THE STRUCTURE OF PLATO'S PARMENIDES Edward F. Little (c) Copyright 1982, 1986, 1989 Edward Filene Little CONTENTS THE STRUCTURE OF THE DIALOGUE AS A WHOLE . . . . . . . . . 1 UNITY, BEING AND NEGATION . . . . . . . . . . . . . . 1 PARTICULARITY AND ABSTRACTION . . . . . . . . . . . . 2 THE EIGHT HYPOTHESES . . . . . . . . . . . . . . . . 3 CONTEXT . . . . . . . . . . . . . . . . . . . . . . . 7 THE STRUCTURE OF THE DIALOGUE AS A WHOLE . . . . . . 9 THE INTRODUCTORY PART . . . . . . . . . . . . . . . . . . 10 THE STRUCTURE OF THE INTRODUCTORY PART . . . . . . . 10 THE CONVERSATION BETWEEN ZENO AND SOCRATES: FORMS . . 10 PARMENIDES' CRITIQUE OF THE THEORY OF FORMS . . . . . 12 THE SUMMARY AND EXHORTATION TO SOCRATES . . . . . . . 15 PARMENIDES' PLAN FOR TRAINING . . . . . . . . . . . . 15 THE PROPOSAL FOR A DEMONSTRATION . . . . . . . . . . 16 THE MAIN PART . . . . . . . . . . . . . . . . . . . . . . 17 PRELIMINARY OBSERVATIONS . . . . . . . . . . . . . . 17 OUTLINE OF THE HYPOTHESES AND THEIR ASSUMPTIONS . . . 20 THE INTERNAL STRUCTURE OF THE HYPOTHESES . . . . . . 21 OUTLINE OF THE HYPOTHESES AND THEIR ARGUMENTS . . . . 22 THE FIRST HYPOTHESIS . . . . . . . . . . . . . . . . 25 THE SECOND HYPOTHESIS . . . . . . . . . . . . . . . . 28 THE THIRD HYPOTHESIS . . . . . . . . . . . . . . . . 42 THE FOURTH HYPOTHESIS . . . . . . . . . . . . . . . . 45 THE FIFTH HYPOTHESIS . . . . . . . . . . . . . . . . 46 THE SIXTH HYPOTHESIS . . . . . . . . . . . . . . . . 49 THE SEVENTH HYPOTHESIS . . . . . . . . . . . . . . . 50 THE EIGHTH HYPOTHESIS . . . . . . . . . . . . . . . . 52 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . 53 This is a substantial revision of an essay first completed in 1982. It is the result of work commenced with the encouragement of Philip Wheelwright in 1963. Philip was my teacher at Dartmouth College in 1938, and at the University of California (Riverside) in 1963. He died Januarya 5, 1970 at Santa Barbara, California. I am deeply grateful for his help all those years. This text was converted to WordPerfect, and a few minor corrections were made, August - September, 1989. References to lines in Plato's dialogues use the customary system established by Stephanus and followed almost universally. The reference, DK, refers to Diels-Kranz, Die Fragmente der Vorsokratiker, 6th edition, 1951, chapter 28 (Parmenides), section B (Fragments), also the reference system customarily used. THE STRUCTURE OF PLATO'S PARMENIDES THE STRUCTURE OF THE DIALOGUE AS A WHOLE The key to the Parmenides is its structure. The dialogue as a whole may be divided into two parts: an introductory part, from the beginning to 137C3, and the main part, from 137C4 to the end. It is the main part, a demonstration by Parmenides, eight hypotheses about unity, that claims most of our attention. This is an intricate demonstration of dialectic that has puzzled readers for more than two thousand years. The ancient neoplatonists treated it as a metaphor, as it were, or point of departure for their quasi- religious philosophy of the One. Modern readers have considered it variously as an exercise in dialectic, as a serious philosophical exposition (with many interpretations), and as a joke. As a work of art, as well as of philosophy, the Parmenides must be allowed many interpretations. This is the quality of all great works of art. Here is another interpretation, one which accepts the Parmenides in a straightforward manner as a serious, albeit artful, philosophical demonstration of important problems. It is based upon an analysis of its structure. UNITY, BEING AND NEGATION The Parmenides deals with three simple and universal human experiences, but it weaves these in a complex pattern with a weft of a fourth not-so-simple human experience. The three simple and universal experiences are: unity, being and negation. Consider first: unity. It is an ambiguous experience for all of us. One may be a single individual, one man, one stone, one thing, one being. Or it may be an abstraction: just unity. A collection is both of these: one group of people, one heap of stones, one class of things or of beings. In short, one may be one or many. Consider next: negation. It may mean non-existence, or it may mean otherness. To say that George Washington is not, is to deny his existence now. To say that a centaur is not, is to deny its existence ever. But to say that George Washington was not Thomas Jefferson, or that you are not I, is not to deny the existence of either (George in the past, of course), but to attribute otherness. Thus negation is either non-existence, or otherness that does exist. This is a problem that Plato took up in his dialogue, the Sophist (esp. 254-259). The Sophist has marks of being an earlier effort to deal with two of the three experiences mentioned here, the specific combination of negation and being. Nothing had so puzzled Plato's predecessors. Here in the Parmenides Plato considers negation, being and unity, all three together. Consider then thirdly: being. It may be any one being, any thing, or it may be all being, everything. It may be a particular or an abstraction. It displays the same ambiguity as unity and negation. Single palpable things, like this page, the chair you sit in, or any stick, stone or such, are well known to all of us. Their being is an obvious and common experience. But the idea of all being, the abstraction, Being, is not quite the same kind of experience. Here is the difference: we can conceive it, but it is rather difficult to be in touch with it, to perceive it, as we do individual things. Indeed, we have here the same sort of ambiguity that we encountered with unity and negation. Those too were particular and abstract, with the particularity of one thing not another, and the abstraction of absolute unity and absolute non-existence. It is just this common character of all three of these ambiguous experiences that constitutes the fourth not-so-simple experience that we have mentioned. The ambiguity of particularity and abstraction shuttles through all three of these experiences, in all eight of the Parmenides' hypotheses. PARTICULARITY AND ABSTRACTION To reiterate, all three of the primary experiences that Plato chose to investigate in the Parmenides show a profound ambiguity. This ambiguity is not just a matter of human imprecision. It is rooted in the very natures of unity, being and negation, and in ourselves. It is the dichotomy of particularity and abstraction. The one may be one thing, or it may be conceptual, absolute unity. Being may refer to a particular thing, or to all being. Negation may mean not this, or not at all. Thus many may be one, what is may or may not be, and others may not be others (they may be ones). These three simple experiences, the most universal of all, turn out to be not so simple. Their ambiguity constitutes the pattern of the eight hypotheses of the Parmenides (137C4-166C5). THE EIGHT HYPOTHESES The eight hypotheses ask what happens, 1-2, to the one, if there is a one, 3-4, to the others, if there is a one, 5-6, to the one, if there is not a one, 7-8, to the others, if there is not a one. These are the questions actually asked at the beginnings of the respective hypotheses. This conforms to the plan which Parmenides outlined in the introductory part of the dialogue (136A5-B1). If you substitute "one" for "many", and "others" for "one", making also the appropriate changes in genders of pronouns, thus reversing the viewpoint of that plan from many to one (Zeno had done just the opposite to Parmenides at the beginning of the dialogue), you have the above scheme. At first sight this scheme appears to contain two dichotomies: (1) being v. not-being ("there is . . . there is not"); hypotheses 1 - 4 v. 5 - 8; (2) unity v. multiplicity ("one . . . others"); hypotheses 1, 2, 5, 6 v. 3, 4, 7, 8. These were, to be sure, problems of primary importance to Plato and his contemporaries, but this scheme of four pairs of hypotheses also conceals the more important dichotomies of being, unity and negation. At first sight there is no suggestion of two kinds of being and unity, although there is a suggestion, if one is alert, of two kinds of negation: not-being (5, 6, 7, 8) v. otherness (3, 4, 7, 8). The two kinds of unity and being are revealed only when one analyzes the pairs, 1 - 2, 3 - 4, 5 - 6, 7 - 8, as Cornford did in 1939 (Plato and Parmenides). Then the abstraction and particularity of unity and being are revealed. Whereas the two kinds of negation, absolute and particular, may be seen in the abbreviated scheme given above, it takes the following expanded schemes of the eight hypotheses to reveal the ambiguities of unity and being. Strictly speaking, two schemes are necessary, since we are dealing with a protasis and an apodosis, or an hypothesis and a conclusion, in each case. The generalized form would be: if there is (or is not) a one, what are we to say or conclude about it (or about the others)? The first scheme here refers to the protases, or hypotheses proper, i.e. the "if" clauses. The parentheses will enclose the kind of one or being that is meant in each case. 1. One (Form) is 2. one (copy) is 3. one (copy) is 4. One (Form) is 5. one (copy) is not 6. One (Form) is not 7. one (copy) is not 8. One (Form) is not The second scheme refers to the apodoses, or conclusions: what kind of one or others is the conclusion talking about? 1. One (Form) is not 2. one (copy) is many 3. others (copy) are ones 4. Others (Form) is not one 5. One (Form) is 6. One/one (Form/copy) is not 7. others (copy) are 8. Others/others (Form/copy) are not Or, more briefly (consolidated): if: then: 1. One is 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 Hypotheses six and eight deserve special comment: both Form and copy are not. Why? The text of six is clear: not-being in no way whatsoever is, nor does it in any way participate in being (163C6-7). There is no one of any kind, Form or copy. Of course, we may logically omit reference to the Form in the conclusion, since it has already been negated in the hypothesis, but we follow the text here, which is a sweeping denial of any sort of one whatsoever. The text of eight also includes a sweeping denial of the others, albeit in its own special way: they neither are, nor are conceivable. Again we may omit reference to the copy in the conclusion, if we wish, since it has been made clear: no Form, no copy (#6). In these schemes the particularity and abstraction of unity and being, as well as of negation, are brought clearly into view. But Hypothesis 1 has to do with the Form of the One, or absolute or abstract Unity. ei hen estin, allo ti ouk an eiE polla to hen, "If there is a One, the One may not be anything else [or] many." The definition of the One here is pure unity, an abstraction. Even the word "is" (estin) is extraneous, as the conclusion of this hypothesis shows (141E9 - 10). We could have deduced that right away, had we been alert. Plato confirms this too near the beginning of the second hypothesis (142C2-3) where he emphasizes the distinction of it from the first, distinguishing the hen hen ("One One") of the first hypothesis from the hen estin ("one is" or one that exists) of the second. Unity and being are other or many. Hypothesis 2, having to do with the one that is (and that's two, as is immediately established, therefore many), has to do with particulars, with things. All the hypotheses examine their assumptions and definitions about the one in terms of a series of attributes or what Plato calls "contrary characters" (tanantia). The list is nearly the same in all cases, although the later hypotheses make short shrift of it. In the first hypothesis, the One has none of them, while in the second it has all of them. This is not hard for us to understand, given what we now already know, at least for the first five in each, because these are bodily or spatial characteristics, which obviously abstractions do not have, but particular things do have. The next five (omitting one bodily character in the second hypothesis, touch, which seems strangely out of place there) have to do with relations. Their status is more problematical. The arguments about these are more difficult, and appear more sophistical, but most of them make use of the ambiguity of Form and particular to effect their conclusions. One of the reasons that the second hypothesis is so much longer that the first is that it seems to take more argument to show that the one possesses both of two contrary characters, than to show that it has neither. Another reason is the problems encountered with the presence of time. As the charts above show, the remaining hypotheses also pair up to deal with the one in its abstract and in its particular states. Hypothesis 3 assumes that the others somehow participate in unity (157C1). This is indeed true of other things. They are a multitude of individual things. They also have all the attributes. They are, of course, other than a particular one. Hypothesis 4 assumes (159B6-C4) that the Others and the One are utterly separate from each other. These are Forms. Hypothesis 5, especially at 162A1-B3, shows us Plato's Parmenides taking issue directly with the real Parmenides' famous dicta in DK VII, 1 and DK II, 3. ou gar mEpote touto damnEi einai mE eonta and ouk esti mE einai forbid us to say that not-being is. How does this come about? The last four hypotheses repeat the pattern of the first four, but for the one that is not, and with some other differences. The situation is tricky. The One of hypothesis 5 has all the contrary characters. Extrapolating our experience in the first four, we would expect it to be a particular one. Not at all. It is a particular one that is not, but that leaves the One as a Form that is. The presence of the negative has reversed the field. The fact that there is knowledge of it confirms this: it is conceptual, not perceptual knowledge. So does the admission (160B7-8) that the one