Download - Counting the Hypotheses in Plato’s Parmenides

Ron Polansky and Joe Cimakasky

Counting the Hypotheses inPlato’s Parmenides

Abstract: Parmenides’ exercise assists Socrates who is perplexed about formsand participation. The exercise assumes the one is and is not, and traces con-sequences for the one with respect to itself and the others and for the otherswith respect to themselves and the one. There appear to be eight or ninehypotheses. Counting the third makes all the odd-numbered hypotheses drawneither … nor … conclusions, while the even-numbered draw both … and …conclusions. Odd and even thus link with limit and unlimited principles, so thethird hypothesis on the instant clarifies forms and all beings. We also cast lighton the Presocratic origin of the theory of forms.

Keywords: Plato Parmenides Hypotheses, Participation, Forms, Principles, Ana-xagoras, Plato, Parmenides, hypotheses

Prof. Ron Polansky: Duquesne University, Pittsburgh, Pennsylvania 15282, United States;E-mail: [email protected], Joe Cimakasky: [email protected]

In Plato’s Parmenides, the youthful Socrates boldly counters Zeno’s paradoxi-cal argumentation by introducing the forms and participation. Parmenidesthen subjects Socrates to withering elenctic argumentation. Fortunately, Par-menides is prepared to assist the befuddled Socrates by providing a helpfulexercise. This exercise has Parmenides making the hypothesis that a one isand tracing what follows with respect to itself and with respect to the others.Moreover, he further assumes that the one is not and again determines theconsequences for the one and the others. This might lead to four series of de-ductions, but perhaps surprisingly there turn out to be eight or nine series ofdeductions.1 All commentators comment upon the number of hypotheses. Yetwe believe that we have a rather obvious, though so far as we know, unno-ticed observation to make about the counting of the hypotheses in the second

1 Many commentators, e.g., Cornford 1957, 194; Meinwald 1991, 124–129; Miller 1986, 251n53;Sayre 1996, 240–241; Scolnicov 2003, 134; Turnbull 1998, 112, count eight hypotheses. Allen1983, 261 counts four hypotheses with two deductions each, except for the first hypothesis withthree deductions. The Neoplatonists, e.g., Proclus 1987, 402–403, typically count nine hypoth-eses, with their numbering relating to their theory of emanation.

DOI 10.1515/apeiron-2013-0014 apeiron 2013; 46(3): 229–243

Brought to you by | Michigan State UniversityAuthenticated | 35.8.11.2

Download Date | 9/14/13 11:50 AM

part of this dialogue. This observation, along with our interpretation of thehypothesis on the instant, clarifies the numbering of the hypotheses and theposition of the third hypothesis. By way of this attention to numbering andordering of the hypotheses, we believe that we arrive at a comprehensive inter-pretation of the entire exercise.

The assumption that the one is gives rise to at least four series of deduc-tions rather than merely two. Two deductions develop the consequences forthe one itself, and two further deductions produce the consequences for theothers. And the assumption that the one is not gives rise to four deductions ofconsequences, two with respect to the one itself and two with respect to theothers. Moreover, there is an additional line of deductions that is third in order(155e–157b). Because this deduction seems unlike the others, yet looks to bebringing the first two together somehow, there is disagreement about whetherthere are eight or nine hypotheses (or series of deductions). Most modern com-mentators refer to this third deduction on the instant as an ‘appendix’, ‘coda’,‘auxiliary inquiry’, ‘corollary’, ‘insert hypothesis’, or such, and they may num-ber it 2a.2

Parmenides seems quite aware of the difficulty with the numbering becausethis third set of deductions is in fact the only one that gets explicitly numberedwith an ordinal numeral.3 Parmenides clearly announces that this is his thirdset of deductions: ‘Let’s speak of it yet a third (τϱίτον) time’ (155e4).4 Thus thisdeduction that commentators dispute about counting in relation to the schemeof hypotheses is the only one that Parmenides actually counts. Some commen-tators point out that this is the only deduction explicitly numbered, but we donot find anyone attempting to explain why Parmenides counts only this one.This we clarify and show as a key to the entire exercise.

