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

Despite its plural uses over the course of Jacques Lacan’s teaching, lack is arguably the central concept of negation to be found there, as well as the crucial framework for thinking through the phenomenon of subjectivity in Lacanian thought. For Lacan, lack is intimately related to desire; all desire is born from a lack, or indeed a manque-à-être (which Lacan proposed should be translated as a ‘want-to-be’). This lack operates on many levels crucial to psychoanalysis, e.g., symbolic castration is the experience by which the subject comes to recognize that he lacks the imaginary phallus possessed by the real father. Likewise, the infant’s lack of access to the real breast of the symbolic mother results in an imaginary frustration that is essential for the infant’s own ego formation. For Lacan, however, lack came to have a properly ontological remit, or more precisely a ‘pre-ontological’ one. In Seminar XI, in response to Jacques-Alain Miller’s questions concerning the ontological status of lack and the subject, Lacan remarked that the ‘structuring function of lack’ is itself predicated upon a pre-ontological ‘gap’ [‘béance’] that is precisely ‘the gap of the unconscious’ (S XI, 29).

What this means in philosophical terms is that Lacan conceives of lack as the primordial phenomenon, anterior to being itself. As such, being can never be thought of as a totality or a plenitude marked by completeness or closure; rather, lack itself, by virtue of being constitutive via the subject, marks being as such, condemning it to permanent incompleteness. In Lacan’s account of language, this translates into his claim that the signifying chain is always incomplete; there is always one more signifier to be added to the chain that is nonetheless never added. In the Lacanian algebra, this ‘missing signifier’ is -1, a primordial negation or lack that is constitutive of the subject as such. In this regard, lack is both what causes the subject to emerge and what binds the subject to the chain of its discourse, which is bound in turn to the web of desire structured by the big Other of language.

In the Cahiers pour l’Analyse

In the inaugural article of the journal, ‘La Science et la vérité’, Lacan addresses the ‘lack of truth about truth’ at the heart of scientific discourse, which is to say, science’s repression of the fact that the truth of its own discourse is constituted by a lack. Lacan affirms there is nothing ‘noumenal’ about this lack; it is simply psychoanalysis’s task to identify it. As such, ‘there is no other truth about truth that can cover over this sore point than proper names, Freud’s or my own’ (CpA 1.1:19; E, 868). In his conclusion, Lacan remarks that psychoanalysis differentiates itself from religion and magic, as well as science, by ‘revealing that the phallus itself is nothing but the site of lack it indicates in the subject’ (CpA 1.1:28, E, 877).

In Jacques-Alain Miller’s ‘La Suture: Éléments pour une logique du signifiant’ (CpA 1.3), one of the seminal articles of the journal, the concept of suture is intimately tied to the lack that is constitutive of the subject. Miller writes: ‘Suture names the relation of the subject to the chain of its discourse; we shall see that it figures there as the element which is lacking in the form of a stand-in [tenant-lieu]. For, while there lacking, it is not purely and simply absent. Suture – by extension, the general relation of lack to the structure of which it is an element, inasmuch as it implies the position of a taking-the-place-of [tenant-lieu]’ (CpA 1.3:39, trans. 25-6).

Miller pursues his analysis of suture through an engagement with Gottlob Frege’s Foundations of Arithmetic (CpA 1.3:44-48). For Miller, the absolute zero, as the concept for an object that is not identical to itself, is at once summoned and annulled in order to establish the sequence of whole numbers. This movement of evocation and rejection, summoning and annulment, is the movement that is essential to the logic of the signifier, and that grounds logic and language itself according to Miller. If one is not cognizant of this fundamental procedure of ‘evocation and revocation’, one will miss that there has been a conversion from an ‘absolute zero’, or a zero as ‘lack’, to the relative zero, or zero as number. The zero, understood as a number, can thus claim to be ‘the first non-real thing in thought’ (CpA 1.3:44/30).

