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Plato’s Parmenides and The Knowable Many: Cosmos as Discursive Order in Hypothesis 3

Darren Gardner

Résumé

In this paper, I argue that hypothesis 3 of Plato’s Parmenides presents a kind of cosmological lesson that shows why the “one” needs to be understood as an essential principle of order when examining what the “others” to the “one” would be like. At face value, the “others” are defined as opposite to the “one,” and so they cannot be “one.” Nevertheless, Parmenides claims that the “others” must not be entirely devoid of the “one.” This is because the kind of “one” in question, a form-like principle rather than a unit, is responsible for the “others” to be a discursive “many” which is required for them to be considered as “others” in the first place. I argue against the view that pairing of hypothesis 3 and 4 is merely aporetic, and propose that the lessons of hypothesis 3 can be sustained in light of hypothesis 4. The benefit of this reading is that Parmenides’ claim that denying forms would destroy the power of dialogue at 135c2 can be seen as upheld. And it contributes to the task of learning to think through the relationship of forms and participants by examining the way that discursive “others” are different from, but essentially dependent upon on a form-like principle of order.

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  • 1 This paper was composed on the occasion of the Société d’Etudes Platoniciennes 2018 workshop “Cosmo (...)
  • 2 See Sophist 237b-ff.
  • 3 I am making the claim that the unintelligible as such is unknowable in its own right, and yet still (...)

1 Central to the meaning of cosmos is a notion of order1. Indeed, the broad sense of cosmos is an expression for something like “the order of the all,” which includes the arrangement that gives “the all” a coherent sense in the first place. For example, if Parmenides calls the all “one,” such a claim can be understood as cosmological because the “all” is arranged in such a way as to be called “one.” Whereas, if it were posited that “the all is unintelligible,” such a claim would be problematic as a cosmology unless there is a determinate way to understand what is unintelligible as such. To comprehend an unintelligible “all” as such, (i.e., not merely in a figurative way) would be to find order in what eschews order. Much like the problem of the being of non-being,2 it stands as a question if an unintelligible object of inquiry, or in what we will examine in this paper – an indeterminate many – strictly speaking can be known as such. For, if there could be an understanding of an unintelligible, rendering it discursive, it would challenge or even undermine the “unintelligible” claim in the first place.3

  • 4 128e5-ff.

2I take Zeno’s argument from the first part of the dialogue [127e1-ff] to touch on a similar problem, even if his argument is a bit (perhaps intentionally) naive. Zeno argued that those who go against Parmenides’ view must hold by way of its contrary an even more problematic view. Namely, they contend that “the many is,” opposed to Parmenides’ view that posits “one.” And since the “many” would be both “like” and “unlike,” a contradiction would ensue making the premise false. The upshot of Zeno’s argument (according to Socrates at 128a4) is an indirect affirmation of Parmenides’ position, refuting its opposite premise by revealing a contradiction. To be sure, the contradiction is disarmed by Socrates’ distinction between forms and participants.4 But for the purposes of this paper it is noteworthy that the premise if “the many is” (εἰ πολλά ἐστι [127e1]), which is seemingly undermined by Zeno, constitutes what Socrates considers to be the obvious state of affairs; arguing against the view that there exists a plurality of things is unreasonable. “Is this the point of your arguments – simply to maintain, in opposition to what is said, that things are not many?” (ἆρα τοῦτό ἐστιν βούλονταί σου οἱ λόγοι, οὐκ ἄλλο τι διαμάχεσθαι παρὰ πάντα τὰ λεγόμενα ὡς οὐ πολλά ἐστι; [127e8]). Socrates, however, is not fully sure of the scope of the forms, doubting if they are necessary for all kinds of things [130c].

  • 5 Parmenides notes that the manner of the exercises that he offers to Socrates are similar to the str (...)

3Zeno’s argument juxtaposes the “many” things to the “one,” which prefaces the oppositional pairings that occur later in the hypotheses.5 Such oppositions, for example, in the first four hypotheses that examine the premise “if one is,” juxtapose conclusions concerning “one” in the first two hypotheses and its correlative “others” in the second two hypotheses. These contradictory conclusions, however, offer additional and very considerable challenges beyond the mere opposition of “one” and the “others.” In fact, the hypotheses are not restricted to depicting the “one” in the first two hypotheses and the “others” in the second pair. Rather, the hypotheses include explicit conclusions for both, integrating the interrogation of the pair.

  • 6 For various views on the hypotheses as antinomies, see: Ryle 1939; Cornford 1939; Schofield 1977; F (...)
  • 7 See: Sophist 238c-ff. There, the Visitor and Theaetetus consider the possibility of applying number (...)

4Nevertheless, what is affirmed in one hypothesis is generally denied in the other. This makes the “one” and their “others” seem to have contradictory depictions.6 For instance, the summary conclusions about the “one” in the first hypothesis depicts a “one” that is radically not, denying all types of spatial and temporal predication, which is opposite to the conclusions drawn about it in hypothesis 2; and the conclusions about the “others” in the hypothesis 4, in opposition to hypothesis 3, deny the unity to the “others” that would be required to grant any spatial or temporal predication. So hypotheses 1 and 4 appear to depict a “one” and “others” respectively that cannot be discursive. Can a “one” and its correlative “other” both be understood as an unknowable object of reflection? The answer, I believe, depends upon what we can discover about the “one” and its relationship to the “others.”7

  • 8 I do not claim that the “others” are phenomenal things per se, only that the “others” will be under (...)
  • 9 A form-like “one” or what I later call an “idea-like one” is a “one” thought of as unifying princip (...)

5If there is a principle of order, or a cosmological account to be found in Plato’s Parmenides, we would be wise to look at what is presented to the young Socrates in the third hypothesis. For it is here that Plato has Parmenides thematize how the “others” (which are a “many” by definition) must be constituted as a whole of parts. As such it must have at a minimum some aspect of order. And if we can understand the “others” in question in some way as informing the “many” things (i.e., the “many” perceptible things like the those challenged by Zeno) such that, if they are knowable, they must be ordered, then such an understanding would constitute a cosmological aspect to the dialogue8. To this end, I argue that the third hypothesis in fact shows that an organizing principle is at work in even a basic notion of the relationship of part/whole or one/many, and that such an organizing principle is a form-like “one”9 that is essential in even the most basic order of things. This principle of order and the “others” it determines, I believe, functions as a propaedeutic model to show that forms bestow discursive order to participants. Moreover, the lessons of hypothesis 3 and 4 begin to show Socrates that all discursive things rely on the unity of a form, and would serve to help him overcome his hesitation about the range of forms.

6First I will examine the argument at 157d-ff which reasons that the “others” as a “many” have a necessary part/whole constitution. The point here is to show that the “others” cannot be entirely “other” to the “one,” but rather that they must participate with the “one” in some way. Second, I will turn to 158c-ff where Parmenides proposes a thought experiment, the upshot of which shows that if the “others” are considered just by themselves, prior to any communion with the “one,” then they would be an unlimited multitude that is unknowable as such. In both cases, the necessity of participation in a unifying “one” will become apparent. First, as a discursive “many” the “others” need to be construed as a whole, and second, because the “others” simpliciter, taken prior to participation, are simply unknowable, proving the necessity of the principle “one” for the “others” to be “others.”

  • 10 That is, the “others” as the basic category of phenomenal things would require a principle of order (...)

7The consequences of the denial of any communion of the “others” with the “one” will reveal an essential need for the “one” in order for any whole or part to be knowable, have limit, and in general for anything to be discursive as such. And, if the “others” under consideration can be taken as a nascent model for phenomenal things (like the “many” brought up by Zeno) then their essential relationship to the “one” can be understood to make not only a cosmological or ordering claim but also a metaphysical one.10

8In addition, the “many” will be examined as requiring even a basic notion of order. Because a “many” is composed of “ones” (for a “many” must have individual members) the account of what makes a “many” discursive will also include an account of member “ones.” I will argue that the “ones,” understood as individual members of a “many,” draw upon and contextualize an earlier depiction of a “one,” in particular, from the second hypothesis. To do so, I will show that the members of a discursive “many” (or an “other”) align with the depiction of the kind of “one” in the second hypothesis insofar as that “one” and the members of the “many” are similarly subject to predication and have being.

