Natural Hearing (Aristotle's Physics)
35. Anaxagoras Refuted: Fewness, Infinity and the Limits of Natural Quantity (Part 1)
https://berquistcourse.com/course/philosophy/3-natural-hearing/035-anaxagoras-refuted-fewness-infinity-and-the-limits-of-natural/

[0:09] So you have to see how it makes sense to say that the letters in the order of the letters are parts of the word cat

[0:19] before you can see what it means to say we're body and soul, although it's not identical; it's only proportional. Okay. So we should stop here before we go into reading nine, huh? Okay. We're not too late tonight. My other grandchildren are arriving tonight too. so we and Matt, I mean, there are three little girls. So Lady Catherine and Lady Anne, Sarah, rather, Sarah and Lady Cecilia, the last one.

[0:55] You know, you know, we haven't seen Cecilia since she was born. So Then we've been we've been working downstairs there. We had the Catena Aurea's commentary on the Epistle to the Hebrews in the very beginning there, the first chapter. Saint Paul says, quoting the Psalms, "He's made his angels spirits, and his ministers I think a flame of fire." So Thomas says, "Well, two names for the the angels, right?

[1:29] Which means, say, what messenger, and then minister, which is one who what does things, right? Or its lord, our master." And so, I like this there, insofar as the angels are called spirits, which is taken from the word for breath or air. He says, for the purpose of messenger, is to receive the message from the one who's sending it, right, and then pass it on to somebody else.

[1:57] So he says he speaks of them as being spirits or air because air quickly what receives something and passes it on. You can see that with sound and color how they what are easily received by the air and carried to our eyes and our ears, right? And it's a swift thing too, right?

[2:18] And so that's why they're called spirits. Then he says, and then they're called what? And his minister is, which is another name for the angels, but for their other function, and they're called a flame of what? Of fire, right? He says, "Well, why is that? Well, of course, fire. He says three things about fire: that it's the most active of the four elements—earth, air, fire, and water—and therefore appropriately applied to their functions, doing things, right?

[2:49] And then, of course, it warms things, right, which is their role in encouraging what charity? And then the flame always goes upward, and everything they do, they refer back to the glory of God. Kind of beautiful passage, also. We ask the guardian angels and Thomas we to pray for us here, help us. We comment on the cause of what Thomas says about the angels there in that little passage there.

[3:16] It's kind of a nice one though, huh? Fire also enlightens, too. didn't you mention that? What? Fire also enlightens. Yeah, but he's tying up fire there with the likeness for them as ministers, right? Rather than as as messengers, they're more a teacher. I see. Okay. Because you know you're kind of speaking of the likeness of, the metaphor there, right? And you know how fire can be, or like a lion can be, you know, a metaphor for Christ.

[3:44] It can be metaphor for the what? Yeah, see, so when to adapt the metaphor when it's being used, you know, what is it like this? Why do you call Christ the lion, right? Well, because he's courageous and he triumphs, right? And he's a king, right? He's the king of the beasts and so on, right? But why do we call, you know, St. Peter calls him a lion, boy around seeking whom he may devour, right?

[4:05] Kind of prowling around, right, looking for weaknesses to attack and so on. And then there's a likeness there to the devil, right? Okay, so fire can be, you know, metaphor for charity. It can be a metaphor for anger or concupiscence or something else, right, by different qualities that it has.

[4:24] Okay, so up to reading nine here. I believe that's where we left off. We're going to start reading nine. And the reason why I attached reading nine to this is for a better understanding of this first matter. And so you might ask this question: Is the first matter?

[4:48] The box. Is the first matter? Matter before other matters, right? Is the first matter an actual substance or a substance in ability only? Now the Greek philosophers up before Aristotle, they thought the first matter is some actual substance. It might be Mother Earth. It might be water. It might be air. It might be fire, right? Or it might be, you know, all four of these, as Empedocles said, right?

[5:49] Um, but if there is change of substance, the really is change of substance. Then the subject underlying change of substance would have to be what?

[6:06] Not actually a substance. Yeah, because in that case, right, all change would be what? Accidents, huh? If the matter underlying all change, right, the very first matter was an actual substance, right? Then that actual substance would be eternal, you might say, huh? It didn't come into existence and go out of existence. Now you do would be to have what? Accidental modifications of the substance.

[6:37] But they couldn't understand how that first substance could be an ability only, and we talked before a bit about how ability is hard to understand, and how we tend to

[6:55] imagine the first substance, the first matter, to be something actual, right? But they have all kinds of problems, and in a way, in our friend Anaxagoras, you see the difficulties you get into when he tries to make the first matter a combination of the act of actual substances. Okay. But now that goes back. Now, if we go back to Aristotle's categories and say, "Give me an example of a substance," he would give us an example of a substance, a man, or a second example would be a dog or a cat or horse.

