NEAR-FINAL TEXT: For official citation purposes, please use published version Platonic Ring-Composition and Republic X In Book I of the Iliad, anger and social rupture are transmitted in a chain reaction: from the grieving father Chryses to Apollo, from Apollo to Agamemnon and Achilles, from Achilles to his mother Thetis, and from Thetis to Zeus and the other gods. In Book XXIV acceptance and reconciliation flow in the other direction, from the divine to the human. In Book I, the aged Trojan priest Chryses travels to the Greek camp to ransom his daughter, and his pleas are rejected; in XXIV, the elderly Trojan king Priam travels to the Greek camp to ransom his dead son, and his pleas are accepted. In Book I, Achilles quarrels publicly with his leader Agamemnon and rejects his role as warrior; he appeals to his divine mother Thetis, who appeals to Zeus on his behalf. In XXIV, Zeus directs Thetis to appeal to Achilles, who then reconciles privately with his enemy Priam and accepts his fate. In short, the first and last Books of the Iliad are mirror-images of each other. Similar, though less marked mirrorings structure Books II and XXIII, and to a lesser extent III and XXII. The Iliad is thus structured by ring-composition, so that the work as a whole has the pattern ABCDCBA.1 Smaller ring structures pervade it as well, most notably in the famous Homeric similes (in which, for instance, a warrior is likened to some force of nature, usually in an ABA pattern) and many of the important speeches. Homeric ring-composition is never pressed to the point of rigidity or artificial display. There are profound differences between even Book I and Book XXIV – for instance, there is no real correlate in Book I to the mourning for Hector which ends the Iliad as a whole. The resonances are just quietly powerful enough to give the reader a sense of order, harmony, and completion. The ring structure also seems to have a 1 The locus classicus for Iliadic ring-composition is the work of van Otterlo 1944, which also reviews earlier applications of the concept to Greek texts, and 1948. A fascinating discussion in English is Whitman 1963; for a state-of-the-art account, cf. Schein 1997, 345-59. Douglas 2007, 101-124 devotes two chapters to the Iliad, emphasising the symmetrical pattern of days and cognitive import: it is part of the reason that in reading Book XXIV we feel we are learning something fundamental about human life as the Iliad has been depicting it all along. Ring-composition makes it possible for the culminating insights and conclusions of a work to be experienced as moments of recognition. It is impossible to discuss its aesthetic function without being reminded of the famous lines from T.S. Eliot's Four Quartets: We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time.2 I. Ring-composition is found in every kind of temporally extended artistic composition, on every scale, and in a bewildering variety of patterns: ABA, ABBA, ABCBA, ABCCBA, and so on indefinitely. Beowulf is ring-composed;3 so is Meleager's self-referential Garland;4 so is almost any movie told in flashback form. The standard sonata form, used for first movements of symphonies, sonatas and chamber works since the mid-18th century, is a kind of ring-composition. I will adopt musical terminology and speak of exposition and recapitulation for the rings found in the opening and closing halves of a work respectively. One useful distinction we can draw is between what I will call 'bookend' and 'pyramid' forms of ring-composition. By 'bookends', I mean a form in which the closing part gestures back to the beginning, without any rings being discernible in between -an ABA in which the great bulk of the work falls into the central B. Most movies in nights over which the events are distributed. Cf. also Myres 1932, 264-96. Ring-composition in the Odyssey is discussed by Tracy 1997, 360-79. 2 Eliot 1944, 'Little Gidding', lines 239-42. 3 Tonsfeldt 1977, 443-452. 4 Cf. Höschele (ms). flashback form follow this pattern; so does a poem in which the last line repeats or rhymes with the first. A pyramid structure (one might also think of a coastal shelf, or a Russian doll) is more elaborate and pervasive, with a regress of multiple rings: e.g., an ABCDCBA structure. We can also distinguish between various kinds of recapitulation. The obvious distinction here is between simple repetition, as when a musical motif from a work's opening is reiterated, and mirroring, in which the order of events is reversed as in Iliad XXIV, creating a kind of chiasmus or husteron proteron. But perhaps a more important distinction is between mere repetition and the kind of transposition we find in Iliad XXIV (and most uses of sonata form), where the reappearing content is transposed -even inverted -in ways which add meaning. Instead of a live daughter, Priam ransoms a dead son; instead of a public quarrel with his allies, Achilles shares a private meal with an enemy; instead of anger being transmitted from the human to the divine, reconciliation is passed on in the other direction. I will call this kind of transformed recapitulation a resolution, and will represent such ring-structures as ABB'A': the point is again to suggest the musical term, since the effect is often that of a dissonance resolved. The 'Eliot' experience of recognition tends to be the mark of a certain kind of resolution. In truth the distinction between resolutions and other recapitulations is a matter of degree, for even in a limerick pure repetition is rarely to be found: There was an Old Person of Hurst, Who drank when he was not athirst; When they said, 'You'll grow fatter,' He answered, 'What matter?' That globular Person of Hurst.5 Here the first and last lines are bookends, and the repetition is reinforced by the rhyme scheme; but the 'globular' in the last line is a significant addition, giving the upshot of the intervening lines. In more sophisticated works, exposition and resolution may differ dramatically, and the ring-structure may be very messy and incomplete. The only perfectly ring-composed work is a palindrome: in high art, asymmetries, blurring, partial melding and interleaving of rings are all par for the course, whether the composition is a Pindaric ode or a Beethoven sonata. None of this prevents the ring form, and the resolution in particular, from serving its structural, aesthetic and cognitive functions. II. Ring-composition is characteristic of some major works in elevated style with roots in oral tradition: the Iliad, Beowulf, parts of the Pentateuch, some Sanskrit epic and drama, and the Zoroastrian Gathas.6 Scholars have inferred that it is a marker of oral composition;7 but ring-composition of various kinds is pervasive in later Greek literature as well, including Pindar, Herodotus, Thucydides, and various orators and epigrammatists.8 It has tended to go undetected in philosophical texts -or perhaps to be ignored as philosophically insignificant. My aim in this paper is to partially remedy this for the case of Plato, and the Republic in particular. We can warm up by noting some other instances of ring-composition in Plato and Aristotle -though to do so will require dogmatizing about some endlessly controversial texts. (1) Bookending is present in several Socratic dialogues. The Charmides reverts near the end to the opening topic of Socrates' Thracian charm (155b-7c; 175a-6a); the Meno ends 5 Edward Lear 1862, 21. 