In Plato's Parmenides

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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 instrumental 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

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 demonstration, 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 investigation 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 notion 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.

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38 Gardner general, and I focus here on the educational character of the dialogue, examin- ing the hypotheses as gymnastic (γυμναζω) 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 understood 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 recommends [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 denying 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 philosophy [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 hypothesis 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 particular 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.

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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 indeterminate ‘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 undetermined ἓν which allows for the consequences drawn for each premise to serve to clarify what kind of ‘one’ Parmenides’ conclusions describe in each case. Sometimes the conclusions about ‘one’ depict a monad that has properties or predicates, while other times conclusions about ‘one’ depict a monad that transcends properties and predicates. The indeterminacy of the use of ἓν also allows for the conclusions to depict what an astute learner, such as the young Socrates, might recognize as a form-like ‘one’ and a participant-like ‘one’. This recognition helps the student of the exercises to consider a model of what a form and participant might be without necessarily exemplifying any particular form or participant. As far back as Plotinus, and perhaps further, the subject ‘one’ has been seen as indeterminate in some way, depicting different kinds of ‘ones’.9 Recent views put forth by McCabe (1996: 17, 22–24) and Sanday 2015 (2015: 78–81) also rightly indicate the broad and open way in which the ‘one’ is used by Parmenides. My view recognizes the value of this important insight, and I argue that the indeterminate nature of the subject is helpful in underappreciated ways for understanding the educational exercise program put forth in the dialogue. In what follows, I first present a description of gymnastic practice in order to help situate my view, and then I present four main arguments for reconsidering the ‘one’ as indeterminate. First, I examine 135e, where Parmenides claims that Socrates has tried too soon (before having been properly prepared) to turn to defining forms. I show that this passage indicates that the subject taken under investigation ought not be understood as a form as such but only a potential

8 The “one” in the Parmenides is famously underdetermined. See Sayre (1996: 99), Gill & Ryan (1996: 139 footnote 21); Sanday (2015: 81–82), McCabe (1996: 23–24). 9 There is a tradition of reading the subject of the hypotheses as ambiguous, starting with Plo- tinus, who understood the hypotheses to articulate different types of ‘ones’, marking different hypostases. More recently, Miller (1986) shows that the hypotheses take different ‘ones’ at different points. McCabe (1996) argues that the ambiguity of the ‘one’ suggests that subject is an individual, “abstractly conceived.” This I believe to be correct, however, she sees the work of the hypotheses cashing out the ambiguity of the subject in two ways: a generous way and an austere way, whereas I maintain that the subject is abstract and the conclusions drawn are actually opposed, not viewed in different ways. Sanday (2015) also argues that the ambiguity of the ‘one’ situates the hypotheses to be about an abstract ‘one’.

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40 Gardner candidate for what a form might be like. Second, I examine the description of the exercises themselves that Parmenides recommends to Socrates at 136a4. This description makes it clear that the work is schematic. As such, it is open to any subject and it is not restricted to “the one” or any other specific or determined ‘one’. Third, I show that the demonstration of the hypotheses that begin at 137c reveal contradictory sets of conclusions that follow from the same premise concerning the subject ‘one’. The conclusions at various points conflict with the subject ‘one’, if that ‘one’ is understood as a form per se. However, if we adopt the view that the subject is an indeterminate ‘one’, the differing sets of conclusions can very well depict opposed and even contradictory ‘ones’ without any issue. In fact, the indeterminate view of the ‘one’ allows for two different types of ‘ones’ to be considered, rendering the ‘one’ in the hypotheses as essentially ambiguous. Finally, I show that the language Plato uses both in the premises and in the concluding moments, which at first appears to be the language of forms (e.g., “the one” and “the one itself”) need not indicate forms as such. Rather, I show that the language is actually consistent with the subject taken as an indeterminate ‘one’.

Gymnastic Practice

A gymnastic practice, as the name suggests,10 helps strengthen an athlete or in this case, a thinker; it is the practice originally proper to the gymnasium which, much like today, was a place for exercise and training. One way to understand Parmenides’ ‘gymnastic exercise’ is to regard it as a practice that helps the trainee improve in an indirect way. Some exercises, for example, the kind for strength development, employ work that is unrelated to or different from the competition that an athlete trains for: a wrestler may improve his or her strength by exercising without engaging in the activity of wrestling itself, or even engaging in the skills required for a wrestler.11 If we imagine, generally, how an athlete might train, we can differentiate between what I am signifying as a gymnastic practice (say, lifting weights) and the practice of wrestling

10 lsj, (1940). s.v. γυμν-άζω A.The verb γυμνάζω means to train and refers to gymnastic exercise. Exercising naked took place in the palestra, an exercise and wrestling place that also functioned as a meeting place for philosophers. Plato sets Socrates in discussion with young thinkers in the palestra, for instance, in Lysis, Charmides, and the young philosopher students Theaetetus and young Socrates are both trainees, συγγυμναστής [Statesman 257d]. See also Isocrates Panathenaicus, Diogenes Laertius on Antisthenes (6: 1–13). 11 See Meinwald 1991, p. 6.

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The Ambiguity of the ‘One’ in Plato’s Parmenides 41 itself (sparring or repeating specific maneuvers). In a similar way, the gymnastic exercise for Socrates need not employ the work of thinking about or defining forms directly, but can be seen to help to prepare him to consider forms in a way that strength training helps the wrestler prepare to be a success- ful competitor. An untrained or unexercised wrestler is unprepared for excel- ling in competition, and likewise an untrained or unexercised philosopher is unprepared to define forms. The exercise that helps the wrestler, however, is not restricted to specific kinds of wrestling work, but rather is indeterminate in nature. It is in the competition of wrestling itself (or a similarly determined practice) where the indeterminate exercises have a specific context in which their indeterminate nature can be understood as determined. It is possible, then, to understand the gymnastic activity in at least these two ways: the first way, as above, where the practice does not directly employ the activity being trained for (a wrestler’s strength training), and a second way where the activity is the task being trained for (the wrestler sparring). With respect to the practice offered to Socrates in the Parmenides, the first way views the gymnastic as a practice that does not take a form as the subject of the hypotheses, and the second, a version that does. Whereas some scholars argue that the training program in fact employs a form as the subject, aligning with the second version of training, I am suggesting that the hypotheses can be taken in the first way, and in doing so, the hypotheses are properly understood as the kind of exercise that Parmenides claims that they are. The indeterminate nature of the subject of the exercises has the effect of restraining the precocious young Socrates from rushing into defining forms before he has properly considered what a form, as a subject of inquiry, is like. This is because the indeterminate subject of the exercises that Parmenides offers has the effect of helping Socrates take a step back and consider two different ‘ones’ before turning to the later task of defining forms. The exercise helps manage the ambitions of the young athlete, who might otherwise too quickly jump into the ring. The hypotheses, nevertheless, are clearly not unrelated to the task of thinking about forms. In fact, Parmenides suggests that the young thinker Socrates requires a proper preparation before defining forms. After Socrates admits that he does not understand how to overcome the problems that Parmenides raised about the notion of forms, Parmenides responds:

“What will you do about philosophy? Where will you turn, while these things remain unknown?” “I do not see, at least not at present.”

