In parmenidem parvi comentarii.

March 22, 2004

"Surely the greatest artistic achievement [Kunstwerk] of the ancient dialectics." This is how

Hegel, in a famous passage at the end of his "Preface" to the Phenomenology of Spirit,

describes Plato's Parmenides. "A curious vanguard" of psychoanalysis is how Lacan

describes the same dialogue. What in this arid-looking, bizarre, and proverbially difficult

text can give support for such judgments? For our present purpose, why can this "work of

art" be seen as relevant, and even crucial, for psychoanalytic theory? And can

psychoanalysis shed any new light on this text, which has been heavily commented on for

2,500 years, giving occasion to a proverbial delirium of interpretations, hardly matched by

any other?

Lacan, in his seminar "... ou pire" of 1971-72, spent much time embroidering on the axiom

"There is One" (Y a de l'Un). In the brief summary (first published in Scilicet in 1975), he

says:

Anyway, I was not occupied by the thought of One [pensee de l'Un],

but, taking the dictum that 'there is One' as the starting point, I

pursued it according to the terms of its usage in order to make

psycho-analysis with it. This is already present in Parmenides, i.e.

Plato's dialogue, by a curious vanguard [par une curieuse avant-

garde]. I proposed this reading to my audience, but have they read it?

(Lacan 2001: 547) (1)

The Parmenides, which dates to 370-367 B.C.E., is part of Plato's Middle Period (if we are to

follow the standard periodization), together with Theaetetus, Sophist, and Republic.

According to Plato's own textual hints, (2) the dialogue is the first in this series, and the

others would have to be seen as its follow-ups (a point I will come back to). The Parmenides'

notoriety springs from two sharply opposite reactions to it. On the one hand, it was

extensively used by the Neoplatonics, who treated it as a mythical sacred text, as it were, as

a paragon of philosophical and theological depth and perfection, the disclosure of divine

essence by a series of subsequent emanations--what Hegel calls "this misunderstood

ecstasy" (44), and Lacan "the Neoplatonic confusion" (2000: 547). On the other hand, the

text is so odd and bizarre that it has frequently produced the very opposite effect--not the

mythical ecstasy, but an unease, a consternation, a disbelief, which occasionally takes the

form of a serious doubt as to its authenticity. Ueberweg, the great German nineteenth-

century authority on the history of philosophy (his history was widely used as a textbook for

almost a century), thought that this curiosity (monstrosity?) could not possibly have come

from Plato's own hand, and many followed his opinion. (The dialogue's authenticity is now

universally accepted.) Others speculated, less radically, that the two parts of the dialogue

could not have been written together, or that there must be a missing third part that could

put things in order and make sense of the whole.

Such philological speculations have been driven by something like an anxiety in face of the

dialogue's aberrant nature. There are two principal sources of this perplexity, distributed

between the two parts of the dialogue:

1. How could Plato, in the first part of the Parmenides, have written what seems like a

radical criticism of his own theory of ideas, and thus have anticipated the bulk of Aristotle's

later objections? Plato would seem to have been a better critic of himself than all his

subsequent critics, since he was able to beat them to it, to outwit them in advance, to outrun

them. What sense can be assigned to this self-criticism, if this is what it is? (3)

2. And why does Plato, in the second part, engage in a logical exercise that, apparently, lacks

the point, or does not provide anything remotely resembling a satisfactory answer?

Furthermore, this part does not really furnish an answer to the harsh criticism of the first

part, nor does it deliver a clue, or a clear solution, to what appear to be insurmountable

difficulties (or does it?). And how are we to understand the conclusion, which is almost

unlike anything in the history of philosophy--the hardly ever matched point of paradox, or

nonsense?

"Let us then say this [if one is not, then nothing is]--and also that,

as it seems, whether one is or is not, it and the others both are and

are not, and both appear and do not appear all things in all ways,

both in relation to themselves and in relation to each other." "Very

true." (Prm. 166c) (4)

Is this a conclusion? The ending of one of Plato's dialogues? Is Plato pulling our leg? Can

one continue from here? Is the conclusion to be taken seriously, as a declaration of

philosophical faith? Does this not rather sound very much like a paramount example of

sophist extravagance, as the very epitome of the kind of philosophy that Plato spent his

whole lifetime fighting? To sum up, Plato would thus appear to be both a greater

Aristotelian than Aristotle, and a greater sophist than the Sophists.

The beginning, as always with Plato, is a very strange place to start. The dialogue opens with

an intricate web of displacements: Cephalus brings his friends, philosophers from

Clazomenae, to Athens, where they run into Adeimantus and Glaucon (Plato's brothers).

Through Adeimantus they try to get to Antiphon, his maternal half-brother, who is a great

friend of Pythodorus, who in turn was the witness, in his youth, of the great discussion

between Socrates, Zeno, and Parmenides, and who committed this exchange fully to his

memory. Antiphon, to whom Pythodorus related the whole story, likewise memorized it,

and now Cephalus and his friends would like to hear it from him. Thus, in the beginning

there is hearsay. The discourse had to traverse the distance of time and space, the web of

mediations and transmissions, from mouth to mouth, from memory to memory, from

generation to generation, in order to wind up with Plato, who is merely the transcriber, the

man who keeps the minutes. The initial great event becomes initial, great, and event by the

retroactive web of transmission that produces it as the source and the treasure. Plato is but

the last link in this chain, merely the faithful chronicler, the addressee to whom the long-

sent letter has finally arrived and who is but remailing it for us. Plato is the bearer who is

not writing in his own name but has taken the risk to break the spell, to translate the ideality

of the inscription into memory, and the circulation by the word of mouth, into the

materiality of the letter (and thus to destroy it?)--a step that Socrates never risked or was

brave enough to avoid. The letter is sustained by the previous history of voice and memory,

and would lose its substance and consistency without this prehistory. One cannot simply

start with the letter, for it has to rely on the mythical trace of the voice as its inner part, a

trace that endows the letter with authority and roots it in an impossible presence. (5)

Plato's diegetical hints lead us to believe that the dialogue supposedly took place c. 450

B.C.E., that is, some eighty years before being written down; however, all interpreters for

once unanimously agree that the encounter is fictitious (indeed Plato's strange device of the

triple framing of his narration may well be read as a hint that he is presenting us with a

fiction). The cast appears to be a rather fantastic condensation of the ancient Greek

philosophy, its dream team: not only do the Presocratics (Parmenides and Zeno) meet

Socrates, not yet knowing that they are Presocratic and that this will be their historic fate,

but we also have an Aristotle, a young lad who acts as the sparring partner in the logical

exercise with Parmenides and who is being chosen for that role on the basis of his youth and

inexperience. (6) The story goes that Aristotle (the "real" one) was so offended by the use of

his name in this dialogue that he never mentioned this dialogue in his entire corpus (though

one can find some textual parallels, as Dies has shown, to say nothing about the extensive

use of Plato's own arguments against the theory of ideas). But this mythical text has always

been surrounded by a host of legends.

As if the labyrinth of displacements of an absent origin is not enough, the dialogue itself

starts off with an absent text, a non-lieu, as it were. Zeno has just finished reading his paper

on multitude, and we can only surmise its content on the basis of Socrates' objections. Zeno

argued, roughly, that multitude does not exist, despite the appearance to the contrary, for if

it existed, it would be contradictory, at one and the same time identical and nonidentical to

itself, etc. Zeno seems to have argued for the fundamental Eleatic thesis about the existence

of One, and he did so a contrario, that is, by demonstrating the absurdity of the hypothesis

to the contrary. If the thesis about Oneness is often reproached as being contradictory, then

the opposite hypothesis is even more so.

Socrates' objection to this argument outlines and condenses the basic problem: the doubling

of the order of ideas and the multiplicity of things. Socrates suggests that contradictions can

supposedly disappear with a compromise; for example, he is in certain respects multiple,

since one can discern his multiple qualities, while at the same time he is numerically one

(otherwise the audience would be a company not of seven but of six). The contradiction

between Oneness and multitude may thus be taken care of: there is nothing strange in the

fact that things are in certain respect one, insofar as they participate in Oneness, and in

other respects multiple, insofar as they participate in multitude. Each thing participates in

many ideas; but what has to be excluded as unthinkable is the possible contradiction in the

very realm of ideas:

"If he could show that kinds and forms themselves have in themselves

these opposite properties, that would call for astonishment. But if

someone should demonstrate that I am one thing and many, what's

astonishing about that?" (Prm. 129c)

Thus, each thing can be shown to be one and many at the same time without contradiction;

but it does not follow that the one in itself includes multitude, or vice versa. Oneness and

multitude can be clearly discerned in things, precisely because their forms are clearly

discerned and noncontradictory. But everything would fall apart, and great havoc would

follow, if it turned out that there can be a contradiction in the order of forms themselves.

