Fig. 7. Plato’s Proportion.
Plato, Timaeus
Part 1 (27d–32c)
MCKEON: The first reading that we shall engage in is a series of selections from Plato’s Timaeus.1 Let me remind you that the purpose of our reading is not to penetrate the thought of Plato but, rather, to lay down the structure of different conceptions of motion. We begin with Plato largely because in many respects he lays down the conception of motion—and, therefore, of space, time, and cause—which has had a great influence in the development of Western thought. Consequently, the initial reading should have a kind of explosive effect on you. The key thing that I shall be interested in, then, is laying out the argument in this sense.
Let me remind you what I said in the second lecture. The Timaeus itself is divided into three parts. The first of your selections, which begins at 27d and goes on to 37c, comes from the first part, where the nature of change is explained in terms of reason. Your second selection, from 57d to 59d, is from the second part; this is the explanation of motion in terms of necessity. And the third selection, which begins at 88c and goes on to 90d, is from the third part, which deals with motion as it is perceived, calculated, measured as part of the experience of man. Therefore, three sets of problems are separated, and I wanted you to have this initial information.
From this point, I think that as we go along in these readings I will probably relax and open up the mode of discussion somewhat, but not in the first several discussions. What I’m particularly anxious for is to have you explain what you think the argument is. Therefore, what I propose to do is to break up the first selection into a series of steps and merely ask, What is Plato doing at this stage? Let me clue you, however, into one piece of psychological advice. Answering that question in the form “He says . . .” always has a bad effect on you: I act unpredictably because I know what Plato says; therefore, don’t tell me what he says. Explain, rather, what is going on in the argument. Anything that occurs that seems important or even just silly bring up as part of this.
In your initial selection, the first stage of the argument covers from 27d down to 28c. I have the sheet that you signed last time. Miss Frankl,2 do you want to tell us what function this has? Bear in mind that this is a dialogue in which Timaeus gives what amounts to a lecture. It is not a dialogue in which there is much to-and-fro questioning; Socrates even promises not to speak. Our opening selection is from the beginning of Timaeus’s speech, not quite the first sentence, but for all practical purposes he’s just starting out. Plato has explained that on the previous day, while the company was going through the dialogue of the Republic, dealing with the perfect city, they decided that they needed a little physics in order to understand what’s involved in the perfect city; and Timaeus, therefore, has undertaken as his contribution to supply the second part of the general education. The first part was, obviously, the social science course; the second part is the natural science. This, Miss Frankl, has given you some time to assemble your thoughts. What do you think is going on? Where is he starting? What is the function of this? What’s this got to do with our problem on the nature of motion?
FRANKL: It seems to me he wants to set up a division between what has being and what has becoming on the basis that being is apprehended by reason and becoming is what is conceived by the senses.
MCKEON: I’ll take that as an answer. It’s a good beginning. Let me elaborate it since it would take a long time to get it out of you dialectically. One of the things which I hope you will observe as we go along is that the structure of the argument will vary and the conditions which will be taken as being the conditions of objectivity or of verification, of warrantability, will differ from philosopher to philosopher. Some of them will start out by establishing a proportion, and here in Plato the basic proportion is stated in the opening lines with three sets of terms which we’ll use as we go along. There is the always existent, and there is the always becoming—obviously, a ratio there. You can construct the proportion when you bring into account that the way in which you know the always existent is by reason, whereas the way in which you know the always becoming is either by opinion or by sensation—opinion and sensation are put together. But there are two other terms that come into this proportion and will become more important as we go along. What else do we know by reason? Or what else is characteristic of the always existent?
STUDENT: Its perfectness?
MCKEON: No, that’s a later part of the argument. Yes?
STUDENT: It is becoming, and, therefore, it is created? No, it’s the same.
MCKEON: It’s the same and the other. Notice, all that we have thus far is a proportion (see fig. 7).3 If you feel this is old-fashioned, think of it in these terms. What you know by reason is an equation which will deal with everything that the equation applies to; in that sense, it is always existent. You never see the equation: you know it by reason. It is related to what you see, however, in that if you apply it, you get a lot of instances that you can distinguish, although they are the same in the respect indicated by the equation. Yet the things you apply it to are constantly changing, either in respects relative to the equation—and then the thing ceases to be an instance of it—or in respects that don’t affect the equation. Therefore, if we take this as our fundamental schematism of intelligibility, we can then go on and ask our questions. Miss Frankl, what question would follow?
