By means of the characters of Adeimantus and Glaucon, who together with Socrates create the theory of forms in the Republic, the frame (126 a-127 a) indicates the weight that Plato claims for the Parmenides : the effort is great, poly ergon. In his praiseworthy and original monograph, R. immediately refers to the result of the effort: the theory of forms undergoes an evolution here, which is indispensable for the last phase of Plato, for the Sophist, the Statesman, and the Philebus. But it is difficult to establish an evolution without contradiction or to postulate for the theory of forms an evolution that can withstand scrutiny. From the early phase to the text of the Laws, Plato does not reveal a coherent theory of forms.1
The Parmenides receives from modern-day critics either a logical interpretation or a metaphysical one. The logical interpretation, from Ryle to Owen and Vlastos, either detects in Plato a polemical goal, that of demolishing the result of Parmenides, or a more positive goal, that of raising a solid basis for semantic research. This array of scholars finds its most recent exponents in Allen, Sayre, Meinwald, Moravcsik, Turnbull and Scolnicov. R. borrows method and material from this interpretation and freely acknowledges his debt.2 He offers a logical interpretation in a positive direction: the Parmenides not as a field of semantic research, but as a meticulous discussion of the theory of forms. There is an immense distance to a metaphysical interpretation, either the great theme of Halfwassen that the Parmenides is a colossal monument to the one beyond being, or to the reconstruction of Migliori and Horn that the Parmenides is a prefiguration of the one and the dyad, the doctrine of oral communication documented by Aristotle.3
In his analysis, R. recalls the theory of forms that Plato offers in the central phase, in the Meno, the Phaedo, and the Republic (10-52). Of course, it is not difficult to perceive the theory of forms already in the aporetic phase, in the need to find the definition of eusebeia or the definition of sophrosyne. But here Plato does not explain the status of the forms, their relationship with becoming, and he does not see the forms as a peak of knowledge.4 The theory of forms is born from the substitution of a method with a polemical function, the elenchos, by a method with a positive function, the hypothesis. And it is born by means of axioms and auxiliaries, which R. wishes to distinguish: two axioms—One-over-Many and Itself-by-Itself—and seven auxiliaries—polarity between properties, polarity between forms, the necessary consistency between properties and things, the transmission theory, the intrinsic ambiguity of things, knowledge in relationship with its aim, knowledge in noetic perspective. With axioms and auxiliaries, Plato is said to weave a sequence of fourteen assertions of central weight, for example, the existence of the forms, their uniqueness, their participation, self-predication, non-contamination, non-identity, accessibility and separation. R. has abbreviations for all: for the axioms, OM and II, for the auxiliaries, CON, PC, NCC, TT, IS, SOK and PHK, and for the fourteen assertions,
R. begins with the famous answer of the young Socrates to Zeno’s book and the monistic conception of Parmenides, in which he illustrates the forms in relationship with the many (127 a-130 a). R. detects here the higher version of the theory of forms, and offers a subtle examination of it. He divides the speech, and recognizes in the last section a Radical Purity, RP, beyond P and
But the highest theory of forms, the highest for its Radical Purity, has a weak nature that Parmenides quickly indicates (130 a-134 c). Parmenides rejects the relationship between the axioms or between the auxiliaries and one or more of the fourteen assertions. Here Socrates recognizes eight situations of aporia. In his second chapter R. sums them up in his abbreviations (53-94). For example, for the “third man”: it is the combination of OM, SP, NSP, O and RP in the presence of an insuperable resistance to the combination of OM, SP, NSP and U. The reflection on the “third man” starts in the Phaedrus, the Republic and the Timaeus. But is it correct to underline the function both of OM and of SP, both of NSP and of O, both of RP and of U? Does Plato choose the route that R. outlines? Clearly, the problem is the participation of the many in the forms. But R. indicates more than one combination that does not find adequate support in the text.5
Immediately afterwards, the Parmenides has a section dealing with the method that may be useful to save the theory of forms, checking the force of the refutation (134 c-137 c). R. offers a reconstruction of this in his third chapter (95-111). It is not possible to admit a drastic solution, the refusal of One-over-Many and Itself-by-Itself, the starting axioms: without One-over-Many and Itself-by-Itself, the theory of forms vanishes. But, without the theory of forms, it is not possible to develop the inquiry R. does not forget the definition suggested by Book VI of the Republic : the inquiry transcends the sensible, with its method, hypothesis;it advances among the forms, and in the forms finds knowledge. This leads in the Parmenides to a technical interpretation of gymnazesthai. Here the inquiry is to apply to the forms, and not to the sensible. But in order to understand gymnazesthai, the value of pros in relationship with hen and polla is undoubtedly a problem. Quite rightly, R. rejects the hypersemanticisation that critics mostly prefer, the Meinwald Reading: pros has the common value, the value that the Parmenides indicates, the value fixed in the Symposium, by Diotima, or in the Hippias Major.