  • 11 My view builds upon the arguments of Miller 1986 p.137-139 and Sanday 2015, p153-154 who read hypot (...)

9Finally, I will turn to the fourth hypothesis in order to show how it relates to the conclusions drawn out from the third hypothesis. I will suggest that hypothesis 4 is a reductio ad absurdum in support of hypothesis 3, securing that the “others” require participation in the “one.” While it may be argued that hypothesis 4 undermines the work established in hypothesis 3 because it ostensibly refutes conclusions about the “others,” I contend that the contradictions are only one aspect of the relationship of the hypothesis, and moreover, the contradiction can be understood in the context of a reductio argument.11 If hypothesis 3 and 4 are merely contradictory then they stand as an indissoluble antinomy and the project of the hypotheses may be considered broadly as aporetic. However, following my view, the two hypotheses do not stand together merely as opposed, but also as an exercise, the challenge of which is to understand how the two accounts can be integrated. Under this view, the student of the exercises (and of the dialogue in general) will be more ready and able to affirm that a discursive “many” is dependent upon a “one” understood as an ordering principle.

  • 12 If someone, having an eye on all the difficulties we have just brought up and others of the same s (...)
  • 13 The destruction of “dialectic” could also be translated as the destruction of the power of discursi (...)
  • 14 The examination of Parmenides’ challenges to Socrates about forms, including the range and scope of (...)
  • 15 Recently Priou 2018 argues that the dialogue helps train Socrates, but he sees this as predominantl (...)

10Since the ordering principle in question will be depicted as a form-like “one” or an “idea” that orients the “many” as a discursive whole, my reading aligns with Parmenides’ position about the hypotheses as it is put to Socrates at 135b5-d6.12 There, Parmenides explicitly endorses the essential necessity of forms for philosophy. Without forms, Parmenides tells the young Socrates, one would have nowhere to direct thoughts, destroying the power of dialectic.13 Denying forms would disallow one’s thoughts to be directed at a fixed or unified object of discursive inquiry. In other words, discursive inquiry is dependent upon forms. In light of this conclusion, Parmenides claims that Socrates’ issue is that he has turned to defining forms too soon, before he is properly trained [135c8]. The problem raised in the Parmenides is not that forms per se are undermined by Parmenides’ famous challenges,14 but rather that Socrates as a young learner is not yet prepared to properly think through what a form would be like as immune to the critical refutations of the sort that Parmenides had challenged Socrates with. His remedy for Socrates is to strengthen or develop his thinking through the hypotheses as exercises in order to help him better secure his initial insight about forms.15 In this light, I argue that hypothesis 3 stands as an essential contribution that shows how a form-like “one” is necessary with respect to a discursive “many.” It provides a model for how an ordering principle must be at work for any discursive account, and suggests that an ordering principle is required for any discursive subject.

1. If the “Others” are deprived of the “One”

  • 16 The viability and scope of Plato’s notion of participation is a point of much debate. I argue here (...)

11Parmenides posits at 157c-ff that the “others” are not “one” because they are by definition other to the “one” and therefore cannot be “one.” However, Parmenides continues, it must be the case that the “others” are not entirely deprived of the one [οὐδὲ μὴν στέρεταί γε παντάπασι τοῦ ἑνὸς τἆλλα (157c)]. Working out why he claims that the “others” are not entirely deprived of the “one,” while not being “one” per se, will characterize the “one” as an ordering principle. This ordering principle is responsible for the relationship that the “one” has to the “others” in virtue of participation.16

12Let’s look at the text. At 157c1 Parmenides tells Aristotle:

  • 17 οὐδὲ μὴν στέρεταί γε παντάπασι τοῦ ἑνὸς τἆλλα, ἀλλὰ μετέχει πῃ.
    πῇ δή;
    ὅτι που τὰ ἄλλα τοῦ ἑνὸς μόρια
    (...)

“The others are not entirely deprived of the one, but somehow partake of it”
“In what way?”
“In that things other than the one are surely other because they
have parts; for if they didn’t have parts, they would be altogether one.”
“That’s right.”
“And parts, we say, are parts of that which is a
whole.”
“Yes, we do.”
“Yet the whole of which the parts are to be parts must be
one thing composed of many, because each of the parts must be part, not of many, but of a whole.”17

13Parmenides’ claim is that since the “others” are by definition not “one,” they must have parts [158c]. And the parts that comprise the “others” must be parts of a whole, which is a “one” composed of constituent member parts. So, though the “others” are not “one” per se, they cannot be deprived of the “one” and constitute a whole. But why are the parts that comprise the “others” necessarily constituent parts to a whole rather than of a many? The answer begins with a deduction based on the premise that the others could be parts of a many.

  • 18 εἴ τι πολλῶν μόριον εἴη, ἐν οἷς αὐτὸ εἴη, ἑαυτοῦ τε δήπου μόριον ἔσται, ἐστιν ἀδύνατον, καὶ τῶν (...)

“If something were to be part of many, in which itself is, it will, of course, be both part of itself, which is impossible, and of each one of the others, if in fact it is part of all of them. For if it is not part of one, it will be part of the others, that one excepted, and thus it will not be part of each one. And if it is not part of each, it will be part of none of the many.”18 [157c8-d5]

14The argument here is compact and seemingly obscure if not circular. If something were part of a “many (a “many” that is in no way “one”) it would (a) need to be part of itself – and that can’t be – and (b) it would need to be part of all of the “many.” Since the part ostensibly must be part of all of the “many,” which includes itself, it renders the strange claim that the part would have to be part to itself, which is not possible. For this reason, that part cannot be included in the “many.” Since that part cannot be part of all of the “many,” the parts would not be part of all of the “many.” And, because the part is not a part of all of the “many,” it cannot be part to any of it. This is true because the “many” is not in any way a whole with discrete parts (it cannot be in any way unified as any kind of “one”), but only a mass “many.” As such, a “many” that entirely lacks wholeness requires its parts to be understood either distributively across it, or not at all. Lacking wholeness, parts of a “many” cannot be ordered relative to any predicate, for there is no referent that does not require the unification or the making a whole out of the parts. In this way Parmenides claims that such a part could only be a part of none, rendering that part as not a part at all, and proving the premise to be false.

  • 19 ὅτι που τὰ ἄλλα τοῦ ἑνὸς μόρια ἔχοντα ἄλλα ἐστίν: εἰ γὰρ μόρια μὴ ἔχοι, παντελῶς ἂν ἓν εἴη.

15The argument shows that lacking one-ness undermines any part/whole relationship for the “others” by making the “others” merely a mass many” that cannot admit of specific discursive parts. If the “others” do not have parts, they must be a “one” and not any kind of “other.” But this is a contradiction, because the “others” are by definition [157c3-4] composed of “many” parts.19 Therefore, the conclusion drawn is that the “others” cannot be wholly deprived of the “one.” And, they cannot be “others” as a “many” (which they are by definition) unless they are a whole which is dependent upon a “one.”

  • 20 See Gill 1996, 89.

16But could a part of a “many” be part of some rather than “part of none” as Parmenides has concluded?20 A “many” not being in any way “one” must be an indeterminate “many.” And parts to an indeterminate many, lacking any unity, must be parts only in an obscure way, only distributively. Take, for instance, the distributive way that moisture is part of clouds. It cannot be that moisture is in one section of clouds and not in another. Rather, if it is a part of clouds, it is part of all clouds or if not, none. But this example, of course, has a unifying aspect insofar as clouds and moisture are discursive referents.

17Since the “others” as a non-unified “many” cannot be a discursive whole or otherwise allow for a portion which we could call ‘some’, the only remaining way a part of the “others” can have parts is distributively, which it cannot have because, as deduced above, without the absurdity of a part being a part to itself. The “others,” in order to be discursive “others” and not an indeterminate mass “many” must be such as to have a part/whole constitution [157c8]. This requires that the “others” are not completely deprived of unity.

