Wisdom (Metaphysics 2005)
Lecture 17: Leucippus, Democritus, and Atomic Determinism

Transcript
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But, you know, in the old days there, I remember reading an article on God's plan in Moscow during the eight days. And God's plan was 1,000 economists and 1,000 engineers who planned or misplanned the whole Russian economy, right? Well, we have what we call market economy, right? But does government influence the economy in the United States? All kinds of ways, right? And was there no market at all in Russia? There had to be other things that could completely break down. So why do you call this a market economy in that? Well, we call things the way it has most stuff, right? But I noticed that when we divide the Bible, the books, say, the Old Testament, and we say that the book of Psalms is a book of, what, prayer and praise, huh? It proceeds, or it to you, I think, Thomas says, and now it to you, prayerful and praising. Why, Isaiah is a book of, what, prophecy, right? But are there no prayers in Isaiahs? Well, there are prayers, yeah. And is there no prophecy in the Psalms? Well, yes, there is. Well, why call this a book of prayer? Well, we use it in an ex-Korean way of speaking, right? We call it, but what it has, what? Most of, right, huh? Why do we call it the comedy of errors? A Shakespeare comedy, right? Because a man has been sentenced to death there, right? Mm-hmm. You know? It's a rather serious matter, right? But we call it what it has most of. There's a little bit of humor in Macbeth, right? Yeah. A little comedy, you know, for this terrible tragedy, you know? But we still call it a tragedy, right? Mm-hmm. Because it's mainly that, most of it. We call it a thing, but what it has most of. Either absolutely right, or in comparison to other things, huh? I was tasting a carbonate, somebody's house the other day, and this is sweet, you know? That's really sweet, but I mean, compared to other carbonates, it's kind of sweet, you know? But you're calling it now, not maybe what it has most of all, but what it has more of in comparison to other carbonates, huh? Mm-hmm. Yellowtail carbonate, you know? Mm-hmm. I recommend Wolf Bloss, you know? Yellow labels, that's good. Yellowtail, not. That's disgusting. In comparison, right? So, that's more, you know, as I say, about matter than about the mind, right? So you have these ten things about the mind. That's pretty good, huh? Pretty good for a, it's like a book in miniature, about the mind. Now, sometimes, apart from that comparison to Einstein, I'll compare it also to theology, and I say, what is the mind that Annex Acres has arrived at here? They call it the greater mind. Is it the human mind, or is it the divine mind, or is it the angelic mind, huh? Well, it's not the human mind, because that's the lesser mind, obviously. But is it, is it, is it arrived at the divine mind, or the angelic mind? Yeah. Because is this a mind that's responsible for the existence of matter? No. It's a mind that can act upon matter by, what? Local motion, right? Now, when you study the angels, they can act upon matter through local motion. But they cannot produce or create matter, huh? So, in a sense, he's arrived at the angelic mind, rather than at the, what, divine mind, huh? You see? This mind acts upon things only by motion, right? Not by creation. I remember in the kind of saying one time in class, in passing, that it's easier to know the existence of the angels than of God. He didn't unfold himself, or I don't know why he said that, you know? But it's always kind of stuck in my mind, you know? It's one thing he said in passing one time. But you can see it here, in a sense, huh? He's actually arrived at the angelic mind, although he would, you know, we'd think of it as being the divine mind, you know? This mind that is completely separated from matter, you know, and it's a greater mind. But he's actually arrived at more the angelic mind, huh? Than the divine mind, huh? Do you see why you say that? Mm-hmm. Yeah. And therefore, you know, when Karl Marx and Engels, they have a division of all thinkers, huh? And they divide them into materialists and the idealists, as they call them. And the difference is very interesting, because materialists say that matter is the beginning of all things, even of what? Mind, huh? And so, Karl Marx, Lennon, who's one of the materialists, right, says that mind is the highest product of matter. In a way, the evolutionists are saying that, aren't they, right? Yeah. Mind is the highest thing that is evolved out of matter, right? Yeah. Okay? And then, on the other hand, you have the idealists, like Hegel and St. John the Evangelist, and so on, for whom mind or thought is the beginning of all things, right? In the beginning was the Word, and the Word was of God, and all things are made through the Word, right? So, that's an interesting division, right, of all thinkers, right? But I ask the question, is that a good division? Does it exhaust them, right? All thinkers either say that mind is the beginning of all things, even of matter, or that matter is the beginning of all things, even of mind, right? But where do you put Anantiagris, they say? Although he does make the greater mind superior