[7:36] Okay. Now, if man is a substance, then there is change of substance, isn't there? Because men do come into existence, right? They do go out of existence, In, the same way for a dog, right? Okay. Now,

[8:03] if you deny that man or a dog is a substance, then you're going to probably end up saying that man or a dog is something composed of many what? Other substances. Yeah, yeah, and therefore something like a like a word that's made out of many letters, right? Arranged in some way. Well, the question is, is a man one thing with many parts, no, or is many things in some way arranged or put together, huh?

[8:42] Which is it? Well, the early Greeks, like many modern natural scientists and people in general, followed them. They imagined a man or a dog to be composed of. Let's say earth, air, fire, and water, or to be composed of atoms and molecules, right? As if these were all many distinct substances, right? In some way, poured together. Which case would a man be really one thing?

[9:16] He'd be no more one thing in a way than an army is, right? Or a family is, or you know, city is, huh? So, what do you think a man is?

[9:30] One thing. Yeah, is that part of your your inward experience of being a man that you're one thing? First, I will take the example then of the fact that a man dies, or a man comes into existence, or even that a dog dies, or a dog comes into existence, as an establishment of the fact that there is change of substance, huh? And then going back to our understanding. of change in general.

[10:03] there's a change from man, let's say, any other substance. Let's take man to dog, but there must be some subject or matter underlying that change, just as if there's a change from, let's say, a sphere to a cube, there has to be something underlying that, right? Okay. What underlies sphere and cube being accidents would be some actual substance. Now we take my example here of clay. if you take the other example on the tape.

[10:36] Well, what underlies a change from man to dog? What does that? Well, if it were actual substances like clay, then man and dog would be not what substance is. It is contrary to our starting point there. So the subject underlying that must not be an actual substance, but substance and ability. What is able to be a man or a dog, but not at the same time, right?

[11:09] Aristotle said, but you have to know this first matter by a proportion, right? Because you could say that the first matter is to man and dog something like the clay is to sphere and cube, okay?

[11:27] But you could be even more explicit and say that it seems to be knowable only by this proportion, right? And why isn't it knowable by itself?

[11:41] Well, if you try to consider this first matter by itself, it'd be a substance only in ability. So it'd be in itself or by itself anything actual? No. It certainly can't be an actual substance if it's only substance in ability, and so it can't be an actual what accident? Again, an accident underlying substance? Therefore, it must be something only in ability. But now ability, as, we said in general, is difficult to know because ability is not knowable by itself or through itself, and that's true not only about this ability, but any kind of ability.

[12:25] The ability to see, the ability to walk, the ability to think, and so on. These abilities are known only through the acts which their ability. They're never known by themselves, and this being an example of pure ability, huh? Would be most of all this would be true. It's not knowable by itself, so it easily escapes our understanding, right?

[12:54] Okay. Now, when you get down to something less known than man or dog or substance. when. You get down to what we call sometimes the elements. Greeks call elements. You get down to the most basic forms of matter that we know, which for the Greeks of the earth, they're fire and water, right? Okay. For us in modern science, the most basic forms of matter we know are the so-called elementary particles.

[13:27] But if earth, air, fire, and water are the first forms of matter, if there is no form of matter before earth, air, fire, and water, are earth, air, fire, and water eternal, or do they change? Changed.

[13:47] Yeah, it seems that you can burn up these things, right? We can dissolve them, right? So, if the very first forms of matter are not eternal, but fire becomes water, or water becomes fire, eventually, right? Then underlying that change must be something which is only what substance and ability, right? Okay. Now I say that argument for the existence of substance and ability is not as sure as man and dog because you are not so sure that earth, air, fire, and water are the first forms of matter as we are that man and dog are substances, huh?

[14:28] Okay. Now, modern science, huh? Um, they found out that water was not the first form of matter, right? That before water is something called hydrogen and what oxygen, right? Another elements, but are hydrogen, oxygen the first forms of matter? No, because underneath them are proton and electron and neutron, and they call those things not atoms, but what? Elementary particle. Yeah, that's the name for them in science, right?

[15:07] Okay. So the molecule is not the first form of matter because before that is the atom, right? The atom is not the first form of matter because before that is the elementary particles, huh? Now, you might say, "Well, are the elementary particles though eternal?"

[15:26] Well, in the high-energy experiments with elementary particles, they found out that no elementary particle is what eternal, right? Okay. Everyone is. It showed, as Heisenberg said, the complete mutability, right? The complete changeability of matter, okay. Now, some might say, "Well, maybe." Below Earth, air, I mean not with air, water, proton, neutron, there's a more basic form of matter, right? Just as the atom was found to be below the molecule, and the elementary particles to be below, right?

[16:07] Okay. Now, that's a new question now because what happened was in the experiments something very strange happened when they accelerate one particle, shoot it against another particle, and that particle shoot against doesn't remain, right? Disappears. What do you end up with? Well, sometimes you end up with particles of more mass than the original particle. Actually. Which isn't true when you what break water down to hydrogen oxygen.