2. The “Idea” as the Unifying Aspect

  • 21 See also Harte 2002, 123-125.

18How are the “others” not “one” per se, and yet not entirely deprived of the “one”? Since the “others” cannot be an indeterminate or non-unified many and still have parts, it follows that they must be unified as a whole with respect to something. “So the part would not be part of many things or all, but of some one character [idea] and of some one thing, which we call a “whole” (ἀλλὰ μιᾶς τινὸς ἰδέας καὶ ἑνός τινος καλοῦμεν ὅλον ) since it has come to be one complete thing composed of all (ἐξ ἁπάντων ἓν τέλειον γεγονός)” [157e]. That which constitutes a complete whole out of a many is some one character or one idea that in principle unifies the many into a whole. And this idea-like “one” must be at its most basic a foundational principle of order.21

  • 22 Many have argued that the hypotheses take up the form of unity as the subject. For instance, Rickle (...)
  • 23 One might object to the idea that the language of forms is not explicitly employed until the third (...)

19The reference to the “idea” is the first explicit connection of a form-like aspect that is applied to the subject “one” in the hypotheses.22 Furthermore, the use of the “idea” does not appear in the examination in the first two hypotheses. We might expect to find the language of forms in the first hypothesis which ostensibly articulates the most abstract nature about some “one.” Rather, it arises only from the examination of the correlative “others” in hypothesis 3 by showing that the “others” are dependent upon being unified by such a principle. More specifically, the language of the “idea” arises as the essential way to consider the “one” that addresses the contradictory conclusions that would otherwise hold for the “others” if they would be completely deprived of the “one.”23 If the “others” are unified by an “idea” or form-like “one,” then they escape the fate of being an unknowable mass “many” that admits of no parts. In this way the “others” owe their discursive nature, having a whole/part constitution, to a “one” thought of as an idea or a principle of order.

  • 24 The “one” cannot be a form per se exclusively on the basis of the first hypothesis because it is un (...)

20The use of the “idea” comes up in the third hypothesis only after traversing through the lengthy arguments about the “one” that precede it. The late emergence of the language of forms contextualizes the kind of “one” being considered, and supports a reading of the hypotheses that develops, rather than the more standard view that sees the hypotheses as a static series of antinomies, a collection of aporias, or that the form of the ‘One’ is the subject of examination from the very start of hypothesis 1. The “one” considered in and by hypothesis 1 is not defined as a form explicitly, and it can only be understood there as a form in a very problematic way;24 it is only in virtue of hypothesis 3 that the student of the hypotheses is directly invited to reconsider what kind of “one” might be needed as a principle relative to the “others.”

  • 25 See Gardner 2018

21The development view of the hypotheses allows us to see the initial investigations about the “one” in the first two hypotheses as preliminary or foundational work for what will continue to develop over the course of the exercises as a whole. The explicit use of the term “idea” in hypothesis 3 contextualizes what was previously an ambiguous employment of the term “one” as now a necessary ordering or unifying principle.25 Nevertheless, the use of “idea” is still a broad way to describe the “one” in hypothesis 3. All that is specified is that there is some one “idea” by which parts and wholes are unified as a whole, and which thereby come to be one complete thing [157e]. While it is necessarily one form-like thing insofar as it is a unifying principle, I believe it is still an open “idea” to the extent that it can be any unifying “idea”: any potential candidate for a form would seemingly apply.

22The “one” in the first hypothesis, while perhaps sharing attributes that we equate to forms (i.e., that forms are in some way without spatial or temporal characteristics) still remains ambiguous, particularly in light of the opposite conclusions arrived at in the second hypothesis. I contend, however, that the opposed conclusions about the “others” in hypothesis 4 do not contribute to an ambiguous or contradictory account of the “others” in hypothesis 3 because hypothesis 4 can be understood as a reductio ad absurdum argument and therefore its negative conclusions are in support of hypothesis 3.

23The ambiguity of the “one” in the first two hypothesis is due to the fact that the “one” is depicted twice, seemingly as mutually exclusive types of “ones.” At some points the “one” admits of all sorts of spatial and temporal predication (such as in hypothesis 2) and at other times transcends spatial and temporal predication altogether (such as in hypothesis 1). The “idea” in hypothesis 3 that is required to unify the “others,” helps us to understand the kind of “one” in hypothesis 3 beyond the ambiguity of the previous hypotheses. Moreover, we will see that hypothesis 4 is best understood not to propose a different “other” than in hypothesis 3, but rather as arguing for the necessity of the kind of unified “others” that are depicted in hypothesis 3. The contradictions from the conclusions in hypothesis 4 show via negativa that hypothesis 3 must be affirmed.

24There is yet another striking implication for the “others” as they are unified by the “one.” The idea-like “one” is not only necessary for unity and therefore the discursive aspect of the “others,” but it is also equally necessary with respect to the parts of the “others.” Since the “others” consist of parts and wholes, both of which are also unified and composed of parts, both come under the aegis of an ordering principle “one” considered like an “idea.” Wholes are unified parts, unless they are simple monads without parts (and therefore are not “others”), and this is true also of parts. Insofar as they can be a ‘single’ part, they are a unified whole such that they can be a ‘single’ or individual member.

25Parmenides makes this point quite clear: “The same account applies also to each part” (καὶ μὴν καὶ περὶ τοῦ μορίου γε ἑκάστου αὐτὸς λόγος) [157e5]. So each of the parts of the “others,” as an individual member(s) are also a unity and they therefore must likewise not be deprived of the “one.” In both instances, the parts and the wholes cannot be completely deprived of the “one” without running into contradiction; neither the part that is part to a whole, nor the part that is part to a part. In this way, Parmenides claims that things that participate with the “one,” would be unlimited in multitude [158b5] since wholes and parts (and even parts of parts, etc.) must participate in a unifying idea in order to be a whole or a part, which we will turn to next.

3. The “Others” as Such

26Having motivated the position that the “others” require participation with a unifying principle, the upshot of which also suggests that the “others” and the parts that compose them are unlimited in multiplicity, the question remains to be asked: what about the “others” as such, taken just by themselves? If the “others” must participate in the “one,” perhaps they can be conceived of prior to or outside of participation? In order to examine the “others” in this way, Parmenides employs a thought experiment to try and consider the “others” simpliciter. By taking up the “others” just in thought [τῇ διανοίᾳ], Parmenides has the student of the hypotheses try to consider what they would be were they not participants in the “one.” However, by making a special case “in thought” in order to consider the “others” as such, stepping around the issue of participation, is Parmenides suggesting that the separation of the others from a unifying “one” is somehow problematic? Otherwise, why would the inquiry be qualified in such a way as specifically relegated to conceptual abstraction? It will turn out that even if the “others” could be thought of separately or prior to participation in the idea-like “one,” they could not be understood properly as “others,” but only as an undifferentiated, unknowable, unlimited multiplicity.

27The thought experiment runs as follows:

  • 26 ὧδε ἴδωμεν. ἄλλο τι οὐχ ἓν ὄντα οὐδὲ μετέχοντα τοῦ ἑνὸς τότε, ὅτε μεταλαμβάνει αὐτοῦ, μεταλαμβάνει;(...)

“Let’s observe the following: isn’t it the case that, at the time when they [the others as a whole or part] get a share of the one, they get a share, while not being one and not partaking of the one?”
“Quite clearly.”
“While being multitudes, then, in which oneness is not present?”
“Certainly, multitudes.”
“Now, if we should be willing to subtract, in thought,
the smallest we can from these multitudes, must not that which is subtracted, too, be a multitude and not one, if in fact it doesn’t partake of the one?”
“Necessarily.”
“So always, as we examine in this way its nature,
itself by itself, different from the form, wont as much of it as we ever see be unlimited in multiplicity?”
“Absolutely.” [158c1-ff]
26

  • 27 The thought experiment appears to have two distinct educational aspects for the student of the gymn (...)