2 Cornford 1957, 194 argues that the third hypothesis ‘has no claim to the status, which manyassign to it, of a ninth independent Hypothesis. That would destroy the symmetry of the wholeset of Hypotheses.’ We reject Cornford’s view and will show that far from destroying symmetry,counting nine hypotheses enhances the symmetry and clarifies the general structure of the ex-ercise.3 Sayre 1996, 240–241 claims that ‘the deduction that ensues, accordingly, should be under-stood as a further step in a series of inferences already underway, and not as the beginning ofa fresh set of inferences.’ Miller 1986, 251n53 believes: ‘Plato’s reference to the “third time”announces not a new, third hypothesis, but rather, as the Greek proverb has it, a “third timefor the savior,” that is, an insight which will rescue the inquiry by getting beyond the seemingmanifold absurdity of hypotheses I and II.’4 We use the Gill and Ryan translation in Cooper ed. 1997.

230 Ron Polansky and Joe Cimakasky



I Counting the Third Hypothesis

A reason for counting just this third deduction is to call attention to the countand the importance of the position of this deduction, which, as many have re-cognized, is intended somehow to bring the first two hypotheses together, aswell as indicating how the subsequent pairs of hypotheses can be brought to-gether. The first two series of deductions assume that the one is. But the first ofthese immediately urges that the one that is, since it is one, cannot be many inany way (137c4–5). Consequently, the one cannot have any further attributes orplurality, which would make it more than one. Thus the assumption that theone is simply one leads to many neither … nor … conclusions concerning theone, such as that it is neither like nor unlike itself or the others.5 And thereforeit turns out that the one can neither have any being nor even be one(141e9–142a1). In contrast to this result from assuming that a one is, the secondset of deductions allows that the one that is, since it has being, can be manyand have all sorts of attributes. Along this line, there develop both … and …conclusions, such as that the one is both like and unlike itself and the others.Whereas the first hypothesis then results in neither … nor … conclusions, thesecond hypothesis produces both … and … conclusions.

Looking toward the remaining sets of deductions, when we count the thirdas third, we find that the fourth, sixth, and eighth sets lead to both … and …conclusions, while the fifth, seventh, and ninth produce neither … nor … conclu-sions. Hence, through inserting the third hypothesis, Parmenides arranges forall the odd-numbered hypotheses to have neither … nor … conclusions, while allof the even-numbered hypotheses have both … and … conclusions.6 The follow-ing diagram displays how inserting the third hypothesis creates clear order andsymmetry:

Hypothesis ConclusionsOne Neither … Nor …Two Both … And …Three Neither … Nor …Four Both … And …Five Neither … Nor …Six Both … And …

5 These many denials about the one, as denials, should not be supposed to give plurality to it.6 No previous interpreter to our knowledge has recognized that insertion of the third hypothe-sis has the consequence of lining up the odd-numbered hypotheses as neither … nor … and theeven-numbered hypotheses as both … and … deductions. Of course interpreters have not thenattempted to explain this. We need not raise the issue whether ‘one’ is in fact a number for theancients since what we go on to say accords with viewing ‘one’ as the principle of number.

Counting the Hypotheses in Plato’s Parmenides 231



Seven Neither … Nor …Eight Both … And …Nine Neither … Nor …

What might be the significance of this arrangement of odd- and even-numberedhypotheses?

II The Function of the Third Hypothesis

The first hypothesis of a one with no manyness leads to neither… nor… conclu-sions such that it is not even one. This initial deduction responds to Socrates’supposition in the first part of the dialogue that each form is merely the oneform that it is. Socrates there insists that he will wonder exceedingly if it can beshown that the forms themselves admit opposites and mix with each other (see129c–e). The first deduction of the exercise provided by Parmenides discloses toSocrates how problematic it is to keep his principles, the forms, from havingany association with each other. Viewing any form as solely one with no many-ness about it whatsoever prevents it from even being what it is. Socrates wastherefore mistaken in trying to have each form be an isolated island unto itself.Forms, to be what they are, must be in some association with other forms. Forexample, each form must be the same as itself and other than all other forms.Thus in order for a given form to be the same as itself it must participate insameness, while being different from other forms requires it to share in other-ness. Evidently, contrary to Socrates’ supposition, the forms must associate witheach other.

