Concept and Form:
The Cahiers pour l'Analyse
and Contemporary French Thought

This project is funded by an Arts and Humanities Research Council (AHRC) research grant and is supported by the Centre for Research in Modern European Philosophy (CRMEP) and Kingston University's Faculty of Arts and Social Sciences.

Jean-Claude Milner first presented this article as a paper on 2 June 1965 at the 21st session of Lacan’s Seminar XII, Crucial Problems for Psychoanalysis. It appeared in volume 3 of the Cahiers pour l’Analyse alongside Xavier Audouard’s essay ‘Le Simulacre’ (CpA 3.4), under the rubric ‘Sur Platon. A propos du sophiste.’ Both papers are readings of Plato’s Sophist.¹ In opposition to Audouard’s Hegelian transformation of the concept of non-being into a concept of difference, Milner identifies an irreducible function of non-being in Plato’s text that parallels the movement implied in the theory of suture proposed by Jacques-Alain Miller (in CpA 1.3). According to Milner, Plato’s generation of non-being in the Sophist should be understood from the vantage point of the logic of the signifier.

In their two pieces on the Sophist, Milner and Audouard are taking up a request by Lacan in the session of 12th May of Seminar XII. In Sophist 254-258, the dominant character in Plato’s dialogue, the Eleatic Stranger, sets out a minimal ontology of terms comprised of the five largest genera or forms: movement, rest, being, sameness, difference (or ‘the other’; to heteron). According to Lacan, this passage demonstrates how ‘the signifying dyad’ of opposition between being and non-being ‘requires the introduction of the other as such’.² Lacan draws attention to the analogy between this passage in the Sophist, where a hierarchical order is introduced into ‘dyadic, oppositional thinking’, and the process by which the child enters speech through the navigation of signifying oppositions (as expressed in Freud’s account of the child’s ‘fort-da’ game; SE 18:14-15). For Lacan, Plato is anticipating an elementary linguistic structure whereby ‘the signifier can represent the subject for another signifier’. As Lacan puts it, ‘in order that being and non-being should not be contraries equally existing, thus giving shelter to all the conjuring tricks of the sophist, it is necessary that non-being should be established as other, in order [in turn] that the sophist can be rejected there.’ Milner’s and Audouard’s papers are responses to Lacan’s request for an analysis of this crucial sequence in Plato’s Sophist. ‘Everything that I will say about this other in what is going to follow, emerges, is already perfectly articulated at the end of the Sophist, which I invoked for you just now under the rubric of the Other.’³ Audouard constructs a Hegelian account of the shift from non-being to difference, Milner’s paper focuses on the central account of the genera themselves, closely following Plato’s generation of the category of non-being.

The piece begins with a reflection on the historical relation between ontology and number. Milner cites a text by Isocrates that distinguishes between Greek ontologies on the basis of the number of entities they assume. The ancient sophists say that there are an infinity of beings, Empedocles says that there are four, Ion three, Alcmaeon two, Parmenides one, and Gorgias none. Milner suggests that Plato’s position lies between the One of Parmenides (who is represented by the Eleatic Stranger in the dialogue) and the absolute negation of Gorgias. In the Sophist, Plato’s ‘guiding desire is to establish the status of non-being’ (CpA 3.5:73).

Milner’s analysis takes the following passage of the Sophist as its point of departure:

Since we are agreed that some of the classes will mingle with one another, and others will not, and some will mingle with few and others with many, and that there is nothing to hinder some from mingling universally with all, let us next proceed with our discussion by investigating, not all the forms or ideas, lest we become confused among so many, but some only, selecting them from those that are considered the most important; let us first consider their several natures, then what their power of mingling with one another is, and so, if we cannot grasp being and non-being with perfect clearness, we shall at any rate not fail to reason fully about them, so far as the method of our present inquiry permits. Let us in this way see whether it is, after all, permitted us to say that non-being really is, even though it is not, and yet come off unscathed (254b-d).⁴