28If one were to consider the “others” as prior to the point at which they get a share of the “one,” the “others” would only be an unlimited multiplicity or plethe. As such, they would lack all discursive characteristics that depend upon the “one.” This would render them unknowable as “others,” and therefore unknowable per se. And moreover, even if we take away from that unlimited multiplicity, the very smallest possible amount, even that would be an unlimited multiplicity, rendering any bit likewise unknowable as such. Why? Because lacking any “one-ness” – any discernible unifying character with which a multitude can be a discernible whole, even the smallest amount must already be an unlimited multiplicity. And, the least amount of that would also be an unlimited multiplicity. Any ‘amount’ of the plethe (if you will, any “part” of it taken “in thought”) cannot be in any way discernible or enumerably different from any other, or the original plethe. The kind of abstraction that is required to consider the plethe, or more properly, the manifold plethe, is in some way beyond our capacity to refer to directly. Indeed, what could it mean to apprehend a manifold of unlimited multiplicities?27

29Next, Parmenides turns to address how it would be that such a multiplicity could be knowable and how limit comes to bear on the plethe:

  • 28 καὶ μὴν ἐπειδάν γε ἓν ἕκαστον μόριον μόριον γένηται, πέρας ἤδη ἔχει πρὸς ἄλληλα καὶ πρὸς τὸ ὅλον, κ (...)

“Furthermore, whenever each part comes to be one part, the parts then have limit in relation to each other and in relation to the whole, and the whole has a limit in relation to the parts.”
“Quite so.”
“Accordingly, it follows for things other than the one, that from the one and themselves gaining communion with each other, as it seems, something different comes to be in them which affords a limit for them in relation to each other; but their own nature, by themselves, affords unlimitedness.” [158c7-ff]
28

30The “others” come to be different, or rather, something different becomes of them [ἕτερόν τι γίγνεσθαι ἐν ἑαυτοῖς] which bestows limit and thereby endows the plethe as a “many” with a part/whole constitution. Lacking limit, the plethe is no more than a non-knowable object of reflection: it remains available as a mere conceptual abstraction.

  • 29 καὶ ταὐτὰ δὴ καὶ ἕτερα ἀλλήλων, καὶ κινούμενα καὶ ἑστῶτα, καὶ πάντα τὰ ἐναντία πάθη οὐκέτι χαλεπῶς (...)

31Parmenides brings hypothesis 3 to a close by marking off a series of summary conclusions about the “others”: They are both unlimited (that is, in and of themselves an unlimited plethe) and partake of limit (having a part/whole constitution in virtue of the “one”). They are both like and unlike. Why? Because insofar as the “others” are unlimited, they are alike, and insofar as they are delimited they are also alike. Yet the others can in some sense be both unlimited and partake of limit, so they are also different. “Thus the others would be both like and unlike themselves and each other” [159a5]. Parmenides wraps up this depiction of the “others” claiming that there would be no problem concluding that the “things other than the one are both the same as and different from each other, both in motion and rest, and have all the opposite properties…” [159b1].29

32The list of characteristics is a return to the kind of conclusions that generally populate the other hypotheses, and they invite us to consider both what we have come to understand about the “others” insofar as they are not wholly deprived of the “one,” and how they relate to the summary of conclusions in the other hypotheses. This is particularly telling with respect to the second hypotheses. There, the “others” are concluded to be subject to all types of opposite properties [159b1], and this is similar to the characteristics that are given to the “one” as it is depicted in hypothesis 2: both admit of all the opposite properties including spatial extensions and temporal modes of being.

  • 30 142b-ff. Parmenides revisits the premise “if one is” a second time emphasizing the being of the one (...)
  • 31 Thus the one would touch itself and the others.” οὕτω μὲν δὴ ἅπτοιτο ἂν τὸ ἓν αὑτοῦ τε καὶ τῶν ἄλλ (...)
  • 32 The ambiguous “one” in the second hypothesis is not, as it where, equal to the “others” in the thir (...)

33The “one” of hypothesis 2 is like the “others” of Hypothesis 3 insofar as it is both limited and unlimited [145a/158d7], like and unlike [148c/158e1], same and different [146b/159a6], in motion and at rest [146a/159a7]. And moreover, the “one” in the second hypothesis, the “one” that has being,30 is a kind of “one” that is inclusive of all properties including spatial and temporal attributes.31 Insofar as the “others” are not deprived of participating in a idea-like “one” as Parmenides shows in hypothesis 3, the “others” can be seen to this extent as similar to the kinds of “ones” described by hypothesis 2: they have being and admitting of all sorts of predicates including spatial and temporal ones.32

  • 33 See 142b1-ff

34The “ones” depicted in hypothesis 233 share the basic characteristics that the “others” have, both as instances of wholes as instances of members of a whole. And therefore the “others” in hypothesis 3 can also be understood in this respect to describe what would be required for the kind of “one” in hypothesis 2 to be discursive or knowable. They would require participation with an “idea.” This is due to two essential points: First, the kind of “ones” in hypothesis 2 and the unified “others” of hypothesis 3 similarly admit of all kinds of spatial and temporal predication which would be determinate for any discernible thing. And second, because both parts and wholes require unification by an idea-like “one” in order to be discursive, both parts and wholes are “ones” as instances or members of a whole only by virtue of the ordering power of the unifying “one.” If a part of the unified whole requires an “idea” for any discursive aspect, so too does just a “one,” since that is what a single part is.

35The “ones” of hypothesis 2 can in this way be seen in light of what is claimed about the parts and wholes of the “others” in hypothesis 3 [157e5]. The connection of the characteristics of the “ones” and “others” in the two hypotheses allows the “ones” in hypothesis 2 to be recognized, albeit only after working through hypothesis 3, as setting out basic parameters that would be required of phenomenal things: having a part/whole constitution in virtue of the unifying idea or “one.” Lacking the unifying power of the idea-like “one,” a “one” in hypothesis 2 would also remain undifferentiated and unknowable.

36To sum up so far, we have discussed how hypothesis 3 shows that the “others” can be understood as a unified whole of parts in virtue of not being denied participation in a form-like “one.” It must be the case that: (a) the “others” are a many; (b) that such a many must have a whole/part constitution where the whole and the parts are likewise unified by an “idea” and thereby are also “ones” as members of a whole; (c) that the “others” prior to or lacking participation in the “one” would be an unlimited plethe, which is not knowable as such, and; (d) when a part comes to be a part of what is otherwise a plethe, something different comes to be, namely, a discursive part with respect to a whole.

37If it were not the case, the “many” would not constitute a whole in any way (as demonstrated at 157b-ff) and the “others” would be merely an unknowable unlimited multitude (158c-ff). What would remain, lacking participation in the unifying “one,” would be an unknowable that simply goes against what is minimally recognizable as any discursive object of consideration. This would be the same lamentable situation that Parmenides warns us of at 135b5-ff: “If someone…won’t allow that there are forms for things and won’t mark off a form for each one, he won’t have anywhere to turn his thought, since he doesn’t allow that for each thing there is a character that is always the same. In this way he will destroy the possibility of dialectic (i.e., discursive inquiry) entirely.” And since the “others,” which would be an unknowable unlimited multiplicity, would simply not be “others” in any sense, the contradiction refutes the premise that the “others” are altogether separate from the “one.” This establishes the necessity of participation with an “idea,” or a principle of order, not only for any epistemological claim about the knowability of a plethe, but for the possibility of things to be discursive.

38This summary can now be set against Socrates’ objection to Zeno’s anti-pluralist view at the beginning of the dialogue; as Zeno would have it, the argument that “the many is,” is false. Socrates countered, pace Zeno, that there are many things, and that this is the state of affairs that would be absurd to argue against. We may now see on the basis of hypothesis 3 that the “many” as the correlative other to the “one” can be understood as a propaedeutic model that shows the necessity of an ordering principle for any discursive or even phenomenal many. If the “others” are wholly deprived of a unifying “one,” then intolerable contradictions ensue, like the contradictions that Zeno indicated in his book.