6 For the Pentateuch and the Gathas, see Douglas 2007, 2-5, 12-6, 43-71 and 6-7 respectively; for Beowulf, Tonsfeldt 1977. 7 Notopoulos 1951, 98; but the further claim that ring-composition died out early in the history of Greek literature ("it is a stylistic device which terminates with the fifth century" (97)) is clearly false. In fairness, much of the early scholarship on ring-composition, Notopoulos' paper included, focusses on the small-scale rings used to structure speeches and digressions in epic and tragedy, not the larger structures I am concerned with here. 8 For Pindar, see Race 1997, vol. 1, 20ff. and Kirkwood 1982; for 'pedimental' structure in Herodotus, Myres 1953; for Thucydides, Hornblower 2004, 271, 282-3, 315, 328, 338, 346-7; 349; for the orators, Worthington 1991 and 1993; for the Hippocratic corpus, Wenskus 1982; for epigrammatists, Höschele, n. 4. with an answer to Meno's opening question (70a; 99e-100b); in an amusing 'transposed' resolution, the Laches opens with the question of how the young (the sons of Lysimachus and Melesias) should be educated and ends with the subject of how the old (Socrates and his friends) might yet be (178e-80a; 200a-01c). In these cases the bookending serves to prompt reflection on how far the opening questions of the dialogue have been answered by the intervening dialectic -and perhaps hints that Socrates and his interlocutors have in some sense ended up where they began. (2) The dialectic of the Theaetetus is also quietly bookended. Theaetetus' first attempt at a definition of knowledge consists in a list of epistemai (146c-d); Socrates objects that this is as if one were to define 'clay' by listing 'potters' clay', 'brickmakers' clay' and so on (147a). This is obviously doomed: "a man who does not know what knowledge is will not understand 'knowledge of shoes' either" (147b).9 At the close of the dialogue, the last definition of knowledge Socrates considers is that knowledge consists in correct judgement together with an account of the differentiating feature of an object. But this is ambiguous: is mere judgement of the differentiating feature required, or knowledge of it? The latter option provokes an objection which is the same as Socrates' first: "it is surely just silly to tell us, when we are trying to discover what knowledge is, that it is correct judgement accompanied by knowledge, whether of differentness or of anything else" (210a). In short, both the first and last definitions are vitiated by inclusion of the term to be defined -that is, by being circular. This circling back to circularity reinforces the aporetic character of Socrates' conclusion: the dialectic of the Theaetetus as a whole ends where it began. (3) The Sophist has a pyramidal structure, though two steps are more or less fused in the first half. We work through (A) preliminary definitions of the sophist (217a-236e); (B and C) the puzzles raised by false statement and by any kind of thought or speech about Not-Being (237a-41d); and (D) the puzzles raised by Being (241d-51a). The 9 Quotations from the works of Plato are by the various hands in Cooper 1997, including the translation of the Republic by G.M.A. Grube revised by C.D.C. Reeve, in some cases with revisions. recapitulation revisits the same topics in mirror order, resolving the puzzles raised in the first half: (D') Being and the other greatest kinds are explained as distinct but interacting forms (251a-56d); (C') Not-Being is identified with the form of Difference (256d-59e); (B') false statement is explained and shown to be possible (260a-64b); and (A') the final definition of the sophist is produced (264d-8d). (4) The Cratylus has both bookends and a somewhat messy pyramidal structure.10 The bookending is through a small motif: at the start, Cratylus denies that 'Hermogenes' is really the name of Hermogenes (384e); at the end, Socrates hands Hermogenes' name back to him by calling on him to escort [propempsei] Cratylus to the country, as a son of Hermes pompaios would do (440e). 11 The name 'Hermogenes' is also discussed more extensively near the mid-point of the dialogue (408b): as Mary Douglas notes, ringcomposed works often have a marked 'turn' at mid-point tied to the outermost rings in some way.12 The pyramid is shaped roughly as follows (pairing exposition and recapitulation rings): (A) Cratylus and Hermogenes are introduced as being at odds (merged with the exposition of conventionalism) (384a-5e), then later (A') they are reconciled, or at any rate sent off together by Socrates (440e); (B) the stability of things is accepted as a necessary assumption by Hermogenes (385e-7b), then later (B') argued for by Socrates (439b-440d); (C) truth and falsity in logoi are said to depend on truth and falsity in naming, and thus on the possibility of false names (385b-d, following Schofield in shifting 385b2-d1 to follow 387c5, though even on this reading there is some interleaving of rings in the recapitulation),13 then later (C') the possibility of false names is shown to make truth and falsity in logoi possible (432e); (D) conventionalism is rejected (387d-91a), then later (D') rehabilitated, in connection with the understanding of names as pictures (433a-5e). All this is oriented around a kind of two-fold dialectical core, (F) the account of natural correctness (391cor perhaps 387b-427d) and (G) its critique (427d-33a). 10 Cf. Barney 2001a, 17 n. 25. 11 Barney 2001a, 160. 