Wisdom (Metaphysics 2005)
Lecture 47: Definitions, Numbers, and the Nature of Form

Transcript
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These artificial things, in other words, are substances at all, right? For one would lay down only nature as substance in corruptible things. So Plato didn't put a house itself, right, and a chair itself, and a glass itself, and so on, right? But he took only substantial things, like man himself, or God himself, huh? Now, this last part of this fourth comparison there. You see, as we've mentioned before, Plato seems to have answered yes to the central question of philosophy. Does truth require that the way we know be the way things are? And Socrates, or Plato rather, seems to have answered yes to this question, or thought yes to this question. And then he was convinced with his studies with the Pythagoreans, and so on, that we didn't know the truth in John and Canipodeck. Because these are very certain sciences, huh? And since we're knowing sphere and cube and triangle in separation from sensible matter and motion, and we're knowing them truly, and truth requires it the way we know be the way things are, then there must truly be outside of our mind in separation from sensible matter and motion, triangles and spheres and cubes and so on. And therefore you have this mathematical world, huh, corresponding to the character of the science of mathematics, huh? Aristotle says, that doesn't follow Plato. Our mind can consider in separation sometimes things that don't exist in separation, huh? When one can be understood or known without the other. So if I can understand the shape of a sphere without rubber or glass or steel or anything else that might be any other kind of matter, I can think about sphere in separation from those kinds of matter, even though it doesn't exist in separation from them. But Plato had not yet seen this, right? And then he came under the influence of Socrates, and Socrates is famous for trying to define things. And you read the dialogues where Plato represents Socrates in conversation. And that's the most common thing in the dialogues, that Socrates would be asking, what is something, right? What is virtue in the meno? Or what is piety in the euthyphro? Or what is courage in the laques? Or what is temperance in the karmides? Or what is justice in the republic? Or what is epistemia sciencia in the theotetus and so on, right? He's always asking, what is something, huh? And when he's being pushed, right, by our friend Sibis and the Phaedo there to come up with a necessary argument, right? For the immortality of the soul, he's trying to use definitions, right? And, you know, if he's going back to say, even in mathematics there, why are you so certain that no odd number is even? Well, it's the definition of odd number, even number, that you see that no odd number can be even. Or no prime number can be composite. Or no circle can be a square. And so on. So definitions seem to be the way to know things truly, and with certainty, right? Well, of course, in a definition, you're knowing the universal in separation from the, what? Singulars, right? So if truth requires that the way we know be the way things are, and we're truly knowing through definitions, then universals must truly exist in separation from the singulars. And this is his so-called world of forms, right? With a capital F, right? So he's introducing that in order to save his knowledge by definition. And Aristotle would say, well, no, you can know what's common to two men, what they have in common, in separation from the individual differences, truly, even though it doesn't exist, right? In separation from these two individuals outside of our mind. Separating them. The falsity comes in when you say that what is separated in our knowledge, truly, our true knowledge, is separated in things. Then you've got a real, what? Mistake, yeah? Okay? But, as Socrates teaches, say, in the Euthyphro, he's trying to help Euthyphro define piety. And it's natural, kind of, to begin with saying what a thing is in a general way, what the logician calls, give it the genus of the thing, and then add the, what? Differences, right? So if he asked a student, you know, out of the blue in class, what is a dog, he began by saying it's an animal, right? And then you add the differences that are wrong. So the definition is composed of the genus and differences, huh? Well, as you know from your study of porphyrin, the genus is the difference a bit like matter is to form. Not that the genus is exactly the same thing as the matter, or the difference is the same thing as form, but the genus comes from what is more material than a thing, and the difference from what is more formal. So if man is defined as a rational animal, animal is taken more from his body and what's material than man, and rational more from his soul, and the difference is taken from his form, therefore. So it seems to have a definition that, composed of genus and difference, you've got to have something like matter and form. Now, these