[16:45] The molecule water has more mass, more size, and so on than the hydrogen atom or the oxygen atom, right? When you break those up, you know the protons, say, or the electron have less mass, less size, right? So it makes some sense to say that the water molecule is composed of the hydrogen nitrogen, and they're composed of the hydrogen atom, right? But now when you try to repeat that with the elementary particles and you shot other particles at them, what they found out was that the result of this showed that that form of matter didn't remain, right?

[17:23] But you didn't necessarily get smaller particles. You got what? Sometimes one with what? More size and more mass. And that seemed to show that these basic forms of matter called the elementary particles are not, in fact, made up of something smaller, right? See. Yet, since there's change from one of them into the other, there must be what?

[17:51] Something. An underlying subject, but that subject would not be an actual substance. That's why Heisenberg says that we know matter only through the forms of matter. He's saying you don't know matter by itself, right? I was going to bring in a fact too, but I'll bring in sometime Heisenberg's lectures there, unified field theory of elementary particles. Heisenberg and Wolfgang Pauli got the Nobel Prize and quantum theory.

[18:19] They went on to study elementary particles afterwards, right? And this is the theory they came up with. But when they began to study elementary particles, it seemed that any elementary particle could eventually get all the rest. Yeah. And therefore, you find Heisenberg saying, quoting several times in the book, the well-known formula: every elementary particle is composed of all the rest, right? See, what's interesting that that way of speaking will be exactly like Anaxagoras' speaking, and of course it's going to run into the same difficulties if you take that exactly what it says that Aristotle pointed out for what, Anaxagoras, but both that well-known formula, of the students of elementary particles, and Ana Xavier's as their similar way of speaking.

[19:15] I think both reveal the difficulty our mind has in understanding the first matter, right? In understanding that there can be you can get out of something something that isn't actually in there.

[19:33] Can you get money out of my pocket? You know, you know, there's no money in my pocket. Where's my chapstick here? But there's no money in my pocket. How can you get money out of my pocket, right? And

[19:45] now, in Japan I was using class. There we have wooden chairs there, maybe in one of the classrooms, and I say, occasionally you get a class, you know, and it's over enrolled or whatever it is, and someone will have to borrow a chair from another room, right? Mhm Now can you get Chairs out of the other room if they're not chairs in the other room. No, okay.

[20:05] It's not too hard to see what that means to get a chair out of another room. You've probably done that time in your life, right? Got a wooden chair out of another room, right? But originally these wooden chairs we got the wood of what? Trees. Trees. Now were there in fact wooden chairs and the trees out there? Potentially. Potentially, yeah, but not actually, right? But the way we get a chair out of a tree is much more hidden than the way we get a chair out of the next room.

[20:38] And so, notice, huh? The way in which chairs are in the trees out there in the camp and the grounds here, and the way a chair is in the next room, has a much different sense of in, isn't it? In the case of in the next room, that's the first meaning of in in some place, right? And what is in something is in a place is actually there.

[21:09] When you get to the sense in which something is in matter before the matter has been formed, is that actually in there? it's in there in what? Ability, right?

[21:21] Okay. And so you can say that the most common fallacy too of equivocation is involved here because one is imagining the way something is in matter to be like the way something is in a place. And that's in there only what? Actually, huh? Okay.

[21:50] I mentioned before how Weizsäcker, the student of Heisenberg, said that when we imagine something, we make it actual in our imagination. And so, the fundamental cause of deception on the side of our knowing powers, what the philosopher calls false imagination, right, is especially active here.

[22:16] When we study place there in the fourth book of the actual philosophy, the fourth book of the Natural Hearing Aristotle there will distinguish the various meanings, the very central meanings of the word in. And he gives eight different meanings of the word in. And Thomas orders those eight meanings in the way Aristotle teaches us to do so in the fifth book of Wisdom. And just to recall those meanings, the first meaning of in or being in, if you want to take the old phrase, the first meaning is in place, okay?

[23:00] Like you and I are in this room, right? The chairs. In this room, right. The second meaning he gives of in is that of a part in a whole, like my teeth in my mouth, right? Okay.

[23:22] Now the second sense of part in a whole is very close to the first sense, because if you hit me in the jaw here and loosen one of my teeth so I can take it in and out, then that tooth would no longer be in my mouth as a part in a whole, but as in a place, right? Okay. In the same way, if I was to, you know, was to take my electric saw here and cut a round hole in the top of this table and take out a piece of wood, right?

[23:50] Take it in and put it back in again, would it be in the table? Would it be a part of the table anymore? No. You see how a very close part in a whole is to like in place, okay?

[24:04] Then the third meaning he gives is the sense in which a genus is said to be in the species, okay? And in general, the part of the definition in the definition. So genus is in the species. Okay.

[24:26] Again, that's still a sense in which something is actually inside of something, right? So if you take the definition of of square, let's say, as equilateral and right-angled quadrilateral, in that definition of the species square is quadrilateral and equilateral and right-angled, right? But they're actually parts of that, right? Okay. But notice this here is something more in the mind, right? Right. This here is something more that the senses can get at, huh?