to matter, right? Because it moves matter, right? And separates things and orders them, right? It's nevertheless not the origin of what? Of matter, right? So, in a way, he's a dualist, in the sense that he has matter and the greater mind, one of which is not the beginning of the other, right? Although one is superior to the other, right? So, it's kind of a middle position, right? And they say whether it be, you know, by their thought or by the devil's, right? But leaving out the middle position, you make it very difficult to go to the truth, right? Which is that, you know, that there's a mind that is the source of all things, even of matter, right? That created matter. But our mind naturally begins with Mother Earth, and thinking that matter is the beginning of things, right? And until you see mind as something, what? Distinct from matter. It can be without matter, right? You never get to the idea that there's some mind that is the creator of matter, right? It's the source of the very being of matter, right? So, if you leave out the middle position, you're like on one shore with no bridge over to the other shore. And so, you just get kind of stuck in that first position, right? But, when you see the mind as something distinct from matter, superior to matter, then you have kind of a bridge to seeing eventually that there's a mind that is so superior to matter that it's responsible even for the existence of matter, and not just for moving it around. You see that? Now, Plato in the Timaeus sound speaks of the Demiurgos, this greater mind, right? As, what, acting upon matter and reducing it to some kind of order from the chaotic motion of matter. But, again, that's the position, like Yank Segrist's, kind of a dualist position, huh? But, until you see the mind as something immaterial and independent of matter, you wouldn't even begin to think that there could be a mind that might be responsible for the existence of matter. So, this is kind of the middle position, huh? Aristotle really is getting to the idea of what? Of the creator, huh? And, Thomas thinks he's arrived at that, right? But, when you read the third book, where we'll be looking at the questions he raises, right? One of the questions is, is there anything a cause without motion, right? You see? And, that's a problem for the Greeks, right? And, he's still in the position of thinking, you know, that this greater mind is a mover, or a cause, only in the sense of being a, what? A mover, right? You see? And, it's interesting, you know, if you look at Thomas' ordering of the priestesses of God, right? Which are not original with him, really, but he understands him better than most. In both Sumas, right? You begin with God as being the, what? Showing that he's the unmoved mover. Showing that he's the unmoved mover. And then you show that he's the, what, first maker, first deficient cause, right? And then you're starting to get more into what's altogether proper to God, right? Because here you may almost see it. This mind here is an unmoved mover, too, right? But notice the order there, right? He's saying God is a cause of, what, motion, right? Doesn't do full justice to God, but that's where we begin, right? But even in the highest, you know, consideration of God in the two Summas, he begins with, he's being an unmoved mover, right? He doesn't say he's a creator, does he? No. And then eventually you come to understand him as the maker, in a sense, of the creator, right? He's responsible for the very existence of matter, and not just the motion of matter. But you see the order there, right? Perfectly ordered. So it's interesting to compare him. Usually when I get through with this, I'll compare him to Einstein, you know, and say, well, what they have in common is that they both come to the conclusion that there's a greater mind that reveals itself in the order of the natural world, right? They both come to this not as a believer or a religion that is around them, right? But simply as a natural philosopher, right? But Einstein, you know, has it mixed up with things, why Anaxagoras sees it cannot be mixed with things. And he has a reason for thinking so, right? Which I don't think Einstein has. And then I compare him, you know, to us, and I say, well, no. In theology, we talk about three minds. The human mind, the angelic mind, the divine mind. But he's actually arrived more at a description of the angelic mind here, a mind that is not responsible for the existence of matter, but can move and act upon matter, huh? You see that? Now, when you turn to Socrates there in the Phaedo, you can see that Socrates is expecting Anaxagoras to give the end or purpose of things in the actual world. But now you're introducing, with Socrates now, and Plato, a fourth kind of cause, namely what? End, right? So you had matter, right, in the earliest Greeks, and that's all you had. Then you had something of form with Pythagoras, with Heraclitus the bed, and more so with Empedocles you have the mover. But with Empedocles, you know, he has matter with the four elements, form with the ratios they combine, and he's got the movers, love and hate. And here you've got another mover, but you've got, what, the door open now to seeing the end or purposes of cause. And