THE SPEECH OF PYTHAGORAS IN OVID'S METAMORPHOSES
KARL GALINSKY
(University of Texas at Austin)
1. Introduction
First, with over 400 lines, this is one of the longest episodes in the Metamorphoses. As it comes in the final book, we can assume that it has some kind of programmatic purpose or, as is always the case with Ovid, several purposes. In terms of literary traditions alone, Ovid has regaled us in the preceding 14 books with a vast array of styles and genres; it is clear that this variety, rather than interpretation in terms of generic constraints, is the real significance of the role of genre in the Metamorphoses.2 Absent, until the last book, have been a long philosophical disquisition and a speech yet longer than that of Ulysses in Book 13. One of the reasons, therefore, for Ovid's inclusion of this philosophical rodomontade is simply to round out his whole bravura collection with yet another bravura piece.
Secondly, the choice of Pythagoras was congenial for that purpose and several others. By Ovid's time, "Pythagoreanism" stood for a syncretistic collection of the teachings of various philosophical schools, mysticism, pseudo-scientific speculation, and religious and spiritual dispensations. 3 Accordingly, Ovid's Pythagoras offers an eclectic farrago indebted to all kinds of philosophical teachings: his own, Heracleitus', Empedocles', and the Stoics', along with frequent allusions, mostly for the sake of counterargument, to Lucretius and the Epicureans. The procedure finds its fitting analogue in Ovid's choice of material for the Metamorphoses, which is similarly varied, not doctrinaire, and not consistent. Ovid's poem is, "among other things, an anthology of genres" and styles; 4 Pythagoras' speech is an anthology of philosophies.
And more than that. Philip Hardie, with his typical learning and astuteness, has recently argued that through the speech of Pythagoras, in conjunction with the cosmogony in Book 1 and the historical passages in the second part of Book 15, Ovid is claiming his place in the Roman epic tradition, exemplified by Ennius and Vergil. 5 According to Hardie, Ovid does so by linking philosophy and history in an Empedoclean key, and I will come back to this argument later. For right now, let me simply state the obvious fact, acknowledged by Hardie in a footnote, 6 that Empedoclean coloring is absent from fully half of Pythagoras' speech, the catalogue of yaumastã and parãdoja (15.259-452). Not surprisingly, we are dealing again with the typically Ovidian invitation, which in this case was facilitated by the very nature of the phenomenon of Pythagoreanism, to reader response. 7 Some highbrow readers may concentrate on the philosophical evocations and pursue them beyond the text. For differently oriented readers, what is memorable is the vignettes from Pythagoras' version of Ripley's Believe or Not, such as the birth of green frogs from mud (15.375-77), dead people's spine marrow mutating into snakes (15.389-90), and putrefying war horses generating hornets (15.368).
Thirdly, then, there is the question of the relationship between the philosophical and scientific mode on the one hand, and mythological and poetic on the other, as indicated especially in Ovid's cabinet of mirabilia that are proffered by the same philosopher Pythagoras. Are these modes of explanation merely juxtaposed or is one privileged over the other? A similar issue is raised by the pendant to Pythagoras' speech in Book 1, the cosmogony-is Ovid there indebted to philosophy rather than poetry? These dichotomies, which have often been used to frame the discussion, may in fact have to be modified in view of the low content of science and philosophy proper in Roman Pythagoreanism. Fourthly, given the fact that the Metamorphoses in many ways was meant to be an alternative to the Aeneid, how does Ovid's treatment of philosophy contrast with Vergil's? Vergil's most sustained use of philosophical models, including Pythagoreanism, occurred of course in Book 6 or, to put it with Ovidian insouciance, in hell from where Ovid studiously omits it. 8 Moreover, Vergil studied philosophy with Philodemus and that fact is relevant to some of his characterizations in the Aeneid. 9 Vergil's integration of myth and philosophy was in many ways a response to Lucretius, whom we must also consider in this context. Finally, and without my going into all the details of narratology, Pythagoras' presentation of the subject and of exempla of change clearly calls for a comparison with Ovid's own narrative presentation in the rest of the Metamophoses. Is the philosopher a foil for the poet or a complement?
For the Roman audience, Ovid's choice of Pythagoras as the archetypal philosopher made excellent sense. Since the time of Aristotle, he was credited with being the eÍretÆw of the very word filÒsofow. 10 Modern scholarship suggests scepticism about the claim, but it found huge resonance in antiquity and became a staple in handbooks up to the time of Isidore of Seville; Cicero furnishes one of the lengthier attestions in Tusc. 5.8-9. Secondly, Pythagoras had a Roman affiliation that was particularly suitable for one of the main themes of the last book of the Metamorphoses, the transfer from Greece to Rome. The theme is continued with the story of Asclepius' arrival in Rome and, for that matter, with Julius Caesar's catasterism; a further link is that one of the appellations (coined at Croton) of Pythagoras was "Hyperborean Apollo"11-Apollo was, of course, the father of Asclepius and the patron god of Augustus.
The Roman component of Pythagoras needs some further comment. One aspect is the development of Pythagoreanism in Italy and Rome. The other is the association of Pythagoras and Numa. My aim, in both instances, is to work towards defining the horizon of expectations of Ovid's contemporaries.