Contradictory attributes can be ascribed to things, but not to ideas, whose very status

depends on univocal predication. The problem, then, seems to be elegantly solved by the

strict distinction of two orders, but it is now displaced by the question of how multiple and

changing things participate in the non-contradictory and unchangeable realm of ideas.

Socrates offers a strategy to eliminate the paradox. Where Zeno took the extreme stance that

there is no multitude, no movement, and no changing (a stance that can be underpinned

only by a firm footing in the signifier against the massive evidence of the senses), Socrates

takes the position of a compromise, the ecumenical position that everything can be sorted

out if one establishes the division of labor between two spheres; he repeats three times that

there is nothing to be astonished about. This position may well sound Platonic, but it will

quickly turn out that it is full of tricks and traps, and the entire second part of the dialogue

will ultimately demonstrate precisely what Socrates tries to avoid at all costs at the

beginning: that there are paradoxes and contradictions in the very midst of the realm of

ideas. Thus, Platonism (par excellence?) only starts at the point where it can sustain a

paradox far greater than the one proposed by Zeno.

After the short initial dialogue, Zeno mysteriously keeps silent. Has his cause been utterly

defeated? Maybe one of Plato's intentions was to humiliate and then dispose of Zeno so as to

promote Parmenides, who now takes over Zeno's cause, as an ally of the theory of ideas. The

strategy--to make alliance with the master, to get rid of the cumber-some disciples--seems

common enough.

In the ensuing dialogue between Parmenides and Socrates, we witness a most extraordinary

scene where Socrates--who later so magisterially and artfully twists his sparring partners

with the ability to outwit anybody--is here in the position of an ignorant pupil, a beginner,

clumsy in his thinking, easily confused and constantly contradicting himself, unable to think

through the consequences of his own thought. The very idea of participation, one of the

cornerstones of the Platonic position, seems to crumble in front of his eyes, with himself

entirely powerless, the cornerstone being revealed as shaky, corroded, porous, and

unusable. The first part is a slow but sure way to Socrates' defeat.

Parmenides' objections to the theory of participation quickly put Socrates at an impasse. If

ideas exist separate from things, then Socrates has no problem in admitting this status first

to the mathematical and logical entities; then to the ideas of one, multitude, identity,

difference; further to the ideas of the good, the beautiful, the right; and finally, with some

misgivings, to the ideas of man, fire, water, etc. The question already emerges whether these

latter ideas are on the same rung as the former, but the real trouble arises at the end of this

progression, or rather this descent. If every genus has to have its eidos, is there a form for

"things that might seem absurd, like hair and mud and dirt, or anything else totally

undignified and worthless?" (Prm. 130c). Is there an eidos of shit? Of garbage? Of refuse? Of

scum? It would be strange if those things had a form that can simply be put alongside the

above-mentioned elevated notions, that can be part of the same series; but then again, are

they not covered by eidos? Socrates, faced with this dilemma, is seized with panic:

"When I get bogged down in that, I hurry away, afraid that I may fall

into some pit of nonsense and come to harm; but when I arrive back in

the vicinity of the things we agreed a moment ago have forms, I

linger there and occupy myself with them." "That's because you are

still young, Socrates," said Parmenides, "and philosophy has not yet

gripped you as, in my opinion, it will in the future, once you begin

to consider none of the cases beneath your notice." (Prm. 130d-e)

If I had to choose but one quote from Plato, this passage would be it. Indeed, it should be

placed on the frontispiece of Plato's works, or perhaps as the inscription on the gate of the

philosophical edifice (if such a thing existed).

Socrates escapes. Faced with the object "in the form of" refuse, that is, without a form, he is

terrified by the menacing pit of nonsense; after all, if the doxa is to be trusted, it is so much

more comfortable and pleasant to consider the elevated and sublime notions that are

deemed to be the proper business of philosophy. Thus, at the margin of the theory of forms

and at the very beginning of its scrutiny, there suddenly arises the phantom of an object not

covered by eidos, the formless object, the castoff--or, if we give it a little push in the

Lacanian direction, an object not covered by the signifier, a being not represented by a

signifier. Parmenides, as opposed to the young Socrates, is prepared to follow the thought to

the extremes: the dignity of philosophy ultimately consists in being able to consider the

object without dignity, and it takes a far greater courage to consider the refuse rather than

the good and the beautiful. This is where psycho-analysis should pay attention.

Indeed, when Lacan tried to establish the theory of the objet a, he found no better

foundation to pin it down to than Plato. In his seminar on transference (the eighth in a row,

from the school year 1960-61 and published in 1991), Lacan took recourse to the

Symposium, in order to single out there the object as agalma (cf. Symp. 215a-b), the infinite

treasure supposedly detained by Socrates (in another incredible scene where Socrates is

treated as an object of erotic seduction, but this is another story). The object as agalma was

then taken as the pivotal point, the clue to transference (cf. Lacan 1991: 163ff.)--specifically

the object as sublime, as the supposed hidden treasure, the object to which, ultimately, love

is addressed (or rather, love is addressed to the supposed holder of that unfathomable

object). It was the object qua agalma that presented the phantom of knowledge, as well as

that of the good and the beautiful, the specter that appeared to detain their secrets. But here

we have the object--the very same object?--in a dramatically different, indeed the opposite,

outlook: the object as refuse, deprived of any sublimity, the object provoking horror and

anguish, the object that cannot be the proper object of knowledge (let alone the object of

love), the refuse of the episteme itself, its garbage. Yet, perhaps we have here the necessary

counterpart, the Platonian missing half, as it were, for a theory of the object a. There are two

very different, sharply opposed views of the object in Plato, agalma and junk; these views

should ultimately be made to converge in the concept of object a, and the theory of the

object has to account for them both from the same pivot. Admittedly, the present passing

remark, insightful as it may be, may seem rather meager to base great theories on, but let us

not make haste, for the continuation of our dialogue provides a most remarkable and strict

foundation for a theory of the object a.

All this is but a prelude to the first part of the dialogue, where Parmenides, with a sort of

sadistic clarity, exposes the weaknesses of the theory of participation, that is, of what is

ultimately the cornerstone of Plato's theory. This part would require much more detailed

reflection, but since this is not my aim here, a few very brief summarizing strokes are all that

are in order. The objections are roughly these:

1. How can a multitude of things participate in a form without the form itself becoming

multiple and divided? If the form is whole in things, then it is outside itself; but if only part

of it is in things, then it is divided and not one, or else its part should be the same as the

whole.

2. It does not help if we conceive of the form as the principle underlying multiple things, the

form that they would all have in common and that would thus form their unity. Big things

would thus be big by participating in the form of magnitude as their common trait, and so

forth. But this approach would demand another idea of magnitude that would encompass

both the big things and their form, for the form and the things do not have a common

measure; they can find their tertium comparationis only on a metalevel that would cover

both things and forms and thus secure their unity and participation. This is, of course, the

notorious argument that gained fame under the name of "the third man." (7) But once we

introduce a third, there is no way to stop the amassing of metalevels: the new entity will

need an entity of a superior order in order to insure the unity of inferior levels. The

metalevels will expand, in what seems like the nutshell of Russell's paradox, into infinity.

3. We fare no better if we try to conceive of the idea as a thought present only in the soul; we

would thus preserve its unity, in a stance that looks like a brand of nominalism. But if the

form is a thought, then it should be the thought of something that is common and identical

in the multitude of things. Forms can only be thoughts inherent in things, or else one would

have to give up the whole idea of participation. Thus, either everything is a thought, or

things are thoughts that do not think.

4. We could try to disentangle ourselves by positing forms as models (paradigms), and

things as their copies. But here again, the third man lurks behind the corner (like Orson

Welles in Carol Reed's great film of that name, suddenly springing up in a deserted square):

how can copies resemble the supposed models without presupposing a third form that

would encompass both and thus enable resemblance in the first place? And so forth into

infinity.

5. At the core of all these failed strategies, there may be the biggest impasse of them all: if

forms are what they are supposed to be, if they constitute an order of their own and are kept

well apart from things, then they should be inaccessible to knowledge. The absolute entity

should not be in us and for us, if it is to be absolute. The ontological status of forms is

separate and they can be adequately grasped only at their own level, just as the things can

only be considered in relation to other things that are of the same rank. Thus, the ideas

would, in principle, be inaccessible and there would be an unbridgeable gap between the

forms and things. (8) This argument also works in reverse: since the divine mind possesses

the absolute knowledge, our world is beyond its reach; divinity cannot understand the finite

human world any more than we can understand the absolute. There is an unsurpassable

precipice.

