PLATO'S PARMENIDES THE INTERNET SEMINAR In December, 1994, Lance Fletcher, LISTSERV@FREELANCE.COM, asked Edward Little, ELITTLE@THUBAN.AC.HMC.EDU, to host a reading of Plato's Parmenides, as one of his (Fletcher's) "slow reading" groups on the Internet. What follows now is a transcription of the weekly commentaries that ensued, commencing 2/17/95, and some of the queries and comments accompanying them. These commentaries were posted regularly Thursdays from THUBAN at Harvey Mudd College in Claremont, California to over sixty recipients worldwide. PLATO, PARMENIDES, 127D6-128E4 Here we get down to business with the opening conversation between Zeno and Socrates. A hypothesis of Zeno is presented by Socrates (the treatise Zeno had just read); Zeno objects to some of Socrates' ad hominem remarks, but agrees that he has got the gist of the argument right. (Let me remind you that such a conversation as this never actually happened. Plato is using Socrates as mouthpieces to introduce his own ideas. He is presenting Zeno and Parmenides as themselves, or pretty much true to themselves as far as we know them from other sources, at least here in these early stages of the conversation. Later on, not so, but let's leave that 'til we come to it.) Following this Socrates enters upon a critique of Zeno's hypothesis just presented, which brings up the theory of Forms, at 128E5, but let's leave that for our next reading, and concentrate upon the above text, 127D6-128E4 for the time being. It's all of one piece, of course. The whole dialogue is. But a bit at a time. The otherwise historical Socrates we know fairly well, from some of Plato's other dialogues and from other sources, and it is thought that Plato got the germ of his Form theory from Socrates, in some such manner as described perhaps in the Euthyphro where Socrates was searching for the "one single idea" (mian tina idean) that represents piety, but here we are far beyond that. The Socrates of the Parmenides, right here, is probably a voice for Plato's later stages of speculation. This is, in short, Plato speaking in a drama of his own invention. Who was Zeno? Aside from what is said here, we know him best from the later books of Aristotle's Physics. He became famous for his four paradoxes presented there, the dichotomy, the Achilles, the flying arrow, and the "ogkoi" (bodies, objects) in the stadium. Without going into extensive discussion of the significances of these paradoxes right here and now, it is fairly said that, whatever else they do, they do involve an argument for the denial of motion. If Achilles can't catch Hector, or whoever the slower runner might be, or if you can't get across the any distance because you have to cross an infinite number of half-ways first, then motion would seem to be impossible. Such arguments would tend to corroborate the position represented by Zeno here, from the point of view of movement instead of (here) plurality. Zeno here would seem to be in character. I am rather loathe to present alot of bibliography. I am not too happy about presenting all that on the TMA, but I mainly did it to show how tied up in knots we can all get. My own preference is to come to these texts and their problems fresh, concentrating on the texts. But I will welcome any suggestions you have, and in the present instance, will anyone tell me if there has been anything improving H. D. P. Lee's book, Zeno of Elea (1936), supplemented perhaps by what Guthrie has to say in his History? If you want references of course Cornford in Plato and Parmenides, and Kirk and Raven on the Presocratics, are tried and true reliables. I will now go out on a big fat limb, and make a statement that is sure to be controversial, and will have a great deal to do with how we approach the Parmenides. It comes up now because we are speaking of the Eleatics, here Zeno, and shortly Parmenides, and it is my suspicion, nay contention that we have utterly misunderstood what they were about. Zeno and Parmenides are already linked in their claims that everything is one, Zeno, as said here, backing up Parmenides in a reverse manner, denying plurality. So the question comes up: just what did they mean by this? They have always been understood to mean that the whole universe is just one big unmoving undifferentiated mass. How could they be so dumb? It has been suggested that they were playing games with us, or that - well, you know, philosophers are like that (tapping the head, as it were). But no, I think that they were dead serious, and that they, at least Parmenides, were on to something. He dimly sensed what we now call an abstraction, what Plato, who alone saw through this, called an Idea. Being, just being. Not beings. I think that Parmenides had a very tentative and not too firm grip on this novel notion, and it was Plato who took it on and developed it. There wasn't just Being. There were all sorts of Forms and abstractions. He saw what Parmenides was up to, and no one else did. No one else ever has. The Parmenides, the dialogue, seems evidence that Plato saw this. Instead of dealing with Being, the abstract Form of such, as opposed to beings, he picks up Parmenides' other and correlate notion, the One, and treats it as such a Form or abstraction, using Parmenides as his mouthpiece. There were all sorts of problems with this theory of course. We will get to them. But just now I ask you to consider this underlying possiblity that I have just mentioned, that we have mistaken Parmenides' One Being. Nun, estin homou pan, hen, sunecheis (DK VIII, 5-6). It explains so much, and our own repeated confusion of ideas and things is so notorious. Even Plato's Forms became hypostasized, "thingified." Perhaps this is getting ahead of the game, except that Zeno had entered the picture, Parmenides is soon to enter, and we had to look at the famous Eleatic position. Returning to the immediate text at hand, what about Zeno's argument at 127E1, if things are many . . . ? Surely it did not go down in history as his other arguments have done. And perhaps for very good reason. It is not a very good one. Socrates' immediate riposte is somewhat fresh: you have offered, Zeno, many proofs that there are not a many! This was the sort of thing, however, that those ancient Greeks seemed to love: a self-contradiction. The ad hominem remarks remarks referred to above follow, and then at 128E6 Socrates' more earnest reply to Zeno's argument follows. It is for the moment not a bad try, but it too is not without difficulties, as it will turn out, but we leave it to the next pass. PLATO, PARMENIDES, 128E5-130A2 Zeno had argued, as Socrates summed it up at 127E, that: "If existences are many, they must be both like and unlike, which is impossible . . . " This is a very primitive argument about on a par with the quibbles of Euthydemus and Dionysodorus in the Euthydemus dialogue. Some call this sort of argument on the part of those men sophistical. I rather call them unsophisticated. Socrates won't take such a statement at that face value, as we are going to see shortly. " . . . for the unlike cannot be like, nor the like unlike." Of course they can. Not only can things be like some others, and unlike other others, but, to anticipate a bit, so can Forms. To put it succinctly, the Form of Likeness is like the Form of Unlikeness insofar as they are both Forms, both unitary, and maybe some other things. They are unlike insofar as they are different Forms. Plato seems to approach this problem in the Sophist 256A-B, where he makes out Motion to be same and other. Here in the Parmenides, the difficulty is quite obvious, and Socrates is about to pounce on it. He does so at 128E5. In what follows please be assured that the words, "absolute" and "abstract" which translators (at least H. N. Fowler) use, did not exist in Plato's vocabulary, although they are a fair translation into our modern English of what he did use: auto kath' auto eidos, the Form itself by itself, and auta ta , itself. I think it is worthwhile to remind ourselves, as I do from time to time, that Plato's (and others' of his contemporaries) language is simple and straighforward. Such a reminder has a tendency to keep us from bringing in considerations that would have been far from Plato's mind, or at least to remind us, when we do, that we could easily be drifting away from Plato's intent. Sometimes indeed it is helpful to introduce our own language. Our conversation with Plato, and our understanding him, must be a compromise in this respect. Just let us be careful. There is no rule, except to be fully conscious of what we are doing. In the argument that follows, especially 129B, this simplicity of Plato's language leaves room for much ambiguity. The phrase, ei men gar auta ta homoia tis apephainen anomoia gignomena e ta anomoia homoia, teras an, oimai, "if anyone showed that the absolute like becomes unlike, or the unlike like, that would, in my opinion, be a wonder," is ambiguous. And it is wrong. Toward the end of the passage we have under discussion today, 129D and E, Socrates (Plato) makes himself much clearer, but it is still not quite right. Using (ourselves) capital letters to distinguish Form from copy, Likeness is indeed not Unlikeness, but Like can be unlike. What confusion this entails! What problems, for the Forms! Socrates is not out of the woods, although Parmenides' ensuing critique of his (Socrates') suggestion seizes upon others, not this difficulty. I suspect strongly that it is not Plato's intention to offer a solution to Zeno's paradox here, but to show rather what a difficult problem it is. In passing, note 129B6, "But if he shows that absolute unity is also many, and the absolute many are again one, then I shall be amazed." This indeed Parmenides implies in the First Hypothesis, as we shall see: The Absolute One does not exist; if it did, it would be many. And the second clause, "The Absolute Many are one?" Well, - think of that. Are Ideas unitary or not? But this last clause reveals what Parmenides does NOT do in the ensuing dialogue. He does not undertake eight more hypotheses from the Zenonian point of view , which well he might have. We are spared that effort. But you can do it. I did, very briefly, for the fun of it. What this implies is that this introductory part is not where to look for Plato's most earnest effort to solve these problems, but seems intended to introduce it. The eight hypotheses are a start. To recapitulate: Zeno's argument is very unsatisfactory, and Socrates shows us why. But Socrates' explanation, although it seems to put Zeno in his place, is not without its difficulties too. As we shall shortly see. * * * * * Before leaving them, there is still something bothering me about these two passages that comprise the exchange between Zeno and Socrates. I have been having a hard time putting my finger on it, but I think it is this: Plato is giving us here an argument on a very early and crude level of philosophical discourse, true no doubt to the dramatic date of the mid-fifth century. We would do better to NOT to analyze it too closely in an effort to pick out what is wrong with it, than otherwise. We would do better just to listen to it, accepting it as a valid effort by Plato to portray the state of the art at that early time. The same remark might apply to the sections we are going to study next, Parmenides' critique of Socrates' theory, but not quite so much. Parmenides is going to raise problems, not solve them, or may we say Plato is going to do that. But he is going to do it on a level above what we have just been engaged with, but still somewhat cruder and more naive that he will be doing later in this dialogue in Parmenides' eight hypotheses. Plato is an utter master of dramatic presentation. In my personal estimation he ranks with Shakespeare. It is not at all beyond him to appreciate and represent such fine nuances of development. We should not let our inclination to rush in and do philosophical battle blind us to this aspect of this dialogue. In short, let's not try to justify or correct Zeno's or Socrates' arguments here. Let's accept Zeno's as one of his poorer efforts, and Socrates' as deserving the criticism that is about to follow. PARMENIDES, 130A3 - 131E7 "You are still young, Socrates." We now come to Parmenides' response to Socrates'theory. I have initially outlined it in seven parts, as follows: Parmenides' critique of Socrates' theory 130A3-136C5 Seven problems raised by Socrates' theory A3-134E8 a. the extent of the Forms A3-E4 b. is the whole of the Form E4-131C11 in the participant? c. is a part? C12-E7 d. infinite regress (first mode) E8-132B6 e. are Forms just thoughts? B7-C11 f. infinite regress (second mode) C12-133A10 g. relation of Forms to us A11-134E8 in order to make it somewhat more amenable. In this section we look at the first three of these seven problems. First Parmenides raises a question about the extent of the Forms, which Socrates admits is troublesome, even before, note, they get down to some of the seamier aspects of reality, mud (pElos, mud, mire) and dirt (hrupos, dirt, filth). As a matter of fact Plato seems rather restrained. One can easily think of some even more extreme examples that would put an even sharper point on the question. It is left a problem, in any case, unresolved, although Parmenides (Plato) does imply that there is a case to be made for Forms of base and material things. (For a note on this problem, see Ross' edition of Aristotle's Metaphysics, vol. I, p. 191F.) Parmenides passes on to the next question, "does each participant partake of the whole idea, or of a part of it . . . ?" and he examines the matter from both sides, assuming first that it is the whole, and then the part of the idea that is in the participant. Socrates is undone by Parmenides' arguments here, but even Parmenides arguments are unsatisfactory, for they ignore the difference between the world of particulars and the world of Forms. Do Forms, abstractions, immaterials have wholes and parts? Are they greater, or smaller, etc.? What is a part of a Form? The notion is nonsense. Note that at one point Socrates makes an effort to get around this difficulty, at 131B3-6, where he suggests the"day" analogy. It is not a bad suggestion, as Parmenides makes it out to be, brushing it quickly aside. Although "day" may not be as thoroughgoing an intangible as is wanted, it is at least a step in the right direction. There will be another, better such effort, coming up soon. There was an implication of this immaterial-material question in the very first argument, the one asking if there were Forms of dirt, and so forth. Socrates' hesitation seems to imply that he thought the Form of dirt would be dirty, a notion that would also tie in to the next argument in the series, the TMA. I only point this out to suggest that there is something tying these many arguments together. What is it? It is the confusion of the material and the immaterial, for the last thing that Forms are is material. Yet they are treated as such here. I am for my own part more interested in this particular oversight in these arguments, than in whatever detailed logical or other objections may be found in them. It is enough to disqualify them from being taken too seriously, as