[25:00] You see that? Okay. So this one is more sensible and therefore more known to us. That means, in this sense, right? And then the fourth sense. It's actually good, like Thomas is already teaching you. The more you study it, the fourth sense is the sense in which the species is in the what? Genus. Yeah. Now, the sense in which man is in what animal, right? That's very interesting.

[25:37] Animal is in man in the third sense of in. Man is in animal in the what? Fourth sense, right? Okay. Um. Now, in what sense is this third sense like the earlier senses, and especially like the third sense that follows directly after? More part and

[26:04] whole. Yeah, yeah. The genus is a universal what? A whole, right? Okay. The species or the definition of the species, as well as the whole we have in mind here, are composed holes, right? So here you have composed holes, but the one that's in the material world and in the sensible world, right? Or the other one is only in the mind, right? So one is more known to us than the other, right?

[26:35] But in both cases, the part is in that kind of a hole, actually, right? So, but then you have another sense of hole, which is universal hole, right? Okay. Which you also sometimes call the the general, right? Okay. We talked about that in the beginning of the course, there, where in Greek the word for general is katholou which comes from the Greek word for holon Katholou kata according to the holon the whole.

[27:11] In English, we had for the less universal the term what particular, right? Which obviously comes from what part, right? Later on in Greek, you see the word just like particular merikon, which comes from the Greek word merasa. So they have the word for part is gives rise to the word for what species, right? Species of part of the genus. So this is somewhat like this, right? It's also in the mind, though, but it's likely part of the whole.

[27:48] Okay. But here, what is in something is not actually an ability, right? And then comes the fifth sense, form in matter, form the matter's been formed, right? Okay. And that's very much like species in the genus, the form in matter. But here you have if you can take these three senses actually in, right? And here it's in only in ability. You see that? Now later on you get to the sense which I got you in my power, and that's again a sense where what different kind of ability there, the active ability, right?

[28:40] I got you in my power, right? Okay. Or as we say in English sometimes it's out of my hands, right? You know, I can't control it, right? Or we're in God's hands, right? Okay. But see, that's that's like the sense of form and matter. That's a different kind of ability.

[29:01] But for a person right now, we'll stop here at the fifth sense, right? Okay. Now. I think I mentioned how John Locke, right? He's trying to understand the general idea of triangle, okay. But he can't really transcend his imagination, right? So he's trying to. He says that the what is a triangle in general? What's a three-sided plain figure, right? Now, those three sides equal, or just two of them, or none of them.

[29:34] He says it's all and what? None of these, right? He's trying, in a sense, to imagine triangle general. Now, can you imagine triangle general? No. Any triangle you imagine will be a particular triangle, right? Yeah. Either equilateral or isosceles or scalene, right? Yeah. So he's trying to to imagine it, right? So i if he Says it's none of these, then it wouldn't fit any of them, apparently, right?

[30:04] And so it must be all of them, but it can't be all of them because then wouldn't fit. So he ends up by saying it's all and none of them, right? Okay. And then I mentioned how Berkeley, right, in his next work, I mean, after Locke, he says, "Well, doesn't make any sense at all. " Therefore, we have no general ideas. It's a lot of impossible, right?

[30:26] Well, the point is, what would you say about the three straight lines? The definition of triangle general. Are they equilateral, or the equal, or unequal? What would you say? Not actually. Yeah, there, there, none of these actually, but it's all of them in what? Ability, right? But he can't understand the ability of the genus, right? See, and so he ends up in that confusion of mind, right?

[31:02] Well, you can see the same confusion would arise down here, right? You could say that all of these things that come to be out of matter, right? They're all in there. None of them in there, right? I mean, Anaxagoras is going to say that they're all in there in a way, but infinitely small pieces, and nothing is distinguishable. So the way they're not in there, right? And Aristotle, in another place, think in metaphysics, I guess, must be, he says that if he listened to what Anaxagoras is trying to say, he'd have the truth, right?

[31:29] But what he actually says gets him into difficulties, huh? Um. Now, another interesting thing here about the order here of the fourth and fifth meanings, huh?

[31:43] A little paradox here. If you look at the order of the second and third meanings, and then the order of the fourth and fifth meanings, um. I mentioned how part in the whole is more sensible than genus in the species, and since the natural road for us is from the senses, obviously part in the whole is before genus in the what species, right? Okay. And then, of course, what's most like that is not form and matter, but species in the genus, right?

[32:17] But now, species in the genus is something mental, like genus and species, right? While form and matter might seem to be something that you find in the sensible world, like there's a shape in that in the metal, there's a shape in this piece of chalk, right? There's a shape in my my sensible body, right? Um. So it's kind of amazing to see that, right? See. Now you can see that Thomas is ordering them correctly, you know, in terms of what is nearer to the third meaning, right?

[32:47] Okay, but if you just look at these two meanings by themselves, you might first think that form and matter would come first, right? Okay, but. This is kind of some why I show this, right? And you've kind of prepared for it now, but try to answer like an unprepared person, okay?