But here we have reached a point where the argument cannot be sustained any longer. If

Parmenides is trying to display the contradictions of the theory of participation, his aim is

not to undermine the very reality of forms altogether. Participation may have grave

problems, but the extreme position that seemed to be the result, or the source, of the

objections turns out itself to be untenable. The radical unknowability of ideas entails the

impossibility of thought itself, of language, the annihilation of discourse, for only forms

enable any nomination and predication, and should they be withdrawn, we would find

ourselves in a universe of chaos, of the undistinguishable, or in a void. Even though the

contradictions of participation may seem insurmountable, the forms are the only support

for our thought. We may not be able to get to them, but we cannot do without them. So how

to wriggle out of this loop?

Parmenides, on the face of it, does not offer any clear advice or handy solution. What he

does offer seems rather bizarre: a dialectical exercise whose aim is not simply to look for an

answer, but rather to test all the logical possibilities, investigate all the conceivable

hypotheses, and fearlessly draw from them all the consequences, however extreme and far-

fetched they may appear. And even more: "... you must not only hypothesize, if each thing is,

and examine the consequences of that hypothesis; you must also hypothesize, if that same

thing is not" (Prm. 135e-36a). The dialectical exercise must be able to sustain the nonbeing

of each entity, and probe it on the same level with its being. Each entity must be investigated

against the backdrop of its possible absence, the presence and the absence taken at the same

level, and the consequences drawn from each in cold blood, regardless of habits of thinking

and the evidence of perception. Only such an exercise, if rigorously pushed to the end, can

perhaps show the way out of the predicament of the initial discussion.

Socrates requests a demonstration, and after some persuasion Parmenides is finally willing

to undertake it, but not without tremor and anxiety. Just like the old poet Ibycus, who,

before engaging in the game of love, compared himself to an old horse, a past champion who

has to race again in his old age, trembling with advance excitement and past memories, so

Parmenides engages in the exercise, thrilled as the horse before the race, or an old man

before the act of love. Anxiety, desire, trembling, expectation, rapture, shudder, dread,

hope--those are the proper attributes of the subjective stance corresponding to this exercise

that may seem as the most tedious and the dullest of drills with no place for subjectivity. But

the stakes are high, the highest possible, and Plato has given us a notice, however strange,

that the stakes involve the very topology of the subject. The philosopher's trembling is not a

psychological trait, not a description of a particular feeling or something to depict the

atmosphere; it is a precise subjective--that is, nonpsychological--counterpart to the

seemingly arid deduction of hypotheses.

The logical exercise proposed by Parmenides deals with the problem of one, the central

problem of Eleatic philosophy. It does not lead to some clear-cut conclusion, but to the

bizarre ending quoted above, which, at least on the face of it, seems to make the initial

predicament even worse, and we might well ask what we have gained (if anything). Indeed,

we are rather faced with a maze where all the possible tracks will be carefully examined, and

all the consequences deduced from all the stances that we can possibly take, only to find out

that each of them leads to an impasse, that each of them must be rejected because they all

lead to absurdities. (9) The one, the axis of the entire discussion, will give rise to an

articulate totality, a paradoxical structure; but it is precisely by the paradoxes, the impasses

it entails, that the one pertains to the Real. It may well be, as Dies says (xvi), that Plato, in

the last instance, endeavors to find "the intellectual intuition of a unity which would

generate multitude without splitting itself." This is a noble and impossible endeavor, but the

one displayed in front of our eyes is overwhelmingly a split one, the one inherently broken

on the rocks of multitude and alterity, and which will never be whole again, whatever the

Neoplatonics may try to say on its behalf. This is no doubt the scandal of this dialogue, and

we cannot but admire Plato's immense heroism. (10)

First Hypothesis

As the dialectical exercise must scrutinize the being as well as the nonbeing of its entities,

the nine hypotheses are from the outset distributed roughly into two groups: the first five

follow from the being of one, the second four from its nonbeing. But the being of one, the

starting point of the first group, becomes rather dramatically convoluted already in the very

first hypothesis, which will lead to the bizarre conclusion that "the one in no way partakes of

being" and "as it seems, the one neither is one nor is" (Prm. 141e-42a).

The first hypothesis, "if one is one," investigates what can be ascribed to one. If one is one,

what follows? On closer inspection, it seems that the first hypothesis calls for caution since

it does not claim that one is, but rather merely analytically dismembers the one and

examines its possible predicates. And since the one is taken "in itself," in isolation, as it

were, the predication fails. It keeps failing. One, taken in itself, cannot be many, cannot have

parts, and therefore cannot be a whole either, since being whole means having all the parts,

and hence being divisible. Having no parts, it cannot have a beginning or an end or a middle

or a limit; it is, therefore, limitless and formless. It cannot be in another, since it would then

be contained by this other and thus have a border with it; this would already presuppose the

division into a middle and a periphery. But it cannot be in itself either, since that would

entail an inner division into the containing and the contained. It can be neither active nor

passive, nor can it move, for all of that would entail some form of division. But it cannot

stand still either, since it could only stand still in relation to something that would contain

it. It cannot be identical to something else, since it would thus cease to be one; but it cannot

differ from it either, since it would thus turn into something differed, marked by the

difference. Furthermore, and more dramatically, one cannot be identical to itself, since

identity "always already" presupposes difference, some minimal and purely formal form of

duality that identity then "identifies," that is, evens out, equalizes, or tries to abolish and

annul, but too late, too late. If it were not so, identity would coincide with oneness, but to be

one is not the same as to be the same. The argument, which will become notorious in

Hegel's majestic and magisterial strokes, is already here in a nutshell: "If the one is to be the

same as itself, it won't be one with itself; and thus it will be one and not one. But this surely

is impossible. Therefore the one can't be either different from another or the same as itself"

(Prm. 139e). One will thus not be similar to another, since that would entail a common

measure, and it will not be similar to itself, since similarity too entails inner division. It will

be neither like nor unlike itself, neither equal nor unequal to itself; it is excluded from any

comparison. It cannot be older or younger than anything else, which further means the

exclusion from any form of temporality. Time can basically be understood as becoming

unequal to oneself, and so one is thus also excluded from becoming and passing. Being

outside time it is also outside being, since being can only be conceived in relation to a past, a

present, a future. To be is to be in time:

"Therefore, if the one partakes of no time at all, it is not the case

that it has at one time come to be, was coming to be, or was; or has

now come to be, comes to be, or is; or will hereafter come to be, will

be coming to be, or will be....Therefore the one in no way is." (Prm.

141e)

It follows from this radical exclusion that "one neither is one nor is" (142a) and

consequently cannot be the object of speech (logos), of knowledge (episteme), of opinion

(doxa), or of perception (aisthesis). In one sentence, in a most remarkable metaphorical

condensation, we have all the key philosophical entities of classical antiquity: the one

escapes logos as well as sensory perception, it escapes the stringency of epistemic science as

well as the nonbinding opinion. It shuns both truthful and untruthful speech; it pushes us

against the limit of the speakable. The one, which should be the basis of the possibility of

speech and the minimal foundation of the theory of forms, the inner principle of eidos as

such, when taken in itself, is in this first hypothesis revealed as void, an entity to which one

cannot ascribe anything at all. In place of one, we suddenly have the precipice of a lack.

Second Hypothesis

If the first hypothesis, which considers the one in itself, produced a disjunction between the

one and being (the one is not), then the second hypothesis starts from their conjunction. It

proposes that "one is"; there is, as it were, an existential judgment. And where the first

hypothesis proceeded analytically, merely unfolding the consequences of the "one in itself,"

or rather the impossibility of its consequences, here the second proceeds "synthetically" (to

borrow the largely inappropriate Kantian diction of Jean Wahl's commentary on this). It

ascribes something to one that is not inherently contained in its concept, namely, being.

Lacan's famous dictum "Y a de l'Un" can be read as a paraphrase of this second hypothesis.

Translating it simply by "There is One," we lose the paradox of the French formulation,

where the partitive article de treats the one as an indefinite quantity (as in Il y a de l'eau

["There is water"], that is, an indefinite quantity of it), implying, first, that there can be an

immeasurable quantity of one, of what is itself the basis of any measuring, and second, that

if the quantity is indefinite, then it is divisible (like water). But into what, if one is the

minimal unity? This peculiar (mis)use of Plato's wording is perhaps not so far from Plato's

point, as we shall see.