Pythagoras, ortu Samius (15.60), migrated to Croton and in Magna Graecia was reputed to have taught the Romans along with Lucanians, Messapians, and Peucetians. 12 Testimonia of continuing Roman interest in him include, besides the link with Numa, the Romans' selection of Pythagoras as "the wisest Greek" to be honored with a statue in the Comitium sometime in the fourth century B.C., 13 and the gens Aemilia's deriving its name from one of Pythagoras' sons. 14 As for Pythagoreanism, Aristotle called it simply "the Italian philosophy." 15 But what was it? The ancient sources acknowledge that the old, authentic Pythagoreanism became extinct. That, however, did not mean the end of a thriving production of pseudo-Pythagorica especially in Hellenistic times that obviously responded to considerable demand. There was, in Walter Burkert's words, a flood of Pythagorean writings, but there were no Pythagoreans. 16 By the late Republic, that had changed: Varro wanted to be buried Pythagorio modo (Pliny NH 35.160), Nigidius Figulus was exiled; and Sextius was credited with establishing a Pythagorean sect that, however shortlived, was roboris Romani (Sen. NQ 7.32.2). 17
The character of this new and Roman Pythagoreanism, however, was quite different from the old. It shared, as I briefly noted earlier, a trend toward syncretistic convergence as it incorporated aspects of Platonism and Stoicism, due to the influence of Posidonios in particular. 18 The phenomenon is part of a yet wider panorama. On the one hand, it relates to the kind of poetic and intellectual eclecticism that informs, for instance, Horace's thought in the first Roman Ode, 19 i.e. a sort of philosophical Allgemeinbildung. 20 On the other, and on a more popular level-in contrast to Horace, Ovid never proclaimed odi profanum vulgus et arceo-hard science never had any appeal in Rome and serious philosophy had a limited audience. What was in demand was the "popular, the watered down, and the coarsened . . . A Roman, who inquired about the cosmos, and the forces and laws that ruled it, did not come upon Plato's Timaeus, nor upon Archimedes and Eratosthenes, but upon an extract from Platonic, Aristotelian, and Stoic cosmology which, in combination with some isolated and half-understood insights into science, had been melded into a pseudoscientific whole and been put under the name of Pythagoras." 21 In so many words, Ovid's audience would not look to "Pythagoras" for hard science or philosophy, and we should not either. This does not mean that (Neo)Pythagoreanism and its titular founder were being held in low, derisive regard. Rather, the gibes of Horace and Laberius, just like those directed by Aristophanes at Socrates, further confirm that Pythagoras and his supposed teachings were a matter of topical fascination among a large public. If Ovid wanted to mix some "philosophy" into the Metamorphoses, he could not have made a better choice. Further confirmation of its suitability comes from the mythological decorations, 28 in all, of the Pythagorean underground "basilica" at the Porta Maggiore: "La singulière architecture et la proliférante richesse du décor semblent avoir été conçues pour défier à jamais toute tentative d'exégèse systématique"22-an apt characterization of the Metamorphoses, too.
The association of Pythagoras and Numa was an equally fascinating topic. The earliest testimonium is that of Aristoxenos, 23 which should not lead us to believe that Aristoxenos' writings reached Rome in the fourth century and forthwith led to the acceptance of the story there. It accords well with the Hellenistic fascination for things Pythagorean. There can be little doubt, however, that the tale gained further currency and was well established in Rome by the early second century. It was hard to dislodge; as has been observed correctly, the vehement attacks on it by Cicero, Dionysius, Livy, and others are indicative of the legend's strength. There was no need for these writers to pound away at its chronological absurdity if only a few misguided souls believed that Numa had been taught by Pythagoras. Plutarch's account is a good example of the stubborn longevity of the story. He confronts the problem in the very first chapter of his Life of Numa, offers various explanations and justifications, and then proceeds, in chapter 8, with a recital of Numa's relation to Pythagoras, including a list of his Roman institutions that were due to the philosopher's precepts. Much as he likes the traditional story, Plutarch is forced to restate, in he concluding sentence, that there is a great deal of dispute (émfisbhtÆseiw) about "these matters" and that it would be contentious to pursue them further.
One of the most clamorous incidents in the tradition of the tale took place in 181 B.C. According to the earliest account, that of Cassius Hemina, 24 the stone arca of Numa turned up on the Janiculum in the course of excavation. It also contained several books, and in his libris scripta erant philosophiae Pythagoricae-eosque combustos a Q. Petilio praetore, quia philosophiae scripta essent. In the subsequent annalistic tradition, the usual accretions occur: the books, varying in number, are now said to consist equally of Numa's pontifical laws and philosophical (Graecos or Pythagoricos) writings. In Livy's account (40.29.2-14), there are two arcae and both sets of books are burned, whereas Valerius Maximus (1.1.12) has it that only the Greek books were burned quia aliqua ex parte ad solvendam religionem pertinere existimabantur, a version followed by Lactantius (Div. Inst. 1.22.1, 5-6). Plutarch (Numa 22.2-3) does not miss the opportunity to point out that Numa followed Pythagorean practice in commanding that the (pontifical) books he wrote should be buried with him while their precepts should be memorized and passed on by the living. Accordingly, when the books were found in conjunction with "twelve others of Greek philosophy," the praetor has them burned because it was not ius or fas that they should be made public (Numa 22.8).
As can be expected, the episode has received different, and sometimes elaborate, interpretations. My own inclination would be to rely mostly on Hemina's report, which is closest in time to the event and free from embroidery. He speaks only of the Pythagorean books found with Numa. Subsequent authors added the pontifical books because they were de rigueur for Numa, and this could lead to the absurdity of both sets of books having to be burned. Hemina's version, and the action taken by the Roman magistrate, makes sense in the context of the quackery that produced pseudo-Pythagorica en masse. What is important for our purposes is that the tradition linking Pythagoras and Numa was widespread, lively, and disputatious.
Ovid wrote his own version against this backdrop and could expect his readers to be familiar with much of it. Therefore he did not have to subject the legend to the same overt, rationalist, and chronological critique as other late Republican and Augustan writers; his readers could do so for themselves. The conclusion that Ovid disregards the problem or even accepted the legend ignores the implied reader and the more nuanced nature of poetry. As so often, Ovid's own hints are unobtrusive but plentiful.
He disassociates himself from most versions of the legend by not speaking of Numa as actually meeting with Pythagoras. In his quest of rerum natura (15.6), Numa journeys to Magna Graecia. One of the indigenous seniores (15.10)-a favorite Ovidian narrator especially when distance from a tale is sought25-tells him about the foundation of Croton. The events belong to veteris aevi (15.11); Numa and Pythagoras are not contemporaries. The addressee, therefore, of Pythagoras' speech is not Numa, but coetus silentum (15.66); the shift from Numa to them is emphasized by the repetition of rerum causas (15.68), now a theme in Pythagoras' discourse to that group. But what group is it? Elsewhere in Ovid and Latin poetry, silentes are the defunct. 26 The reader again has the choice to understand the phrase in that sense or as referring to the proverbial silence preached by the Pythagoreans. In addition to not being the original listener, Numa qualifies on both counts. From the temporal perspective of Ovid's readers, Numa was, of course, long dead and, as for his silence, we do not hear a word from or about him for the duration of his informant's recital of Pythagoras' disquisition. He reappears at the very end as the purported recipient of Pythagoras' instructions (15.479-84):
talibus atque aliis instructum pectora dictis
in patriam remeasse ferunt ultroque petitum
accepisse Numam populi Latiaris habenas.
coniuge qui felix nympha ducibusque Camenis
sacrificos docuit ritus gentemque feroci
adsuetam bello pacis traduxit ad artes.