keys to doctrine. Need I remind you of the further implication of all this? Here is a dialogue, which, whatever its precise date is, shows signs of being fairly late in Plato's career. It is highly developed in style and substance, we shall see. Yet here Plato is not making firm doctrinal, not to mention dogmatic, statements. He is showing weaknesses of a proposed hypothesis. He is showing problems. This should speak for itself. These reflections will come up again in the next reading, in the TMA. 131E8 - 133A10 TMA "If in your mind you look at all these thus . . . " Much ink has been spilled over the TMA, especially in the last forty years. You might add to the bibliography supplied earlier to you on this network, the chapter on the TMA in Terry Palmer, The Ascent from Nominalism, Dordrecht, 1987. This suggestion from Sean Kelsey of Princeton. Also there are some relevant notes in W. D. Ross' edition of Aristotle's Metaphysics, vol. I, p. 194 ff. And for other, contemporary references to the TMA, see Republic, 597C; Timaeus, 31A; Aristotle, Metaphysics, 990B17 (whence the name), etc. I do not feel inclined to enter into many of these discussions, because it is my belief that by and large they miss the point. Whatever reason Plato in his time may have had for using the TMA, a point that he does in fact raise has never been solved: those old questions of Forms, of what are they? of what is their relation to things? are an ancient approach to what we now call the mind-body problem, the problem of abstractions. One can conceive of Unity by itself, without reference to anything else. That's what this dialogue is all about eventually. But the status of such a conception and its relation to percepts, like the status of Forms and their relation to things, remains a mystery: they seem to be related and unrelated, and you can't get agreement on the question. What are they? Plato was hard put to say. And so are we, and let us admit it fairly. To use the language of Plato for the moment, Forms and the things that participate in them are like and unlike, same and different. The TMA siezes upon their likeness alone, and ignores their difference. It treats the Form as if it were just another thing. But Forms and things obey different rules, as it were, and cannot be treated together as having the same requirements and the same effects. This is a simple observation, which you may accept or reject. If you reject it, you may continue with the TMA. If you accept it, you cannot. I accept it, but either way, this is the problem: our assumptions about mind and body. Plato was a very intelligent man (to use understatement). But he was feeling his way into a problem that we, if not nearly as intelligent, can see somewhat more clearly with the benefit of over two thousand years' added experience. Indeed it is perhaps only now that we can begin to see what the problem really is. Because, up to very recently, highly capable thinkers have achieved abstractions, and, backsliding, hypostasized them, re-conceived them as things. As material or at least quasi-material things. Consider for example the immortal Descartes: who distinguished mind from body, and then went looking for this mind or soul in the pineal gland. Consider what the scholastics did to Aristotle's hulE, matter, an abstraction which they hypostasized over the later objection of George Berkeley. Consider Ryle's "ghost in the machine," which comes through as a very material wraith. Consider the materialist tendency of all of us in our religious beliefs, and consider too what Xenophanes said about this. What about self-predication? By its light, not only is the Idea of the Good good and the Idea of the One one, and so forth, but the Idea of the Many is many, and, if we accept Parmenides' advice to the young Socrates at 130E3, then the Idea of Blue is blue; of Dirt, dirty; and on this route we quickly arrive at some Ideas that are rather malodorous. See how soon we slip from the sublime to the ridiculous. On this basis too I must reject the TMA. The second version of the TMA is no better than the first. Calling the Ideas paradigms, and calling participation likeness or assimilation, are semantic quibbles. Ideas and things are still only treated alike. "Is there any possibiity that the like can be unlike its like?" By all means there is, even though the word translated as "possibility" here (mEchanE) casts some derision on it (mEchanE is an artificial contrivance, whence deus ex machina). Between these two versions of the TMA comes the suggestion of Socrates that the Forms are thoughts, "that it belongs to them to arise nowhere else but in minds" (132B4-5). Plato's Parmenides cries it down with what seems to us a rather childish argument: if such were the case, then "each thing is [made] out of thoughts and everything thinks, or thoughts are thoughtless" (132C9-11). Superficially it might seem so, and it is enough to turn Socrates, here. Again, any distinction between thoughts and things is ignored, but this is just the issue that is not settled. Plato, here at least, did not put it in such terms, but it is the case: the problem is not where the Ideas are, but what the mind is! What is wrong with this explanation? Obviously there are many who know quite well what the mind is: it is brain, and nothing more. There is no such thing as mind. Well, - that depends upon what you mean by "is." If you mean only corporal being and such, you are right. You need accompany us no further. If you assume some other kind of is-ness (being), different and abstract, then you may want to continue. What kind of being could that be? What is its nature? This is beginning to sound like the TMA, isn't it? Rightly so, except I suspect that it will go around in circles. The only thing that will put an end to it, will be an assumption. The assumption will be a choice between one or two natures, one or two kinds of being, one or two states of the thinking apparatus: brain, or brain-and-mind. That there is also a dualist strain in Greek philosophy, evident elsewhere as well as here in the Parmenides, (not in the least in Aristotle's Metaphysics and in Parmenides himself), is demonstrable. But you are going to have to decide whether it is worth following up, and seeing where it leads. You have to decide whether you wish to enlarge your understanding, or confine it. 133A11 - 134E8 PARMENIDES' SEVENTH PROBLEM "None of them [the Ideas] exists in us" The seventh and last of the problems raised by Socrates' Forms, which he used to counter Zeno's hypothesis, is the relation of Forms to us. It may be outlined summarily as follows: 1 Forms are unknowable to us A11-134C3 a difficulty convincing the agnostic A11-C2 b Forms are not in us (or in our C3-7 world, en hEmin); they are by themselves c Forms of relation are related to C8-D6 themselves, not to our world, and vice-versa d examples: (1) masters & slaves v. absolute D7-134A2 mastery and absolute slavery (2) absolute knowledge is of absolute truth A3-5 (3) and each kind of absolute knowledge is A6-8 of each kind of absolute truth (4) our knowledge is of our truth, A9-B2 and each of our kinds of knowledge is of each of our kinds of things e recall of major premiss: the Forms B3-5 are not in us (refers to 133C5) f each absolute class is known by B6-8 its own kind of knowledge g we don't know them or any of the Forms B9-C3 2 God has no knowledge of or relation to us C4-E8 a absolute knowledge is more accurate C4-9 and better than our knowledge b no one has better title to this than God C10-12 c God cannot have knowledge of us D1-8 d concluding summary D9-E8 This is a rat's nest of ambiguities, non-sequiturs and question beggings. It sidesteps the main question: what is the relation of Ideas and things. It appeals to different notions of relation. The relation of a slave to a master is not comparable to the relation of a slave to the Idea, Slave, etc. Or, to put it more generally: the relation of a pair of relative Ideas is not the same as the relation of those Ideas to their participants. There are two, maybe three different sorts of relation here, and they are like and unlike. Parmenides is being cleverly sophistical, and Socrates falls for it, hook, line and sinker. What are Ideas? Where are they? They are not en hEmin, or par hEmin, says the text. Ouk echomen, we do not have them. What do these words mean? (They have been variously translated, "in us," "in our world," etc.) We are not told. Plato also fails to distinguish between absolute knowledge and knowledge of the absolute (134B). It may be argued on the basis of Parmenides' denial (encountered above - 132C) that Forms can be thoughts, that Plato did not entertain the notion which we have expressed, that Forms are abstractions. It is possible that, whether Parmenides' answer to Socrates' suggestion was or was not any good, Plato really felt that way. Yes, it is more than possible. It was simply too early for Plato to envisage mind after the manner we do, however bright he was. Psychology didn't exist then, as we know it. It was another generation before Aristotle even approached the subject. The mind, hE psuchE, and thought, to noEma, were still somewhat mysterious. Bruno Snell addressed this problem in The Discovery of the Mind (Hamburg, 1948; Cambridge, MA, 1963). Whatever the case may be, we may rest assured that to the extent that Plato did understand mind and thought, it was an early and unfinished understanding, compared with later achievement. It is often thus, that when someone discovers something, he does not know what he has discovered. So Christopher Columbus. The question arises: if these arguments of Parmenides are as poor as we make them out to be, why has Plato used them? Could it be because they are typical arguments of the day that were floating around earnest discussions? Could it be that they represent a stage in thinking about problems that Plato, as well as all the rest of us, went through (and some of us still go through)? Or that he has put them behind him, yet wishes to record the travail that led up to better approaches to these problems, such as will follow? They do not lack some drama, and drama is not easy to bring to philosophy. Or again, might it be that he wishes to lead the listener or reader through these fallacies for the sake of the latter's education? Or might it be all of these? Whatever the case, we are left with the fact that this part of the text is a collection of poor arguments that altogether fail, because they assume that Forms behave like the particulars that participate in them. There is nevertheless some truth to the remark (134E) that God does not know us, "nor do we know anything of the divine." Centuries of neo-platonist and Ps.-Dionysian theology were built on this insight. Our relation to God is matter for some other day. Here the question is: what is the relation of our world and Ideas, and of bodies and minds? Here too there is some truth in their utter otherness. There is a paradox behind all this that looms on our horizon. 134E9 - 136C5 "What will become of philosophy?" We have just seen Parmenides counter Socrates' proposal of Ideas with a series of arguments involving their extent, their integrity, their nature and their relation to ourselves - arguments on which Plato reverses himself, and now brings all into question again. We may organize the ensuing text for our convenience as follows: 1. Parmenides' conclusion of his objections to Ideas 134E9-135B4 2. He reverses himself 135B5-C3 3. His praise and advice to Socrates C4-D6 4. Socrates' request for explanation D7-E7 5. Parmenides' explanation, or plan for training E8-136C5 There are here two points that should claim your special attention. (1) The reversal speaks for itself. Whatever difficulties we have with Ideas, whatever quandaries remain, we cannot do without them (literally, "he will not have anywhere he will direct his thought," oud' hopE trepsei tEn dianoian hexei). Parmenides also was expressly pleased with Socrates' bringing them up. But it reinforces our impression of the uncertainty on Parmenides' (Plato's) part throughout this introductory section. Those arguments that he brought up against Socrates are not to be taken as settled doctrine. Rather they are one half of the problematic character of Ideas. The "seven arguments" of Parmenides were all perfectly legitimate questions that one might initially raise about Ideas. It is only upon closer inspection that one is led to see their inadequacies. And these point to just one inadequacy: the Ideas and their copies cannot be measured by the same yardstick. In any judgement, or in any hypothesis we propose, it makes a difference whether we are asking about Ideas or things. You cannot be talking about both at once. Parmenides' plan for Socrates' training (E8-136C5) seems designed to point this out. The same dichotomy occurs in the hypotheses that comprise that plan. If there is a many, what will happen to them, themselves, will be one result if they are considered by themselves, and another result if they are considered in relation to the one. The Many all by themselves are a Form. Related to one they are things. And, to make matters worse, the opposite can also be true! In any case, it is sure that Parmenides takes these options alternatively, not simultaneously. This is just the sort of ambivalence that Parmenides will point out in the eight hypotheses of the main part of the dialogue, where he proceeds in the same manner. (2) Then look very carefully at that plan, lines 136A5 ff. Parmenides asks, what will happen, if there is a many, to themselves, the many, by themselves (pros auta), relative to the one (pros to hen), and to the one, by itself (pros te auto), relative to the many (pros ta polla); if there is NOT a many, to the one and to the many, by themselves and in relation to eachother? These are eight hypotheses. You are going to see this same scheme followed in the eight hypotheses of the main part of the dialogue, only substituting one for the many in the protases (the "if" clauses), and others (talla) for many (polla) in the apodoses (conclusions). It will also appear in the final lines of the dialogue. So what will become of philosophy? We will retain the Ideas, Parmenides, but we will puzzle over them for centuries, under various names like form, universals, sets, mind, and we will continue to mix ideas and things, mind and matter, hypostasizing ideas and materializing the mind. I rather think that Plato was exceedingly honest, and that here in this introductory conversation is recorded his puzzlement over the relation of Ideas and things, over the fact that they are related and NOT related (this time) at the same time. Perhaps it will help us understand Plato, if we acknowledge that we have today the same puzzlement over the relation of mind and brain. They both are and are not related. Obviously there is no mind without brain to support it. But just as obviously, mind is not nothing-but-brain. It is capable of flights of its own. It is more than the automation that is brain. It is not only inventive; it is itself an invention. I am not a spiritualist, not do I entertain the notion that mind is something apart by itself, in the manner that many things are apart by themselves. But it is somehow sui generis. The rub is that our materialist culture is incapable of expressing this, and cannot refrain from remaking it in our materialist image. We are much puzzled by this. Is it any wonder if Plato was puzzled by it, twenty four hundred years ago, when this was quite all quite new? 136C6 - 137C3 THE TRANSITION "I am filled with terror when I remember through what a fearful ocean of words I must swim, old man that I am" We are reading now the final lines of the introductory part. Straightforward, they supply some color to this conversation, but do not appear to me to contain any great problems. It might be a good place for us to review the accomplishments of the introduction as a whole. 