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“That is because, Socrates, you are trying too soon to mark off some beau- tiful, and just, and good, and each one of the forms,” he said, “before you have been properly trained” [135c–d].12

The hypotheses, in this way, can be understood as an example of the training required for the still young Socrates in order for him to be prepared to turn to the task of defining forms. And, if we take Parmenides at his word that Socrates needs to go through this exercise before he turns to forms [135d], then we should suspend considering the subject of the hypotheses as forms per se. We can, however, consider how the exercises can help Socrates strengthen his thinking in such a way as to prepare him to conceive of forms more properly prior to turning to the work of defining forms as such.13

The Subject Apprehended by Reason

At 135e, Parmenides gives the first clue about the subject of the exercises he will provide. While this passage is usually understood to secure the view that forms themselves are the subject of the hypotheses, I argue that a careful re- view of the text actually supports a different view. The passage shows that the subject is not exclusively forms or even a form. It is a subject that is described as apprehended by reason, and this description does not exclusively depict forms. I argue here for an inclusive reading of this passage that allows for the subject of the hypotheses to be considered as indeterminate. Let us examine the passage. Socrates, unclear himself about the kind of exercise he needs, asks Parmenides to describe it: “What is the manner [τρόπος], Parmenides, of this gymnastic?” Parmenides replies: “It is like what you heard from Zeno. Except, I also admired what you said to him, because you would not allow him to investigate the wandering in the visible things or in relation to them, but about those things that could be most apprehended by reason and could be regarded as forms [καὶ εἴδη ἂν ἡγήσαιτο εἶναι]” [135e3].14

12 τί οὖν ποιήσεις φιλοσοφίας πέρι; πῇ τρέψῃ ἀγνοουμένων τούτων; οὐ πάνυ μοι δοκῶ καθορᾶν ἔν γε τῷ παρόντι. πρῲ γάρ, εἰπεῖν, πρὶν γυμνασθῆναι, ὦ Σώκρατες, ὁρίζεσθαι ἐπιχειρεῖς καλόν τέ τι καὶ δίκαιον καὶ ἀγαθὸν καὶ ἓν ἕκαστον τῶν εἰδῶν. [135c5]. 13 See Ferrari (2004; 100–108) on the methodological aspect of the hypotheses as a gymnastic practice for elenchus. 14 πλὴν τοῦτό γέ σου καὶ πρὸς τοῦτον ἠγάσθην εἰπόντος, ὅτι οὐκ εἴας ἐν τοῖς ὁρωμένοις οὐδὲ περὶ ταῦτα τὴν πλάνην ἐπισκοπεῖν, ἀλλὰ περὶ ἐκεῖνα ἃ μάλιστά τις ἂν λόγῳ λάβοι καὶ εἴδη ἂν ἡγήσαιτο εἶναι [135e].

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The Ambiguity of the ‘One’ in Plato’s Parmenides 43

This passage suggests to some, notably Sayre, Allen, Peterson, and Rickless,15 that the gymnastic exercises will take forms as such as their subject. They contend that the “things that could most be apprehended by reason” must be forms, and therefore the hypotheses will take up forms directly. However, it is not at all clear that the “things that could most be apprehended by reason” are exclusively forms. For example, a geometrical figure such as a square need not be understood as a form itself, but only a figure grasped by reason, which remains an example that participates in the form of ‘the square’. The subject ‘square’ could be considered as the form ‘Square’, but as an example of what Parmenides means by something “apprehended by reason,” it need only be a candidate for what could be the subject as a form. Moreover, Parmenides clearly states that what he admired of Socrates’ response to Zeno was the inclusion of the “things that could most be apprehended by reason” which only potentially “could be regarded as forms.” The indication of the things that “could be regarded as forms” is crucially phrased in the optative and marks the kind of thinking that locates candidates for forms rather than exclusively a form per se. The sentence at 135e also emphasizes that Socrates would not allow Zeno to merely investigate the wandering [πλάνη] of the visible things or the wandering with respect to them. The problem is not the investigation of the wandering of things as such, but rather merely or exclusively investigating them. Because they are subject to wandering, visible things that are grasped merely by the senses can be seen in many different and sometimes contradictory ways. For instance, a tree can be seen as an acorn, a sapling, a tall oak, and a felled log;

15 Peterson (2003: 250–251) argues that the hypotheses are about a form even though the optative makes it potentially ambiguous. Allen (1997: 210) claims: “That the subject matter of the deductions is an Idea is required by 135d–e.” Further, Allen on Miller [Footnote 40, 210]: “A version of the ambiguity theory has been restated by Mitchell Miller in Plato’s “Parmenides”: The Conversion of the Soul, Princeton, 1986: Parmenides refers “to each one form and each one thing” in various hypotheses, so that sensible unities are subjects of hypothesis. This is inconsistent with the claim that the inquiry will be restricted to the intelligible world (135d), which requires that the subject of Parmenides’ hypotheses be the character or Form of Unity. Miller’s version of the ambiguity theory, like any other, makes the overt structure of the hypotheses only apparent.” The unexercised Socrates need not take up forms themselves to receive the training that could help him define forms properly. Moreover, it is not required that the subject matter is an “Idea” or a form, only that the hypotheses take up that which Parmenides admired of Socrates, namely, things grasped most of all by reason [μάλιστά τις ἂν λόγῳ λάβοι]. Reason need not be restricted to forms because it also includes such things as a rational account of geometrical and sensible objects and things that have not yet been distinguished as a form. See also: Sayre (1996: 99), Rickless (2007: 117).

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Socrates can be seen as one single man, or as a many that includes legs, arms, hands, and a snub nose. Then Parmenides clarifies what was admirable about Socrates’ response to Zeno, namely, his demand for the inclusion of the consideration of a stable aspect with which the wandering visible things should be considered. Parmenides admired that Socrates pushed Zeno to include a consideration of the things “that could most be apprehended by reason,” but not to the exclusion of the sensible objects.16 I believe that Socrates’ insistence that Zeno include forms in his investigation is what is appreciated by Parmenides, and this appreciation pertains to the inclusive aspects of Socrates’ response to Zeno, whereas Allen and Peterson consider the subject of the hypotheses to be exclusively forms. Moreover, the use of the optative “could” helps to clue us into the indeterminate nature of the subject that will be taken up in the hypotheses. Because the subject could be a form, it need not be taken as a form simpliciter. In fact, this is an accurate depiction of what occurred in the early part of the dialogue: Socrates extended Zeno’s investigation to include what could be a form [129a], while not excluding the sensible objects that the appeal to forms was meant to sort out. The admirable move is to make room for what could be forms in the investigation so as not to run afoul of what is evident and conclude whatever one may wish by appealing to the variable nature or the “wandering” of the merely visible things. Because the passage need not be read as exclusionary, both the things apprehended by reason and visible things can be included in what Parmenides appreciates of Socrates, and they mark the kind of learning that Socrates needs in light of Parmenides’ criticism of his underdeveloped intuition about forms. It should be no surprise, then, that Parmenides can be understood to call upon an indeterminate ‘one’ in the hypotheses that allows for both.