separated forms that have no matter in them would not be, what, definable, right? So kids invented a whole row of forms. They have something that you can define, truly. And the position seems to make it impossible to define, see? And this was something like, and Thyssen is, one of the guys who's saying, you know, you can't really say what anything is. You can only say what it's like, huh? Well, he said, that's maybe kind of the stupidest saying, but it would have some truth now, Plato. How can you define an angel, right, when there's nothing proportional to matter and form in it, huh? And therefore, any basis for the genus and the difference, huh? It's a little bit like, you know, the problem of Heraclitus and those who want to say that day and night are the same, right? And the heart and the soft are the same, and the hot and the cold, and the waking and the sleeping, because one becomes the other, right? And the healthy are the sick, and the sick are the healthy. All these other contradictions and words that they seem to be admitting, and, you know, how Parmenides react in saying, well, then this is an all illusion, right? Day cannot be night, the hard cannot be soft, the healthy cannot be sick, right? And if the healthy cannot be sick, then the healthy cannot become sick, because become means what? Comes to be. So if the healthy cannot be sick, the healthy cannot come to be sick. So if you're healthy, you'll always be healthy. And if you're sick, you're going to always be sick. And you're bad, you're going to always be bad. But if you're good, you're going to always be bad. So in order to save the reality of change, right, they seem to say then that the healthy can be sick, right? And day can be night, and the famous fragment of Heracles, you know. They admired Hesse of the Poet, you know, but he didn't even know day and night. In fact, they're two different things, you know. You get up in the day and do your work and go to bed at night and get your rest. As if day and night were two different things. They're the same thing, because day becomes night and night becomes day. But the point is, if day and night were really the same thing, and the sick and the healthy the same thing, and the hard and the soft, would you have any change at all? The change is from hard to soft, or soft to hard, right? But if you're both soft and hard, there couldn't be any change from hard to soft. So he's admitting that something can both be and not be, he's admitting, in words, the impossible contradictions, right, in order to save change, but he ends up, what, not saving change, even. Why go to all the work of denying something as obvious as it's impossible to both be and not be, in order to save change, but you don't end up saving change even by doing so. Well, Sarasdala's saying, hey, Plato, what are you doing? You're inventing this, imagining this world of forms in order to have truth in your definitions, but if these things were really just form, then would you really have a definition of them? If genus is to the difference as matter is to form, the definition is composed of genus and what? Differences, huh? So, too bad, Plato, huh? Shall we take our break now, because that makes a logical division here of the reading, huh? This is the end of the four comparisons between form and substance, or substance as form, and the forms or species of Plato, right, huh? And I was going to make a four-fold comparison to what? Numbers, huh? Starting with the second paragraph here on page five, right, so. You get it. You get it. Okay. So, let's begin here now, the second part of the third reading. Now, what Aristotle is going to do here is compare definitions which are expressing the formal thing with, what, numbers, right? Okay. It is clear also why his substances are in some way numbers. You see, it's in the likeness there. They are so thus and not, as some say, as of units. For a definition is a number in a qualified way. For it is divisible and indivisibles, for definitions are not unlimited, and number is also such. Well, as Thomas explains in the commentary, Aristotle will compare to this, so here in the Thessalonians 3, in the first book about the soul. He compares thoughts and definitions to numbers, right, okay, rather than to the continuous, huh? Now, the continuous is divisible forever, right? Okay. You can recall the argument of that, right? But the geometrists assume that. Now, the geometrists say you can always bisect the line, right? Now, you bisect the line, you get two lines that are shorter than the original line, huh? Now, you bisect those lines into two even shorter lines, and does this go on forever, or does it ever come to an end? It goes on forever, and you can kind of show that it never comes to an end, because the only way to come to an end is, would be, if, when you divided a line, you got either two nothings, in which case the line would be made out of two nothings, and that's obviously absurd, right? Or else you had a line that was two points long, right? Remember