1. Its naturalness, its fluency, its color need not surprise us. Plato shows himself a master of this sort of thing in many of his dialogues, even here in what is reputed to be his driest and most difficult. He was no fool: "You gotta get 'em in the tent, before you can sell 'em something," and he certainly does. If this is philosophy (which it is), it is philosophy at its most palatable. 2. Part of what makes it this way is his willingness to put his arguments in ways that common men in the street (or the agora) must have batted some of these problems about, before getting down to tackle them in earnest himself. This may explain the poor arguments of the introduction. Let us not take them too seriously. Now in the main part, coming up, is when he really gets down to business. Perhaps this is also a good time to look forward, and view the forest before we get entangled in the trees. For entangled we will be. To this end I propose to append here a little parody I wrote recently. This does to Zeno's hypothesis in the introductory part what Parmenides did to his own in the main part of the dialogue. PARMENIDES II "Omne tulit punctum, qui miscuit utile dulci" - Horace Returning to Claremont from Cleveland, and going downtown to lunch one day, I met a couple of friends, who are connected with the Colleges there. John greeted me with a handshake, and "Welcome back, old fellow, we have missed you. What are you up to, these days?" Well, I replied, As a matter of fact I have a rather interesting project in hand. I am glad to see the two of you, because, as old friends and scholars, it may interest you. So what is it? they replied almost in unison. I'll be glad to tell you, if you have some time to listen. Let's sit down here and have a cup of coffee. I took a trip to Egypt last Fall, and, while we were poking around out in the desert, I met an old man who was trying to peddle a papyrus he had dug up out in the sands. I looked at it closely, and warned him that he had better take it to the Department of Antiquities. In fact I did more than this. I escorted him there myself. In a moment you will understand why. At least I gained for myself the opportunity to read through the old roll, and it was more than interesting. I can't remember it all, of course, but I can give you a pretty good idea of what it contained. You are familiar with Plato's dialogue, the Parmenides. In it Plato recounts a conversation between Zeno and Socrates and Parmenides, about the nature of Forms. In the beginning, Parmenides criticizes a theory which Socrates has advanced in reply to a hypothesis of Zeno's. He does not reject Socrates' ideas, but admits that they raise questions that remain unresolved, and he goes on to urge Socrates to prepare himself to pursue them by a careful training. Indeed, he even suggests a plan to Socrates for this training. Whereupon they all join in an entreaty to Parmenides to give a demonstration of what he means, and Parmenides goes ahead to do just that. Parmenides' demonstration, you recall, is to take up serially eight hypotheses: If there is and is not a one, what shall we say about it, and about the others. That only makes four hypotheses, but he considers each of those twice, coming up in each case with a contradictory conclusion. At the end of the dialogue Parmenides sums up what has been said with these somewhat astonishing words: It seems that, whether there is or is not a one, both that one and the others alike are and are not, and appear and do not appear to be, all manner of things in all manner of ways, with respect to themselves and to one another. His demonstration is so full of contradictory conclusions that it has baffled readers ever since, that is at least until Professor Cornford partly untangled them in 1939 by showing that Plato's Parmenides (Plato himself, of course) was in every case treating the one in two different manners: once as a Form (we would say, abstraction) and then again as a particular. Well, this old roll turns out to be a sort of continuation of that dialogue. Whoever did this we don't know. It could have been old Plato himself, or it could have been someone else, even long after him. In any case it is very clever: it has a very authentic feeling to it. What the old man found is essentially a reprise of the main part of the original dialogue, that is of the eight hypotheses, except that in it Parmenides takes them up as hypotheses about the many, instead of about the one. As a matter of fact, this was just the way they had initially been suggested by Zeno, and repeated by Parmenides in the early part of the original dialogue. Parmenides had suggested in effect that Socrates consider, if there is or is not a many, what shall we say about them and about the one, both with reference to themselves and to each other. That is what he now does here. But he goes on to say that he is no longer up to the exhaustive and exhausting inquiry that he went through before, so that he is going to be briefer, and he hopes it will be clearer. Evidently Plato, if it was Plato, or whoever wrote this, wanted to take some of the mystification out of the original dialogue. If there is a many, he asks once more, what shall we say about them and about the one, both with reference to themselves and to each other, and again if there is not a many, what may we say . . . you remember the litany. Apparently out of consideration for his interlocutor and his hearers he does something else, as he starts out, to make the whole situation clearer. He warns them explicitly that, since they got into this conversation as a result of some difficulties that they discovered in a discussion of Forms, he will be treating each hypothesis twice, as he did the first time, once taking up the Form of the others, and once the particular others. And furthermore, he says, I want you to notice that it is not just the many (or the others) and the one that are ambiguous terms here, in that we may treat them as Form or particulars, but there are two others that are equally ambiguous, and in the same way: namely `be' and `not.' Existence and negation may also be Form or particular. Absolute existence is an idea. In fact it was the idea I was groping for in that poem I wrote years ago. A particular existence a thing. Negation too may be absolute non-existence, or just otherness. And there are countless other ambiguities, of course. I am going to make this as simple as possible, he says, in hopes that it will help you to unravel the puzzles of our first conversation, in which I teased you a bit, albeit for a serious purpose. I will leave out the contrary characters and try to address these hypotheses directly in a common sense way. Well, then, he continues, turning this time to Socrates, if there is a many, what shall we say about it? We have an idea of it, don't we, since we speak about it? Yes, answers Socrates. But does an idea exist? This of course is one of the questions we have considered before, and others have asked it. It is a valid one. It certainly doesn't exist like you and I do here and now, or our friends, or the stools we are sitting on, does it? No. Then this is a sense in which we can say that it doesn't exist? Agreed. I am glad of that. There are lots of others who would agree, too. For sure. But that doesn't prove it so. Perhaps it is a better argument for us to say that if we have an idea of it, if it is an idea, it would have to be one (all ideas are ones). Therefore it would not be many. There would be no many. That is certainly so, answered Socrates. But if there are many, they are all ones, aren't they? I mean, each of us is a single person, and each of these stools is a single thing. Also the Many (the Idea) is one isn't it? How can anyone argue with that? You're right, they can't. But don't you see now that the many do and do not exist, and are and are not one, depending upon how we look at them, on whether we consider them as an idea or as things? And don't you see that this is the game I was playing with you in our first conversation? It amounts almost to a trick, except that I was very serious. I can see it now, alright. And can you see that in raising the question about the many, we have not avoided at the same time raising the question about existence, or being? Do they mean things, or do they mean ideas? Any one may have his own views about the answer to that, but he cannot evade the question. Assuredly. Now, then, what are we to say about the one, if there is a many? Well, I think that you've already said it. If there are many, they are ones, lots and lots of them. Of course, but then again, how can the many have anything to do with one? Now I am beginning to catch up with you. It can't, if we are thinking about the Idea, the Form of the many. So you see that we have the same predicament with the many, if we consider it by itself, or if we consider it in relation to the one. Yes. Good. Now what are we going to say about it, if there is not a many. I am not quite sure yet. Well, let me help you. What do we mean when we say the many is not. Do we mean there is not such thing at all, or that it is other than something else? Well, I suppose we could mean either. But if we mean the latter, that it is other than something else, isn't then there a many after all? Yes. So, strange as it may appear, by these lights, if there is not a many, there is a many. So it seems. But on the other hand, if we mean the former, that there is no such thing at all, in any way, shape or manner, then we cannot even think of it, and there are not any things either. But there could be one! Right you are, if it is an idea, but there would be no particular ones, which is all we just said. I am glad you saw that. You are beginning to catch onto my game. Well, if there are not many things, there are no single things either, that is no ones. Bravo! You have caught my meaning exactly, and are taking the lead from my hands. If you continue in this way, you will be engaging in just the sort of training that I urged upon you before. You might for example explore these hypotheses in terms of the contrary characters that we took up in our first discussion, or even other possible characteristics. One, many, being, and negation are not the only ambiguities in our thoughts and speech. If you don't, someone else perhaps will do it some day. Thank you, but with this much progress what I want to do first is to go back and examine your first eight hypotheses, using what I have learned here. For now I'll leave the other ambiguities to some one else. Alright, but before we part I want you to notice a couple of other points. This whole exercise is not just about the one Form of the many, or about others we pointed out, that is being and negation, but it is about all Forms and things. And I want you to notice something else: what we have said here also uncovers the root of the difficulty that you and others have had with my statement in that poem that somehow got to Athens long before I did. You have all thought that my great `Being,' `now whole all one continuous,' meant the whole universe. Nonsense. How could you credit me with such a howler that so obviously flies in the face of everything we see and hear and feel. What you have done is understand what I said in only one of two possible ways, and the wrong one at that. Try the other way and see if it doesn't make more sense. I will admit that when I composed that poem I, myself, was only dimly aware of what I was searching for, of the other kind of one, so I am not surprised if others misunderstood me. Had I had a firmer grip on the idea, I might have expressed myself better. But we all have to learn to walk before we learn to run. Furthermore I predict that there will be no end to the confusion, and that people are going to have the same trouble with your Forms as they did with my one. They will always try to think of them as things again, albeit ghostly sorts of things but still things. There will be no end to it. It is in our human nature to do it. It is as my friend from Colophon says: mortals even suppose that the gods have been born, that they have voices and bodies and wear clothing like men. If they put clothes on their gods, what won't they do to Forms? 137C4-139B3 BEGINNING OF THE FIRST HYPOTHESIS Eien ("Well, then") . . . Ei `en ("If there is a One") The first hypothesis begins with a question and an answer that, taken together, amount to an assumption. Parmenides asks, if the One exists (or: if there is a One), the One could not be anything else, many, could it? Aristoteles answers, How could it? This is auto to hen, the Form of the One, One absolutely by itself. Very quickly (C5) we are launched upon the consequences of this hypothetical assumption. First of all, there can be no part of it, nor can it be a whole. How come? asks Aristoteles. And we find out very quickly that wholes imply parts; parts are many; therefore the One would be many, which we assumed it was not. >From this other consequences ensue, in the remainder of the first five arguments (137C5-139B3): no beginning, no end, therefore infinite (in extent), no shape, no place, no motion or rest. What sort of a One is this, then? (It sounds like the original One of the real Parmenides, doesn't it?) It is not physical, surely. It must be abstract: a Form. It is the careful distinction right from the outset that saves these consequences from the fate of those of the introductory part. In following the tortuous text, an outline may be some help to you. The One has no parts, nor is a whole 137C5-D3 has no beginning or end; is infinite D4-D8 has no shape, not round or straight D8-138A1 is nowhere, not in itself or another A1-B6 cannot move or rest B7-139B3 A word about these attributes of the One that we have started to list above, whole, part, limited, unlimited (finite, infinite), shape (straight, curved), place (in itself, in another), at rest, in motion, etc. You are going to see alot more of these. In fact, you might just get a bit tired of them. There are ten pairs of them, and Parmenides will use them to measure each of his hypotheses, although as we move along he seems to get out of breathe on this particular line, and he cuts it down somewhat. The second hypothesis will be the "worst" on this score, you will see. The ten pairs of "opposites" or tanantia, as Plato calls them, are whole part limited unlimited straight curved in itself in another at rest in motion same other like unlike equal unequal older younger in contact not in contact Where do these come from? Three of these pairs you will recognize having seen in the list of Pythagorian "sustoichia" given by Aristotle in A, Metaphysics, 986a24. Are they all Pythagorean pairs? Or possibly common coin of contemporary discussion? We have no way of knowing, but may guess that there is some tradition or other behind them. These first five pairs we are now looking at are all material attributes. If you think some of these problems, which may seem silly to us latter day readers, were not real problems to those fifth and fourth century Athenians, take a look at Aristotle's Metaphysics, Z, xvi, and I. At the end of the fourth century it still seems necessary to Aristotle to devote time to putting to bed the notion that the one was a substance! Plato's dialogues, the Euthydemus and others, also do so with other notions. This should tip us off to the way we should approach some of these passages before us. Sometimes they look like quibbles, but do not be too sure. (By the way, if you have been finding that my line references are slightly out of sync with yours, it is because I am not using the line references in the Loeb edition. Lacking a copy of Stepahnus' edition princeps - wouldn't that be a joy! - I am using what seems to me to be the next best thing: the present Oxford Classical text, John Burnet's edition. The differences are very slight.) 