FRANKL: “Was the world . . . always in existence and without beginning?” [28b].
MCKEON: That is the question, but let’s generate the question. Why would we have this question?
FRANKL: I don’t understand.
MCKEON: Well, let me read you the sentence. “Now everything that becomes or is created must of necessity be created by some cause, for nothing can be created without cause” [28a]. In other words, the only place that we’ll look for causes is below the line in our proportion; and since we’re dealing with physics, which is changing things, we’re going to need to look for a cause. Notice, if it always is, it’s meaningless to look for a cause; if it is an equation, the equation would be a substitute for a cause. But if this is the case, what would we mean by a cause? . . . There is an artificer here, but the artificer is going himself to look for something that’s beyond. In fact, this is going to be our first question, and it’s a very modern question. What’s he going to mean by a cause? The rest of you can come in and help Miss Frankl.
STUDENT: A pattern?
MCKEON: He’s going to mean a model—the modern word is model—and the first question, therefore, will be, What kind of a model? What kind can it be? We’ve only two possibilities. What kind can it be?
STUDENT: A model for any of the always existent . . .
MCKEON: That’s right.
STUDENT: . . . and one for the always becoming—the created object is the always becoming.
MCKEON: And which will it be?
STUDENT: Well, it’s going to be a pair of creations, but here we need a model for the second.
MCKEON: Well, all right, let’s leave it. Obviously, we could look for a cause in the sense of an antecedent efficient cause; but what we are saying, in effect, is that we want a cause in the sense of an inclusive formula. The model will be, therefore, not something that pushed the universe but, rather, the formula that we will set up. I’m deliberately going into detail on these opening lines; they may seem of slight importance unless you watch them carefully. But you’ll notice what we have said thus far.
We now turn to the first question and then later to a second question. Mr. Davis, what question do we ask in order to get started?
DAVIS: I didn’t hear what you said.
MCKEON: What questions do we ask in the first part of the reading for today. There are two, I’ve already suggested; and I asked, What are the two questions, and why?
DAVIS: One question is dealing with the world: Was the world created after a model which is a pattern or one he just invented?
MCKEON: No, we’ve already answered that. That is to say, if we are going to look for a model, it will be an eternal model. What’s the first question we will want to ask? . . . Yes?
STUDENT: Who its maker is.
MCKEON: Is that the first question? Let me read you what it says in my book. “[T]he question which I am going to ask has to be asked about the beginning of everything—was the world, I say, always in existence and without beginning?” [28b]. In other words, we’re asking, Is the world invented or did it not have a beginning in time? Actually, you could still have had it created even if the world didn’t have a beginning in time. In fact, during the middle ages one of the regular doctrines that was held for the created universe was the creato attamen aeterno, that is to say, the eternal creation. Still, of course, there is also the creation in time. Plato, however, is not arguing on this question here. Now, how do we answer the question whether the world has a beginning or not?
STUDENT: It’s created in the sense of a sensible creation. If it’s sensible, then it must be created.
MCKEON: It had to have a beginning in time, and we read it off the proportion we began with. That is to say, if you are talking about something which is sensible, you’re talking about something which is changing, and anything which is changing had a beginning in time. So, you give an answer right away. Let me point out, this is exactly what he says: “Created, I reply, being visible and tangible and having a body, and therefore sensible; and all sensible things which are apprehended by opinion and sense are in process of creation and created” [28b–c].
What’s the second question we go on to?4 Is Mr. Rogers here?
ROGERS: Yes. The second question is the question of the order of knowledge.
MCKEON: The second stage of the argument has three parts. It begins at 28c. What are the three parts to this stage?
ROGERS: He seems to be asking what the efficient cause is here, corresponding to what he calls the maker.
MCKEON: He’s asking a question of method. He’s asking, How do I know about that stuff? And what’s the second thing he asks?
ROGERS: Is this the question where he’s asking what it’s thought to mean to us?