that's all there is. Aristotle takes over those four, right? So one thing that comes, this is a little different than what I'm doing here than what Aristotle does in the rest of Book One of Wisdom, but one reason why he goes over what they say is to see if they touched upon any kind of cause other than the four kinds, right? Anaxagoras is not touching very clearly upon the end here. That's what Socrates has kind of let down, right? But then Socrates will talk much more explicitly about the end and the purpose of things. Then you have no causes other than the four that Aristotle has distinguished. Now, sometimes I compare him, like I compare Anaxamandru with Thales, right? Which is a better guess, air or water, right? Which is a better guess as the mover or maker? Love and hate? Or what? The greater mind, huh? So, notice, hate separates things, right? Okay. And mind separates things, right? So I say, which is a better separator, hate or mind, huh? Well, was it hate that split the atom? And sometimes, when people go around destroying things, hate, they destroy sometimes even their own friends, right? Don't distinguish, right? Between friend and enemy, right? But, I mean, is it, is it, you know, when you study logic, you find out that logic is very much about seeing distinctions and divisions and definitions, right? Hate? Can hate do that? Can hate do that? Is it hate that makes you distinguish the senses of a word? God's talking about the word in there, you know? Was it just how I hated that word, so I didn't see what to distinguish there? He's separated from everything else. Was it hate that made us divide triangle into these equilateral satsalites, scale? Hate, do your numbers make you distinguish between prime and composite numbers? See, mind is more able to separate than hate can do, right? So, as far as separation is concerned, mind is a better cause than hate, right? Now, love brings things together, right? But, Empedocles went so far as to say that love brings together things in different ratios. Now, what's you bring in ratio? Which is a better cause of ratio? Mind or love? Well, the word itself suggests that mind is a cause of ratio, right? And, of course, in Latin you have the same word for reason, ratio, and ratio. The Greek word for ratio is vocasum. Same as the word. So, and to bring things together in some kind of order, obviously mind is better than that, right? But even if mind or no were just as good as love, one is better than two, right? Kill two birds with one stone, huh? So, mind can do what love and hate can do, maybe better than love and hate can do them, right? And it's one cause, so, it's better, huh? Okay. But now, you've got to be careful, because maybe that's not the whole truth, though, right? Because, as Socrates and Plato and Aristotle point out, there's the same knowledge of opposites, right? So, knowledge without love of one rather than the other, without appetite, won't produce anything, right? So, I can teach you or deceive you, right? My knowledge enables me to do both. The doctor can heal you and kill you. Make you healthier, make you sick, right? And so, there needs something besides knowledge, that you do one rather than the, what? The other, right? And that brings in the will, right? So, that's interesting, right? That's one of the reasons why we think that God has a will, right? As a philosopher, we think that, right? Because his knowledge enables him to do opposites, but he does one rather than the other, depends upon will, huh? But just looking at it here, in the way that these early Greeks did, mind seems to be a better guess than love and hate. Sober man among the drunk men, huh? You notice the first thing he says about the mind, it's unlimited. That's kind of anticipated by Heraclitus, when he says, you know, you're not fine in the ends of the soul, no matter how far you travel, remember that fragment? Okay, we've got to stop now, around 4.30 or whatever. Yeah, I guess we're better. Okay. Now, we'll look at Leucippus and Demarchitus next time, and then we'll go back to the, start to look at the second book of wisdom, you know? Okay. Um, I can give you that enough. I'll do it. Good. Yeah, you sure. Okay, let's say a little prayer. In the name of the Father, and the Son, and the Holy Spirit, amen. God, our enlightenment, guardian angels, strengthen the lights of our minds, orden and illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor, and help us to understand all that you have written. In the name of the Father, and the Son, and the Holy Spirit, amen. Okay, we've got to look at Leucippus and Democritus, the last two thinkers here. And they share a lot of thoughts apparently together, so we kind of take them together. Kind of strange, now, that in the Greek fragments, there only are a few on the natural world here from Democritus. Although when Aristotle talks about Democritus, he says that he lived in a greater familiarity with nature, you know, and he must have written more, but almost all the fragments are in ethics or domestics or a political philosophy than, you know, the first quotes, you know. So let's look at Leucippus here first. Nothing happens at random, he says, but everything comes to be from reason or by reason and by necessity. So