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Synopsis of Alain Badiou, ‘Marque et Manque: à propos du Zéro’

[‘Mark and Lack: On Zero’]

CpA 10.8:150–173

With this, the penultimate article in the last volume of the Cahiers pour l’Analyse, Alain Badiou offers a sustained critique of Jacques-Alain Miller’s ‘Suture’ (CpA 1.3), the key article of the journal’s inaugural issue. What is at stake is nothing less than the guiding concern of this collective theoretical enterprise: the relation between science and subject. Badiou rejects Miller’s attempt to conceive of a general ‘logic of the signifier’ that both expresses, and is engendered by, the subject’s lack of identity with itself, in favour of a strictly formal conception of logic purged of any reference to non-self-identity, subjectivity or lack. He insists, in particular, that the implications of Gödel’s famous incompleteness theorem undercut rather than reinforce Miller’s efforts, and Lacan’s gestures, on this score, in effect reasserting the integrity of formalised science and restricting the ‘logic of the signifier’ to ideology alone.

Remarkable both for its remorseless ‘theoreticism’ and its clipped Mallarméan style, ‘Mark and Lack’ is one of the most forbidding articles in the whole of the Cahiers. Written before the tumultuous watershed of May 1968 (but published afterwards), it is nevertheless a critically important text, not only for assessing the theoretical legacy of the Cahiers pour l’Analyse but also for illuminating Badiou’s own intellectual itinerary. If the challenge of Badiou’s work after 1968 has been to develop a new articulation of formalisation and subject (precisely via the vanishing mediation of a non-self-identical term, or ‘event’), in ‘Mark and Lack’ he argues, in keeping with Althusser’s familiar distinction of science and ideology, for their mutual exclusion. Althusser’s position was implacably clear: ‘an ideology is a distorted representation of reality: it is necessarily distorted, because it is not an objective but a subjective representation of reality [...]. Science, in contrast, exists only on condition that it struggles against all forms of subjectivity, class subjectivity included (consider Lenin’s struggles against the “spontaneous” ideology of the proletariat); science is objective.’1

Badiou wrote ‘Mark and Lack’ at a time when, as he remembered later, ‘I was freeing myself from Sartre, existentialism and phenomenology. I would say that what first seduced me in my mathematical education was the non-subjective, the making possible of a capacity to think outside of all intentionality and subjectivity.’ ‘Mark and Lack’ ultimately affirms a conception of science as literally ‘psychotic’ in the Lacanian sense. Science is a formal practice that forecloses subjectivity - and with it, any susceptibility to the process of suture.2

In 1990 Badiou returned to consider anew Miller’s article - ‘the first great Lacanian text not to be written by Lacan himself’ - in a chapter of his book Number and Numbers.3

Born in 1937, Badiou was several years older than founder-editors of the Cahiers like Miller, Milner and Duroux, and by the time the journal was launched in the mid-1960s he had already left the Ecole Normale for a teaching position in Reims. As a result he joined the editorial board late, in 1967, and his distinctive contribution - a more rigorous approach to questions of science and mathematical logic - is most apparent in the last two issues of the journal. By the time ‘Mark and Lack’ was published the editorial collective had already disbanded, and it’s hardly an exaggeration to say that the philosophical significance of this early debate between Miller and Badiou would be more or less ignored, at least in mainstream philosophical circles, for several decades. It might be even less of an exaggeration to say that the revolutionary theory of the subject that Badiou went on to develop in the 1970s and 80s has its origins precisely in a sort of disjunctive synthesis of Miller’s (neo-Lacanian) ‘Suture’ and his own (neo-Althusserian) ‘Mark and Lack.’