If one is, it participates in being and is therefore something different from being, for

otherwise it would make no sense to assert that one is. One and being are distinct, so that

"the one that is" is necessarily innerly split by their difference. "The one that is" falls apart

into one and being, but in such a way that each part includes the other as its part. This inner

division, once it has started, cannot be stopped: the moment we have two parts, we have

infinitely many of them, for each new one, and each new being, fall apart in its turn into

being and one:

"So again, each of the two parts possesses oneness and being; and the

part, in its turn, is composed of at least two parts; and in this way

always, for the same reason, whatever part turns up always possesses

these two parts, since oneness always possesses being and being always

possesses oneness. So, since it always proves to be two, it must never

be one.... So, in this way, wouldn't the one that is be unlimited in

multitude?" (Prm. 142e-43a)

The difference between one and being cleaves both from inside, turning them into

something split and divided ("chopped up"). The couple of one and being makes already

three, for difference and alterity have sneaked in between them, and once one has started

counting, there is no way to stop it. "The one that is" is difference and multitude, by the very

fact of being:

"Therefore, the one itself, chopped up by being, is many and unlimited

in multitude.... So not only is it the case that the one being is

many, but also the one itself, completely distributed by being, must

be many." (Prm. 144e)

The equation of one and being does not add up, and if the entire Eleatic philosophy, with

Parmenides as its founding father, came into history under the auspices of this equation,

(11) then it is extraordinary to hear Parmenides saying here that the equation cannot

possibly work--though we must also bear in mind that this is but a provisional stage of an

uncertain whole, a step in a progression.

It is already here that we can see Plato's dealings with the Presocratic problem par

excellence, the problem of "the count of being." Can being be counted, be seized by a

number? How many beings are there? The most economical evocation of this problem is the

quote by Isocrates: "For some there is an infinite number of beings, for Empedocles there

are four, for Ion just three, for Alkmaion two, for Parmenides and Melissos one, and for

Gorgias none at all" (quoted in Dies 11). In order for logos to be possible, being must be

divided and counted; it has to be calculable and calculated. But Plato here draws the line

under this problem, and especially under the Eleatic equation of being and one: it seems

that this equation made being one and all-encompassing, a whole (hen kai pan). Yet Plato

here demonstrates the very contrary, that the equation cleaves them--both cleaves them

apart and cleaves each of them from the inside. The one that is will never be one, and its

being will disintegrate into infinity.

A number of paradoxical consequences subsequently follow that are directly opposed to

what we encountered in the first hypothesis. One is now, at one and the same time, the

whole and the part, and so into infinity; it is both limited and unlimited, it moves and stands

still, both identical and different, like and unlike itself and others, both equal and unequal to

itself and to others, etc. Insofar as it participates in being, one is in time; it becomes older

and younger than other things, and is subject to becoming, to "now," "before," and "after."

The conclusion of this deduction, which I cannot follow into detail here, is that we may well

have "one that is," but only at the price that it can now be ascribed all the contradictory

attributes--just as in the first hypothesis it was not possible to ascribe any to it at all. It

seems that we have avoided one kind of catastrophe only to fall into its opposite:

"And indeed there would be knowledge and opinion and perception of it,

if in fact even now we are engaging in all those activities concerning

it.... And a name and an account belong to it, and it is named and

spoken of. And all such things as pertain to the others also pertain

to the one." (Prm. 155d-e)

We have gained the one that is--the one that can be known, spoken about, perceived,

defined, etc.--but on the way we have lost its oneness.

The basic preoccupation, roughly designated above by the problem of "counting the being,"

offers the basis to propose a "didactical scheme," a device to help us conceptualize all the

different wonders that Parmenides proffers in the nine hypotheses, and to help us to

consider together the different strategies displayed here. Let us use the intersection of two

circles, so familiar from Lacan's various demonstrations, a simple device that Lacan was so

fond of and used for a variety of purposes. This time, if we recast it in such a way that one of

the circles designates "one" and the other "being," it suddenly appears that the hypotheses

quite naturally take their places in the slots waiting for them: if the first hypothesis takes the

place of "one without being," then the second has to be located at the very intersection of

being and one, in the areas where the two circles overlap.

[FIGURE 1 OMITTED]

Lacan's scheme of intersection of two circles was designed (Lacan 1986: 210ff.) to

demonstrate the mechanism of forced choice, that is, a choice that in spite of the seeming

freedom has been decided in advance, a choice that entailed a loss. (12) We can see that the

scheme here is of a different nature: it confronts us with an even more difficult situation

where all the possibilities have to be taken, while, at the same time mutually exclusive, they

all turn out to run into an absurd. We are free, or rather we are forced, to adopt them all, in

good time, but each choice comes with a vengeance. The forced choice here means not only

that there is no free choice, but also that there is no "right choice," that what we are forced

to choose is the logic of concatenation--where every impossible choice leads to another

impossible choice--which traces a pattern of impossibilities but is perhaps the only way to

pursue the real.

Third Hypothesis

The third hypothesis, a consequence of both the first and the second hypotheses, radicalizes

their impasse. (13) If the one can be ascribed contradictory predicates, this ultimately also

applies to the existential predicate itself: one, therefore, is and is not, and can be ascribed

being as well as nonbeing. This consequence, after all, follows from the fact that one, insofar

as it is, is situated in time (subject to "being and time," as it were), and if it is in time, it

becomes and it passes; there is a time when it is and a time when it is not, and it passes back

and forth from being into nonbeing, and vice versa. This is also true of all the other

contradictory predicates: the becoming of one is the passing of multitude and vice versa, a

splitting and a coupling, a permanent passage from movement to standstill and vice versa,

etc. It is as if Plato were suddenly speaking with the tongue of Heraclitus.

But the point of this hypothesis is elsewhere: how can one grasp the very moment of

passage? Is it thinkable at all? Insofar as something is in time, it can either move or stand

still, but it cannot be somewhere in between. If time is a continuum, it seems impossible to

comprehend the passage from one state to another. When, at what point in time, does the

passage take place?

"Yet there is no time in which something can, simultaneously, be

neither in motion nor at rest.... Yet surely it also doesn't change

without changing.... So when does it change? For it does not change

while it is at rest or in motion, or while it is in time." (Prm.

156c-d)

The moment of passage and change is a "suddenness," something that cannot be located in

time. It does not fit into time, and time cannot accommodate it. It is an impossible instant

when an entity does not rest nor is it set in motion, an evasive and intangible instant that

does not occupy any point in time. It is the time of "not yet" and "not any more," a passage

that can never be something present--as if, suddenly, we are in the company of not only

Heraclitus, but also Hegel. Hegel, however, uses the paradox of retroactivity to deal with the

evasiveness of passage: one has "always already" become the other; in the very process of

progressing it turns out that the passage has already taken place, that it is not somewhere

ahead but somewhere behind, so that one can only progress to where one has already been.

It follows that the place, where one "always already" was, is not some primordial identity

but otherness from the outset. The passage as a "now" is structurally lacking, and this is

what pushes forward Hegelian dialectics.

But Plato tries to resolve the problem in a very different manner, by opposing the instant--

the suddenness--and time. The instant does not belong to time, not to the time seen as a

series of "nows." It has no place in the present, in any presence; it is excluded from being,

and yet not simply falling into nonbeing. It is the very limit between the being and the

nonbeing. The problem of the instant may well arise with all passages, but its emphatic

touchstone case is no doubt the passage from being into nonbeing and the other way

around. The instant is the moment of suspension when something is not yet, and not any

more, and thus the instant cannot be situated in the seemingly exhaustive division between

being and nonbeing; it is on neither side of the seemingly sharp limit, the sharpest of them

all. It embodies the very boundary between being and nonbeing:

"But in changing, it changes at an instant, and when it changes, it

would be in no time at all, and just then it would be neither in

motion nor at rest.... Whenever the one changes from being to

ceasing-to-be, or from not-being to coming-to-be, isn't it then

between certain states of motion and rest? And then it neither is nor

is not, and neither comes to be nor ceases to be?" (Prm. 156e-57a)

This is, Plato says, a physis atopos (atopical entity), a creature without a place, an

unplaceable location, a point outside time and space, where the law of noncontradiction and

the law of the excluded middle do not apply--the proper object of the third hypothesis. In

our scheme, its place will be precisely the limit, the boundary between one and being, the

place where one neither is nor is not.

Fourth Hypothesis

The following hypothesis places the one into a relationship to the other, or rather to a

plurality of others, the multiplicity of entities other than one (and by not being one, they are

necessarily multiple). Otherness appears here in a rather rough and abstract manner as the

non-one. No doubt, on the one hand, the otherness has to be considered on the level of

forms themselves, that is, as the eidos other than one, and not simply on the level of

material things of the senses. Yet on the other hand, Plato envisages a certain limit: what

makes others others is something that cannot simply be subsumed under the eidos. Are we

going too far if we say that the otherness here is located in a paradoxical verge where it

touches upon something irreducible to eidos and yet not simply coinciding with material

things?