39I have argued that the reliance of the “others” to the “idea” or form-like “one” in hypothesis 3 can been understood as a propaedeutic, showing the need of a unifying principle to escape the contradictions that ensue from lacking this kind of “one.” Hypothesis 3 shows the necessity of an organizing principle by demonstrating that all discursive “others” are in fact dependent upon it. This conclusion helps Socrates and those who are not fully sure about the range of things that forms cover. For, at 130c, Socrates admits that at this moment he is unsure if forms are required for all kinds of things (human being, fire, water, hair, mud and dirt seem to perplex him). On the basis of what we, and Socrates, have learned from the exercise of hypothesis 3, however, all discursive objects of reflection require participation in a unifying principle in order to be knowable.

4. Hypothesis 4: The Counterfactual View

  • 34 ἆρ᾽ οὖν οὐ χωρὶς μὲν τὸ ἓν τῶν ἄλλων, χωρὶς δὲ τἆλλα τοῦ ἑνὸς εἶναι;

40Parmenides gives a second set of conclusions about the “others” in the fourth hypothesis. Yet this hypothesis concludes opposite to the third. Because the “one” here must be wholly separate from the “others,” it cannot be the case that there is any participation with the “one,” which would bestow a part/whole constitution on the “others” as a “many.” Nor can it be the case that there is any limit bestowed upon an otherwise unlimited and unknowable multiplicity. Lacking the unifying power of the “one,” neither of these aspects, either a part/whole constitution or limit can be part of the “others.” Rather, the proposal in hypothesis 4 is that the “others” are totally separate from the “one,” and because of this they are not “one” in any way whatsoever. “Must not the one be separate from the others, and the others separate from the one?” [159b7].34 The conclusions drawn are opposed to the concluding remarks about the “others” as not completely deprived of the “one.”

  • 35 See: Meinwald 1999, Peterson 1996, Sayre 1996.

41It is tempting to say that since the conclusions of the fourth hypothesis seem to be completely opposed to the conclusions of the third hypothesis that a determination of the “others” is aporetic. After all, the depictions are mutually opposed. For instance, the “others” are both like and unlike on the basis of hypothesis 3 [158e1], and neither like nor unlike on the basis of hypothesis 4 [159e2]. Perhaps the two hypotheses are contradictory in such a way as to warrant two different approaches, as some scholars have proposed.35 However, if the opposed contradictory conclusions of hypothesis 3 and 4 can be considered not merely as contradictory, but also as complementary as I suggest that they can, then the notion of an ordering principle can be sustained. This reading is also preferable because it aligns with Parmenides’ stated purpose of the exercises, as we have seen, which is to help Socrates strengthen his notion of forms since they are necessary for dialogue and discursive articulation. Following this line, hypothesis 4 reflects a similar argument to the thought experiment in hypothesis 3. Insofar as we understood the thought experiment as a reductio, I argue that the argument in hypothesis 4 can also functions as a reductio.

  • 36 οὐδ᾽ ἄρα πολλά ἐστι τἆλλα: ἓν γὰρ ἂν ἦν ἕκαστον αὐτῶν μόριον τοῦ ὅλου, εἰ πολλὰ ἦν: νῦν δὲ οὔτε ἓν (...)
  • 37 οὐδὲ ὅμοια ἄρα καὶ ἀνόμοια οὔτε αὐτά ἐστι τῷ ἑνὶ τὰ ἄλλα, οὔτε ἔνεστιν ἐν αὐτοῖς ὁμοιότης καὶ ἀνομο (...)
  • 38 The “others” would hold no attributes and would not even be enumerable: So the others are neither t (...)

42Hypothesis 4 depicts by way of its conclusions that the “others” are not in any way the same as the “one”; they do not have parts [159d4]; they do not constitute a whole [159d5]; they cannot participate or commune with the “one” [ 159d7]; are not a many, and therefore they are not numerable [159d7] ; they are neither like nor unlike [159e2]; same or different [159e3];36 in motion or at rest [160a4]; coming to be or ceasing to be [160e5]; neither greater or lesser or equal [160e6].37 Since there is nothing that both the “one” and the “others” share, “there is no further thing, different from them, in which the same thing the one and the others could be” [159b5-ff]. Furthermore, since what is “truly one” does not have parts, the “others” cannot be in the “one” as a whole or as a part because the “one” admits of no part. “In no way, then, are the others one, nor do they have any oneness in them” [159d1]. If this is the case the “others” cannot participate with the “one,” have a part/whole constitution, or have any numerable or discursive aspect as such. Lacking the unifying power of the “one” what remains is outside recognition because no attribute can be said of the “other” without subjecting it to the delimiting function of an idea or an ordering principle.38 Lacking participation with an “idea,” the “others” are an undifferentiated multiplicity that defies discursive articulation. The “others” would not be such as to be “others” to anything.

43Things that are neither whole nor part, nor in any way participate in a “one” are like the unlimited multitudes or plethe that was considered in hypothesis 3: they are likewise unknowable as such. The conclusions of hypothesis 4, in this way depict the “others” like the thought experiment at 158c. There, the “others” are considered as they would be prior to any participation with the “one.” What remains for both examples would be some multitude that does not admit of discursive articulation and is unknowable as such.

  • 39 I agree with Miller 1986, pp.137-139, who also proposes that hypothesis 4 is a reductio. I disagree (...)

44The conclusion of the thought experiment in hypothesis 3 is similar to the conclusion of hypothesis 4 insofar as they both show that the same absurd results that would follow for the “others” if they lack participation in a unifying “one” or if the “one” would be considered prior to participation. Lacking any participation in the “one” (hypothesis 3 thought experiment) is another way of claiming that the “others” are completely separate from the “one” (hypothesis 4). And because both concluded that the “others” would not be knowable and to this extent not even “others,” both show that they depend on the “one” to be knowable in any way at all. Therefore in order for the “others” to be “others” they require participation in the “idea.” Both arguments can be understood to function as instances of a reductio ad absurdum in favor of participation with a principle.39 And moreover, to argue against a discursive many by insisting on the separation of the “one” would be to argue against what is simply basic about objects of reflection or phenomenal things, a point that Socrates points out to Zeno at 129d-ff.

  • 40 Yet on the other hand, Socrates,” said Parmenides, “if someone, having an eye on all the difficulti (...)

45In conclusion, (1) because of its similarity to the thought experiment, hypothesis 4 can serve as a reductio reinforcing the necessity of the participation that is presented in hypothesis 3, and (2) the discursive nature of the “others” that are made manifest only from participation with the form-like “one” can be extended to the characteristics of “ones” as instances or members of a whole. And if we add to that the view that the “others” could be taken as propaedeutic for a phenomenal many, then the upshot is that such a phenomenal many would be necessarily delimited only by participation in a unifying idea, or what I am calling a cosmological or ordering principle. This view is a preferred reading of hypothesis 3 and 4 because it aligns with Parmenides’ stated task to help Socrates to consider the necessity of forms, for the sake of saving philosophical discourse [135c3].40 And we have seen that the ordering principle or “idea” is responsible for the discursive aspect of all participants, which is an essential lesson for Socrates. Lacking participation in the “one,” the “others” would be an unknowable unlimited plethe that would disallow a thinker to “have anywhere to turn his thought” [135c] and the objects under consideration would not be discursive.

  • 41 See 141e9: Therefore neither is it in such a way as to be one. οὐδαμῶς ἄρα ἔστι τὸ ἕν.
  • 42 See 130e5-135b2. Much has been made of this issue, in particular Vlastos 1954 and the discussion of (...)