139B4-140D8 Hyp. I - The One vis-a-vis Relatives If the first five argumemts seemed fairly straightforward because they were obvious spatial or material characteristics that non- material abstractions would utterly lack, then the next three are different. They all have to do with relatives. The One is not same or other 139B4-E6 like or unlike E7-140B5 equal or unequal B6-D8 In each case, add "than (or "as" etc.) itself or others", doubling each. So to begin with, the first two alternatives become four. The One is not other than itself B5-6 same as another B7-C3 other than another C3-D1 same as itself D1-E6 We are probably comfortable with the first two of these because, even if it is a Form we are talking about, it is behaving like things, with which we are quite familiar. They can be said of things as well as Forms. It is the second two that compel us to consider this is the Form of the One under our eye here. Single things are other than another and same as themselves, but not the Form of the One. And other Forms may have relations, but not the Form of the One. It is just One, not other, not same. And Parmenides is careful to point this out: "so long as it is one", eOs an E hen (C4), and "but since itself is not other at all", auto de mEdamE on heteron (C8). It can have no relations. The second pair, like or unlike, doubled in the same manner, is argued on the basis of the first: likeness and unlikeness involve sameness and difference. to tauton pou peponthos homoion, "like is that which is affected in the same way," is the key to this section which seems somewhat simpler than the first. The One is not like another or itself E7-A6 Unlike another or itself A6-B5 The third pair, equal or unequal, begins with a definition of equality (B7-C4) in terms of measures (metroi). Then come the arguments themselves, that the One is not equal to itself or another C4-C8 < no sameness unequal to self or another C8-D4 where more or less measures C8-D1 < no parts where One is the measure D2-D4 < no equality You can see there on the right where he draws upon prior arguments. D4-8 is a recapitulation. The One is as devoid of relations as it is of matter and extension and all their attributes. It is something apart, alone, all One. But keep in mind that it is because it is both One and a Form that this is so. Forms that are not One, and ones that are not Forms may have these and other relations. Let me remind you: as we plunge deeper into the details of these hypotheses, you are going to have to return from time to time to the outline of the larger structure of each, and occasionally of all, if you want to avoid the feeling from time to time of being lost. The old saw about the forest and the trees is especially true of this dialogue. Here is an outline of the first hypothesis: If there is a one, It has none of the contrary characters. C4-5 The One is not other or many. allo ti ouk an eiH polla to hen. The One = absolutely One, nothing else. 142C2 calls it hen hen, One One. a. it has no parts, nor is a whole C5-D3 b. it has no beginning or end, is infinite D4-8 c. it has no shape, is not round or straight D8-138A1 d. it is nowhere, not in itself or another A1-B6 e. it cannot move or rest B7-139B3 f. it is not same or other, as (than) B4-E6 itself or others g. it is not like or unlike itself or others E7-140B5 h. not equal nor unequal to itself or others B6-D8 i. it is not nor becomes older or younger E1-141D6 or the same age, nor is it in time, nor has anything to do with time j. it does not exist or participate in being D7-142A8 nor IS one; there is no name, account or knowledge or perception or opinion of it. f., g., and h. are this week's text. We will enlarge this outline and structure, as we proceed from this one to other hypotheses. 140E1-142A8 TIME "The One has no participation in time whatsoever" We arrive at the question of time, 140E1-141D6. It is divided into two parts: the One IS not older or younger or the same age as itself or another 140E1-141A4 it does not BECOME older, younger or the same age as itself 141A5-141D6 The first part is founded upon the arguments of likeness and of equality and their opposites. The second addresses the question of becoming, since time is something dynamic as well as static. It is a flow as well as an instant or an extent. "Something in time is always getting older than itself", ean ti E en chronO, aei auto autou presbuteron gignesthai (141A6-7). Thus it brings up that question of becoming, as opposed to "is". Let us look at the second part, since the first reiterates now familiar ground, but the second brings up something new. After the preamble, it is structured thus: what becomes older than itself becomes younger 141B1-B2 explanation B3-C4 itself is being compared to itself older self is being compared to younger self yet it becomes for an equal time, & is, & will be C4-7 so what is in time is of the same age, and C8-D3 becomes older & younger than itself BUT the One does none of these D4-5 How could it? It is just One. Nothing else. It doesn't have a single one of these properties, alla mEn tO ge heni tOn toioutOn pathEmatOn ouden metEn, D3-4 (pathEmatOn = properties, accidents; see Liddell, Scott, Jones). This leads to the concluding argument of the first hypothesis, 141D7-142A8, that the One does not exist at all. We cannot even know it. (Here is a huge contradiction!) This argument is ostensibly based here upon the argument from time, just preceding. But that in turn leads us back to the very beginning of the hypothesis: the One is nothing but One, nothing else at all; otherwise it would be many. This would seem to be the real reason it does not exist, and what is to prevent us from jumping there right away? If it is absolutely One, auto to hen, the One by itself, how can it even be? (This of course raises the question of what is meant by existence. Do the kinds of knowledge mentioned in 142A offer us any hints? Sensation, opinion, perception are prominent. Naming and reasoning are mentioned. This would seem to be the ordinary sort of knowledge we are accustomed to, associated with things, with mundane reality.) Now Plato has his Parmenides here contradict what the real Parmenides had said nearly a century before: the famous One of the real Parmenides does not exist. Unless perhaps there is some other mode of existence than the one relentlessly rejected in this hypothesis. Do you think that Plato wrote this to contradict the real Parmenides, or was he rather trying to elucidate what the real Parmenides was really getting at? The real Parmenides, if you look closely, even contradicted himself, when he attatched several pathEmata to his One. So at least Plato would seem to think. Or do you take this all as evidence that Plato thought that Parmenides did not envisage an absolute, separate, what we would call abstract, One, because such a thing did not exist? Contradicted itself? You can, but I don't. It would only beg a number of questions that Plato seems to be trying to delve into here. Thus ends the first hypothesis. It raises the great question of an abstract One, a One that is not anything else or many: allo ti ouk an eiE polla to hen. Even if Parmenides, the real Parmenides, had not even faintly suggested this (and to me he did), surely Plato does here. The argument might look simple-minded to you, but nevertheless the insight is, as the saying goes, "on the beam". It must be re-iterated that these detailed arguments about the tanantia, which engross so much of our time and attention now, are not the main points of this dialogue. They may be supporting arguments and context, but Plato's main argument could be made without most of them. We are apt to lose sight of this while we are in the midst of them. The main argument is the double nature of the one, being and negation, their ambivalence. This will be revealed more in the overall structure of the dialogue, when we reach a point where we can view that. More than in the detailed arguments we are laboring under now. Nevertheless we are going to have to go through the detailed arguments. We cannot afford to dismiss anything that Plato says, and who knows what we may find? If this labor causes anyone to throw up his hands, it should be no surprise. To a newcomer they must look crazy. 142B1-145A4 Hypothesis II, The one is The second hypothesis is the longest of all. It comprises not quite forty percent of the lines of the dialogue. Why is this? In the first hypothesis we met one fundamental ambiguity. Here we will find numbers of them. It takes more time to show that the one does have attributes (and opposite ones, at that) than to show that the One does not. Lastly, time is the most ambivalent attribute of all. The one of Hypothesis II, it is immediately assumed, IS; hen ei estin, ara hoion te einai men, ousias de mE metechein (B5-6)? In case we don't get the point, Plato immediately makes it clear: is and one are not the same thing, hE ousia tou henos eiH an ou tauton ousa tOi heni (B7). And he pointedly distinguishes hen hen and hen estin (C3). These are the ones of hypotheses I and II respectively. They stand in stark contrast. 142B and C are pivotal lines. To begin with, the one of hypothesis II is a. a whole, with parts 142C7-D9 b. infinite and limited D9-145A4 c. has shape, round or straight A4-B5 d. in itself and in another B6-E6 e. moves and rests E7-146A8 These are the material attributes (the first 5 pairs of tanantia) we met together in the first hypothesis, 137C5-139B3. There the One had none of them. Here the one has all of them. a. The first argument that hen on is a whole with parts is short and clear. It reiterates the distinctive subjects of hypotheses I and II: hen hen and hen on. But one might well argue that being and one are hardly material parts. A rejoinder to this is that they are at any rate considered so here, and must be, unless one concedes the existence of immaterials as in the first hypothesis. The point is (and this is not a quibble) that either way one argues one must fall back upon a dichotomy of the one. One might also argue that the matter is obviously partible, if it is insisted that it be the subject of the argument here. These are of course our explicit arguments, not Parmenides' (Plato's). b. The scheme of the second argument is as follows: (1) the parts have parts, ad infinitum 142D9-143A3 (no recourse to numbers) (2) infinity of multiplication, using numbers A4-144A9 preparation of the argument 143A4-143B8 multiplication 143C1-144A9 (3) infinity of division, still using numbers B1-E7 (4) the one is limited E8-1454A2 (5) recap of hypothesis II to this point A2-4 (1) The beginning of the section on the infinite, 142D9-143A3 is fairly clear and simple, except notice in passing, that infinity is a positive attribute here (an infinite number of parts), whereas in the first hypothesis it was a negative attribute (no beginning or end). (2) Lines 143A-B appear at first to confuse hypotheses I and II, but they are merely a recapitulation of hypotheses I (auto to hen) and II (ho dE phamen ousias metechein), before adding ean auto tE dianoia monon kath' hauto labOmen, etc. What is this "one only in thought"? It turns out to be an intermediate one, the number one, an entity whose status was not quite clear at that time. Even Aristotle (the great one) was still calling number ta metaxu a generation later. In 143B Parmenides begins the evolution of this one into all number and infinity. Throughout much of this section of the text the distinctions are three-fold: One is not; one is; the (intermediate) number one participates in being somehow (ousias meteschen, B3). The continued evolution of infinity by multiplication follows: being and other, etc., are two, 143C1-144A9 and infinite number (a) they are both C1-9 (b) both = 2 D1-2 (c) both + each = 3 D2-7 (d) 3 is odd; 2, even D7-8 (e) 2 is double; 3, triple D8-E2 (f) 2x2, 3x3, 3x2, 2x3, etc. E3-7 (g) even x odd, odd x even, etc. E7-144A2 (h) this leads to endless number A2-5 (i) as well as to an infinite A5-9 multitude of beings Do not be put off by the seeming simplicity of that argument. It is not far from Georg Cantor's proofs of countably infinite numbers in the late nineteenth century. (3) In the next section, infinity by division (B1-E7), it does not occur to Plato here, as it would to you and me, that the number, one, can be divided into fractions. Instead, he gives us (a) the cutting up of existence into B1-C2 an infinite number of parts, (b) and of the one into as many, C2-D5 (c) go hand in hand, are equal and infinite D5-E5 (d) the one distributed among existents is many [and of course infinite] E5-7 So this number one connected with ousia is many and infinite. Plato would have been very uncomfortable with numerical division, and takes the alternative of dividing existing things, then relating numbers to them. (4) The one is limited (E8-145A2), on the up side, if not on the down side. Has the notion of limit changed from numerical to spatial? It seems so. A2-4 is a recapitulation. We are entering an area, in these detailed arguments about the attributes, in which there is much room for error or difference of interpretion, largely on account of the ambiguities involved. This is another reason why I am much more comfortable with the overall structure and symmetry of the dialogue, and with certain key passages (not difficult to identify) wherein Parmenides is stating assumptions or definitions, as he does at the beginnings of his hypotheses. Once again, please do not be put off by the seeming simplicity of these arguments. It is very easy to be so. But remember, in spite of their sophists and their philia sophias, those IV century B.C Athenians were not as sophisticated in some of these matters as you and I are. Evidence of that are their inability to conceive of fractions and their hesitation about what numbers are, their as yet incomplete "discovery of the