that is not differs from the not-one that is not. Furthermore its participation in Others is participation in other Ideas, after the manner of the Sophist, 253B-259B. So this one that is not, in hypothesis 5, is a copy, but the One that is is a Form. Absolute Not-being is distinguished at 160C4 from particular not- being, which is otherness. Thus is broached the question of the two states of negation, to parallel the two states of unity and being, broached in the first and second hypotheses. The two states and the reversal of their application are summed up at 160E7: einai men dE tO heni ouk hoion te, eiper ge mE esti, metechdk viiiein de pollOn ouden kOluei, alla kai anagkE . . . The negative absolute possesses characteristics of the positive particular. Hypothesis 6 deals with the One that is not in any way whatsoever: oudamOs oudamE estin oude pE metechei ousias to ge mE on (163C6-7). This one is not even a Form, much less a copy, and of course, not existing in any way whatsoever, neither can there be any contrary characters. Thus the sixth denies what the fifth affirms, and it is to this state of not-being that the real Parmenides' strictures, noted just above, truly apply. Hypothesis 7. With the last two hypotheses we have come to a double negative: if there is not a one, what happens to the others? The others are not the one that is not, in seven. If we are talking about particular things, this makes perfectly good sense: just because one is not, others need not be not. They may well be. Furthermore, the field being reversed again by the double negative, they have the contrary characters. Thus: Hypothesis Contrary Characters 1 no 2 yes 3 yes 4 no 5 yes 6 no 7 yes 8 no The 8th hypothesis parallels the sixth. It is again the Form of the One that is not; otherwise, as in the seventh, there would be others - and there are not, neither one nor many (165E4-8). And since there are no others, there can be no Others. Others would be other in such a case. And there are no contrary characters. There is nothing at all. Taken all together the eight hypotheses exhibit various symmetries of structure. Three have been exhibited. Here is a fourth. One may tabulate their relationships with each other, according to their subjects and assumptions, as follows: A B C Form/copy one/other being/not-being 1 2 4 6 2 1 3 5 3 4 2 7 4 3 1 8 5 6 7 2 6 5 8 1 7 8 5 3 8 7 6 4 This table of pairings is helpful in discovering and keeping in mind what Plato is saying, and it exhibits again how highly structured is the main part of the dialogue. CONTEXT What is the point of all this? Do you think that it is just a game or a puzzle or an exercise? For one thing, it deals with problems, being and not-being, unity and multiplicity, that had bothered the ancient Greeks for a long time. For another, it deals with central doctrines of both Parmenides and Plato: being and the Forms. We can see here that Plato recognized what few if any others recognized: Parmenides' One Being of DK VIII, 5 - 6, etc., epei nun estin homou pan, hen, suneches, etc., was not an immobile, undifferentiated universe - a notion that no one could rightly put up with - but it was an abstraction, as we would call it, a Form! Dimly recognized, perhaps, but nevertheless just that: the Form of Being. Plato surpassed Parmenides by recognizing that there were other abstractions, other Forms, too. But Parmenides' estin was in fact the first, even though not named as such by him. We have seen above how the Parmenides, 162A1-B3, addresses directly the problem of not-being raised by Parmenides in DK VII, 1 and DK II, 3. Plato had dealt with this after one fashion in the Sophist. We can see now that the solution there was based upon the ambiguity of negation: not-being and otherness. Here in the fifth and sixth hypotheses he argues from the ambiguity of Form v. copy, abstract v. particular. As a Form (abstraction) Not-being is; as a particular it is not. There seems little question that Plato in the Parmenides has the real Parmenides very much in mind. His own Form theory is also part of the context for these eight hypotheses. A number of the problems and paradoxes that attend the theory are raised here. What sort of being does the Form of the One have? In the first hypothesis it does not exist. In the fifth, if there is not a one, the Form of the One somehow is. In the fourth hypothesis the Form of the Others has no unity, certainly an aberration in Plato's theory as we know it otherwise. Not only did the Parmenides have a context in the traditions of its time, but it also provided a possible context for later times that was ignored, probably because it was not even understood. I do not refer to the stimulus it provided for the great neoplatonic tradition. That was something else. But it embodies a way of thinking in terms of paradox, a logic, that was completely lost 66rom sight. Aristotelian and Stoic logic became the Greek legacy to the following ages. The fundamental rule of thought was and still is Aristotle's famous law of contradiction (Metaphysics, G, iii - vii). The rule of Plato's Parmenides is: the same can belong and not belong to the same subject, the same can be and not be, opposites can be attributed to the same at the same time, contradicting Aristotle's three formulations of the law, omitting only "in the same respect", kata to auto. But that is precisely the point. There is no same respect where Form and copy, abstract and concrete, mind and body are involved, and these are basic suppositions of the human condition. We will return to this point later. THE STRUCTURE OF THE DIALOGUE AS A WHOLE The dialogue as a whole is divided into two parts, an introductory part and a main part. The introductory part creates the setting and relates a conversation between Zeno, Socrates and Parmenides. This leads easily to the main part, which is a demonstration by Parmenides. Here is briefest statement of the structure of the whole dialogue: I. Introduction 126A1-137C3 A. The setting and characters 126A1-127D5 B. Conversation between Zeno and Socrates 127D6-130A2 1. Zeno's hypothesis: if things are many . . . 2. Socrates' reply: the theory of Forms C. Parmenides' critique of Socrates' 130A3-136C5 theory and of Zeno's method D. Proposal for a demonstration by Parmenides 136C6-137C3 II. Parmenides' demonstration: eight hypotheses 137C4-166C5 about the one A. If there is a one, 1. what must we say about it? (two hypotheses) 2. what must we say about the others? (two hypotheses) B. If there is not a one, 1. what must we say about it? (two hypotheses) 2. what must we say about the others? (two hypotheses) The second part (II) is the raison d'etre of the whole, and the part which usually causes the most amazement and difficulty. But let us first take a closer look at the first and introductory part. This may be outlined in greater detail as follows. THE INTRODUCTORY PART, 126A1-137C3 THE STRUCTURE OF THE INTRODUCTORY PART A. The setting and the persons 126A1-127D5 B. Conversation between Zeno and Socrates 127D6-130A2 1. Zeno's hypothesis: if things are D6-E5 many, they are both like and unlike, which is impossible, etc. 2. Socrates' reply E6-130A2 a. preliminary exchange between E6-128E4 Socrates and Zeno b. Socrates' critique of Zeno's 128E5-130A2 hypothesis: the theory of Forms; things can participate in oppos- ite Forms. See esp. 129B1-C1. C. Parmenides' critique of Socrates' 130A3-136C5 theory and of Zeno's method 1. 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 2. summary and exhortation to Socrates 134E9-135E7 3. Parmenides' plan for training, E8-136C5 expanding Zeno's method D. Socrates' proposal for a demonstration, and C6-137C3 the entreaty to Parmenides to conduct it. THE CONVERSATION BETWEEN ZENO AND SOCRATES: THE THEORY OF FORMS (127D6-130A2) This outline indicates how easily and naturally the conversation led up to the climax at the end of the introductory part, wherein Parmenides was persuaded to undertake the demonstration that comprises the whole of the main part of the dialogue. Zeno's hypothesis led to Socrates' rebuttal, which led in turn to Parmenides' rejoinder to them both, explicitly to Socrates, implicitly to Zeno in his plan for training. This in turn led to the entreaty to Parmenides to demonstrate what he meant. But there is more than art at stake here. Several of the terms are introduced in this conversation which will figure in the later demonstration: the One and the Many of course (established Eleatic themes), also likeness and unlikeness, whole and part, and the Equal, the Large and the Small. All these will be explicitly mentioned in the main part. There are others that are not so explicitly mentioned later, but nevertheless play a part: above all the theory of Forms. Although Zeno's hypothesis initiates the conversation, there can be little doubt that the theory of Forms, which we know of course as Plato's theory, is the main theme of the introduction (126A1-137C3). Socrates' exposition of it, and Parmenides' critique and ultimate partial approval (135E5-C3) of it, form the larger share of this part. The significance of this will become apparent in the eight hypotheses, where it plays a major role. One must always keep in mind the historical background, so far as we know it, of this conversation and of the main figures in it. The conversation is part fiction, part fact. It is fiction with a factual background. Such a conversation never did take place, and some of the views of the speakers are not their views as we know these from other sources. But some of the views are views that we know from other sources that they held, and yet other views seem to be fairly drawn implications of views that they did hold. Here we are on the borderline between fact and fiction. For example, the theory of Forms is generally accepted without question as Plato's invention, not Socrates' as this dialogue would have us believe. But Plato himself in his early and (it is widely believed) more historical dialogues (e.g., Euthyphro, 5D, 6D; Phaedo, 65D, 74A-B, 100B-D) seems to indicate that the germ of the idea came from Socrates. Aristotle confirms this in Metaphysics, 987b1-11, 1078b17-34. The Form theory which Socrates raises in the dialogue as a criticism of Zeno is really being raised by Plato as an explanation of the real Parmenides. Parmenides had in fact become notorious for the problem he had raised in his philosophical poem, perhaps a hundred years or so before this dialogue was written: . . . epei nun estin homou pan, hen suneches, . . . (DK VIII, 5 - 6) Everything is one! This statement we accept as a historical fact. It is also a fact that all his contemporaries and successors (so far as we know) understood that Parmenides was making the absurd and impossible suggestion that the whole universe is one single, immovable, impartible unity. There could be no plurality or change. Hence Zeno's supporting hypothesis, with which this dialogue commences. It was the famous Eleatic thesis that he was supporting. But this dialogue may be evidence that Plato saw through this, and in his eyes there was a sense in which Parmenides was quite right and not the least bit absurd. This sense is supplied by the theory of Forms, as we shall in due course see. The theory of Forms plays a majaor role throughout the whole of the second and main part, Parmenides' demonstration. It can also be seen to have played a part, however unconscious he may have been of the fact, in the real Parmenides' real statement about the unity of being. If Being was a Form, he was right. PARMENIDES' CRITIQUE OF THE THEORY OF FORMS, 130A3-135E7 The critique of the theory of Forms, which Plato puts into the mouth of Parmenides, in the introductory part, deserves closer inspection. The text appears to contain seven problems, which may be outlined as follows: a. the extent of the Forms 130A3-E4 1 One and Many? B5 2 Beautiful and Good? B8 3 Man? C1 4 Hair, and Mud and Dirt? C6 5 Socrates' hesitant response D3-9 6 Parmenides' fatherly advice E1-4 b. is the whole of the Form in the participant? E4-131C11 1 Parmenides explains the difficulty E4-131B2 2 Socrates' rebuttal; non-material B3-6 analogy of "day", ignored by Parmenides 3 Parmenides' analogy of "sail"; B7-C11 Socrates agrees that the Form is a part c. difficulties that ensue, if it is a part C12-E7 1 the Great C12 2 the Equal D4 3 the Small D7 4 recap: neither whole nor part E3-7 d. infinite regress (first mode) E8-132B6 1 one common Form in many individuals 132A1-5 2 another in the Form and individuals A6-9 3 and again and again ad infinitum A10-B2 4 Socrates' rebuttal: Forms are B3-6 thoughts, and only in the mind e. if Forms are thoughts, and things part- B7-C11 icipate in them, then either things are thoughts, or thoughts are things f. infinite regress (second mode) C12-133A10 1 Socrates suggests that Forms are para- digms, particulars are likenesses D4 a if particulars are like Forms, D5-8 then Forms are like particulars b both share in and are like a Form D9-E5 c then there is another Form, and E6-133A4 another, ad infinitum d conclusion: likeness won't do A5-10 g. relation of Forms to us A11-134E8 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 fairly straightforward outline of Parmenides' critique just as Plato gives it, aimed first of all to assist us in following the text. It does not however emphasize the key points or elicit the significant implications. To these ends, one might reorganize the outline along the following lines. The first problem, or question, a., is in effect postponed. The next two, b. and c., are really two parts of one question, and they include an important suggestion by Socrates, i.e., his non-material analogy ("day") that is ignored by Parmenides. It will come up again shortly, only slightly altered. The third part of this critique comprises the two arguments based upon infinite regress. The second one, f., is really only a revision of the first, d., brought about by an