that? Okay. Now, if a line was two points long, when you divide that line, you've got two points and they have no links, you can't divide anymore, right? Okay? But that's assuming that you can put together a line by points, huh? And if you try to put a line together by points, like the mathematician sometimes says that a straight line is composed of an infinity of points, and composed is really the last word to put together, well, the points have to come up and touch each other, right? And you may recall the argument that we use, or it still uses, that two things touch, either part of one touches part of the other, right? Or part of one touches the whole of the other, right? Or the whole of one touches the whole of the other, they coincide, huh? I can't draw the circle twice. And perhaps if you distinguish a fourth way, they could touch at their, what, edge, right? Okay? Because the edge is not really a part in a strict sense, right? Well, two points can't touch part touching part, because the point has no parts, right? So that eliminates the back of the future of the other. The same reason, part of one cannot touch the whole of the other, because one has no parts, right? So you eliminate that. In fact, can you distinguish between the point and its edge, such that there's some part of the point within that is not the edge? Well, then you'd be giving it as a little circle, not as a point, huh? So that way is impossible. So the only way that two points could touch would be like when the whole of one touches the whole of the other, which is to say they coincide. Well, if two points coincide, they have no more length than one point, which is no length at all. If a hundred or a million or infinity of points touched, the only way they could touch would be to coincide. If they coincide, they have no more length than one point, which is no length at all. So you can't put together a line from what? Points, huh? So when you cut a line, you always get two smaller lines, huh? And then they can be divided, but if you divide them, you divide a line, you always get two smaller lines. So this goes on forever, right? Okay? Aristotle has other arguments, like he does where he combines the infinite divisibility of time, which is continuous, and indivisibility of the line. And he takes something we all know about, that one body is faster than another. So the faster body, if you represent what these lines say is distance, another one is time. Well, the faster body, at the same time, that the faster body, say, covers its distance, the slower body is going to cover what? A less distance. Well, that lesser distance, the faster body would have covered in any what? A lesser time. But in that lesser time, the slower body would cover a lesser distance. So just to alternate the fact, right, that the faster body covers the same distance in less time, and the slower body covers less distance in the same time, both time and distance can be seen to be what? Divisible forever. If you're not divisible forever, then the faster body would cover only the same distance in the same time, which would be faster. Or vice versa, right, the slower body would cover the same distance at the same time. So given what the faster and slower body are, then time and distance must be divisible, what, forever? Now, our thoughts like that, see, because, say, Euclid will define square, right, huh? So you divide the definition, you divide square into parts of the definition. It's an equilateral and right-angled quadrilateral. And then he defines quadrilateral, right? As a rectilineal plane figure contained by four lines and so on. And then you define rectilineal plane figure. And then you define plane figure. And then you define figure. So you keep on dividing, right, the definition, and the part of the definition to the definition and so on. But does that go on forever? See, if it did, then the division of thoughts and definitions would be like the division of what? Continuous, huh? It would be divisible forever. But you know how we're showing, in logic, that not every, what, genus is a species. That not every genus is a genus above it, huh? That eventually you would come to a, what, a highest genus, right? Now, there's a number of ways that they show that, right? But one way that we show that not every genus has a genus is that if that was so, you'd have to know an infinity of genus, right, before you'd know anything. In which case, you would know nothing by definition. But as you know, you came to know what a rhombus is or what a square is by definition. But also you could say that if, what, every genus had a genus above it, it would always be a more universal, more universal name than any name, right? But is there something more universal than being or something? Could there be something more universal than something? Could there be, you know, something more universal than being, huh? Okay. So definitions are not like, what, lines, huh? But now if you take the number, say, take the number seven, well, you can divide it into two and five or