mind," etc. 145A4-146A8 Hypothesis II - The material attributes, cont. The one that is (hypothesis II) has all the attributes, the pairs of contraries. It is a. a whole, with parts 142C7-D9 b. infinite and limited D9-145A4 c. shaped, curved or straight A4-B5 d. in itself and in another B6-E6 e. moves and rests E7-146A8 f. the same and other as itself and others A9-147B8 g. like and unlike itself and others C1-148D4 h. touches & does not touch itself & others D5-149D7 i. equal & unequal to itself & others D8-151E2 j. does & does not partake of time, be & become younger & older than itself & others E3-157B5 This is a long section, of which we have covered the first two subsections. We continue here with the three remaining material attributes: c. it has shape, curved or straight (A4-B5). This is based upon the prior arguments about the limited, and the whole. But note that they are now taken in their spatial or extended sense, not in their numerical sense. That such wholes have such parts as beginning, middle and end, is an intuition readily accepted here. Previously (in the first hypothesis) we translated stroggulos as "round", as does Fowler. "Curved" might be better. Curved and straight are accepted as two opposite typical shapes, from Pythagorean tradition (Aristotle, Metaphysics, 986a25, except stroggulos for kampulos). d. it is in itself and in another (145B6-E6). (1) it is in itself: the one qua parts B6-C7 is in the one qua whole (2) the one qua whole is in another C7-E3 (a) it is not in its parts (i.e. C7-8 wholly in, or in qua whole) 1) it is not in all, because D1-4 it is not (wholly) in any one part, en tini gar heni 2) it is not in some, because the D5-7 larger would be in the smaller (b) if not in its parts, one, many or all D7-E3 1) it must be in another D8 2) if it were nowhere, it would be E1-2 nothing (3) recap E3-6 Here is another ambiguity of the one (similar to the ambiguity of the collection and the individual): it can be a whole or a part. Furthermore, whole can be its parts, or not its parts. In section (2) there is a distinct meaning assumed for being "in its parts" (in = wholly in) which reflects this ambiguity. Then in (2) (a) 1), i.e. 145D1-4: not in all = not in all of all* not in any of all = not in any (all) not in any one* confounds the two starred meanings of "not in all." This is a briar patch, when you consider the compounding of ambivalences: the one qua whole and the one qua part, and the whole qua parts and the whole not qua parts (or whole qua whole). And is it all necessary? Is it not obvious that any thing is in itself, i.e. it occupies the space it occupies? And in another, since it must be somewhere (unless it is the whole universe)? Perhaps it is to you and me, but Plato chooses to argue these points in his own way, for his own reasons. However, his argument is valid, given his ambivalent criteria. e. it moves and it rests (145E7-146A8). (1) it is at rest (145E7-146A3) is derived from the recent argument that it is in itself (145B6-C7). (2) it moves (146A3-A8) is derived from the argument that it is in another (145C7-E6), but notice again an ambivalence: there it was an encompassing other; here, a separate other. By now you are probably ready to ask again, how much is Parmenides (Plato) playing games with Aristoteles and us here, or how much is he serious? Intentions are difficult to prove, although the games theory has been seriously advanced as an explanation for this whole dialogue. That strikes me as a "cop out". Certainly there are some serious points being made here, but Plato was not above mixing some fun and games with the serious. Other dialogues, not excepting the Euthydemus and the Sophist, for two, provide us with examples of this stylistic ambivalence of Plato's. At the same time, some of what may seem like fun and games may be pursued on account of the cultural naivete (from our standpoint) of Plato's wider audience. This brings us to the end of the material attributes. Next we will begin to take up the relational attributes of the one. 146A9-148D4 Hypothesis II - relative attributes, same & like, etc. Continuing with the attributes of the one, having done with the five material attributes, we now take up the first two of the relative attributes, same and other, like and unlike. f. it is the same and other as (than) itself and others, 146A9- 147B8. This section has five subsections: (1) same as itself B2-C4 (2) other than itself C4-D1 (3) other than others D1-D5 (4) same as others D5-147B6 (5) recap B6-B8 (1) same as itself (B2-C4): Is this all necessary to prove what seems obvious? Furthermore the argument as it is trades on ambivalent meanings and inconsistencies: (a) In 146B5-6 he asks, is the one part of itself? and the answer is no. Back in 142D4-5, near the beginning of this hypothesis, he asked, must not the existent one be a whole of which the one and being are parts, and the answer is yes. What has changed? In the first instance (142) the parts are one and being (hen and on); in the second (here) the sort of parts are not specified, but probably they are spatial or extended parts that are meant. (b) 146C1, Nor can it be other than itself. Certainly not (answers Aristoteles). This is immediately contradicted in the next sub-section. We may look for this. (2) other than itself (C4-D1): This argument seems to be based upon the argument d. of last week (145B6-E6), although en heterO there is exchanged for heterOthi here, creating an ambivalence of "in another place", inclusive there, exclusive here. This raises an important point: what is our attitude to be toward these short, detailed arguments, some of which seem quite shaky, if not eristic? Are we to reject them? Do they invalidate the overall argument of the dialogue? I do not think that they do. The main argument and the important argument of this dialogue does not depend upon some of these details, for which we could probably find better arguments anyhow. It is revealed in the overall structure of the dialogue. This dialogue is not a proof, but a dialectic. It is probably the product of an intuition. (3) other than others (D1-5), very brief, is a reaffirmation of the duality of otherness as stated in 139C4-5 (Hyp. I): others must be other than others. (4)same as others (D5-147B6): the main headings of this argument are as follows [my comments in brackets]: (a) the (absolute) Other can never be in the (absolute) Same (D5-8) [eliminating this as a possibility] (b) there is no existing thing in which other is, or other would be in the same (D9-E4) [over a time span] (c) other is not in the one or the not-one (E4-5) [these are eqivalent to same and other] (d) thus, not by reason of the other will the one and the not-one be different [other] from each other (E5-6) (e) nor by reason of themselves (E7-8) (f) they cannot be other than oneanother at all [lit: they wholly escape being other than oneanother] (147A2-3) (g) participation, number, part/whole relation are eliminated (A3-B3) (h) conclusion: they are same as oneanother (B3-6) Parmenides (Plato) does not consider the possibility that other can be same, and same, other, in the world of things, or one, not-one, etc. Note also, not-being as other is suggested here. g. like and unlike itself and others (147C1-148D4) has four subdivisions, slightly asymmetric: (1) like the others C2-A6 (2) unlike the others A6-C3 (3) like & unlike, another argument C3-D1 (4) like and unlike itself D1-D4 (1) like the others: based on (3) of f. above they are other than each other "to the same degree", mEte mallon mEte Etton, homoiOs. Aristoteles is a little slow to catch the drift of this argument (147D1-E6), and needs some explanation, but you won't. Is this brief interlude intended for dramatic effect? (2) unlike the others: this seems obvious, and you might think of simpler arguments than the one used, an argument from opposites. Here are the bare bones of it: (a) the one is the same as others (from f. (4) above) (b) same is the opposite of other (c) other is like the others (g. (1) above) (d) same must be unlike the others Rather than subject this to the analysis of, say, mathematical logic, let's just wonder why Plato used this tortuous means. (3) like and unlike the others: another argument, much simpler than the two preceeding, and parallel to 139E7-140B5 in the first hypothesis, excepting of course that, assuming an opposite one, it reaches an opposite conclusion. (4) like and unlike itself again draws upon sameness and otherness (f. above), parallel to 139E7-140B5 in the hypothesis I. 148D5-151E2 Hypothesis II, relatives, cont. h. it touches and does not touch itself and others (148D5-149D7). This argument was altogether lacking in the first hypothesis. The one (1) touches itself and others D6-E4 (2) does not touch itself E4-149A3 (3) does not touch others A3-D5 (4) recap D5-D7 (1) it touches itself and others (D6-E4) because it is in itself and others. Reference is to 145B6-E6: the one qua all the parts is in the one qua whole. (1) and (2) here use different reasonings for their contradictory results. (2) it does not touch itself (E4-149A3) because it would have to be in two places, therefore two, which it is not. This argument is out of place here, as we will see shortly below. (3) it does not touch others (A3-D5) because it takes two to touch. But the one is only one. However, this is not the one of the second hypothesis, which is two from the very beginning. It is the One of the first. And both these arguments, (2) and (3), are the sort of arguments that belong in the first: they are negative, or privative arguments. Have these passages, (2) and (3) slipped? Is this why they were missing in the first hypothesis? Did they displace something here by accident? It looks suspiciously so. But not surely. In such a dialectical conversation as this, would Parmenides (Plato) be above a covert appeal to the One of the first hypothesis here in the second? There remain many perplexities in these detailed arguments, and this is one such. i. it is equal and unequal to itself and others (149D8-151E2 is divided as follows. It is (1) equal to others D9-150E1 (2) equal to itself E1-E4 (3) unequal to itself E5-151A2 (4) unequal to others A2-B5 (5) recap B5-B7 (6) argument extended to number B7-E2 (1) equal to others: since most of our difficulties will be found in the first subsection, let us outline it briefly: (a) The Forms of Greatness and Smallness exist, and the one is equal, greater or smaller than others not by its own nature, but by virtue of them (D9-A1) (b) Smallness is not in the one (A1-B7) 1 in the whole, or it would be equal to it or greater (A3-B2) 2 in the part, or it would be equal to it (B2-B7) (c) nor is Greatness in the one; where no smallness, there is no greatness (B7-C6) (d) not greater or smaller, the one must be equal to the others (C6-E1) This is not only a roundabout argument from the negative, but it makes definite assumptions (probably erroneous) about the nature of participation, a process which Plato was hard put to explain. Surely Forms are not "in" things in the same manner as things are in things. Once more is begged the question of wholes and parts in participation (recall 131A), but with a difference: there it was whole and part of the Form; here, of the thing. Also, in (c) the question of the nature of comparisons is raised. Again, in all this you may suspect conscious trickery, or genuine puzzlement, or an effort to get his hearers to analyze these matters. Motivations are very, very difficult to prove, if even possible. You might like to know that Cornford (p. 171) calls this section "the hardest in the whole dialogue." The involved language may account for this. (2) equal to itself (E1-E4) calls upon the same argument (3) unequal to itself (E5-151A2) relies on argument d. of this hypothesis (145B6-C7), that it is in itself, therefore contained by itself, etc. (4) unequal to others (A2-B5) appeals to our common sense (5) recap (B5-B7) (6) these comparisons are extended to include number (B7-E2) We are a little more than half way through this dialogue. Haven't you ever been tempted to throw up your hands, and say, "This is a fraud," or some such words? Even if it were (which it is not), there is something more to this dialogue than these detailed arguments, whatever their meaning or merit. It will take younger minds than mine, and much time and effort to explain and evaluate these details. Meanwhile, my purpose is to pursuade us to take it all seriously, and to find our way through this thicket of arguments, without too much evaluation, and then to take a look at the whole when we have done with the parts. The whole, Plato's Parmenides notwithstanding, will turn out to be more than the parts! 151E3-155E3 TIME The ensuing section is the one I think (pace Cornford) "is the hardest in the whole dialogue", on account of the complexities presented by time. Notice right away that the One of the first hypothesis is not in time, while the one of the second both is and is not. There, it had nothing to do with the opposites; here, it has to do with both them, like the other attributes. In the case of time, this means the one does and does not partake of it. If we were to speak in the fashion of the other sections of this hypothesis, we might say that the one is timely and untimely, but that is awkward to our ears. It is this opposition that adds to the complexity of this section of this hypothesis. So do the many ambiguities of time. These are compounded by the facts that we may regard time subjectively or objectively, as a continuum or an instant, in two directions (looking forward and back), and in various other ways, as you will eventually see. It is enough to lead one to think that this is a climax of Parmenides' roguery. An outline will be especially helpful. Let us take time in two "bites": j(à) the one DOES partake of time, be and become 151E3-155E3 older and younger than itself and others (this week) j(á) the one DOES NOT partake of time, be and become 155E4-157B5 older and younger than itself and others (next week) j(à) it DOES: (1) become older than itself 151E6-152A5 (2) become younger than itself A5-B2 (3) it is older than itself B2-D4 (4) it is younger than itself D4-E3 (5) it is not and does not become E3-10 older and younger than itself (6) it is older than others E10-153B7 (7) it is younger than the others B8-D5 (8) it is the same age as the others D5-154A4 (9) it does not become older or A4-C5 younger than the others (10) it does become younger than the others C5-E3 (11) it does become older than the others E3-155B4 (12) recapitulations B4-C7 (13) there is knowledge, opinion, and C7-E3 sensation of it, a name for it, reasoning about it (1) it becomes older than itself (E6-A5). Time is a measure. each of us gets older every day; older = more time has passed. It is easily overlooked, that we get older, not time. (2) it becomes younger than itself (A5-B2): what is older from time's yardstick is younger from ours, and vice versa. We are older and younger than our grandparents (e.g.), depending on whether we use time or ourselves as the measure. (3) IS older (B2-D4): in the instant that is the present, it is whatever it has been becoming. Time is a series of instants as well