12 Douglas 2007, 31-2, 37. (5) Its authenticity is a matter of perennial dispute, but for whatever it is worth the Platonic Seventh Letter is also ring-composed. It centres on a philosophical 'digression' (341a-45c) surrounded on both sides by historical autobiography; and that digression is itself ring-composed. It progresses through (A) references to Plato's conversations with Dionysius (341a-b; with extended criticisms in (A'), 344d-5c); (B) criticism of writing (341b-c; (B') at 344c); (C) affirmation that dialectic alone can lead to knowledge (341c; (C') at 343e-4b); (D) the difficulties of communication (341d-e; (D'), 343c-d); and at the core, (E) an exposition of the metaphysics of the 'five' and a critique of language itself (342a-3b). (6) Before turning to the Republic, a few words about Aristotle by way of comparison. First, both the NE and EE exhibit marked 'bookending': this falls out so naturally from the flow of Aristotle's dialectic that it hardly registers as a formal feature at all, but it is exceptional -whether by authorial design or not, most of Aristotle's works seem to follow a strictly linear trajectory, with nothing of significance at the end reverting to the start. But in the Nicomachean Ethics, both the first and last books are concerned with the nature of happiness, the 'choice of lives', and the roles of excellence and external goods. Book X reverts to these opening themes in order to give conclusive answers to the questions posed (and addressed in a preliminary way) by Book I, answers informed by the account of the virtues (and pleasure, friendship, etc.) given in the intervening books. It is of course enormously controversial exactly what those answers are, and how exactly the various claims of Books I and X fit together. But it should be uncontroversial that the general relation of Book X to Book I is one of ring-compositional resolution. And this structure is no accident if, as seems likely, the N.E. is in many ways Aristotle's answer to and replacement for Plato's Republic, which (as we will see) is strongly ringcomposed itself.14 The Eudemian Ethics likewise reverts at the end to its opening themes. The ringcomposition here is both more exact and, because of the superficially chaotic nature of EE VIII, harder to spot. But the EE opens in I.1 with (A) the question of the relation of 13 Schofield 1972, 246-53. 14 For the structural parallels between the Republic and the NE, see Sparshott 1982, 483-99. the good, the beautiful and the pleasant, and turns immediately to (B) the question of whether happiness comes from nature, teaching and knowledge, divine inspiration, or chance and good luck -Meno's question, rephrased as a question about happiness rather than virtue. Book VIII returns to this list of candidates ((B'), VIII.1-2). Aristotle first considers puzzles raised by his opting for a version of 'knowledge' as his answer to Meno's question; the solution is to distinguish wisdom from mere knowledge (VIII.1, cf. esp. 1246b31-35). Second, in VIII.2, he considers again the roles of good fortune, divine influence, and chance, asking whether these in turn could be due to nature -in other words, he reverts to the rival candidates of (B), and confirms their rejection (VIII.2). The EE then closes in VIII.3 with a reversion to the outermost ring (A). Here Aristotle gives a final accounting of the relation of the good, the noble, and the pleasant: the highest life, that of the 'noble and good', is one in which all three converge ((A'), VIII.3).15 In section III I will suggest that this sort of ring-composition expresses a conception of philosophical method common to Plato and Aristotle. Yet, given the size of the oeuvres of these two philosophers, the examples I have listed are relatively few -which should at least quiet fears that I have defined ring-composition so broadly that it could be found anywhere. So my claim is not that ring-composition is a pervasive feature of Platonic composition. In some cases he even seems to duck obvious occasions for it, perhaps to preserve an air of lifelike spontaneity: for instance, the introductory frame of the Theaetetus and the regress of narrators which opens the Symposium are not resumed at the end of those dialogues (apart from a few passing references to Aristodemus, Symp. 223b, d). But the instances I have noted are none the less real for that, and it is striking that the most interesting cases -the Cratylus, Theaetetus and Sophist – come from a group of dialogues closely related in themes and probable order 15 For whatever it is worth, the other Aristotelian work with the strongest suggestions of ringcomposition is the Metaphysics. For Books M and N revert to some of the topics of A, at times to the point of being a 'doublet' text. Since (in part for this very reason) it is very hard to believe that the Metaphysics as we have it is a work completed by Aristotle, all formal bets are off: but I suspect that the Metaphysics should be seen as (incompletely and abortively) ring-composed, with ΖΗΘ (or an intended account of metaphysical principles for which they serve as a placeholder) as the dialectical core, and Λ and ΜΝ (ditto) working through its positive and critical implications, thus resolving the opening aporiai (Β). of composition. The kind of ring-composition we find in the Sophist, and more murkily in the Cratylus (and the Seventh Letter as well), is also of particular interest. For in these cases literary form follows philosophical function: the ring-composition is an expression of a dialectical strategy in which one problem or hypothesis leads to another more basic one, which leads to another; the solutions and explanations then unfold in reverse order, from prior to posterior, after a dialectical core articulating the principles which make the solutions possible. And the Cratylus, Theaetetus, and Sophist are all plausibly read as composed not long after the Republic, which I will now argue is ring-composed in much the same way. III. That the Republic is structured by ring-composition seems to belong to the common folk wisdom of Platonic scholarship, in a way which (so far as I can discover) outruns anything reflected in the published literature. The copy of the OCT Republic which I used for undergraduate courses at the University of Toronto in the 1980s has 'ring composition' written in the margins at various points -alas I failed to give any references, though J.M. Rist must have been the principal direct source.16 In a recent account of the structure of the Republic, Georges Leroux cites the oral tradition rather than any published precursors: "cette structure en forme de 'grande voûte', pour reprendre une expression de Jacques Brunschwig".17 Platonic ring-composition has also been noted under various guises in works by Eva Brann ('concentric circles'), Holger Thesleff ('pedimental' or 'two-level' composition), Kenneth Dorter, and, in his discussion of Plato on mimetic art, Myles Burnyeat.18 Burnyeat uses the general claim 16 Likewise, my talk of the upwards and downwards paths in this section is endebted to the teaching of Stephen Menn. 17 Leroux 2002, 30. 