The Schema of the Exercise Program

The plan of the gymnastic exercise is explained to Socrates at 136a4. As Par- menides describes it, this program is not restricted to the subject ‘one’ that is used in the hypotheses that follows from 137c–166c. Rather, Parmenides makes it very clear that any subject will work:

16 I agree with Cornford (1939). Differing from Allen (1997) and Peterson (2003), he trans- lates: “There was one thing you said to him which impressed me very much: you would not allow the survey to be confined to visible things or range over that field; it was to ex- tend to those objects which are specially apprehended by discourse and can be regarded as Forms.”

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The Ambiguity of the ‘One’ in Plato’s Parmenides 45

concerning whatever you might hypothesize as being or as not being or as having any other property, you must examine what follows for what you hypothesize in relation to itself and in relation to each one of the others… if after completing your gymnastics you are to have a masterful view of the truth [136b7–c5].17

I will stress three major points concerning the description of the exercises. First, the manner of exercising has a four-part schematic structure that will align with the eight-part demonstration. In the hypotheses, the four parts are doubled and each premise is worked through a second time; once with positive conclusions about ‘one’ and once with negative conclusions, revealing an ambiguous ‘one’. This will help show that the indeterminate subject ‘one’, having two different depictions, must be an ambiguous ‘one’. The open indeterminate ‘one’ in the premises can be seen to be two different kinds of ‘one’ from the conclusions drawn. The ‘one’ from the premises can then be reconsidered as an ambiguous ‘one’ (i.e., a ‘one’ that has two opposed characterizations). Sec- ond, I argue against the view that Parmenides presents eight premises, contra Meinwald (1991), and I show why it is essential to see that there are exactly four. And third, I show that the schematic program, following Parmenides’ remark, is broadly open to any subject the trainee may wish to examine, further em- phasizing that the subject ‘one’ is indeterminate.

The Four Premises

We can see the general schema of Parmenides’ program from his description that begins at 136a4. He uses several examples to describe the process. Here he uses Zeno’s hypothesis about the ‘many’ as the subject to map out the program he has in mind:

If many are, what must follow both for the many themselves in relation to themselves and in relation to the one, and for the one in relation to itself and in relation to the many? And, in turn, on the hypothesis, if many are not, you must again examine what follows both for the one and for the many in relation to themselves and in relation to each other? [136a]

17 περὶ ὅτου ἂν ἀεὶ ὑποθῇ ὡς ὄντος καὶ ὡς οὐκ ὄντος καὶ ὁτιοῦν ἄλλο πάθος πάσχοντος δεῖ σκοπεῖν τὰ συμβαίνοντα πρὸς αὑτὸ καὶ πρὸς ἓν ἕκαστον τῶν ἄλλων … εἰ μέλλεις τελέως γυμνασάμενος κυρίως διόψεσθαι τὸ ἀληθές.

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There are two inquiries, each with two parts, revealing the four lines of inquiry. If Zeno’s ‘many’ is hypothesized, the exercise investigates the ‘many’ [1] with respect to itself and to the ‘one’ (its correlative other), and [2] the ‘one’ is investigated in relation to itself and to the original subject ‘many’. Then, [3] if ‘many’ is not, it is investigated with respect to itself and the one, and then [4] with respect to the one and the original subject ‘many’. There are exactly four premises in the description, and the actual demonstration of the exercise that follows, we will see, takes only these four, albeit taking each premise twice, comprising the eight hypotheses. The program Parmenides offers Socrates, therefore, has the following general structure: First, the subject (whatever that may be) should be examined, if it is, and considered with respect to itself and its correlative other(s) (i.e., all that the subject is not). Second, the correlative other should be considered, if it is, with respect to itself and to the original subject. Parmenides then claims that not only should the subject, whatever it may be, be considered “if it is,” but that subject should also be considered “if it is not.” For the third part, then, the subject should be considered, if it is not, with respect to itself and its correlative other. And forth, the correlative other is taken, if it is not, and considered with respect to itself and with respect to the original subject.

Against the Eight Premise Model

The description of the exercise marks off a four part program, as the above example with Zeno’s ‘many’ clearly shows, but this view is not without controver- sy. Some scholars, following Meinwald (1991), unearth an eight part program in the initial description [136a4-ff], possibly to find parity with the eight hypotheses themselves. This view is achieved by separating out the distinctions “with respect to itself” from “with respect to others” as individual or distinct lines of inquiry.18 This approach, however, is problematic because it misconstrues the

18 Sayer (1983), Meinwald (1991), and more recently Peterson, (2000, and 2003) mistakenly understand 136a4-ff as marking off the eight part program of exercise that corresponds to the practice that Parmenides demonstrates. But Miller 1986 shows that each hypothesis takes the subject and considers the conclusions that are drawn with respect to itself and with respect to others, whereas Meinwald and Peterson see that ‘with itself’ as pros “heauto” and ‘with another’ “pros ta alla” are separate lines of inquiry. By not recognizing that the passage at 136a4-ff describes a four part program and only in demonstration are we witness to an eight part program, a major gymnastic aspect of the hypotheses remains obscure. When we see that the four part description of exercise is doubled, and that that doubling reveals the intended juxtaposition of contradictory conclusions, then we are

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The Ambiguity of the ‘One’ in Plato’s Parmenides 47 description in the text, as I have shown it, and it glosses over the importance of seeing the contradictory pairs of conclusions which will establish the essential ambiguity of the subject. The twice-examined premise reveals opposed conclusions that show that the indeterminate subject—having different and contradictory depictions—must be ambiguous. For example, a ‘one’ that transcends predicates (hypothesis 1) and a one that accepts all predicates (hypothesis 2) are mutually opposed, contradictory ‘ones’ if the ‘one’ in question is considered in a determined way. Confronting rather than avoiding the contradictory conclusions, I believe, is an essential aspect of the gymnastic training, and it is clear that Parmenides has this in mind when he presents opposed conclusions about the seemingly selfsame ‘one’.19 If, however, just for argument’s sake, the summary description that follows from 136a is interpreted to depict eight distinct premises following Meinwald (1991) it would look as follows:20

1 The subject (if it is) is examined relative to itself. 2 The subject (if it is) is examined relative to its correlative other(s). 3 The subject (if it is) whereby the correlative other(s) to the subject are examined relative to themselves. 4 The subject (if it is) whereby the correlative other(s) to the subject are examined relative to the subject. 5 The subject (if the subject is not) is examined with respect to itself. 6 The subject (if the subject is not) is examined with respect to the correlative other(s). 7 The subject (if the subject is not) whereby the correlative other(s) to the subject are examined relative to itself. 8 The subject (if the subject is not) whereby the correlative other(s) to the subject are examined relative to the subject.