The Stranger selects movement, rest, and being as the largest genera. Milner says, ‘if, of the three selected genera, rest and movement are unable to mix with each other, while being can mix with both, then Plato has in effect constituted the minimal series proper to the support of the binary opposition between mixture and non-mixture, which is nothing other than the law of the entire collection’ (CpA 3.5:74). Among the genera, the concept of being has a special property: as well as being a term in its own right, it is mixed in with the other genera. If ‘movement’ and ‘being’ were the only genera, then, because movement is, ‘being’ would become indeterminately mixed with ‘movement’. Hence, as Milner puts it, ‘in order to make non-mixture manifest, two mutually exclusive terms, quite apart from being, are necessary: rest and movement’ (74). Milner claims that this ‘minimal series’ of three terms, on account of the distinctive features of the genus of being, already yields up the principle for a ‘hierarchy’. ‘It is being alone among all the terms that must support the binarity of the founding opposition, through an alternating duality of functions: capable of being mixed with everything, it effects the trait that defines it as an term assignable to the class of mixtures, while however ceasing in the same movement to subsist as the delimited term that this effectuated trait should define’ (75).

The Stranger then adds sameness and difference (otherness) as further essential genera. He shows dialectically how movement and rest must participate in the ‘same’ and the ‘different’ (254-56). Like Audouard, Milner highlights how the notion of the ‘the other’ (or ‘the different’) allows Plato to grant mutual determination to the forms or genera while displacing the spectre of non-being. The Stranger argues that ‘when we say non-being, we speak, I think, not of something that is the opposite of being, but only of something different’; he will go on to say that ‘having shown that there is a nature of the other, and that it is distributed among all beings in their mutual relations, we have dared to say of every part of the other opposed to being - that it is really just this that is non-being’ (Sophist, 257b, 258e). Unlike Audouard, Milner focuses in on the role of the fleeting, flickering manifestation of ‘non-being’ in Plato’s dialogue. If non-being is converted into difference, it is due to a misperception by Plato of its real movement, the effects of which will continue to be generated throughout the series.

In what follows, Milner expounds Plato’s presentation of the genera from the perspective of Jacques-Alain Miller’s conception of suture (CpA 1.3:39), identifying in the lineaments of Plato’s text a logic of the signifying chain and its retroactive causality (77).

Non-being first appears in Plato’s text as a result of the ‘internal dissymmetry’ between being as ‘expansion’ and being as ‘term’. By virtue of its unlimited generalised expansion, ‘being’ has a special function of ‘double participation’. It is this feature of ‘redoubling’ that gives rise to an ‘other that it is powerless to deny: non-being’ (75). ‘The vacillation of being as expansion and of being as term’, Milner says, ‘through the play of being and the other, generates non-being’. Noting that Plato refrains from making ‘non-being’ a sixth genus (which would complete a series of binary oppositions: movement/rest, same/other, being/non-being), Milner argues that non-being ‘surges forth in the series of genera’, manifesting itself as the movement of determination and annulment. Every time that being confirms its function of expansion, it is denied as a definable term; conversely every time it ‘collects itself as a term’, or ‘countable unity’, it denies its own expansion, refusing itself to other terms and rejecting them into the ‘abyss’ of non-being. He suggests that the notion of ‘non-being is developed through a play of vacillations between expansion and term, between place and repetition, between the function of abyss and the function of mark [cerne]’ (76). While the form of non-being clearly cannot be a counted as a ‘unity [...] among the number of forms’, the effects of its movement are discernible in Plato’s presentation, in which Milner goes on to identify a ‘cycle in which non-being is enumerated’. Before appearing as ‘the abyss which erases all terms’, non-being appears as a ‘mark repeated without a fixed place, the displacement of a fall from being’ (76). In the initial series, ‘the terms, by coming to be, deny being as a term (moment of the other)’, in turn making non-being ‘appear under all the terms as a term without fixed place, as a mark that is repeated’, and then, at the final point in the cycle, as the abyss in which all terms are effaced. The structure of non-being thus mirrors the twofold aspect of ‘being’, insofar as it is ‘at once a term of the chain, and, as term, the collapse of any chain’. It is the ‘reverse side of the struggle between term and expansion within being’ (77).

From the point of view of this ‘vacillation’, the genera can be seen as points where being is bound, but where it simultaneously ‘disappears’:

Unable to proceed without vacillation, this series is confirmed as a chain whose elements entertain relations that are irreducible to a simple succession. Some sites of interdependence are revealed therein; through the sequential linearity of the series, they sketch a profound space for the play of strict cycles alternately positing and suppressing the same, the other, being and non-being (76).

