you admit that if A is so, then B will be so, right? That necessarily follows. Yeah. Then you admit that in fact B is so, obviously you've got to admit that B is so, right? Now, the one that is more difficult. I saw some room here. Mm-hmm. One form is obvious. If A is so, then B is so. A is so, in fact, and therefore B is so. Yeah. Okay. So notice you're admitting up here when you say if A is so, then B is so, admitting that B follows necessarily from A, right? You're not yet saying that A is in fact so, or that B is in fact so. You're saying if A is so, then B will be necessarily so, right? Yeah. So if you admit that in fact A is so, then you must admit that B is so, right? That's some squareness. Now, the other form of style is if A is so, then B is so. B is not so, therefore A is not so. Now, that's not so obvious, right? And so we show what is not obvious through what is obvious, right? We say if A were so, then B would have been so, right? But we're given that B is not so, right? Therefore A is not so, right? What we're showing, in a sense, is that these three statements, if A is so, then B is so, and the statement A is so, and the statement B is not so, those three statements are incompatible, right? Okay. Because these two together, by the first case, contradict that, don't they? So these three statements can't be true together, can they? Okay? So if you're given this as being true, and you're given this as being true, right? Then the third one must be what? False, right? Because if they were true, then this would have been so rather than that, right? Yeah. So, this is the second case, but we show it through the first case, because it's not as obvious like the first one is. Okay? You see? Because if A had been so, then B would have been so, but B is not so, right? So they cannot be so, right? So those are the two forms. So if you want to show a statement by the if-then argument, you have to look before, right? If you want to overthrow it, you look after it. This is what Socrates does in Divino, right? He's arguing with probability, but he argues that if virtue is knowledge, then virtue can be taught. And then he tries to show that virtue is knowledge, therefore virtue can be taught, right? And then he argues if virtue can be taught, there will be teachers of it, given the importance of it, right? And then he argues there are no teachers of it, therefore it cannot be taught, right? So he uses these two forms that are good. But now the other two forms. If A is so, then B is so, then A is not so, and if A is so, then B is so. He can show that nothing follows necessarily from these two by a very simple example, right? If I am a dog, then I am an animal, but I am not a dog, therefore I am not an animal, okay? And if I am a dog, then I am an animal, but I am an animal, therefore I am a dog, okay? And that's why you can disprove this by examples. You can't prove these by examples. You can disprove by examples because one example shows that something is not always so, and it's not always so, it isn't, what, necessarily so. Right. In this form here. If it's necessarily so, then it's always so. Oh, huh. It's not always so, therefore it's not necessarily so. Yeah, okay. So one example is enough to show that something is not always so. Sure. So if I say man is always white, how many black men do you need to disprove me? Just one, right? But how many white men would prove that man is always white? The world went on forever, you know? So white men are always being produced, but still not prove that man is always white, huh? I can give you an infinite examples of numbers that are odd, right? Sure. That prove that every number is odd? No. Three, five, seven, nine, how many examples do you need? Go on, can't you see? So you can't prove a form by examples. You can disprove it by examples. So in this form here, it's really obvious if you understand what it means to say if he is so, then be so. You're saying that be necessarily follows me, right? So if you say that it is in fact so, you must obviously say that be is so. And then we use that to prove this. And we use this form to disprove these. If it follows... See, here people are going to have to see that be is not so, as you don't think, right? Okay? And here they'll think it follows that be is so, right? But if that follows necessarily, then when these are true, that would always be true too. But it's not always true when these are true, is it? If I am a dog, then I am an animal. That's true. It's true. It's true. I'm not a dog. Therefore, I'm not an animal. That's true. I'm not a dog. Therefore, I'm not an animal. That's false. I'm not an animal. Same over here. If I am a dog, then I'm an animal. That's true. I am an animal. Therefore, I'm not an animal. Now we have to go to a particular example to see that clearly, is that right? Well, yeah, but notice what the example does, you see. By this form here. If this is a syllogism, right, something follows necessarily. If something follows necessarily, then it's going to always be so. And the premises are so. But one example is enough to show that something's not always so. And therefore, it's not necessarily so. You don't have a syllogism. All right. So, if the brain is around the thought, then a blow on the brain refers to thinking. A