Such a plan would distinguish the subject from two different perspectives: first, with respect to itself, including all the variations; and second, with respect to the other(s). The list above helps illustrate this, for it shows half “with respect to itself” (1,3,5,7) and the other half “with respect to others” (2,4,6,8).

prepared to recognize an important gymnastic practice for the trainee: to try to hold together the contradictions under the same premise. 19 Confronting the contradictory conclusions about “one,” will have the effect of disabusing the trainee from thinking that the subject “one” is a form itself, and prepares that trainee to reconsider what a form might be. 20 Meinwald (1991: 35–39) offers this interpretive model as “Reading ii.”

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48 Gardner

Such an arrangement could allow for the contradictions that arise between, say, the conclusions of hypothesis 1 and the conclusions of hypothesis 2, to be dissolved by an appeal to the different respects from which those conclusions are drawn. If the conclusions that are drawn from the subject as it is examined “with respect to itself” are opposed to the conclusions that are drawn “with respect to the correlative other,” no contradiction need be sustained.21 This kind of ordering (or reordering)22 attempts to avoid the contradictory conclusions altogether. In doing so, however, the exercises are misunderstood to merely map out the consequences that follow for the subject as it is viewed from those two different respects. The point of this reordering, following Sayre and Meinwald, is to suggest that the subject (conceived of as a form) with respect to itself has a wholly different set of characteristics from that which participates in a form. While I do not argue against the view that a form and a participant are in fact different, the dialogue already assumes that point.23 It may be tempting to avoid the contradictory conclusions by separating the inquiry into two different respects, but there are two major problems. First, it is in no way supported by the text, either in the description of the exercise [136a-ff] or in the hypotheses that follow it [137c3-ff]. The description clearly indicates that the inquiries conclude both “with respect to itself” and “with respect to its other” for each premise [136a5–136c5].24 And the demonstration that follows the description bears this out by including “with respect to itself” and “with respect to others” conclusions for each hypothesis.25 Second, the hypotheses

21 Turnbull (1998: 47–50) rearranges the program to describe “with respect to itself” inquiries as separate from “with respect to others” inquiries, the former he names Parmeni- dean, the later Platonic. While it is clear that two different perspectives are taken, I argue that they are both presented for each query. 22 See: Sayre (1978: 135–141 and 2005: 41–49). 23 Socrates already makes this difference clear to Zeno, for example, at 129a–c and 130b–c. 24 For instance, at 136a5–6, Parmenides outlines the program of exercise taking up the example of Zeno’s premise. “If many are, what must follow both for the many themselves in relation to themselves and in relation to the one, and for the one in relation to itself, and in relation to the many” τί χρὴ συμβαίνειν καὶ αὐτοῖς τοῖς πολλοῖς πρὸς αὑτὰ καὶ πρὸς τὸ ἓν καὶ τῷ ἑνὶ πρός τε αὑτὸ καὶ πρὸς τὰ πολλά. There is a clear parallel structure to the sentence, suggesting two inquiries: First, the many themselves in relation to themselves and in relation to the one; Second, the one in relation to itself and in relation to the many. Here the infinitive συμβαίνειν takes the datives τοῖς πολλοῖς and τῷ ἑνὶ, signifying that the inquiry is a two-part inquiry, and that the “many” and the “one” are investigated both with respect to itself and its correlative other “many,” both πρὸς αὑτὰ and πρὸς τὰ πολλά. 25 For example, in the first Hypothesis, “one” is queried not only with respect to itself but with respect to “others” at 139b–c, 140a–b, 140b–d, and 140e–141a. See Miller (1986: 226–227).

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The Ambiguity of the ‘One’ in Plato’s Parmenides 49 have eight parts that specifically repeat each premise twice with opposed sets of conclusions, setting up the learner to contend with the oppositions that establish the ambiguity of the subject ‘one’.26 The double use of each premise shows that the eight hypotheses are not differentiated by two separate respects (with respect to itself / with respect to its correlative other), but rather what are opposed are the sets of conclusions themselves. For example, the first and second hypotheses have the very same premise “if ‘one’ is”, and both consider what follows for it “with respect to itself” and “with respect to others.” The double use of the premise (e.g., “if ‘one’ is” at 137c and 142b) reveals opposed contradictory conclusions from the same premise that I claim are instrumental for the gymnastic training of the student. And the confrontation of the two different and opposed depictions from the same premise instigate a reconsideration of subject. The sets of conclusions about the subject ‘one’ sometimes depict a spatially and temporally extended ‘one’ (such as in hypothesis 2) and at other times depicts a ‘one’ that transcends extension and temporal modes of being (such as in hypothesis 1). In order to hold these opposed depictions, the very same premise under which both sets of conclusions are drawn must be seen as ambiguous and must be reconsidered as having been indeterminate.27 The educational value of the exercise, I contend, lies in part in the difficult work of contending with opposite sets of conclusions that stem from the same premise. It is difficult to consider a ‘one’ that both is and is not spatially and temporally extended. Avoiding this essential confrontation by separating the double inquiry into two independent inquiries has the effect of avoiding the exercises as such in place of something like listing the descriptions of the two different depictions of ‘ones’ from two different respects. But because the premise of hypothesis 1 and 2 is the same, in this case “if ‘one’ is”, (and the premise is likewise the same for the pairs of hypotheses 3–4, 5–6, and 7–8) then hypotheses 1 and 2 are in some sense one exercise moment comprised of 2 parts. This double aspect is emphasized by Parmenides, because at the concluding moment of the first, third, fifth and seventh hypotheses, Parmenides

26 An important caveat is the so-called appendix to the second hypotheses [155e–157b]. I take the view that this section properly belongs to the second hypothesis. The determination of the “instant” in the appendix does not have a corollary in the first hypothesis because while the second hypothesis admits of temporality that makes the “instant” a point of inquiry, the first hypothesis, in denying all modes of temporal extension, pre- cludes the “instant.” 27 For any indeterminate subject x, if the conclusions drawn are contradictory and hold both x and ~x, then the initial subject x must be ambiguous.

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50 Gardner asks his interlocutor if they should return to the original premise, while they look for a different result [142b, 159b4, 163b6, 165e3].28 The difficult work of the gymnastic exercise is avoided if the opposed conclusions are seen as independent inquiries from different respects. It amounts to a form of throwing the baby out with the bath water. I think that the tempta- tion to separate “with respect to itself” from “with respect to others” is based upon the belief that a form itself is being examined in the hypotheses. Free from the misconception that the hypotheses specifically take up and explain forms directly, the hypotheses can now be more properly viewed as exercises as an educational propaedeutic for the sake of being prepared to define forms at a later time.