It should be the case, then, that understanding the way perceptible thingsparticipate in the forms necessitates an understanding of the way the forms, asthe principles of perceptible things, participate in each other. Consideration ofparticipation has to be raised up to the level of the forms themselves. Subse-quently, the second hypothesis of the exercise with the both … and … conclu-sions shows how any one form may participate in all sorts of other forms. Surelyall these both … and … conclusions are as dizzying, however, as the neither …nor … conclusions of the first hypothesis. Can the third hypothesis offer clarifi-cation?

The discussion of the third hypothesis about how to speak of the one beginsthis way:

Let’s speak of it yet a third time. If the one is as we have described it (οἷον διελ-ηλύθαμεν) – being both one and many and neither one nor many, and partaking of time(ἕν τε ὂν καὶ πολλὰ καὶ μήτε ἓν μήτε πολλὰ καὶ μετέχον χϱόνου) – must it not, because




it is one, sometimes partake of being, and in turn because it is not, sometimes not partakeof being? (ὅτι μὲν ἔστιν ἕν, οὐσίας μετέχειν ποτέ, ὅτι δ᾿ οὐκ ἔστι, μὴ μετέχειν αὖ ποτεοὐσίας; 155e4–8)

This summarizes the results of the first two series of deductions: the one is bothone and many, and the one is neither one nor many, and it is temporal. Parme-nides rather strangely adds ‘partaking of time’, but he leaves out that the onethat is neither one nor many, i.e., the one of the first hypothesis, lacks any tem-porality or relation to time at all (see 141d–e). By leaving this out he may makeit seem that participation in temporality explains how the one both partakes ofbeing and does not partake of being, or both is one and is not one. Accordingly,he says that because it is one, it sometimes (ποτε) partakes of being, and be-cause it is not [one], it sometimes does not partake of being, as if there is atemporal shift from the one condition to the other, occasioning no violation ofthe principle of non-contradiction. But this can hardly be taken straightfor-wardly if the one of the first hypothesis never has anything to do with time.

We propose alternatively that when Parmenides here says ‘sometimes’, hereally refers to just those times when he and his interlocutor Aristotle werespeaking of the one. Sometimes they were saying that the one partakes of being,and sometimes they were saying that it does not partake of being. Consequentlythe phrase οἷον διεληλύθαμεν, ‘as we have described it’ (in 155e4–5) harmo-nizes with this interpretation insofar as it refers to the different times when theywere saying one thing or the other about the one.7

If our interpretation regarding ‘sometimes’ is correct, what Parmenides saysin the third deduction does not have to do with a shift in the one itself but intheir reflections upon the one. Of course once Parmenides puts it this way, andAristotle makes no complaints or raises no queries, Parmenides can shift moreand more to the view that it is the one itself that is undergoing these changes.But the shifts have in actuality rather been in their accounts of the one becausethe one allows for such shifting perspectives.

Thus Parmenides is initially talking about the way they have been speakingabout the one: he is really saying that when they were saying that the one is,then surely it must partake of being, and when they were saying that it is not, itwas not partaking of being. He goes on to get agreement that when the oneparticipates in being – or when they were saying that it participates – it is un-able not to; and when it does not participate in being – or when they were say-ing that it does not participate – it cannot participate in it (155e8–10). Therethen seem to be different times, a time when the one participates in being and

7 We have not found this interpretation in the literature.




another when it does not (155e10–11). In fact this is most plausibly read as wesuggest such that Parmenides has the different times be the different times inwhich they were making the two different deductions.

Parmenides subsequently inquires,

Isn’t there, then, a definite time when it gets a share of being (μεταλαμβάνει τοῦ εἶναι)and when it parts from it (ἀπαλλάττεται)? Or how can it at one time have and at anothertime not have the same thing, if it never gets and releases it? – In no way. – Don’t youin fact call getting a share of being ‘coming-to-be’ (τὸ δὴ οὐσίας μεταλαμβάνειν ἆϱά γεοὐ γίγνεσθαι καλεῖς)? – I do. – And parting from being ‘ceasing-to-be’ (ἀπόλλυσθαι)? –Most certainly. – Indeed the one, as it seems, when it gets and releases being, comes tobe and ceases to be. (156a1–b1)

If we are right that Parmenides should really be speaking about the way theyspoke differently of the one at different times, then we may wonder whether theone’s getting or losing a share of being has to do with its coming into being orceasing to be. But perhaps either Parmenides comments generally here aboutwhat occurs in time, or Aristotle usefully misunderstands what he says. What-ever the case, the one seems able not only to be and not to be, but also there-fore to become and to perish. It surely appears that the becoming and ceasingto be of the one is its change to being and not being respectively, i.e., it goesbetween the one of the first and second hypotheses. Yet Parmenides quicklyrevises our thinking about this, which might not be so surprising if we recognizethat he has actually been referring to how they were speaking of the one ratherthan primarily of the one itself. The change in the one does not occur betweenthe two deductions but just within the one of the second hypothesis that allowsfor opposed attributes.