18 Brann 2004, 93ff., 116ff. with chart of concentric circles at 117; Dorter 2006, 3ff. with chart at 7; Thesleff 1993; and Burnyeat 1999. Burnyeat remarks, "The structure of Republic II-X is, in broad outline, a ring composition: poetry/city and soul/Forms/city and soul/poetry", while "Book I stands outside the structure" (288 with n. 8). This is to bring out a point which I too mean to argue for in section IV: "Book X... is designed to be consistent with Book III and to give a retrospective, theoretical commentary on its major claims".19 No two scholars carve up the Republic in exactly the same way, and I will not here be concerned to compare and assess the different analyses on offer; but the 'rings' are for the most part evident enough, running roughly as follows: (A) and (A') Katabasis and Return: Katebên is the first word of the Republic, which begins with Socrates' going down to the Piraeus (327a); the Myth of Er with which it closes depicts a more literal katabasis to the underworld (though Er himself remains in an intermediate-level limbo, 614b-d), ending in a return to the light by both Er himself and the other souls (617d, 621b). As Mary Douglas has noted, ring-composed works often reinforce the outermost rings at the 'mid-turn';20 it cannot be a compositional accident that at the dialectical mid-point of the Republic, we have another descent in the Cave allegory. (Strictly speaking what is depicted there is an ascent followed by a descent on the part of the prisoner; but the reader surely experiences the description of the cave and ascent as a katabasis and return.) (B) and (B') Death: The first topic of discussion between Socrates and Cephalus is how we should face the end of life (328d-31b); Book X ends with a vision of the afterlife in the Myth of Er (608d-21d).21 (C) and (C') The Challenge and the Answer: The impetus for the argument of the Republic is the challenge to the value of justice presented by Thrasymachus in Book I and reformulated by Glaucon and Adeimantus in Book II. Glaucon's central demand is that Socrates explain why justice is in itself a good thing, leaving out its 'rewards' (358b). Books IX and X revert to this challenge in systematic stages. First, Socrates very different from how I would identify the 'rings', but it enables Burnyeat to be unusually appreciative of how closely Book X relates to the earlier discussions. 19 1999, 319. 20 2007, 31-2, 37. 21 Tae-Yeoun Keum has also drawn my attention to a number of respects in which the Myth of Er is internally ring-composed, though I cannot explore this here. reintroduces the 'choice of lives' trope (580a-88b, cf. 360d-2c), arguing that the just philosopher is happiest. An allegory of the soul (588b) is used to bring out that it is absurd to suppose that injustice could be beneficial to the doer, however far the appearances may diverge from the reality (the guiding theme of Glaucon's opening challenge). Finally, in Book X, the rewards of justice are restored. (D) and (D'): The City: Development and Degeneration: Socrates meets Glaucon's challenge by sketching the stages by which a city might develop into a maximally just one, beginning with a 'first city' which harbours only moderate appetitive motivations. In Books VIII-IX he sketches the stages by which the just city might degenerate into a maximally unjust one, in which only the most immoderate appetitive motivations have any sway. The two accounts belong to the same genre, presenting analyses of permanent psychological and political forces in the manner of genetic myths (rather than being historical or even pseudo-historical accounts of particular cities). (E) and (E'): Poetry and the Arts: Blurring together with (D) (and recapitulated out of order in Book X -i.e., (E') is interleaved between (B') and (C')) is an account of the appropriate standards for poetry and the other arts, as needed for the education of the 'guardian' class in the just city. This is recapitulated in Book X when Socrates returns to give a more fully grounded account of art, one explicitly based on the intervening discussion: I will return to this account in section IV. So much by way of an outline of the 'rings'. It should be obvious that the recapitulation steps here ((A')-(E')), presented in more or less mirror order, are a matter of 'resolution' rather than mere repetition. In the case of (B') and (C'), we might say that the relation of exposition to resolution is one of question and answer: how should we face death? is it advantageous to us to be just or not? And, to state the crashingly obvious, the answers given in (B') and (C') are informed by the intervening core of the work. The relation of (A) to (A') calls for a somewhat different kind of analysis, and I am not sure quite how to describe the philosophical import of the katabasis motif. The relation of (D') to (D) seems different again: in addition to their being symmetrical as narratives of progress and decline, I would suggest that among other things (D') corrects the earlier exposition, being based as (D) was not on the true tripartite psychology.22 That resolution can take the form of correction is clear from a small-scale example. Though it makes a mess of my divisions (by belonging to all of (A'), (B') and (C')), the 'choice of lives' depicted in the Myth of Er (617d-21b) clearly stands in a ringrelation to Glaucon's Book II speech and the myth of Gyges' ring in particular (C) (359c60d). As Sarah Broadie has noted, both passages are images of 'context-free choice', the selection of a destiny in a magical absence of social constraints and moral convention.23 In choosing his next life in the Myth of Er, a nameless person who 'participated in virtue through habit without philosophy' (619c-d) throws his moral habituation aside to lunge at tyranny: "in the next world, where no impediments surround us, what had been a fantasy becomes an automatically self-fulfilling choice".24 Now the Gyges story was presented by Glaucon to show that, freed of social constraints, anybody will gravitate to his most selfish desires, of which tyranny is the perfect expression. When the Myth of Er revisits this claim, it is to specify that it holds only for the unreflective person; and to show that he will not be happy with his choice. The genuinely virtuous person, who understands the necessity of justice for happiness, will not even feel tempted by such a mistake. So it seems fair to say that the Myth of Er serves to (among other things) correct the Ring of Gyges story, showing that it only depicts human nature in its uneducated state and thus misrepresents the powers of justice. But this correction is (like most philosophical resolutions, I would think) not exactly a matter of contradicting or rejecting the earlier account. The Gyges story is not simply wrong: for one thing, it is right empirically about how most people would behave. But as initially presented it is at best a half-truth. Socrates' correction is thus a matter of clarification – of relocating Glaucon's insight, we might say, putting it in its place as only half the story, and showing that if properly understood it points the opposite of the moral initially intended. 