intervening incident, e. In e., Socrates again suggests that the Forms are non- material: they are thoughts, he says, and are only in our minds. Parmenides replies with a question that seems unanswerable (132C9-11), and Socrates drops it and passes on to another suggestion, the one that leads to the second infinite regress argument, f. That it seems unsatisfactory here, does not mean that Socrates' suggestion is a bad one. On the one hand it raises a question that, although unanswerable, has remained with us for nearly twenty four hundred years, and is still with us today. It was the universals question of the twelfth century and is the mind-body question of our time (Are thoughts things? Are things thoughts? What is the relation between things and thoughts?). On the other hand, it is the question that the present critique by Parmenides returns to in its last part, g.: Parmenides' question about the relation of the Forms to us. Plato himself calls this the "greatest" problem (133B4). What is it? The text in its simplicity of language is not easy to interpret here. The basis of the argument is that the Forms are not en hEmin. What does this mean? "In us"? "In our world"? Later he uses also the words, par hEmin (133C9-10, 134B4). He also uses the verb, echomen (134B3): we do not "have" them. He probably does not mean here "in us" in the sense of "in our minds". He has already had his Socrates make the suggestion and his Parmenides reject it. Plato did not think of the Ideas as just in the mind, even though later generations did. It was not his way. He seems to mean here something more like "in our world" (as Cornford indeed translates here). The purport of this whole section, g., is the contrast between the world of Forms and our world, the world of bodies. The world of Ideas may not be only in the mind, to Plato, but still it is approachable only with the mind, and again, although he does not put the world of Ideas in the mind, he most emphatically severs it 66rom our bodily world. He took the first step; others took the second. And even if he failed to take the second, he implied it explicitly here in Socrates' key suggestion in the very middle of this critique: aren't these Forms thoughts, in our minds (133B3-5)? So this critique by Parmenides of Socrates' theory of Forms discloses to our inspection the gradual development of this profound problem: what or where are the Forms? 1. Are they material or non-material (ignored)? 2. Are they thoughts, in the mind (not really answered, but only turned into another question)? 3. How can there be any relation between the Forms in one "world" and us in another? How can we know anything about them? In short, Parmenides' critique does not deny the existence of Forms. Far from it. The critique is concluded by his avowal to Socrates that we must believe in them in any case (135B5-C4). They exist, and are apprehended with the mind. It simply raises questions that we are still struggling to answer. What are these Ideas that we apprehend with the mind, and how are they related to our bodily world and selves? Whatever they are, we will find that the main part of the dialogue is organized with them in view. THE SUMMARY AND EXHORTATION TO SOCRATES, 134E9-135E7 The important thing to note about this section is that Plato goes to some length to show that Parmenides has far from rejected Socrates' arguments out of hand, nor thinks that he has proven Socrates wrong. The question has not been resolved. It remains an aporia, which Socrates is encouraged to prepare himself carefully to pursue. Of course we must keep reminding ourselves that what we have here in this dialogue between Parmenides and Socrates (and others) is really Plato talking with himself, and perhaps also to us. In any case, the Forms, the Ideas, these abstractions remain to be explained. It is a brief exchange, 135B5-C4, that throws everything in question again. PARMENIDES' PLAN FOR TRAINING, 135E8-136C5 The plan which Parmenides now outlines briefly (136A5-B1) is precisely the scheme which he himself follows in the second or main part of the dialogue (137C4-166C5), substituting there the one for the many as the subject of the inquiry. He says here: "If there is a many, what must we say about them (or attribute to them, ti chrE sumbainein), with regard to themselves and with regard to the one, and about the one, with regard to itself and with regard to the many; and again, if there is not a many. what are we to say about the one and the many with regard to themselves and to each other (136A5-B1)." Compare this with the scheme of Parmenides' own inquiry which follows in the main part of the dialogue: If there is a one, what are we to say about the one itself? 1 the one in relation to the others? 2 the others in relation to the one? 3 the others themselves? 4 If there is not a one, the one itself? 5 the one in relation to the others? 6 the others in relation to the one? 7 the others themselves? 8 Aside from reversing the inquiry, commencing from the standpoint of the one instead of that of many, the only other substantive difference is the substitution of the others (talla) for the many (ta polla). THE PROPOSAL FOR A DEMONSTRATION AND ENTREATY TO PARMENIDES This section, 136C6-137C3, concludes the first part, and fluently and naturally introduces the second or main part of the dialogue. We might easily overlook the reference to Ibycus and his horse here (136E9-137A4) as merely another piece of rhetoric on Plato's part. However, it is especially significant in revealing Parmenides' state of mind. The easiest place to take the measure of Ibycus, after the brief articles in the Oxford Classical Dictionary and Der Kleine Pauly, is in the second volume of the Loeb Classical Library edition of Lyra Graeca, p. 78-87. Beside being a poet of note in the sixth century, he seems to have had a reputation of being what we would call today a "great lover." gegone de erOtomanestatos peri meirakia (Suidas), "he was mad with love for young lads." Apparently he just couldn't quit, as he got older, even though it was getting a bit difficult for him. Thence his lines about the old race horse, and quite apt they are. Parmenides, likening himself to Ibycus and his horse, reveals the intensity of his love for dialectic, his inability to refrain, and the difficulty of performing the task that he is faced with in the main part of the dialogue. THE MAIN PART: THE DEMONSTRATION BY PARMENIDES (137C4-166C5) PRELIMINARY OBSERVATIONS Plato has introduced the main part of his dialogue, and given us a hint about its structure, but before proceeding further these observations are in order: 1. First of all, there has been disagreement about the number of hypotheses that Parmenides considers. The neoplatonists counted nine. This view began perhaps with Plotinus (Ennead V, 1, 8, lines 24-27) and is most evident in Proclus (for a fuller account see H. D. Saffrey and L. G. Westerink, ed., Proclus, Theologie Platonicienne, Livre I, Paris, 1968, esp. chap. I, sect. 7). It was peculiar and appropriate to the neoplatonist theology. F. M. Cornford adopted a middle course. In his arrangement there are eight hypotheses and a corollary, hypotheses 2a. The latter is Proclus' third hypothesis. In our outline there are eight hypotheses. The neoplatonists' third, and Cornford's corollary, are part of the second hypothesis in our scheme, nothing more. This leaves us with the task of explaining a textual peculiarity at 155E4-5, and this will be done when we come to it. Meanwhile, a justification of eight hypotheses has already been suggested by Parmenides' own words above (135E8-136C5). Such a structure conforms to his stated intention. In addition the symmetry of the eight is a strong argument in their favor. 2. Secondly, the internal structure of the hypotheses will be easier to understand if we anticipate a special feature to be found in them. Parmenides develops and tests (so to speak) each of his hypotheses with a peculiar set of terms, a fixed list of contraries. Cornford called them "contrary characters," and we adopt that term here. Plato himself gave them a name, alluding to them several times in hypotheses 3 and 4 (157B1, 159A1 and 7, E5, 160A2). He called them ta enantia pathE or simply ta enantia. Mostly he just uses them, pair by pair. They can be listed, thus: 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 This list is unique to the Parmenides. Many of these pairs appear elsewhere, but not as part of just such a list. One is reminded of the list of ten pairs of contraries, the sustoichia, that Aristotle ascribed to the Pythagoreans (Metaphysics, A, 5, 986a23-26). Indeed, three of Plato's pairs appear on the Pythagorean list. Whatever its origin, it is this list of contrary characters that Parmenides used in each of the hypotheses of the ensuing demonstration. We will meet them over and over again. 3. The arguments large and small are frequently framed around an ambiguity. The apparent contradictions that the one does and does not have the contrary characters (hypotheses 1 and 2) or that the one has both of a pair of contrary characters (hypothesis 2), for example, make use of ambiguities in our notions of one, or in our notions of the various contrary characters. It is these contradictions and by implication their underlying ambiguities that have elicited the varied responses to this dialogue, causing some to see it as a game, others as a parody, yet others as an exercise, and so forth. Little wonder. They could be taken in any of these ways. If we are going to ask if there is a serious point to this demonstration of the Parmenides, it is precisely these ambiguities that we are going to have to identify and evaluate. We will be able to signal some of them, such as of the one and the others, by capitalizing the initial letters when it is clear that it is the Form that is meant, and by using lower case when it is clear that it is not. But even this is not always clear, and in some cases, when both or either are meant, the lower case will be used. The Greek text makes no such use of capitals, of course. It will be the purpose of the outline and commentary to help make these ambiguities clear. 4. One of the difficulties of this demonstration is the need to keep in mind at the same time several arguments that are going on at several structural levels. For example, if one is following a detailed argument in the middle of the second hypothesis, one has also to keep in mind the developing contrast with first. When one comes to the third and fourth hypotheses, one has their contrast with the first two to think about, as well as their contrast with each other; and in the last four, theirs with the first four, as well as their pairs with each other, and singly with each other. This is, needless to say, sometimes rather taxing. The outlines should help us to cope with these multiple demands. 5. We must be on our guard to distinguish between (1) terms used to refer to or deal with the subjects of the argument, and (2) terms used as subjects of the arguments themselves. The distinction is similar to the distinction that computer programmers make between (1) address arithmetic and (2) calculation. It is an especially vexatious problem here where so many of the terms that we will be talking about will be the same as the terms that we use to talk about them. To make up a brief and exaggerated example, consider the following statement: this demonstration deals with two topics; one is the other, and the other is the one. That statement contains two words, each of which is used twice, one time as a term of address, the other time as a term of substance. 6. We must keep in mind that we will be dealing in this demonstration with two kinds of negatives. This ambiguity does not stand out quite so obviously as the other two ambiguities of one and being do. Abstraction and particularity of unity and being are evident in the pairings of 1 and 2, 3 and 4, 5 and 6, 7 and 8. The abstraction and particularity of negation are to be found in the comparison of 5, 6, 7 and 8 with 4, 5, 7 and 8. The last four hypotheses deal with the one that is not ("If there is not a one . 2E . "). The third, fourth, seventh and eighth deal with the others. They also are not one. In the last two hypotheses, in which we deal with both of these together (others than the one that is not), we will be dealing with double negatives. All of these ambiguities of unity, being and negation have tended to be obscured by the starker contrasts of being and not being, one and others that stands out in the pairings 1 - 4 v. 5 - 8 and 1, 2, 5, 6 v. 3, 4, 7, 8. When Parmenides first enunciated his plan (136A5-B1), he used the words pros hauta, pros allEla and so forth. He might as well have used kath' hauta, kath' allEla, etc. kath' hauta is one of Plato's customary ways of referring to abstractions. In any case, the subjects of hypotheses 1, 4, 6, and 8 are abstractions, the Form of the One, and the subjects of hypotheses 2, 3, 5 and 7 are particular ones. The conclusions follow a somewhat different pattern, but the ambiguity of Form and copy of unity, being and negation remain controlling. Ambiguity, complexity, terms of address and substance, double negatives - all these are going to make the ensuing demonstration difficult to follow. Outlines will help. OUTLINE OF THE HYPOTHESES AND THEIR ASSUMPTIONS A. If there is a one, 1. the first hypothesis deals with the abstract One, i.e. One as a Form. It is only One. allo ti ouk an eiE polla to hen. It is neither other nor many. It is called hen hen at 142C3. It does not even exist. 