But by establishing the singularity of this category, Frege is able to generate the 1 out of the 0; in effect, 1 becomes the ‘proper name’ of 0. Crucial here is the relation between verticality and horizontality, a relation which maps on to Lacan’s concept of metaphor’s relation to metonymy. Miller argues that the ‘verticality’ of the movement from zero to one, by which ‘the 0 lack comes to be represented as 1 […], indicates a crossing, a transgression’; the successor operation installs a ‘horizontal’ sequence of numbers on the basis of this primary ‘verticality’ (CpA 1.3:46/31). The exclusion of the absolute zero, as a concept inimical to truth, is an instance of suture; what establishes the horizontal or metonymic chain of discourse is a suture which covers over the primordial lack of the absolute zero that made the chain of discourse possible in the first place.

In the first lesson of his seminar, ‘Compter avec la psychanalyse’, reproduced in Volume 1 of the Cahiers (CpA 1.5), Serge Leclaire develops a critique of the abstraction of Miller’s presentation, aiming to reconnect the ‘logic of the signifier’ developed therein with the bodily surface and the signifiers which mark it. He writes:

It is necessary to grasp the fundamental relations of the signifier with this indelible mark that is the detachment installing the cut [coupure] within the non-dual, and which makes emerge the radical transgression that institutes the zero of lack. There alone does the zero of lack appear as zero and not only as lack. There the signifier ‘incarnates’ itself, insofar as the cut makes the zero of lack and the polarising one of the trait emerge (CpA 1.5:68).

Near the conclusion of his ‘Réponse aux étudiants en philosophie sur l’objet de la psychanalyse’ (CpA 3.1), Lacan writes: ‘The object of psychoanalysis is not man; it is what he lacks – not an absolute lack, but the lack of an object. Even then agreement must be reached as to the lack in question – it is that which excludes the possibility of naming its object’ (CpA 3.1:12, trans. 113). Here lack is tied to the Lacanian concept of the objet petit a. Moreover, Lacan’s claim here functions as a contribution to the general debate in the Cahiers launched by Miller’s theses in ‘La Suture’ (CpA 1.3). Not being absolute – that is to say, an aspect of a general ontology indifferent to subjects – lack is specific to unique subjects.

Similarly to Leclaire, André Green seeks, in his contribution to Volume 3 of the Cahiers (CpA 3.2), to provide Miller’s arguments with a firmer base in bodily affect and the basic terms of psychoanalysis grounded in childhood experience. In the first place, Green enumerates the process by which the child undergoes an imaginary castration to receive the symbolic phallus or ‘Name-of-the-Father’, a signifier which marks a radical absence or lack (CpA 3.2:17). Green then explores the function of lack in terms of the developmental concerns of Freudian theory, with specific focus on the objet petit a as an object of lack that remains, in its essence, ‘non-specularisable’ (CpA 3.2:19-21).

In his reading of Plato’s Sophist in ‘Le Point du signifiant’ (CpA 3.5), Jean-Claude Milner addresses the peculiar phenomenon of the proper name as that which covers over that which lacks in the chain of discourse, but that at the same time condenses discourse itself, making of the subject precisely that which does not lack (CpA 3.5:81).

In the instalment of his ‘Compter avec la psychanalyse’ seminar in Volume 3, Leclaire affirms again that his analysis is guided by Lacan’s teachings concerning the unconscious and the ‘central function of lack’, which together make manifest the ‘impasses of knowledge and the order of the phantasm’ (CpA 3.6:83). In the discussion following Leclaire’s lesson, Miller insists that the ‘impossible object’ is not a remainder, but a lack, and that as a result the ‘object (a) is zero as lack’ (CpA 3.6:95). Milner, likewise, reaffirms his theses from ‘Le Point du signfiant’ (CpA 3.5) in claiming that the proper name can cover over the place of the object (a) and act as a calming element, playing the same role as the zero in Miller’s reading of Frege. Leclaire concedes that there may be a homogeneity of places, but that the terms themselves remain heterogeneous, which leads Milner to call for a firmer theoretical distinction between terms and places (CpA 3.6:95). In the next and final instalment of Leclaire’s seminar in Volume 8, lack will emerge again as a key term in the assessment of the objet petit a in the play of sexual pleasure (CpA 8.6:96).