Others are by definition not one, but this does not mean that they are without one or outside

one: by virtue of being other, they can participate in one. Others have parts, insofar as they

are not one; but having parts means that they are parts of a whole, and "the whole of which

the parts are to be parts must be one thing composed of many" (Prm. 157c). Multitude is in a

necessary relationship with one that unifies it and thus makes it a multitude. Others, insofar

as divided, participate in one and in the whole, and participation presupposes difference,

since others must differ from one in order to participate in it. Without participation they are

just an infinite multitude that cannot be related to one, and even the smallest part of this

infinite multitude would still be infinite. Thus, "one" can be seen precisely as a limit to this

limitless multitude; it is only by virtue of one that others can become parts and wholes and

be limited against one another. The others, then, show two faces--the limitless face of

ungraspable infinity, and the face of participation in one that enables any distinction. The

others are thus placed precisely on the limit between one and alterity:

"[I]nsofar as they are both limited and unlimited, they have these

properties, which are opposite to each other.... And opposite

properties are as unlike as possible.... So in respect of either

property they would be like themselves and each other, but in respect

of both properties they would be utterly opposite and unlike both

themselves and each other.... Thus the others would be both like and

unlike themselves and each other.... Things other than the one are

both the same as and different from each other, both in motion and at

rest, and have all the opposite properties ..." (Prm. 158e-59a)

This hypothesis can easily be seen as standing in symmetrical terms to the previous

hypothesis: both of them are placed in a limit, or they embody a limit, but while with the

third hypothesis it is the limit between being and nonbeing, with the fourth we have the

limit between the one and the others beyond the one. The third hypothesis is ruled by the

logic of "neither-nor," but the fourth by "one as well as the other." The former leads to the

exclusion of the instant, while the latter leads to the inclusiveness of all properties of the

others. The others are placed on the borderline between form and the amorphous, but in

such a way that both sides pertain to them; the others live in both worlds.

Fifth Hypothesis

The fifth hypothesis continues the examination of the consequences of one for the others,

but this time the others are considered with respect to their nonparticipation in one, which

entails their exclusion from the realm of one. "So the one could not be in the others as a

whole, nor could parts of it be in them, if it is separate from the others and doesn't have

parts" (Prm. 159c). Thus, in the others one cannot distinguish parts, nor can one speak of

them as wholes. If they are not one, they cannot be many either, "for each of them would be

one part of a whole, if they were many" (159e). Multitude is only thinkable in relation to one,

as its counterpart and its consequence; there is no multitude without counting, and there is

no counting without one. Others are then uncountable, and therefore neither like nor unlike

the one, nor can they be like or unlike themselves. If they were to be that, we would have to

compare one part of them with another and so produce their division, which cannot be done

without one. Thus, they are neither identical nor different, neither bigger nor smaller; they

neither move nor stand still, neither do they come to be nor do they pass. No predicate can

be assigned to them.

In the end, after the trajectory of five hypotheses, we get stuck in the impossibility of

discourse with which we started in the first hypothesis. The fifth hypothesis mirrors the

first: just as it was impossible to say anything about one, taken in itself, so it is equally

impossible, at the opposite end, to say anything about things (other than one) that are taken

in isolation from one. At the opposing extremities we face the precipice of the impossibility

of predication. We can now see the exact symmetry of the first and fifth hypotheses, as well

as the analogous symmetry of the third and fourth hypotheses, so that the pivot of this

matrix appears to be the second hypothesis, which asserts the being of one and which I

placed in the intersection of the two circles. The possibility of discourse stuck to this

intersection and to its boundaries, although even there this possibility turned out to be

highly paradoxical and problematic. It seemed that it contained too much or too little, that it

did not have the air of the firm ground we were looking for. But discourse pertains to being

precisely through those paradoxes, not in spite of them; if we want to isolate the one as the

basis of the possibility of discourse, the pure signifier in itself, or if we want to isolate being

for itself and outside the realm of the signifier, then in both these opposite directions we

wind up with the impossibility of speech, the abyss of the unspeakable.

I have already proposed that the five hypotheses can be most economically disposed with

the little help of our didactical diagram, the intersection of two circles. If the left circle,

arbitrarily, covers "one," and the right circle "being," this obviously entails a simplification

and a condensation. To be sure, the provisional massive opposition between one and being

actually condenses two different oppositions: that between the one and the others (things

other than one), and that between nonbeing and being. As we have seen with the first

hypothesis, one taken in itself is excluded from being and falls into the nonbeing. In the

symmetrical fifth hypothesis, the exact opposite takes place: things other than one, despite

the impossibility of predication, do not fall into nonbeing, but rather coincide with pure

being without any attributes. We are confronted, then, with being without one, with that

dimension of being that escapes oneness, which is heterogeneous to one and hence

"inexpressible." This symmetry allows for our makeshift condensation from which some

clarification may be gained.

[FIGURE 2 OMITTED]

This diagram makes immediately clear why Lacan sees in Plato's Parmenides the forerunner

of psychoanalysis and how he could read it as a deduction of the basic concepts of his own

theory. Obviously, in the intersection of the second hypothesis we are faced with the "unary

signifier," with "Y a de l'Un" or "There is one," as the basis of all signifying logic, its minimal

presupposition, the root of any possibility of distinction. The function of the signifier occurs

precisely through the emergence of a "unary trait," (14) which, in Lacan's algebra, is pinned

down by the symbol [S.sub.1], the "first" signifier, the signifier of pure oneness, the signifier

without a signified. And since it is without a signified, all attributes can be assigned to it,

that is, any and all of [S.sub.2] can be attached to it. [S.sub.2], the second signifier, thus

condenses the entire signifying chain that can always be prolonged into infinity. In our

condensed scheme, the one of the second hypothesis stands at the intersection of one and

being (as the one that is), and hence at the intersection of one and the others (since being

introduces difference into it, and hence alterity).

On the left side of our scheme, the space of the first hypothesis, there is the empty space of

one in its pure form, the void of the pure difference that is not the difference of any positive

entities, the void that is invisible the moment we deal with positively-given signifiers, but

that enables their differences and glides along their chain, shifting from one link to another,

although it can never be apprehended as such and for itself. The moment we have the unary

signifier (one), we also have the void that pertains to it, not as something external or added

to it, but as the embodiment of the very evasiveness of its existence. To put it in another

way, this void represents the very place of the inscription of the signifier, insofar as this

empty space is different from it, so that its own lack is, as it were, part of the one. The lack

forms a single part, the signifier another. The circle of one, the left circle, is quite

demonstratively split into the unary trait and the lack: signifier is the paradoxical entity split

into itself and into its own absence as its own part. (15) This empty space is precisely the

location of the entity that, in Lacanian algebra, is designated by $ (the barred S), and this is

where Lacan spots the subject, the place where subjectivity enters speech. The place of the

subject is the place of this lack, this void, which, however, cannot be present as such in itself.

This is why it has always to be represented, that is, represented by a signifier for other

signifiers. This structural place can be isolated in Parmenides in its explicit and pure form,

yet one should not be quick to draw from it too many conclusions. Plato produces it as a part

of his deduction, but the idea never crosses his mind that this could be a place of

subjectivity. The structure that he produces is not a structure with a subject; we will have to

wait for Hegel for this. (16)

There remains the last slot in the matrix, the space of the fifth hypothesis, reserved for pure

alterity, the place of pure being outside of the realm of one, the being not covered by forms.

It is the otherness that is stubbornly recalcitrant to any seizure by one but, in spite of this,

does not simply coincide with materiality, sensuality, and objectivity. What else can that be

but precisely what Lacan calls the objet a? Can a better designation of this paradoxical

object be given? The specter of mud, hair, junk, etc., which for a moment haunted Socrates

in the first part, here finds a proper logical site.