Not only do these few compact lines deliberately contrast with the verboseness of Pythagoras, but they do nothing to establish Numa as his follower. The Romans' main interest in philosophy was in ethics and there was plenty of relevant Pythagorean material around. Ovid systematically ignores all of that, relegating it, at best, to the unarticulated aliis dictis. He reduces Pythagorean ethics to vegetarianism-this is the subject of the peroratio in lines 459-78 to which talibus dictis refers-and, yet more important, "presents it in a position more extreme than that usually ascribed to Pythagoras." 27 This does not make Pythagoras' speech a parody-such labels are too facile because the speech is more than one-dimensional-but it reduces Pythagoras' credibility qua philosopher. Furthermore, strident vegetarianism, of course, was not one of Numa's teachings nor is it likely to have figured in the writings of Castor of Rhodes, a pro-Roman chronographer (1st cent. B.C.), who "accepted that early Roman institutions had been influenced by Pythagoreanism." 28 Once more, Ovid deliberately passes up a connection that could have been made, as we know from Plutarch. Plutarch (Numa 8.8) relates that Numa's sacrifices "had great similitude to the ceremonials of Pythagoras, for they were not celebrated with effusion of blood, but consisted of flour, wine, and the least costly offerings." Ovid rejects this tradition in two ways. In the first instance he credits Egeria and the Camenae, and not Pythagoras, with helping Numa establish sacrificos ritus for the ferocious Romans. 29 Secondly, he says nothing about their bloodlessness, nor, in the parallel version in the Fasti (Book 1.337), does he attribute the origin of bloodless sacrifices to Pythagoras. In fact, later in the Fasti, in connection with the incubation oracle of Faunus, Numa is shown to be sacrificing sheep and a pregnant cow (4.652, 671).
Ferunt, as has been noted, 30 serves both for distancing and for giving the story the patina of antiquity. In this instance, the former effect appears to be predominant: in his catalogue of teacher and disciple pairs in Ex Ponto 3.3.41-44, Ovid uses the same qualifying expression only for Numa and Pythagoras. At the same time, and as throughout the Metamorphoses, Ovid leaves enough latitude even for the true believer. 31 While he does not make Pythagoras and Numa coevals, he refrains from pointing out, as Dionysius had done at some length (Ant. Rom. 2.59.3-4), that Croton was founded four years after Numa's accession. In addition, the determination of the range of aliis dictis is left entirely to the reader. It is elastic enough to allow for the inclusion of the philosophical-scientific topics which Pythagoras outlines initially (Met. 15.66-72), but completely fails to develop. 32
Ovid does not take long to disabuse the reader of any expectations for serious philosophical discourse. The primary theme, concisely rendered in lines 177-78 (nihil est toto, quod perstet in orbe. cuncta fluunt) is, of course, Heraclitean, though it belonged to popular philosophy, if not simply the realm of proverbial expression, by Ovid's time. 33 At the first opportunity (15.186-236), moreover, Ovid ignores the actual cosmic tenets of the Pythagoreans and others and instead has Pythagoras present some routine, if not banal, examples of change: i.e. night, day, the seasons, and the ages of man. The issue is not a complex philosophical doctrine, but an everyday insight into the obvious. The equation of the ages with the seasons may go back to Pythagoras, 34 but clearly was one of his least challenging intellectual properties. The narrator happens to be a philosopher; we are dealing, to use Quintilian's phrase for the impressionistic unity of the Metamophoses (Inst. Or. 4.1.77), with a species, with the appearance of philosophy rather than anything of substance.
Similarly, the subsequent discussion of the elements (237-51) had become the common property of just about any philosophical school. This is reflected by the variety of sources modern scholars have identified, such as "peripatetic eclecticism", "jungepikureisch," and Stoic, especially Posidonian. 35 Empedocles figures in the mix, too, but hardly in a privileged position. 36 We are dealing with an eclecticism-a very Augustan characteristic-that implies the convergence of different philosophical schools. In Horace's first Roman Ode, they could be summoned in support of the mos maiorum; in Pythagoras' speech, they illustrate that change is a topic common to all philosophical schools. In both cases, the effort is to produce some philosophical coloring and not a sectarian attempt to deal thoroughly with the specific tenets of one philosophy or the other. It has been well noted that Ovid, in this passage, "uses (philosophical) terms without being concerned about the meaning they had in previous literature." 37 The lack of concern about terminology, however, is only a result of the more fundamental lack of concern about the subject itself: no sooner has Pythagoras proclaimed that haec quoque non perstant (15.237), echoing the theme of cuncta fluunt (15.178), than he promptly speaks of the aether as aeternus (15.239), which may be a witticism. Fittingly, he had used aether in line 195 devoid of the numerous connotations the term had acquired in previous philosophy and science. 38
The remainder of Pythagoras' "philosophy" is his injunctions, with which he brackets his speech, against animal sacrifices and the consumption of animal meat. It appears that in the teachings of the Sextii, the reason for the emphasis on vegetarianism was not metempsychosis, but hygiene and the avoidance of cruelty to animals. 39 Ovid follows that emphasis: his depiction of the sacrificial victim (15.130-40) is rendered with unusual sympathy as is Pythagoras' concluding appeal (462-9). 40 But we are not dealing with philosophy here. Spirituality and metaphysics are eschewed and while Ovid strikes a humanitarian note, this extreme vegetarianism was, as we saw earlier, not part of the Roman mainstream or of Numa's legacy.
Ovid's refusal to develop Pythagorean philosophy proper has been prepared for in the preceding books and belongs in the general context of his endeavor to distance himself from philosophical creeds. For instance, in contrast to Lucretius' rationalist critique that denied the existence of mythical portenta such as Scylla and Centaurs, Ovid of course makes them the centerpieces of some of his own stories. 41 Similarly, Lucretius (2.700-703, 707) had rejected the possibility of Metamorphoses of humans into trees; in the Metamorphoses, the transformations of Daphne and Phaethon's sisters figure prominently near the beginning of the poem. Ovid deliberately chose these exempla for contrast because they showed Lucretius at his most doctrinaire, an attitude that does not consistently inform the Epicurean poet's treatment of myth. 42 We should keep in mind, of course, that Ovid is uncanonical all around and not just vis-a-vis philosophers and philosopher poets: whereas the depiction, for instance, of dolphins in trees and boars in the waters is the hallmark of the bad artist in Horace's Ars Poetica (29-30), it does not take long for these vignettes to materialize in Ovid's description of the deluge (Met. 1.302-3, 305).