The broader philosophical background for the argument of ‘Mark and Lack’ was establishedin a substantial article on Althusser that Badiou published in 1967, under the title ‘Le (Re)commencement du matérialisme dialectique’ (RMD). Unlike ideology or lived experience, ‘science is precisely the practice that has no systematic sub-structure other than itself, no fundamental “ground” [sol]’ (RMD, 443n.10). Whereas ideologies are concerned with the way objects and conditions are lived, represented and experienced, the specific and ‘proper effect of science - the effect of knowledge - is obtained by the rule-governed production of an object that is essentially distinct from the given object’ (RMD, 449). Science is concerned with a sphere in which, as Bachelard succinctly put it, ‘nothing is given, everything is constructed.’4

The only practices that might qualify as unequivocally scientific in this sense are mathematical, and more precisely mathematical in an axiomatic-formalist sense (as developed, for instance, in David Hilbert’s account of The Foundations of Geometry [1899]). A suitably formal mathematical logic, Badiou explains, manipulates nothing other than the ‘marks’, letters or symbols that it prescribes for itself, in the absence of any external relation to objects or things. ‘Neither thing nor object have the slightest chance here of acceding to any existence beyond their remainderless exclusion’ (CpA 10.8:156). As Badiou was soon to explain in his contribution to the 1968 ‘Philosophy Course for Scientists’ that Althusser organised at the Ecole Normale, ‘mathematical experimentation has no material place other than where difference between marks is manifested.’5

The whole of ‘Mark and Lack’ presumes, then, an ‘inaugural confidence in the permanence’ and self-identity or self-substitutability of logico-mathematical marks or graphemes (156). Given any mark x, logic must always treat x as strictly and unequivocally identical with itself. Badiou thus takes for granted a position that Miller associates, in ‘Suture’, with Leibniz and Frege (CpA 1.3:43): scientific knowledge depends on the exclusion of the non-identical, with the proviso that ‘the concept of identity holds only for marks’, i.e. mathematical inscriptions. ‘Science as a whole takes self-identity to be a predicate of marks rather than of the object’, a rule which applies to the ‘facts of writing proper to Mathematics’ as it does for the ‘inscriptions of energy proper to Physics’, along with the instruments used to measure them:

It is the technical invariance of traces and instruments that subtracts itself from all ambiguity in the substitution of terms. Thus determined, the rule of self-identity allows of no exceptions and does not tolerate any evocation of that which is withheld from it, not even in the form of rejection. What is not substitutable-for-itself is something radically unthought, of which the logical mechanism bears no trace [...]. What is not substitutable-for-itself is foreclosed without appeal or mark (CpA 10.8:157).

In RMD Badiou had already acknowledged the significance of Miller’s contribution to structuralist epistemology. ‘The fundamental problem of all structuralism’, Badiou recognises after Lévi-Strauss, ‘is that of a term with a double function, which determines the belonging of the other terms to the structure insofar as it itself is excluded from it by the specific operation that makes it figure there only in the form of its representative (its place-holder [lieu-tenant], to use Lacan’s concept).’ The ‘determination, or “structurality”, of the structure’, Badiou suggests, is thus governed by the ‘location of the place occupied by the term indicating the specific exclusion, the pertinent lack.’ Badiou applauds Miller’s article ‘Suture’ as an ‘essential reference’ in the conceptualisation of such determination. Although ‘extraordinarily ingenious’, however, Badiou warns that Miller’s approach is ‘epistemologically inadequate’ and involves a ‘duplication of the structure of metaphysics’ (RMD, 457n.23).

The Lacanian ‘logic of the signifier’ that Miller proposes in ‘Suture’ turns essentially on the representation of an irreducible lack. A signifier represents (i.e. treats-as-identical or counts-as-one), for another signifier, that essential lack of self-identity which is the subject. This logic of the signifier envelops or sutures lack (i.e. the subject) to a signifier that represents it only in the vanishing movement of its successive references to another signifier.

Badiou counters that such a logic isn’t really ‘logic’ at all. A properly scientific logic is a wholly ‘positive’ process, one that ‘lacks nothing it does not produce elsewhere’ ((151)). The pseudo-scientific logic proposed by Miller and Lacan thus serves merely to blur if not to ‘erase the epistemological break’ by which science distances itself from the domain of ideology, i.e. the domain of the subject and lived experience. Their logic of the signifier remains a form of ‘metaphysics: a representation of representation, an intra-ideological process’ (151; 151n2; see also 156).