22 I have argued that the psychology presupposed by the 'first city' of Book II is false in 2001b, 207-227. 23 See Broadie 2005, 97-114 at 100-04 with 111 n. 25. 24 Broadie 2005, 102. I will turn in section IV to consider another, more obvious and large-scale instance in which Book X operates as a resolution of an earlier discussion, namely its critique of mimetic art. But first it is worth trying to say something about how the ringstructure I have noted relates to the dialectical methodology of the Republic. So far as I can see the pyramidal 'steps' of the Republic end at (E)-(E'), with no further rings internal to the dialectical core of Books IV-VII. But there is at the same time a shape to Books IV-VII which harmonizes with the ring structure in which it is placed, if only at rather a high level of abstraction. For we begin in Book IV by establishing that the city, being good, must be ruled by wisdom (427e-9a); and we end Book VII with, for the first time, a full understanding of what wisdom entails and how exactly it qualifies its possessors to rule. We end where we began, knowing the place for the first time: here too there is what we might call a structure of explanatory regress, though just how best to spell it out is a tricky question. Now I think that we can see ring-composition in Plato and Aristotle, and explanatory regress more generally, as expressing a distinctively Platonic-Aristotelian conception of philosophical method. Aristotle alludes to that conception in Nicomachean Ethics I.4: Let us not fail to notice, however, that there is a difference between arguments from and those to the first principles. For Plato, too, was right in raising this question and asking, as he used to do, 'are we on the way from or to the first principles?' There is a difference as there is in a racecourse between the course from the judges to the turning-point and the way back. For, while we must begin with what is better known, things are so in two ways -some to us, some without qualification. Presumably, then, we must begin with the things better known to us.25 The phrase 'arguments from and to first principles [archai]' recalls (if it is not an outright allusion to) the Divided Line in Republic VI, where the highest level of thought, noêsis, is contrasted with the kind of mere thinking [dianoia] used by mathematicians. The difference between the two lies in their different relations to hypotheses. Dianoia proceeds from hypotheses as unquestioned assumptions and relies on sensible particulars as images; but noêsis works its way 'up' from those hypotheses, without treating them as assumptions and without the aid of images. Philosophical dialectic "does not consider these hypotheses as first principles but as stepping stones to take off from, enabling it to reach the unhypothetical first principle [archê] of everything" (511b4-6). Then, "having grasped this principle, it reverses itself and, keeping hold of what follows from it, comes down to a conclusion without making use of anything visible at all, but only of forms themselves, moving on from forms to forms, and ending in forms" (511b6-c2).26 The obvious precursors to this dialectical noêsis are the kinds of 'hypothetical method' discussed in the Phaedo and Meno.27 In the Phaedo the Forms are themselves to be adopted as hypotheses in order to prove the immortality of the soul (100b); in the Meno, it is by adopting a hypothesis that Socrates hopes to answer Meno's question whether virtue is teachable (86d-7c). 28 Neither passage is terribly informative about the method, and inasmuch as the hypotheses seem to be treated as assumptions we are presumably at the level to be distinguished in the Republic as dianoia rather than noesis. But the Phaedo does gesture vaguely towards a complementary 'upwards' path: when you must give an account of our hypothesis itself you will proceed in the same way: you will assume another hypothesis, the one which seems to you best of the higher ones until you come to something sufficient, but you will not jumble the two as the debaters do by discussing the hypothesis and its consequences at the same time...29 25 NE I.4, 1095a-b, trans. W.D. Ross in Barnes (ed.) 1984. 26 As Annas 1982 has pointed out, the imagery which comes naturally to us here is the reverse of Plato's: we think of proceeding downwards to foundations where he speaks of a movement upwards to a first or governing principle, archê (104 n. 21). 27 On the method of hypothesis, the state of the art remains Robinson 1953, now joined by Hugh Benson's paper in this volume. 28 Exactly which proposition(s) here count as hypotheses is very controversial. I discuss these texts and the method of hypothesis more fully in another paper currently in preparation, 'Socrates, Virtue and the Method of Hypothesis'. The Phaedo does not envisage a transformation of reasoning from hypothetical into demonstrative by way of an unhypothetical first principle. But it does here adumbrate the Republic by distinguishing 'upwards' and 'downwards' lines of argument, and insisting on the importance of the distinction. Socrates' language here is almost as abstract as in the Line, but I think it is possible to get some sense of how the two directions differ. Upwards reasoning to a hypothesis will be a matter of finding nondeductive reasons to adopt some principle as 'strongest' [errômenestaton, 100a4] or 'sufficient' [hikanon, 101d8]: presumably this is a matter of both explanatory power and inherent plausibility. And we may advance upwards indefinitely, in each case adopting a 'higher' hypothesis which will serve to explain (we would find it natural to say 'ground') a lower one. Downwards reasoning from a hypothesis then takes the form of deducing its consequences and testing them for coherence, presumably by taking the hypothesis in conjunction with plausible auxiliary assumptions. Variations on this pattern are to be found, I believe, in a number of Platonic dialogues.30 In the Republic, the upwards path operates as a dialectical progession from practically immediate but posterior questions to more general and prior ones. Q: In what spirit will we face death? A: It depends on where we stand in relation to justice. Q: But is justice really a good thing? A: To know that, we need to know what justice really is. If justice is common to the just person and the just city, perhaps we can grasp the former by seeing the latter. Q: But what makes a city just? A: A just city is plausibly one in which what is appropriate is rendered to each – ie, each class does its own work, so that it is ruled by the wise. Q: But who are the wise? A: The philosophers: those who have been well educated. Q: But what is a good education? A: One which leads us to know and love the Good. A: But what is the Good, and what does it mean to know it? Dialectically, the buck stops here: whatever exactly is being claimed for it in the Divided Line, the Good does function in the Republic itself as an unhypothetical first 29 101d6-e2, trans. G.M.A. Grube. 