We can here observe Parmenides helpfully having the change take placewithin the opposed attributes within the second deduction:

And since it is one and many and comes to be and ceases to be, doesn’t its being manycease to be whenever it comes to be one, and doesn’t its being one cease to be wheneverit comes to be many? – Certainly. – Whenever it comes to be one and many, must it notseparate and combine? – It certainly must. – Furthermore, whenever it comes to be likeand unlike, must it not be made like and unlike? – Yes. – And whenever it comes to begreater and less and equal, must it not increase and decrease and be made equal?(156b1–8)

The envisioned change is between one and many, like and unlike, greater andlesser and equal, that is, attributes that pertain exclusively to the one of thesecond hypothesis. Hence, the change is merely within the one of this secondhypothesis. Moreover, he adds that the way the one comes to be one from manyand many from one, i.e., the way the one ceases to be and comes to be, isthrough separating and combining (διακϱίνεσθαί τε καὶ συγκϱίνεσθαι). And




when it becomes like or unlike this is through likening or unlikening(ὁμοιοῦσθαί τε καὶ ἀνομοιοῦσθαι). Whenever greater and lesser and equal, itseems to grow and to diminish and to equalize (αὐξάνεσθαί τε καὶ ϕθίνειν καὶἰσοῦσθαι). Thus the changes are within the both … and … determinations of thesecond deduction. Parmenides suggests that the opposites arise only by chan-ging between them, and he spells out the various sorts of motion or change.

This appeal to change may appear strange and unnecessary because the co-presence of opposites in the second hypothesis occurred when the one waslooked at from different perspectives not requiring any real contradiction. Theone could be one and many, like and unlike, and so on in various respects atone and the same time. Yet now Parmenides supposes that there is changegoing on between the opposite determinations, so that the one never seems atthe same time to have opposed attributes. Whereas it initially might have ap-peared that they were going to have motion back and forth from the first to thesecond hypotheses, as the one was in these conditions at different times – in factas we have been suggesting at different times in their discussion of the hypoth-eses –, the motion now is all within the determinations of the second hypoth-esis. Again the different conflicting things they said about the one of the secondhypothesis were at somewhat different times. How, then, is there any synthesiswith the first hypothesis? And why is the motion solely within the second?

So far Parmenides has considered change between being and not being,one and many, like and unlike, greater and lesser and equal. Now he cruciallytakes up the most unusual change, the shift between motion itself and rest itself(156c1). He states,

And whenever, being in motion, it comes to a rest, and whenever, being at rest, itchanges to moving, it must itself, presumably, be in no time at all (ὅταν δὲ κινούμενόντε ἵστηται καὶ ὅταν ἑστὸς ἐπὶ τὸ κινεῖσθαι μεταβάλλῃ, δεῖ δήπου αὐτό γε μηδ᾿ ἐν ἑνὶχϱόνῳ). – How is that? – It won’t be able to undergo being previously at rest and laterin motion or being previously in motion and later at rest without changing (μετ-αβάλλειν). – Obviously not. – Yet there is no time in which something can, simultane-ously, be neither in motion nor at rest (χρόνος δέ γε οὐδεὶς ἔστιν, ἐν ᾧ τι οἷόν τε ἅμαμήτε κινεῖσθαι μήτε ἑστάναι). – Yes, you’re quite right. – Yet surely it also doesn’tchange without changing. – Hardly. – So when does it change? For it does not changewhile it is at rest or in motion, or while it is in time. – Yes, you’re quite right. – Is there,then, this queer thing (τὸ ἄτοπον τοῦτο) in which it might be, just when it changes? –What queer thing? – The instant. (τὸ ἐξαίϕνης, 156c1–d3)