The sequence of the eight deductions occupies the fourth, fifth, sixth, and the seventh chapters, with the last covering the last four deductions. The asymmetry is striking, but it is coherent with both the number of pages that Plato offers for the eight deductions, and the value that the last four deductions possess for the reconstruction.6
R. advances along the rugged paths of the one (112-137). And he observes the separation between the one and the many, between the one and to holon, the arche or the teleute, between the one and peras, kinesis, rotation, the similar and the tauton, between the one and the time, between the one and the becoming, between the one and the knowledge as science or as an opinion (137 c-142 a). The result is commendable, because it enables us to understand the connection between the arguments. Quite rightly, R. affirms that the connection between the arguments is lacking for the one. But he burdens the system of abbreviations for axioms, for auxiliaries and for the fourteen assertions with a further web of abbreviations for the arguments. Hence the style: “assuming RP, if the one is, then the one is not in time (DIA16
Among the eight deductions, the second occupies fully fourteen Stephanus pages (142 b-155 e). The aim is to demonstrate by thirty-three arguments that it is not possible, for the one, to exclude the presence of the opposite forms. The strength of the arguments gives rise to more than one contradiction: the theory of forms is considered to be at risk. R. proves that here, Plato rejects Radical Purity to save the theory of forms. The relationship that Plato has here with the poem of Parmenides, with his sequence of aletheia (8, 1-49 Diels-Kranz) is evident. But the discussion that R. offers, though excellent, does not place the text in a historical perspective (139-187). Not surprisingly, there is no reference to the Theaetetus (147 d-48 e), at a short distance from research on the one as regards the mathematical arrangement, or to the Philebus (23 c-31 b), if not for the one and the dyad, for the function of the peras. And there is no reference to Aristotle’s Physics (226 b-227 a), which recalls the Parmenides for the hapsis and the arithmos. R. does not renounce the outline of the thirty-three arguments. As a positive result, he describes the weak characters of D2A4, D2A12, D2A14: want of consistency, lacunas, flimsy relationship with axioms or auxiliaries, flimsy relationship with the fourteen assertions. But the force of D2A3 is great, with the many that invades the status of the one. Quite rightly, R. discovers here that the support both of P, Purity, and of U, the correspondence of the forms to their properties, is undermined.
It is difficult to distinguish the kind of articulation that Plato indicates for the Parmenides. The result will always reveal an interpretation of the research on the one. Among the scanty words, a to triton emerges for the section on the exaiphnes, the fundamental and elusive moment that witnesses the becoming of the one (155 e-157 b). But R., in the sixth chapter, affirms that the section has a marginal status (188-211). However, the section on the exaiphnes proceeds by means of the inextricable combination of four arguments that Plato offers: D1A1, D1A17, D2A3, and D2A5. Without Radical Purity, the section undoubtedly does not show the force to crush the theory of forms. R. immediately indicates the problem: Radical Purity is not reconcilable with time, the inexorable dynamics that participation requires. Plato arrives at the difficult relationship with things, talla, in order to demonstrate that the one gives rise to the existence both of the forms and of the opposite forms (157 b-159 b). Soon the result is turned upside down (159 b-160 b). Hence a contradiction that finds an evident solution: time. But, it is obvious, time is not reconcilable with Radical Purity.
For the last four deductions, Plato offers no more than six Stephanus pages (160 b-166 c). The style, with rapid words mainly in an elliptical sequence, derives from a tiredness that by itself hinders the peaceful investigation of the first two deductions. But R. observes them scrupulously: this is the seventh chapter (212-239). For the fifth of the eight deductions, Plato indicates a new basis: the negation of the one. But the aim is similar, because the negation of the one immediately indicates the existence both of the forms and of the opposite forms. It is possible to detect in embryo here the perspective that inspires the reflection against Parmenides, the “patricide” in the Sophist (241 d-242 b and 258 c-259 d). But R. proceeds with his web of abbreviations. He obscures the result of the sixth: the existence of the one, existence that requires time, which is indispensable for assuming both participation and non-participation. R. affirms here that the existence of the one proves by itself the existence of the forms. But is this an obvious “exercise” for the addressee? The refusal both of P, Purity, and of U, the correspondence of the forms to their properties, prompts a solution to overcome the problem of the “Piece-of-Pie”, the image for the highest theory of forms. The existence of the forms soon arrives, as the result of the negation of the one. But the negation of the one makes more than one contradiction between appearance and reality inevitable. In his commentary, Damascius (IV 128, 17-129, 11 Westerink) indicates the relationship with the Timaeus (48 e-56 c). It is not difficult to think of Book V and Book VI of the Republic (478 c-480 a and 522 e-526 c). But this is not the purpose: R. here regards the Parmenides as a monument of a sterile consistency. Not surprisingly, the style of the section dealing with the passage where Plato affirms that the negation of the one prevents knowledge is flat.