The symmetry of the first and fifth hypotheses also reveals affinity between $ and a, the

Lacanian concepts of subject and object. What they have in common is that they cannot be

simply pinned down by a signifier. They are recalcitrant to being fixed by a signifier and

therefore are recalcitrant to meaning. They are both "inexpressible" in and by themselves,

although they constantly and necessarily stick to any speech, the two strange creatures

pertaining to any discursivity: on the one hand as the pure lack produced by the incidence of

the signifier ($), and on the other hand as the pure heterogeneity that the signifier cannot

seize, capture, and appropriate, yet not as something preexistent that would evade its grasp,

but something that emerged through its very incidence. What it cannot seize is its own

product, not the illusory infinite wealth that preceded it. Thus we arrive at the following

simple scheme:

[FIGURE 3 OMITTED]

This matrix, which follows directly from Plato's sequence and arrangement of the minimal

elements in the first five hypotheses, offers perhaps the best clue to the matrix of Lacanian

concepts. In a single elegant move, all the basic entities are brought together, inserted in

their proper slots, clearly delineated, and their mechanism displayed. Lacan himself uses

this didactical device in a somewhat different way and for other purposes; most notoriously

he tries to explain with their help the mechanisms of alienation and separation (cf. Lacan

1986: 210ff.). But the matrix that we have uncovered here is perhaps even more elementary

than those developed there; it may well be the matrix at the bottom of those, which can then

be seen as its further elaborations.

Sixth Hypothesis

We now turn to the last part of the dialogue, the second half of the logical exercise, and to

the four hypotheses that start from the supposition opposite to that which served as the

basis of the previous five hypotheses. We are to suppose now that "one is not" and see what

follows from there. This part, as we have seen, has the same necessity and the same dignity

as the part that started from "one that is." The same rigor must preside over our

examination; and the same matrix has to be submitted to equally strict scrutiny, but with

the great difference that now we have a void at its very core: the place of the intersection, the

space of overlapping of being and one--the slot occupied by the second hypothesis--must

now be left empty. "There is one," the coinciding of being and one, has to be left out, and so

there remain only four hypotheses that now encircle the central void. Can they have any

consistency without this anchoring?

The sixth hypothesis begins with the paradoxes that emerge if one speaks of nonbeing. If we

assert that something is not, we yet name in the same breath this nonexistent entity; we

define it, conceive of it, distinguish it from other entities. The nonbeing is the object of

speech, and speech endows it with a kind of existence, however much one tries to assert the

contrary. It is an existence recalcitrant to negation. If we speak of one that is not, we still

know what we are talking about; we can delineate it and acquire certain knowledge about it.

However much one does not "really" exist, it has an existence in the symbolic all the same;

even more, it appears that the symbolic existence is completely indifferent to its being or

nonbeing:

"Then we must state from the beginning as follows what must be the

case, if one is not. First, as it seems, this must be so for it, that

there is knowledge of it; otherwise we don't even know what is meant

when someone says, 'if one is not.' ... Furthermore, the one that is

not partakes of that and of something, this, to this, these, and so

on; for the one could not be mentioned, nor could things be different

from the one, nor could anything belong to it or be of it, nor could

it be said to be anything, unless it had a share of something and the

rest." (Prm. 160d-e)

The one that is not, despite its nonexistence, is thus in a necessary relationship with others

and participates in others. It can be said to be like or unlike others. Its nonbeing is not a

nonrelationship; it is caught in the web of differences with existent entities, and it is from

that web that it acquires a meaning. Even more, it has to partake of a certain part of being if

it is to be spoken about at all. It has to participate both in nonbeing and in being, so that the

boundary between the two again seems to be put into question: being must include a part of

"existent nonbeing," while nonbeing must comprise some part of "nonexistent being," as it

were:

"So if it [sc. one] is not to be, it must have being a not-being as a

bond in regard to its not-being, just as, in like manner, what is

must have not-being what is not, in order that it, in its turn, may

completely be." (Prm. 162a)

Once again we are witnessing a strange scene of Plato's fictional Parmenides in opposition

to the historical Parmenides and his thesis of the clean cut between being and nonbeing,

Plato thus circumventing the prohibition that should prevent nonbeing from surreptitiously

acquiring a being of some sort. Throughout Parmenides this boundary will be put to the test

and into question, but Plato's criticism will achieve its full swing in the Sophist, which,

precisely on this precarious edge, will demand nothing less than the murder of the father,

the parricide, the symbolic murder of the father Parmenides:

Stranger: "That you will not think that I am turning into a sort of

parricide." Theaetetus: "In what way?" Stranger: "We shall find it

necessary in self-defense to put to the question that pronouncement

of father Parmenides, and establish by main force that what is not,

in some respect has being, and conversely that what is, in a way is

not." (Soph. 241d)

If this dividing line--the mother of all dividing lines--is put into question, it follows that

what is not participates in being as well as in nonbeing. And if it participates in both, it is

also subject to changing, to the becoming and the passing, that is, to the acquisition and the

loss of being. The nonexistent one moves, but on the other hand its movement is well

impossible, since it is deprived of being and consequently cannot move and change in

relation to some being. It cannot occupy a place in the midst of being, which would enable a

comparison, and so it has to stand still. If one is not, it cannot be somewhere and cannot

move either.

The final consequence of this is that this one, which is not, has to be assigned contradictory

predicates: being and nonbeing, movement and rest, becoming and passing, etc.:

"Therefore also the one, if it is not, comes to be and ceases to be,

if it is altered, and does not come to be or cease to be, if it is not

altered. And thus the one, if it is not, both comes to be and ceases

to be, and doesn't come to be or cease to be." (Prm. 163b)

The sixth hypothesis is thus located on the same boundary between being and nonbeing as

the third hypothesis, which is its counterpart. But this time its value is inverted: the third

hypothesis yielded "neither being nor nonbeing," but here we have "being as well as

nonbeing." The corresponding entity in the third hypothesis was the evasive instant, "the

suddenness," whereas in the sixth, the counterpart in the realm of one that is not is the

evasive symbolic existence of nonbeing.

Seventh Hypothesis

The one that is not must now be considered from the perspective of its nonparticipation in

being. The nonbeing of one has to be taken as excluded from being, not as its paradoxical

subspecies. If nonbeing does not in any way partake of being, then one cannot assign any

qualifications to it. The one that is not can neither come to be nor cease to be nor change; it

can neither acquire nor lose being, if it is devoid of it. It cannot move or stand still, since

there is no correlative place in relation to which it could do either. It can be neither like nor

unlike other, neither different nor the same. It cannot be the subject of knowledge, opinion,

perception, definition, or name. "Thus one, since it is not, is not in any state at all" (Prm.

164b).

The seventh hypothesis thus arrives at the same conclusions as the first: whether one is or is

not, in both cases nothing can be said about it, if it is taken in itself. The same consequences

follow if we depart from examining "if one is" or the contrary supposition "if one is not."

Eighth Hypothesis

Now we have to explore what follows from "one that is not" for the others; to do this, we

must revisit the terrain previously covered by the fourth and fifth hypotheses. But in this

new constellation, what makes the others others? On what basis can they be ascribed an

alterity? For they cannot be others in relation to one, since we are now in the realm of the

supposition that one is not. Thus, they can be others only in relation to others; there can be

otherness only in their mutual relationship, as it were--there can only be an otherness that

sustains itself as otherness. Others without one can only be indefinite quantities, and so an

indefinite quantity of others can be other in relation to another indefinite quantity. We

cannot compare the others one by one, since they are deprived of one, and hence

uncountable and indivisible. There is no counting, no dividing into parts. Every

infinitesimal part will dissolve in our hands into another infinity, "just as in a dream" (Prm.

164d). All we have, then, are masses, unlimited multitudes, which are mutually

heterogeneous and incommensurable, with no common ground. With these masses every

identity, counting, equality, likeness, etc., can only be appearance and illusion. It will only

seem that some unity pertains to them, but it really does not. It will only seem that they are

equal, like, different, comparable. They will appear to have a beginning, a middle, and a

boundary in relation to others, but "in fact," every beginning will be preceded by another

beginning and every end followed by another end. Therefore, we find ourselves in a universe

of a multitude without a hold which consists only of appearance. If anything is to be pinned

down by thought, we would need to use one, and without one we are stuck with masses

without any unity or footing:

"So every being that you grasp in thought must, I take it, be chopped

up and dispersed, because surely, without oneness, it would always be

grasped as a mass.... So must not such a thing appear one to a person

dimly observing from far off; but to a person considering it keenly

from up close, must not each one appear unlimited in multitude, if in

fact it is deprived of the one, if it is not?... Just as, to someone

standing at a distance, all things in a painting, appearing one,

appear to have a property the same and to be like.... But when the

person comes closer, they appear many and different and, by the

appearance of the different, different in kind and unlike themselves."