These are extraordinary lines. Parmenides has been speaking about the timeduring which the one comes to have and to lose one or another of its oppositeattributes. But he now turns to coming to be in motion and to be at rest, i.e., thechange from one of these to the other. There seems to be no time left for such a




change or transition. That which is in time in the sense of taking time and hav-ing duration must be either at rest or in motion. Yet when something changesfrom motion to rest or rest to motion, it is neither at rest nor in motion, andhence not in time as having duration. So Parmenides says, ‘there is no time inwhich something can, simultaneously, be neither in motion nor at rest’. Onlysomething outside time could be neither at rest nor in motion. We should not besurprised that eternal beings can be neither at rest nor in motion, yet even assensible beings change from one of these to the other, the moment of transitionis not extended in time.

The way neither in motion nor at rest is used here for what is occurring inthe instant can definitely refer to the one of the first deduction, which was apartfrom time. The ‘change’ or transition between the conditions of motion and restcannot just be an ordinary change.8 This is a transition unlike the basic sorts ofchange, e.g., locomotion or alteration, because this transition must occur out-side time, for during this transition the one is neither at rest nor in motion (andwe recall that what is not in time has no being [141e]).

The ‘change’ or transition from motion to rest or vice versa occurs in theinstant (τὸ ἐξαίϕνης). In the instant the one is neither at rest nor in motion, andnot in time. In the instant the one can be neither at rest nor in motion, but alsoit will be neither being nor not being, neither one nor many, neither like norunlike, and so on. The one in the instant thus matches perfectly the one in thefirst hypothesis, with all its neither … nor … conclusions. If the one in the instantis the one of the first hypothesis, what can be at rest and in motion and have allthe opposite determinations previously mentioned: one and many, like and un-like, greater, lesser, and equal? The one of the second hypothesis should beviewed as having the collection of opposed determinations due to its rest andmotion, i.e., it rests in opposite determinations and is in motion between them.But as it transitions to motion or to rest regarding any of these, it could not yetbe in motion or at rest (156d3–e3). The instant is the strange crossroads lyingbetween motion and rest, not taking time, and the one that changes from rest tomotion or from motion to rest enters into and leaves from this (156e3–7). Duringthe instant the one is neither … nor …, i.e., the one then neither is nor is not norcomes to be nor is perishing. Yet, when the one enters into rest or motion, theone has the various opposing determinations, and hence in a way is both …and… with regard to every one of them.

In line with what we have said about the one in the instant lacking any andall determinations, Parmenides announces,

8 As Aristotle argues in Physics VI 5–6, there is no beginning or change to change.




Indeed, according to the same argument, when it goes from one to many and from manyto one, it is neither one nor many, and neither separates nor combines. And when itgoes from like to unlike and from unlike to like, it is neither like nor unlike, nor is itbeing made like or unlike. And when it goes from small to large and to equal and viceversa, it is neither small nor large nor equal; nor would it be increasing or decreasing orbeing made equal. (157a4–b3)

Parmenides is denying that in the instant the one has any of the determinatefeatures that they deduced, but leaving from the instant the one can take onany of these. This permits the one as it transitions from rest to motion or viceversa to take on all the opposite determinations of the one of the second deduc-tion. Parmenides thus discloses that during the instant, when the one isneither… nor …, it is in precisely the condition of the one of the first hypothesis,while going from this instant it takes on the opposing attributes of the secondhypothesis. The instant, or the one of the first hypothesis, is just the neither …nor … condition needed so that there can be the both … and … determinations ofthe second hypothesis. To the extent that the one is ‘changing’ between op-posed determinations, i.e., participating in various forms, it must keep enteringthe instant during which it is none of them and not in any time. In fact the onemust always be in the instant, and so unchangingly outside time, and yet al-ways be associated with many other forms.

The third hypothesis shows how the first and second hypotheses combineby virtue of the instant. It clarifies and resolves the perplexities of the first twohypotheses and discloses how the remaining hypotheses are also in pairs andsimilarly combined through the instant. But how should we understand this sortof combination of the pairs of hypotheses?