As most commentators have noted, almost half of Pythagoras' discourse, the catalogue of mirabilia and paradoxa (15.259-452), has next to no basis in Pythagoreanism, whether old or new. The closest connection we can make is (Pseudo)Sotion's treatise on the paradoxa of rivers, springs, and pools, 43 but the more important point is that Ovid's preceding treatment of Pythagoreanism has set the tone: we should not now expect an exploration of the phenomena in terms of probing science and philosophy. The relation of paradoxography to Greek science corresponds to that of the pantomime to Greek tragedy: anything serious and substantive is eliminated in favor of small, easily digestible snippets concentrating on the fascinating and the sensational. 44 Both developments are the result of the taste of a large public, and Ovid knew his audience. By his times, pseudoscience and science were intermingled in Hellenistic Greece and Rome, and the elder Pliny's massive collection provides continuing attestation. 45 Even if the distinction between the two may be clearer to us than to Ovid's contemporaries, Lucretius' De Rerum Natura had shown that rational, scientific thought was not incompatible with poetry. The presentation of an elaborate contrast, then, between philosophical and poetic modes is not one of the objectives of Pythagoras' speech. In its first part, Ovid flattens out philosophy to the point where it is indistinguishable from generalized, popular ideas, while in the second part he simply juxtaposes, rather than opposes, scientific-philosophical and poetical-mythical explanations in his large catalogue of miraculous happenings.
Franz Bömer and Sara Myers have thoroughly documented this procedure with example after example. 46 I will limit myself, therefore, to a few additional comments. One involves the mention of the spring of wondrous waters near the town of Clitor in Arcadia (15.324-8). Whoever drank from them would abstain from drinking wine in perpetuity. Ovid compresses the scientific explanation into one line; in fact, it is not an explanation as much as it is a matter-of-fact observation: seu vis est in aqua calido contraria vino (324) ["there is some force in the water that is opposed to the warmth of wine"]. He then goes on to summarize the mythological tale (325-8):
sive, quod indigenae memorant, Amythaone natus,
Proetidas attonitas postquam per carmen et herbas
eripuit furiis, purgamina mentis in illas
misit aquas odiumque meri permansit in undis.
The mythological explanation is four times the length of the scientific one. Before we construe this, however, as Ovid's privileging poetry over natural philosophy, we need to look only at Vitruvius. Vitruvius treats such phenomena in the first part of Book 8, which deals with hydrology. In many cases, including that of the wine-blocking springs of Clitor, he does not even bother to suggest a scientific cause. Instead, he simply tells the tale, expanding it, in the case of Clitor, to cite in full the ten-line epigram that was inscribed at the site (8.3.21). If a prosaic, nuts-and-bolts writer like Vitruvius, who stressed that an architect should diligently study philosophy (1.1.3), could come to the realization that natural philosophy would not go very far in such instances, so would Ovid.
Moreover, the mention of alternative explanations for wondrous phenomena has ample precedent in Metamorphoses 1-14, even if they are not immediately collocated with another. 47 Ovid tips off the attentive reader in his very introduction of Pythagoras. The sage's subjects include quae fulminis esset origo, / Iuppiter an venti discussa nube tonarent (15.69-70). As for the cause of lightning, Ovid already provided a naturalistic cause at 1.56 (cum fulminibus facientes fulgora ventos) only to proceed to depict it as the traditional mythological accoutrement of Jupiter (1.197, 253); the thunderbolts now are tela . . . manibus fabricata Cyclopum (1.259). Small wonder, then, that Pythagoras really has nothing more to say about the subject. Similar dual explanations are given for the creation of man (1.78-83, cf. 1.363-4), the support of the aether and air above the earth (1.26-31, 2.293-7), and the cause of the rainbow (6.61-4, 11.589-90). One explanation is no better than the other.
Nor is their credibility, and this produces another commonality of poetry and philosophy. Just before the philosopher starts speaking, Ovid comments that his teachings may be learned, but not altogether believed: primus quoque talibus ora / docta quidem solvit, sed non et credita, verbis (15.73-4). 48 In their position, the lines refer to the entire speech, and not just Pythagoras' injunctions about vegetarianism or metempsychosis. Ovid, in turn, in his apologia to Augustus explicitly characterizes the titular subject of the Metamorphoses as not to be believed (Trist. 2.63-4):
inspice maius opus, quod adhuc sine fine tenetur, in non credendos corpora versa modos. (Look at my major work, which is still unfinished, look at the bodies who were transformed unbelievably).
The assertion is reinforced by the enumeration of mirabilia asadynata in Tristia, 4.7.11-20: the majority are myths that occur in the Metamorphoses. 49 To be sure, there is a distinction between natural wonders, such as the spring of Clitor, and transformations of human bodies, as the former verifiably exist and call for an explanation, whether scientific or mythological. But Ovid deliberately blurs the line by sprinkling, throughout Pythagoras' speech, references to myths he had told earlier and by failing, in the case of the Symplegades (15.337-9), to give a "scientific" reason altogether. Similarly included are transformations from inanimate to animate (375-7), and decomposing to live matter (368, 389-90). Several assertions of disbelief, therefore, are a constituent part of Pythagoras' speech (282-3, 359, 389-90). It is not possible to put stock either in the fides poetica or the fides philosophica. As a result, Ovid's poetic immortality, to which I will return, is not based on the traditional claim of the vates to have revealed the truth, but on the truthful prediction of the vates-and that is the only truth they may possess-that Ovid and his fame will be immortal (15.878-9):
perque omnia saecula fama,
siquid habent veri vatum praesagia, vivam.