[33:10] Suppose you have a piece of clay, right, in the shape of a sphere, and you mold it into a cube, right? What has changed, the clay or its shape? What would the average person answer that question? You think? Shape, shape. Yeah. Has the shape changed? You're saying the shape, which means that's the genus, right? You're saying the shape has changed. from spheric cube, right? As if the genus were the subject underlying the two species, huh?

[33:48] But there's a certain likeness between between those two, huh? But notice the fact that you you speak as if the genus had changed rather than the matter is a sign in a way is more known to you, huh? Okay.

[34:14] Okay. So a lot of things you can learn from this comparison, but if you go back to John Locke, you can see that he gets confused about the way the species in the genus. He's trying to, in a sense, make the genus triangle contain differences, actually, right?

[34:33] And he gets into trouble. Gets into contradiction, right? It's all none of these, huh? Okay. So let's look at Aristotle's text here now. Now, in the first three paragraphs, Aristotle is recounting the position of Anaxagoras, but more fully the the line of reasoning whereby he apparently arrived at this, huh?

[35:10] And basically, the starting point of his thinking, you might say, are two premises, right? One that he gets by induction, right? And the other that he gets by something being what something that seems to be obvious to all the Greeks, right? Okay. You can't get something from what nothing, right? Okay. But then he saw that in the in the natural world you could start with anything in the natural world and eventually get everything else.

[35:44] And I think I did that before when he talked about Anaxagoras, huh? But I say let's start with the with the grass, right? Okay. And take the example of the cow eats the grass, and you get what more cow out of grass, right? And then uh, Berquist has a stake, right? Or the cow, right? So now you get more what man, right? Then we feed Berquist to the lions.

[36:12] who he discovered as a Christian, you get more lion, right? Huh? The lion dies and get worms, right? And then you get from the worms more bird, right? And from the bird more cat, right? And the cat dies and pushes up daisies. So you're getting from the original grass more cow, right? Eventually, more man. Eventually, more what? Lion, more worms, more birds, more cats. It seems to go on and on and on, right?

[36:41] Okay. Now, there is something similar to that in the study of elementary particles. It seemed in their experiments you could start with any elementary particle, and eventually, by acting upon it, get all the other elementary particles. They put those two together. You can't get something from nothing, right? And out of any thing and everything else, and the conclusion that arises is what? Everything is inside of everything, right?

[37:09] Okay. Okay. Now you are imagining, right? Although maybe falsely, that everything that is in everything else is actually in there, right? Okay. In that case, everything would be composed of everything else. Yeah. Or in modern science, every elementary particle is composed of all the rest. That was the well-known formula. You know, Heisenberg. You know, I see it used at several times in in the book there, right?

[37:37] And I assume well-known among the students of elementary particles. See, but they're thinking like the Greeks. You can't get something from nothing, right? Okay. If you can get hydrogen oxygen from water, then water must be composed of hydrogen oxygen, right? If out of any elementary particle we can get all the rest, any elementary particle must be composed of all the rest. Huh? Clear as mud, right? Clear as day, right?

[38:03] It seems to be, doesn't it? See, okay. But there is going to be an obvious difficulty in that, and the same difficulty Aristotle would point out with Anaxagoras. Okay.

[38:18] So let's look at the text here a little bit. Anaxagoras would seem to have thought the beginnings, the causes, are limited, infinite, in this way, because he assumed the common opinion of the naturalists to be true, that nothing comes to be from what is not, right? Can't get something out of nothing.

[38:40] For an account of this, they speak thus: all things were together, coming to be such is alteration. what others say is putting together and separating. For the reason from contraries coming to be from each other; therefore, they exist within.

[38:57] Okay. For if everything that comes to be necessarily comes to be either from what is or from what is not, and of these coming to be from what is not is impossible, for all those tweeting about nature or one mind about this. He thought the rest followed necessarily, right? That coming to be was from what is is and exists within. Okay. But an account of the smallness of their sizes to be from what is unable to be sensed by us.

[39:25] Hence, he said that everything is mixed with everything because he saw, you could say, by induction, everything coming to be from everything, right? Okay, but basically everything coming to be for everything, and you can't get something out of nothing. Those are the two premises from which he draws his basic conclusion, right? Everything is inside of everything, right? Okay.

[39:48] Now we can add to that that he thought, like with all the early Greeks, the things keep on coming to be in the natural world without end, right? So there must be an infinity of pieces of everything inside of what everything to keep on coming to be forever, right? Well, how do you fit an infinity of infinitely of pieces of everything inside of everything? How would you fit inside a blade of grass, which is finite, an infinity of things?

[40:22] Only by making them infinitely small. Something like the modern mathematicians speak of a line as composed of infinity of points, right? Which we say is false, but they have the same difficulty, by the way. They're imagining right the line to be composed of all the points that are able to be on the line, right? See, so they're falsely imagining what is their own inability to be actually there.