into three and four, or you want to divide it. You can divide three into two and one, but then you can divide two into two ones. Well, then it stops, right? Unless you're one of these crazy mixed-up modern mathematicians. But the one which is the beginning of number is even simpler than the point. Because the point is, what, a position, right? In addition to being simple. But the one at the beginning of number has no position, right? And, of course, if you divide three into, say, two one-and-a-halfs, then you can divide three points into... So, numbers are not divisible forever. So, Aristotle compares definitions to, what, numbers? There's an unlikeness theorem. And the definition is tied up with the, what, form, which completes what the thing is. The definition signifies what the thing is. So, that's the way he makes a connection, right? Between form and numbers, through definition. The definition, the right number, is not being divisible forever. And the definition expresses what the thing is, and the form is what completes what the thing is. So, forms are like, what, definitions? Definitions are like numbers. They're not divisible, what, forever. Incidentally, the same thing is true about, what, statements? In fact, those things are really proportionate. So, there must be something which is known without, what, definition. And there must be some statements that are known, but not known through, what, other statements, huh? And those are the first statements, and they're naturally known. Notice, another thing about this here is that because of the infinite divisibility of the continuous, between any two lines, say, of unequal length, right? You can always find a line, what, in between, right? So, between, say, this line and this line here, which is longer, right? There is a, what, line that is longer than the first, but shorter than the second. And between these two, there's always a line. Because there's a divisibility, right? You can say, between two unequal lines, there's always a line in between, in length, huh? Okay? And if you're going from one to the other, you come to that in between, before you come to the greater or lesser line, huh? But, is that true about thoughts? You see? Well, isn't that true about numbers, right? Between six and eight, there's a number of seven. But, now, between six and seven, is there a number? No. Oh, it goes crazy mixed up models. I don't say six and a half. But, between six and seven points, there's no point. Now, our thoughts, like numbers in that respect, too. There's, what you could say, a mixed thought, right? There's a mixed, bigger number. You take any number, say six. There's a mixed, bigger number, which would be seven, right? And a mixed, lesser number, which would be, what, five. Well, what about thoughts, huh? Is there a mixed thought? So, take an example of the syllogism that I had there a minute ago. What changes is composed, right? God is not composed, therefore. Yeah. Now, is there any thought between the premises and the conclusion? Yeah, yeah. See? So, there's a next thought, right? Okay. And, you go through the definition, and you say, well, what's a square? Well, it's a quadrilateral, right? And then you add, what? Well, maybe it's right-angled, right? You get a rectangle, right? And then you add, what? Equilateral, and then you're at square, right? Nothing in between that. Yes. That's it. Okay. So, definitions are like, what? Numbers, huh? Okay. That's the first comparison he gives, but especially insofar as the, just as a number is not divisible forever, so definitions and thoughts are not divisible forever, right? Okay. Now, in the third paragraph on page five, he has a second comparison, huh? If you add or subtract even one from a number, you have a different, what? Number, huh? And he's saying the same thing as, what? Definition and the what was to be, what it is. You add or subtract anything, you don't have the same number, huh? Now, notice a way of speaking there, huh? And Shakespeare uses it in the definition of reason when he's touching upon man, huh? He says, what is a man, if his chief good and market of his time be but to sleep and feed? A beast no more. He'd be no more than a what beast, right? Okay. Now, sometimes to give the likeness between definitions there and numbers, I say, what is a five if it be half of eight, I say? Because half of eight is to four, like the chief good of the beast is to the beast, right? And half of ten would be to five, right? Okay, like the chief good of man is to man, huh? But notice, they use the word more there, right? Okay. So, if you have a body and you add to body life, you've got a what? A living mind. A plant, see? Now, if you add to body life and then you add a sense, then you have a what? An animal, see? But animal is the sense of a beast, right? Okay. Then you add to body and life and sense, you add reason, and now you have a what? Man. If you take away reason, you have nothing but a what? Peace. If you take away sense, you have nothing but a what? Plan. If you take away