It is only at this point, after the exposition of Plato’s text, that Milner makes explicit the context provided by Miller’s ‘Suture’. The signifying chain is the ‘sole space suited to support the play of vacillation’. Wherever an element in a linear sequence is replaced by an element which, as element, transgresses this linearity (as in the mechanism of structural causality identified by Miller in ‘Action de la structure’, CpA 9.6), a ‘vacillation’ is produced within the chain. Milner gives the examples of (1) the founding exception of a chain, and (2) any marking of the place of an erasure. The institution of a linear sequence is governed by a vacillation that testifies to a ‘double formal dependence’, and which ‘retroactively defines the signifier as a chain’ (77). Plato’s chain of genera thus points towards the possibility of an ‘order of the signifier in which being and non-being would regain those traits whose very coupling guarantees truth and authorizes discourse’ (77).

Milner speculates that the notions of being and non-being might borrow their traits from the order of the signifier itself in its basic constitution. In a passage cited by Leclaire in CpA 5.1:12, Milner mentions three aspects of vacillation. First, there is ‘the vacillation of the element’ is ‘the effect of a singular property of the signifier’, and develops in a space ‘where the only laws are production and repetition: being and non-being recover this relation through their inverse symmetry, dividing themselves between term and expansion, between mark and abyss’ (77). There is also a ‘vacillation of the cause’ insofar as both being and non-being cannot posit themselves as cause except by revealing themselves to be the effect of the other. Finally, there is the movement of vacillation whereby the term that initially ‘transgresses the sequence’ calls up a transgression that annuls the whole chain.

Milner claims that grounding Platonic ontology on the logic of the signifier also makes possible a new understanding of the opposition between being and subjectivity. On the one hand, there is being as the order of the signifier, the ‘radical register of all computations’, totality of all chains, and on the other hand, the ‘one’ of the signifier, the unity of computation, the element of the chain, non-being, as the signifier of the subject (77). This latter reappears as such every time that discourse deploys its power to ‘annul’ signifying chains.

Moreover, this system also helps us to formalise Lacan’s conception of the objet petit a, which Milner refers to as ‘like the stasis of a fall’s cyclical repetition’ (78; cf. CpA 3.1:6; trans. 107). For Lacan, the splitting of the subject is coeval with the ‘dejection’ or evacuation of the objet petit a. Milner suggests the term ‘fission’ to describe what is formally common to the division of being and non-being on the one hand, and the splitting of the subject and the emergence of the objet petit a on the other. Milner and Miller return to the issue of the objet petit a in the discussion following the second of Serge Leclaire’s ‘Compter avec la psychanalyse’ seminars (CpA 3.6:95).

Following Miller's lead, Milner presents his reading of Plato as an attempt to trace ‘the lineaments of a logic of the signifier’ (78). He claims that Plato himself occludes this basic structure, and reflects on Plato’s theory of names in Sophist 262-264. According to Milner, the logic of the signifier accounts for the mirage-effects produced in Plato’s discourse, allowing us to perceive the structural necessity of its misrecognition.

Plato’s guiding aim in the Sophist is to court the concept of non-being in order to defeat the Sophist with it, i.e. to align non-being and sophistry. Milner identifies two ways in which the concept of non-being and the Sophist are interrelated. First, there is the ‘thematic relation’ of non-being to lie, error and falsity: Plato will eventually situate non-being in discourse as a type of false discourse (Sophist 262e-263d). Second, however, there is a relation of ‘homology’ between the appearances and traces of the Sophist in the dialogue and the re-emergence of non-being within discourse as false speech. In order to demonstrate this homology, Milner turns to the final pages of the dialogue, where Plato introduces a discussion of the act of naming.

Milner proposes that ‘the object of the whole dialogue [...] is the onoma [name] of the Sophist’. The Sophist appears throughout as an indeterminate figure under pursuit, pushed from definition to definition. As soon as the Sophist is named, he will cease to be. But he never appears in the dialogue as an I or a you (pronouns which designate the partners of speech). At 246e, Plato describes the role of the hermeneut capable of lending their mouth to another voice and then interpreting the utterance. The Sophist is excluded from approach by this hermeneutic art: nobody lends him their mouth, and he is excluded from replying.