he's what we'd say in the modern world is a believer in determinism, right? Complete determinism, complete necessity. And perhaps Leucippus and Democritus here are, Leucippus in particular, is already influenced by the mathematical science of nature. There's an interesting text in, I think it's the third book of the Nicomachean Ethics, where Aristotle says there are four causes. And one is nature and one is man, right? His will and so on. One is luck or chance and one is necessity. And of course, nature is a cause you would think is appropriate to natural things and choice and so on, to ethics and so on. And luck and chance can be applied in both, because neither one of them are 100% achieving their results. But necessity might refer to what you have in geometry, right? It's not nature there, it's not choice. Pythagorean theorem is a matter of necessity. And so someone who's accustomed to this mathematical knowledge could come up with his opinion, that all things are what? Necessary, huh? Now, in modern science, they often state this principle in terms of past and future, and say the past necessarily determines the, what, future. And this is actually finding Galileo and Kaplan Newton, and they always quote Laplace there in the 19th century, saying that if you do the position, the momentum of every particle in the universe at any moment in time, and you have a super calculating mind, you can predict the whole future course of the history, that the universe is a complete necessity, you know, there'd be nothing at random, huh? Well, you might say that determinism, or the principle of determinism, as it was called in modern times, which is being stated here already by the SIPPIS, that that principle was the absolute principle of modern science in the 17th, 18th, 19th centuries, and to some extent in the 20th century until quantum theory and modern science, when Heisenberg formulated the principle of indeterminism. But the reason for saying that that was the, quote, absolute principle of modern science is, in the oldest part of modern science, which is the most mathematical of physical sciences, you get this partly from mathematics. But when the other things like biology or psychology or something try to be more scientific, they would think of determinism right away. And one famous work we used to use sometimes in philosophy of science was a book by Claude Bernard, the French physiologist in the 19th century, who made important contributions to physiology and so on. But he also had a book called An Introduction to the Study of Experimental Medicine, around the 1860s, I think it was. A book which was to encourage biologists to be more scientific. And the book has three parts to it. And the first part is a description of the scientific method in general. The second part is a description of the experimental method in biology in particular. And the third part is very concrete with examples from his own research, using that method and illustrating it and so on. Now, if you go back to the first part, we're describing the scientific method in particular. I mean, in general, rather. He has a very good understanding in some ways of the probable character of the scientific method. And he makes the famous statement that doubt is intrinsic to the experimental method. That no matter how many times a theory or hypothesis has been tested and confirmed, it can still be tested again, right? And may still be, what? Overthrown, right? And if you know a little bit of elementary logic, you know that the confirmation of a scientific hypothesis is not a syllogism. You're saying, you know, if my hypothesis is correct, then there will be an eclipse of the sun today, right? Well, there is an eclipse of the sun at the time I predicted, right? Therefore, my hypothesis is what confirmed. But is that a form of reasoning, a syllogism? You're saying, if A is so, then B is so. But B is so. Does it follow necessarily that A is so? You've heard my example in logic, huh? If Perkowitz dropped dead last night, they say, then I predict you'll be absent from class today. But he is absent from class today. Therefore, he dropped dead. I tell them that's wishful thinking. But it's not logical thinking, see? Like that. And notice, huh? Day and night follows from what? The sun going around the, what? Earth, right? As well as from the earth turning on its axis, huh? So there could be, what? The same prediction made by different hypotheses. And so if the prediction made by one of those hypotheses comes true, because I think that hypothesis is the correct one. And Einstein, huh? Says that Newtonian physics had been so phenomenally correct in its predictions that they began to think it must be true. And one kind of very striking thing, I guess, in the 19th century, when they were, you know, always precising things, they found out that some of the planets didn't exactly go in the paths they should have according to Newtonian physics. But Newtonian physics can't be wrong. There must be planets we don't know about, right? And they're mathematically so exact they could predict where those planets were. And so they found some of the last planets. That shows you an amazing thing, right? And so, as Einstein said, some people came to the conclusion