life, growth, and so on, you just have a body, a stone, right? So, it's like a what? A number, right? You add or subtract something, you have a different kind of thing, right? Just like you add or subtract one from a number, and you have a different what? A number, huh? Okay. Well, that's very important to see, huh? It's funny. Thomas was going back to this in the Trees of the Trinity, huh? When he says to, you know, in the article that, what was the article where the Holy Spirit proceeds from the Son as well as from the Father, and there has to be some order between them, right? You have to order new material things because they're like numbers. I'm interested, you come back to this text for that. So, that's the second comparison, huh? Now, the third comparison here, to, again, two definitions here. And it is necessary that a number be one by something which these thinkers cannot state by what it is one, if it is one. Now, some people think of a number as just a collection of what? Ones. In which case, a number would be like a heap or a pile, right? It wouldn't be one thing, huh? Okay. What is it that makes a number to be one? We've got to see, and not as being simply a collection of ones, but you have to see each one as making actual what the previous number was able to be. Okay? So, six is able to be seven by the addition of one. So, one makes actual the ability of six to be seven. And that's why you have a unity, and it's like the unity of what? Act and ability, matter, and form. And that's the way a definition is what? Is one, huh? Because the difference, strictly speaking, determines the ability of the genius, huh? Remember the famous difficulty there of John Locke that we maybe mentioned before, huh? And John Locke is having some difficulty with the understanding of the general idea, right? Okay? We've talked about that before. And he's trying to understand the general idea of a triangle, right? And he's looking at... He's confused as to whether it's a thought or an image, right? He's thinking of it kind of as being an image, huh? Now, any triangle you imagine will be what? Equilateral, or isosceles or scaling, but it won't be all of each, right? Now, what's the definition of triangle in general, huh? What's a plane figure contained by three straight lines, something like that? And are those three lines equal, or just two of them, or none of them? Well, if you take just one of these, then you seem to exclude the yellow ones, right? So it seems that it's all or none of these, he says. Okay? Well, then Barton, in the next generation period, says that doesn't make any sense. It can't be all or none of them. Therefore, there are no general ideas. So they're all messed up, these period systems. They can't distinguish between an image and a thought, huh? Because any triangle you imagine will be one or the other. But you understand what they're having in common, leaving aside the differences. But now, going back to the original question there. You say, what's the definition of triangle in general? Well, it's something like a plane figure contained by three straight lines, huh? Now, excuse me, it's a reasonable question to say, are those three straight lines equal, or just two of them, or none of them, right? You see? But in the definition of triangle in general here, what would you say? It's indifferent to it, it doesn't determine that. Well, you could say, it's all of them in ability. None of them in act. But Locke can't see that distinction. So he just says they're all none of them. Well, unless it's all of them in one way, and none of them in another way, you've got a contradiction. And Barclay can't see his way out of the contradiction either. So he says, there aren't any of them in ideas. You know, it's like talking about a square circle, right? You know? He can't obviously, you know, read those things in a square circle, right? So there's no triangle that is all of these things in another way. So, when you add that, right, equilateral to triangle, right, you are determining what is already in the definition of triangle in ability. It's not that you're bringing in something entirely like other, it's not that you're bringing in another individual, right? But equilateral is determining those three straight lines, making actual something they're able to be, okay? So he said, he said, these three straight lines, equal or unequal, what's able to be both, right? But it's none of them in act, right? So what it's able to be, or one thing it's able to be, is made actual by the what? Difference, huh? And that's like matter, again, in form, isn't it? So the piece of clay is able to be a sphere, or a cube, or a pyramid, right? But its ability to be one or another of these, one of these abilities is made actual by the form it receives from my hands or something. So it's not like you're bringing in two things, right? You know, like when my hand picks up the chalk, right? Like that, well, my hand is not actualizing some ability of the chalk to be something, is it? No, you have kind of a