30 I cannot make the case for this here, but other instances I have in mind include the Theaetetus and Gorgias, where the positions of Theaetetus-Protagoras-Heraclitus and Gorgias-Polus-Callicles represent a kind of explanatory regress of false higher hypotheses. principle, in the sense that our questions about it are answered, not by a further explanatory regress, but -if at all -by evocative allegories and analogies. So the rings of the Republic are united to the inner dialectical core by this shared, more general pattern of explanatory regress, which becomes visible as a ringstructure in the outer zones. And the latter, recapitulation half of the Republic covers much of the terrain we might expect from 'downwards' argument, retracing the 'upwards' steps and putting to work the principles established in the dialectical core. The higher education of the Guardians sketched in Book VII is explicitly informed by the account of the Forms in Books V-VII, as the earlier account of their early education could not be. The depiction of corrupt constitutions and psychological types in VIII-IX is explicitly informed by the tripartite theory of the soul in Book IV, as the earlier account of the first city and its successors could not be. The final choice of lives in Book IX brings together the Book IV psychology and the Book VI-VII metaphysics to establish that the life of the philosopher is happiest and most pleasant, in answer to and correction of Glaucon and Adeimantus in Book II. This same combination of 'core' principles is brought to bear in the Book X account of the arts: I now want to give this a closer look, as a case study of ring-composition in action. IV. Socrates' critique of mimetic art in Book X is explicitly presented as a resolution of his earlier exposition in II-III. That is: he announces both that his discussion will reaffirm the earlier account and that it will draw on the principles articulated in the intervening discussion, and the partition of the soul in particular: Indeed, I said, our city has many features that assure me that we were entirely right in founding it as we did, and, when I say this, I'm especially thinking of poetry. What about it in particular? Glaucon said. That we didn't admit as much of is as is imitative [mimêtikê]. Now that we have distinguished the separate parts of the soul, it is even clearer, I think, that such poetry should be altogether excluded. (595a-b) His conclusion, addressed to the defender of poetry, reiterates this claim to consistency: "Then let this be our defense -now that we've returned to the topic of poetry -that, in view of its nature,31 we had reason to banish it from the city earlier, for our argument compelled us to do so" (607b). That the intervening arguments do invoke the principles of the dialectical core - the theory of Forms as well as the tripartition of the soul -is obvious and uncontroversial. But the exact machinery and import of the argument here have been the subject of enormous interpretive controversy. I cannot engage with this fully here, and will offer only a brief and somewhat dogmatic sketch of my own reading: my aim is simply to take seriously Socrates' presentation of his account as a resolution, and shows how it operates as such. I will proceed from what seem to be the clearest points to ones which are more problematic: 1. In its general upshot, it is easy to read the Book X account as a resolution of the discussion of art in Books II and III. For the earlier account is (again, in its general upshot) an argument for the expulsion of tragedy and comedy from the well-run city (394d, 397d-8b, 568a-c).32 That is why Socrates recalls the ban as one not on mimesis as such, or mimesis of bad models, but 'poetry insofar as it is mimetic' (595a5). The reference here is to the type of poetry distinguished as 'narration through imitation' at 392d-4d, viz dramatic poetry; whether the results extend to the third class distinguished there, the partially mimetic poetry of Homer, is left an open question (394d). And this is just the question taken up in Book X. Hence the strong and otherwise 31 Literally 'being such', toiautên ousan, picking up the introductory hoia tugkhanei onta, 'of what sort it is' in the introduction of the critique (595b7). It is only in Book X that we find out what poetry as such is: the Book III discussion thus was necessarily hypothetical and provisional, as are all attempts to determine the qualities of an object without first defining its nature (cf. Socrates' strictures in the Meno, 71a-c, 86d). 32 Cf. Burnyeat 1999. puzzling focus on Homeric poetry and in particular on Homer as a tragedian, at 595c ('the first teacher and leader of all these fine tragedians'), 598d ('tragedy and its leader, Homer'), 605c ('Homer or some other tragedian'), and in Socrates' peroration: And so, Glaucon, when you happen to meet those who praise Homer and say that he's the poet who educated Greece, that it's worth taking up his works in order to learn how to manage and educate people, and that one should arrange one's whole life in accordance with his teachings, you should welcome these people and treat them as friends, since they're as good as they're capable of being, and you should agree that Homer is the most poetic of the tragedians and the first among them. But you should also know that hymns to the gods and eulogies to good people are the only poetry we can admit into our city. If you admit the pleasure-giving Muse, whether in lyric or epic poetry, pleasure and pain will be kinds in your city instead of law or the thing that everyone has always believed to be best, namely, reason. (606e-607a) Now that we are in a position to see what mimesis really is, we can also see that its defining and objectionable features are, alas, equally (or even more) present in the work of the greatest of poets. 