that Newtonian physics must be the truth, huh? The truth and nothing but the truth. And then Einstein himself, with the two theories of relativity, showed that he could predict the same things that Newton predicted with a different, what? Hypothesis. Plus he could predict some things that Newtonian physics did not predict, right? And then Einstein said it became perfectly clear to them, right? That a scientific theory is never known, in a strict sense, to be true. The more predictions you make, and the more exact they are, huh? The greater probability, you might say, for your hypothesis. But by the very form of the reasoning, it's not a syllogism. That is to say, the conclusion doesn't follow necessarily. If A is so, then B, C, D, E, F, G, H, I, J, K, L, M, M, P will all be true. And they're all so. It doesn't follow necessarily that A is what? So. Well, Claude Bernard, as I say, sees that, right? And so he says, doubt is intrinsic to the experimental method. But despite all that understanding, he says, but you cannot doubt determinism, he says. To doubt determinism would be to doubt science, he says. So he excludes determinism, the principle of determinism. which is being stated here by Sippel already, he's excluding that from this doubt that he sees quite correct in hypotheses. And in the 20th century, it's in quantum theory that Heisenberg saw this consequence. And so he formulated the principle of indeterminism, and this was quite a shock to the physicists. And this was part of what was called the Copenhagen Interpretation of Quantum Theory because it was situated around Niels Bohr at Copenhagen and people like Heisenberg, who were very close to Niels Bohr. And you could get all kinds of descriptions of the big meeting of the physicists from around the world, the famous ones, at the Solvay Congress in 1927, I guess it was. And Einstein didn't want to go along with the rejection of what? Determinism, huh? So Einstein would come and would present what we call thought experiments, right? Trying to break down the Copenhagen Interpretation. And Bohr would stay up at night, you know, and come back the next day and refute Einstein's objection, right? And finally, Einstein produced his final objection at the conference, and it was quite convincing to everybody there. And they had actually seen a photograph of Einstein and Bohr leaving that session, right? And Einstein walking out kind of, you know, you know, kind of cocky a little bit, always, you know. And Bohr's, you know, kind of walked out, looking kind of worried, like, you know. Einstein's fighting. Well, Bohr's day, of course, another night, huh? And he discovered a mistake in Einstein's argument, a mistake that was due to overlooking the applications of the relativity theory itself, Einstein's own theory. Well, that was the last time Einstein publicly tried to, what, overcome it, huh? You see? But it shows you how strong entrenched that thing was, right? So even if Heisenberg is right, and this is not true, you could say Josephus here is stating what was the absolute principle, right, of modern science in the 17th, 18th, and 19th centuries, huh? That when they tried to make something like biology, let's say, more scientific, right, the thing they saw as being indispensable is this determinism, huh? Or the same way like in psychology, right? When Freud or something like that is trying to make psychology more scientific, right, what they see as fundamental is determinism, right? And kind of an obvious example of that is dreams, right? See? Now, if anything seems to be not by necessity and not by reason, it's some of the dreams we have, huh? And my cousin Donald used to have these crazy dreams and he'd tell them to us in the morning and we'd laugh about them. But I remember one dream, you know, where he was being chased by a tiger, huh? He's running away to escape from the tiger and so on, and he finally runs down one street and it's a dead end. No place to go, right? So he turns around to face the tiger, right? And as the tiger comes up, the tiger says, how would you like to buy a raffle ticket? No, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no It's simply at random and by chance, and, of course, there is sometimes something in our dreams that does tell something about us, right, and, but you can see that what Freud is saying, even something apparently irrational and contingent as a dream, if it's going to be scientific, you know, psychology, it's got to have determinism even, what, there. Aristotle will reject this idea of determinism, we'll see some of that later on in the sixth book and in the ninth book of wisdom, right, but in the far as the natural world is concerned, Aristotle will be doing so partly by his understanding of the potency or ability of matter, and it's interesting that when Heisenberg rejected it, he said that quantum theory introduced a version of the potency that Aristotle Heisenberg talked about it, so again here, you have sometimes in history what I call a spiral, right, as opposed to a circle, where you come back to the same place but at a different level of experience, so let's say in the ancient Greeks there, they began like we saw a little bit in, in Pedocles, especially in Anxagoras, the only