Like non-being, the Sophist cannot enter discourse without warping it. If the Sophist or non-being are allowed to emerge as such, discourse will disappear, so they maintain subsistence solely through their warping of discourse. In the dialogue, the Stranger’s task is to prevent the Sophist from undermining the truth of discourse, and, by suppressing the notion of non-being, to construct a mediate form of non-being that will allow for the local possibility of false propositions (i.e. propositions that state what is not the case). Against Audouard’s interpretation, which claims that Plato successfully transforms the notion of non-being into a species of falsity or appearance, Milner argues that such a transformation, if it occurs in Plato’s text, is rather symptomatic of a denial of non-being of which Plato himself is not explicitly aware. Plato, however, ‘did not misrecognise, but simply knew nothing of the structure of the zero’ (82).⁵

Milner suggests that at the end of the Sophist, Plato tries to brush over the traces left by the Sophist and non-being. The cycles of being and non-being henceforth become abstracted from their matrix and acquire the status of ‘hypotheses’. Therefore it is necessary to read Plato against the grain. Rather than try to render a pre-existing ‘suture’ (82) in Plato’s text legible, the task here must be to ‘invent’ a suture in order to make a statement or text readable. Milner suggests that the figure of the ‘chain’ has served this purpose in his own approach to the text.⁶

Milner concludes that to make manifest the play of ‘the diffracted reflection of the signifier’ in Plato’s text, ‘one must imagine Plato directing a blind eye towards a point whose unicity, position and validity can only subsist as strangers to the gaze itself, just shy of misrecognition’ (82). He cites André Breton: ‘In order to situate the point that renders the object alive’, it is necessary ‘to place the candle well’.⁷

Notes

1. Benjamin Jowett's translation of Plato's Sophist is online via Project Gutenberg, at http://www.gutenberg.org/ebooks/1735. ↵

2. Lacan, Seminar XII, Crucial Problems for Psychoanalysis, 12 May 1965, 18th session; Gallagher version, 6-7. ↵

3. Lacan suggests that ‘the modern status of the subject’ can already be discerned in Plato’s ontology of the genera, but that ‘the tension that there is between this Other and the One, and which would allow us to ground this Other as what I call the One-more (Un-en-plus)’ has to wait until ‘the theory of the One-more that you only see emerging in the theory of numbers with Frege’. Lacan, Seminar XII, Crucial Problems for Psychoanalysis, 12 May 1965, 18th session; Gallagher version, 6-7. ↵

4. Jowett's translation of this passage reads as follows: ‘Since, then, we are agreed that some classes have a communion with one another, and others not, and some have communion with a few and others with many, and that there is no reason why some should not have universal communion with all, let us now pursue the enquiry, as the argument suggests, not in relation to all ideas, lest the multitude of them should confuse us, but let us select a few of those which are reckoned to be the principal ones, and consider their several natures and their capacity of communion with one another, in order that if we are not able to apprehend with perfect clearness the notions of being and not-being, we may at least not fall short in the consideration of them, so far as they come within the scope of the present enquiry, if peradventure we may be allowed to assert the reality of not-being, and yet escape unscathed.’ ↵

5. In the version of the text given in Lacan’s seminar, Milner appears to state (although the transcription is corrupt) that ‘it remains impossible … for us to welcome the concept of simulacrum into analytic discourse’. Seminar XII, 2 June 1965, 21st session, Gallagher version, 12. ↵

6. The final sentence is removed from the text as it appears in the Cahiers, but included in the seminar: ‘I found that Plato himself articulated the laws of the locus of discourse … [This] calls for a reading whose order would depend on a unique point whose validity only revealed itself to be foreign to Plato on the hither side of a misrecognition’. Seminar XII, 2 June 1965, 21st session, Gallagher version, 13. ↵

7. The citation is from Breton’s ‘Ideas of a Painter’, on the work of André Derain: ‘The object whose being I paint only lives insofar as I can make a “point blanc” (blank point) appear. Everything is in placing the candle well’ (Breton, Oeuvres complètes, 1, 248). ↵