Science

SIX Science Ray Brassier Rationalism and scientism Badiou is a rationalist: he holds that mathematics captures whatever is sayable about being qua being and names science (alongside art, politics and love) as one of the generators of the truths that condition philosophy. It would be difficult to overstate the extent to which this sets him apart from the main stream of post-Hegelian continental philosophy. From Kierkegaard and Nietzsche, through Heidegger and Adorno, up to Foucault and Derrida, continental philosophers have sought to radicalize Kant's critique of reason by exposing the limitations of conceptual rationality in general and of scientific reason in particular. For continental philosophers, scientific reason is congenitally deficient, whether because of its disregard for the concretely existing individual (Kierkegaard); its "religious" reverence for objective truth (Nietzsche); its persistent reduction of time to space (Bergson); its subordination to the prejudices of the natural attitude (Husserl); its inability to understand entities in any terms other than that of presentat-hand actuality (Heidegger); its blind submission to the utilitarian imperatives of instrumental rationality (Adorno and Horkheimer); or its unwitting compliance with power-knowledge complexes (Foucault). This list is by no means exhaustive; it could be expanded to include similar assertions about the debilities of science made by other influential continental philosophers such as Marcuse, Merleau-Ponty and, more recently, Michel Henry.1 If pressed about their overwhelmingly negative characterizations of science, continental philosophers are liable to protest that they are 61

A L A I N B A D I O U : KEY C O N C E P T S criticizing "scientism" rather than science itself (for which, they assure us, they harbour nothing but respect). The facility with which this distinction is routinely brandished invites suspicion. What exactly is meant by "scientism"? On the face of it, the distinction between science and "scientism" points towards the difference between an unobjectionable practice that consists in observing, experimenting and inducing law-like regularities to explain natural phenomena, and an objectionable ideology that presumes to draw broader philosophical conclusions about the nature of reality from this practice. On this account, then, science would be an ideologically innocent practice that becomes perverted into "scientism" when contaminated by the pernicious philosophical presumption that it can limn the ultimate structure of reality. The trouble with this definition of "scientism", however, is that it ignores the way in which ideology is necessarily implicated in practice and in doing so it unwittingly indicts the scientist's own understanding of her activity. Is it not part and parcel of the scientist's own conception of her practice that her methods and procedures provide a more reliable basis for investigating reality and uncovering truths about the world than the armchair intuitions habitually brandished by metaphysicians? And is not this practice necessarily informed by the scientist's conviction that her theorizing is more credible than metaphysical speculation precisely in so far as it is constrained by standards of deductive and evidential stringency that cannot be matched by any other type of theorizing about the world? The attempt to dissociate the denunciation of scientism from the denigration of science quickly founders upon the observation that so-called "scientism" is inextricable from scientific practice. Such denunciations of "scientism", so prevalent among continental philosophers, cannot but imply an attack upon the autonomy of scientific rationality, insisting as they do that science is internally conditioned by factors that it is intrinsically incapable of comprehending (as when Bergson asserts that quantification depends upon the utilitarian conception of space or when Heidegger claims that chronological time depends upon existential temporality). These critiques mount a direct challenge to the conviction - espoused by educated non-scientists and scientists alike - that mathematized natural science is our most authoritative source of knowledge. Moreover, it is important to note that the "scientism" habitually vituperated by continental philosophers does not target just those who proclaim science to be infallible and indubitable (an indefensible claim that no scientifically literate person would maintain) but also those committed to the more modest assertion that science, although fallible, continues to provide the basic epistemological 62