kind of change is change of place, only gradually they realize another kind of change, that same thing takes place in the level of, more particular, more particular of experimental science, where a change of place seemed to be the only kind of change, and then you get to quantum theory, then you begin to force to say there's other kinds of change in the world, and so, same way here, you begin with this determinism, then you give it up at a different level, maybe, of experience. It's turned out to these fragments of the Democritus, and these are the ones that are dealing with the natural world, but I've got the interesting ones of his, dealing with ethics and domestics and so on. What did he say, Democritus, you shouldn't, you shouldn't generate children, you don't know what you're going to get, he says. You should adopt children. Kind of a rationalist, it's like a modern almost, doesn't it? Take it, the good Lord sends you, right? Yeah, from the modern, they call them designer babies. Yeah, yeah, it's the same idea, yeah, but for him, not having all that technology, the idea was, you don't generate, you don't know what you're going to get, anything, you know? You go and you pick one out there, that seems to be. But there are other interesting fragments, like there's one where he says, don't try to understand everything, he says, lest you become ignorant of everything. That would be good advice to the moderns, right? Or try to understand everything, and we end up understanding nothing. Now, sweet exists by custom, the bitter by custom, the warm by custom, the cold by custom, color by custom. None of these things really exist, none of the sense qualities, huh? What truly exists are the atoms and the, what? Empty. Now, this is very common among the modern philosophers, and even the modern scientists, to say that these sense qualities don't really exist. And just the way they appear to us, or something of that sort. This could be also influenced by mathematical studies, right? Because in mathematics, there's no what? Sense qualities, huh? It's interesting, in mathematics, there's no substance, either, and no purpose. So if you're accustomed to think of the world mathematically, and this is the only way that, once you think about the world, then the world seems to have no sense qualities, no substance, and no purpose. Which is exactly the way the modernists kind of think, huh? But now what truly exists are the atoms, he says, and the empty, huh? Now, let's look at that for a moment, huh? Let's look at the word atom, huh? Now we have two common words in even modern science, in English now, that come from that same root, huh? T-O-M. We have the word atom, and we have the word anatomii. And in both of those words, you have the root T-O-M, right? Well, what does that mean in Greek, huh? T-O-M. Well, it means... But now, the prefix in these two words is different, right? In anatomy, ana means up. So anatomy means cut, huh? And so an hairstyle is biological works, more particular ones, where you cut up animals and lift their parts and try to figure out the order of them and so on. Because I'm in Greek, that's anatomy. That's how you get to do it, right? Okay? So if you take a class in anatomy in a college or medical school or something, you will do what? Cut things up. Yeah, yeah, okay? But now, the prefix A is just a negative, right? So active means literally, I'm cut, okay? Just like amoral means without morals, right? You see? Agnostic, I suppose, huh? A is a negative, and Kenosi's not knowing, right? You see? But in the account that we have from Aristotle of how he arrived at the idea of the heavens, it has a sense not only of uncut, but uncuttable, right? Okay? Now, Democritus apparently did what Einstein would call a thought experiment, right? An experiment conducted, that is to say, in the imagination, right? Which helps you to clarify certain things. And so Democritus says, imagine the bodies around us, our own body for that matter, cut up in every way it can be cut, right? Okay? What would you have left? Well, you couldn't have nothing, right? Pieces. Because as Einstein would say, you can't cut something up into nothing, right? Can you? Because the thing is cut up into what it's made out of, right? So, if when the bodies around us, our own body, was cut in every way that could be cut, if you had nothing left, then these things would have been made out of nothing, which is obviously absurd, right? So, therefore, when these bodies are cut in every way they can be cut, there must be something uncut left over, right? But given that this is what's left, right? Uncut, when you cut it in every way you can cut it, these are uncuttable, right? Okay? Now, there are some passages in Aristotle, when he discusses this position of Demarchus, where the atoms seem to have some size, right? They're very small, but they can have a shape and things of this sort, so they have some size. But you just can't cut them, right? There are some passages in Aristotle, where he almost speaks as if the atoms of Demarchus were like points, huh? Well, it's interesting, huh? If you're in mathematics, huh? In pure mathematics, as you might call it, in geometry, the only thing uncuttable is the point. A line, as long as it has