The Schema is Open to Any Subject

The program as described is schematic, laying out a plan of inquiry both if the subject is (the first two premises), and if the subject is not (the following two premises). The schematic nature of the program also makes it clear that the subject is not restricted to be a form, or any ontological principle as such, but rather is open ended. Parmenides’ description of the program not only maps out the plan of the exercise, implying an open structure, but it also specifically claims that any subject can be employed for exercising. Parmenides gives several examples to illustrate the structure of the exercise (we have looked at the example employing ‘many’), but he also specifically notes the openness of the scheme to other subjects: “If you like, said Parmenides, take as an example this hypothesis that Zeno entertained: if many are…” (εἰ βούλει, περὶ ταύτης τῆς ὑποθέσεως ἣν Zήνων ὑπέθετο, εἰ πολλά ἐστι) [136a4]; “And again, in turn, if you hypothesize if likeness is or is not…” (καὶ αὖθις αὖ ἐὰν ὑποθῇ εἰ ἔστιν ὁμοιότης ἢ εἰ μὴ ἔστιν) [136b1]; “And the same reasoning applies to unlike, to motion, rest, generation, destruction and to being itself and not-being” (καὶ περὶ ἀνομοίου ὁ αὐτὸς λόγος καὶ περὶ κινήσεως καὶ περὶ στάσεως καὶ περὶ γενέσεως καὶ φθορᾶς καὶ περὶ αὐτοῦ τοῦ εἶναι καὶ τοῦ μὴ εἶναι) [136b4]; “And in a word, concerning whatever you might ever hypothesize as being or as not being or as having any other property…” (καὶ ἑνὶ λόγῳ, περὶ ὅτου ἂν ἀεὶ ὑποθῇ ὡς ὄντος καὶ ὡς οὐκ ὄντος καὶ ὁτιοῦν ἄλλο πάθος πάσχοντος) [135b6]. This makes clear that Parmenides’ program is not specific to a single subject. So far, the program has been depicted in such a way that the subject of the hypotheses is something that is apprehended by reason, and is a candidate

28 See the section: The Hypotheses and the Ambiguous ‘One’.

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The Ambiguity of the ‘One’ in Plato’s Parmenides 51 to be a form. The subject, in these cases, is to be investigated through a schematic exercise program. The schematic investigation of the consequences of a subject, if it is, and if it is not, is open and not restricted to any particular example, or any particular form. With this in mind, we can turn to the way that Parmenides demonstrates the program for Socrates and consider the hypotheses themselves.

The Hypotheses and the Ambiguous ‘One’

As we have seen, the description of the exercise at 136a articulates a four part program, and yet the demonstration of the hypotheses have eight rather than four parts. The eight parts, nevertheless, follow from the same four premises, but they conclude twice for each one.29 So, for instance, the first hypothesis and the second hypothesis take the first premise “if ‘one’ is” but conclude differently about it. It is clear that the second hypothesis takes the premise from the first, not only because it examines “if ‘one’ is” [142c7] and investigates ‘one’ both with respect to itself and its other, but also because Parmenides asks his interlocutor to return to it specifically: “Do you want to return to the hypothesis from the beginning?” [142b1], marking the second hypothesis as a return to the first premise. The same is true for Hypothesis 4 which returns to the premise of 3: “Let’s say from the beginning, if ‘one’ is, what must follow for the others and for the one.” [159b4]. The same is true of Hypothesis 6, “Let’s go back to the beginning to see whether things will appear the same …” [163b6], and Hypoth- esis 8 at 165e3. Insofar as Hypotheses 1 and 2 both follow the first of the four premises, they can be seen as a pair that corresponds to the first part four part schema. In demonstration, then, the hypotheses examine “if ‘one’ is”30 twice,

29 The premise in question is “if one is” εἰ ἓν ἔστιν describes the inquiry for the the first and the second hypothesis at 137c3 and 142b4. It is possible to object to the claim that the second hypothesis sustains the same inquiry as the first because Parmenides appears to change the way he puts the premise. For instance, at 142b7 he rephrases the premise: ἓν εἰ ἔστιν. Parmenides does this to emphasize that the ‘one’ can be considered as distinct from the “is,” and in that separation, he shows how this ‘one’ can be two, comprising both ‘one’ and ‘is’. Further, Parmenides articulates the outcomes of this rearrangement, underlining the being of a ‘one that is’ in order to survey this one as a different ‘one’ from the first hypothesis. Nevertheless, at the outset of the second hypothesis, the phrase once again is εἰ ἓν ἔστιν [142b], and then reinforcing this view at the start of the third Hypothesis, Parmenides refers once again to the premise εἰ ἓν ἔστιν [157b6] in order to begin to deduce what follows for the correlative others. 30 The premise of the first hypothesis differs from the second hypothesis only in word order. In the first, εἰ ἓν ἔστιν, in the second, ἓν εἰ ἔστιν. This serves to help Parmenides stress the

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52 Gardner concluding in both cases what a ‘one’ is with respect to itself and its correlative other(s). The four premises, as before, are the following: First, if ‘one’ is, what follows with respect to it and its correlative other(s); second, if ‘one’ is, what follows for the correlative other(s) with respect to it and to a ‘one’; third if ‘one’ is not, what follows with respect to it and its correlative other(s); if ‘one’ is not, what follows for the correlative others(s) with respect to it and to a ‘one’. Hypotheses 1 [137c3] and 2 [142b] take the first premise; 3 [157b6] and 4 [159b2] take the second premise; 5 [160b7] and 6 [163c1] take the third premise; and 7 [164b5] and 8 [165e1] take the final premise. For the purpose of my argument here, I will be restricting my example to the first two hypotheses, but the other pairs also could be used to make the same point. The first hypothesis, inquires “if ‘one’ is” and describes through the conclusions drawn a one without any spatial attributes or relations or any temporal mode of being. Following a long list of attributes that this ‘one’ cannot hold the first hypothesis comes to a stop with self-undermining conclusions: “if ‘one’ is” it follows that “the ‘one’ in no way is” (οὐδαμῶς ἄρα ἔστι τὸ ἕν) and moreover, “it is in no way as to be ‘one’” (οὐδ᾽ ἄρα οὕτως ἔστιν ὥστε ἓν εἶναι) [141e10]. “Is it possible that these things are so for the ‘one’?” asks Parmenides. “I don’t think so” replies Aristotle.With that, Parmenides and Aristotle agree that they should return to the hypothesis from the beginning “and see if, returning to it, something different appears to us” (ἐάν τι ἡμῖν ἐπανιοῦσιν ἀλλοῖον φανῇ) [142b2]. Indeed, something different will appear. The return employs the very same premise: “If ‘one’ is” (εἰ ἓν ἔστιν) [142c3], but concludes differently and describes another kind of ‘one’. It begins again with the indeterminate ‘one’ and concludes with a different depiction than before. As expected, something different does appear to them, and the conclusions drawn are inclusive of all spatial aspects, all relations, and all temporal modes of being. Whereas the first hypothesis describes a ‘one’ that is not, admitting of no predicates or modes of temporal being, the second affirms that this other ‘one’ is, and admits of all qualities and modes of temporal being. Two different ‘ones’ are depicted: a ‘one’ that holds no predicates nor has any mode of temporal being, and a ‘one’ that is inclusive of predicates and has temporal being.31 These two ‘ones’ are contrary and they have mutually

difference between “one” and “is” in the second hypothesis, but need not be understood as different in meaning. Moreover, Parmenides will return to the first phrase at 142c3. 31 The view of two different ‘ones’ requires that we accept the conclusions drawn by Par- menides. I believe that the confrontation of the different depictions is instrumental to the practice and we should not undermine the view before we see the benefit that they offer

