Section 1
Detaching from Derrida?
The Future of Deconstruction after Malabou
Chapter 1
Is Science the Subject of Philosophy? Miller, Badiou, and Derrida Respond1
Catherine Malabou
Translated by William Samson
I wish to make you aware of two reading experiences I have had. The first is that of reading Alain Badiouâs 1969 text, published in Cahiers pour lâanalyse, titled âMark and Lack,â where we can find the affirmation that gave rise to my title: âScience is the subject of philosophy.â2 This chapter is a response to Jacques Alain Millerâs âSuture: Elements of the Logic of the Signifier,â3 published a few years prior to Badiouâs essay in the same journal. Despite their specific and very dated contextâtheir questions about science had to confront, in that time, both psychoanalysis and Marxismâthey contain very important elements for thinking the relations between science and philosophy today, and they have import that, in my opinion, goes well beyond their time.
The second discovery is altogether different. While, for other reasons, I was recently rereading Derridaâs âPassions: An Oblique Offering,â4 I was struck by the coincidenceâif not the similarityâof the analyses developed in that book with those developed by Badiou about the situation of philosophy. The word âsituationâ is being taken here in its proper sense, as venue, place, and orientation, all at the same time. This coincidence is more surprising given that the two thinkers have little in common with each other, as is attested to by the extreme difference in the points of departure of their respective discourses. Badiou undertakes the analysis of the relations between philosophy and mathematical logic, while Derrida concerns himself with the relations between philosophy and literature. Despite it all, their conclusions strangely and mutually echo each other.
In both cases, what I will call the law of the fault of philosophy (la loi du défaut de philosophie) emerges. For both thinkers, philosophy is in need of an answer. It wants to answer for everything, even, which is the problem, for that which does not respond. What does not respond, for Badiou, is science. For Derrida, literature. Examining these two types of nonresponses more closely will constitute my subject, which is precisely the question of the subject. There is no subject of science, says Badiou; there is no subject of literature, says Derrida. This double absence of subject constitutes precisely, for them, the subject of philosophy, which is supposed to respond in their place by wrongly characterizing this absence as a lack. A lack which it is possible not to fill, but at least to make speak.
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Let us start with Miller. He undertakes to show that science, and in particular mathematical logic, proceeds from a denial of lack, and sutures closed all that could leave the place of the other of science (which is to say, the subject-function) empty. By definition, science is âobjectiveâ and admits no lacuna or void, no desire nor gap. This constitutes the âsutureâ or foreclosure that Miller, with the help of Lacan, intends to deconstruct. To this end, Miller begins with a reading of Fregeâs The Foundations of Arithmetic, where he defends the idea that zero, in mathematics, is precisely not a void or a lack.5 Miller will then demonstrate that zero in reality marks the place of the subjectâs foreclosure.
In The Foundations of Arithmetic, Frege defines number. A number refers to no particular thing. It does, however, have an object. What is the difference between a thingâthat empirical Xâand an object? The difference between four balls as things and what the number 4 measures? What do things become once they are numbered and numerable, in other words? They become units. Because of this, they obey particular syntactic determinations, which are ordered by a fundamental rule or structure, which Frege outlines in the following way: Numbers are extensions of concepts. The number 4, for example, is the extension of the concept âfour.â The two are equinumerical. âThe number which belongs to the concept F,â says Frege, âis the extension of the concept âequinumerical to the concept F.â â6
What does âconceptâ mean here? âConceptâ signifies self-identity. Saying that a number is an extension of a concept signifies that a number is identical to its concept, that it is identical to itself. In other words, as Miller rightly says, all numbers presuppose âthe concept of identity to a concept.â7 This rule of identity to a concept is valid for all numbers. âThe concept of identity to a conceptâ works for every number. This is the rule of unity: being self-identical means to âbe one.â There is thus some âoneâ in all numbers. âThis one [that of the singular unit] ⊠is common to all numbers in so far as they are first constituted as units.â8
The object is the thing become one (self-identical), and thus numberable. âThat definition, pivotal to his concept,â continues Miller, âis one that Frege borrows from Leibniz. It is contained in this statement: eadem sunt quorum unum potest substitui alteri salva veritate. Those things are identical of which one can be substituted for the other salva veritate without loss of truth.â9 Numbers are substitutable for one another insofar as in them, at any time, the self-identical repeats itself, that is, the âoneâ of the unit. We can thus âpassâ from one number to another without losing truth, since identity is preserved.
But the problem then arises of knowing how one âprogressesâ from one number to another. How the number can âpass from the repetition of the 1 of the identical to its ordered succession: 1, 2, 3, 4, 5?â The answer is for that to occur, âthe zero has to appear.â10 And Miller here makes reference to the very influential Fregian analysis of zero.