2. the second hypothesis deals with particular ones. They participate in existence. hen ei estin, ara hoion te auto einai men, ousias de mE metechein? - ouk hoion te (142B5-7). It is not only one. It is at least two, and by extension many. 3. the third hypothesis deals with particulars, one and others. The others somehow participate in unity. Oude mEn steretai ge pantapasi tou henos talla, alla metechei pE (157C1-2). This is indeed true of all the everyday things around us. 4. the fourth hypothesis deals with the Forms of the One and the Others. They are both utterly separate from each other. Ar' oun ou chOris men to hen tOn allOn chOris de talla tou = henos einai? Nai. . . Oudeni ara tropO metechoi an talla tou henos . . . (159B6-7, D1). Plato's vaunted unity of the Forms breaks down here, as did their existence in the first hypothesis. B. If there is not a one, 5. the fifth hypothesis makes it clear that it is something quite distinct that is not, thus the one that is not somehow is. heteron ti legei to mE on (160C4) . . . einai men dE tO heni ouk hoion te, eiper ge mE esti, metechein de pollOn ouden kOluei, alla kai anagkE (160E7-161A1) . . . kai mEn kai ousias ge dei auto metechein pE (161E3). There is knowledge of it. This One that somehow is, is a Form. It is a copy that it is not. 6. the sixth hypothesis states that when we say that it is not, we don't mean anything else than to deny it all being. To de mE estin hotan legOmen, ara mE ti allo sEmainei E ousias apousian toutO hO an phOmen mE einai? - ouden allo163C2-3). . . oudamOs oudamE estin oude pE metechei ousias to ge mE on (163C6-7). The one in no way whatsoever is. No way at all. Neither Form nor copy. In the hypothesis here it is the Form that must be meant, since, as we saw in the fifth, if it were a copy, such a conclusion would not hold true. There might be a Form, and thus it might somehow participate in being - which it does not, here. We conclude that in this hypothesis neither Form nor copy exist. houtO dE hen ouk on ouk exei pOs oudamE (164B3). There is not one thing, nor any Idea. 7. the seventh hypothesis commences with the assertion that the others must be somehow, otherwise they could not be spoken of. alla men pou dei auta einai. ei gar mEde estin, ouk an peri tOn allOn legoito (164B6-7). The others here are both things and Form, and the one is one thing. Clearly, if there is not one thing there are others. And if they can be spoken of, there is an Idea of them. 8. the eighth hypothesis states that, if there is not a One, the others will not be one. oukoun hen men ouk estai talla (165E4). Nor many. oude mEn polla ge, en gar pollois ousin eneiE an kai hen (E5). The One that is not must be a Form. If it were a copy, there would be others, as we saw in the seventh, above, and they would be ones. The others that are neither one nor many (again, mE enontos de henos en tois allois, oute polla oute hen esti talla, 165E7-8) are Form and copies. There is nothing: hen ei mE estin, ouden estin (166C1). THE INTERNAL STRUCTURE OF THE HYPOTHESES Although the subjects and assumptions differ in each hypothesis, the internal structure of each of them is the same or similar. Each examines its subject in terms of ten pairs of contrary characters. The parallelism of their treatment is attenuated as the demonstration proceeds, but it remains to the end in some measure. For example, up to a point (g. in the following outline) the first two hypotheses follow the same arrangement. Thereafter some differences appear. And the first four hypotheses all start with the consideration whether their subjects are wholes with parts, while the last four start with the consideration of other characters. Also the later hypotheses tend to be briefer than the earlier ones. This internal symmetry of the hypotheses (and its attenuation) is evident in an outline, and such an outline will also be a useful guide as we proceed to examine the hypotheses individually and in greater detail. OUTLINE OF THE HYPOTHESES AND THEIR ARGUMENTS A. If there is a one, 137C4-160B4 1. it has none of the contrary characters. C4-142A8 The One is not other or many. allo ti ouk an eiH polla to hen (C4-5). The One is absolutely One, nothing else. It is hen hen (142C2). 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. 2. it partakes of being: hen ei estin, ara 142B1-157B5= hoion te auto einai men, ousias de mE metechein? - ouk hoion te (B5-7). Its being is not the same as its unity: oukoun kai hE ousia tou henos eiE an ou tauton ousa tO heni . . . (B7-8). Again: esti de ou to auto hE te ousia kai to hen (D2-3). This hypothesis is not ei hen hen, but ei hen estin (C2-3). It has the contrary characters. a. it is a whole, with parts C7-D9 b. it is infinite and limited D9-145A4 c. it has shape, round or straight A4-B5 d. it is in itself and in another B6-E6 e. it moves and rests E7-146A8 f. it is the same and other as (than) A9-147B8 itself and others g. it is like and unlike itself and others C1-148D4 h. it touches and does not touch itself D5-149D7 and others i. it is equal and unequal to itself and D8-151E2 others j. it does and does not partake of time, E3-157B5 be and become younger and older than itself and others. 3. the others are not one, but they do not 157B6-159B1 wholly lack unity; they participate in it somehow. oukoun eipeiper alla tou henos estin, oute to en esti talla . . oude mEn steretai ge pantapasi tou henos talla, alla metechei pE (157B8-C2). It is as particulars, rather than abstractions, that they participate in unity as well as plurality. They have all the contrary characters. a. they have parts and are 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 A6-B1 contrary characters 4. The Others and the One are utterly separate 159B2-160B4 ar' oun ou chOris men to hen tOn allOn, chOris de talla tou henos einai? - nai (159B6-7) . . . oudeni ara tropO metechoi an talla tou henos (D1). The Others, as the One, are a Form. They have none of the contrary characters. 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 contrary characters A4-B2 e. recap of the first four hypotheses B2-4 B. If there is not a one, 160B5-166C2 5. it is something distinct, and there is 160B6-163B6 knowledge of it, an idea (Idea) of it. dEloi oti heteron ti to mE on (C4) . . . gnOston ti legei (C78). It is a Form, and it participates in many Ideas, metechein de pollOn ouden kOluei, alla anagkE (E8-161A1). It has the contrary characters: a. unlikeness and likeness A6-C2 b. inequality, equality, greatness, smallness C3-E2 c. being and not being E3-162B8 d. it moves and rests B9-E3 e. it changes and does not change E4-163A7 f. it comes into being and passes away, and A7-B6 does not come into being and pass away 6. it simply is not, and does not participate 163B7-164B4 in being in any way whatsoever, ara mE ti allo sEmainei E ousias apousian toutO hO an phOmen mE einai? ouden allo (163C2-4) . . . oudamOs oudamE estin oude pE metechei ousias to ge mE on (C6-7). Neither Form nor copy, it has none of the contrary characters. a. it does not come into being or pass away D1-8 b. it does not change, move or rest D8-E6 c. it has no greatness, smallness, equality, E6-164B1 = likeness, difference, thisness, thatness, etc. d. there is no knowledge or opinion or perception B1-2 or reasoning or name of it, or anything else e. recap: it is not, in any way whatsoever B3-4 7. the others must be somehow, otherwise 164B5-165E1 one could not speak of them. alla men pou dei auta einai, ei gar mEde alla estin, ouk an peri tOn allOn legoito (B6-7). They must be as a Form, since they can be spoken of, and if the one that is not is a particular thing, then the others may be particular things too. Surely, if there is not one thing, there may be others. And they must be other than others (B8-C8). In any case they have the contrary characters. a. they appear unlimited and limited, C8-165C6 one and many, etc. b. they appear like and unlike C6-D4 c. same and other D5 d. in touch with each other and separate D5-6 e. moving and at rest D6 f. coming to be, passing away, and neither, D7 g. and all other such D8-E1 8. the others are neither one nor many. 165E2-166C2 oukoun hen men ouk estai talla . . . oude mEn polla ge (E4-5) . . . mE enontos de henos en tois allois, oute polla oute hen esti talla (E7-8). Nor do they appear one or many, or have or appear to have any of the contrary characters. a. they are neither like nor unlike B3-4 b. nor same nor different B4-5 c. nor in touch nor separate B5 d. nor anything else B5-7 e. there is nothing B7-C2 C. Recap of the eight hypotheses C2-5= It is not a waste of time to repeat these outlines and commentary with slightly different emphases or levels of detail. This dialogue is sufficiently complicated that repetition is a help in grasping its contents. Thus we will go through the hypotheses once more, examining their assumptions and arguments in still greater detail. This is especially important for the verification of the scheme. THE FIRST HYPOTHESIS The first hypothesis commences with a succinct statement of its assumption, albeit in the form of a question and response: ei hen estin, allo ti ouk an eie polla to hen? pOs gar an? "If there is a One, it can't be other [or] many, can it? How could it be?" (137C4-5). This One is in our modern terms an abstraction, in Plato's terms a Form, although nothing more is made of it now but to go on with the argument. The argument has ten parts, as we have outlined above. They involve the ten pairs of contrary characters that have also been outlined above. There is however more to the organization than just that. These ten sections, upon closer inspection, may be divided into three groups. 1. The first five arguments (137C5-139B3) are developed on the premiss of the very first (137C5-D3), that this One has no parts and is not a whole. They all have to do with physical characters, and Forms have no physical characters. The infinity under consideration here is a case in point. There are several kinds of infinity, raising possibilities of ambiguity that are played upon later on, but here only one kind is meant: it is an infinity of spatial (physical) extension, such as results from having no beginning or end. These are parts. Beginning, end, shape, place, motion, rest, all these are physical. Being interrelated, if the One has no parts, it has none of them. So the key to this group is the initial conclusion, that the One has no parts nor is a whole. That it has no parts is obvious, else it would be many. That it is not a whole depends upon the additional assumption or definition (as you will) that parts and wholes reciprocally entail each other. ouchi hou an meros mEden apE holon eiE? panu ge (137C7-D1). It seems a valid assumption about the physical world, that parts and wholes entail each other. The one will have both or neither (parts and whole): both if it is a physical thing, neither if it is not. Here it has neither: it is a Form. In the first five arguments, then, it is the Form of the One that is assumed, and it is from physical things that this Form is distinguished. Once this is done in the case of the parts, the rest seems to follow quite naturally. 2.The next four arguments (139B4-141D6) have to do with relatives. These arguments are also interrelated, and they are more complex in their organization. This makes them a bit more difficult to follow. The complexity is due in part to the fact that opposite relatives are taken up together, and both of these are referred both to the subject itself (the One) and to oneanother. This raises acute problems about the nature of relations: can they be considered per se, to or by themselves? Plato sometimes thought not (Sophist, 255D; Parmenides, 139C4-5, etc.; Aristotle, by the way, thought not; see Metaphysics, A, 9, 990b16; see also Asclepius, In Metaph., ed. Hayduck, p. 76). If not, then how can there be Forms of relations? The first of these four arguments has itself four parts. The One is not a. other than itself B5-6 b. same as another B7-C3 c. other than another C3-D1 d. same as itself D1-E6 The first two (B5-C3) of these four parts seem self-evident to us. In them the One is identified with itself or distinguished from the other. These are conclusions that are comfortable, because they are true of things as well as Forms, and thus are easy for us to recognize. The third part (C3-D1) depends upon a peculiarity of otherness just referred to above: ou gar heni prosEkei heterO tinos einai, alla monO heterO heterou (139C4-5). Only an other can be other than another. Since the One is not other, it follows that it cannot be other than another. If it were not a Form, it could be other than another. The fourth part (D1-E6) is also based upon the supposition that the One is an utterly separate Form. Sameness would compromise this. Recapitulating, the first two parts of this argument (B5-C3) state consequences that apply equally to Forms and things, whereas the last two (C3-E6), to Forms only. Although these are negative consequences, the acute problem mentioned above is present, if partially concealed. It should be clear by now that in such a series of arguments which have the appearance of verbal trickery, it is not mere trickery at all. The arguments are based upon the distinction of things and Forms, and upon the peculiar natures of each, and upon the ambiguities that result. This will continue to be the case throughout the remainder of the dialogue.