MCKEON: We’re asking, After we’ve found the cause, how will we formulate it? He’s asking a semantic question. First, how do you know what the cause is? Second, how do you state it to all men? And, then, third?
ROGERS: What is it for?
MCKEON: What does that mean?
ROGERS: Well, what models are they choosing?
MCKEON: Yes, what model will we use? And you notice, in terms of what we have said, these tend to collapse into the third, so that it’s the third that we answer first. What model will we use?
ROGERS: Oh, oh, the model that’s always existent.
MCKEON: Yes, we’ll use the always-existent model. And you notice, what we mean by saying that the maker, the model, and the world are good is simply that the model which we will use will be an orderly one. On the semantic side, this is easy because the Greek word kosmos, which we still use for the universe, the “cosmos,” has as its original meaning order.
Let me sum up, then. At the beginning of Timaeus’s speech we lay down the fundamental model of our argument: it is an argument by means of a proportion, namely, being is to becoming as reason is to sensation as same is to other; and in terms of this we are now going to seek the cause. And our last sentence is that the world will be a copy, which is to say, in more modern terms, that it will be an applied equation.
Next comes a passage [29b–d] which involves the statement that we are going to proceed according to the natural order. Is Mr. Dean here? Mr. Dean, this is not an easy question, but what is the rest of that passage about? It begins, “Now that the beginning of everything should be according to nature is a great matter.” What’s he do from this point on?
DEAN: I believe he talks about how certain our thoughts about the creation can be. He does this by saying that since, after all, the world is a copy of something perfect, our words about it cannot easily be entirely, unchangeably certain; rather, they can’t. In other words, our words about the world are in a proportion to our words about truth as the world is in proportion to essence.
MCKEON: This is correct. He is here taking up the semantic issue. In other words, it is not just a question of what we say; rather, we will proceed according to nature, that is, we will first deal with the beginnings of things and we will make our words apply to the beginnings of things. But this leads him to state the proportion, Mr. Dean. In your translation, which begins, “What essence is to generation . . .” [29c], I suggest that you cross those two words out and make the proportion—it’s a better translation—“What being is to becoming, that truth is to belief.” Mr. Dean, what’s his conclusion on this?
DEAN: That we shouldn’t worry if we can’t speak with the precision of absolute knowledge. We’re telling tales about the gods to mortal men.
MCKEON: I know, but get it out of the aphoristic frame. What does it mean about the nature of scientific knowledge of physics?
DEAN: That it’s not certain, that it is only probable.
MCKEON: Yes. Knowledge of physics is probability. Knowledge of mathematics will give you certainty; but since it is a copy we’re dealing with, it is probability which will be true of all physical laws. Let’s take this, then, as the second stage of the argument.
The third stage begins at 29d, after a slight interruption of Timaeus. Miss Marovski, he’s now going to talk about the way in which his proof will proceed. Can you tell us what it is that the proof in this paragraph is going to involve? What is it that he says it will be?
MAROVSKI: Well, the basis of it is that the person who created the world must have been good and that, having no jealousy of anything, he wants the world also to be good; and, therefore, he . . .
MCKEON: What would this mean? Leave the word good out, and tell me what he’s driving at.
MAROVSKI: Well, I think that . . .
MCKEON: To begin with, is this a creation ex nihilo, out of nothing?
MAROVSKI: No.
MCKEON: What was the state that he found things in?
MAROVSKI: He says, “[A]lso finding the whole visible sphere not at rest, but moving in an irregular and disorderly manner” [30a].
MCKEON: It’s irregular and disorderly. What’s that?
MAROVSKI: This person, I think, is going to need to use reason.
MCKEON: Well, even this doesn’t tell me because the word reason is one of our most ambiguous words. We found the world, the visible world, in disorder. What is it that the creation will consist in?
MAROVSKI: Bringing order out of disorder.
MCKEON: All right. To bring order out of disorder, what will he do? Among other things, he will, it says, be involved in a construction of all becoming; that is, everything is going to be constructed. Incidentally, let me give you a little more Greek. In Greek, the creator, the maker, is the poiétés, the poet. The poet is the maker, and all the way through we are talking about god or the maker or the demiurge in this way. Now, to bring order out of disorder, what is it that he’s going to do?