collection of chalk in my hand now. And, or it's not like a heap or a pile, you know. A book here, and I've got a glass here, and I've got a piece of chalk, and I've got something else, right? You're bringing one thing to another thing. No, one is the, what? Actuality of the other, right? So what makes seven to be seven? It's the seventh one that makes it to be seven, right? And strictly speaking, it's six that is able to be seven. But it becomes actually seven by the addition of one. So that's the connection you're seeing there, right, huh? Of ability and what? Act, matter, and form. Definitions are like numbers in that sense, huh? Just like an animal is able to be a man by the addition of what? Reason. And a living body is able to be an animal by the addition of what? A sense, huh? And a body is able to be, you know, a living body or a planet by the addition of some kind of life, huh? So six is able to be seven by the addition of one, and seven is able to be eight. So it's like act and ability, matter and form, huh? So that's another subtle comparison he's making between the two, huh? Definition-like numbers, huh? But you can say that the positive thing is that just as the number, if it's really one thing, it's not simply a collection of ones, so the definition is really a definition, right? It's not just a collection of names, huh? Or not just a collection of different things, huh? But one is the act of the other's ability, huh? Okay? Just like form is the act of it. And Aristotle mentions, you know, in the study of the soul there, people say, what makes a soul and a body one, right? And he says, in a way, once you realize there is matter and form as act and ability, then it's kind of stupid to ask what unites them, right? Because one is the actuality and there is ability. So you don't need a glue or a nail or a rope or something to hold them together, right? But say, the different parts of the chair are what is not the act of the other's ability, right? So you've got to screw them together or nail them together or something or glue them together or something, right? You need some third thing to unite them. But matter and form, you don't need a third thing to unite them. Because form is the actuality of the matter's ability. So the clay, say, in the shape of the clay, you don't need a third thing, huh? You know, to screw them together, you know? I don't usually screw together the shape of the clay and the clay. I don't know what you guys do, but I assume it's the same as us, right? In the same way you don't bundle together the ones and the number, right? But the last one actualizes the previous number, right? It makes an actual next number. And you have something like that in the definition, right? But the difference actualizes the genus, right? It makes actual what is there in ability. So, and since you have to understand the genus first before you can see the differences, that would, what, contract that, right? Because the differences are determining something intrinsic to the genus. The ability that's already intrinsic to the nature of the genus. And I got my number. I got the number. It's a good little expression, huh? I may not be exactly that. To get the nature of the thing is to get its number, right? But there's a likeness, right? Between getting the number of a thing and getting the nature of a thing, huh? And this is the third, what? Comparison he has, huh? Okay? That number and definition are not divisible forever. It was the first one, right? Yes. The first one. And the second one was that you add or subtract something, however small, from a number, and you have a different number, right? And so you add or subtract something from the definition, and you have a different, what? Definition, right? Different nature. And Thomas was offing them back to this. The nature of the things are like, what? Numbers, huh? It's like you go from the stone to the plant to the animal to man, right? It's like going from one to two to three to four. And then that the parts are, as well, a built-in act, right? In the definition, like with matter and form. And this is necessary if the number is going to be one thing, huh? There'd not be a collection of units, but lift the unit. that completes the number completely, right? The actual one it's able to be, right? And it's interesting how, you know, when we, there's one way of naming things kind of equivocally that I've spoken about, where sometimes the one that adds something noteworthy gets a new name, and the other one keeps, right? Now, like the example, you know, how many fingers do I have in one hand? And you hold it up like this, and you've got five fingers, I'll say, right? And sometimes you say, now, what do you have? And they'll say, you've got four fingers and a, what? Thumb. So somehow the thumb stands out. They call it the opposable thumb, right? Which means it has some distinction. So it's something special. So these four keep the name, and this one gets the, what? Yeah, okay. Now, maybe a more clear example of that, huh? Sometimes