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The Ambiguity of the ‘One’ in Plato’s Parmenides 53 opposed sets of conclusions. Opposed as such, the two depictions cannot be subsumed under a single determined notion of “one,” but rather remain two opposed and different ‘ones’.32 The two depictions of the subject can only be sustained as opposed under an indeterminate subject. Since the premise for both sets of conclusions is the same, if the subject ‘one’ under consideration in the first hypothesis is a form, for arguments sake, it should likewise be a form in the second hypothesis. This is because the ‘one’ in the premise ranges over the depictions of both of the ‘ones’ that are concluded about. But, since the two sets of conclusions are opposites, either the kind of ‘one’ depicted in the first hypothesis articulates the form ‘one’ in the premise, or the kind of ‘one’ depicted in the second hypothesis. If both hypotheses are to be viable, then the different depictions defy the possibility of the ‘one’ of the premise being a form. However, the incompatibility dissolves when the ‘one’ in the premise is understood as indeterminate: a one rather than the one. On my reading, the contradictions cease to undermine the premise. The problematic view of the contradiction becomes clear if we rephrase the premise and the conclusions in the following way, taking the assumption that the ‘one’ is the form of the ‘one’: ‘If the form ‘one’ is’ (premise), then the form ‘one’ in all ways is not (conclusion of hypothesis 1); and, ‘If the form ‘one’ is’ (premise), then a form ‘one’ in all ways is (conclusion of hypothesis 2). Finally, if the form ‘one’ could admit of two contradictory accounts, then that form would not be “itself by itself,” which is a defining characteristic. For, having two contradictory and mutually opposed articulations, the form admitting of both would betray the essential unity required of a form. On the other hand, seen as an ambiguous subject, the indeterminate subject of the premise can allow for different sets of conclusions. If we embrace the idea that the premise is not inquiring about the form of ‘one’ but instead suggests in the conclusions an ambiguous ‘one’, the two different depictions can be opposed and even contradictory without undermining the premise: ‘If some ‘one’ is’ then one conclusion can be that this one is ‘a one-that-is-not’ and another ‘a one-that-is’.

the trainee. Parmenides’ selection of Aristotle as a partner in the demonstrations shows us that what Parmenides wishes to convey requires that his interlocutor not object, and Aristotle is chosen precisely because he is the most tractable [137b7]. 32 The “one” of the first hypothesis can be seen, not merely as opposed, but also as an essential partner to the one of the second hypothesis in the small passage on the instant at the end of the second hypothesis. However, the way that the two “ones” are related in such a way as to dissolve their oppositional character requires a separate investigation. See Miller (1986: 112–121).

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54 Gardner

The Language of the ‘One’ Does Not Exclusively Imply Forms

I have argued that the description of the gymnastic exercise claims that the subject taken for exercise is an indeterminate and ambiguous subject. When we turn to the language that Parmenides uses in the exercises the ambiguity of the subject becomes even more conspicuous. First, Parmenides asks to use his hypothesis about the ‘one’ for the exercise demonstration. This hypothesis may seem at first to suggest that the subject for the exercises is his ontological principle of the one, as mentioned by Socrates in the first part of the dialogue,33 but upon closer inspection, I show that this is not the only possibility. Rather, his ‘one’ can be taken in a way that is still undefined as such, and this is a pref- erable and less restrictive reading. I will then clarify how what appears to be language that could be seen to invoke forms, (such as the phrase “the one itself”) is actually in support of my view that the ‘one’ is intentionally indeterminate and therefore ambiguous. At 137b Parmenides agrees to go through the work of the exercises, and he suggests that he should first take his hypothesis about the one. He says: “… shall I begin with myself and my hypothesis, hypothesizing about the one itself, whether one is or one is not, what follows?” [137b].34 First, because Par- menides claims that this is his hypothesis, it is tempting to assume that the exercise articulates his own ontology about the one, the one that is “the all” (τὸ πᾶν) that Socrates alluded to earlier in the dialogue at 128b. This view, however, is also untenable. Parmenides’ notion of the ‘one’ as “the all” [128b] pre- cludes the possibility of taking the correlative others as part and parcel to the schematic inquiry he clearly described at 136a4.35 For, as I have argued above, each premise requires that the trainee investigate a ‘one’ with respect to itself and its correlative other. But, if that one is taken to be “the all” then this dis- tinction cannot be made, and the schema cannot be followed. Therefore the ‘one’ as the subject of inquiry in the hypotheses cannot be “the all.” It is also a mistake to view the ‘one’ in question at 137b as any defined principle or form. As I have argued, the ‘one’ should be understood as indeterminate, along the lines of the description at 135e as that which merely could be a form or a

33 ”You say that the all is one in your poem” σὺ μὲν γὰρ ἐν τοῖς ποιήμασιν ἓν φῂς εἶναι τὸ πᾶν [128b]. 34 πόθεν οὖν δὴ ἀρξόμεθα καὶ τί πρῶτον ὑποθησόμεθα; ἢ βούλεσθε, ἐπειδήπερ δοκεῖ πραγματειώδη παιδιὰν παίζειν, ἀπ᾽ ἐμαυτοῦ ἄρξωμαι καὶ τῆς ἐμαυτοῦ ὑποθέσεως, περὶ τοῦ ἑνὸς αὐτοῦ ὑποθέμενος, εἴτε ἕν ἐστιν εἴτε μὴ ἕν, τί χρὴ συμβαίνειν; [137b]. 35 See Allen (1997: 208–209).