MAROVSKI: He’s going to make something that’s old and tired itself rational and with a soul.
MCKEON: Well, I know, but what does that mean? We have a chaos, to use physical language, and I’m going to bring order out of chaos, to use a cliché. If I’m doing it for the universe, what do I have to do?
STUDENT: You need a principle of organization to determine a pattern of motion.
MCKEON: I know, but how does this happen?
STUDENT: Do you mean, How would you go about it?
MCKEON: What is the relation of body to soul to intelligence?
STUDENT: It’s in a hierarchy?
MCKEON: Leave the hierarchy out. At 30b is what I want: “For these reasons he put intelligence in soul, and soul in body, and framed the universe to be the best and fairest work in the order of nature.” In effect, what I’m asking you is, What does this mean, treating it intelligently and treating it as if it were science, which it is, and not poetry?
STUDENT: Well . . .
MCKEON: Yes?
STUDENT: Namely, he bound it in a form?
MCKEON: But that doesn’t help any. Let’s begin with soul. What do you mean by soul? . . . If you wanted evidence that there was a soul in something, what would you look for? Yes?
STUDENT: Couldn’t you say the soul was the essential element of . . .
MCKEON: The word essential is a modern invention; I don’t know what it means. I hold up this book. Does it have a soul?
STUDENT: Well, there’s a certain essence of the book.
MCKEON: I don’t know what essence means. I just said that I thought I would want an empirical proof that it had a soul or didn’t have a soul.
STUDENT: You would look for self-movement.
MCKEON: You would look for self-movement. This, incidentally, is broadly the Greek approach. If you take a hand and you want to know what the difference between a live hand and a dead hand is, you find out if it moves itself. If it is moved only externally, if it is moved only when the physician lifts it and then it falls again, it’s dead. What would it mean to say that the universe has a soul in it?
STUDENT: It moves.
MCKEON: It moves, and it moves in such a way that something outside it isn’t moving it. Now, let me ask the question in general terms. Do you think the universe has a soul? Is there anyone here who thinks it doesn’t have a soul? The criterion, bear in mind, is that if it didn’t have a soul, there’d have to be something outside of the universe moving it externally. If you are conceiving of the universe as a whole in motion, then it is alive. This is all that Plato means by it; he doesn’t mean that it’s got a respiratory system or that it has blood circulating. It is self-moving.
Let’s take it a step beyond that. Mr. Brannan? What does intelligence mean in this formulation? Notice, I’ve answered half of my question. I’ve answered what it would mean to say that you put the soul in the body; that is, he made the universe a self-moving whole. But he also put the intelligence in the soul. What does that mean?
BRANNAN: It means the pattern was one that was of being, not becoming.
MCKEON: I’m not sure I understand. His words like essence and being are private. I mean, suppose—I used the example of the hand—I’m wiggling my fingers at you now. What is the intelligence?
BRANNAN: The intelligence would be in that they didn’t just twitch indiscriminately.
MCKEON: It’s wiggling. You don’t know what it’s doing, but I have five fingers and I’m wiggling my hand at you. It’s a pedagogic device to affect your mind. [L!]
BRANNAN: The pattern that it wiggles in, if it has one, would be it.
MCKEON: The pattern would be an extremely difficult one to trace, even with our modern machines. If you laid out on graph paper all the positions that were occupied by the five fingers in their successive series of movements, it would take a team to tear it apart. What’s the intelligence in this motion?
BRANNAN: Well, whatever would organize this movement.
MCKEON: That’s suspect. Even in Swift Hall we cannot tolerate this mysticism.5 Yes?
STUDENT: Is it that if it’s internal, then it moves through order rather than chaos?
MCKEON: Any others? Yes?
STUDENT: Regularity?
MCKEON: What would you mean by regularity? This is the right answer, but it is like the word essence and needs specifying.
STUDENT: Well, we could see if there’s any purpose achieved.
MCKEON: Oh, no, no. Leave purpose out.
STUDENT: Why can’t we use the term pattern to see if there’s anything recurrent in the movement?
MCKEON: Because if it is recurrent, then we’re down on the level of time and becoming, and we’ve come up from that.