III An Outline of the Exercise

As we have explained, the first hypothesis about the one that is just one, andconsequently not even one because it is just one, initially has the critical func-tion of exploding Socrates’ assumption about the forms, i.e., that each singleform F-ness solely is F. This leads to the one of the second deduction with allits both … and … oppositions due to the need for the one to have being. The firsthypothesis therefore has the negative role of turning youthful Socrates from iso-lated forms having no association with other forms. Thus the first deductionleads into the determinations of the second hypothesis since without them wefall back into the first hypothesis. But then we should further understand, bythe illumination of the third hypothesis, an additional vital constructive role forthe one of the first hypothesis. The first two hypotheses must be combined, or




more precisely the first is within the second. The opposing determinations ofthe second hypothesis are possible of an eternal being because the instant, i.e.,the one of the first hypothesis, stands between all the conflicting determina-tions. As the third hypothesis clarifies, the first hypothesis is a constant ele-ment, component, or delimiter of the second. We should not really count two inany ordinary way.

We might wonder why the first is really needed since the co-presence ofopposites in the second is not actually contradictory insofar as there are differ-ent respects in which the conflicting opposites are participated in simulta-neously. And why is the one, if possibly a form, really in motion and in time atall? The forms are presumably timeless, eternal beings. As outside time theremust be a sense in which the forms are always neither … nor … while also al-ways being both … and …, since in order to be at all the form must associatewith other forms. Any form as a form, then, is always in the instant, i.e., eternaland outside time, while also having participation in opposing determinations.

Stated in another way, the instant or the one of the first hypothesis is somesort of principle of any being whatsoever, whether a form, a perceptible being,or any other kind of being. It is a principle as a ‘limit’ principle. As a limit prin-ciple, the one of the first hypothesis does not itself have limits or any of theother determinations, but it is a most strange unity with no plurality. Hence,while they are rejecting Socrates’ conception of isolated forms by going throughthe first hypothesis, they are also acknowledging that Socrates has correctly dis-cerned an element or principle of the understanding of forms, and any otherbeings, i.e., sheer unity as a limit principle that is only in the surprising mannerof the instant.

What goes along with a limit principle would be an unlimited principle.9

On our interpretation, the one of the second hypothesis with all its both …and… determinations is not itself the unlimited principle. Instead the secondhypothesis introduces the principle of unlimitedness, but because the third hy-pothesis reveals how the second hypothesis already combines with the first hy-pothesis through having the instant always within itself, the one of the secondhypothesis depicts the being of any form or any other being, which is a productor combination of limit and unlimitedness. The subsequent hypothesis that justdepicts the unlimited principle, as it is with no unity or limit involved with it atall, is the eighth hypothesis on our counting. This is the hypothesis from164b–165e, where the others are amorphous masses, other than the others, thatmerely appear to have any determinations at all.

9 Our account fits with Aristotle’s in Metaphysics I 6 that Plato is close to the contemporaryPythagoreans.




On our interpretation, then, while the odd-numbered hypotheses are thelimit principle, the even-numbered either are or include the unlimited principle.Of course the third hypothesis discloses the way the principles of limit and un-limitedness combine and separate, and allow for the one of the first hypothesisto perform as limit principle ‘in’ any being. The one of the third hypothesis, orthe corresponding limit principle, plays this role for all the pairs of hypoth-eses.10

IV Forms in the Exercise

Our understanding of the hypotheses clarifies the forms as paradigms and prin-ciples of perceptible beings. Parmenides has shown that no change occurs inthe now (152b). The ‘now’ is in time and a limit of time. The ‘now’ is the sensibleanalogue to the ‘instant’, which is not in time at all. Sensible beings are alwaysin the ‘now’ and also changing, i.e., they have the possibility of rest and mo-tion. Consequently, they imitate the paradigm forms. The instant is a nature thatthought posits to account for the transition from motion to rest and vice versa,or really for the forms to have being through associating with each other. Theone in the instant has the features of the deductions of the first hypothesis, thisone of the first hypothesis being a fundamental principle of all beings. Any formin its association with other forms keeps entering and leaving the instant. Toparticipate in other forms, it in a manner of speaking goes outside itself to an-other, and thus it ‘changes’ or undergoes a sort of transition from the one of thefirst to the second hypothesis, only not at different times but eternally. Change-able perceptible things take time while doing their version of this, i.e., becom-ing other, and they thus offer, in the words of Timaeus 37d5, ‘a moving imageof eternity’. The becoming of perceptible things thereby imitates the being of theforms.