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The Ambiguity of the ‘One’ in Plato’s Parmenides 55 principle, but it is not the ‘one’ as such but a ‘one’ that marks an indeterminate subject. Supporting my view the phrase “hypothesizing about the ‘one’ itself” (περὶ τοῦ ἑνὸς αὐτοῦ ὑποθέμενος) is better read as “the one by itself ” meaning ‘just a one’. Such a ‘one’ can be construed as the hypothesis used, even Parmenides’ hypothesis, without meaning anything more than the subject ‘one’ that he concerns himself with, which in this case is an indeterminate monad. This view does not require that the ‘one’ employed in the exercises is his principle, only that a ‘one’ is taken as the indeterminate example ‘one’. Moreover, Par- menides then clarifies that his subject is indeterminate in his formulation of the premise: “if one is or if one is not, what must follow?” (εἴτε ἕν ἐστιν εἴτε μὴ ἕν [137b4]). The ‘one’ is given without a pronoun and without an article signifying the very openness that an undetermined one, by itself, would need. In addition to the conspicuous way that ἓν is used without the definite article at 137b4, Par- menides will continue to do so in the exercises, reinforcing the indeterminate- ness. Let us take a closer look. Each hypothesis has an orienting premise that establishes the conclusions that follow. For the eight hypotheses, there are four premises that are used, each one deployed twice, once with affirming conclusions, and once denying. In every case, the premise is stated without the use of the definite article. In some cases, the word order is modified, but the meaning is unaltered.

Hypothesis 1: εἰ ἕν ἐστιν, ἄλλο τι οὐκ ἂν εἴη πολλὰ τὸ ἕν; [137c3]. Hypothesis 2: ἓν εἰ ἔστιν, ἆρα οἷόν τε αὐτὸ εἶναι μέν, οὐσίας δὲ μὴ μετέχειν; [142b5]. νῦν δὲ οὐχ αὕτη ἐστὶν ἡ ὑπόθεσις, εἰ ἓν ἕν, τί χρὴ συμβαίνειν, ἀλλ᾽ εἰ ἓν ἔστιν: οὐχ οὕτω; [142c2]. Hypothesis 3: τί δὲ τοῖς ἄλλοις προσήκοι ἂν πάσχειν, ἓν εἰ ἔστιν, ἆρα οὐ σκεπτέον; [157b6]. Hypothesis 4: οὐκοῦν, εἰ ταῦτα μὲν ἤδη ἐῷμεν ὡς φανερά, ἐπισκοποῖμεν δὲ πάλιν ἓν εἰ ἔστιν, ἆρα καὶ οὐχ οὕτως ἔχει τὰ ἄλλα τοῦ ἑνὸς ἢ οὕτω μόνον; [159b2]. Hypothesis 5: τίς οὖν ἂν εἴη αὕτη ἡ ὑπόθεσις, εἰ ἓν μὴ ἔστιν; [160b6]. Hypothesis 6: οὐκοῦν ἓν εἰ μὴ ἔστι, φαμέν, τί χρὴ περὶ αὐτοῦ συμβαίνειν; [163c]. Hypothesis 7: ἔτι δὴ λέγωμεν, ἓν εἰ μὴ ἔστι, τἆλλα τί χρὴ πεπονθέναι. [164b5]. Hypothesis 8: ἔτι δὴ ἅπαξ ἐλθόντες πάλιν ἐπὶ τὴν ἀρχὴν εἴπωμεν, ἓν εἰ μὴ ἔστι, τἆλλα δὲ τοῦ ἑνός, τί χρὴ εἶναι. [165e1].

This strange phrasing εἰ ἕν ἐστιν / ἓν εἰ μὴ ἔστι underlines the ambiguity of his use of ‘one’ in the premises. By leaving out the definite article Parmenides marks the openness that a ‘one’ needs in order to sustain multiple depictions of different ‘ones’.

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56 Gardner

This phrasing contrasts with the concluding remarks that often have an article prefacing ἕν. We can already notice this from the lines that follow the premise of hypothesis 1 quoted above. “If ‘one’ is” is the premise, followed by the concluding remark that “the one is such that it is not in any way many” (ἄλλο τι οὐκ ἂν εἴη πολλὰ τὸ ἕν [137c4]). The concluding statement with the article, however, should not be understood as ‘the form one’ because of the included τὸ, but rather, it is better read in a demonstrative sense: “This one is such that it is not in any way many.” It is the first of many concluding remarks about that ‘one’, which will follow in the same way. In each case, however, the demonstrative sense of the τὸ will disambiguate and emphasize for that moment which ‘one’ is being referred to and concluded about, rather than signaling that a form is being considered. This demonstrative sense of τὸ ἓν becomes even more clear in the second hypothesis, where it is used to indicate a ‘one’ that has predicates and temporal modes of being, which is opposed to the previous determination of a ‘one’ that transcends predication and temporal modes of being. For, having two opposed sets of conclusions requires that Parmenides indicate that ‘this one’ in the second hypothesis is not that other kind of ‘one’, the ‘one’ of the first hypothesis. The article τὸ in this way is disambiguating the ‘one’ under scrutiny in its deduction. The two different conclusions about ‘one’, again, follow from the same premise that lacks the definite article, supporting the view that this ‘one’ is indeterminate, and that the opposed conclusions show that ‘one’ is therefore ambiguous. Now, along these lines of disambiguation and clarification, Parmenides also employs the term “the one itself” and the “being of the one” which can also appear at first to be indicative of a form or a determined subject. However, under our current line of reasoning, these phrases actually align with the view that the subject is ambiguous in the premises and the concluding remarks are defining and distinguishing what kind of ‘one’ follows from each deduction. In this case, the use of the “the ‘one’ that is” (τὸ ἓν ὂν) [143a5] clearly differenti- ates the second hypothesis from the first which established a one that is not: “therefore this ‘one’ in no way is” οὐδαμῶς ἄρα ἔστι τὸ ἕν [141e9]. As for the phrase “the ‘one’ itself” (αὐτὸ τὸ ἕν) which may appear to invoke the language of forms, the context makes clear what is meant. Parmenides had just concluded in the second hypothesis that this ‘one’ partakes of being and its ‘one-ness’ can be distinguished from its ‘being-ness’ [142e]. Because he distin- guishes these two parts, and two parts are a multitude, this ‘one’ is a many. He continues: “What about the ‘one’ itself, which we say partakes of being? If we apprehend it in thought alone by itself, without that which we say it partakes of, then will this appear one alone or will this same thing appear also as many?” (τί δέ; αὐτὸ τὸ ἕν, ὃ δή φαμεν οὐσίας μετέχειν, ἐὰν αὐτὸ τῇ διανοίᾳ μόνον καθ᾽ αὑτὸ

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The Ambiguity of the ‘One’ in Plato’s Parmenides 57

λάβωμεν ἄνευ τούτου οὗ φαμεν μετέχειν, ἆρά γε ἓν μόνον φανήσεται ἢ καὶ πολλὰ τὸ αὐτὸ τοῦτο;) [143a6]. The “one itself” simply serves to indicate the one alone, and does not require considering this phrase as a determination that the subject is a form. In fact, this “one” taken alone in thought, underlines once again the intermediate stage of thinking about the subject, not as a form, but as an open ‘one’ that is subjected to examination prior to thinking about forms. The αὐτὸ τὸ ἕν is best understood not as a form alone but just a ‘one’ simpliciter; not as a multitude, just one. In sum, then, the language that refers to the subject ‘one’ is not unambigu- ously referring to forms simply by employing the definite article or by using the intensive pronoun. In fact, the way that Parmenides explicitly leaves off the definite article in the formulation of the premises, using it only to clarify the concluding points about a particular ‘one’, aligns with the view that the subject in the premise ‘one’ is not a form or a principle, but an ambiguous subject that can sustain the opposed sets of conclusions. Second, the intensifying pronoun, which seems to invoke the language of forms, can in fact be seen to further emphasize a particular ‘one’ rather than the form of ‘the one’. “The ‘one’ itself” can be understood to specify a ‘one’ simpliciter.