as a continuum. In the instant it stands still. With this alteration, it is derived from (1). (4) and if it is older than itself, itself is younger than itself (D4-E3). (5) it is not and does not become older and younger than itself (E3-E10) because whatever it is or does, it is or does for an equal time as itself. Derived from i (2) above (150E1-4). (6) it is older than the others (E10-153B7) because one must precede multitude. The one here is considered as a number, and the ordinals as temporal. (7) it is younger than the others (B8-D5). Now the one is considered as a whole with parts, parts as if being assembled. There is also one nagging little problem. It is clear from the context that we have been for some time and are now dealing with the one of the second hypothesis, which Parmenides (Plato) has occasionally referred to as auto to hen. Usually this phrase is reserved for Forms, but he does seem from time to time to use it for ones that are things (153C3-4, D1-2, E6). (8) it is the same age as the others (D5-154A4). The one that was the whole in (7) is now a part. At 153C1 it has parts; at D6 it is a part; in each case, the subject of the argument. (9) it does not BECOME older or younger than the others (A4- C5). Older and younger now mean not difference in age, but a change in difference in age. Compared with (11) following, this is an absolute difference in age (say, so many years, or other unit). (10) it does become younger than the others (C5-E3). Younger now means a diminishing proportional difference in age, rather than absolute difference. The one becomes proportionally less older than the others, therefore younger. (11) it does become older than the others (E3-155B4). The others become proportionally older (less younger), from (10) just above. But being "born" later the others become less older than the one (reversal of viewpoint again, as in (2) above). Thus the becoming older become younger, and the becoming younger become older, both by this enantiodromia. (12) recap of (9)-(11), 155B4-C4, and of J(à), C4-C7. (13) (C7-E3) needs no further elucidation. It parallels 142A, the end of hypothesis I. The One of hypothesis I does not exist. The one of hypothesis II does, etc. This defines existence as described in hypothesis II. What then is the One of hypothesis I? If it doesn't exist, what does it do? Nothing? But why did we even speak of it, which we most assuredly did? Or think of it? What is speech; what is thought? Nothing? How un-Platonic! How un-Greek! We have seen that time flows or endures (1), and may be viewed in two directions, forward and back (2). "Older" may mean further back in the past, or something has been around longer; "younger" of course, the opposite. The first meaning would seem to be objective; the second, subjective, related to the subject. Time may mean an instant, rather than a duration (3). In (4) as in (2) one may reverse one's viewpoint. In (5) we revert from comparison of instants to duration again. In (6) time is treated as a number; in (7), as a whole, assembled of parts; in (8) as the parts. In (9) difference in age (as in older or younger) gives way to change in difference in age; and in (10), to change in proportional difference in age. (11) treats it the same, but reversing the viewpoint again. And there is more to come. 155E4-157B5 TIME, cont. "Let us discuss the matter once more and for the third time" That line brings up an important question. What does it mean, the third time? Is this a separate hypothesis, as the neoplatonists thought, making altogether nine? Cornford seems to compromise, calling this hypothesis IIa. I would urge upon you that "entia non sunt multiplicanda praeter necessitatem," and there is no need here to call this a separate hypothesis, of equal status with the other eight. What is this "third", then? It is the third approach to time in this dialogue: (1) in the first hypothesis, the One does not participate in time at all because it is transcendent, (2) in the second hypothesis, the one does participates in time, but is subject to the opposites, as we saw last week in j(à), and (3) here, it does not participate in time for a special and different reason than any given before: time comes to a stop in the instant of change. This brings in an opposite attribute of time, timelessness, as is done in the first and second, in their own respective ways. It does it here in another way. Last week, the one did not be or become older, younger, or the same age as itself or the others, just like the negative attributes heretofore (unlike, unequal, no beginning or end, no shape, and so forth). Now it does not participate in time because an instant in time is timeless in another sense: like Zeno's arrow, time stops in the instant. Notice he did not use this argument in (5) and (9) of j. (à); he used it in (3) but not in a negative. And it is timeless not because it is transcendent, as in the first hypothesis, but because this is a peculiar feature of time. It is, as you doubtless recognize, much of a piece with Zeno's puzzle about the flying arrow, the third of his paradoxes (logoi) of motion mentioned by Aristotle in the sixth book (Z) of the Physics, only here Parmenides argues that it is not just the arrow that stops, but time. This section is part of the second hypothesis. We can trace the following structure: j(á) the one does not partake of time, be and become 155E4-157B5 older and younger than itself and others (1) [the one changes] (a) the one is and is not one E4-E8 (b) there is a time when it changes from E8-156A4 being to not being, and vice versa (c) it becomes and decays A4-B1 (d) it divides and combines B1-B5 (e) it becomes like and unlike B6-B7 (f) it grows, diminishes, equals B7-B8 (g) it changes from motion to rest, C1-C2 and from rest to motion (2) [the nature of the change] (a) it is not in time, mEd' en heni chronOi C2-C3 (b) for the resting to move, or for the C3-C5 moving to rest, is change (c) there is no time when something is C6-C7 neither resting or moving (d) it cannot change without changing C8-C9 (e) therefore, it is not in time C9-D1 (f) the instant is not in time D1-E3 (g) the one changes from motion to rest, E3-E7 and vice versa in an instant, not in time (h) and this is true of other changes E7-157B5 The argument seems fairly clear, excepting only the opening lines. 155E4-E8 are ambiguous. This can refer to hypotheses I and II, or just to the second hypothesis. I do not think it will make any substantive difference, but prefer the latter, on account of the kai metechon chronou in what is in effect the subordinate clause of the protasis. Fowler's translation is off the mark in E6-E7 of the apodosis, hoti . . . hoti . . . I would translate, "must it not partake of being when it is one, and not partake of being when it is not?" In order to make smooth the course of the argument, I have supplied a couple of headers above in brackets. 157B6-159B1 The Third Hypothesis (with a glance at the fourth) Having come to the end of the first two hypotheses, it is a good time to pause and take stock. It appears on the face of it that, if there is a one, it does not exist (hypothesis I), and if there is a one, it is two or other or many (hypothesis II). That is a pretty pickle! What are we to do? I suggest that we welcome these paradoxes, and continue, seeing what happens. The introductory part ended in a dilemma raised by Parmenides: Forms raise grave problems, but we cannot do without them. The first two hypotheses raise particular problems of the most acute sort: the paradoxes described above. One could stop right there, and have a complete and self-subsistent dialogue, ending in a question or problem as Plato's often do, but Plato does not. He continues, and in six more hypotheses that follow he rings changes upon the theme of the first two. With this difference: notice that in the remaining hypotheses his treatment of the details of the attributes, the tanantia, are attenuated. We will begin to become more conscious of the hypotheses themselves, the assumptions and definitions and such. What does he mean by one, is, and not? Our growing problem is going to be not the fine details, but how to keep the four, six and finally eight hypotheses in view at once, in order to appreciate their contrasts. To this end some "skeletons" will be of help. These were supplied in "The Structure . . . ", and will be repeated here. To begin with, the order of hypotheses three and four reverses the order of one and two, in respect to absolute and particular, altho whether it is absolute or particular in each it remains the same. (Take note: this will change later.) IF the One is THEN the One is not (1) the one is it is many (other) (2) the one is the others are ones (3) the One is the Others are not One (4) We do know, from the framing of the hypotheses themselves, as well as from the ensuing treatment, that they deal with Absolute or particular as shown there. But why the reversal of order? In any case, we are faced with more paradoxes: not only is the one not, and not one (but many or other) (1-2), but now the others (if there is a one) are one, and have nothing to do with the one (3-4). Is there a clue there to the resolution of these paradoxes? What kind of a one is not, and what kind is many? What kind of other is one, and what kind is not? Meanwhile, an outline of the third hypothesis: III. the others are not one, because they are 157B6-159B1 others, but they do not wholly lack unity; they participate in it somehow (157B8-C2). They have all the contrary characters. a. they have parts, parts are parts of a whole C3-158B4 b. they are infinite in number and limited B5-D8 c. they are like and unlike E1-159A6 d. they are subject to all the other tanantia A6-B1 In hypothesis III the others are not a whole, but belong to a whole, thus partake of unity. Don't be fooled by that word, "partake" (or participate, metechei pEi). It means being, in one of its modes. Like the one, and the others, so also absolute Participation is not Being, but actual participation is being. If they participate in unity "somehow", they ARE one(s), in spite of what he says below (157E5-158A4 and B1-2) ambiguously. a. parts. Why do the others partake of, or participate in unity somehow? 1. they have parts 157C3-C4 else they'd be one, not others; parts are parts of a whole; C4-C5 a whole is one C5-C8 2. each cannot be part of many, or it would be C8-D2 part of itself and each of the others: impossible 3. if not a part of one it will be part of others D3 so not a part of each [any] one D4 so a part of no one of the many D4-D5 if of none, it is not a part at all D5-D7 4. it is a part of some one idea we call a whole D7-E2 5. So the others than one must be a whole, E2-E5 having parts [and, as we saw, a whole is one] Parmenides goes on (E5-158B4), to say that the mere use of the word, "each", implies unity, and then he continues, to distinguish participation in one from being one. The relation of Forms and things and participation is precisely what this whole dialogue is asking about. Here the one that the others are other than, is the One they participate in (metechoi tou henos, A3-4). In this fashion they are ones, too. Did we need to go this long way around to show that wholes and parts participate in unity somehow? Doesn 't "each" imply that it is one (158A1- 2)? What is more, is it not quite clear to common sense that in the world of things (participants) others are ones, both individually and collectively, although they are not ones in another sense? Doesn't it begin to look as if you can't separate the others and the one, even if you must separate the One and the Others? b. infinite and limited (158B5-D8). 1. infinite depends again upon the ambiguous status of participation: the participant is not a Form, but is a participant. But until it becomes a participant (whenever that could be) it has no sort of unity whatsoever (158B8- 9, allo ti . . . metalambanei). Others, without any participation in unity, presumably before participation would be ungoverned multitudes, and infinite. We can imagine the smallest "subtrahend" would still be a multitude, lacking any unity (C2-C4). 2. limited (C7-D8), shifting our notion of limit from number to extension, is easy to see. If we stick with number, a part's limit would be its unity that it participates in. c. and d. (158E1-159B1) are based explicitly on the foregoing, and should cause little difficulty in themselves. I repeat: we have had a new dimension of complications introduced here in hypothesis III. Participation in being is treated here as distinct from being. It was a kind of being in II. It is indeed both, ambivalent. Participating being is the being of palpable things. Participated being is the absolute being, the Forms (whatever the status of those might be). Plato is having his Parmenides play the game both ways here in hypotheses II and III. Notice that other is subtly introduced here as the equivalent of "not". Others, being other than one, are not one. But others are a special kind of negative, that in another sense is. "Not" is as ambiguous as being, as we will see again another day. Notice also, in passing, Plato's phrases, hen ek pollOn (157C6) and hen teleion (157E1 and E4). These are his words for what you and I now call a "collective unity" or a "collective one." 159B2-160B4 Hypothesis IV is short. It is like hypothesis I: in I the One was utterly separate from being (and everything else). In IV the One is utterly separate from the Others. Again it is alone, the absolute One, the Form of the One. The Others also, since ouk esti para tauta heteron (B7-8), are also thoroughly separate, absolute, a Form. We are left with another problematic paradox there: there could be no unity of the Form of the Others, where the Others had nothing to do with the One. Oudepote ara en tautOi esti to hen kai talla (C3-4). The text is rather explicit here. You can also conclude that there are no things. Fowler's "we have included all things" (C1) is not quite correct. A better translation is "we have said it all," or "all has been said." It should be no surprise that the Others here suffer none of the tanantia, but perhaps a bit of a surprise that they are not even many, or any number, in addition to not being one! (One is tempted to ask, if they are not one and not many, what are they?) By now however we should by now be inured to surprise by such a paradox. (Again, we must remind ourselves that there is a sense in which they are not One, and a sense in which they are.) That they are not like or unlike follows for anything so devoid of number and many- ness. Plato at 159E5 and 160A1 uses the words eidE and eidous, which Fowler probably does well to translate as "elements", since it seems unlikely that the usual Platonic sense of Form is meant here. The others cannot partake of any of the opposites, if utterly lacking in unity, tou henos ge pantEi pantOs steromenois (160B1). Here is an outline of hypothesis IV: IV. the Others and the One are utterly separate 159B6-C4 a. they are not parts or wholes C5-D3 b. they are not one or many D3-E1 c. they are not like or unlike E2-160A3 d. they have none of the other tanantia A4-B2 e. recap of the first four hypotheses B2-B4 e. The recap