SCIENCE yardstick by which to measure the credibility of all other cognitive claims. Seen in this light, the distinction between science and scientism is dubious, and invoking it to absolve oneself of the charge of being anti-science is unconvincing. The common thread running through all these critiques of scientific reason by continental philosophers is the idea that science leaves out something fundamental in its account of the world. This remainder is variously characterized depending on the philosopher in question (selfconsciousness, life, being, duration, power, non-identity etc.), but what underlies all these various accounts is the claim that there is something that cannot be captured in scientific concepts and categories. In a gesture that is the exact inverse of the one carried out by those philosophers in the analytic tradition who have sought to realign philosophy with the natural sciences, continental philosophers have opted to fix upon this a-rational residue as the proper concern of philosophy while marking it as forever inaccessible to scientific reason. This leaves us facing a stark alternative: either embrace the positivistic claim that scientific discourse encompasses everything worth knowing about the world; or insist that there is something forever recalcitrant to scientific conceptualization. The choice is between a positivistic conception of immanence and an obscurantist conception of transcendence. Badiou's rationalism allows him to refuse both horns of this dilemma. On the one hand, Badiou's mathematical ontology, indifferent as it is to the varieties of qualitative particularity - phenomenological experiential, perceptual - fetishized by those who reproach science for disregarding the "concrete richness" of experience, can easily accommodate the claim that mathematized natural science has a direct purchase upon being: "In the final analysis, physics, which is to say the theory of matter, is mathematical. It is mathematical because, as the theory of the most objectified strata of the presented as such, it necessarily catches hold of being-as-being through its mathematicity" (Badiou 1998c: 127). On the other hand, Badiou's conception of generic truth renders transcendence intelligible while ruling out any presumptive erasure of the discontinuity between nature and culture. Thus Badiou proposes a non-positivistic (anti-empiricist) conception of immanence and an anti-obscurantist (rationalist) understanding of transcendence, rooted in the post-Kantian distinction between what is and what is knowable - the distinction that Badiou recodes as the distinction between truth and knowledge. Accordingly, although Badiou shuns the kind of vulgar positivism that remains completely beholden to the authority of current science while being unable to understand or explain the discontinuities in scientific history, he also abjures every variety of anti-rationalism that would 63

ALAIN BADIOU: KEY CONCEPTS belittle the power of scientific reason while exalting the a-rational as philosophy's proper concern. Philosophy, science, ideology Badiou accepts the Marxist claim that science is never ideologically neutral (witness for example the recurring attempts to enlist Darwinism and complexity theory in order to legitimate competition, inequality and the free market as ineradicable natural phenomena). However, he refuses the facile inference that science is nothing but technology plus ideology.2 The challenge is to recognize the imbrication of science and ideology without capitulating to the self-serving conceit whereby philosophy (or "theory") would relegate science wholly to the realm of ideology while arrogating the power of critique to itself by virtue of its allegedly privileged access to some transcendent source of truth: Spirit, Being, History etc. What distinguishes Badiou's stance towards science is its simultaneous acknowledgement of the inextricability of science and ideology together with the novel suggestion that it is science itself, rather than philosophy, that proves to be the most acute diagnostician of those ideological prejudices that hinder its development. Badiou's most sustained account of the relation between philosophy, science and ideology occurs at the beginning of his philosophical career in four texts published between 1967 and 1969. These are "The (Re) commencement of Dialectical Materialism" (1967), "Mark and Lack: On Zero" ([1967] 1969b), "Infinitesimal Subversion" (1968), and The Concept of Model (1969a).3 Badiou's account unfolds under the aegis of two fundamental distinctions: 1. The distinction between "historical materialism", understood as the Marxist science of history, and "dialectical materialism", understood as the latter's philosophical counterpart. 2. The distinction between ideological notions, philosophical catego­ ries and scientific concepts. In The Concept of Model, Badiou describes philosophy as constituted by its parasitic relation to scientific innovation on one hand, and its subservience to dominant ideological interests on the other. Philosophy is the practice of an "impossible relation" between science and ideology (CM 50). For the most part, philosophy carries out an ideological envelopment of science: philosophical categories denote "inexistent" objects that combine concepts and notions. 4 The task of a 64