blow on the brain doesn't refer to thinking. No, this is not a syllogism. It doesn't follow. Here in that one, it follows, huh? If the brain is around the thought, then a blow on the brain refers to thinking. Excuse me, if a blow on the brain refers to thinking, then the brains are around the thought. A blow on the brain is around the thinking, therefore the brains are around the thought. It follows blows, but this is not true. If a blow on the brain interferes with thinking, then the brain is the organ of thought. Because it doesn't have a possibility, right? It could be interfering with it on the side of the object, right? If I don't love something, it can be a defect in my heart, or it can be a defect in a thing, right? Sure. If I don't love cancer, right? The defect is in the object, right? If I don't love God, then the defect is in my heart, right? Can you say, if I don't love something, the defect is in my heart? No. No. It could be in my heart, or it could be in the object. So I think most people in the academic world, at least they speak this way, they think that the brain is the organ of thought, right? Yes. And why do they think that, right? Well, it's because there's a connection between the brain and thinking, right? Right. And we use our brain when we think. And we probably all say, use your brain, you know? My wife works for the Mass Brain Injury Foundation, right? And the slogan is, you know, use your brain when you have one, right? Or something like that, you know? I don't think about things of that sort. And so we all think of the brain, you know, as being the organ of thought, but it really isn't. It's inside of the object, right? So it's the organ of phantasms, or the organ of images? Yeah, yeah. And because the object of our reason is the what it is of something imagined, right? That you don't think about the what it is of something imagined without imagining, right? Just like, to use Aristotle's proportion there, right? Just like I don't see the color of your clothes, without your clothes being here, right? But your clothes are not the, what, organ of my sight, are they? They're on the side of the object of my sight. So if you take away your garment, I can't see it. I can't see the color of that robe, because what I'm seeing is not color in some abstract sense, right? But it's the color of that robe there in front of me. And when you understand what a triangle is, but a triangle is not something that exists by itself, huh? You know, that would be the pittany mistake, right? In the world of forms, right? But it's the what it is of something of this individual triangle, right? And the what it is, what a man is, or what a dog is, is the what it is of Rosie over there, right? Or what it is of you and me, I see. And so, we don't think about the what it is of a dog or a triangle without, in some way, imagining an individual dog or triangle. But what we understand directly is the universal, what it is. Next time, we'll do Article 8, and then we'll start on the next one here, right? Mode and Ordinary Intelligendi. Right, so that would be, next time will be... The last one in this thing, and then the first one in the next. Yeah. Yeah. And we'll see you next week, right? Yeah, yeah. Back in school next week, actually. Okay. The Holy Spirit, amen. God, our enlightenment, guardian angel, strengthen the lights of our minds, order and illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor. Great, great, friend. And help us to understand all that you have written. In the name of the Father, and the Son, and the Holy Spirit, amen. So up to Question 84, Article 8 today, right? Yes. Okay, and this kind of ties in with Article 7. To the 8th one proceeds thus. It seems that the judgment of the understanding is not impeded by the binding up of the senses. For the higher does not depend upon the lower. But the judgment of the understanding is above the sense. Therefore, the judgment of the understanding is not impeded by the tying up of the senses. Moreover, to syllogize is an act of the understanding. Syllogism is a, what? Argument in which some statements lay down and other follows necessarily. Because of those laid down. Okay. But in sleep, when the senses are bound up, as is said in the book about sleep and being awake, one of Aristotle's books, huh? It happens sometimes that someone sleeping syllogizes. Therefore, the judgment of the understanding is not impeded by the senses being bound up. But against this, it is that in sleeping, those things which happen against lawful morals are not imputed to sin, as Augustine says in the 12th book, upon Genesis to the letter. But this would not be, if man, in sleeping, had the free use of reason and understanding. Therefore, the use of reason is impeded by the binding up of the senses. Okay. An answer that ought to be said, that has been said above, that the nature of a sensible thing, right, is the object, right, proportioned to our understanding, huh? But a judgment, a perfect judgment about some things, or about a thing, is not able to be given unless all those things which pertain to that thing are known. And especially, if, be ignored, that which is the term or limit, and the end of the judgment. Now, let me point that out a little bit. The definition of judgment, at