To turn from the end of the poem to its beginning: as it is Ovid's overture to the Metamorphoses, the cosmogony (1.5-75) is poetic rather than philosophical. This introductory passage and the speech of Pythagoras have rightly been considered thematic pendants, 50 but it is important to be alert to the differences, too. Like the discourse of Pythagoras, the cosmogony does not fit the simple matrix of (mythological) poetry vs. (natural) philosophy. Its suggestive model is far more emphatically poetic: it is Homer's description of Achilles' shield, imago mundi, as Stephen Wheeler has recently argued. 51 Two brief observations may be added to his cumulative argument. First, reading Ovid's cosmogony to some extent as poetology, he identifies deus et melior natura (1.21)with "a figure for the poet" (117); I would argue that this notion is picked up by Ovid's phrase in the sphragis (15.875) that melior pars mei, exactly his esprit créateur and the works produced by it, 52 will escape oblivion and live on forever. Secondly, as Wheeler points out, by Ovid's time there had been a joining of poetry and philosophy in the interpretation of Hephaestus' shield, which had come to be considered as an allegory of the creation of the universe by a demiurge. The primacy, of course, belonged to Homer, just in purely chronological terms. "As a result of this type of exegesis, Roman poets came to regard the shield as a primary model for describing the origin and structure of the universe." 53 I would add that Ovid's choice of the Homeric shield as a model, therefore, suggestively enhances his placement of the Metamorphoses directly in the Homeric, rather than the Empedoclean, tradition. The ancient view was that all the literary forms took their origin with Homer. He was the "Ocean"-how curiously relevant this is to the shield description-from which all literary streams flowed. 54 Over time, they had been disjoined, but the Metamorphoses was Ovid's grand attempt to bring them back together. In this light, Ovid's procedure of presenting "not merely one cosmogony, but a series" and "suggesting that the cosmogonic process is one that will continue throughout the poem: ad mea tempora"55 takes on its true dimension. It is his poetic program of recreating and reuniting the various literary forms, which originated with Homer.
Philosophy is assimilated and subordinated to this purpose. As in the case of the discourse of Pythagoras, numerous attempts have been made to identify philosophical sources in Ovid's cosmogony. Once again, Ovid includes enough allusions to lend philosophical coloring to the piece. At the same time, and befitting the poet of metamorphosis who changed many poetic traditions, he makes some changes in the received philosophical tenets. Significantly, these changes apply to Empedocles and his doctrine of Love and Strife. 56 In the first instance and in contrast, too, to Orpheus' song in Apollonius' Argonautica 1.497-511, Ovid presents Strife not as triggering the evolution of the cosmos, but as perpetuating chaos. What creates order is not an abstract philosophical principle, but a benevolent creator who is easily assimilable, as we have seen, to the pohtÆw: deus et melior natura (1.21). Similarly, despite all the importance of love as a theme in the Metamorphoses, Ovid excludes it as a natural-philosophical agent from his cosmogony. The avoidance of emphasis on serious philosophy is the same here as in Pythagoras' discourse.
By raising issues that are central to his work, Ovid appeals to the reader to reflect on the nature of mythological poetry and to compare him, in this important respect, with his two major Roman predecessors, Vergil and Lucretius. I have already commented on Vergil; what about Lucretius?
It has traditionally been argued that Lucretius, because of his ostensible attacks on myths, demythologized myth and that Vergil and Ovid subsequently remythologized it. In actuality Lucretius' attitude is more complex. 62 He wanted to be an Epicurean and a poet, and being a poet meant he had to use myth, which seems to have been precisely one of the reasons Epicurus had rejected poetry. Lucretius proceeded to combine the two hitherto irreconcilables by devising his own, Epicurean "theory" of myth on the basis of several differentiations. Parallel to the Epicurean theory that sensations bear some relation to (external) reality, he posited that myths have a hyponoia, an underlying phenomenon that needed to be explained. In both cases, the problem is not reality or the phenomenon itself, but faulty inferences and interpretations, in this case, the traditional myths. Myth, therefore, can be retained for its power to attract and charm readers, provided the vera ratio is pointed out at the same time. "The mythological passages in the DRN," therefore, "act as a powerful polemical and didactic tool: at one and the same time, Lucretius is able to dispose of rival theories of myth satisfactorily by substituting his own account of its origins and nature; and to use myth didactically to illustrate and enhance his own argumentation." 63 Lucretius, then, appropriates myth, which was formerly deceptive, for his own philosophical purposes; hence his use of the "myths" of Venus and the plague to bracket his poem-just as Ovid does with the ostensibly "philosophical" episodes of the cosmogony and Pythagoras.
This is only part of Ovid's response to Lucretius. Another involves the juxtapositions we have observed of mythical-poetical and natural-philosophical explanations. Such juxtapositions are frequent in Lucretius, and they have a deeper reason: the demonstration of vera ratio. The theme is sounded in his apologia for poetry (1.921-50, repeated at 4.1-25): id quoque enim non ab nulla ratione videtur (1.935). We reencounter it in the pivotal exempla of Magna Mater (2.596-645) and Phaethon (5.396-415). Both times, the traditional mythological version is ascribed to veteres Graium poetae (2.600, 5.405). Both times Lucretius emphasizes that longe sunt tamen a vera ratione repulsa (2.645) and procul a vera nimis est ratione repulsum (5.405-6). The difference from Ovid is clear: for Ovid, there is no vera ratio of myth and serious philosophy is next to non-existent in Pythagoras' discourse. In the catalogue of yaumastã the juxtapositions, therefore, become a mere literary device without any profound significance. 64 And just as Lucretius had appropriated the language and evocativeness of mythology for his philosophical tenets, Ovid uses the Lucretian language of natural philosophy for some of his most fantastic transformations. 65 The inversion is complete: these portenta now are dressed up as if they were phenomena that can be explained in terms of rationalist science. A paradigm is the transformation of Lichas (9.216-25):
dicentem genibusque manus adhibere parantem
corripit Alcides et ter quaterque rotatum
mittit in Euboicas tormento fortius undas.
ille per aerias pendens induruit auras,
utque ferunt imbres gelidis conscrescere ventis,
inde nives fieri, nivibusque molle rotatis
adstringi et spissa glomerari grandine corpus,
sic illum validis iactum per inane lacertis
exsanguemque metu nec quicquam umoris habentem
in rigidos versum silices prior edidit aetas.
We are looking at multiple appropriations and inversions from Lucretius. The slingshot in line 218 recalls a bit of "pseudo-science taken on trust by Lucretius (DRN 6.177-9, 306-7)," 66 with a venerable pedigree that included Leucippus, Democritus, and, possibly, Anaxagoras. 67 Ovid treats this "scientific fact" accordingly by turning it inside out: he has the slingshot freeze and harden rather than heat up. 68 Ovid proceeds to explain the actual petrifaction of Lichas as a meteorological phenomenon; the model is Lucretius 6.495-523 and 527-34. Moreover, he mimics and inverts Lucretius by distancing himself from this event that is now garbed in natural philosophy: ferunt (220), which hints at the borrowing of the explanation from Lucretius, and prior edidit aetas (225) correspond to Lucretius' distancing himself from the mythological stories of the Graeci vates. This also provides the larger context for Ovid's use of ferunt to disavow Pythagoras' influence on Numa (15.480).