46This conclusion raises the specter of taking into consideration the “one that is not” depicted in the first hypothesis. In spite of the self-undermining nature of that depiction (it is concluded that that “one” cannot even be such as to be a “one”),41 that “one” could be understood as a basis for the kind of abstract “one” that would be required for an “idea” or a principle of order. It would lack spatial and temporal being in such a way as to be immune to whole/part distinctions that phenomenal things have in virtue of having limit come to bear upon them. As such, a “one” that lacks being in that way would be immune to the famous dilemma of participation at the center of Parmenides’ challenges to Socrates.42

47Finally, it is also worth noting the possibility that the “one” of the first hypothesis may be knowable only virtually, like the virtual way in which the plethe can be considered in the thought experiment while not being a discursive knowable as such. While it is beyond the scope of this paper to investigate, the “in thought” abstraction that is required to consider an unlimited plethe, could very well be a propaedeutic model for the task of considering the principle as an abstraction that cannot be like the “others” it unifies. Regardless of this hypothetical leap, I hope to have shown that the idea-like “one” in hypothesis 3 should be seen as an ordering or even cosmological principle. This “one” is responsible for the discursive articulation of the “others,” which is the very basic foundation for the “others” to be “others.” And, moreover, that this reading connects young Socrates’ insightful but underdeveloped view of forms relative to the “many” things [129a-ff], with Parmenides’ claim about the necessity of forms for discursive inquiry, and for philosophy in general [135b5-ff].

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Bibliographie

Allen, R.E. (1997). Plato’s Parmenides. Yale University Press, New Haven.

Brisson, L. (2002). “‘Is The World One?’ A New Interpretation of Plato’s Parmenides.” Oxford Studies in Ancient Philosophy. XXII p. 1-20

Burnet, J. (1901). Platonis Opera, Tomus II, Tetralogia III-IV. Oxford University Press, Oxford.

Calogero, G. (1932 [1977 edition]). Studi SullEleatismo, La Nuova Italia, Florence.

Calogero, G. (1974). Plotino, Parmenide e il ParmenideAtti del Convegno Internazionale sul Tema: Plotino e il Neoplatonismo in Oriente e in Occidente. Accademia Nazionale dei Lincei, Rome, 49-59.

Cornford, F. M. (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.

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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.

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Gonzalez, F. (2002). “Dialectic of Forms.” in Welton W. (ed.), Plato’s Forms: Varieties of Interpretation. Lexington books, Maryland, 31-83.

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Peterson, S. (1996). “Plato’s Parmenides: A Principle of Interpretation and Seven Arguments”. Journal of the History of Philosophy, XXXIV No.2 April, 167-192.

Peterson, S. (2003). “New Rounds of Exercise of Plato’s Parmenides”. The Modern Schoolman, LXXX, 245-278.

Priou, A. (2018). Becoming Socrates: Political Philosophy in Plato’s Parmenides. University of Rochester Press, Rochester.

Rickless, S. (2006). Plato’s Forms in Transition. Cambridge University Press, Cambridge.

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, 23:2, 133-150.

Sanday, E. (2015). A Study of Dialectic in Plato’s Parmenides. Northwestern University Press, Evanston.

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Turnbull, R. (1998). The Parmenides and Plato’s Late Philosophy. University of Toronto Press, Toronto.

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Notes

1 This paper was composed on the occasion of the Société d’Etudes Platoniciennes 2018 workshop “Cosmology in Plato’s Parmenides.” Following this theme, this paper engages the idea of cosmology in the broadest terms. It attempts to locate in the Parmenides a notion of order implicit in any cosmology; namely, the possibility of order as the necessary precondition for discursive articulation.

2 See Sophist 237b-ff.

3 I am making the claim that the unintelligible as such is unknowable in its own right, and yet still be referred to in language. To this extent, an object of inquiry can be located as an abstraction while still being unintelligible per se.

4 128e5-ff.

5 Parmenides notes that the manner of the exercises that he offers to Socrates are similar to the structure of Zeno’s work: “‘What manner of exercise is that, Parmenides?” he asked. ‘It is that which you heard from Zeno’ he said.” τίς οὖν τρόπος, φάναι, Παρμενίδη, τῆς γυμνασίας;

οὗτος, εἶπεν, ὅνπερ ἤκουσας Ζήνωνος. [135e1]. All translations from Gill and Ryan 1996 except where emended.

6 For various views on the hypotheses as antinomies, see: Ryle 1939; Cornford 1939; Schofield 1977; Fronterotta 1998. Others have attempted to mitigate the contradictions prevalent in the hypotheses by various means, either by reordering or arranging the arguments with an eye to dissolving aporiai, recently Sayre 1996; 2005, or by distinguishing that the arguments hold different respects that avoid aporia by contradiction most famously by Meinwald 1991; and Peterson 1996; 2006. A more dialogical approach to the hypotheses can be found in Gonzales 2002 and Trabattoni 2016 that begins to contextualize the arguments more broadly. Others like Calogero 1939; 1974, argue that the subject of the hypotheses have an anti-Zenonian irony which deflates the antinomies as such. I argue elsewhere that the subject “one” of the hypotheses initially remains as ambiguous and that the apparent, rather than terminal antinomies, are part of an educational challenge for Socrates and the student of the dialogue to overcome. See: Gardner 2018.

7 See: Sophist 238c-ff. There, the Visitor and Theaetetus consider the possibility of applying number, or even a “one” to something that is not.

8 I do not claim that the “others” are phenomenal things per se, only that the “others” will be understood to reveal, in a nascent manner, the basic parameters that make any “many” comprehensible.

9 A form-like “one” or what I later call an “idea-like one” is a “one” thought of as unifying principle in general. The “one” in hypothesis 3 is not specified as any particular form, and need not be exclusively the ‘One’ itself. It remains open such that one could consider a “one” without the demands of any particular definition of any particular form. In this sense, the “one” in question is a place holder for any form. See section 2.

10 That is, the “others” as the basic category of phenomenal things would require a principle of order by which the “others” are in fact “others.” Such a principle could be considered metaphysical since lacking order, the “others” would not only be unknowable (an epistemic issue) but also the “others” would not be “other.”

11 My view builds upon the arguments of Miller 1986 p.137-139 and Sanday 2015, p153-154 who read hypothesis 4 as a reductio rather than as an antinomy of hypothesis 3. The oppositional structure of the two sets of conclusions is contradictory, however, they need not be seen as merely opposed. I argue that the contradictions can dissolve when the student of the dialogue recognizes the “one” in hypothesis 3 as an organizing principle that prepares the way for considering it as a form-like object of thought. While Sanday argues from the get-go that the “one” and the “others” are forms and participants, I differ slightly, maintaining that the “one” remains crucially ambiguous, particularly in Hypothesis 1 and 2 (Gardner 2018). It is only at hypotheses 3, 157d8 that there is anything like an explicit reference to the form-like aspect of the “one”: ἀλλὰ μιᾶς τινὸς ἰδέας καὶ ἑνός τινος καλοῦμεν ὅλον. Therefore looking at the arguments as they unfold from 137c onwards shows a step by step learning that leads the student to consider the unifying or ordering aspect of a “one” only after the open and ambiguous aspects of the “one” and its correlative “other” have been presented in the first two hypotheses.

12 If someone, having an eye on all the difficulties we have just brought up and others of the same sort, won’t allow that there are forms for things and won’t mark off a form for each one, he won’t have anywhere to turn his thought, since he doesn’t allow that for each thing there is a character that is always the same. In this way he will destroy the possibility of dialectic entirely. But I think you are only too well aware of that.”
“What you say is true,” Socrates said.
“What then will you do about philosophy? Where will you turn, while these difficulties remain unresolved?”
“I don’t think I have anything clearly in view, at least not at present.”
“Socrates, that’s because you are trying to define some beautiful, and just, and good, and each one of the forms, too soon,” he said, “before you have been properly trained.” [Gill 1996 emended].