= The second of the four arguments of this group is that the One is not like or unlike itself or another (139E7-140B5). This is fairly simple and straightforward. It reiterates the prior argument, and adds the stipulation that likeness involves sameness, and unlikeness, otherness. It has two parts: the first (139E7-140A6) concludes that it is not like another or itself; the second (A6- B5), that it is not unlike itself or another. The third of the four arguments (it is not equal or unequal to itself or another) has three parts, following its announcement in 140B6-7. The first part (140B7-C4) is a series of definitions of equal and unequal, unequal being represented by greater and smaller. The definition of equal (tOn autOn metrOn, B7-8) is simple. The definition of greater and smaller (=3D unequal) is somewhat more complex: they have either more or less of the same measures (C1-2), or, if it is their measures that are not the same (in size), it is greater than another of smaller measures and smaller than another of greater measures (C2-4). These last lines are severely elliptical. The second part (C4-8) eliminates equality to itself or another: it would participate in sameness. The third part (C8-D4) eliminates inequality in the guise of greater and smaller. It does so in two steps. First (C8-D1), this third part eliminates greater or smaller on account of having more or less of whatever measures, because measures are parts (tosautOn kai merOn an eiE, C9). Then, secondly (D2-4), it eliminates them in the case where the One itself is the measure (ei de ge henos metrou eiE . . =2E , D2): the argument from parts will not do in this case, but it would be equal and same. D4-8 is a recapitulation. The third prior group for its premisses. The fourth and last of these four arguments of the middle group has two main parts. The first part (140E1-141A4) is devoted to showing that the One is not older or younger or the same age as itself or another, and has for its premisses the prior arguments about equality and inequality, likeness and unlikeness. The second (141A5-D6) is devoted to showing that the One does not become older or younger than itself, or the same age, since if it did it would be in time and partake of time, which it does not. It depends (141A5-6) on the immediately preceding part (140E1-141A4). In the distinction of becoming from being older, younger, etc., there is an ambiguity about time used here: time can mean a fixed or a growing continuum, a period (or instant) or a procession. This distinction is used here in passing from being to becoming, and again when it is argued that something in time is always becoming older and younger (141A6-B3) and always the same age (C4-7). In the first case it is the procession of time that is meant; in the second, the period or instant. This ambiguity will be used again in later hypotheses. Lines 141B3, pOs legeis? . . . C4, eoiken, seem almost a superfluous explanation. In this group of four arguments, all are derived from the first, that the One is not the same or other than itself or another, excepting one case, in which inequality is eliminated on account of its having more or less measures, i.e. parts. And the first of this group, like the first of the prior group, is derived from the original supposition that this is the Form of the One which we have under scrutiny here, the utterly separate and abstract One alone, supposed in the beginning, which cannot be a whole or a part or same or other, because it cannot be other or many: allo ti ouk an eiE polla to hen (137C4-5). 3. The last of the ten arguments of the first hypothesis (141D7-142A8) denies it being. This argument is ostensibly based upon the preceding argument, that the One does not participate in time, etc., and upon the contention that being is in time. However, that preceding argument is ultimately derived, as we just saw, from the original supposition that the One is an utterly abstract Form. This, its utter aloneness, is the real reason that the One cannot be, and you could argue directly from this reason to this result, with no intermediaries. The intermediate argument may be deceiving, taking our attention away from the real reason. The final argument then could have been the initial argument, with all else following. In fact one could also criticize the original statement, ei hen estin, allo ti ouk an eiE polla to hen (137C4-5) as self- contradictory. Plato's Parmenides himself implies this near the beginning of the next hypothesis (142C2): nun de ouk autE estin hE hupothesis, ei hen hen, ti chrE sumbainein, all' ei hen estin. But do not let the semantic problem (how do we speak of this One Form, of the abstract One?) obscure the underlying problem: contradictory modes of being, i.e. Forms (abstractions, concepts, Ideas, ideas) v. things. These are what this hypothesis, this dialogue, and modern mind-body controversies are primarily about. Finally we can compare this hypothesis with its complementary hypotheses: if there is a One (Form), it is not (#1), but 1. (being) if there is not a One, there is not a one either (#6), 2. (negation) if there is a One, the Others (Form) is not in any way one (#4), 3. (unity) if there is one (copy), it is many (#2). THE SECOND HYPOTHESIS The second hypothesis is the longest by far of all the eight. In its structure it parallels the first very closely. The first eight arguments in both (a. - g.) deal with the same topics. The second hypothesis adds a new topic in the ninth argument (h.) that is not found in the first hypothesis: touch, haptesthai. It appears to omit reference to the tenth or final topic of the first (existence and its concomitants) but really this occurs at the very beginning of the second, as we saw that it should or could have in the first. The chief difference between the two hypotheses, which may account for the greater length of the second, is that the second attributes to the one all the characters that the first denies it. Since these are contrary characters in all instances, they require lengthier explanations. The attribution of contrary characters will involve some fancy dialectic, and the use of a number of distinctions that have not been needed so far. Having called attention to the tripartite division of the contrary characters in the first hypothesis, we will ignore that feature here, and take them up one by one. It may make the study of this long hypothesis a bit easier. But first of all there is the assumption to consider. hen ei estin, ara hoion te auto einai men, ousias de mE metechein? ouk hoion te( B5-7). This is the opposite of the assumption of the first hypothesis. So much is immediately evident. The one, instead of being so utterly abstract that it cannot even be, here must partake of being, if it is. In case there might be any mistaking this, the difference is restated in the ensuing lines, B7-C7. Seldom in this dialogue is Plato as emphatic and unequivocal as he is in these lines. Everything that follows issues from this difference and from the plurality of the one being, which also mark it as not the Absolute One, but one thing. a. First of all it has parts: one and being, C7-D5. It is also a whole (D6-9). Thus we see right away that things are both one and many, as opposed to the Absolute One or Form of the One, which is utterly separate and alone. The one thing can be a collection (of parts in a whole) or an individual (part or whole), many or one, and other such ambiguities. Parts and wholes are one and many. They too are ambiguous. This section is so closely knit in the text with the assumption above, that it barely escapes being confused with thus close to the assumption of that hypothesis. b. It is infinite and limited (142D9-145A4). Each of the parts has parts, since each part is and is one. This division may be carried on endlessly, like an infinite regress, the parts always possessing being and unity (142D9-143A3). Thus begins the second argument of this hypothesis. But there is much more to it than just that. It corresponds to 137D4-8 of the first hypothesis, but it is much longer and more complex. There the One was simply infinite, for negative reasons, with an infinity of extension: it had no beginning or end. Here the existent one is infinite in division and extension (by multiplication), and it is infinite both non- numerically and numerically. Then it is also limited. The argument runs to ninety two of Stephanus' lines, as opposed to five in the first hypothesis, and it begins and ends in the midst of his paragraphs. Here is an outline of the major headings of the argument: 1 the parts have parts, ad infinitum 142D9-143A3 (infinity of division, without recourse to numbers) 2 infinity of multiplication, numerical A4-144A9 3 infinity of division, parallel with B1-E7 existents 4 it is limited E8-145A2 5 recap A2-4 Section 1 gives little difficulty. It simply carries out the logic of the prior argument so faithfully that at first sight it may strike the reader as a part of that argument rather than the beginning of a new one. Section 2 (A4-144A9) is deceptive. At first it may appear to the reader to be a digression that resuscitates the abstract One of the first hypothesis, and that mixes the two hypotheses. auto to hen, ho dE phamen ousias metechein (A6-7). Plato's absolute Ideas or Forms (auto . . . kath' auto, 143A7) were never for him only in the mind (tE dianoia monon, ibid). But this turns out to be another argument for the infinity of the one, in endless number, an infinite multitude of beings. In Plato's system numbers are not Ideas or things, but something in between, ta metaxu (Aristotle, Metaphysics, passim, see Bonitz, Index, p. 461). Here he is concerned first of all to distinguish them from the existents (things) which he has just been talking about. The structure of section 2 is as follows: a distinction of the existent 143A4-8 and conceptual ones b is the latter one or many? A8-9 (1) it is different from being, and B1-8 difference is other than oneness (2) one and difference, etc., are two, C1-144A9 and, by extension, infinite number=D4 (b) both =3D 2 D1-2 (c) both + each =3D 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 At the conclusion of the argument (144A5-9) numbers are associated with being, pas arithmos ousias metechei (A7), in contrast to the situation at the beginning. Perhaps the most important aspects of the argument are the insights it gives us into Plato's realistic view of Forms and his compromising view of numbers (metaxu). Forms are not mere figments of the mind (en tE dianoia monon, 143A7). The difference of one and its being, effected in the mind by our mental analysis, is different from the difference of Form and copy, and it requires the separate treatment given it here in this argument. This treatment by mental analysis makes use of numbers with their peculiar intermediate status. Plato's ontology is still imperfect in some respects. Section 3 (144B1-E7) runs as follows: a the cutting up of existence into B1-C2 an infinite number of parts b and of the one C2-D5 c goes hand in hand, is equal and D5-E5 infinite d recap E5-7 The assumption that oneness parallels existence seems appropriate to the second hypothesis. The assumption that beings are infinitely divisible may be unobjectionable to us, but some of Plato's contemporaries might not have found it so. The transition preceding this section, A5-9, might be assigned to this section rather than the preceding one. Section 4 (144E8-145A2) is a brief argument for the limitedness of the existent one, based upon the premisses of a parts being parts of wholes, and b wholes being limits. The first of these two premisses, the minor, kai mEn hoti ge holou ta moria moria (E8), is the same as the one used at the beginning of the first hypothesis, to meros pou holou meros estin (137C6). The second refers only to limit or infinity of extension, spatial or otherwise. Section 5 recapitulates the assumption and the first two consequences of the second hypothesis, that is up to this point. c. It has shape (A4-B5). The premiss is the preceding argument, or that last part of it which demonstrated that the existent one is limited. In this argument limit is now taken in its spatially extended sense. d. It is in itself and in another (145B6-E6). This argument exhibits the following structure: 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 it D1-4 is not in any one part (wholly) (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 the other ambiguity of the one (related to the ambiguity of the collection and the individual): it can be a whole or a part. In section 2 there is a distinct meaning assumed for being "in its parts" (in wholly in) which reflects this ambiguity. Note that there are other ways to argue that the existent one is and is not in itself and in another, if one is to use such ambiguities. The greatest one of all, i.e. to pan, the universe, is in itself and not in another, while all lesser ones are in another and not in themselves, if identity is not place (this was addressed by Aristotle in Physics, IV, iii - v). This argument also leans on the ambiguity that the existent one is a whole or a part (a.). e. It moves and rests. It stays put in relation to itself, but moves qua in another. The meaning of "in another" has changed from a static meaning (in the prior argument) to a moving one (in this). This argument has the immediately preceding one for its basis. It is the last of several arguments devoted for the most part to physical properties of the existent one, as in the first hypothesis. As in the first also, these arguments have for the most part their basis in the first of the series, that the existent one is a whole with parts. The exception is the argument for a numerical infinity of multiplication (143A4-144A9). f. It is the same and other than itself and others (146A9-147B8). This argument has four parts, followed by the usual brief recapitulation: it is 1 same as itself B2-C4 2 other than itself C4-D1 3 other than others D1-5 4 same as others D5-147B6=D4 Section 1 gives little difficulty. One thing is the same as itself, in the sense of identity or individuality, one of several possible senses of the one. The one as a part or a whole is ruled out (146B3-7) explicitly since these involve a collective sense of the one (collection of parts). If the statement that the one is not different from itself, oud' ara heautou ge heteron an eiE (C1-2), is plainly contradicted by the next section, that is because a different definition is assumed there. Section 2, other than itself (C4-D1), refers to the conclusions of the second prior argument (d., it is in itself and in another, 145B6-E6), which in turn depends upon definitions of the one as a whole and a part. Section 3, other than others (D1-5) tersely treats the argument as self evident. The