In the first of the four main parts of his article, Badiou demonstrates that the essential operation of (genuine or scientific) logic - for instance the sort of logic at work in formal propositional calculus - involves the ‘separation’ or distinction of statements as valid or invalid, i.e. as consistent with a system or inconsistent with it. He then goes on to show that what Gödel calls ‘incompleteness’ does not threaten the essential integrity and self-sufficiency of such a logical system. Vague semantic (i.e. ideological) associations aside, logical incompleteness does not introduce any sort of ‘lack’ into the domain of science.

The ‘production’ that is logical separation proceeds across several levels, i.e. it operates via several stratified ‘mechanisms’. The primary level or mechanism (M1), the mechanism of ‘concatenation’, produces arrangements of a discreet set of elementary marks or letters, as a sort combinatorial ‘alphabet’ (by way of illustration, consider for instance all the possible combinations of the letters used in the English language). At a second level, the level of ‘formation’ (M2) - i.e. the level of ‘syntax’ - certain expressions are deemed acceptable or ‘well-formed’, and separated from those that are rejected as ill-formed (152). To pursue our linguistic analogy, at this second level we might distinguish between syntactically valid (though not necessarily coherent or meaningful) sequences of words, as opposed to random series of letters. The third level (M3), the mechanism of ‘derivation’, will separate sequences that can be derived or ‘proved’ as valid ‘theses’ from sequences or statements that cannot be thus proved, i.e. from ‘non-theses’. We might call this third level the domain of intelligibility or coherence, the level at which coherent expressions are distinguished from incoherent albeit ‘well-formed’ strings of words.

Whereas the separation of well-formed from ill-formed expressions (at level two) is absolute and straightforward, the relation between derivable and non-derivable expressions at level three may, in any system complex enough to formulate basic arithmetical expressions, be either decidable or non-decidable. ‘An undecidable statement is not the remainder of a cut [i.e. separation], but a statement such that neither it nor its negation is derivable’ or provable (153). The crux of Badiou’s argument here is that Gödel’s demonstration of the incompleteness of any relatively complex logical system applies to this level three (M3) alone.

In other words, in any relatively complex logical system which is sufficiently ‘strong’ to allow for the articulation of statements that relate any given statement to its negation, it is not always possible to decide on the meaning or coherence of all such statements. Some may remain undecidable, and thereby involve a certain ‘tearing of structure’ (154). This means that in such a system, the negation of some non-theses at level M3 cannot simply be identified with valid, provable theses; these negative statements thus remain unrelated to the domain of theses, and consequently evoke a sort of ‘distance without concept.’ They testify not to a failure of separation (i.e. a failure clearly to divide theses from non-theses) but, on the contrary, to the ‘place of separation’s greatest efficacy’ (i.e. a division that leaves no relation at all between the terms it divides).

The derivation of the undecidable must be understood, then, 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’ (155).

Badiou unpacks this compressed assertion in the second of the four parts of his article. The essential point again involves the self-identity, as far as logic is concerned, of the marks or letters it uses to articulate its statements. Any mark x must always be identical to itself. As a sign or mark, every x must be and remain this same x. It is perfectly possible, however, to express a lack of equality between x and itself, with the well-formed (albeit unintelligible) expression ‘x x’. (In terms of Badiou’s three mechanisms of separation, both x = x and x x are legitimate expressions at M2, i.e. the level of formation, but the expression x x is excluded as non-derivable or unintelligible from level M3 [158-59]).

What then is the logical status of this incoherent but well-formed expression, x x? The key thing to remember is that ‘it is necessary that one be unable to conceive that x, qua mark, is “other” than x - the same mark placed elsewhere - in order for this statement to be logically produced. The mere convocation-revocation of x’s non-self-identity, the shimmering of its self-differing, would suffice to annihilate the scriptural existence of the entire calculus.’ In other words, we can formulate logically coherent statements of non-self-equality (on the model x x) only if we first exclude all that is ‘scripturally non-self-identical. The lack of the equal is built upon the absolute absence of the non-identical’ (158). Miller’s evocation of a non-identical and thus non-substitutable thing (i.e. a subject) is thus ‘foreclosed’ here in advance, ‘without appeal or mark’ (157).