[40:48] But just as they could fit that infinity of points, it seems that are finite lines are making them infinitely small, infinitely short, right? So Anaxagoras is fitting everything into matter by making it infinitely what small, right? So his grand position is, as we saw in the fragments, that there's an infinity of infinitely small pieces of everything inside of everything. Or to speak English, there's an unlimited right multitude of everything, but unlimitedly what small without limit, right?

[41:23] Now, if that's so, you know the objection is, well, why call this a dog and that a tree? For everything inside of everything. Everything's a mishmash, right? Well, he says we call them by what they have most of. And I I call that the Anaxagorean way of what naming things, right? Okay, we follow that a lot, though. Okay. Um.

[41:50] So mentioning how we even define the books of Scripture, we follow that way of naming things, right? So the Book of Psalms is a book of what? Prayers, right? It's not one of the historical books, is it? But there's some history in the Psalms, right? Okay. There's some prophecy. It's not one of the prophetic books, but we classify it as one of the sapiential books, right? Because of that, right?

[42:15] What it has most of, either absolutely or in comparison to other things. Okay. I mean Shakespeare's comedy of errors, right? We call it a comedy, right? But there's some kind of. You know, serious scenes in there, right? Okay.

[42:37] Now, at the bottom of page four, and going on through the rest of the reading now, Aristotle is going to give eight arguments against an exaggeration And we might number them first so we can refer to them. The first argument is in the bottom of page four, the last paragraph. This is a little different. Okay. If then unlimited as unlimited is unknown. Okay, that's the first argument.

[43:06] Then okay. Then just number them. Second, third, fourth would be in addition, right? Fifth would be further, right? Then six would be it is not knowingly said, right? Seven would be nor does he rightly take the coming to be. Then the eighth argument is better to take fewer limited beginnings, which Empedocles does. Okay. That's numbered properly there. Now,

[43:48] Thomas divides these arguments. How Aristotle is ordered there? He says we have seven arguments. The first seven ones against what? Anaxagoras's position, considered by itself, right? And then the eighth argument is refuting his position in comparison to Empedocles. Okay. So Thomas divides the first seven against the what? Last one, right? Okay.

[44:21] The first seven arguments, he divides the first five against the last two, right? Because the first five arguments are basically refuting what's essential to the position here, Anaxagoras. But six and seven are dealing with more particular difficulties, right? Okay. The more particular difficulties need to be avoided if you're more careful, right? Okay. But the first five arguments are dealing with the difficulties inherent in this basic position that there's infinity of infinitely small pieces, everything inside of everything.

[45:00] Okay. So the same Thomas then divides the first seven arguments against the last one, and the first five against the sixth and seventh argument, right? Okay.

[45:18] Now I sometimes group these a little differently because I used to make kind of a comparison between the critique of Anaxagoras here and the modern science, right? Okay.

[45:37] And sometimes I put eight and five and one together, right? Okay. Because eight and five and one has something in common with the whole of modern physical science, starting with Galileo, Kepler, Newton, right, and going down to Einstein and beyond. Yeah. What they all seem to have in common, as useful to explain these three arguments, they all seem to touch upon what we call the principle of fewness, huh?

[46:14] Or sometimes called the principle of simplicity. Okay. If you read Galileo, Kepler, Newton, you'll see that they have this principle of fewness or simplicity. And uh Einstein in the 20th century still follows that principle, right? And he says this is the underlying idea of all actual science from the Greeks, right? Through our work, right? Okay.

[46:44] A principle of fewness could be stated by saying that fewer beginnings, fewer causes, are better if they are what enough, enough right? Okay. So Newton for example, for example, if you look at his rules of reasoning that he follows, right? That's the basic rule. Nature says is pleased with simplicity, right? It affects not the pompous and superfluous causes, huh? I think we gave you that text earlier, right?

[47:16] We saw Galileo, right? He's investigating the actual accelerated motion when you drop a stone and it falls to the ground going faster. He looks the simplest way it might what increase its speed, right? So right away the mind goes that way, right? Kepler spent 10 years trying to find the simple what geometrical figure to fit the movements of the planets, huh? So he tried to find the simplest what that still fits the facts, right?

[47:47] Okay. So Kepler came up with what figure? Ellipse. Yeah. Now the ellipse is not as simple as a circle, but the circle went into difficulty, right? The Ptolemaics saw and they were constructing what circles saw and they were constructing what circles on top of circles on top of circles, circles, right? You had something going around something and then imaginary center and around that and imaginary one, it started to get too complicated, right?

[48:16] So though the circle by itself is simpler, when you start adding circles on top of circles, it gets kind of complicated. Why the ellipse has what two centers rather than one, right? And so each point in it is what any distance from a point in the interior called the center, like in a circle, but the sum is always the what same, right?

[48:40] So here's a man spending 10 years looking for a simple thing. So it's very clear that Aristotle in the eighth argument is reasoning from this, huh? And we saw that argument earlier when we talked about whether there's an infinity of beginnings, right?