same assumptions seem implied as in the first section. Compare 139C4-5 contradicting. Section 4, same as others (146D5-147B6), must obviously sieze upon the ambiguities of these terms. Let us outline this section, in an effort to detect them, as follows: a the one and the others are not different D5-147A3 (1) the Same and the Other are opposite D5-l8 to each other, auto te tauton kai to heteron enantia allElois (2) there is no other in any thing, D9-E4 since it would be in a same thing (anything that endures in time is the same), ouden esti tOn ontOn en O, etc. (3) whether one or not-one E4-5 (4) the one and the not-one are not E5-147A3 different (a) it is not by otherness or on E5-A1 account of themselves that one is different from the not-one, and vice versa (b) they cannot be different A1-3 b elimination of other possible relations A3-B3 (1) participation ruled out A3-4 (2) the not-one is not a number A5-6 (3) nor are they part and whole A7-B3 c conclusion: they must be same as B3-6 each other The first ambiguity to leap to the eye is at the beginning. Parmenides (Plato) begins by establishing a premiss about auto te tauton kai to heteron, the Same and the Other, or Different, themselves. These are Forms. Then he draws therefrom a conclusion about things, ouden esti tOn ontOn en O estin to heteron chronon = oudena. auto . . . is usually Plato's term for absolutes or Forms. Whether he means such here, or whether he means concepts (as Cornford, p. 159, suggests), is not certain. Plato seems to have made a distinction between the two (as at 143A7), which some later investigators have not. There is less question about what tOn ontOn en hO . . . chronon oudeni are. If the presence of ontOn does not suffice to mark these as things, surely the reference to their duration in time does. Let us concede Plato's uncertainty about Forms, attested well enough in the introductory part of this dialogue and in unanswered contradictions to be found in the main part. Whatever Forms or dianoetic absolutes (143A7) are, or whatever their relations to each other are, may be questions, but there is no question that they play a role in these hypotheses. They perform a function right here in this argument. This argument aims to show us that there is a sense in which ones in the world of things are the same as others. Even common sense tells us this: they are both unities. This argument is not that the Form of the One is the same as Others, nor that one thing is the same as another, but in a third way that somehow mixes Forms (or concepts) and things: if many things or copies participate in one Form (many ones in one One, for example) it is the same Form, not another, in all of them. Or if it is concept that is meant, the same observation applies. Is this then what Parmenides' argument means here? If it is, the two hypotheses that we have so far encountered, the first and the second, divide the one analytically into Form and copy between themselves, yet the treatment of each is not wholly independent of the other. If Parmenides' treatment here of the one thing takes into account its Form or concept, we cannot help recalling that his corresponding treatment of the Form of the One, not other than the others, in the first hypothesis (139C3-D1), called upon a premiss taken from the world of things (the inverse of the situation here): only another can be other than another (139C4-5). If there are no Forms without copies, ones without others, being without not-being, and vice versa, it should not be surprising that at some point these pairs of hypotheses should depend upon one another. It is possible that they are inseparable, even when separated, and that this inseparability makes itself manifest again on the detailed level. In this argument in the context of the second hypothesis, which treats of the one being, not the One Form, Plato is talking about things, while appealing to some sort of non-things, absolutes, Forms or concepts. g. It is like and unlike itself and others (147C1-148D4). This argument is organized somewhat asymmetrically as follows: it is 1 like the others C2-A6 2 unlike the others A6-C3 3 another argument, or restatement C3-D1 4 like and unlike itself D1-4 In section 1 the likeness of the one to the others is the likeness of their reciprocal difference. They differ from each other in the same way; they are affected alike; in this they are alike. D1-E6 is a long explanation in response to the young Aristotle's query, demonstrating that, when we say that the one is different from the others and the others are different from the one, "different" in both cases means the same thing. This first section of the argument depends upon the third section of the preceding argument (f.) that the one is different from the others (146D1-2). Section 2 (A6-C3) refers to the fourth section of the preceding argument (the one is the same as the others, 146D5-147B6), and to the first section of this argument (the one is like the others, 147C2-148A6) for its premisses. It presumes opposite consequences from opposite premisses. If the one is like the others, because it was different from the others, then oppositely the one is unlike the others because it was the same as the others. This compounding of opposites (he began in the first section with an argument that was opposite of what we might have expected) is enough to confuse the young Aristotle, if not the rest of us. Section 3 (C3-D1) introduces an ambiguity of a new sort. If we are quite strict, we must admit that we do not have enough evidence here to be certain whether this is a new argument, or a restatement of the two preceding sections. The first section called the one and the others, differing from one another, tauton peponthota, tauton peponthos and other inflections of these same terms, and on account of this same affect called them like: to de pou tauton peponthos homoion (148A3). This third section does the same. It is possible that the tauton peponthe (and its opposite) here (148C4-6) refers to some other affect (pathos, paschein) than that of difference, but it is not explicitly stated that such is the case. This amounts to a restatement. But if Plato had something else in mind, it might be a new and opposite argument. Such is possible but not a necessary inference, taking the text as it stands. This more permissive reading differs from Cornford's (Plato and Parmenides, p.166). Section 4 (D1-4) tersely applies the same sorts of reasoning as in the first three sections to the first two sections of the preceding argument (f.), 146B2-D1. h. It touches and does not touch itself and others (148D5-149D7). This argument presents peculiar problems. First let us identify the three main sections of it, exclusive of the heading and the recapitulation: 1 it touches others and itself D6-E4 2 it does not touch itself E4-149A3 3 it does not touch others A3-D5 The first section (D6-E4) is brief, and it refers for its premiss to the fourth prior section, d. (it is in inself and in another), 145B6-E6. This gives us no problem. It is the second and third sections that give trouble. Their arguments are good enough. It is their premisses that are questionable. A premiss of the second section is that the one is not two: heOs d' an hE hen . . . mEte duo einai, 149A1-3. A premiss of the third is that the one is only one, ei de ge hen monon estin, 149C4. The trouble is that it is a presupposition of this hypothesis that the one is two (this is precisely what distinguishes it from the first hypothesis), and it is a presupposition of the first hypothesis that there is only one alone. What then is wrong? Has Antiphon misremembered the conversation? Do these two sections belong in the first hypothesis? Has the text been corrupted? Or is this another instance of deliberate shuffling of assumptions? This is the only argument in the second hypothesis that did not appear in the first, excepting the slightest of references at 135A5-7. These two sections would fit well there, restoring an almost perfect symmetry. On the other hand, it must be admitted that he has mixed references to Forms and concepts into these arguments about things before (143A-144E; 146D- E), and will do so again very soon, in fact in the very next argument. i. It is equal and unequal to itself and others (149D8-151E2). This argument is divided into five sections, and may be outlined as follows: it is 1 equal to others D9-150E1 2 equal to itself E1-4 3 unequal to itself E5-151A2 4 unequal to others A2-B5 5 all these arguments (1 - 4) are B7-D8 extended to discrete quantities What difficulties there are, will be found mostly in the first section. These will be much alleviated if our attention is directed to three points. In the first place, the argument of the first section is a negative argument. It demonstrates that the one is equal to the others by showing that it is not unequal. to ge mEte huperechon mEte huperechomenon pollE anagkE ex isou einai, ex isou de on ison einai (150D7-8), etc. In the second place, throughout most of the argument it substitutes for unequal the terms greater or less, or greatness and smallness, meizon E elatton, megethos kai smikrotEs (passim). In the third place, it appeals for its premiss to the Forms of Greatness and Smallness and Equality. The first two points merely render this argument somewhat more complex, but the third must be the main object of our attention. Once again Parmenides (Plato) seems to be blurring the distinction between the first two hypotheses, and appealing to the nature of Forms to establish arguments about things. Notice also that such a tactic is tantamount to adopting the tactic of Socrates against Zeno in the introductory part (128E5-130A2): Forms are called upon to support an argument about things (albeit a different argument). Further, it raises a same assumption as was raised in one of Parmenides' criticisms of Socrates' use of Forms, namely that Forms have the physical characteristics that they are Forms of (i.e., the Form of Largeness is large; of Smallness, small; etc.; 131C12-E7, etc.). Any possible objections to such an assumption are again ignored. All of this raises more questions than it provides certainties. It is perhaps useless to try to guess what Plato was trying to do. It is better to admit that whatever else may have been the case, the relation of Forms and things, and thus of the first two hypotheses (perhaps also others), may be uncertain and paradoxical. The presence of Forms is the main point to be considered in the first section. Section 1 (D9-150E1), equal to others, may be divided thus: a establishment of Forms: things are D9-A1 equal, greater or smaller only by their participation in such Forms b there is no Smallness in the one A1-B7 (1) in the whole of it A3-B2 (2) in part of it B2-7 c there is no Greatness in the one B7-C6 d the one, not smaller or greater than C7-E1 the others, must be equal to them Section 2 (150E1-4), equal to itself, simply applies the same argument to the one in relation to itself. Section 3 (E5-151A2), unequal to itself, relies upon argument d., it is in itself (145B6-C7), for the premiss. It no longer exhibits the reliance upon Forms, found in the first two sections.= Section 4 (A2-B5), unequal to others, also relies partly upon argument d., but not explicitly and this time to the second section of that argument (145C7-E3), it is in another (others). It also relies upon an argument that the one and others are in one another (A2-9). Section 5 (B7-E2) recognizes that greater, less and equal are measures; measures are parts; parts imply numbers. Thus the arguments of the preceding sections are extended to numbers and discrete quantities. j. It does and does not partake of time, be and become younger and older than itself and the others (151E3-157B7). This argument is divided into two major parts: 1 the one does partake of time, etc. 151E3-155E3 2 the one does not partake of time, etc. 155E4-157B5 It is one of the arguments that seems as if it does not have a symmetrically opposite argument in the first hypothesis. This lapse of symmetry has been mentioned before, but it is perhaps appropriate that the aberrations be summarized: all the arguments= =D4 except (a) the last argument of the first hypothesis is the negative of the assumption of the second; (b) the argument h. of the second (touch) is not to be found at all in the first, and covers both positive and negative; (c) the second arguments of each appear at first to reach similar conclusions (i.e., infinity) but really they do not, since opposite notions of infinity are at stake; (d) in the arguments of the two hypotheses about time, the One of the first is not in time, etc., while the one of the second both is and is not. There will be found, of course, a distinction, or what we have called an ambiguity, in the meaning of not being in time. This lack of opposition between the two hypotheses may be more apparent than real, but it may add to the complexities that will be noted below. That the one does and does not partake of time, etc., has not always been seen as two parts of a single argument terminating the second hypothesis. To the neoplatonists, e.g. Proclus, the part 2, 155E4-157B5 (the one does not partake of time, etc.), was a separate hypothesis. To Cornford it was a corollary to the second, which he calls hypothesis 2a. This question will be examined more closely when we come to this section of the text. Let us take up the first part first: 1 the one does partake of time, etc. 151E3-155E3 a it becomes older than itself E6-152A5 b it becomes younger than itself A5-B2 c it is older than itself B2-D4 d it is younger than itself D4-E3 e it is not and does not become E3-10 older and younger than itself f it is older than the others E10-153B7 g it is younger than the others B8-D5 h it is the same age as the others D5-154A4 i it does not become older or A4-C5 younger than the others j it does become younger than C5-E3 the others k it