the word animal is kept as a name for the beast, huh? And so we distinguish man against the animals, right? And man gets no name because he adds something, right? Okay. Well, it's a little bit like, you know, let's talk about five and five plus one. Well, we're just going to keep the name five. The one that is just five, right? But the one that is five plus one, that's only more, right? It's a big addition. You have a new name. Which happens to be six, right? Okay. I told you how my mother didn't like me calling man an animal. You know, she didn't like that way of speaking. And I said, well, Mama, I don't mean he's just an animal. I say, well, okay, that's better, she said. But it would be very much like saying, you know, to call man an animal, I'd say you'd better call him six or five, right? You know, and say, well, it's not just a five. It's a five plus one. Okay, that's better. See the likeness there. Now the last comparison next to the comparison of definitions and so on. He says, and as number does not have the more and the less, neither does substance according to the form. But if any does, it is one with what matter, right? Remember one time in a class, quoting one of our founding documents, we hold these truths to be self-evident, that all men are created equal, right? I say, now, if I get up in slave-owning Athens or slave-owning Rome and said, we hold these truths to be self-evident, that all men are created equal. What do you mean? Some are free, some are noble-born, some are slaves, huh? But even apart from nobles, you might say that some men are born more healthy than others, right? Some men are born stronger, right? Some babies are kind of weak. Some are born more handsome. Better looking, right? Some are born more intelligent, right? Okay, some are born more courageous, I think. Some more, maybe, temperate, huh? Some more mild, some more irascible, right? What do you mean we're all born equal? What the heck does this mean, right? You know, it seems like a fiction there, maybe, huh? But, is one man more a man than another? Now, if I man, I'm encouraged, yeah. But that's not what a man is, right? That's something added. That's a virtue or a disposition. But is one man more what a man is? Or is one dog, huh? One cat would be more beautiful than a cat, right? And I went to get a cat there for my daughter. So, let's get a male cat. I would be, by the way, kittens, you know. All the male kittens are kind of ugly. And if he's a cat, he's all good-looking, you know. And it's kind of funny, because even I remember the trash man coming, you know. But it didn't have any too great aesthetic sense, as you say. So, everybody, you know, kind of, you know, admiration. What a beautiful cat, he said, you know. Now, you know, I say, see, it's not just enough, you know. Tabitha was beautiful. So, but was Tabitha more a cat than the other cat? We used to give her the title of the Queen of Bumblebee Circles, you know. The neighbor there, you know. And they were because, excuse me, I was the superior cat in the whole neighborhood. But Tabitha was not more a cat than the other cat, son. And that's the, what a thing is, right? If you add and subtract anything, you'd have a different kind of thing, right? Wouldn't be a cat anymore, right? So, he says, about the generation corruption of the four set of substances, how it can happen, how impossible. This kind of is like a little summary. And it was touched upon a little bit here. We saw that, right, in the first group of the Paris, right? Where form is not generated and corrupted as such. But the composite. And about the reduction of things number, right? Leading them back to us in a lightness number. Let it be determined as far as these, right? So, that's kind of an epilogue to chapter 3. But you'll find as you read through Thomas, and even in theology, he's always coming back to this thing when he's trying to explain things. You're talking about, you know, how God can, what? By knowing himself and everything else, right? Well, I mean, Thomas, we'll go back to comparison numbers, right? If ten really knew itself, right? Would it know nine and eight and seven and six and five and four, right? You see? Because in a sense they're contained, right? In perfection of ten, right? But there's something less, huh? So, but we kind of know animals, huh? Because they're like, what? One unit less than us. Without reason, right? But they have something, right? Like what we have, huh? The plants, you know, a little bit less, because they're less like us. I feel closer to the plants and to the stones myself. Mm-hmm. And the plants grew much better with the Mozart and grew straight, and so rock and roll together. You know? I don't know how scientific these experiments were, but the results, at least, it kind of pleased me, you know? I mean, the, uh... Tell the students what this music is doing to them, you know, and what the good news is going to do for them, huh? I guess we'll have to stop there, huh? Because we just want them to do a chapter, let's see.