In part three Badiou moves on to consider the nature of the paradoxical mark that is zero itself, understood as the mark which serves to enumerate all those marks that are not equal to themselves. Zero is the number of x’s that fit the relation of x x. The symbol zero can be understood as an abbreviation of a statement produced at level M2, i.e. the proposition 0(x), which can be read: ‘x is a zero, it has the property of not being equal to itself’ (160). Unlike Miller, however, Badiou does not infer from this predication of zero to x, i.e. the attribution to x of the property of being-unequal-to-self, that x itself, qua mark or sign, has in any sense become non-self-identical and thus non-substitutable with itself.

Defined in this way, zero is simply a shorthand for the expression ‘there are no non-self-identical objects or marks.’ Zero serves here as the ‘abstraction’ or ‘proper name’ of a construction produced at M2 and then rejected as non-derivable at M3 (and strictly speaking the attribution of such a name itself operates at a further, fourth level, M4). In short, ‘the zero marks in M4 (in predicative form), not the lack of a term satisfying a relation, but rather a relation lacking in M3. But it is necessary to add immediately: if the relation can be lacking in M3, it is only insofar as it figures in M2’ (161). 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. 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’ (161).

The fourth and final part of Badiou’s article develops the properly 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 (161-62).

The ‘science of psychoanalysis’, consequently, can have ‘nothing to say about science’ per se, precisely because it serves to analyse the ‘functioning’ and ‘efficacy’ of ideologies. Psychoanalysis helps to establish ‘the laws of input and connection through which the places allocated by ideology are ultimately occupied.’ It is on this basis that psychoanalysis and historical materialism might be articulated together, as a double ‘determination of the signifiers’ at work in lived or ideological discourse, thereby ‘producing the structural configuration wherein ideological agency takes place’ (162).

Whereas science ‘relates only to itself’, such that ‘no signifying order can envelop the strata of its discourse’, Badiou (again following Althusser) defines ‘philosophy’ as ‘the ideological region specializing in science, the one charged with effacing the break by displaying the scientific signifier as a regional paradigm of the signifier-in-itself. This is Plato’s relation to Eudoxus, Leibniz’s relation to Leibniz, Kant’s relation to Newton, Husserl’s relation to Bolzano and Frege, and perhaps Lacan’s relation to Mathematical Logic’ (163). 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, very neatly, 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’ (163). Purged of any reference to a subject, science i.e. mathematics remains an austere ‘archi-theatre of writing’, the articulation of marks, traces, and traces of traces ‘indefinitely substituted for one another in the complication of their entangled errancy’. In terms reminiscent not only of Mallarmé, Blanchot and Foucault, but also of the Derrida whose reflections on arche-writing had shaped most of the fourth volume of the Cahiers (CpA 4.1), science here prescribes a signifying movement in which ‘we never risk encountering the detestable figure of Man’ (164), no more than God, Spirit or any other figure of the subject.

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’ (163).

* * *

In the semi-technical appendix to ‘Mark and Lack’, Badiou demonstrates how Gödel’s theorem serves to ‘limit’ any sort of undertaking that seeks to establish itself on the basis of its own internal coherence or closure, and that (by appearing to reconcile philosophy with science) might thereby seem to heal or at least ‘efface the wound which was historically opened within the weave of ideology by the fact of science’. At the most general level, Gödel’s theorem confirms and ‘illustrates philosophy’s failure to prescribe to mathematical inscriptions even the unity of a space of existence. It indicates stratification’s resistance to the schemes of closure that philosophy has sought to impose upon the former for the sake of its own salvation’ (164).

What is basically at stake in Gödel’s theorem is the production ‘of a statement that exhausts itself in stating its own falsity’ (165). The work of ‘limitation’ at issue here ‘comes down to the possibility of constructing a predicate of non-derivability in a formal language and applying this predicate to a representative of the statement formed by this very application.’