does become older than E3-155B4 the others l recapitulations B4-C7 m there is knowledge, opinion, C7-E3 sensation of it, a name for it, and reasoning about it This is the most complex section of a complex dialogue. It is also the longest. Up to this point the most complicated argument has turned around two pairs of alternatives, or at the most three: positive and negative of a character in relation to self and others (e.g. like and unlike itself and others), with one case of a splitting in two of a character (e.g. unequal =3D greater or lesser). Here there are at least four major pairs of alternatives: positive and negative, self (one) and others, being and becoming, younger and older. These are evident in the headings (151E3-6, 155C4-7, etc.). They result from the complex nature of time. Time presents us with its own ambiguities. Time may signify an instant or a duration, hence the attention to both being and becoming. Duration may be viewed forwards or backwards, or two times may be compared two ways, taking either as a base of reference, hence older and younger. Furthermore, an instant may be viewed as in a duration (part of time), or not (in this sense, not in time), hence the two major parts of this argument, as we shall see. Subsections a - d make use of the first two of these ambiguities. a and b treat time as duration; a, as the normal process of aging; b simply reversing the viewpoint, the older in duration being younger or newer in its present state (the reference at 152A6 is to 141B1-C4). c and d view time as an instant: what becomes older or younger is, at any instant, older or younger. Starting with e additional ambiguities are introduced. e negates all the preceding four conclusions by treating time as duration, but in a different manner than heretofore: it is not comparing two separate instants in a duration, but measuring the quantity of the duration. In other words, duration is ambiguous: it is expressed by two separate instants or by the amount of time between them: you can stay from Wednesday to Friday, or three days. Whereas in a - e the one is any one thing, in f the one is a number, the first of a series of numbers. Notice that Parmenides (Plato) is also careful to distinguish others from other. In g the others are within the one as parts of it; elsewhere they have been externals (there are references to 142D1 in 153C1, and to 145A6 and B1 in 153C2). In h the same age is substituted for not older or younger, i.e. a positive expression for a negative expression. The oneness of the parts of the one is now invoked (A2-4 refers to 152E10-153D5). In i older and younger refer to the change in difference in age, rather than difference in age (ei kai estin, etc. in 154B1-2, refers to sections f and g, 152E10-153D5). j and k compare durations proportionately, instead of absolutely, as elsewhere (154C6-7 refers to 153A1-D5). k merely reverses j. There follow two recapitulations in subsection l, 155B4-C7. First, subsections i, j and k, 154A4-155B4, are recapitulated at 155B4-C4. Then the whole section, 151E6-155B4, is recapitulated at 155C4-7. Finally this first part ends (m, 155C7-E3) with the ascription of knowledge, opinion, perception, name, reasoning and all the other things that we have of the others also, just the opposite of the situation described at the end of the first hypothesis. That brings us to the second major part of this argument: 2 the one does not partake of time, etc., 155E4-157B5. dielEluthamen can mean anything. hen te on kai polla mEte hen mEte polla kai metechon chronou (E5-6) is the critical phrase. It modifies the subject, providing a clue to whatever the subject might be. It is the one of course, but which one? This phrase seems to establish that it is the one of the second hypothesis. It sums up its self-contradictory character very succinctly in saying that it is one and many and not one and not many, adding that it participates in time, not as an afterthought but to remind us of the immediate context, the final question about time. Unfortunately the remainder of this sentence, oti men estin hen, ousias metechein pote, oti d'ouk esti, mE metechein au pote ousias, clouds the issue. This predicate seems to refer to the one of the second hypothesis and the One of the first (cf. 141E9-10). So the subject seems ambiguous. It can be either the one of the second hypothesis or the one (One) of the first two hypotheses. Thus there are two possible contexts for the ensuing discussion. But either context will do. Whether we consider change from the One of the first hypothesis to the one of the second, or change of the one of the second from contrary to contrary, in either case we have the basis for the point that Parmenides wishes to make: the one changes, and it changes in time (155E8-156A4). Various kinds of change are enumerated (A4-B8). Parmenides' argument now follows (156C1): precisely due to the fact that it changes, the one does not partake of time. But it does not partake of time (note well) for quite a different reason than the reason that the One of the first hypothesis did not partake of time. There (in the first, 140E1-141D6) the One did not partake of time because of its utter transcendence of all the characteristics of existence. Here its non-participation is due to a peculiarity of change and time themselves. There seem to be three options altogether: 1. participation in time, by the one of hypothesis 2, j., 1 (151E3-155E3), 2. no participation in time, because it is utterly transcendent, the One of hypothesis 1, 3. no participation in time, because time stops in the instant of change, the one of hypothesis 2, j., 2 (155E4-157B5). Is it possible that this last is "the third" (to triton) that Parmenides (Plato) refers to at 155E4? Whatever the answer to that question, it seems that the present argument is an integral part of the second hypothesis, and in no way represents a separate one. Hypotheses non sunt multiplicanda praeter necessitatem. It exhibits the following structure: a the one changes (1) the one of hypotheses one and two E4-8=D4 partake of being (2) it changes E8-156B8 (a) it changes participation E8-A4 and being (b) it becomes and decays A4-B1 (c) it divides and combines B1-5 (d) it becomes like and unlike B6-7 (e) it grows, diminishes, equals B7-8 (f) it changes from motion to C1-2 rest, and rest to motion b the nature of change C2-D1 (1) it is not in time (en heni chronO) C2-3 (2) demonstration C3-D1 (a) repetition of definition in C3-5 (f): for the resting to move or moving to rest, is change (b) syllogism C6-D1 1 there is no time when some- C6-7 thing is neither resting or moving 2 when something changes, it is C8-9 neither resting or moving 3 it is not in time C9-D1 c the instant is not in time: a paradox D1-E3 d the one changes from motion to rest, E3-7 and vice versa in an instant, not in time e and this is true of other changes E7-157B5 All of this rests upon the ambiguity of change and time as durations v. change and time as instants. The notion of the instant was something quite puzzling to the early Greeks, as Parmenides (Plato) makes plain right here in his extended discusssion of it (D1-E3) as a paradox. It had been the subject of one of Zeno's paradoxes about motion, i.e. the flying arrow, and it was to be the subject of Aristotle's attention in Physics, IV, xi. Surely the One of the first hypothesis changing to the one of the second (if it does), and even much more surely the one of the second, going through any of the numerous changes which Parmenides has just put it through, encounter this problem of change and time. It was a problem which had not in Parmenides' or Plato's time been resolved, and which deserved the attention that was called to it here. To sum up, the second hypothesis exhibits a carefully crafted internal structure, and a structure that is (for the most part) symmetrical with that of the first hypothesis. One difference is that whereas the first denies the attribution of the contrary characters to the One, the second affirms their attribution to the one. Being contraries, their affirmation in the second requires a lengthier logical exercise. More distinctions and ambiguities are required. The hypothesis is longer. It is the longest of the eight. Some exceptions to the complete symmetry of the two hypotheses have been noted. For the one-sided treatment of touch in the second, missing in the first, there seems to be no sure explanation. The special treatments of infinity and time are due to the peculiar and problematic nature of these. Nevertheless one can hardly finish the reading of these two hypotheses without a strong impression of their close relation. Taken together the two hypotheses emphasize the two possible states of being, and of unity: as Form and copy. The theory of Forms is not new here in Plato's writing but it receives here a problematic treatment that is new and deeper than before. Here is a Form that does not exist! And if the one is and is not, what does "is" or "to be" mean? The fact that one thing is also many need not surprise us; it is a commonplace. But it was not so simple a matter to Plato and his contemporaries. The remaining hypotheses will also exhibit, in pairs (3-4, 5-6, 7-8), other contradictory consequences of changes from Form to copy, or vice versa. That there are two kinds of one and two kinds of being seem now established. But there will be other problems, and we will shortly see two kinds of negation. The Form theory, the existence of Forms alongside things, raises acute problems. THE THIRD HYPOTHESIS The third hypothesis is much shorter than the first two. Its arguments - there are only four of them - seem quite different than any that have gone before. Parmenides (Plato) is now concentrating his attention for the first time upon a new problem, a matter that had previously been taken for granted. a. In the first two hypotheses, the arguments about parts and wholes were used prominently, and were premisses for a number of other arguments. It was a question of the One having no parts and not being a whole (first hypothesis), or of the one being a whole with parts (second). The relationship of parts and wholes itself was not questioned. At 137C5-8 it was simply accepted that a part must be part of a whole. Here in the third hypothesis this is investigated more deeply. At 157C8 it is asked, why? pOs touto? At 157C8-E2 a demonstration appears to be offered, why parts must be parts of a whole. The argument is complex and tricky (due in part to a concatenation of negatives). At the risk of being tedious, we will outline and examine this section, 157B9-E5, in detail: 1 If there are others than one, they are not B9 one, because they would not be others [if they were one] eipeper alla tou henos estin, oute to hen esti talla, ou gar an alla tou henos En. 2 But the others are not entirely lacking unity C1-2 (the one) but participate in it somehow, oude mEn steretai ge pantapasi tou henos talla, alla metechei pE. 3 [Why the others somehow participate in unity] C3-E5 a the others have parts; otherwise they'd be C3-4 one, ta alla tou henos moria echonta alla estin, ei gar moria mE echoi, pantelOs an hen eiE, b the parts are parts of a whole, moria de C4-5 ge phamen (137C6), toutou estin ho an holon H, c the whole is one, because each of the parts C5-8 is not part of many parts but of a whole, to ge holon hen ek pollOn anagkE einai, ou estai moria ta moria, hekaston gar tOn moriOn ou pollOn morion chrE einai, alla holou (this too looks back to 137C6, but now the young Aristotle asks, why? pPs touto?). 4 [Why the whole is one, and why each of the C8-E2 = parts is part of a whole, not of many - this is the apparent demonstration we spoke of, answering the young Aristotle's "Why?". It deserves close examination.] a each cannot be part of a many, because, if C8-D2 it were, a part would somehow be part of itself and of each of the others, which is impossible, ei ti pollOn morion eiE, en hois auto eiE, heautou te dEpou morion estai, ho estin adunaton, kai tOn allOn dE henos hekastou, eiper kai pantOn, b [why that is impossible] D3-7 (1) not being a part of one (>B9), it will be D3 part of the others, henos gar mE on morion, plEn toutou tOn allOn estai, (2) and so it will not be a part of each one, D4 kai houtOs henos hekastou ouk estai morion, (3) and not being a part of each, it will be D4-5 part of none of the many, mE on de morion hekastou oudenos tOn pollOn estai, (4) being some (ti) of none of all these of D5-7 which it is none of any, it is impossible for it to be a part or anything else, mEdenos de on pantOn toutOn ti einai, On oudenos ouden esti, kai morion kai allo hotioun adunaton. c so the part is not a part of many or all, D7-E2 but of some one Idea, and of some one thing which we call a whole, become one completion of all: this is what the part is part of, ouk ara tOn pollOn oude pantOn to morion morion, alla mias tinos ideas kai henos tinos ho kaloumen holon, ex apantOn hen teleion gegonos, toutou morion an to morion eiE. 5 Thus if the others have parts, they participate E2-5 in the whole and unity. The others than one must be one complete whole having parts, ei ara metechoi. Hen ara holon teleion moria echon anagkE einai talla tou henos. This apparent demonstration makes use of an ambiguity of "one" (in 4, b, (1) it is a whole; in 4, b, (2), a part). Of more importance, its negative assumption in 4, b, 4 begs the question: can a part be part of something else, namely a whole? This is just what the argument here is trying to prove, albeit in a negative way (it can't be part of a many that is not a whole; it is not a part of each; if it is not a part of each, it is a part of none, etc.) Its negative assumption (being none of all these, it cannot be a part or anything else) begs the question: can it not be part of a whole? That is something else. The arguments about wholes and parts, it should be clear by now, are equivalent to the arguments about ones