2. The principles drawn on for the resolution are, as Socrates tells us at 595a-b, to do with the partition of the soul. This claim might seem surprising or incomplete, since the first of his arguments, to the effect that the products of imitation are 'third from the truth', actually depends on the theory of Forms and the accompanying epistemology sketched in Books V-VII. However, the concluding arguments of the Book X discussion are psychological, and do indeed draw on the analysis earlier of the lower parts of the soul. So what Socrates' allusion suggests is that we are to read what follows as a single continuous argument: the metaphysical and epistemological principles introduced in its early stages are salient because of their implications for human psychology. 3. So read, as a continuous chain of argument, the trajectory of the Book X discussion is in broad outline clear. It runs as follows (cf. Socrates' recap, in mirror order, at 605b): (i) Mimesis is the creation of objects at a 'third' remove from the truth (596a-8b); (ii) the imitator should not be supposed to have knowledge of the truth, and cannot be trusted (598b-600e); (iii) the imitations created by poets are actively misleading, like optical illusions (601a-2b); (iv) such illusions persuade, appeal to, and gratify the lower, irrational parts of the soul (602c-5c); (v) when we exerience empathetic emotion and aesthetic pleasure at Homeric poetry, we are indulging and strengthening the lower parts of our soul at the expense of reason, which can only be a dangerous and corrupting course ('the most serious charge', 605c-7a).33 Exactly how each of these steps leads to the following one is a complex and difficult question which I cannot properly address here; on the face of it, each seems to establish a crucial necessary condition for the following claim, which is further elaborated and supported by independent argument. An important point to note is that only the final argument, (v), is presented as a warrant for the expulsion of the poets. Plato is not worried about the presence in his just city of ontologically low-grade entities as such -there is no hint that painting, which is equally mimetic, is to be banned (let alone that the Guardians are to fret over the presence of shadows and reflections). The point of the earlier stages of the argument is rather to clarify what mimesis is (argument i) in order to establish that (ii-iii) and show how (iii-v) mimetic poetry in particular is able to do the damage it does. 4. The crucial turning point (and greatest source of interpretive difficulty) is thus the claim in (iii) that mimetic poetry is inherently deceptive, as per the optical illusion analogy: it is here that Plato pivots from the comparatively straightforward claim that 33 These last two, allusively presented steps leave any number of residual puzzles, including: how exactly does an imitative representation register as normative -why does the audience admire and sympathize with Achilles and not with Thersites? And what exactly is the role of pleasure in mimetic poetry? Plato seems to present it as an important factor in the capacity of poetry to rouse emotion and deceive, but how exactly does this work? the poet is as such ignorant (ii) to the damning argument that his work is actively harmful (iv-v). This part of Plato's argument has been the subject of enormous controversy, and raises a number of issues I cannot go into here. But the basic move is easy to grasp so long as we do not shrink from taking Plato at his word. When we take Ajax for a hero, enjoy weeping with him, and form false moral beliefs accordingly, it is because something primitive and irrational within us takes him as a real hero, and takes the poet's representation of him as true in a literal and straightforward sense.34 To find this absurd or incredible is to miss the point of Plato's analysis of the tripartite soul, which shows how irrational emotions and magical thinking can coexist with a rational self which 'knows better'. Our rational part does of course 'know better' than to think that the tragic Ajax is a real hero, just as it does in cases of optical illusions. But what makes tragedy so dangerous is that, through pleasure, it puts our rational part off guard, and encourages it to give in to our irrational selves. Tragic poetry is a kind of statesponsored akrasia; and tragedy includes epic. 5. Now we still might well wonder how the Book X account so understood can function as a resolution of Books II-III. For the account given in II-III was of 'mimesis' understood as oratio recta within poetry, not as representation in general (393d-4b). And the objection to mimesis so understood was that (unless restricted to good models) it corrupted its practitioners – not its audience (394d-8b). So it might seem that Plato's two discussions are really saying quite different things about different things, even if the two can be misleadingly lumped together as 'critique of mimesis' – less an exposition and resolution, then, than a bait and switch. The general question this raises is the delicate one of how a philosophical resolution can complete and correct the 34 In the terms of Belfiore 1983, the 'veridical mistake' is mediated by the 'ontological mistake'. For after all, "doesn't your soul, in its enthusiasm, believe that it is present at the actions you describe, whether they're in Ithaca or in Troy or wherever the epic actually takes place?" (Ion 535c). When I suspend disbelief, I turn over my thinking, including my formation of evaluative judgements, to a part of me too foolish and childish to distinguish between appearance and reality. I then take Ajax for a real warrior, and it is because I do so that I take his virtues 'in the fiction' to be real ones. Once the play is over, the first mistake is shrugged off; the second remains (cf. the ancient accounts of actual reactions to tragedy noted by Stanford 1983, 1-10). correlative exposition without either simply contradicting it or replacing it as irrelevant. One way it can do so – and this is, I think, the answer in the present case – is by interlocking with the earlier argument in a complementary way. Here the crucial point to note is that, according to the Book X account, epic and tragedy corrupt by stimulating the very emotions they depict. When I take pleasure in Achilles' lamentation,35 I share his sufferings [sumpaschontes]: I take seriously what he does, and feel grief as a result (605d); I may even weep as he does. In other words, poetry makes imitators of its audience. (Obviously I do not pretend to be Achilles when I weep with him; but I do make myself like him, which is what counts (cf. 393b-c).) So the Book II-III argument, that the activity of imitation corrupts, turns out to have a far wider reach than we might have thought -and the