Some conclusions can be drawn at this point. Ovid's treatment of the discourse of Pythagoras is viewed best not as a unifying philosophical pivot of the Metamorphoses, but as a contribution to an ongoing discussion about the roles of myth and philosophy in the grand poetic tradition. One of Ovid's uses of this extended passage is to call attention to his poetic aims and to his place in the poetic tradition. 69 He does not limit himself to writing Empedoclean epic; if anything, he places his poem in the tradition originating with Homer, a tradition that he Metamorphoses throughout his poem by numerous innovations. The speech of Pythagoras and related passages in the Metamorphoses highlight the nature of Ovid's contribution and his differences both from Lucretius' insistence on vera ratio and Vergil's reinvestment of myth with great spiritual, moral, and historical meaning. Ovid downplays the historical component, i.e. the connection of Pythagoras and Numa, and banalizes philosophy. The didacticism of Lucretius and philosophy in general are deflated by the jarring disjunction of the "hyperdicactic" mode of the speech, 70 which is marked by a profusion of protreptic injunctions and didactic pronouncements, 71 and the minimalism of both philosophical content and a substantial addressee-the latter, as we have seen, is not Numa, who receives Pythagoras' ramblings only second- or third-hand, but the shadowy coetus silentum (15.66). Pythagoras's discourse itself, therefore, is a dubious vehicle for the poet to lay a serious claim to Empedoclean epic. At the same time, Ovid uses the speech of Pythagoras, by way of contrast, to call attention once more to his distinctive contribution to mythological poetry on a grand scale. It lies, to restate stubbornly what I said more than a score of years ago, in the realm of narrative. 72
In terms of narrative, Pythagoras' presentation of change is designed to invite comparison with Ovid's in the previous books of the poem. To be sure, Pythagoras' speech is not a deliberately bad piece of poetry; Dryden and others singled it out for praise, and E.J. Kenney has observed that "the speed and fluency of the writing match the theme." 73 The reason is simple and does not have to be over-determined by narratologists "carried away by [their] hyperfunctionalist enthusiasm." 74 As always, Ovid has it both ways (although, as we could see from Lucretius' utilization of myth, Ovid was not alone). He is the narrator al fondo who demonstrates, through his handling of Pythagoras' discourse, that he can assimilate "philosophy" to his mythological poem just as easily as any other subject, genre, style, or tradition. The up-front narrator is Pythagoras. The basic point is that Ovid, by presenting the subject through Pythagoras in this particular manner, alerts us to the fact that the material could be presented in other ways. This is true, as we have seen, of his failure to develop the multiple connections, discussed by other writers, between Pythagoras and early Rome, and it is implicit in his refusal to develop a significant philosophical discourse. Ovid makes no more than a bow to both traditions: he also knew that, as Cicero had pointed out, 75 philosophy and oratory were thought of as being united; hence the length of Pythagoras' speech is a running contrapposto to the thinness of its philosophical content proper. But, as we have already seen on several occasions, the speech looks back to the first 14 books as well. There is reference after reference to stories that Ovid had told earlier: the Cyclops, Lucifer, Hercules, Scylla, Salmacis, the Centaurs, Phoebus, Myrrha, Phaethon, Aurora, the underworld. They are a constant reminder of how differently stories such as these could be told. Or take a subject like sex change: Pythagoras baldly mentions the hyena (15.408-10); Ovid tells the stories of Iphis and Caeneus at length and with gusto. Ovidian polyphony is replaced by the monotone of Pythagorean taxonomy.
Simultaneously, Ovid uses Pythagoras' discourse as a reminder of the challenge he himself faced in stringing together a mass of often heterogeneous material. Ovid's solution was to create imaginative and, sometimes, deliberately outrageous transitions, whereas those of Pythagoras lack such brio and can be artless and mechanical, an aspect that has been repeatedly commented upon; the connective et quoniam, for instance, is used twice here (15.143, 176) and does not occur elsewhere in the Metamorphoses. Along the same lines, I am still convinced that Pythagoras, or Ovid through Pythagoras, articulates the realization that the listener's attention may be flagging due to Pythagoras' narrative mode. At least this is the strong implication of lines 418-20: "The day will wane, the Sun beneath the waves will plunge his panting steeds before my tale recounts the sum of things that take new forms" (Melville transl.):
desinet ante dies, et in alto Phoebus anhelos
aequore tinguet equos, quam consequar omnia verbis
in species translata novas.
Taking issue with my observation, Bömer in his commentary (ad 418) avers that it is not boredom that is suggested here. Rather, and borrowing a phrase from the Italian scholar Cupaiulo, he writes that we are dealing, in the Ovidian trope, with "accorgimenti tecnici e stilistici consueti nella prosa retorica." That is an even better way of making my point.
One of the main differences is, of course, that Pythagoras' speech deals single-mindedly with change whereas most of the stories in the Metamorphoses do not; Kenney's observation is still on the mark that love or, as I would put it, love in all its variations (or Metamorphoses in that sense), rather than metamorphosis pure and simple, is the principal theme of the poem. Just as important, while the philosopher, represented by Pythagoras, proclaims change to be the controlling principle of the world, Ovid ends Book 15 and the Metamorphoses by emphasizing that he and his poetry will be impervious to it. /i>Nihil est toto, quod perstet, in orbe: cuncta fluunt, says Pythagoras (177-8). Ovid, by contrast, will transcend /i>theorbis terrarum: super alta perennis / astra ferar, nomenque erit indelebile nostrum (875-76). 76 The contrast is played out yet further in the phrase Pythagoras had used to introduce his maxim. He employs a well-known metaphor for poetry: magno feror aequore followed by i>plena ventis vela dedi, but his poetic pretensions are subverted from the start by yet another et quoniam, his second such use of that connective within less than 35 lines. It is a formula that is at home, e.g., in Cicero's De Officiis, 77 but not in poetry.