In the last chapter, R. reaches the ambitious goal of his reconstruction (240-250). The idea that Plato does not play is plausible in itself: Plato discovers that, in order to save the theory of forms from refutation, it is necessary to renounce auxiliaries or one or more of the fourteen assertions.7 But the result, which is perhaps reconcilable with the need for order, for mathematic sapheneia, is repellent: “at the apex of the theory stand the two axioms, OM and II, II entails S, NSP and NSE, OM entails both O and E and … NMTO (O also follows from the conjunction of PC and CON)”.
The list of References is extensive and very useful: more than 125 works, essays and reviews. Apart from the comment by Wundt, of 1935, all are in English.
At the end of this densely reasoned monograph, it is difficult to detect the research of Plato, his concrete, laboured effort to conquer the theory of forms. It is true that for the axioms or auxiliaries, and for the fourteen assertions, R. recalls, all in English, the words of Plato. But is it right to understand the Parmenides only with axioms or auxiliaries and to postulate in Plato a consciousness of the fourteen assertions? The web of abbreviations is too thick for a reconstruction faithful to the text. Among the fourteen assertions, there emerges KF, Knowledge of Forms, which substantially recalls PHK, at the end of the auxiliaries, and among the fourteen assertions, there is no precise motivation for the presence, after NMTO, No More Than One, of U or of O. R. then claims a central value, among the fourteen assertions, for
Notes
1. One indispensable datum is undoubtedly missing: the sequence of the works. For example, the problem of the Timaeus is well-known. R. insists on the short distance from the Republic. And not by chance: the initial dialogue (17 a-20 d) recalls the Republic. But critics mainly drift towards the Laws, apart from the stylometric question, for the relationship with the sensible or for the conception of mimesis. Cf. M. Erler, Die Philosophie der Antike 2/2, Platon, Basel 2007, 262-272.
2. C. H. Zuckert, “Plato’s Parmenides: A Dramatic Reading”, The Review of Metaphysics 51 (1998), 875-906 should be added to the References along with A. Graeser, who, with his contributions “Wie über Ideen Sprechen? Parmenides”, in T. Kobusch, B. Mojsich (ed.), Platon, Seine Dialoge in der Sicht neuer Forschungen, Darmstadt 1996, 146-166, and Platons Parmenides, Stuttgart 2003, 3-84, recalls the study of Speusippus on the one and the debate in the Academy.
3. Cf. L. Brisson, Platon, Parménide, Paris 1994, 293-306, and F. Ferrari, Platone, Parmenide, Milano 2004, 9-18.
4. Cf. M. Erler, Platon, München 2006, 101-124.
5. Cf. L. Brisson, “Come rendere conto della partecipazione del sensibile all’intelligibile in Platone?”, in F. Fronterotta, W. Leszl (ed.), Eidos – Idea, Platone, Aristotele e la tradizione platonica, Sankt Augustin 2005, 25-36.
6. It is difficult to establish the text of the passage from which the sequence of the eight deductions derives. R. expunges, with Wundt, the second hen from eite hen estin eite me hen, on the basis of the content. But he neglects the weight of B, of T, of W, of a mediaeval tradition which offers undoubtedly the second hen. Cf. A. Carlini, “Marsilio Ficino e il testo di Platone”, in S. Gentile, S. Toussaint (ed.), Marsilio Ficino: fonti, testi, fortuna, Roma 2006, 25-64, and for the Parmenides, “PVindob G 3088 and PDuke G 5”, in Corpus dei Papiri Filosofici Greci e Latini, I 1***, Firenze 1999, 146-154.
7. The idea that Plato does not play clearly entails the refusal of an ironic interpretation, the refusal of Cherniss or of Calogero, who gives a more fruitful interpretation for the aporetic phase. Cf. G. Giannantoni, Dialogo socratico e nascita della dialettica nella filosofia di Platone, Napoli 2005, 89-140.
8. Other reviews of the book: J. Palmer, Philosophy Reviews 2007.11.20, K. M. Sayre, Journal of the History of Philosophy 46 (2008), 169-170, K. Thein, Rhizai 2 (2007), 339-349.