least in looking reason, what's the definition of judgment? Well, it's the separation of the true from the false. But you could add to this definition, by some beginning, okay, or you could say, limit in our knowledge. And of course, the very beginning of our knowledge is our what? Senses, huh? And so is Berquist standing, or is Berquist not standing now? Standing, we know by our senses. Yeah, but you're going to separate the true, Berquist is standing, from the false, Berquist is not standing, in this case, right by your senses, huh? And that's especially done in, what? Natural science, right? Mm-hmm. And he gives this famous text of Aristotle in the third book of the universe, about the universe. For the philosopher says in the third book about the universe, that just as the end of a making science is the work, huh? Now what's the proverb, huh? The proof of the pudding is in the work. Is in the eating. In the eating. Yeah. Self-eating pudding. Wow. So you have to go back to the work, right? So likewise, the end of natural science is what is seen chiefly according to the what? So Aristotle will say sometimes that, and Tom is following him, that natural science, natural philosophy, begins in the senses, right? And it also ends in the senses, huh? And what we say about the natural world is judged again by going back to the senses. And Albert Einstein said the same thing in the 20th century, that natural science begins and ends in the senses, right? And then there's a certain likeness between that and the way we judge a recipe or something of that sort, right? And if it doesn't taste good, right? Because you get a recipe and it sounds interesting, and you make something according to the recipe, and if it tastes good, then you maybe decide to keep the recipe, right? But if it doesn't taste good, you forget about the recipe, right? And someone says, I know how to make something that will fly. You say, well, that's interesting. And so you make something according to my plan, and if it, what? Gets off the ground and stays off the ground, then you acknowledge the goodness of my idea. But if it doesn't, then as we say, it's black, back to the what? Joy, boy. Yeah. And the engineer in my father's company there, you know, would say, we have some interesting ideas, and we're going to see if they're any good, right? Because you would make something according to the engineer's blueprint, and they'd go out to the experimental farm, and they would test it and see how it works, right? And, of course, Detroit, or the automobile producers, they make a new car, and after it's been on the road for a while, they discover something that is what? Falsy. Yeah, and then you get a better than mail or something, you know, to replace some part of the automobile, huh? That's causing problems, huh? So the proof of it is in the work there, right? And this is why you could have in modern experimental science, too. To some extent, a union of natural science and the mechanical arts, union of natural science and technical science, as they call it sometimes, because you judge both of them in a way, in the same, what? Way, right? By going back to the sentences. Okay, for the father there, the workman there, does not seek a knowledge of the knife except in account of its work, right? And he makes a certain particular knife. And similarly, the naturalist does not seek to know the nature of the stone or the horse, except that he might know the reasons of those things which are seen according to the sense. It is manifest that there cannot be a perfect judgment of the artist about the knife if he ignores his work. And similarly, there cannot be a perfect judgment of natural science about natural things, if sensible things are ignored. But all the things which we know in the present state are known by us in comparison to sensible things, in comparison to natural sensible things. Whence it is impossible that there be in us a perfect judgment of the understanding with the senses being bound up, to which we know sensible things. Of course, this happens in a dream, right? You don't have the use of your senses and you're often deceived in a dream, right? And one way you're deceived, of course, is by taking images for what? Real things, huh? And then sometimes you wake up and you're either relieved or you're disappointed, whatever it is, right? Depending on what you're dreaming about, huh? I can say that's talking about how ultimately it all goes back to the senses, right? When you go into other sciences, like, say, the mathematical sciences, that goes back immediately to what? The imagination. And remember that Mark pointed out there about the fifth postulate, you know, sometimes the fifth postulate of Euclid, they'll call a postulate about parallel lines, right? Well, it's never really about parallel lines. Because can you really imagine parallel lines? Not lines, at least, you can't imagine, at least, you know, the definition of parallel lines is lines which extended forever never meet. Well, you can't imagine something going on forever. Right. The actual fifth postulate says that if a straight line falls upon two lines and make angles less than two right angles on one side, those lines, no, straight lines, those lines of extended will, in fact, what, meet, right? But