STUDENT: Didn’t you say before that this would be up at the level of formula, and your formula is something?
MCKEON: All right. What’s the difference between a formula and a recurrence?
STUDENT: Well, couldn’t you use recurrence in defining what a formula is?
MCKEON: No. You could use recurrence in deciding whether or not to apply a formula, but all you need in a formula is a series of variables which have a relation to each other. Each finger of my hand is an articulated set of levers. It’s relatively easy to write the mathematical equation of the motion of a lever, even a double lever. The instrument is prehensile, that is, the levers come together. So even with five fingers, one of which is opposable, the mathematical equation for this would be one, it would be the same; that is, for all of them it would be the same equation in spite of the fact that my thumb is shaped mainly into my fingers. I could write, therefore, the mathematical equation for the motion that is possible. The length of the finger, the comparative length of different ones, the amount of flexibility I have, all of this is on the level of becoming; and I would get that out of my equation by putting in constants. But the equation would be the same for all fingers, for all hands, for all living hands.
Consequently, what we are saying here—and we’ll have triple steps fairly frequently—is that you have the regularity of the equation: that is reason. You have, next, with respect to becoming, the inclusive self-motion: that is the soul. And you have the manifestation of that in the body. The bodily motion, therefore, depends on reason. If we have reason as well as sensation, we can not only see the series of positions occupied by the hand; we can also determine whether this is going on because it’s rigged up with an electric charge—it’s a dead hand moving—or because it is in self-motion, and then we can, in turn, reduce it to the scientific form in which we could write the equation. To bring order out of chaos, consequently, involves a rational schematism manifested in physical motion. This is perfectly reasonable, isn’t it, in spite of the poetic form in which it is put?
Let me call your attention, however, to one point which will be of use to you as you watch what happens to motion. This is a hypothesis which is exactly the contrary of the atomistic hypothesis. The hypothesis we are working on here is that there is an organic equation, what we would now call a general field equation, and that the field equation is such that it will account for the entire universe and will get down to the parts of the universe in terms of their contexture in this equation. The atomic hypothesis begins with the supposition that we have least parts and that we can construct wholes out of the least parts, eventually getting to the universe. Stated in the abstract, these are two plausible hypotheses; there’s no reason why you shouldn’t go in either direction. You can get started, then, if you have your general equation; this would be pretty good. If, on the other hand, you have an exhaustive list of the initial particles, this would also be pretty good. Yes?
STUDENT: In this description of intelligence, are you thinking of these things as being independent or dependent variables?
MCKEON: What I’m talking about, which Plato says in other words, is that E=mc2. No, there aren’t any independent variables in the other equations. That is, what you have here is a general field equation, and you will get down to something other than the universe as a whole only if you construct frames that are influenced by this general equation, frames which will then require more specific, lower equations.
STUDENT: That is, the variables in these lower equations would have to be dependent, then.
MCKEON: Yes. And let me add, incidentally, that in philosophy, this form of approach is quite frequent. In many respects, for instance, the main outlines of Whitehead’s philosophy is Platonic. He himself said the history of philosophy is “a series of footnotes to Plato.”6 He makes a similar set of assumptions about his philosophic approach.
Let’s begin, now, with the fourth stage. This is the question which begins at 30c and runs through 30d: “in the likeness of what animal did the Maker make the cosmos?” Mr. Milstein?
MILSTEIN: Well, he asks what animal the creator would pattern the world after. He says that it would be more reasonable . . .
MCKEON: This is the form of the answer which always makes it go hard on the student I’m talking to. Tell me what he means rather than what he says.
MILSTEIN: Beings which are whole and not in parts are fairer.
MCKEON: What does this mean in terms of the discussion we’ve just had?
MILSTEIN: It means that they would have one unified principle of organization or order.
MCKEON: Yes. If we are going to build a universe, stressing universe, it will have to be on the model of something which is a whole and not the part of anything else. That’s our first principle. What’s our second one?
MILSTEIN: That would be when he raises the question of having an organizing principle.
MCKEON: No, that’s the next question, stage five. There’s still a subdivision of your question, which is stage four. . . . It’s essentially the question of what it is we’re making an imitation of and what the relation between the model and the imitation is . . . . The rest of you can come in if you wish. Yes?