In his reading of Balzac’s Sarrasine in Volume 7 of the Cahiers, Jean Reboul notes how the Lacanian phenomenon whereby that which is repressed or avoided in the symbolic returns in the real is in play in Sarrasine’s relation to the castrato Zambinella. Zambinella is ‘castration personified’. Sarrasine, meanwhile, is the bearer of ‘an uncertain penis’. Having avoided the test of symbolic castration, he ends up encountering lack and castration ‘in the real’ [dans le réel] (CpA 7.5:96). His narcissism fragments before a ‘profaned mirror’. He cannot re-appropriate himself as a desiring being, and now, insofar as the imaginary other literally does not have the phallus, he becomes permanently ‘excluded’ from possessing a ‘specular other’. ‘For him, there are no more women, nothing but mutilated men’. Hence the shadowy, vampiric apparition at the ball at the beginning of the story. ‘Castration and death, the fatal cycle is closed’ (CpA 7.5:96).

Lack performs a crucial function in Jacques-Alain Miller’s ‘Action de la structure’ (CpA 9.6), one of the Cahiers’ central programmatic texts. In effect, lack, as the site of suture that produces the subject, is the motor of the ‘action of the structure’ itself. Miller argues that the relation of the subject to the structure is mediated by a misrecognition. A system of representations is established, built around ‘the fundamental absence in the structuring process’, and ‘compensat[ing] for the production of lack’. The imaginary is thus both an effect and, more profoundly, a means of structuration with its own specific mechanisms of production (CpA 9.6:96).

Miller outlines a complex account of how ‘the totality of structure’ may be reconstituted. Although overdetermination must be ‘relate[d] back to lack as to its principle’, lack itself never appears as such, and is instead always misrecognised by the inhabitants of the structure. It is at this juncture that Miller attempts to fuse his conceptions of suture and structural causality: ‘We must deduce from this that, in this place where the lack of the cause is produced in the space of its effects, an element interposes itself that accomplishes its suturation’ (CpA 9.6:96). Every structure includes a ‘lure’ or ‘decoy’ [leurre] which takes the place of the lack [tenant lieu de manque], but which is at the same time ‘the weakest link of the given sequence’, a ‘vacillating point’ which only partially belongs to the plane of actuality.

In the final section of this article, Miller applies his arguments to the domain of science itself. The closure proper to scientific discourse, Miller insists, should not be confused with the suture of non-scientific discourse. Its procedure of negation is in fact more radical: it actually expels lack [elle met le manque à la porte], in the manner of a foreclosure:

Thought from within the field it circumscribes, this closing [fermeture] will be given the name: closure [clôture]. But the limit of this circumscription has a density, it has an exterior; in other words, scientific discourse is not marked [frappé] by a simple lack – rather the lack of a lack is also a lack (CpA 9.6:102).

Miller calls this ‘lack of a lack’ that is itself a lack a ‘double negation’: ‘It is this double negation that confers positivity on the field of the theory of discourse’. This conception will be taken up and put to the test by François Regnault in ‘Dialectique d’épistémologies’ (CpA 9.4) and Alain Badiou in ‘Marque et manque: A propos du zéro’ (CpA 10.8). Miller’s point is that, although scientific discourses do not have utopic elements such as are found in ideology, this special ‘lack of a lack’ nevertheless creates a space for ideology at the borders of scientific discourse.

In its essentials, Badiou’s ‘Marque et manque’ is a defence of scientific discourse against the claims developed by Miller in ‘Action de la structure’ (CpA 9.6). In effect, the quarrel between Badiou and Miller turns on the relation between the concepts of suture and foreclosure. In Badiou’s reading of Kurt Gödel’s undecidability theorems, scientific discourse is accomplished through an exclusion of lack, that is to say, a foreclosure that prevents the possibility of any suturing operation. The derivation of the undecidable must be understood, not as ‘the suturing of lack, but rather the foreclosure of that which is lacking through the failure to produce, within what is derivable, the entirety of the non-derivable as negated’ (CpA 10.8:155). Crucial to Badiou’s argument is his insistence that, in scientific discourse, marks (e.g., x, 1, or 0) are self-identical, which is also to say, that in each instance of the discourse they are functionally the same. Miller’s evocation in ‘La Suture’ (CpA 1.3) of a non-identical and thus non-substitutable thing (i.e., a subject) in Frege’s gestation of the whole number line out of the zero is thus ‘foreclosed’ here in advance, ‘without appeal or mark’ (CpA 10.8:157). Whatever is presented as lacking (as zero) can only be so presented insofar as it was first presented, precisely, on a different level - i.e., only insofar as it was first positively marked in a different layer of discourse. Badiou thus refuses Miller’s own conception of foreclosure (in ‘Action of the Structure’, CpA 9.6:102) as a sort of redoubled lack, a conception whereby the ‘lack of a lack is also a lack’ (CpA 10.8:161).

