méthexis 30 (2018) 36-59 brill.com/met The Ambiguity of the ‘One’ in Plato’s Parmenides Darren Gardner Department of Classics, University of Groningen, the Netherlands [email protected] Abstract This paper examines how the exercises offered to the young Socrates in the Parmenides can be understood as an educational practice, or a gymnastic that is prior to and in- strumental for defining forms. To this end, I argue that the subject of the exercises given to Socrates can be understood as an open and indeterminate ‘one’, rather than a form per se. I show that the description of the gymnastic exercises, the demonstration of the hypotheses themselves, and the language concerning the ‘one’, are consistent with an indeterminate subject ‘one’. Keywords Greek philosophy – Plato – Parmenides – Exercise – One The hypotheses that comprise the later part of Plato’s Parmenides are a no- toriously difficult set of arguments. They are presented as an exercise that the elder philosopher Parmenides provides to the still young but promising thinker Socrates. Having first criticized Socrates’ notion of forms, leaving him in aporia, Parmenides affirms that in fact thinking about forms is necessary not only for the possibility of dialogue but also for philosophy [135c–d].1 He then offers Socrates help in the form of a salutary exercise so that he will be able to * I wish to acknowledge Inger Kuin, Matthew Lau, Mitch Miller, and Charles Snyder for their help in preparing this article. They offered invaluably keen insights and comments that helped to clarify this study. Their erudition is only matched by their generosity. In addition, I thank Ruurd Nauta and the department of Classics at the University of Groningen for their support. 1 ἀλλὰ μέντοι, εἶπεν ὁ Παρμενίδης, εἴ γέ τις δή, ὦ Σώκρατες, αὖ μὴ ἐάσει εἴδη τῶν ὄντων εἶναι, εἰς πάντα τὰ νυνδὴ καὶ ἄλλα τοιαῦτα ἀποβλέψας, μηδέ τι ὁριεῖται εἶδος ἑνὸς ἑκάστου, οὐδὲ ὅποι © koninklijke brill nv, leiden, 2018 | doi 10.1163/24680974-03001003Downloaded from Brill.com09/26/2021 04:47:31PM via free access <UN> The Ambiguity of the ‘One’ in Plato’s Parmenides 37 overcome the aporia he has been placed in, and so that he will be prepared to properly reconsider the notion of forms. Parmenides’ help is presented first as a description of the exercises he should undertake, and then as a clarifying demonstration of those exercises. The dem- onstration, which discloses a series of premises and conclusions, has come to be known as the “hypotheses,” a term I will use to refer to the set of exercises. As a specifically gymnastic exercise (γυμνάζω) I believe that the hypotheses are intended to help strengthen Socrates’ conception of forms, following from Par- menides’ stated purpose of the exercises [135d–136d]. This casts Parmenides as a benevolent figure for Socrates, a critical but generous interlocutor in the spir- it of a gymnasiarch, rather than merely an eristic challenger. However, there is no agreement concerning precisely how these hypotheses help Socrates. In fact, there is no strong consensus about the meaning of the hypotheses. Even more problematically, there is no clear agreement about the very subject or subjects that the hypotheses take under examination. One interpretation of the hypotheses claims that the subject under inves- tigation is the form of unity or the form of the ‘one’.2 Another view ascribes Parmenides’ own principle of the ‘one’ to the subject, and suggests that some sort of Eleatic influence on Plato’s forms is presented in the dialogue.3 Alterna- tively, a more hermeneutic or dialogical approach has also emerged as a viable interpretative model. For example, Miller (1996) and Sanday (2015) argue that the dialogue presents a turning from the sensible participants to the dialectical thinking about forms.4 I agree with and build upon the dialogical approach in τρέψει τὴν διάνοιαν ἕξει, μὴ ἐῶν ἰδέαν τῶν ὄντων ἑκάστου τὴν αὐτὴν ἀεὶ εἶναι, καὶ οὕτως τὴν τοῦ διαλέγεσθαι δύναμιν παντάπασι διαφθερεῖ. τοῦ τοιούτου μὲν οὖν μοι δοκεῖς καὶ μᾶλλον ᾐσθῆσθαι. [135c]. ἀληθῆ λέγεις, φάναι. τί οὖν ποιήσεις φιλοσοφίας πέρι; πῇ τρέψῃ ἀγνοουμένων τούτων; 2 See Rickless (2007: 117), Peterson (2003: 250–251), Sayre (1996: 99), Dorter (1994: 47-ff), Allen (1997: 210). See also Fronterotta (1998) and (2001) on the exercises as they relate to the notion of participation in light of the ostensibly insoluble aporias given to Socrates in the first part of the Parmenides. 3 σὺ μὲν γὰρ ἐν τοῖς ποιήμασιν ἓν φῂς εἶναι τὸ πᾶν [128b]. See also Brisson (2002: 6) who argues that the view of the historical Parmenides is indeed on display in the Parmenides. Brisson suggests that the hypothesis ‘if one is’ takes as its subject ‘the all’ of Parmenides, i.e., the physical world: “According to the interpretation I am defending, the expression τὸ ἕν does not refer to a metaphysical entity, beyond existence, or even to a Form, but to the one that is being discussed, i.e. to the whole that is the world.” 