[49:02] He says Anaxagoras introduces an infinity of things in order to explain how you can keep on going forever, right? And Empedocles explains the same thing by what just earth, air, fire, and water. Well, if you can explain the same thing with four principles instead of infinity, that's an obvious example of what. The principle of fewness, right? Okay. Now, basically, it's because Anaxagoras is trying to explain things coming to be by a kind of straight line coming to be, right?

[49:45] So if you keep on getting things out of the blade of grass, a little more cow, a little more lion, a little more man, a little more worm, and so on, keep on taking things out of there forever. How many things you have to have inside there to go on forever? Infinitely. Yeah. See. But Empedocles has what a circle a circle, right? Where love brings together earth, air, fire, and water, and he what separates them, right?

[50:21] We can go on forever doing that, can't you? And so I used to say to kids at Christmas time, you know, you buy your child or your nephew toy, you know, buy him a bag of blocks rather than a finished toy, because the finished toy gets broken the next day anyway. So you got to buy another one, right? Another one, another one, right? If buy a bag of blocks, you can build something out of it, knock it down, build something else, knock it down, can go on forever, right?

[50:47] There's something superior about that. So I call this is the Empedoclean principle by Christmas time, as opposed to the Anaxagorean way, right? Is it? In other words you've got always something new for the kid to amuse them today, right? You've got to have the Anaxagorean principle, infinity of toys to keep them. But this is a much better idea. For the other example I give is what that of the rich man who wants to get his exercise, right?

[51:15] The running on a road, wants to run every day. He's going to run forever every day. He's going to run in a straight line. How long's the road have to be? Infinite. Yeah. But if he, it's wise, like they have a tractor around, right? Circular thing, more or less. You can go running forever in a circle, right? And yet the circle is what finite. You see that?

[51:40] Superiority the circle to the what straight line. And so you get these people caught up now with the idea of recycling, right? That presumably doesn't use up resources in the same way that straight line production does. You see, you can recycle things, you can go on, it seems, right? And this is superiority to that, right? Even economic terms or in terms of very honest things. So, because resources are not infinite, right?

[52:14] Once you realize resources are infinite, then you've got to recycle or you're going to run out of them, right? But on the other hand, if you see in nature things never run out, and you still got this idea of what. The straight line motion—you've got to need an infinity of things in there to go on forever. So isn't it simpler to explain it this way than to explain it this way?

[52:37] Yeah. So notice you can invoke then the principle of funism. If Empedocles explains with earth, air, fire, and water, and love and hate, right? How you can go on forever, he explains the same thing that Anaxagoras requires infinity of beginnings to go on forever, right? Then you can invoke the principle of fluence, right? Of course, our mind kind of naturally inclines to the simpler explanation.

[53:09] I told you my standard example in classes—you know, you assume it's the same guy coming in to teach the class each day, learns the same thing. Even though you could explain this by assuming that there are what a number of people that are look alike, right? Each of which has the same training, education—that's very complicated. Right, if you don't see any need to say it's a different man, because it comes up for each Tuesday, right?

[53:36] You know, you've got hundreds of left alikes, right? If I can explain it with one man why not do it? Right? The mind of man is inclined to that simpler explanation. You know I take the famous dispute between the ancients and the moderns. You know, what's the cause of day and night? Huh? Is it the sun going around the earth, or is it the earth turning on its axis?

[54:05] But notice in both of those guesses as to what is the cause of day and night, they both assume that there is one what sun,

[54:16] rather than a new sun every day, right? Well, why have a new sun every day if you can explain two hundred sixty-five days and nights with one sun? That kind of circular thing, right? But if the earth turns on its axis, or the sun around the earth, it's a circle, not a straight line, right? Rather than thinking of the earth maybe being stationary here and a new sun shot across each day, you know, kind of some kind of mechanism here to shoot it across the sky and so on each day, right?

[54:45] But that would explain day and night, right? A new Sun being shot across each day, right? You see, being extinguished over here, as he said sometimes, you know, in poetry, you know, the sun is extinguished there. But that's going to require eventually an infinity of suns if days and nights go on forever. Do you see that? Okay. Okay.

[55:11] You see how the argument is very clearly based upon that? Why not your conclusion? Okay. Yeah. There you go. Okay. Now, let's go back to the fifth argument, right?

[55:31] Now, notice, huh? I think the fifth argument is explaining how really complicated is this position of Anaxagoras, because he's saying inside of everything there's an infinity of infinitely small pieces of everything else, right? If you see that's true of everything, then inside each one of those infinitely small pieces, there must be what?

[55:58] Infinity of infinitely small pieces of everything, right? And inside each one of those, there must be what? And this is going to go on what? Forever. Yeah, could hardly be more complicated than that, right? You see, there must be something wrong with that, right? At the surface, right? Okay. And I think I quoted you know the passage there from Max Born, right? He said the genuine physicist, right, believes often.

[56:29] In the unity and simplicity of nature, despite any appearance of time frame, right? And the context where he's making that statement in the book there,

[56:43] the restless universe, right? He's talking about the periodic table of elements. The periodic table of elements was saying there was what I guess originally it was in 92 and then they had some more, but roughly 100, right? First matters, right? That's too many. That's too many, right? There had to be something fewer than that behind that, right? Well, that's nothing compared to infinities. of infinity. There must be something wrong with this, right?