Why is the âengendering of the zeroâ11 necessary for Frege? At this point, weâve posited the self-identity of the concept of number, and thus of the number itself. Thatâs to say that ânon-identity with itself is contradictory to the very dimension of truth.â How then to designate nonidentity? âTo its concept, we assign the zero,â says Miller, reading Frege. Nothing falls under the concept ânonidentical with itselfâ if not, Miller continues, a void or a gap. Zero is the name of that nothing. Yet Frege defines zero as a number, to which he assigns the cardinal 1. This is where the âsutureâ comes from, from that eclipse of the zero by the one.
The nonâself-identical answers fully, for Frege, to the principle by which, for any object, it must be possible to say under what concept it must be subsumed. Yet zero can be subsumed under the concept of non-self-identity as âidentical to zero.â Thus, zero is identical to its concept, the concept of non-self-identity. Let there be a concept âidentical to zero.â One and only one object, zero, is subsumed under that concept. âOneâ is thus by definition the cardinal number that belongs to that concept. Zero is âoneâ in the sense of self-identity. Now, in trying to make the number 1 appear, it must be shown that something can immediately follow zero in the series of natural numbers. âZero,â Miller says, following Frege, âis the number assigned to the non-self-identical. This number is 1 [marked zero]. It follows that 1 follows immediately from 0 in the series of natural numbers.â12 And from there we can deduce the set of numbers, following the structure of âfollowing from,â with the restriction that no number can follow itself in the natural series of numbers beginning with zero. Inscribing zero as a point of departure for the series of numbers makes it possible that the rule n + 1: 0 (self-identity of the concept ânot identical to itselfâ) is followed by 1, which itself is followed by 2, then by 3, and so on.
Examining the Fregean argument, Miller concludes that the zero is at the same time summoned and dismissed. âThat which in the real is pure and simple absence finds itself through the fact of number (through the instance of truth) noted 0 and counted for 1.â13 The word âsutureâ signifies (1) the uniting, by use of thread, of divided parts after an accident or surgical intervention and (2) the immobile articulation characterized by two jointed surfaces united by fibrous tissue, like those which from the cranium, the apparent line constituting the conjunction of two parts. The suture is thus always at the same time a division and conjunction. In every case, the seam, the conjunction, remains visible.
What is really sutured in Fregeâs discourse in particular and in formal scientific language in general? Miller responds: the subject-function. âTo designate it I choose the name of suture. Suture names the relation of the subject to the chain of its discourse.â14 The appearance-disappearance of the zero in the series of numbers figures the appearance-disappearance of the subject in the chain of its discourse.
Frege affirms, however, multiple times that logic does not follow from a subjective act, which is always psychological. Yet it is precisely this which appears to Miller as a denial. According to Frege, the subject counts for nothing. From this, it follows that suturing the zero can be read as suturing the subject. Indeed, for Miller, only the subject-function can subtend the operations of abstraction, of unification, and of progression. There is, therefore, identity only for a subject. It is the subject that produces the primary unity; it is impossible to think self-identity outside of the subject, since the subject-function is the identity-function. Weâve known since Descartes that a subject is, by definition, a power identical to itself. The subject is the form of identity. At the same time, like the zero, the subject is never self-identical. Like the zero, it receives its identity from a lack, it misses itself. The relationship of the zero to the chain of numbers is the same as the relationship of the subject to the chain of discourse. Like the zero, the subject is both present and absent at once. âIt figures [in the chain] as the element which is lacking, in the form of a stand-in. For, while there lacking, it is not purely and simply absent.â15 Lacan shows that, in the same way that the zero is excluded from the beginning from the chain of numbers, the subject is excluded from the field of the Other, which is what comes to bar the subject. The subject displaces this bar onto the A, âa displacement whose effect is the emergence of signification signified to the subject.â16 Yet âuntouched by the exchange of the bar, this exteriority of the subject to the Other is maintained, which institutes the unconscious.â17 The summation of the subject in the field of the other calls for its annulment.18 The subject, in this way, is always alienated from and by the very process of its signification.
Regarding Frege, we have spoken of (1) unity and (2) the role of 0 in succession, its status as number, and finally of its eclipse by the 1. This structure of appearance-disappearance, of suture, would be the point, emergent or derived, of a more originary logic which Miller, with Lacanâs help, proposes to name the âlogic of the signifierââa logic that proposes to âmake itself known as a logic at the origin of logic,â19 which retraces the steps of logic, a âretroaction,â20 or a repression. âWhat is it that functions in the series of whole natural numbers to which we can assign their progression? And the answer, which I shall give at once before establishing it: in the process of the constitution of the series, in the genesis of progression, the function of the subject, miscognized, is operative.â21 Zero is the placeholder of the subject, which is itself, insofar as...