The remainder of Badiou’s article develops the philosophical implications of his argument. The logic of suture applies only to the domain of ideology, i.e., to the domain of the (‘castrated’ or barred) subject’s speech and experience. The signifying order of science itself, however, is ‘stratified in such a way that no lack is marked in it that does not refer to another mark in a subjacent order differentiated from the first. Science does not fall under the concept of the logic of the signifier. In truth, it is the fact that it does not fall under it that constitutes it: the epistemological break must be thought under the un-representable auspices of de-suturation.’ The essential conclusion follows immediately:

Accordingly, there is no subject of science. Infinitely stratified, regulating its passages, science is pure space, without inverse or mark or place of what it excludes.

Foreclosure, but of nothing, science may be called the psychosis of no subject, and hence of all: congenitally universal, shared delirium, one has only to maintain oneself within it in order to be no-one, anonymously dispersed in the hierarchy of orders. Science is the Outside without a blind-spot (CpA 10.8:161-2).

Philosophy is thus constitutively committed to an impossible task. It seeks ‘to mark, within its own order, the scientific signifier as a total space. But science, indefinitely stratified, multiple foreclosure, difference of differences, cannot receive this mark. The multiplicity of its orders is irreducible: that which, in philosophy, declares itself science, is invariably the lack of science. That which philosophy lacks, and that to which it is sutured, is its very object (science), which is nevertheless marked within the former by the place it will never come to occupy.’

This logical articulation of mark and lack then allows Badiou to return to Miller’s conception of the subject (the subject as lack of self-identity) and use it to confirm his own characterisation of the relation between science and philosophy. He thereby ‘claim[s], in all rigour, that science is the Subject of philosophy, and this precisely because there is no Subject of science’ (CpA 10.8:163). This lack of a subject in science, i.e., this radical lack of any lack, persists as the eternal ‘torment’ of philosophy. An ideological practice, philosophy is the endlessly futile effort to locate a subject (be it logos, God, man, speech...) at the very point, indicated by science, where every figure of the subject is proscribed in advance. ‘Through science we learn that there is something un-sutured; something foreclosed, in which even lack is not lacking. By trying to show us the contrary, in the figure of Being gnawing at itself, haunted by the mark of non-being, philosophy exhausts itself trying to keep alive its supreme and specific product: God or Man, depending on the case’ (CpA 10.8:163).

Select bibliography

• Badiou, Alain. L’Être et l’événement. Paris: Seuil, 1988. Being and Event, trans. Oliver Feltham. London: Continuum, 2005.
• Lacan, Jacques. Écrits. Paris: Seuil, 1966. Écrits, trans. Bruce Fink, in collaboration with Héloïse Fink and Russell Grigg. New York: W.W. Norton, 2006.
• Lacan, Jacques.Le Séminaire, livre XI: Les quatre concepts fondamentaux de la psychanalyse, ed. Jacques-Alain Miller. Paris: Seuil, 1973. Seminar IX: The Four Fundamental Concepts of Psychoanalysis, ed. Jacques-Alain Miller, trans. Alan Sheridan. London: Penguin, 1977.
• Miller, Jacques-Alain. Un Début dans la vie. Paris: Gallimard, 2002.
• Milner, Jean-Claude. L’Oeuvre claire: Lacan, la science, la philosophie. Paris: Seuil, 1995.