εἴ γέ τις δή, Σώκρατες, αὖ μὴ ἐάσει εἴδη τῶν ὄντων εἶναι, εἰς πάντα τὰ νυνδὴ καὶ ἄλλα τοιαῦτα ἀποβλέψας, μηδέ τι ὁριεῖται εἶδος ἑνὸς ἑκάστου, οὐδὲ ὅποι 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.
ἀληθῆ λέγεις, φάναι.
τί οὖν ποιήσεις φιλοσοφίας πέρι; πῇ τρέψῃ ἀγνοουμένων τούτων;
οὐ πάνυ μοι δοκῶ καθορᾶν ἔν γε τῷ παρόντι.
πρῲ γάρ, εἰπεῖν, πρὶν γυμνασθῆναι, Σώκρατες, ὁρίζεσθαι ἐπιχειρεῖς καλόν τέ τι καὶ δίκαιον καὶ ἀγαθὸν καὶ ἓν ἕκαστον τῶν εἰδῶν. [135b5-135d6]

13 The destruction of “dialectic” could also be translated as the destruction of the power of discursive articulation, as not to restrict the claim to formal dialectic. καὶ οὕτως τὴν τοῦ διαλέγεσθαι δύναμιν παντάπασι διαφθερεῖ

14 The examination of Parmenides’ challenges to Socrates about forms, including the range and scope of forms [130b1], the problem of the divisibility of a form [130e1], the one over many regress (the so-called ‘third man’) [132a] and the “greatest difficulty” [133c], are beyond the scope of this paper. The scholarship on these challenges is vast, perhaps too vast. For some notable views, see Vlastos 1954, Peterson 1981, Meinwald 1991, Allen 1997, Turnbull 1998, Rickless 2007, and many others. I take the view that the lessons in the hypotheses help disarm the challenges that Socrates does not yet see. The kind of relationship that a principle “one” has that entails the discursive aspects of the phenomenal “many” would have helped Socrates escape the view that the forms are subject to predication in the same way that phenomenal objects are. In learning this, Socrates could employ resources to respond to the regress arguments.

15 Recently Priou 2018 argues that the dialogue helps train Socrates, but he sees this as predominantly a political affair that navigates between pluralism and monism. I argue that the educational program here is minimally intended to help develop Socrates’ notion of forms as they relate to the “many” things.

16 The viability and scope of Plato’s notion of participation is a point of much debate. I argue here that on the basis of the third and forth hypotheses that Plato demonstrates the need for participation: the “others” somehow participate in the “one” while not being the “one.” However, it is beyond the ambition on this paper to analyze the working details of participation as such in the Parmenides.

17 οὐδὲ μὴν στέρεταί γε παντάπασι τοῦ ἑνὸς τἆλλα, ἀλλὰ μετέχει πῃ.
πῇ δή;
ὅτι που τὰ ἄλλα τοῦ ἑνὸς μόρια ἔχοντα ἄλλα ἐστίν: εἰ γὰρ μόρια μὴ ἔχοι, παντελῶς ἂν ἓν εἴη.
ὀρθῶς.
μόρια δέ γε, φαμέν, τούτου ἐστὶν ἂν ὅλον .
φαμὲν γάρ.
ἀλλὰ μὴν τό γε ὅλον ἓν ἐκ πολλῶν ἀνάγκη εἶναι, οὗ ἔσται μόρια τὰ μόρια: ἕκαστον γὰρ τῶν μορίων οὐ πολλῶν μόριον χρὴ εἶναι, ἀλλὰ ὅλου. [157c1-8]

18 εἴ τι πολλῶν μόριον εἴη, ἐν οἷς αὐτὸ εἴη, ἑαυτοῦ τε δήπου μόριον ἔσται, ἐστιν ἀδύνατον, καὶ τῶν ἄλλων δὴ ἑνὸς ἑκάστου, εἴπερ καὶ πάντων. ἑνὸς γὰρ μὴ ὂν μόριον, πλὴν τούτου τῶν ἄλλων ἔσται, καὶ οὕτως ἑνὸς ἑκάστου οὐκ ἔσται μόριον, μὴ ὂν δὲ μόριον ἑκάστου οὐδενὸς τῶν πολλῶν ἔσται. [157c8-d5]

19 ὅτι που τὰ ἄλλα τοῦ ἑνὸς μόρια ἔχοντα ἄλλα ἐστίν: εἰ γὰρ μόρια μὴ ἔχοι, παντελῶς ἂν ἓν εἴη.

20 See Gill 1996, 89.

21 See also Harte 2002, 123-125.

22 Many have argued that the hypotheses take up the form of unity as the subject. For instance, Rickless 2007, 117; Peterson 2003, 250–251; Sayre 1996, 99; Dorter 1994, 47-ff; Allen 1997, 210. It is my contention however that the use of “one” is underdetermined and ambiguous. See also Gill & Ryan 1996, 139 n. 21; Sanday 2015, 81–82; and McCabe 1996, 23–24. The ambiguity of the “one” is particularly evident in the first two hypotheses; it is part of the program of the exercises to come to terms with what the subject under investigation is, and this takes traversing through the whole of the exercises. My view helps make clear that the description of the one as an ‘idea’ is not determined in advance but develops over the course of the work. This is why it is striking and important to see the first explicit reference to a unifying ‘idea’ in Hypothesis 3. Parmenides does claim that he will take up the hypothesis about the “one itself” [περὶ τοῦ ἑνὸς αὐτοῦ ὑποθέμενος] at 137b4, prefacing his display of the exercises, but this statement can be read as “one simpliciter” and it need not render the “one” in the hypotheses as explicitly a form from the get-go. Parmenides means to help Socrates clarify and strengthen his notion of forms by means of gymnastic exercises, so it makes sense that the work done from 137c3-157b6 (Hypotheses 1 and 2) offers only an ambiguous “one” that is set up to be contextualized by the work of the remaining hypotheses.

23 One might object to the idea that the language of forms is not explicitly employed until the third hypotheses because at 149e7-9 Parmenides speaks of the forms of smallness and largeness (εἰ δὲ τὰ μὲν μέγεθος, τὸ δὲ σμικρότητα, καὶ μέγεθος μὲν τὸ ἕν, σμικρότητα δὲ τἆλλα, ὁποτέρῳ μὲν τῷ εἴδει μέγεθος προσείη, μεῖζον ἂν εἴη, δὲ σμικρότης, ἔλαττον;…οὐκοῦν ἐστόν γέ τινε τούτω εἴδη, τό τε μέγεθος καὶ σμικρότης;). However Parmenides is not claiming that the “one” is the form in any explicit way, only that smallness and largeness would bestow their large and small quality to some “one,” rather than that “one” have that quality of itself.

24 The “one” cannot be a form per se exclusively on the basis of the first hypothesis because it is undermined by its own concluding arguments: the “one” neither has any being, nor can it even be “one” [141a-ff]. See Gardner 2018.

25 See Gardner 2018

26 ὧδε ἴδωμεν. ἄλλο τι οὐχ ἓν ὄντα οὐδὲ μετέχοντα τοῦ ἑνὸς τότε, ὅτε μεταλαμβάνει αὐτοῦ, μεταλαμβάνει;
δῆλα δή.
οὐκοῦν πλήθη ὄντα, ἐν οἷς τὸ ἓν οὐκ ἔνι;
πλήθη μέντοι.
τί οὖν; εἰ ἐθέλοιμεν τῇ διανοίᾳ τῶν τοιούτων ἀφελεῖν ὡς οἷοί τέ ἐσμεν ὅτι ὀλίγιστον, οὐκ ἀνάγκη καὶ τὸ ἀφαιρεθὲν ἐκεῖνο, εἴπερ τοῦ ἑνὸς μὴ μετέχοι, πλῆθος εἶναι καὶ οὐχ ἕν;
ἀνάγκη.
οὐκοῦν οὕτως ἀεὶ σκοποῦντες αὐτὴν καθ᾽ αὑτὴν τὴν ἑτέραν φύσιν τοῦ εἴδους ὅσον ἂν αὐτῆς ἀεὶ ὁρῶμεν ἄπειρον ἔσται πλήθει;

27 The thought experiment appears to have two distinct educational aspects for the student of the gymnastic hypotheses. First, it serves to disabuse the trainee that the “others” can be knowable if it could be deprived of the “one.” Second, in having the trainee conceptualize an unlimited multiplicity where any possible part is likewise unlimited in multiplicity, points to the kind of abstract thought that is appropriate for the task of considering what a form would be like if it were to be considered. The “others” taken in thought are not forms as such, however the abstract thought experiment itself reflects the kind of abstraction that would be required to consider a form as an object of conceptual reflection.