you can imagine two lines meeting like that. But you go back to the imagination, huh? And, but in a science like, say, logic, we're dealing with the universal. The first thing, as Albert the Great says, to be considered in logic. The universal is something you can't sense or imagine, huh? And, therefore, the judgment goes back, in a sense, to reason itself, huh? Okay? But you could say, if you look at our knowledge as a whole, it all starts in the senses, and, therefore, ultimately, our judgment goes back to the senses. Now, the first objection was saying the higher shouldn't depend upon the lower. To the first, therefore, it should be said that although the understanding is above the senses, nevertheless, it takes or receives in some way from the sense, right? And its primary and principal objects are founded in something sensible. So, I usually state the reason's own object is the what it is, is something you can sense or imagine. And, therefore, it's necessary that the judgment of reason or the understanding be impeded from the tying up of the senses. The second objection is the one taken from the dreams. To the second, it should be said that the senses are bound up in those sleeping, on account of certain evaporations, right? And fumoses resolutas, huh? Certain fumes rising up, right? Resolving. As is said in the book on sleep and being awake, huh? And, therefore, according to the disposition of these evaporations, there happens to be a binding up of the sense, more or less. When there are many emotions of the, what, vapors, not only is the sense bound, but also the imagination is bound, right? So that there appear no phantasms. Just as especially happens when someone begins to sleep after much food and drink, huh? But if the motion of the vapors is in some way remiss, or not as strong, there appear phantasms, right? But distorted and what? Disordered, right? Just as happens in those who have, what, fevers, right? If, however, the motion is more sedate, there appears phantasms in an ordered way, huh? Just as most of all happens in the end of sleep. I guess that's what they say now, when they study dreams, yeah. It's in the end of sleep just before you wake up, I guess, that you have most of these dreams that you think you're dreaming all night, you know? And in sober men, right? And in... those having a strong imagination. If, however, the motion of the vapors was moderate, not only does the imagination remain free, but also the common sense, right, is partly untied. Thus that a man judges sometimes in sleeping those things which seem to be what? Which he sees to be dreams, as it were, judging between things and the likenesses of things. But nevertheless, in some partial way, the common sense remains bound. And therefore, although it discerns some likenesses from things, nevertheless, always in some it is what? Deceived, right? And that's a common thing, right? We all know we're deceived in the dreams, huh? Thus, therefore, in the way in which sense is untied in imagination in sleeping, to that extent the judgment of the understanding is liberated. Now, however, ex total, right? Whence those who in sleeping are syllogized, when they are, what, aroused or awakened, they always recognize themselves to have failed in something, right? It's interesting, you know, when people, they go to bed thinking about a problem and sometimes they wake up in the morning and they've got the solution to it, right? So they haven't been entirely, what, bound up their imagination and their common sense on doing their dreams, right? Yeah. And especially those problems that depend upon, you know, certain use of the imagination, huh? Oh. Yeah. I suppose probably because you're removed from the distractions of the day, too, huh? But you have to add somehow the use of your imagination, at least, right? Yeah. About this stuff with the vapors and stuff, did you say, oh, that's just old medieval medicine, or is there something to it? There's something to that, yeah. Yeah. But that's a question for the particular part, right, of natural philosophy when you go to study it on the side of the body, right? Uh-huh. See, in the three books about the soul, and also the Dhyanima here, I mean the Summa here, you're considering the soul in a kind of separation from the body, right? Sure, right. Okay. And then, as Aristóteles goes forward from that, he goes more and more into the body, huh? Uh-huh. Okay? Yeah. That's the way natural science proceeds from the general of the particular, and it goes towards matter, right? Uh-huh. So this book on sleep and being awake is one of the, what, general books, huh? Sure. Already involving an application to the, what, body, right? Sure. It belongs to what today we call experimental science. Okay? It's just been my experience. I remember when I was going, like, in high school and that, if I would study for something, I wouldn't have it clear at night. Now I'd wake up in the morning and it was clear. Yeah. But now, as I'm older, I don't note that. Is there ever been anything that that process is not as sharp as you get older or something? No, I don't know. There's been any study in terms of youth as opposed to old age, huh? Yeah. I know little children probably have more, what, who wake up screaming or something than we