Gödel’s theorem does not therefore suspend the ‘psychotic’ foreclosure of lack from mathematical logic. Instead it engineers ‘a reprise, within the system’s architectonic transparency, of certain ambiguities produced in language by the (ideological) concept of Truth. If one tries to make the Derivable subsume the True, then like the latter the former operates as a snare at the elusive juncture between science and its outside.’ Understood along these lines, ‘Gödel’s theorem is one of formalism’s fidelity to the stratifications and connectivities at work in the history of the sciences, insofar as they expel from the latter every [ideological] employment of the True as (unlimited) principle’ (166).

The remainder of Badiou’s appendix offers what he describes as a ‘largely intuitive but nevertheless complete and rigorous demonstration of the essential core of a limitation theorem’, adapted from R.M. Smullyan’s Theory of Formal Systems (1961). The basic sequence of the demonstration is as follows:

1. First we posit a set called ‘E’ of well-formed expressions of a logical system, i.e. the existence of a ‘syntax’ or ‘mechanism of formation’ (operative at what Badiou has called level M2, above). Taking for granted the set of integers (or ‘counting numbers’: 1, 2, 3...), we further assume that we can count-off every expression in the system, such that to every integer there corresponds one and only expression (166). By thus ‘diagonally mapping’ an expression onto a particular number ‘we obtain an inscription within the system which thereby “talks” about numbers’ (167).

2. Next, we posit a ‘mechanism of derivation or demonstration’ (at level M3) which operates on the statements produced via M2, and which (a) distinguishes between provable expressions and unprovable expressions, and (b) demarcates a set of refutable expressions (i.e. expressions whose negation is provable). What Gödel then demonstrates are the structural conditions under which it is impossible to determine whether every unprovable statement is (or is not) refutable.

3. Take any given set ‘W’ of provable expressions, and map the expressions in W onto the integers to which they correspond. The set W* will be the set of integers that number these ‘diagonal expressions’. If W* is represented in the system, the system thus includes a predicate which signifies ‘to be a number that represents a diagonal expression contained in W’. If now we further ‘diagonalise’ this predicate, i.e. map it to its own numerical representation, we obtain a further statement, whose meaning Badiou renders as follows: ‘the number that represents the predicate, “to-be-a-number-that-represents-a-diagonal-expression-contained-in-W”, is itself a number that represents a diagonal expression contained in W.’ Such a statement is ‘not provable unless it belongs to W’; in other words it functions as a ‘Gödel statement’ for W (170). A ‘Gödel statement’ serves in effect to express what it means to be ‘provable in the system.’ (The derivation of such statements is typical, Badiou observes, of the ‘underlying structure of the diagonal processes which, ever since Cantor, have provided “foundational” mathematics with its principal instrument: the construction of a statement that affirms its own belonging to a group of expressions which this statement represents or designates’ (170).

4. If now we apply the process diagonalisation to the subset of statements in E that are refutable - call them the subset R - ‘we will thereby quite easily obtain Gödel’s Theorem: if R* is representable, then there exists a statement that is neither provable nor refutable’ (171). The Gödel statement for R will be the diagonalisation of the predicate that represents the set R*, where R* is the collection of numbers corresponding to the expressions in R. Such a statement implies that ‘the number that represents the predicate, “to-be-a-refutable-diagonal-expression,” itself represents a refutable diagonal expression.’ The meaning of such a statement is clearly undecidable, for the same sort of reasons that underlie the classical paradox of the liar (i.e. the impossibility of deciding whether a liar who insists ‘I am lying’ is in fact lying).

Badiou follows his version of Smullyan’s demonstration by listing, with dizzying concision, a series of seven stages in that ‘dialectic of science and ideology’ which determined the context of Gödel’s intervention. These stages run from the historical establishment of ‘intuitive’ arithmetic through the scientific construction (in Russell and Whitehead’s Principia Mathematica) of formal systems that represent such arithmetic (and the ‘ideological re-presentation’ by Husserl of this scientific break in terms of rational ‘closure’ and consistency) to the further scientific break (via Gödel) that constructs a rigorous mathematical syntax and thereby establishes that ‘the structural stratification of the mathematical signifier does not answer the “question” of closure.’ Gödel’s break, in turn, comes to be ideologically re-presented (for instance by Miller-Lacan) as a limitation performed upon aspirations to closure, and thus as testifying to an apparent ‘openness of speech’ and an apparent logic of ‘splitting, suture’ (172).