The speech of Pythagoras has several purposes. Pythagoras personifies the confluence of Greece and Rome, a theme that shapes Book 15 and, in a larger sense, the entire Metamorphoses and the culture of the Augustan age. Pythagoras and his discourse also stand for the synthesis of various philosophies; Pythagoreanism, in fact, had evolved into such a synthesis, especially in Rome, by the first cent. B.C. In that sense, Pythagoras is the compleat philosopher; after all, he was credited with inventing the term. Further, Pythagoras' speech is a tour de force, just like Ovid's poem, but it is a very different tour de force. It is a demonstration of what Ovid could have done throughout the Metamorphoses, but did not. It also suggests what Pythagoras could have done and did not, both in terms of treating philosophy and narrative. The passage is also part of Ovid's ongoing dialogue with his Roman predecessors: with Ennius by recall of the earlier poet's Pythagorean coloring of the beginning of the Annales, 78 and, especially with Lucretius and Vergil. Overall, the passage is a final demonstration of Ovid's inversion of Lucretius by Lucretian means. Lucretius had assimilated myth to his philosophical poem by stripping it of its traditional perspectives. Ovid reciprocates by assimilating philosophy to his mythological poem by divesting it of its real content. As in the case of any Augustan creation-and the Metamorphoses is very Augustan, unless one buys into the usual dichotomies-the main task for the interpreter of Pythagoras' discourse is to be attentive to the multiplicity of aspects and to consider each individual aspect, such as the philosophical coloring, within this totality.
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NOTES
1 Esp. Myers (1994) and Hardie (1995).
2 For the combination and interaction of genres in the Metamorphoses see the useful articles by Horsfall (1979) and Farrell (1992); cf. Solodow (1988) 18-25. W.S. Anderson's review of S. Hinds, The Metamorphosis of Persephone (Cambridge 1987) in Gnomon 61 (1989) 356-8 puts the issue of genre into perspective relative to other issues with which Ovidian scholars should be concerned.
3 See Burkert (1961) 236-46 for a concise and substantive summary; more detail in Ferrero (1955) and, with an excellent collection of the ancient sources, Garbarino (1973)
4 Kenney (1986) xviii.
5 Hardie (1995).
6 Hardie (1995) 205 n.7.
7 A study of the Metamorphoses from this aspect is still a desideratum; for such approaches and their application to Roman literature, cf. Woodman (1992) 208 with n.17.
8 Metamorphoses 4.432-80; see Bernbeck (1967) 4-30 and Galinsky (1989) 82-6.
9 Cairns (1989) chs. 1-3.
10 By Heracleides of Pontus; the various sources are listed and discussed by Burkert (1960).
11 Aelian Var. Hist. 2.26 (citing Aristotle); cf. Iambl. Vita Pythag. 140. Another connection would be Pythagoras' claim to be the reincarnated Euphorbus (Met. 15.261), who was prominently associated with Apollo in the Iliad. According to Diogenes Laertius 8.21, Pythagoras received his teachings from the Delphic priestess; hence Delphos meos . . . recludam . . . et augustae reserabo oracula mentis (Met. 15.144-5). On augustae, see Bömer ad loc.
12 Aristoxenos fr. 17 (Wehrli) = Porph. Vita Pythag. 22; Iambl. Vita Pythag. 241; Diog. Laert. 8.14.
13 Pliny, NH 34.26; Plut. Numa 8.10; cf. Coarelli (1985) 119-23.
14 Plut. Aem. 2.2; Festus p. 23 L.; cf. Burkert (1961) 237 n.5 and Maltby (1991) 12-13.
15 oþ ÉItaliko¤: Met. 987a10, 31; 988a26.
16 Burkert (1961) 234.
17 On the Sextii, see Ferrero (1955) 360-78; cf. von Arnim in RE II.4.2040-41. 18 Ferrero (1955) 268-80; Segl (1970) 103-4 (with reference to Lafaye); Bömer (1986) 269-70.
19 Cairns (1995) 122.
20 Cf. Bömer (1986) 270-71; Due (1974) 30; Segl (1970) 94-6.
21 Burkert (1961) 245; cf. Hirzel (1891) 1308-11.
22 Sauron (1994) 630.
23 See note 11, above. Garbarino (1973) 63-72 has conveniently assembled the ancient sources (20 in all). For extensive discussions see Ferrero (1955) 142-7; Garbarino (1973) 230-38; Gruen (1990) 158-70.
24 Fr. 37 Peter = Pliny NH 13.84-6. The testimonia (12 altogether) again in Garbarino (1973) 64-9. The most recent discussion, which proceeds along different lines from mine, is Gruen (1990) 163-70; cf. Gruen (1992) 259.
25 Cf. Met. 8.721-2, with my comments in Augustan Culture (1996) 232-3.
26 Met. 13.25; cf. Hor. Epod. 5.51; Lucan 6.513; Sen. Med. 740; Verg. Aen. 6.432; Prop. 3.12.33. I follow Barchiesi (1989) 76-7 rather than Bömer ad loc. There may be more to it yet: Plato (Phaedo 64 a and b) mentions a (comic?) tradition according to which philosophers were endemically enamoured of death; cf. Middle Comedies entitled "Pythagorists" (Diels-Kranz 58E).
27 Rawson (1985) 294.
28 Rawson (1985) 293 on the basis of Plutarch Quaest. Rom. 10.
29 Cf. Barchiesi (1989) 79.
30 By Bömer ad loc.
31 The story of Philemon and Baucis is another paradigm; see Galinsky (1975) 202.
32 Cf. Myers (1994) 141-2.
33 Detailed documentation in Segl (1970) 43-4 and Bömer ad loc.
34 Diog. Laert. Vita Pythag. 8.10; full discussion in Segl (1970) 51 and Bömer ad loc.
35 See Haupt/Ehwald/von Albrecht (1966) and Bömer ad loc.
36 Segl (1970) 136 n.223; cf. Bömer ad 252-3.
37 Segl (1970) 47 (with reference, e.g., to quattuor genitalia in line 239).
38 Segl (1970) 45-7.
39 Sen. Epist. 108.18; see Haussleiter (1935) 296-9 and Ferrero (1955) 374-5.
40 Galinsky (1975) 141-3.
41 Lucr. 2.700-29; 4.732-45; 5.878-924; see Myers (1994) 145-7.
42 Gale (1994); cf. below, Section 6.
43 Segl (1970) 57 with n.265; Crahay and Hubaux (1958) 286.
44 See the collections of the Greek paradoxographers by Westermann (Amsterdam 1963) and Giannini (Milan 1965). Cf. Galinsky (1996) 265-6 on the affinities of pantomime and Metamorphoses; from there the road leads to the Ovide bouffon of the 17th century (Moog-Grünewald [1979] 124-56).