do. So maybe we have more, I think we'd have more control in some sense, you know. I mean, of course, a child does more by his imagination than we do. Most of us, anyway. Okay, now we're up to 85, huh? On the way and order of understanding, huh? And about this are asked eight things. First, whether our understanding understands by separating species or forms from the, what, images, huh? Secondly, whether the understandable forms extracted from the images are to the understanding as what is understood, right? Or as that by which it understands. Of course, Thomas is going to say it's that by which we understand, right? But the understanding, you might say, formed by such a thing, right? Begins to think, and in thinking, then it forms, what, thoughts of what it's thinking about, right? So you have to distinguish between the thought formed by your thinking and the form by which you think, right? And the form by which you think was separated from the images by the act of understanding, which is like a light, huh? Okay? And then he starts to talk about something about the order of understanding. And third, whether our understanding naturally understands the more universal. And that's what Aristotle talked about. Didn't we do the physics there, the first reading of the physics? The eight books of natural hearing? Yeah. That's the point that Aristotle, Aristotle's whole, most of that first chapter of the physics, book one, is about that. The fourth thing, whether understanding is able, at the same time, to understand many things, huh? Meaning in second act, right? Not just habitually, but whether it's, what, can I understand what a dog is and what a cat is at the same time, huh? What do you think? We'll find out. Then, whether our understanding understands by putting together and dividing, and he's using these here to refer to the putting together and the dividing in the affirmative and in the negative, what, statement, right? Okay? And the sixth article, whether the understanding is able to make a mistake, to wander, to err. To err is human, to forgive is divine, right? And the seventh article, whether one is able to understand the very same thing better than another. It's because we both understand the same thing, but one of us understands it better. In the eighth article, whether our understanding before knows the indivisible than the, what, divisible, huh? That's something Aristotle also talks about there in the third book about the soul, when he talks about the understanding, huh? If you think back upon the definition of, what, point, huh? Point is that which has no parts, if it says. He seems to be defining the point by the negation of what has parts, right? As if what has parts is known before what has no parts. That's very important when you come to know God, because God himself is altogether simple, right? Mm-hmm. But if we know the simple through the composed, we have to negate the composition of the composed. Mm-hmm. And so in the article on the simplicity of God, Thomas goes through six articles where he negates six different kinds of composition or putting together in the preacher. And then finding the seventh article in university, he says there's no composition in God. And there's reasons for that, huh? And the eighth article is that God has not composed himself with anything else. So let's go back now to article one here. To the first thus one proceeds, it seems that our understanding does not understand bodily things and material things. And notice that's what he's in right now, that section of how you understand material things, right? He's going to talk about how the soul understands itself and how it understands things that are above it, right? And these subsequent questions. So he says it seems that our understanding does not understand bodily and material things through separation from images. First, for whoever, whatever understanding understands a thing other than it is. would be false, but the forms of material things are not abstracted from particular things of which the images are likenesses. If, therefore, we understand material things by abstraction of forms from images, there will be falsity in our understanding. Of course, you know how Plato, in order to keep truth there, said that there's a world of what, these universal forms, man himself and dog himself and cat himself, right? But for Aristotle, outside the mind is only what? This man, this man, this man, this dog, you know, that dog, another individual dog, right? So, is our mind false in understanding dog rather than, is that dog's name, Rosie? Rosie. That's right. Yeah, yeah. See? Because what's out there is Rosie. There's no dog in general out there. I always say to the students, you know, when I read the list, you know, John, Thomas, Mary, man, woman. No, and they never appeared on my list after all these years of teaching. I mean, that's... Man is never replied to my reading of the role. Moreover, material things are natural things, in the definition of whom, of which follows matter, right? And that was Aristotle's argument against Plato, right, huh? That he had these immaterial forms corresponding to definitions of man, dog, cat, and horse. There'd be no matter in the definition of man, dog, cat, and horse. And that's obviously contrary