Conclusion

I have argued that the subject ‘one’ that is employed in the hypotheses is best understood as an indeterminate ‘one’ that is open to the set of contradictory conclusions drawn by the hypotheses. If the ‘one’ is understood in a determined way as, for example, a form per se, then many essential conclusions drawn undermine that subject in a way that contravenes Parmenides’ stated views about the exercises. Rather, Parmenides clearly affirms to Socrates that thinking about forms is necessary, and I believe this claim is the starting point for his recommendation for Socrates to train more before turning to the task of defining forms. To take the ‘one’ as a form or a principle at the outset of the exercises amounts to an immediate departure from Parmenides’ educational proposal, which I believe underwrites the entire dialogue. The purpose of the exercises in the Parmenides that follows from the needs of the young and inspired Socrates, is to prepare the trainee to be in a position to define forms, not to demonstrate or define a particular form itself. To this end, understanding the subject as an indeterminate and ultimately ambiguous ‘one’ is consistent within the plan of the exercises such that the contradictions that arise juxtapose the conclusions drawn under each premise, rather than contradict the subject in the premise. They juxtapose a form-like ‘one’ and a

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58 Gardner participant-like ‘one’ in an instructive way whereby the ‘one’ in question is not undermined because it is intentionally ambiguous. The ‘one’, thought of as ambiguous, simply allows for different and even opposed depictions to follow from the premise. As noted, the doubling of the program, in practice, occasions the trainee to consider the contradictory opposed pairs of conclusions for each of the four parts originally proposed. The key is to undertake the challenge to hold these opposed depictions under one premise, and this challenge is obscured if not missed altogether if the ‘one’ is understood as a form. The challenge of keeping these two contradictory descriptions together acts as a gymnastic, a strength- ening provocation, which helps the trainee to reconsider the subject in a more abstract way. And, it is this type of abstract reconsideration that is the kind of preparatory exercising that is helpful prior to defining forms. In this way, the ambiguous nature of the ἓν is instrumental in allowing under its purview the sets of contradictory conclusions that occasion this kind of training. In disabusing the notion that the ‘one’ as a form is to be taken as the subject under scrutiny in the hypotheses, the hypotheses can be reassessed and reconsidered in such a way that asks the trainee to confront contradictory accounts in a provocative way: a way that makes good on the suggestion that they are a gymnastic training program for the student who is not yet fully prepared to define forms. Much as Socrates, in challenging Zeno’s polemical counterfac- tual, pushed Zeno to raise his thinking to the level of forms, reassessing the way in which the hypotheses ask the student to contend with challenging sets of contradictions will raise his or her level of inquiry from a criticism of forms to a reconsideration of the way that forms are abstractions that exceed direct description. Moreover, the student who reconsiders the nature of the subject in the hypotheses will also reconsider how the forms are not only juxtaposed to their participants, as Socrates had indicated to Zeno, but also how the hypotheses’ contradictions may give way after exercising to reveal a structure of mutual entailment between form-like ‘ones’ and participant-like ‘ones’. This is work that Socrates and we, as readers, are now prepared to undertake.

References

Allen, R.E. (1997). Plato’s Parmenides. Yale University Press, New Haven. Burnet, J. (1901). Platonis Opera, Tomus ii, Tetralogia iii–iv. Oxford University Press, Oxford. Calogero, G. (1932 [1977 edition]). Studi Sull’Eleatismo, La Nuova Italia, Florence.

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The Ambiguity of the ‘One’ in Plato’s Parmenides 59

Calogero, G. (1974). ‘Plotino, Parmenide e il Parmenide.’ Atti del Convegno Internazio- nale sul Tema: Plotino e il Neoplatonismo in Oriente e in Occidente. Accademia Nazio- nale dei Lincei, Rome. Cornford, F. (1939). Plato and Parmenides. Kegan Paul, Trench, Trubner & Co, London. Dorter, K. (1994). Form and Good in Plato’s Eleatic Dialogues. University of California Press, Berkeley. Ferrari, F. (2004). Platone Parmenide. Introduzione. Biblioteca Universale Rizzole, Milan. Fronterotta, F. (1998). Guida alla Lettura del Parmenide di Platone. Laterza, Rome. Fronterotta, F. (2001). Methexis. La Teoria Platonica delle Idee e la Partecipazione delle cose Empiriche: Dai Dialoghi Giovanili al Parmenide. Scuola Normale Superiore, Pisa. Gill, C. & McCabe, M. (1996). Form and Argument in Late Plato. Clarendon Press, Oxford. Gill, M.L. & Ryan, P. (1996). Plato Parmenides. Hackett Publishing, Indianapolis. Gonzalez, F. (2002). ‘Dialectic of Forms.’ from Welton, W., Plato’s Forms: Varieties of Interpretation. Maryland. Meinwald, C. (1991). Plato’s Parmenides. Oxford University Press, Oxford. Miller, M. (1986). Plato’s Parmenides: The Conversion of the Soul. Princeton University Press, Princeton. Peterson, S. (2003). ‘New Rounds of Exercise of Plato’s Parmenides.’ The Modern School- man lxxx. Peterson, S. (1996). ‘Plato’s Parmenides: A Principle of Interpretation and Seven Argu- ments.’ Journal of the History of Philosophy, xxxiv No. 2 April. Rickless, S. (2006). Plato’s Forms in Transition. Cambridge University Press, Cambridge. Sanday, E. (2015). A Study of Dialectic in Plato’s Parmenides. Northwestern University Press, Evanston. Sayre, K. (2005). Plato’s Late Ontology: A Riddle Resolved. Parmenides Publishing, Las Vegas. Sayre, K. (1996). Parmenides’ Lesson: Translation and Explication of Plato’s Parmenides. University of Notre Dame Press, Notre Dame. Sayre, K. (1978). ‘Plato’s Parmenides: Why the Eight Hypotheses are not Contradictory.’ Phronesis, Vol. 23 No. 2, 133–150. Trabattoni, F. (2016). Essays on Plato’s Epistemology. Leuven University Press. Turnbull, R. (1998). The Parmenides and Plato’s Late Philosophy. University of Toronto Press, Toronto.

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