45 Cf. Myers (1994) 150-52 with n. 79.
46 Bömer (1986), esp. ad 15.324; Myers (1994) 152-9.
47 Cf. Little (1970) 349-55. A kindred procedure is Ovid's frequent use of "the language of physics to describe myths of the most fabulous nature" (Myers [1994] 49, with a discussion of several examples on pp. 47-9; cf. Section 6 below).
48 Primus may be a reference to the tradition that Pythagoras was the eÍretÆw of the word "philosopher"; see note 10, above. Also relevant may be Callimachus Iambus 1 (fr. 191) lines 62-3: oi d ar oux uphkousan, ou pantew with the poignant emendation by H. Lloyd-Jones: oi Italoi d uphkousan, ou pantew, with the further remarks by M. L. West in CR 21 (1971) 330-1.
49 Cf. Little (1970) 347-8.
50 Cf. Pythagoras' reference to magni primordia mundi at Met. 15.67.
51 Wheeler (1995), with extensive references to previous scholarship. As always in Augustan poetry, several inspirations coexist; see Helzle (1993) for the Callimachean aspect of the cosmogony. The cosmogony then becomes an immediate illustration of the poetic program announced in lines 1-4: the combination of carmen perpetuum with carmen deductum.
52 See Bömer ad loc.
53 Wheeler (1995) 98, summarizing Hardie (1986) 66-70, 346-58.
54 Documentation in Williams (1978) 87-9, 98-9; cf. Galinsky (1996) 262. Cf., with reference to the Aeneid, Cairns (1989) 150 and Hardie (1986) 22-4 .
55 Myers (1994) 27.
56 Wheeler (1995) 95-7.
57 Cic., Tusc. 1.48; Prop. 2.34.53-4, only a few lines before Propertius' famous reference to the Aeneid (61-66).
58 Cf. Wlosok (1990) 386-7.
59 See the insightful and delightful discussion by Bernbeck (1967) 10-26.
60 Book 5: Ceres and Proserpina (341ff.); 10.40-48 (Orpheus); 14.101-53: Aeneas and the Sibyl. Only 20 lines after his dismissive remarks, Pythagoras lays claim to being vates (15.174: vaticinor); his topic, vegetarianism, is consigned to materies vatum.
61 Trist. 2.63-4, cited above, p. 13. The phrase cannot be restricted to mean "bodies transformed in amazing ways"; cf. Luck ad loc. and Little (1970) 347-8. Ovid was taking no great risk as there was a strong tradition that "veracity" was not to be expected of poets; for documentation and discussion see Feeney (1991) 5-56 and Myers (1994) 49-51.
62 See the sensible study by Gale (1994) on which my following remarks are based. Cf. Myers (1994) 53-9.
63 Gale (1994) 230.
64 Aristotle's comment tÚ de yaumastÒn ¾dÊ (Poet. 1460a17) is apropos.
65 See Myers (1994) 47-9.
66 Kenney in Melville (1986) 390.
67 See Leonard and Smith (1961) ad loc. As Bömer points out (ad Met. 9.218), there is also an element of anachronism.
68 See Bömer ad Met. 9.220 with reference to Met. 2.727-9.
69 I cannot emphasize strongly enough that this is only one aspect of the passage. It is legitimate for academics to be attentive to aspects of poetology, genre, and the like in the Metamorphoses, provided we realize that these are not the immediate reasons for the popularity and appeal of the poem through the ages. The increasing interest in this aspect of the Metamorphoses is gratifying; see the recent the collections of Martindale (1988), Anderson (1995), and Walter and Horn (1995). As I stated initially, the entertainment value of the mirabilia and the topicality of "Pythagoras" would assure Ovid a broad public.
70 Barchiesi (1989) 77, 80-82.
71 E.g., animos advertite (140); animos adhibete (238); mihi credite (254); tollite . . . nec fallite . . . nec includite . . . nec celate . . . perdite . . . perdite (473-8); nonne vides (361, 382); magna. . . canam (146-7); doceo (172); vaticinor (174); docebo (238).
72 Galinsky (1975) 104-7. Cf. Kenney (1982) 435: "If the Metamorphoses is in some sense significant . . . it can only be on the strength of Ovid's treatment of his material, the myths themselves."
73 Kenney (1986) 460.
74 Genette (1988) 48. For a plain exposition of levels of narration and embedded narrative texts see Bal (1985) 134-48.
75 Orator 11-19, cf. 113-19.
76 Paratore (1959) 193 has briefly adverted to the echo of Horace C. 2.20.1-4 (ferar . . . per liquidum aethera . . .neque in terris morabor), but the associations between the ode and the sphragis of the Metamorphoses are more extensive. In addition to dealing with the topos of poetic immortality (cf. the reference to C. 3.30.1 in Met. 15.871), the ode was congenial because of its graphic description of metamorphosis, which anticipates several of the Ovidian depictions. There is also the usual alteration of the model: Horace, who is being transformed into a bird, becomes biformis vates, pretending to immortality, whereas Ovid, the poet of metamorphosis, concedes to the vates the power of predicting his immortality. Another connection is Horace's claim that he will be known among the barbarians at the fringes of the Roman Empire-precisely the kind of place where Ovid completed the Metamorphoses. Similarly, there is yet another point to Ovid's ascent super astra: his deification will be even greater than Julius Caesar's, whom Venus simplycaelestibus intulit astris (15.846); cf. Feeney (1991) 249. Fittingly, Ovid ends the Metamorphoses with a blaze of allusions that add perspective to his achievement; the topic of Ovidian closures bears revisiting.
77 Off. 122, 132, 138; see Haupt/Ehwald/von Albrecht (1966) ad 15.75 and 143.
78 It should be clear from Ovid's treatment of "Pythagoras" and Pythagoreanism that the passage in the Metamorphoses provides no basis for any inferences about Ennius' Pythagoreanism, whatever its nature. Ennius' principal point was to be Homer's reincarnation. By recalling Ennius, Ovid, therefore, also recalls Homer, an aspect that is central to the Metamorphoses.
A very preliminary version of this paper was delivered at the Leeds International Latin Seminar in February 1996. A more extensive version was presented at the Universities of Budapest, Szeged, and Verona later that year. Im grateful to these audiences and, in particular, to Alessandro Barchiesi and my colleague Stephen A. White, for some helpful suggestions.