to the very nature of a man or a dog or a horse. Okay? So he says, material things are natural things, in whose definition follows matter. But nothing is able to be understood without that which follows in its definition. And therefore, material things are not able to be understood without matter. But matter is the source of individuation, huh? And that's why we say, you know, well, how can you have many window panes exactly the same, huh? How is that possible? The simplest answer is you have enough glass, right? So you're saying glass, some kind of matter, right, as quantified, right, is the source of individuation, huh? You can divide it, huh? And you can have many chairs of exactly the same kind, these chairs here, because you have enough metal, right? Okay? So it's matter, as subject to quantity, that enables you to have many individuals, huh? What would, um, would another source of individuation be the form, though, in the fact that you have the way to cut the, let's say it was a stamp or something? Yeah. How would that work? But if you had just, um, uh, why can you have many, you ask the same question about toes in a sense, why can you have many, um, uh, cubes, let's say, right? Mm-hmm. Okay? Well, it's because this cube is in this ice, and that cube is in that ice, right? Mm-hmm. Because you have enough ice, right? Yeah. So it goes back, you do the same thing, huh? But that's the reason why Thomas will say that, uh, there's no two angels of the same kind, huh? Yeah. Because the angels can't have any formal differences, they have no matter. Mm-hmm. So you can't speak of one angel different than the other angel, because one angel is here, and one is there. But because what he is, is different. Yeah. Yeah. What Gabriel is, and what Raphael is, and what Michael is, is all different. Mm-hmm. Couldn't be two identical angels, huh? Thomas will bring that up, too, when he's talking about, you know, the Trinity, you know, there can't be, what, two sons in the Trinity. Mm-hmm. Mm-hmm. You know, the Holy Spirit can't be the son, a son, too, right? Mm-hmm. Because these immaterial things, there can't be two of the same, what, kind, huh? So, material things cannot be understood without matter. But matter is the, what, source of individuation. Therefore, material things cannot be understood by the abstraction, the universal and the articular, which is to abstract understandable forms from, what, images, huh? Moreover, in the third book about the soul, this is a famous proportion now that we talked about before, it is said that images have themselves to the understanding soul as colors to what? Sight. But sight is not by abstraction of some form, some colors, but by this that the colors are pressed upon the sight. Yeah. Therefore, neither does to understand happen through this that something is abstracted from the images, but through this that the images are pressed upon the, what, understanding, right? Moreover, as is said in the third book about the soul. In the understanding soul are two things, namely the possible understanding, that's one that, what, is able to understand, right? But has to be acted upon before it can understand. The undergoing understanding, you could say it, God. And the, what, agent understanding, huh? The active understanding, the one that acts upon it, right? But to abstract from the images understandable forms, does not belong to the possible understanding, but to receive the forms already abstracted. But neither does it seem to retain to the acting upon the agent understanding, which has itself to the images as light to colors, right? Good to Aristotle's comparison there. Which does not abstract something from colors, but more flows into them something. Therefore, in no way do we understand by abstracting from images. Moreover, the philosopher in the third book about the soul says that the understanding understands the forms in the images, right? Not, therefore, by abstracting them, huh? Of course, we touched upon that before when we said you don't understand without turning to the imagination, right? Because reason's own object through which it understands everything it understands is that what it is is something sensed or imagined, right? And when you try to understand that what it is is something sensed or imagined, you have to either sense or imagine at least that thing, huh? Just like when I want to see, to use the proportion there, the color of your clothes, right? I need your clothes there, right? Even though your clothes are not my eye or that in which the act of seeing takes place, huh? But what I'm seeing is the color of your clothes. So I can't see the color of your clothes without your clothes. And so I can't likewise understand what it is of something sensed or imagined without at least, what? Imagining it, huh? But against all this is what is said in the third book about the soul, that as things are separable from matter, so they concern the understanding, huh? And that's why when you distinguish the, what, looking philosophy into three parts, you know, natural philosophy, mathematical philosophy, wisdom, right? It's in terms of their separation from matter and motion, right? So natural philosophy is about things that both depend upon matter and motion for their existence, but also in the