STUDENT: There seems to be another proportion here, which is related in terms of the model’s intelligibility and the imitation’s intelligibility.
MCKEON: Is it the imitation’s intelligibility?
STUDENT: Well, the proportion is between the model in its intelligibility and the copy . . .
MCKEON: The copy is what?
STUDENT: The world.
MCKEON: I know, but instead of intelligibility what’s the right word? . . . It’s visibility. In other words, taking his language, we are going to make a visible animal in imitation of an intelligible animal, and the reflexivity is so great that intelligible here means intelligent. That is, the universe as a model is through-and-through intelligible precisely because it is itself a thinking process. That is, it is an intelligible animal because it’s an intelligent animal. This, then, is the model, which is off beyond. What we are dealing with is a visible animal, an animal that we will experience empirically. We’ll be able to build the intelligible animal only in our thoughts by writing the equations as we find them; but we must bear in mind that, ultimately, there is an inclusive equation which will bind together all of our partial dynamics, all of our partial statics, and so on . . . . Yes?
STUDENT: Is this what the Greeks thought? I mean, that’s what I understood, and I’m a little confused by it. Is what makes the intelligible world one animal that it is the form of all ideas of thought, in other words, that it is thought?
MCKEON: Well, what do you mean by form?
STUDENT: I don’t know.
MCKEON: Well, that’s the reason why I advise you to throw it out. What we are dealing with here, what Plato is saying, is that we begin on the bottom level of our proportion (see fig. 7), that is, we have sensations. The sensations are such that we can deal with them in terms of what we infer to be their cause. Of the cause, we can determine whether it is regular or irregular; and if it is regular, we can write the equation. The equation would give us the intelligibility of the cause; and we argue from this to the more inclusive situation, namely, that any partial intelligible equation is possible only if it is in a total context which is intelligible. Therefore, all of the equations hang together; and they hang together not because something moved down here on the bottom of the proportion but because something thought up there on the top: that’s what the intelligent animal is. The universe thinks itself out as the model, then runs itself out as the imitation.
STUDENT: So this whole conception of thought holds that the pattern is the creator thinking.
MCKEON: Not the creator thinking. The creator’s doing his best to see an intelligibility which is up above him. This is one of the reasons why the Christians thought that Platonism, although it had some good points, was dangerous: it set up a rationality prior to the process of creation, it set up a good prior to the creator. They were right. Here, you notice, there are criteria of being and of goodness that the ordering process which is the creation approximates to.
STUDENT: And it’s the criteria of being which are in the equations that do this.
MCKEON: That’s right. And you see, we can think in ways that we can then test and discover implicit in the universe precisely because the thinking has been done on a more systematic basis before; otherwise, it wouldn’t apply here. That’s a reasonable hypothesis.
Let’s go on to our next stage, the fifth, beginning at 31a. Is there one heaven or are there many? Are they infinite? Mr. Wilcox? . . . O.K., let me give you the answer to it: there’s obviously only one heaven. But why? What I’m trying to do is to get you used to his mode of thought—which I was going to say is not ours, but that isn’t true. We think in a Platonic way more frequently than we do in any other way, certainly more frequently than we do in an Aristotelian way; but we don’t recognize it and, therefore, many of his arguments seem odd. If, on the basis of the argument we’ve been running thus far, we wanted to prove that there was a single heaven and not many, what would our argument be?
WILCOX: Well, first you’d have to give the definition of what a heaven is.
MCKEON: No, this would be semantics. Remember, we are going naturally, not semantically. We threw out the analytical philosophers when we said it’s a natural sequence we will go through. We are saying that if we can show how the heavens came to be, then we can tell what kind of words to use. Our definitions will depend upon our physics. It’s a much simpler reason. . . . Yes?
STUDENT: Well, if we said that it’s made after a pattern, is that pattern one or many? We can then answer that by saying it is one pattern which is involved. When something is all inclusive, there can’t be another one like it.