28 καὶ μὴν ἐπειδάν γε ἓν ἕκαστον μόριον μόριον γένηται, πέρας ἤδη ἔχει πρὸς ἄλληλα καὶ πρὸς τὸ ὅλον, καὶ τὸ ὅλον πρὸς τὰ μόρια.
κομιδῇ μὲν οὖν.
τοῖς ἄλλοις δὴ τοῦ ἑνὸς συμβαίνει ἐκ μὲν τοῦ ἑνὸς καὶ ἐξ ἑαυτῶν κοινωνησάντων, ὡς ἔοικεν, ἕτερόν τι γίγνεσθαι ἐν ἑαυτοῖς, δὴ πέρας παρέσχε πρὸς ἄλληλα: δ᾽ ἑαυτῶν φύσις καθ᾽ ἑαυτὰ ἀπειρίαν.

29 καὶ ταὐτὰ δὴ καὶ ἕτερα ἀλλήλων, καὶ κινούμενα καὶ ἑστῶτα, καὶ πάντα τὰ ἐναντία πάθη οὐκέτι χαλεπῶς εὑρήσομεν πεπονθότα τἆλλα τοῦ ἑνός, ἐπείπερ καὶ ταῦτα ἐφάνη πεπονθότα.

30 142b-ff. Parmenides revisits the premise “if one is” a second time emphasizing the being of the one, thereby scrutinizing what the one is insofar as it has being: ἆρα οὖν ἄλλο ὅτι οὐσίας μετέχει τὸ ἕν, τοῦτ᾽ ἂν εἴη τὸ λεγόμενον, ἐπειδάν τις συλλήβδην εἴπῃ ὅτι ἓν ἔστιν;
πάνυ γε. [142c5]

31 Thus the one would touch itself and the others.” οὕτω μὲν δὴ ἅπτοιτο ἂν τὸ ἓν αὑτοῦ τε καὶ τῶν ἄλλων. [148e3]; “So the one partakes of time, if in fact it partakes of being” μετέχει μὲν ἄρα χρόνου, εἴπερ καὶ τοῦ εἶναι. [152a2]

32 The ambiguous “one” in the second hypothesis is not, as it where, equal to the “others” in the third hypothesis. Rather, the depiction of the “others” insofar as they are a “many” that admits of predicates in the same way the “one” of the second hypothesis does, allows the student to try and understand how the two depictions are dialectical. They will help develop a model for the characterization of a participant relative to a form.

33 See 142b1-ff

34 ἆρ᾽ οὖν οὐ χωρὶς μὲν τὸ ἓν τῶν ἄλλων, χωρὶς δὲ τἆλλα τοῦ ἑνὸς εἶναι;

35 See: Meinwald 1999, Peterson 1996, Sayre 1996.

36 οὐδ᾽ ἄρα πολλά ἐστι τἆλλα: ἓν γὰρ ἂν ἦν ἕκαστον αὐτῶν μόριον τοῦ ὅλου, εἰ πολλὰ ἦν: νῦν δὲ οὔτε ἓν οὔτε πολλὰ οὔτε ὅλον οὔτε μόριά ἐστι τἆλλα τοῦ ἑνός, ἐπειδὴ αὐτοῦ οὐδαμῇ μετέχει.
ὀρθῶς.
οὐδ᾽ ἄρα δύο οὐδὲ τρία οὔτε αὐτά ἐστι τὰ ἄλλα οὔτε ἔνεστιν ἐν αὐτοῖς, εἴπερ τοῦ ἑνὸς πανταχῇ στέρεται. [159d4-ff]

37 οὐδὲ ὅμοια ἄρα καὶ ἀνόμοια οὔτε αὐτά ἐστι τῷ ἑνὶ τὰ ἄλλα, οὔτε ἔνεστιν ἐν αὐτοῖς ὁμοιότης καὶ ἀνομοιότης: εἰ γὰρ ὅμοια καὶ ἀνόμοια αὐτὰ εἴη ἔχοι ἐν ἑαυτοῖς ὁμοιότητα καὶ ἀνομοιότητα, δύο που εἴδη ἐναντία ἀλλήλοις ἔχοι ἂν ἐν ἑαυτοῖς τὰ ἄλλα τοῦ ἑνός. [160e4-ff]

38 The “others” would hold no attributes and would not even be enumerable: So the others are neither the same nor different, neither in motion nor at rest, neither coming to be nor ceasing to be, neither greater nor less nor equal. Nor do they have any other such properties. For if they submit to having any such property, they will partake of one and two and three and odd and even, of which it was shown they could not partake, since they are in wholly deprived of the one. [160a4-ff]
οὐδ᾽ ἄρα τὰ αὐτὰ οὐδ᾽ ἕτερα, οὐδὲ κινούμενα οὐδὲ ἑστῶτα, οὐδὲ γιγνόμενα οὐδὲ ἀπολλύμενα, οὐδὲ μείζω οὐδὲ ἐλάττω οὐδὲ ἴσα: οὐδὲ ἄλλο οὐδὲν πέπονθε τῶν τοιούτων: εἰ γάρ τι τοιοῦτον πεπονθέναι ὑπομένει τὰ ἄλλα, καὶ ἑνὸς καὶ δυοῖν καὶ τριῶν καὶ περιττοῦ καὶ ἀρτίου μεθέξει, ὧν αὐτοῖς ἀδύνατον ἐφάνη μετέχειν τοῦ ἑνός γε πάντῃ πάντως στερομένοις.

39 I agree with Miller 1986, pp.137-139, who also proposes that hypothesis 4 is a reductio. I disagree with Allen 1997, 320-321 who contends that the hypothesis grants similar results to hypothesis 1, setting up a parallel aporetic situation. Allen relies on the view that the “others” in hypothesis 4 cannot participate in the “one” because they must be radically, separate. However, this view is conditioned upon the view that participation requires spatial and temporal predication with respect to the “one,” which is not warranted. in virtue of the “idea.”

40 Yet on the other hand, Socrates,” said Parmenides, “if someone, having an eye on all the difficulties we have just brought up and others of the same sort, won’t allow that there are forms for things and won’t mark off a form for each one, he won’t have anywhere to turn his thought, since he doesn’t allow that for each thing there is a character that is always the c same. In this way he will destroy the power of dialectic entirely.” ἀλλὰ μέντοι, εἶπεν Παρμενίδης, εἴ γέ τις δή, Σώκρατες, αὖ μὴ ἐάσει εἴδη τῶν ὄντων εἶναι, εἰς πάντα τὰ νυνδὴ καὶ ἄλλα τοιαῦτα ἀποβλέψας, μηδέ τι ὁριεῖται εἶδος ἑνὸς ἑκάστου, οὐδὲ ὅποι τρέψει τὴν διάνοιαν ἕξει, μὴ ἐῶν ἰδέαν τῶν ὄντων ἑκάστου τὴν αὐτὴν ἀεὶ εἶναι, καὶ οὕτως τὴν τοῦ διαλέγεσθαι δύναμιν παντάπασι διαφθερεῖ. [135b5-c3]

41 See 141e9: Therefore neither is it in such a way as to be one. οὐδαμῶς ἄρα ἔστι τὸ ἕν.

42 See 130e5-135b2. Much has been made of this issue, in particular Vlastos 1954 and the discussion of the so-called third Man, and the many responses that have been published. I do not make any claims here about the nature of participation except that on the basis of the hypotheses, Parmenides can be understood to show the necessity of participation in a way that aligns with Socrates’ initial insight into forms in his response to Zeno. This reading proposes that the hypotheses do what Parmenides claims, namely, help Socrates develop his thinking about forms, rather than present insoluble aporias.

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Darren Gardner, « Plato’s Parmenides and The Knowable Many: Cosmos as Discursive Order in Hypothesis 3 »Études platoniciennes [En ligne], 15 | 2019, mis en ligne le 01 mai 2019, consulté le 28 mai 2020. URL : http://journals.openedition.org/etudesplatoniciennes/1626; DOI: https://doi.org/10.4000/etudesplatoniciennes.1626

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