The ‘epistemological upshot of this convoluted adventure’, Badiou concludes, ‘reminds us that mathematics operates upon its own existence such as it is designated in ideology; but this operation, conforming to the specific constraints of a science, takes the form of a break, such that the (ideological) questions which make up the material upon which mathematics carries out its working reprise, find no answer in the latter [...]. Such is the law of the alternating chain in which what is known as “the progress of science” consists: it is not because it is “open” that science has cause to deploy itself (although openness governs the possibility of this deployment); it is because ideology is incapable of being satisfied with this openness’ (173). Ideology seeks for new ways to close the ‘wound’ that science inflects upon its aspirations to ‘unlimited’ Truth; science responds by displacing, in new ways, the ‘breach’ that it opens up in ideology.

References to this text in other articles in the Cahiers pour l’Analyse:


English translation:

  • Alain Badiou, ‘Mark and Lack: On Zero’, trans. Ray Brassier and Zachary Luke Fraser. In Concept and Form: The Cahiers pour l’Analyse and Contemporary French Thought, ed. Peter Hallward and Christian Kerslake. London: Verso, 2010.

Primary bibliography:

  • Badiou, Alain. ‘Le (Re)commencement du matérialisme dialectique’ [review of Louis Althusser, Pour Marx and Althusser et al., Lire le Capital]. Critique 240 (May 1967): 438-467.
  • ---. ‘Note complémentaire sur un usage contemporain de Frege’, Le Nombre et les nombres. Paris: Seuil, 1990. 36-44. ‘Additional Note on a Contemporary Usage of Frege’, in Number and Numbers, trans. Robin Mackay. London: Polity, 2008. 24-30.
  • Miller, Jacques-Alain. ‘La Suture: Eléments de la logique du signifiant’, CpA 1.3:37-49.

Selected secondary literature:

  • Badiou, Alain. The Concept of Model: An Introduction to the Materialist Epistemology of Mathematics, ed. Zachary Luke Fraser and Tzuchien Tho. Melbourne:, 2007.
  • Feltham, Oliver. Alain Badiou: Live Theory. London; New York, NY: Continuum, 2008.


1. Louis Althusser, ‘The Historical Task of Marxist Philosophy’, The Humanist Controversy (London: Verso, 2003), 191.

2. ‘I thought that if mathematics were to achieve the secrets of thought’, Badiou remembers, ‘it was because of its a-subjectivity. It seemed like a psychosis; that is to say, it was the automatism, a characteristic of the automatism of thought, a mechanical conception of mathematics that I was concerned with in those days’ (Tho and Badiou, ‘The Concept of Model, Forty Years Later’, 103).

3. Badiou, ‘Note complémentaire sur un usage contemporain de Frege’, Le Nombre et les nombres. Paris: Seuil, 1990. Badiou here contrasts Miller’s argument that number is engendered through the ‘function of the subject’ with his own position in which number, on the contrary, is a ‘form of being’ (36-37), and in which non-self-identity can only be attributed to an ‘event’ (40).

4. RMD, 440n.1, citing Bachelard, La Formation de l’esprit scientifique: Contribution à une psychanalyse de la connaissance objective (Paris: Vrin, 1938), 14.

5. Badiou, Concept of Model, 30. Luke Fraser shows, in his illuminating introduction to Concept of Model, that Badiou’s later conception of truth does not retreat from this point. As Badiou maintains in a 1990 text on Sartre, ‘the true does not speak of the object; it speaks of nothing but itself. And the subject does not speak of the object either, nor of the intention that sights it; it speaks only of the truth, of which it is an evanescent point’ (Badiou, ‘Saisissement, dessaisie, fidélité’, Les Temps modernes 531-533, vol. 1 (1990), 20, cited in Fraser, ‘The Category of Formalisation’, in Badiou, The Concept of Model, lii).