MCKEON: No, it’s simpler than that. Notice what we’ve been doing. We’ve been simplifying in the modern form. What are the alternatives between one or many heavens? This, by the way, is an argument which has come down to us almost continuously. Tennemann,7 for example, had a work on the plurality of worlds, and in the seventeenth and eighteenth centuries they’re all over the place. We are in it in cosmology again; that is to say, do we consider each of the galaxies a world or is there a world which includes all the galaxies? Stated in this way, obviously we are not dependent on more information about the heavens; we are dependent, rather, on the approach in which we’ve already cast our thought. That is, if we are going to talk about a universe in which there is a single inclusive formula, it can’t be more than one. Even if there are galaxies, not merely occasional stars beyond the farthest-seeing telescope, they are by rational proof possible only if they fit in and exemplify the equation—or you may have to change the equation. In any case, the interplay between our empirical knowledge and the equation would be such that, of course, there is only one world. It would have to be by another approach that you could get the plurality of the worlds.
Let’s raise the sixth problem—and remember, I’m trying to get you to read with more speed. The sixth problem is the one which runs the whole paragraph from 31b to 32c. Let me, instead of preparing you for it, ask, What is going on here? Is it Mr. Roth?
ROTH: Yes. Well, he’s talking about what the actual corporeal entities are which make up the universe.
MCKEON: He’s gotten around to asking about the elements—he would call them elements even though he would not call them atoms. How does he make the transition? What’s the opening sentence saying?
ROTH: He’s saying, what is created is sensible.
MCKEON: But we already knew that it was sensible and tangible. We’re now also saying it’s corporeal. If it’s corporeal, it’s made up of bodies; therefore, even with all our talk about equations, he does talk about these bodies. How do we get them?
ROTH: If we’re talking about some things that are corporeal and they’re so good, then they are specific things without which nothing can exist.
MCKEON: You’re not reading what he says. You’re being reasonable, but you’re not being Platonic. “[N]othing is visible when there is no fire”—so our first element comes in with respect to visibility—and “nothing is . . . tangible which is not solid, and nothing is solid without earth” [31b]. We have said, then, that it is corporeal because visible and tangible. If you’re beginning with the empirical experience, all you can say is, “I see it and I touch it.” Touch and sight tended in antiquity to be considered the fundamental senses; in fact, they still tend to be. Consequently, by means of touch and sight we get our first specification of the elements, fire and earth. For a moment, leave out your prejudices that might lead you to think there are over a hundred elements instead of only four. I’m trying to find out what these four are. If we begin with fire and earth, how do we fill in the picture? . . .
Well, let me answer that, since what is going on is in one sense fairly simple. That is, we are again making use of the device we had before. We used the empirical device to discover the first specifications of corporeal things. This gives us the two extremes of material, earth and fire, and now these have to be related in a way which will hold them together. That’s what this “fairest bond” is, and the fairest bond would always be a proportion. If you are dealing with plane figures, then you need only a single proportion; if you are dealing with solids, you need two. And you can write your equation out. What he’s saying is very simple. This is the original equation: A2: AB:: AB: B2. You can then turn it backwards, if you like, and say, B2 : AB:: AB: A2; or you can turn it inside out: AB: A2:: B2: AB. He goes through all of these inversions. Suppose, however, the situation you’re dealing with is a three-dimensional universe. You would then begin with the cube, and you now need two middle terms. The two middle terms between earth and fire are obviously air and water, and so he makes this equivalence. As I’ve said, don’t think of it simply in terms of an ancient doctrine; think of it, rather, in terms of the conditions of solidity that would give you a bodily world which would make an application of our equations.
Well, we’ll go on next time from this point. We’ve reached 32c. It isn’t quite as far as I was aiming; I had wanted to reach 57d and the second selection. Reread the beginning of this first selection and then get going at 32c. I should say that arguments seven and eight appear at 32c and 33b, respectively, argument nine begins at 34a, argument ten, a long one, begins at 34b, and argument eleven begins at 36d. See what the argument is. Ask yourself, then, how you revise this to make the approach by way of necessity and, last, what the final set of problems are. On the basis of this we will have the foundations of the conception of motion. You will also have run into space, time, and cause in the process; but we’ll come back later to those. For the time being it’s primarily motion that we’re interested in. Next time we will try to finish the Timaeus.