[57:14] Okay. So again, that you could say is tied up with the principle of what fewness right? Okay. Now notice that argument was not found back in the readings. In reading what 11, right? Remember in reading 11, we ask: Is there one beginning, or infinity of them, or two or three? What's known, right? Aristotle gave four arguments against there being an infinity of them, right? Okay, he uses, well actually before, if you take the order of his readings, eight and one, we'll see he used in that part as well, right?

[57:58] Why five is something peculiar to Anaxagoras, right? Because there is not only infinity, but infinities of the infinities of the infinities of the infinities of the infinities infinitely, right? Okay.

[58:10] Now the first argument, huh? It's more hidden there. That's why I reversed the order here. The first argument is more hidden. The first argument is saying that if the beginnings are unlimited or infinite, then we can't know them, right? I say, what's wrong with that consequence?

[58:30] It's too bad we can't know. But, I think what Aristotle has in mind is the fact that man has a natural desire to know the causes. And as Sir Isaac Newton said, and the others who say, that nature is pleased with simplicity it affects not the pompous, superfluous causes. Nature does nothing in vain, in other words, right? So if nature gave us a desire for something impossible, then nature would have done something in vain, right?

[59:00] It would have given us something superfluous, right? Okay. So therefore, our desire to know, our desire to understand the causes, must be what for something possible, right? Okay. You can see that in all the other natural desires, the desire to what eat and to drink and so on, right? Which is natural to us and the other animals. It doesn't mean we always get food. We don't always get water.

[59:28] It's not impossible to get food or water, right? See, why would nature give animals hunger and thirst if there's nothing to eat and nothing to drink? It would serve no purpose, right? It'd be superfluous, right? So, likewise, if nature gives us the natural desire to know causes, it must be in some way possible to know them. But if there's an infinity of them, would you know them?

[59:50] So could you know a word that had an infinity of letters? Could be best speller in the country, the one who wins the spelling contest. You know, you know, once they have across the country here sometimes, and they have a national competition, right? Would he know how to spell a word in an infinity of letters. He'd never finish. No, he'd never know that word, right?

[1:00:17] So I sometimes put the eighth and the fifth and the first arguments together because my students can't take too much into account, right? And it enables me to emphasize that principle of fewness, right? And it is relevant to, in a sense, understanding those three arguments. At the same time, it's pointing out something that Aristotle's critique of Anaxagoras has in common with the physical sciences from Galileo, Kepler, Newton, through Einstein and beyond.

[1:00:52] thank you, doctor. It just popped into my head that when you said you're talking about a word of infinite letters, I just thought, well, what about the value of pi? You know, three point one four etc. Etc. We know something about it. We do a lot of work with it, but we don't know it. We can't read it out. That's true. Yeah. So we call it irrational, eh?

[1:01:13] Yeah, true. Yeah, irrational. Yeah. Aristotle talked too about you know an online which is think that the continuous is divisible forever, right? Okay. But you can't what actually succeed in dividing it completely. Then can you? Okay. Okay. To be going in that way, right? But not as infinite. By going through one by one, you can't know it, huh?

[1:01:46] But in a sense, pi kind of results from what the fact that the discovery of the Greeks, right, that not every line has to every line the ratio the number has to a number, right? Yeah. And if you're looking, you know, the Pythagorean, right? You would be trying to see what that every line, right, has the ratio of a number to a number. That was a great discovery.

[1:02:18] One of the great discoveries of the Greeks, huh? That's led if you look at Heath's notes to Book Five, that led to Book Five there of Euclid's Elements, huh? Because originally the Greeks kind of assumed that every line would have to every line the ratio that a number has to another, and therefore you could what, or at least the one has to number, and therefore you could what, kind of have similar understanding, right, of ratios in lines and in numbers.

[1:02:55] But then they found out that not every line has to the line, right? So essentially, kind of know there what isn't in that sense, right? But you can make an approximation there, right? Right. Okay. But let's take another example where it is true that a straight line is in mathematics is divisible what forever, right? Okay. But you can't what divide it forever, right? Okay. But does the mind have a natural desire to do that? And with pi, man has a natural desire to do it too, because they write computer programs to to divide things first.

[1:03:39] Yeah, yeah, yeah. But but I mean, I mean, can a man really be aiming at dividing a line forever? No. See, but he realizes that. Or like with numbers, right? You know, you can keep them going higher and higher, right? But we have a natural desire to go on forever. No, because we have no goal there, right? See. So

[1:04:04] sometimes, you know, to kill many birds with one stone, I put these three arguments together because in explaining them, they all seem to, in some way, have a connection with the principle finis, most explicitly the eighth argument, right, and then the fifth, less so, but also, and then the first argument again, right? Okay. But it also facilitates a comparison with modern science. Now, the second, third, and fourth