reads, "If one exists, the one is all things and nothing at all in relation both to itself and to others" (160B2-3). houtO dE hen ei estin, panta te esti to hen kai oude hen esti kai pros eauto kai pros ta alla hOsautOs, is what Plato says, but it is not quite what he has explicitly shown. What he has shown is that, if there is a one, or if the one exists, then: I. the One is not many, and does not even exist II. the one does partake of existence, and is many III. the others do partake of unity IV. the Others has nothing to do with the One. Yet it is not difficult to construe Plato's meaning thus. The first and fourth hypotheses have to do with Forms: they are absolute. The second and third, with things: they participate in, or partake of existence or unity. That, in simplest terms, explains their contradictions. What are Forms? What is participation? These are the questions that these hypotheses inexorably drive us toward. They have often been given confident and quick answers, but such answers will not do. To say that they are paradigms, or to give them other names - universals, classes, sets - begs the question, what those are. Curiously, Socrates once tried to give an answer that rings true to a modern mind, but this was quickly brushed aside (132B-C). Plato clearly was not prepared for this, and the question remains here, at the completion of the first four hypotheses: What are Forms? We have been shown that the ambiguities of one, others, whole, part, and some others, even participation, can be explained only by distinguishing their absolute and their particular modes. Their particular modes are somewhat more tractable than their absolute. What is being by itself? What is "anything" by itself? What are Forms? We are at the limit of ancient philosophy here, Plato's, Aristotle's, anyone's, although we are not at the limit of philosophy altogether. The Parmenides leaves us with this question (what are forms?) that no one answered satisfactorily. Not Aristotle , not the medieval scholastics, not "modern classical philosophy," Descartes, Locke, Berkeley, Hume. The nature of activity and creations of the mind, which Forms surely are (where else do you find them?) is still being debated, but at least we know WHERE they are. Plato started us down this road. We have only gone this much farther, after much travail, that we recognize this as the mind-body problem. What are Forms? = what is mind? AI (artificial intelligence) enthusiasts and their opponents to the fore! Plato at least admitted here an irreducible dichotomy. 160B5-163B6 Hypothesis V The opening lines of this hypothesis (160B5-C7) explicitly state a new ambiguity of primary importance, the ambiguity of "not being". Here not being = being different. heteron ti legoi to mE on. This heteron ti is some thing that is not some other thing. It is the participative, concrete, palpable sort of being. (Compare Sophist, 257, where it is Forms that are under scrutiny.) The one thing that is not IS a this one, and IS NOT some other one. It is a particular one (160C7-161A5). It is some known thing, therefore different (C7). There is knowledge of it (D5), or you don't know what is meant when someone says "if there is not a one" (D5-6). This is repeated in D8-E2. This one-that-is-not participates in "that and some and this" etc. The mE on that participates is a thing, but participants participate in Forms. eiper ge mE esti, metechein de pollOn ouden kOluei, alla kai anagkE (160E8-161A1). One of the many Forms participated in is the Form of the One, and that is why THIS one-that-is-not is known. So we have here on the one side (protasis) the not-one that is a thing, and on the other (apodosis) the One that is a Form. In each of the first four hypotheses the subjects of the two clauses maintained their mode of being throughout the two clauses. Now they switch modes. I abbreviate severly, concentrating on the subjects, using O and o to distinguish absolute and particular modes, to illustrate: If Then I. One One (not) II. one one (many) III. one others (ones) IV. One Other (not One) V. one One (is) If the one that is not, that is different, etc. is something known, a Form, there has to be an opposition of modes: if we take it that the not-one IS known as the text clearly states, it has to be some other mode of being that is known. If the not-one is a thing (also clearly stated), that other mode must be a Form. It might be vice- versa, if it were not made clear several times that the not one of the protasis is a thing, heteron ti. To sum it up, we can now see after five hypotheses that there are two modes of not (existential and otherness), as well as of one (absolute and particular), of being (Form and participant), and of other. Here is an outline of hypothesis V: a. not one = different; is something known 160B5-E2 b. not one partakes of many (Forms) E2-E7 c. recap E7-161A5 d. has unlikeness, to others A6-B4 e. has likeness, to itself B4-C2 f. participates in inequality C3-D1 g. and in equality, greatness, smallness D1-E2 h. and in being as well as non-being, E3-162B8 i. moves and remains still, B9-163A7 changes and does not change j. it does and does not come into being A7-B6 and pass away The not-one participaties in the attributes, conformably to the fact that its mode of being is one that partakes of a Form (b. above), but it no longer is or partakes doubly, both in respect to itself and others, as it did in the first two hypotheses. Its unlikeness is to others; its likeness, to itself. a. "one does not exist" is not only different, but the oppositely different (pan tounantion) from "not-one does not exist" (B5-C2). The latter (mE hen mE estin) negates the existence of the "not- one"; the former (hen mE estin) merely says it is something else (heteron - C4). (1) "one does not exist" is the opposite of B5-C2 "not one does not exist" (2) "one does not exist" = is different C2-C7 (3) it is something known C7-D6 (4) and different D6-E2 b. this not one, or one that does not exist, partakes of many (Forms), of this and that & so forth (E2-E7) c. recap (E7-161A5) d. has unlikeness to others, on account of difference (A6-B4) e. has likeness to itself (B4-C2), or this discussion and hypothesis wouldn't be about such a thing as the one, but about others. f. partakes of inequality, because it cannot be equal to the others, or it would be like them (C3-D1). g. and partakes of greatness and smallness, on account of its participation in inequality; and of equality, since this is between (metaxu) greatness and smallness (D1-E2). h. (161E2-162B8) And so finally it partakes of existence somehow, ousias ge dei auto metechein pE (E3). Notice that "somehow", pE! A little word, pE, fraught with significance. The association of being with truth (E4-162A1) is offered as the reason. Interesting enough (and foreshadowing Aristotle's Metaphysics, E, iv, and Theta, x), but it is the stunning remark that follows (A1-2) that should arrest our attention: estin ara hOs eoike to hen ouk on, "the non-existent one exists, it seems". What a startling contradiction of the real Parmenides that is! Being and not being are dependent upon each other. To say not-being is not, you have to use "is" (ti tou einai anEsei pros to mE einai). There is a bond (desmon) between between negative and positive, between mE einai and einai, seen in the balanced periods of A7-B3, especially in metechonta . . . to de mE on . . . ousias de tou einai mE on. i. it has motion and rest, changes and does not change (162B9- 163A7). In view of the close association of the various verbs for motion and change, let us outline this carefully: (1) Being > not being = change (metabolE) B9-B10 (2) change = motion (kinEsis). It moves. C2 (3) but not being is nowhere C7 (4) nowhere, it does not change in place C8-D1 (oud' an methistaito < methistEmi; metabainein) (5) it doesn't turn (oude strephoito) D1-D5 (6) it can't change into something other than itself D5-D8 (oud' alloioutai), or it wouldn't be one (7) ergo, it must be at rest D8-E2 (8) recap: it is both at rest and in motion E2-E3 (9) it changes and does not change E4-A7 (associates once more change and motion) He has linked six different kinds of change here: metabolE (change of condition), kinEsis (motion), methistEmi and metabainein (change of place), strephesthai (rotation, i.e. change in place), and alloiousthai (alteration). These were traditionally mixed up. j. it does and does not come into being and pass away (gignetai, apollutai), since it does and does not change (A7-B6). To recapitulate, amid the details do not lose sight of the main thrust of this hypothesis. The one that is not partakes of being, and is not and is "somehow." That "somehow" (pE) is perhaps the most significant word of all here. The being that this one that is not is, or partakes of, must be a Form. Its oneness must be a Form. It is known. It is participated in. 163B7-164B4 Hypothesis VI This hypothesis is short, a page in Stephanus' text, a page and a half in ours (Fowler, or Burnet). And it commences with a clear cut contradiction of the preceding hypothesis V: "Does the expression `is not' denote anything else than the absence of existence in that of which we say that it is not?" to de mE estin hotan legOmen, ara mE ti allo sEmainei E ousias apousian toutO O an phOmen mE einai; (163C2-C3). It "mean[s] without any qualifications that the non- existent is not in any way, shape or manner, and does not participate in being in any way," haplOs sEmainei hoti oudamOs oudamE estin oude pE metechei ousias to ge mE on (C6-C7). How emphatic can one be? Here is the absolute negative, the absolute not, absolute not being. In "if there is not a one" there is no longer any distinction of the one that is not and the not one that is not, upon which to build a participation in being because the one is something different and known, as was done in hypothesis V. Here in VI the supposition is that it just plain is not, period. That is the end of it. Absolute not being (VI) stands in contrast to the not being of a particular not being (V). Again the hypotheses are paired, V dealing with a particular not; VI, with an absolute not. Protasis Apodosis V one One VI One ? What will be the conclusion, the apodosis there? Very quickly we are led to understand that the One that is absolutely not (protasis) a. neither perishes nor comes into being (163D1-D8) b. nor moves nor rests (D8-E6) c. nor do greatness, smallness, equality, likeness, unlikeness, difference or anything else pertain to it, in short none of the attributes (tanantia) (E6-164A7) d. nor of that, to that, some, of this . . . of another, knowledge, opinion, perception, account, name or anything else. "The non-existent one has no state or condition whatsoever," or "doesn't exist in any way whatsoever," houtO dE hen ouk on ouk echei pOs oudamE (164A7-B4). Of course this is true of the Absolute One that is not, but having already said that in the protasis, this must extend to particular ones in the apodosis. V one One VI One one This may have looked like a tautology momentarily: if the One does not exist in any way whatsoever (163C), the one does not exist in any way whatsoever (164B). But it is not tautologous, due to the change in the status of the one: if there is not a One (Form), there is not a one (not one thing). Of course, there are others, as we will shortly see (in VII). And so in other hypotheses: in the first, the Absolute Oneness of the One (137C4) precludes existence, and the conclusion is that it doesn't exist (141E9-10). In the second hypothesis the one partakes of being (142B6), and has all the attributes that other beings have (155E1-2). Only in that peculiar attribute of time ("to triton"), in the instant, does it lack some of these. This was long a puzzle to the Greeks, at least until Aristotle's solution in Book VII of his Physics, 239b7, the incommensurability of the continuum and the point, ou gar sugkeitai ho chronos ek tOn nun tOn adiairetOn, hOsper oud' allo megethos ouden. Thus the long excurse on this unsolved puzzle. In the third, if there is a one, the others are not the one of the protasis (157B9), but they are all sorts of things (159A7-8), i.e. other ones. In the fourth the others are separate (159B6-7), so they are utterly deprived of unity (160B1-2). In the fifth, the one that is not is different (160C4). This hypothesis goes on to assign this not-one-that-is-different contrary characters, not all of them to be sure, but enough to assure it being and not-being (161E ff.) That not-being is difference. In the sixth the One is absolutely not (163C), as we have just seen, so it has no state or condition whatsoever (164B), not even as a participant one thing. In Kantian terms, I believe, these arguments are analytical. They draw out the implications in the initial assumptions, albeit in different ways. In doing so they lead us back to those assumptions, and consequently to their differences. It is the different readings of these protases, the different statuses of the one, that enable us to draw different implications. These different implications, paradoxes if you will, will eventually direct our attention to the structure of the whole list of eight hypotheses. 