(Prm. 165c-d)

To those masses that can be differentiated only in appearance and from afar, we can ascribe

all the contradictory predicates and at the same time none of them. This structure can

perhaps best be summed up by "seemingly the one as well as the other, but in fact neither

the one nor the other." The eighth hypothesis mirrors the fourth; it must be placed on the

edge between the one and the others, but now one is lacking, so that it can no longer serve to

limit the limitless (as in the fourth hypothesis). There is also an affinity with the third

hypothesis as well, but the counterpart of the atopical and unplaceable instant is here the

infinitely stretchy and pliable appearance that dissipates the moment we try to grasp it. (17)

The eighth hypothesis creates a space that is "absolutely relative," as it were, a universe

ruled by the "logic of appearance." Each qualification of this universe is but apparent, yet we

cannot state the truth behind this appearance, for in order to do so we would have to rely on

oneness. This universe is enfolded in itself and cannot be totalized, since it has no boundary.

The one, which in the fourth hypothesis could provide a boundary, is missing here.

Strangely, in this "curious vanguard" of psychoanalysis, on the edge between the

nonexistent one and the others, Plato anticipates the Lacanian logic of the nonwhole. This,

of course, calls for some caution. We must remember at once that the Lacanian nonwhole

includes one, but a kind of one that is not in the position of an exception and is deprived of

all privilege. A way to produce the nonwhole is precisely the inclusion: each "one" is

included in the series, and for that very reason the series cannot be totalized; one cannot

grasp it as a totality, since nothing is left outside as an exception. Totality becomes

impossible by virtue of inclusiveness, and so we find ourselves in a sort of vicious circle

without support and foundation. This is precisely what Lacan is getting at: he takes "Y a de

l'Un" as a starting point (through pointed reference to Parmenides), but the "one" that is at

stake here is not the one of totalization. It is not the one that builds totality or can be

correlative to any totality; it is not the one of exception or a privileged position (cf. the long

tradition of ens est unum, verum, bonum, etc.). Totalization requires delimitation, a

boundary, which is strictly correlative to the exception of "at least one" (au moins un). (18)

We have seen how the second hypothesis introduces the "unary signifier" as the pivotal

point of the entire matrix, and in our Lacanian reading it can easily be converted into

[S.sub.1], that is, into the signifier that is located precisely in the place of exception, the one

that stands apart from the rest of the series (the rest is abbreviated by the symbol [S.sub.2]).

This exceptional status is attested by unary signifier's qualifications: "the signifier without

the signified," "the master signifier," etc. It is by virtue of this exceptional status that it can

serve as the starting point for analyzing a vast variety of effects: the master signifier is the

clue to the analysis of domination, the ideological "quilting point," a logical function, a

poetical effect. Since this signifier is empty in itself (it is the positivation of the pure

difference), it can serve as an ideal support for the supposedly highest and the most

elevated, the ineffability of meaning, the point from which the sense itself emanates. The

combination of the first two hypotheses has perfectly well revealed its nature--the

correlation of one and the void--and also indicated the correlation of the highest meaning

with the absence of meaning. But in this second part of the dialogue, the privileged signifier

is, by the initial supposition, lacking; the pivotal point is missing, and what necessarily

follows is the logic of the nonwhole--a consequence that Plato has fully envisaged and

deduced by a purely logical way. Lacan's corollary would be that the privileged signifier can

be evacuated simply by getting rid of its privileged status, by including it in the series of all

other signifiers. What follows is a universe without a boundary or a hold.

Ninth Hypothesis

The investigation of the consequences of the nonparticipation of others in the nonexistence

of one remains. Others are here seen in a complete incommensurability with the one that is

not, and so we can assign to them neither oneness nor multitude (as in the fifth hypothesis),

neither sameness nor difference, neither knowledge nor opinion nor perception, not even

appearance. Others without one have no reality and no appearance. "Then if we say, to sum

up, 'if one is not, nothing is,' wouldn't we speak correctly?" "Absolutely" (Prm. 166c).

The ninth hypothesis brings us to the familiar situation of the fifth hypothesis, and here we

finally have the entire matrix of the second set of the last four hypotheses:

[FIGURE 4 OMITTED]

The seventh and the ninth hypotheses lead us into the realm of the impossibility of

discourse, just as the first and the fifth hypotheses do. In the first five hypotheses, the

possibility of speech pertain to the intersection of being and one, and to its boundaries,

whereas the external circles (the first and the fifth hypotheses) trail off into the

unspeakable. In the second set of hypotheses (sixth through ninth), based on the

presupposition of the one that is not, we see again that the possibility of discourse sticks to

the limits of the missing one, the boundaries of the intersection. There is a tentative

possibility of discourse only on the borders of this absence, and so the sixth hypothesis dealt

with the capacity of speech to evoke absence, to bring the non-being into being and endow it

with a symbolic reality, so that in speech presence and absence are on a par and so that the

very lack of one is an effect of speech (and can thus be treated at all). The eighth hypothesis

confronts us with a "universality of appearance," that is, the impossibility of a universality;

since universality always relies on one, it has to take support in "the one underneath the

many" (sub pluribus unum). The appearance is the consequence of speech that lacks the

firm footing in one; thus, the eighth hypothesis perhaps does not run out into the

impossibility of speech, but rather a speech that without one will only produce appearances

(cf. the Sophist). The absence of one affects being; it produces a contrived and counterfeit

being of appearance, and the absence of the symbolic one is compensated by the imaginary

that lacks the capacity of distinction. The sixth and eighth hypotheses, which encircle the

central void, the hole of the missing one, can therefore also be read in opposition, as the

opposition between the symbolic "absent presence, present absence," and the imaginary

appearance that comes to inhabit the lack of one. The former is based on the symbolic

distinction (the absent is distinguishable in the same manner as the present; hence, the

distinction of presence and absence is just another symbolic distinction, the symbolic

distinction par excellence), and the latter on the "indistinction," the indistinct character of

the imaginary, its (un)likeness.

The succinct ending of the ninth hypothesis ("if one is not, nothing is") is followed by the

general ending of the exercise, the exit line, the parting shot. If I began this paper by quoting

this passage, the best way to conclude is perhaps to quote it again:

"Let us then say this--and also that, as it seems, whether one is or

is not, it and the others both are and are not, and both appear and do

not appear all things in all ways, both in relation to themselves and

in relation to each other." "Very true." (Prm. 166c)

The conclusion seems to bring this exercise to a complete impasse, with the mien of a cold-

blooded serenity. It is as if in the middle of the stormy ocean Plato, without flinching an

eyelid, suddenly decrees, Here is the harbor.

If the point of Plato's method is reductio ad absurdum, then he succeeds very well indeed;

he manages to lead us into an absurdity of a proper grandeur. But if the point of this method

is to dispute certain claims by displaying its absurd consequences, what is the claim being

disputed? That there is one, that one is not? That whether one is or is not, either is equally

absurd? That one is both necessary and untenable, that we cannot do without it and neither

can we do with it? Mary Louise Gill proposes a useful way of putting it:

The key issue in the second part of the Parmenides is Socrates'

assumption in Part I that the one cannot be both one and many. This is

the false assumption that ultimately leads to the [final] conclusion

... and that conclusion is Parmenides' final response to Socrates'

original challenge in Part I. Socrates' assumption is false, and it

must be false because there is a world to be explained. (107)

In this reading, therefore, the disputed assumption, which led to absurdity, is that one

cannot be both one and many; although it may well look the other way around, the claim

that one is both one and many is absurd enough to disclaim the assumption that led to it. In

order to avoid the absurdity of the conclusion, we are forced to espouse a claim that is

hardly less absurd.

This dilemma causes much of the great unease that Parmenides provokes among

interpreters. It offers only a matrix that, with the minimal elements, delineates all the

possible positions and their logical permutations, without clear "instructions for use,"

without pointing out what follows and which, if any, of the proposed possibilities would be

the right one--or rather, all these possibilities seem to be wrong and equally untenable, their

point being only in the way they are articulated ("the medium is the message," one is

tempted to say), in the logic of their connection, and we have seen that each of the positions

brings forth some essential trait of the "logic of the signifier." What is displayed on the way

is indeed the message that one is at the same time one and many, that it implies a structure

and carries with it alterity.

If the dialogue runs into a complete deadlock and gets stuck in a radical impossibility, what

thread could one attach to this ending in order to continue? We have to wait for the Sophist

for Plato's answer, and ultimately for Hegel and for Lacan. In this impossible exit, Hegel and

Lacan both see the best of entries, and both turn the deadlock into the most formidable

starting point.

Notes

(1) Just for the record, there is already a somewhat enigmatic reference to "the admirable

dialogue with Parmenides" in one of the early pieces in Ecrits ("Propos sur la causalite

psychique," written in 1946 and first published in 1950): see Lacan 1966: 193. This dialogue

there appears in a series of names--along with Socrates, Descartes, Hegel, Marx, and Freud

as the authors who cannot be "surpassed"--against the backdrop of the vogue to "surpass"

philosophy.