problem is not one which could be solved by outsourcing dramatic performance to non-citizens. At the same time, the analysis of the tripartite soul now enables us to see why this experience of imitation is corrupting: it indulges and strengthens the power in us which forms false opinions and low desires, and which is, not by coincidence, what poets specialize in depicting.36 35 Cf. the chain reaction described in the Ion (535a-6d). It is very helpful to Plato's argument in Book X that he uses pity, i.e., sorrow at the sufferings of another, as the case at hand. For one thing, its evocation is important common ground to Homeric and tragic poetry (cf. Stanford, "the supreme tragic emotion" (1983), 23). For another, were the argument to focus on any other emotion, Plato would have to face the objection that even our strongest emotional reactions to art need not resemble the representations which cause them. It is not so obvious that Achilles' anger makes the listener angry, or that fear on stage (as opposed to the sight of the fearful) provokes it in the audience. Also, as the canonical cause of weeping, pity is an emotion which has a demonstrable physical effect on the audience (cf. Gorgias, Helen 8-9): it is all the more plausible that it can affect our beliefs and our character as well. 36 How exactly the two conceptions of mimesis are connected remains a tricky question. Briefly, my answer would be to note, first, that the Book III and Book X senses are never confused or conflated; and second, that neither captures exactly the sense in which both Book III and Book X are properly described as critical of 'mimetic poetry'. Rather, Socrates uses 'mimetic' (and, in Book X, 'tragic') as shorthand for 'poetry which is bad in the way that tragedy is standardly bad': the two discussions work together to gradually define the salient kind by identifying its distinctive features and fixing its scope. What really defines such poetry, as it turns out, is that it strengthens the lower parts of the soul against reason. The fact that all artistic representation is ontologically defective and causally independent of any wisdom in its creators explains how this vicious poetry is possible (cf., perhaps, the way in which the ontological defectiveness of all language explains how false statements are possible (Cratylus 428d-33b)). That In sum, the Book X account of poetry serves as a resolution to the Book II-III exposition in a number of ways. It reaffirms its central result, the banning of tragedy qua mimetic poetry. It clarifies and makes precise the scope of that result, by showing that tragedy properly understood includes Homeric epic. It grounds the earlier argument by deploying the principles set out in the dialectical core, viz the analysis of the tripartite soul, to show how mimetic poetry has its effect. And in doing so it circles back to and supports the earlier line of argument, by showing both how imitative activity is harmful for the imitator and how it makes imitators of its audience. VI. I have argued for five claims. First, the Republic, along with certain other works of Plato and Aristotle, is structured by ring-composition, with a 'pyramid' structure surrounding the dialectical core of Books IV-VII. Second, this is not just an aesthetic and formal strategy, part of Plato's appropriation of and competition with Homer: it also expresses a Platonic philosophical method marked by 'upwards and downwards paths' of argument to and from first principles, or at any rate highest hypotheses. Third, the recognition of ring-structures, and their methodological functions, can help us to solve interpretive puzzles large and small. This is a weak claim: obviously we need to figure out as much as we can about the design of Plato's works in order to get their content right. And inasmuch as structure expresses philosophical method, structure is content. Fourth, by way of a case study, the discussion of mimetic art in Republic Book X needs to be read as a resolution corresponding to the expository discussion in Books II and III, just as Socrates tells us at 595a. irrational, unstable behaviour is better suited than the opposite to pleasure-giving poetic depiction then explains why tragic and epic poetry tend to fall into the vicious class more or less inevitably and universally. And fifth, the cases I have discussed here show that resolution is a complex and variable business. In philosophical works, we should expect a resolution to answer open questions, correct provisional hypotheses, relocate half-truths and revise earlier arguments on the basis of intervening principles – not merely to repeat points which could have been made the first time around. To work out which of these complex operations are being performed in any given case, and exactly how, is the hard part: to recognise a philosophical work as ring-composed is the beginning of interpretation, not the end. In Thinking in Circles, Mary Douglas argues that ancient ring-composed works are chronically misunderstood and underrated by modern readers not attuned to their form.37 It would sound odd to call the Republic underrated: but seeing just how far it is ring-composed should, I think, shift the reader's expectations in a salutary way. For to read a philosophical work as ring-composed is to approach it with the expectation that earlier topics will be reverted to later on, and with the presumption that the earlier discussion is provisional while the later one is complementary, principled and authoritative. To ask whether the critique of the arts in Republic X is 'consistent' with Books II-III (or, I would suggest more provocatively, whether N.E. X is 'consistent' with N.E. I) is thus to put the question too simply, if not to ask the wrong question altogether. The relation between beginning and end in such works will be complicated in all the ways that it is in the Iliad, and the point of the ring form is at bottom the same. It is that at the end of our exploring we may return to the place where we started, and -like the philosophers returning to the Cave -know the place for the first time. 37 Douglas 2007, ix-x, 1, 11, 125-6, 139-48. Bibliography Annas, Julia. "Knowledge and Language: the Theaetetus and the Cratylus" in Language and Logos, edited by M. Schofield and M. Nussbaum, 95-114. Cambridge: Cambridge University Press, 1982. Barney, Rachel. Names and Nature in Plato's Cratylus. New York: Routledge, 2001a. "Platonism, Moral Nostalgia, and the 'City of Pigs'." Proceedings of the Boston Area Colloquium in Ancient Philosophy 17 (2001b): 207-227. Belfiore, Elizabeth. "Plato's Greatest Accusation Against Poetry". 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