164B5-165E1 Hypothesis VII Hen ei mE esti, talla ti ChrE peponthenai; The last two hypotheses are made especially difficult to understand by their double negatives of one-that-is-not and other. In the seventh hypothesis everything seems to dissolve as if into a dream, hOsper onar en hupnO (164D2), before disappearing altogether in the eighth, where we don't even dream. If there is not a one, what are we to say of the others (also not a one)? It seems as though we could say anything we want of them. They exist somehow (VII), and they do not: they are not even conceivable (VIII). It is obvious that, if there is not one thing, there are other things, but the text of VII (allElOn ara esti, etc., 164C5, ff.) might seem to indicate that this is not what Plato meant, since these others are only other than others, and there is not a one. But those others that the others are other than, would be ones that are things, things that (we will shortly see) have no status (cannot even be conceived) without Form. Moreover, if this is all like a dream, who can say for sure? Some semblance of unity does occasionally creep in here. The one exists, to some extent (pou), as can be seen at several points in the ensuing text. Also, for Plato the world of things was not the real world anyway. In hypothesis VII, the others, if there is not a one, a. exist 164B5-B8 b. are different B8-D6 c. masses will appear to be one, but are not D6-D8 d. they will appear to have number, but do not D8-E3 e. the smallest will seem great E3-165A1 f. and will seem equal A1-A5 g. and will seem limited and unlimited A5-C6 h. and will appear like and unlike C6-D4 i. and same, different, in contact and separate, D4-E1 moving and resting, becoming and perishing and neither a. (164B5-B8) they must exist to some extent, alla men pou dei auta einai, because if there were not others, there would be no speaking of them. Does this sound familiar? It seems very like 161E2-8 in the fifth hypothesis, where Parmenides was saying that the one that is not must exist somehow (pE), or ouk an alEthE legoimen, etc. Although Plato is not yet prepared to locate Forms in the mind, as you and I might do, clearly here they are needed as objects of speech, and thought. This is a "somehow" or a "to some extent" existence. b. (B8-D6) they are different. Different is different from different; other is other than other. They aren't other than one, since there is no one. They are other than each other, in large numbers, unlimited masses whose smallest piece dissolves into a multitude, AS IN A DREAM IN SLEEP, hOsper onar en hupnO. This repeated dissolving of dream images is very true and apt. You must have had this experience yourself. c. (D6-D8) The illusion continues: there will appear to be many unit bulks of them, but there are not. polloi ogkoi esontai, etc. This word, ogkos, is very special here. The context is Zeno's fourth puzzle, as reported by Aristotle in VI Physics, 239b35- 240a19. The ogkoi there are objects of an unspecified sort, passing each other in the stadium. They have mass (bulk), motion, unity, countability. It is their indivisibility that counts there, in contrast to their infinite divisibility here. Is this an intentional reference to Zeno, and refutation, on Plato's part? d. (D8-E3) There will appear to be number, but this is another illusion. [How can there be number without units?] e. (E3-165A1) Size disappears in infinite divisibility. The smallest will seem many and great, compared with each of the many small "quotients." f. (A1-A5) Each bulk will seem equal when passing from greater to smaller, since it has to pass through the between-state (to metaxu), but this is just an appearance (phantasma). g. (A5-C6) And seem to have limit and be unlimited (1) (A4-B5) to have limit vis-a-vis another bulk, but no beginning, end or middle vis-a-vis itself, on account of our not being able to conceive of one of them if it has no unity, dia to mE dunasthai henos autOn hekastou lambanesthai, etc. (2) (B4-B7) the whole of being must be cut into pieces, if someone is to think of it, or it would be a bulk somehow without unity. (3) (B7-C3) seen from far away it seems one; from close by, infinite. (4) (C3-C6) recap And so forth. The remainder of the hypothesis poses no difficulty. But in passing here, notice that Forms are needed, to impose limits and definiteness upon things, especially the Form of the One here. If there is not one thing, there are other things, to be sure; but with no Form to "control" them, these other one things lose all definition and even whatever unity they might have had and needed, for them to be grasped by our minds (en tEi dianoiai). This of course is not the way things are, so there must be Forms, and a Form of the One first of all. 165E2-166C5 HYPOTHESIS VIII Hen ei mE esti, talla de tou henos, ti chrE einai The last hypothesis, the eighth, takes a view contrary to VII. The others are not one, nor indeed many, hen men ouk estai talla . . . oude mEn polla ge. If none of these [others] is one, they are all nothing; so they aren't many, ei gar mEden autOn estin hen, hapanta ouden estin, hOste oud' an polla eiE (E4-7). Their nothingness is emphasized by the striking repetition of oudamE oudamOs oudemian koinOnian tOn mE ontOn (166A2) and oudamE oudamOs (A6). Altogether the preamble of this hypothesis assumes the utter nothingness of the one and the others, not being of every conceivable kind (165E2- 166A4). They do not even seem to be, or even to exist to some extent (pou), as they did in VII. a. there is not even any notion (doxa) of not- 166A4-166B3 being for the others, or any phantasm. No way can you think anything at all of them b. they are not like or unlike B3-B4 c. nor same or different B4-B5 d. nor touching or separate B5 e. nor anything else we said they seemed to be B5-B7 f. to sum up, if there is not One, there is nothing B7-C2 It hardly seems necessary to insist on the absolute negativity of all that, and the absoluteness of the One that is not (protasis). All that is left is Parmenides' ostensible conclusion (166C2-C5): hen eit' estin eite mE estin, auto te kai talla kai pros hauta kai pros allEla panta pantOs esti te kai ouk esti kai phainetai te kai ou phainetai. - alEthestata. "Whether the one is or is not, it and the others, relative to themselves or each other, all in all ways are and are not, and appear and do not appear. - Most true." But is this what he has really shown? It is a clever summary that conceals more than it reveals. WHY are and are not the one and the others all these things that it says they are and are not? Why is it that the one does not exist, and does exist (I and II)? Why do the others participate in unity and have nothing to do with it (III and IV)? Why does the one-that-is-not exist as something different, yet not exist at all (V and VI)? And finally, why do others than the one-that-is-not exist, and not exist (VII and VIII)? What are we to make of these contradictions? There is a simple answer. In each pair of cases, the one or the others are taken to be on the one hand absolutely, as a Form, an Idea, and on the other hand particularly, as a thing, a material thing. There is a place for Socrates' Forms after all. But they produce some strange results: a Form of the One that does not exist (unless of course we revise our notions of existence) (I), a Form of the Others that is not unitary (as otherwise Forms might be expected to be) (IV). Forms pose problems. On the other hand, if there is not a Form of the One, there is nothing (VI, VIII). The particular ones give us no such trouble (II, III, V, VII). If we are going to grasp these changes and contradictions, we are going to have to get in mind the eight hypotheses all at once, and compare them. There is only one way to do it. Forget all the arguments we have gone through one at a time. Look at the eight hypotheses more or less bare, and their suppositions and implications, in relation to each other. Ei hen estin, if there is a one 1. allo ti ouk an eiE polla to hen. The one could not be anything else or many - 137C4. It is the absolute One; it cannot even be! oudamOs ara esti to hen - 141E9-10. It is a Form. 2. Hoion te auto einai men, ousias de mE metechein? - 142B6 It partakes of being. Also it has parts, is many - 142C9-D1. Such are things. 3. Oute to hen esti talla . . . oude mEn steretai ge pantapasi tou henos talla, alla metechei pE. The others are not one . . . but they do not wholly lack unity, but participate in it somehow - 157B9-C2. These are things. 4. ChOris men to hen tOn allOn, chOris de talla tou henos. The one is separate from the others, and the others from the one - 159B6-7. Absolutely. They are Forms. Hen ei mE estin, if there is NOT a one, 5. Pan tounantion estin eipein, ei mE hen mE esti tou ei hen mE esti. The not-one is not is opposite of the one is not. heteron ti legoi to mE on. The one-that-is-not is something different (not being is difference) - 160B8-C4. There is knowledge of it (D5). It partakes of many [Forms], metechein de pollOn ouden kOluei, alla kai anagkE (160E8-161 A1). It is a thing. 6. [hen mE esti] haplOs sEmainei hoti oudamOs oudamE estin oude pE metechei ousias to ge mE on. It simply means that it does not exist in any way whatsoever, nor participate in being - 163C6-7. This is Absolute Not Being (a Form). 7. alla men pou dei auta [talla] einai . . . ouk an peri tOn allOn legoito. The others must exist somehow, or we couldn't speak of them - 164B6-7. They are different, ta ge alla hetera estin - 164B8. If "the one is not" = "the one is different", there are particular others, other than particular ones that are not (other particular ones). All of these must be things, which by themselves would be phantasms in Plato's scheme. 8. The others have no communion in any way whatsoever with anything which is [absolutely] non-existent, talla tOn mE ontOn oudeni oudamE oudamOs oudemian koinOian exei (A2), nor is the [absolutely] non-existent conceived of in any way whatsoever as related to the others, oude doxazetai oudamE oudamOs to mE on epi tOn allOn (A6). The non-existence in these two statements has to be absolute; if it were not, there could be others. These are Forms. We have summarized the hypotheses above, to make them easier to understand. Let us tabulate them even more concisely to make them still easier to recall. In the following table the upper case "O" indicates the Form of the One or the Others. The lower case "o" indicates the particular, or the copy. If: 1. One is Then: One is not 2. one is one is many 3. one is others are ones 4. One is Others is not one 5. one is not One is 6. One is not one is not 7. one is not others are 8. One is not Others are not The protases may be remembered easily by this device: OooO oOoO, and that should get you started. The rest follows easily. It seems a silly way to do things, perhaps, but it works. These eight hypotheses are, after all, simple, structured and symmetric. What are we to conclude from them? (Form (Form (Form Existence = ( One = ( Not = ( (copy (copy (copy What IS existence? What IS a Form? In today's view of these matters Plato's Forms are clearly products of the mind. We have outlived the mystery and the religious associations. But we have not outlived the mystery of the mind. In our very mechanical climate of opinion many of us refuse to credit mental phenomena with any more existence than the physical apparatus of the brain. Others think differently. Argument on this point has not stopped. It is what we call today the "mind-body" problem. This is the present version of the problem raised by Plato, and implicitly by Parmenides, nearly twenty five hundred years ago, and subsequently raised in many ways in the intervening centuries. We are long past the point of concern whether this dialogue supports or refutes the real Parmenides, or even important elements of Plato's doctrine itself. It does all of these in various places. But Forms entail as much difficulty as they solve. For Plato they were not a finished doctrine, much as many of his followers liked to make them seem to be. They were an unsolved aporia. THEY REMAIN SO. SUMMARY I continue the search for various devices to help us see the overall arrangement of the eight hypotheses. Here is another scheme, a condensed summary of what Plato says in the beginning of each of them. This is an effort to extract key notions that are his notions, not ours, and see them all together. My interpretation is in brackets at the right. If there is a one, [it/they is/are] is not Absolute [Form] one is partakes/being [thing] are one[s] partake/unity [things] others are not one Absolute (separate) [Form] If there is not a one, is somehow different & known [thing] one is not absolutely [Form] are somehow different & known [things] others are not absolutely [Form] I cannot be briefer. In hypothesis I "is" is treated as another entity than "one," and one is absolutely alone. In II and III Parmenides (Plato) says explicitly that it partakes of being or unity (metechein). In IV he uses the word, "seperate" (chOris). And so forth. In the negative hypotheses he uses the words, heteron and and oudamOs oudamE, etc., to distinguish the different from the absolute. Forms (Ideas) and their copies (things) are different modes of being. What is the pertinence of that observation to us, here, now? We no longer, most of us, consign Plato's Ideas to some heaven or other place, preferring to find them in the mind. But what is mind? This is a now the argument. Is it the brain, an algorithm as the AI people claim, or some other sort of physical function, as others claim? Or conversely is it an utterly disembodied function of the sort that mystics embrace? There is a third alternative. It might be something sui generis based upon physiological brain function yet not just that. It might be a "bootstrap" invention of mankind, discoverable in his history, in his literature and philosophy, a spontaneous creation, based upon but nevertheless transcending the brain, no less real for its immateriality. It is most peculiarly characterized by the power of abstraction. Abstraction is difficult to deal with. There are problems with abstraction: (1) it can mean either (a) removal to some other physical place, such as a heaven or what you will, or (b) removal from the physical and concrete altogether into the mind, conception. This ambiguity will be met head on in Aristotle's Metaphysics. (2) another problem is that we all of us find abstractions difficult to hold on to. We prefer concrete images, whether of God, of numbers, of the world (as in the physics of Galileo and Newton), of anything. Parmenides' One and Plato's Ideas were abstractions which subsequently became re-concretized. We all tend to regress thus, and to rematerialize our abstractions. Their discovery (so far as our record shows) was made initially by Parmenides, and then more clearly by Plato in the Parmenides and other dialogues. But this was lost sight of, and the One and Ideas were hypostasized, turned into some special sort of THINGS. Such is the perennial temptation! I repeat: even Aristotle succumbs to it in his Metaphysics. (3) Finally there is the difficulty of keeping our eyes on the main issue. As any devotee of "Western" movies can attest, mankind loves a contest between opposing forces. Plato's contrast of Ideas and things lent itself to such a categorization. It became a staple of Christian doctrine, and a truism of the history of philosophy. Do you think this was what Plato intended, or was it our own pleasure to interpret him so? One may interpret the Parmenides thus, but it leads us, it seems to me, in the direction of neoplatonism. Here I have preferred not to. The Parmenides raises profound ontological and epistemelogical problems that should have priority over the ethical and the commonplace. CONCLUSION What does this mean for philosophy? It offers a fresh view at a time when old ones have become stale cliches. Logic and metaphysics have no life left in them. The Parmenides offers an exciting vista of a new sort of logic, a logic of paradox, and a new sort of metaphysics that reflects the double nature of man, la condition humaine. And this happens at precisely the time when we need to rethink such questions as: what are the foundations of the human sciences? How do we think about human problems? In the same way and with the same method that we use to think about physical problems? I challenge that! The ultimate fact of human existence is its double nature. It is a bundle of paradoxes, at the root of which lies one great paradox. It is at once physical and mental. Mind is dependent upon the brain and the rest of human physiology, but it is also something utterly independent. What else are abstractions but just that? Paradox has heretofore been a stumbling block for logic from the times of Eubulides and (reputedly) Epimenides, to our time. Modern mathematics sought to evade it by revising the rules. There is no need for that. One can acknowledge an antinomial logic of paradox that meets our nature and our need. There are many traces of it, in fact, in our literary and philosophical tradition. Even the fountainhead of our tradition of metaphysics, Aristotle's Metaphysics itself, is a great paradox. Shall we take a look at it? E. F. Little 8/3/95