Insofar as a form participates in other forms, it may be said to change, iffiguratively, since it does not take time. They ‘change’ or are in ‘motion’ inas-much as participating in another form is somehow to have being in another orto go out to another. When any form participates in the same, the other, being,the one, the like, the unlike, and so on, it is somehow in itself while going out

10 With respect to the role of the third hypothesis in combining the subsequent pairs of hy-potheses, Meinwald 1991, 124 rightly states ‘Having already provided the arguments that showwhat conclusions about becoming, perishing, and change follow for anything that is “such aswe have said,” Plato relies on us to realize that they can be applied again at various points inthe succeeding arguments.’




of itself. Any such association of forms requires in a way being in another,which figuratively introduces ‘motion’ to another, which serves as the basis orparadigm for change among sensible things.

To put this in still another way, any form must be itself and also be all sortsof other things. The form F is essentially the F, and it is a being, one, same,other, like, unlike, and so on. The one of the second hypothesis both is what itis in virtue of itself and is what it is with respect to the others. The instant hasto do with how any being can be itself essentially while yet being able to bewith respect to the others as well. The instant is needed for self-preservation,preservation of self and other. The instant, i.e., the one of the first hypothesis,is the limit preserving self and other. It itself is limitless, as it is the limit princi-ple, but as limit it keeps all else in order. It keeps any form associated with therest of being while also having the form hold its own peculiar being. The one,as the instant outside time and with no plurality, is not nothing, though it hasno being and is in a way beyond being, as the principle of all being.

Each form has its own structure or ‘shape’, i.e., how it connects with spe-cies and genera pertaining to what it is; it also connects with the structure of allbeing, i.e., same, other, like, unlike, etc., so that it participates in many otherforms (see the discussion of ‘shape’ in 145a–b). Motion itself, as itself, has apeculiar structure or essence, since there are various sorts of motions (see156b1–8), but as a being, it shares in being, one, same, other, like, unlike, mo-tion, rest, and so on. It should be the case, then, that ‘self-predication’ is una-voidable for fundamental forms, e.g., being itself must be, the one itself is one,the same itself is the same as itself, the other itself is other than others, andmotion itself is at least figuratively in motion, though other forms do not soinescapably, straightforwardly self-predicate: the large itself is not a very largething.

For each form to be itself, it must somehow be separate from the otherforms, yet nonetheless as any being it must participate in many of the otherforms. The combination of the first two series of deductions thus gives somecredit to young Socrates’ opening position regarding the forms. There must be amanner in which any form is separate from the others while also participatingin many of them. Socrates thought of the one simply, and as mistaken as thiswas in the way he supposed the forms merely absolute unities, this type ofunity does turn out to be a principle for the full understanding of the one itself.In the eternal ‘instant’ the form participates in nothing (or nothing other thanitself) – this is one aspect or moment of itself – but it also thereby enables aform to participate in the other forms and to be itself. Since this is the nature ofthe forms, it also seems the case for all other beings as well, i.e., including allthe things that become. They are separate from each other, are each of them




themselves, and yet they also share in the general structure of being (and sohave multiple connections).

Have Parmenides and Plato here appropriated not only Pythagorean con-ceptions of limit and unlimited principles, but also some of Anaxagoras’ under-standing of principles? For Anaxagoras Mind is alone by itself and not mixedwith anything else (see DK 59B12). That the listeners to the dialogue are fromClazomenae (126a) perhaps calls up Anaxagoras (cf. Miller 1986, 25–28), andSocrates has suggested that participation might be thought (132b3–c12). Anaxa-goras’ Mind as cause of all is pure, simple, and unmixed, which resembles theinstant and the one of the first hypothesis. Has Parmenides not worked out amore appropriate account of Anaxagoras’ Mind in the first hypothesis as thelimit principle involved in any form and in any being whatsoever? And the sec-ond hypothesis, with its both … and … determinations, is Parmenides’ revisionof Anaxagoras’ ‘everything in everything’. ‘Mind’ or limit principle is what com-bines and separates all that must be mixed. So Plato manages to have his Par-menides put together the Ionian and Italian traditions in a truly comprehensiveview.11