4 Gonzalez (2002) and Trabattoni (2016), also following the dialogical model, challenge the no- tion of a “doctrine” or a “theory” of forms more broadly. With respect to the Parmenides, their line of reasoning helps to raise important questions concerning the nature of the hypotheses and how they relate to forms. méthexis 30 (2018) 36-59 Downloaded from Brill.com09/26/2021 04:47:31PM via free access <UN> 38 Gardner general, and I focus here on the educational character of the dialogue, examin- ing the hypotheses as gymnastic (γυμνάζω) exercises. I argue for a different view of the subject ‘one’ [ἓν] as it is present in the exercises. I believe that the ‘one’ taken as the subject of the hypotheses can be understood as an open or indeterminate ‘one’.5 This view has several important benefits: first, it avoids conflicts that emerge between the subject if it is under- stood as a form (or as Parmenides’ ‘one’ understood as “the all” [128b]) and the conclusions that are drawn about that subject; and second, it will bring into view the gymnastic aspect of the exercise program that Parmenides recom- mends [135c]. Indeed, I believe that it is this gymnastic aspect that will help the young Socrates to develop his thinking from a basic intuition about forms to a mature and well-wrought conception. A few examples will suffice to show the conflicts that arise when taking the subject as a form. In the first hypothesis the conclusions drawn show the ‘one’ to be neither “one,” nor “to be” [141e]. In denying the ‘one’ (taken to be a form) any mode of being in the first hypothesis, Parmenides would be deny- ing the being of the kind of intelligible object he has not only praised Socrates for considering [135e], but also set down as required for dialogue and philoso- phy [135b5–c2].6 Another conflict can be seen in the second hypothesis, which concludes about the attributes of the ‘one’ in a way that would undermine the independent character that is basic to a form. For the ‘one’ from this hypoth- esis would hold attributes like multitude and divisibility [144e], which render it a kind of ‘one’ that is a one of many. As such, this kind of ‘one’ is in conflict with the essential “itself by itself” nature of a form [130b7].7 In both cases, the 5 An alternative view is presented by Calogero (1932: 269–311) and (1974: 56–59). He argues that the nature of the exercises are composed with an anti-Zenonian irony having a similarity to the polemics of Gorgias. In doing so, Calogero sees the ‘one’ employed in the hypotheses as neither as a form, nor a metaphysical principle as such. While the hypotheses have an aspect that is similar to Gorgias’ On Being, I do not contend that hypotheses are mainly ironic, but on the contrary, they are at the very least methodologically serious. For the methodological way the hypotheses comprehensively investigate a subject (in eight ways) betrays any partic- ular irony, because en masse they examine all sides of a subject. A potentially ironic position, for instance, located from the non-being of a ‘one’ in the first hypothesis is challenged by its partner argument depicting the mutually opposed scenario, in this case, the being of a ‘one’ in the second hypothesis. 6 The first hypothesis, I will argue, is not about the form of ‘one’ per se. But if it were, the re- sulting consequence makes the recommendation from Parmenides that forms are necessary objects of thought for dialectic, untenable, because this form ‘one’ has no mode of being and therefore is not itself an object of thought as a ‘one’. 7 The conflict that emerges if Parmenides’ “One” as “the all” is taken as the subject will be noted in the section: The Language of the ‘One’ does not exclusively imply Forms. Downloadedméthexis from 30Brill.com09/26/2021 (2018) 36-59 04:47:31PM via free access <UN> The Ambiguity of the ‘One’ in Plato’s Parmenides 39 conclusions drawn challenge the notion that the form ‘one’ is the subject of the hypotheses. I argue that the subject of the hypotheses should be seen as an indetermi- nate ‘one’8 and I explain why this view provides a consistent reading of the dialogue that emphasizes the educational benefits of exercise prior to defining forms. This is particularly crucial with respect to Parmenides’ formulation of each premise of the eight hypotheses. For each premise employs an undeter- mined ἓν which allows for the consequences drawn for each premise to serve to clarify what kind of ‘one’ Parmenides’ conclusions describe in each case.