(2) Cf. Socrates' remarks in Theaetetus: "Parmenides himself is in my eyes, as Homer says, a

'reverend and awful' figure. I met him when I was quite young and he quite elderly, and I

thought there was a sort of depth in him that was altogether noble" (183e). And in the

Sophist: "[T]o use the method of asking questions, as Parmenides himself did on one

occasion in developing some magnificent arguments in my presence when I was young and

he quite an elderly man ..." (217c).

(3) Various hypotheses have been offered to explain this apparent oddity. Just to list a few:

Plato actually never championed a theory that is the object of criticism; what Plato criticizes

here was his early and naive theory of ideas, as it can be found in, e.g., Republic; the theory

under attack can be ascribed to Socrates, and Plato actually settles his accounts with

Socrates through the mouth of Parmenides; Plato criticizes a caricature of his own theory

such as it was simplified and watered down by his disciples; etc. See Dies; Brisson. We can

see that what Freud calls the kettle argument (cf. Freud 4: 197; 6: 100) is alive and well in

classical philology.

(4) For purposes of translation of this dialogue, I use the new translation provided by Mary

Louise Gill and Paul Ryan (1996).

(5) This is part of a much larger problem that I cannot go into here; I reference only Dolar

1996, where the question of the differences with Derrida--the most obvious reference here--

is also taken up and discussed at some length.

(6) The use of this name is certainly a bizarre coincidence. Aristotle, at the time of the

composition of this dialogue, hardly left Macedonia to try his luck in the Academy, and it

really would have been too much if he walked straight into a dialogue of Plato. The name

Aristotle was very familiar at the time--Diogenes Laertes lists no less than eight different

Aristotles--and this particular young lad is probably the one who later became one of the

Thirty Tyrants in Athens after the Peloponnesian War. Being a sparring partner, he could

quite literally be spared: F. M. Cornford, in his English translation of the Parmenides,

simply omits Aristotle's rejoinders (except, most significantly, for the last one). Since this

Aristotle's rejoinders are minimal and he never really expresses any opinion, nothing seems

to be missing--except for the structural function of the interlocutor, who is after all the

subject of the entire exercise. As it has already been argued, the function of the interlocutor,

giving the minimal support to the "feature speaker," is a close and paradoxical kin to the

function of the analyst, whose rejoinders are equally minimal, never express opinions, and

are there purely to fulfil the function of a strawman, as it were.

(7) The designation stems from Alexander's commentary on Aristotle's Metaphysics (though

its origin is attributed to the sophist Polyxenes): "If what is affirmed about several things

simultaneously is distinct from those things and exists by itself, there will be, if man is

affirmed both in regard to individuals and to the Form, a third man distinct from both the

individuals and the Form. In the same way there will be a fourth, then a fifth and so on into

infinity" (Alexander, Comm. in Met. 990b15, quoted in Dies 63; cf. also Dies 21-22). The gist

of the argument can already be found in Republic 597c. I cannot here go into the long,

passionate, and most interesting discussion about the third-man argument that was

triggered by Gregory Vlastos in 1954.

(8) In the inappropriate Kantian diction, one might say that our knowledge would thus be

limited to the phenomenal world, whereas the ideas in themselves would be in principle

inaccessible to us as finite beings.

(9) Cf. Brisson 45: "By a reductio ad absurdum we are led in all cases to reject the

hypothesis, whether affirmed or negated, by seeing that it implies notoriously false

consequences."

(10) The first Lacanian reading of Parmenides was given by Francois Regnault (1968). One

should well note the moment of its publication, namely, in the midst of the revolutionary

events of 1968. What could possibly be more dearly needed in revolutionary times than a

dissertation on oneness and being? I am very fond of the idea of reading Parmenides as a

revolutionary manifesto. Regnault's account has many weaknesses, despite its grand style.

What follows is largely indebted to a different line of Lacanian approach, one proposed by

J.-A. Miller in his seminar in 1986-87.

(11) It has to be noted in passing that the historical Parmenides himself was strangely

reticent on this subject, so that the weight of this notorious equation can be pinned down to

a single explicit quotation.

(12) One necessarily loses the intersection, to cut the long story short; this is indeed the

point where one is always cut short, and this is what the notorious example of "Your money

or your life" tries to demonstrate.

(13) Many interpreters do not count this third hypothesis as an entity on its own (as the

ancient tradition has always done), but classify it as an appendix to the first two (cf., e.g.,

Gill 55, 85-86; Brisson 47), as an attempt to resolve their contradiction. Gill 85: "The

Appendix attempts to reconcile the conclusions of Deductions 1 and 2 by supposing that the

one is in those states at different times. There is no contradiction if an object is F at one time

and not-F at another." Yet I think there is no doubt that there is a separate deduction, that

Plato introduces it as such ("Let's speak of it yet a third time" [Prm. 155e]), and that it leads

to paradoxes of its own.

(14) The French trait unaire is Lacan's rendition of Freud's einziger Zug (a single trait) from

his Group Psychology; see Freud 12: 136.

(15) Let me quote here Zizek's now classic formulation of this paradox: "This paradox is

founded in the differential character of the signifier's set: as soon as one is dealing with a

differential set, one has to comprise in the network of differences the difference between an

element and its own absence. In other words, one has to consider as a part of the signifier its

own absence--one has to posit the existence of a signifier which positivizes, 'represents',

'gives body to' the very lack of the signifier--that is to say, coincides with the place of

inscription of the signifier. This difference is in a way 'self-reflective': the paradoxical,

'impossible' yet necessary point at which the signifier differs not only from another

(positive) signifier but from itself as signifier" (43). For an even more classical formulation,

cf. Miller.

(16) Or at least Descartes, for paradoxically Lacan will read cogito on the basis of the same

scheme, as a certain interpretation of the intersection of one and being. Cf. Dolar 1998.

(17) I can just remind here that the question of appearance will loom large and will play the

pivotal role in the Sophist, since Plato will try to conceive and pin down the sophist precisely

as the producer of appearance.

(18) Cf. Zizek 44: "This, then, is the basic paradox of the Lacanian logic of 'non-all' [pas-

tout]: in order to transform a collection of particular elements into a consistent totality, one

has to add (or to subtract, which amounts to the same thing: to posit as an exception) a

paradoxical element which, in its very particularity, embodies the universality of the genus

in the form of its opposite." And 111: "A totality without exception serving as its boundary

remains an inconsistent, flawed set which 'doesn't hold together', a 'non-all' [pas-tout] set."

Works Cited

Brisson, Luc. 1994. "Introduction." In Luc Brisson, ed. and trans., Platon: Parmenide. Paris.

9-73.

Dies, Auguste. 1956. "Notice generale" and "Notice." In Auguste Dies, ed. and trans., Platon:

Parmenide, Theetete, Le Sophiste. Paris. v-xix and 3-52.

Dolar, Mladen. 1996. "The Object Voice." In Renata Salecl and Slavoj Zizek, eds., Gaze and

Voice as Love Objects. Durham and London. 7-31.

______. 1998. "Cogito as the Subject of the Unconscious." In Slavoj Zizek, ed., Cogito and

the Unconscious. Durham and London. 11-40.

Freud, Sigmund. 1985. The Pelican Freud Library. 15 vols. Harmondsworth.

Gill, Mary Louise. 1996. "Introduction." In Mary Louise Gill and Paul Ryan, eds. and trans.,

Plato: Parmenides. Indianapolis and Cambridge. 1-116.

Hegel, G. W. F. 1977. Phenomenology of Spirit. Trans. A. V. Miller. Oxford. (Originally

published as Phanomenologie des Geistes [Bamberg and Wurzburg 1807])

Lacan, Jacques. 1966. Ecrits. Paris.

______. 1986. The Four Fundamental Concepts of Psycho-Analysis. Ed. J.-A. Miller.

Trans. Alan Sheridan. London. (Originally published as Le seminaire de Jacques Lacan,

livre XI: Les quatre concepts fondamentaux de psychanalyse [Paris 1973])

______. 1991. Le transfert. Ed. J.-A. Miller. Paris.

______. 2001. Autres ecrits. Paris.

Miller, Jacques-Alain. 1975. "Matrice." Ornicar? 4: 3-8.

______. 1986-87. Ce qui fait insigne. Unpublished seminar.

Regnault, Francois. 1968. "Dialectique d'epistemologies." Cahiers pour l'Analyse 9: 45-73.

Zizek, Slavoj. 1991. For They Know Not What They Do: Enjoyment as a Political Factor.

London and New York.