V Conclusion

We see that the count of the hypotheses requires the third to be third so that allthe limit principles turn out to be odd-numbered hypotheses, including thethird hypothesis itself that is another way of looking at the first hypothesis. Theeven-numbered, we have recognized, need not simply be the unlimited princi-ple, though it is in the case of the eighth, while the others involve the unlimitedprinciple. Because the third hypothesis about the instant has clarified the waythe first hypothesis is always contained within the second hypothesis, weshould appreciate that the second hypothesis cannot be separate from the first.Our explanation of the first two hypotheses has the first hypothesis as the sim-ple one, but the second hypothesis is not merely the other, i.e., the unlimited,since the third hypothesis discloses the way the second has the instant and limitprinciple already within it. The second hypothesis obscurely enunciates whatthe third hypothesis confirms. Parmenides thus does not initially separate theprinciples completely and offer the pure limit and unlimited principles, but heoffers the pure limit principle and the combination of limit and unlimitedness

11 Similarly, Aristotle offers an updating of Anaxagoras in Metaphysics 989a30–b2, perhapsinspired by his reading of Plato’s Parmenides.




in the second hypothesis. By having the neither … nor … and both … and … hy-potheses juxtaposed as he does, he puts our thought in motion rather like theforms are in ‘motion’, so that we (and Socrates) are driven to seek a more com-plex, if inevitably partial, understanding of the forms. We must struggle to un-derstand how the first two hypotheses put together somehow deliver to us theone itself, any one form, or any one being. Setting out the hypotheses this waywith the instant as third, we may better appreciate how being involves partici-pation and ‘rest’ and ‘motion’ of the forms.

The counting of the third hypothesis is therefore necessary to get the oddand even hypotheses working out properly. But this third hypothesis is the onlyone counted, and since it in fact turns out to be just the first hypothesis, itmight not really count at all. It is as if we need the third to set the remaininghypotheses in their proper slots, but then the third might be dropped and notcounted, and only the others should be counted. Yet Parmenides has countednone of these others. And as we have shown, the first hypothesis is always con-tained in the second, and similar relationships pertain to the remaining pairs ofhypotheses, so that the count of all the hypotheses arguably reduces to one. Allthe hypotheses fit together to provide a unified account of the one itself, anyone form, and any one being both in relation to itself and to the others. Conse-quently, it looks appropriate that Parmenides does not do any counting of thehypotheses other than the third. Our recognition of the significance of the countregarding this hypothesis leaves us appreciating that we must go beyond count-ing the hypotheses to understand the exercise, though counting is a vital step.

Bibliography

Cooper, John M. ed. 1997. Plato: Complete Works. Indianapolis: Hackett.Cornford, Francis M. 1957. Plato and Parmenides. New York: Bobbs-Merrill.Gill, Mary Louise and Paul Ryan. 1996. Plato Parmenides. Indianapolis: Hackett.Hermann, Arnold. 2010. Plato’s Parmenides. Las Vegas: Parmenides Publishing.Little, Edward F. 2002. Two Essays on the Origins of Metaphysics. Lincoln: Writers Club Press.Lynch, William F. 1959. An Approach to the Metaphysics of Plato. New York: Georgetown Uni-

versity Press.Meinwald, Constance C. 1991. Plato’s Parmenides. Oxford: Oxford University Press.Miller, Mitchell H. 1986. Plato’s Parmenides: The Conversion of the Soul. Princeton: Princeton

University Press.Proclus. 1987. Commentary on Plato’s Parmenides. Translated by Glenn R. Morrow and John

M. Dillon. Princeton: Princeton University Press.Sayre, Kenneth M. 1996. Parmenides’ Lesson: Translation and Explication of Plato’s Parme-

nides. Notre Dame, Indiana: University of Notre Dame Press.




Scolnicov, Samuel. 2003. Plato’s Parmenides. Berkeley and Los Angeles, California: Universityof California Press.

Silverman, Allan. 2002. The Dialectic of Essence: A Study of Plato’s Metaphysics. Princeton:Princeton University Press.

Sternfeld, Robert and Zyskind, Harold. 1987. Meaning, Relation, and Existence in Plato’s Par-menides. New York, New York: Peter Lang.

Turnbull, Robert G. 1998. The Parmenides and Plato’s Late Philosophy. Toronto: University ofToronto Press.




Download - Counting the Hypotheses in Plato’s Parmenides

Top Related