any length, can always be cut again, right? So, you're thinking of quantity as we do in pure math. Yeah, then you say, well, the uncuttables would be points, huh? But there are other places where a Demarchus speaks as if the atoms have some kind of shape and so on, and therefore they have some size. And therefore, maybe he's kind of anticipating something that Aristotle himself will say, and that is that natural things can't have just any size, right? That they have a size that is connected with their nature. But that's something other than just considering quantity abstractly, right? It could be cut forever, right? And there isn't going to be uncuttable to be a point. So, it might have been a little hesitation in his mind, you know, of how to understand the atoms, huh? But basically, he arrived at them through this thought experiment, huh? Imagine your body and every other body in the world cut up and cut every direction and angle the thing could be cut at, right? You must be left with some uncut things, right? And that's what the atoms mean, huh? Now, of course, what we call the atom in modern science should not have been called an atom yet. The atoms, what we called atoms, were uncuttable by chemical means, but then there were other means of cutting them that we discovered, right? So, as Heisenberg said, if you want to compare the thinking of Democritus with us, don't compare what we call an atom with what he called an atom, right? It'd be better to compare our, say, our elementary particles with what he called atoms, or if there's something smaller than that, right? Compare that to the atoms, huh? Okay? But this word atom was taken over by some of the early modern scientists and became familiar, right? It's taken over from Democritus, huh? What about the empty, huh? Well, I think we mentioned before when we talked about Empedocles saying the empty does not exist. But Democritus said the empty existed, and apparently the reason he gave was that bodies couldn't move unless there was some empty space for them to move around in. If nothing was empty, we'd all be packed completely tight, like sardines in a can, or your clothes in your suitcase when you had to sit in the suitcase to close it, right? There would be no give at all. And so, in order to save the reality of change, he thought there had to be the empty. Well, what is the empty, right? Well, it's nothing, right? So now he's saying that nothing is, which is absurd, says Empedocles, huh? But Democritus seems to be willing to admit a contradiction, that nothing is, in order to save what change. And all the way down through history, men trying to understand change, like we saw in Heraclitus a bit, right? To hold on to reality of change, they will sometimes deny the impossibility of something both being and what? Not being, huh? So the next little quote here from Democritus. Man is a little, but, cosmos, a little universe. The Greek word would be like, make one word out of that, micro, small, right? Cosmos, huh? That's a very interesting saying, and even people other than Democritus might agree that there's a lot of truth to that. And if you look at the material world and then the immaterial world, which world am I in? I've got a foot in the material world, my body, obviously. With my understanding and will, I've got a foot in the, what? The immaterial world, right? The stone is only in the material world, and the angels are really in the immaterial world. But man has got a foot in both of them. His body and, what? Soul. And sometimes, you know, when they're talking about incarnation, and why it was appropriate for God to assume human nature, right? They'll refer to this idea that man, in a way, is a microcosm. So God is taking, in a sense, the cosmos back to himself. Because man is a little bit in the material world and a little bit in the immaterial world. And not just purely material or purely, what, immaterial. That's kind of interesting, huh, to see the long life of this. Of course, there are ways, I suppose, man is a little universe, huh? Like in the third book on the soul, when Aristotle's got through talking about sensing, right? And understanding, well, by sensing, I can, what? Take on the colors of all things around me, right? And the sounds and the smells of things around me. And by understanding, I can take on the natures of all things around me. So he says, the soul is in some way all things. So that's a microcosm, right? It's kind of a universe in miniature. And some of these people, you know, when they talk about, oh, gee, man, it's only a tiny part of the universe, you know, and so on. But yet we have a science called cosmology, you know, where man takes in the whole universe, right? Inside of himself, right? Inside of his mind. And so, a lot of truth is to man being a little, what, universe, a microcosm. Now, in this last one, in a kind of tiquant way, he emphasizes the great truth that man is the most imitative of the animals, right? And we imitate, what, nature, right? But sometimes the reason why we say we imitate nature is that our knowledge begins with our senses. And we sense these things, and then we, what, make something like them, right? So the sun is too bright, I get under the tree there, at least in the sun.