and others. Parts are and are not ones, and others; and wholes are and are not ones, and others. And wholes are and are not parts, and parts are and are not wholes, just like the ones and others in these hypotheses. The assumption first stated at 1375-8 that parts are parts of wholes, and referred to elsewhere later, is nothing else than the assumption (ostensible conclusion) of this hypothesis that the others somehow participate in unity. Both of course are well founded on our everyday experience of things. The relations of whole and parts can be run through all the same changes that the relations of the one and the others are run through in the eight hypotheses. b. The second argument, that the others are infinitely numerous (plEthei apeira) and limited, 158B5-D8, has three sections: 1 infinite B5-C7 2 limited C7-D3 3 recap D3-8 The first section, that they are infinite, commences with a reminder of the preceding argument, epei de ge pleiO henos esti ta te tou henos moriou kai ta tou henos holou metechonta. Because of this participation in unity, any argument for an infinity of division, based upon a lack of an atomic limit, might be suspect. Thus a different approach is used: whatever you might wish to subtract from the many others, however small, would itself also be a plurality (C2-4), and this can be repeated indefinitely (C5-7). The subtrahend is a part, and might participate in unity, but in so far as it is not one (plEthE onta, en hois to hen ouk eni, C1) itmay = undergo repeated subtraction. In so far as it is, it is limited (the second section, C7-D3). The recapitulation (third section, D3-8) emphasizes this ambivalence: heteron ti gignesthai en autois. c. The third argument, that the others are like and unlike each other and themselves, E1-159A6, is based upon the second, or preceding argument (b.). Since they all have the two contrary characters of infinity and limit, they have likeness and unlikeness, depending upon which are chosen for comparison. d. The fourth argument, A6-B1, tersely extends the same reasoning to the rest of the contrary characters. Observe: if the one is not, there are still others, or other ones, as here. That is the seventh hypothesis. If the One and the Others are Forms, the Others is not One. That is the next hypothesis, the fourth. THE FOURTH HYPOTHESIS The peculiarity of the fourth hypothesis which arrests one's attention is the great care with which it establishes the separateness of the One and the Others, 159B6-C4. There is no third choice, nothing that is both one and other, as the one of the second and the others of the third hypothesis were. When one has said the One and the Others, one has said it all; there is nothing else in which the One is and the Others; the One and the Others are not in the same; they are utterly separate. All this quite emphatically marks off the fourth hypothesis from the second and the third, and applies to thoroughly separate abstractions, or Forms, as opposed to things. Furthermore, as one saw in the case of the Form of the One in the first hypothesis, the Form of the Others also does not have the contrary characters, not any of them. a. They are not parts or wholes, C5-D3, having no participation whatsoever in the One. The reasoning here appears to reverse itself: the non-participation of the Others in unity appears to be the conclusion of this argument, but it is really the premiss, established in the introductory part, utter separation. b. They are not one or many, B3-E1, for the same reasons: the one and the many participate in unity, just like wholes and parts, with which they are closely associated in D6-7. Still the contrast with the third hypothesis. Furthermore they cannot be numbered (D7-E3).= c. They are not like or unlike, E2-160A3, since they would participate in unity and duality, which the preceding argument (b.) has precluded. d. They have none of the contrary characters, A4-B2, for the same reasons. e. B2-4 recapitulates very tersely the first four hypotheses. The fourth hypothesis may be compared with the third, the first and the eighth. Comparisons with the third and the first have already been made. Comparison with the third requires the distinction of Forms and copies; with the first, of Forms of One and the Others. We have noted that it is emphatically pointed out that the Form of the Others has no unity whatsoever, a rather remarkable thing to say about any Form of Plato's. The fourth hypothesis therewith raises a huge question about Plato's theory of Forms. Our occasional references to this Form in the singular (the Form of the Others), as concessions to grammatical convention, sound awkward.= Comparison of the fourth with the eighth hypothesis discloses another paradox. If there is a Form of the One (fourth), the Others are utterly separate, but if there is not a Form of the One (eighth), the Others are not, either. Thus, while the Others and the One are utterly separate, there is some kind of a connection between them (eighth). THE FIFTH HYPOTHESIS If we pause to reflect upon the surprises that the hypotheses have sprung on us so far, we may recall that the first revealed a Form that does not exist; the second, a one that is many and is the subject of all sorts of contradictions; the third, many that are one; and the fourth, a Form that has no unity whatsoever. These are all remarkable revelations about Plato's metaphysics, but the fifth hypothesis is going to surprise us with yet another novelty. In it Plato addresses the question that the ancient Greeks had found the most vexing of all: can not-being be? Can that which is not, be? The real Parmenides had expressed himself rather forcibly on this question: never shall this be proven, that things which are not, are, ou gar mEpote touto damEi einai mE eonta (DK VII, line 1). Plato brought it up in the Euthydemus, and he offered a solution in the Sophist: not-to-be may mean to be different. It is a solution that applies to things perfectly well. Here in the middle of the fifth hypothesis of the Parmenides he meets this ontological paradox head on, without any assistance from megista genE, and proposes a different solution to a different question: can not- being be, absolutely? The fifth hypothesis begins with a relatively long introduction, 160B5-161A5. About one quarter of the text of the hypothesis is devoted to the elucidation of what is meant here by the hypothesis, if there is not a one. The assumption here is that there is some definite idea of the one to which we ascribe not-being. An outline of the introduction goes as follows: 1 what do we mean by this hypothesis? B6-7 2 distinct things can not be a the one and the not-one B7-C2 b other examples, for differentiation C2-7 3 there is knowledge of them C7-D2 4 recap D3-E2 5 the not-one has "thisness, thatness, E2-7 somethingness," etc.=D4 participate in many (ideas) In other words, there may be Ideas or Forms that do not exist as copies or things; in the present case, of the One. Not-being may be: what is not as a copy of thing, may be as an Idea or Form. This way of putting the connection between being and not-being puts it in terms of the kinds or modes or states of being, rather than in terms of differential negation (as in the Sophist). The one that is not, is the subject of this hypothesis: a. It has unlikeness (A6-B4) and likeness (B4-C2). Notice that the text does not say it is unlike or like, but that it has unlikeness and likeness (autO estin). (And later it does not say that it is unequal or equal, but that it participates, etc.) The one-that-is- not is not assumed to be anything yet, except an Idea (Form). Notice also that the duality of all these relations, to itself and the others, so prominent in the earlier hypotheses, has been dropped, except at 164A3. b. It participates in inequality (C3-D1) and equality (D2-E2). c. It participates somehow in being and not-being, 161E3-162B8. This argument is extraordinary: 1 it interrupts the pattern, established in the prior hypotheses, that goes down the list (gradually abbreviated, to be sure) of contrary characters seriatim; and 2 one might expect that the introduction to this hypothesis (160B5-161A5) had sufficiently established that the one- that-is-not participates somehow in being, when it ascribed to it Formal being, but apparently it had not, and here it requires restatement. The argument is nearly entirely devoted to the being of the one- that-is-not. kai mEn kai ousias ge dei auto metechein pE, E3. Only the final line mentions its not-being. kai mE ousia ara, eiper mE estin, 162B7. It begins with a short section (161E4-162A1) based upon the implied premiss that truth is a kind of being. This seems not wholly unrelated to the stipulations of the introduction, 160B5-161A5, and it also foreshadows Aristotle's classification of one kind of being as truth in Metaphysics, Eta, ii - iii. Then it continues with quite a different, indeed a unique argument. We reproduce it here entire: The one that is not, it seems, is, estin ara, hOs eoike, to hen ouk on, 162A1. [Here is the reason why:] ei gar mE estai mE on, alla pE tou einai anEsei pros to mE einai, euthus estai on, because if not-being will not be, but somehow will give up being in favor of not-being, it will immediately be being, A2-3. dei ara auto desmon echein tou mE einai to einai mE on, there must be a bond [or connection] between being and not-being, ei mellei mE einai, if [not-being] will not be, A4-5, homoiOs hOsper to on to mE on echein mE einai, hina teleOs au E, just as being has not-being not be, in order that it may completely be, A5-6, houtOs gar an to te on malist' an eiE kai to mE on ouk an eiE, because in this way being is, most fully, and not being is not, A6-7, metechonta to men on ousias tou einai on, mE ousias de tou mE einai mE on, ei mellei teleOs einai, to de mE on mE ousias men tou mE einai on, ousias de tou einai mE on, ei kai to mE on au teleOs mE estai, on the one hand, being participating in the being of being being, and in the not-being of not being not-being, if it will completely be, while on the other hand, not-being participating in the not-being of not being being, and in the being of being not-being, if it will completely not be, A6-B3. The last clause is exceedingly symmetrical, a great help in its interpretation. The text then continues, applying these conclusions to the one- that-is-not. Summarizing, the one, if it is not, has being as well as not-being, B3-8. The role of this argument in the present hypothesis will shortly be made clear, in the next argument. Meanwhile we must observe that, taken by itself, it appears to constitute a remarkable passage in Plato's ontology. Elsewhere, as in the Sophist, he addressed the question, whether not-being might be, and answered that it might be, in the Form of Difference. Here however there is no such limitation: it is absolute not-being. = d. It moves and it rests, 162B9-E3. This may be outlined as follows: 1 it moves (kinoumenon) B9-C6 2 it rests C6-E2 a it does not change place (metabainein) C9-D1 b it does not turn in place (strephesthai) D1-5 c it does not alter (alloiousthai) D5-8 d recap and conclusion: it rests D8-E2 3 recap: it rests and moves E2-3 The basis of the argument for movement is the preceding argument: if it has and has not being, it must change from one state to the other; change is motion. The basis for the argument for rest is the denial of place, and consequently motion, to what is not. At this point there is a not too troublesome confusion in the structure of Parmenides' (Plato's) arguments. The argument about motion and rest is not summed up (E2-3) until it has broached the topic of alteration (D5-8), but thereafter Parmenides takes up alteration as an independent topic. e. It changes (alters) and does not change, E4-163A7. This is closely based upon the preceding argument: motion and alteration were closely associated, if sometimes distinguished. Their relation was an on-going problem for the ancient Greeks. f. It does and does not come into being and pass away, A7-B6. This is based upon the preceding conclusions about change. So, if the one is not, at least the Form is, in this the fifth hypothesis. If it were the Form that is not (sixth), there is no copy. And if the one is not, there is a Form of the Others also (seventh). THE SIXTH HYPOTHESIS The introduction, 163C1-D1, makes it very plain that the subject of this hypothesis is the one that is not which lacks any kind of being, oudamOs oudamE estin oude pE metechei ousias to ge mE on, C4-5. Although it is neither Form nor copy, we listed it in the charts above of "The Eight Hypotheses" as a Form, One that is not, since, if it were a copy it would have being as a Form (hypothesis #5), but as a Form that is not, there can be no copy either. Not being in any way whatsoever, it is neither Form nor copy, and it lacks all the contrary characters, of course. These are enumerated, it will be noticed, in the same list as in the fifth hypothesis, but in reverse order, setting aside the section on being (5., c., 161E3-162B8) which this hypothesis has addressed first of all. The arguments are simple and brief: a. If it participates in no way whatsoever in being, it is fairly plain that it cannot come into being or pass away out of it (D1-8). b. If it cannot become or pass away, it cannot change, since change involves those. If it cannot change, it cannot move. If it cannot be, it cannot be in the same place, i.e. rest (D8-E6). c. If it has nothing of being, it lacks the rest of the contrary characters and everything else: greatness, smallness, equality, likeness, difference, relation to itself or others. There are no others than it, if it is not, for it to be related to, or to be like or unlike or same or different from it. It has nothing, is nothing, not this, etc., not before or after or now (E6-164B1). d. There is no knowledge, opinion, perception, account or name of it, or anything else whatsoever having