SCIENCE materialist philosophy informed by the Marxist science of history (as opposed to a "philosophy of matter", which would merely concoct a spurious category called "matter" through the notional envelopment of physico-biological concepts) consists in exposing the reactionary ideologies implicit in various philosophical appropriations of scientific concepts in order to supplant them with materialist categories capable of being deployed in the service of revolutionary ideology. The proper philosophical index of "materiality" in this conjunction between historical and dialectical materialism is that of the "productivity" of a given theoretical practice. In Badiou's words: "The reality of the epistemological materialism which I am trying to introduce ... is indissociable from an effective practice of science" (CM 22, trans, mod.). Badiou's specific aim in The Concept of Model is to isolate the scientific - that is, logico-mathematical - concept of model from its notional envelopment by the categories of bourgeois epistemology - central to which is the distinction between the "formal" and the "empirical" - and to construct a philosophical category of model consonant with a materialist history of the sciences. The broader epistemological import of this project is to develop a materialist account of the nature of scientific theory that challenges both the empiricist assumption that scientific theories merely model empirical reality and the idealist claim that reality is nothing but an inert support for scientific theory. In doing so, Badiou lends a specifically Marxian twist to two ideas of Bachelard's: the idea of the "epistemological break" (rechristened "cut", coupure, by Althusser), and the idea that science cannot be understood in terms of a relation between representation and reality (Althusser and Bachelard are arguably the two key influences on Badiou's understanding of the relation between philosophy and science, both in this initial stage of his thought and throughout his subsequent career). The two principal variants of the bourgeois epistemology that Badiou attacks are empiricism and idealism. Both are coordinated around the notional difference between theoretical form and empirical reality: science is deemed to be a formal representation of its object, whether the representation be characterized in terms of the effective "presence"5 of the object, as in empiricism, or in terms of the primacy of a formal apparatus, that is, of the mathematical code through which the object is represented, as in formalism (the specific variety of idealist formalism that Badiou has in mind here is structuralism). However, the representationalist dualism of fact and form occludes the materiality of science as process of cognitive production. Science neither mirrors nor moulds an allegedly pre-existing "reality"; it is an autonomous process for which mathematics provides the primary 65

A L A I N B A D I O U : KEY CONCEPTS means of production: "[Ultimately, in physics, fundamental biology, etc., mathematics is not subordinated and expressive, but primary and productive" (Badiou 1967: 464). Thus mathematics is not an a priori formal science grounding the empirical sciences' access to reality, but rather the paradigmatic instance of a productive experimental praxis. This is the specifically materialist dimension of Badiou's Platonism. Mathematical productivity (and scientific productivity more generally) consists in "cutting" or differentiating the notational material upon which it operates: science is the production of "stratified differences". Three questions immediately arise here: 1. How does this stratification operate? 2. What does this differentiation consist in? 3. In what way is this production of "stratified differences" an index of "materiality"? 7. How does this stratification operate? Stratification is a function of mathematical formalization. A formal mathematical system is stratified in so far as it divides and separates its own means of production, allotting distinct functions to discrete mechanisms. Badiou gives as an example the elementary mechanisms of concatenation, formation and derivation: a formal system must be endowed with well-defined procedures for (a) assembling symbol strings, (b) dividing these into well-formed and ill-formed statements, and (c) deriving proofs or disproofs of these statements. Formal systems vary in their degree of internal stratification; nevertheless, some minimal degree of stratification similar to that outlined above is the structural prerequisite for any formal apparatus. A formal system is a machine that takes strings of symbols as its input, subjecting these to series of differentiations at distinct levels of stratification, before finally outputting statements whose intelligibility (Badiou will have no truck with the ideologically loaded notion of "meaning") is a function of the system's internally articulated differences. Stratification is the condition for productive differentiation. 2. What does this differentiation consist in? Badiou proposes a dialectical conception of scientific production comprising three moments: in the first, science breaks away (coupure) from its own philosophical self-representation; in the second, this break is re-captured (re-presented) by philosophy (this can occur through 66

SCIENCE scientists' own philosophical interpretation of their practice); finally, in the third moment, science breaks once more with this philosophical re-presentation by reconfiguring (refonte) itself around new limits that it has independently established and that temporarily defeat philosophical appropriation. The first break is the point at which scientific discourse subverts its current ideological representation by producing a difference that cannot be subsumed by extant philosophical categories. Philosophy then represents this break by de-stratifying (re-categorizing) this stratified difference, thereby re-enveloping the new concepts produced by science within extant ideological notions (these will be novel philosophical categories). Lastly, the moment of reconfiguration is the moment of the second break understood as a re-stratification of what philosophy has de-stratified - a re-stratification wherein the parameters of scientific discourse are re-established independently of science's current philosophical representation. In "Mark and Lack", Badiou illustrates this dialectic with regard to the history of mathematics. He identifies seven moments punctuating the dialectic of break and recapture from Pythagoras to Godel: I) The existence of a historical mathematics (namely "intuitive" arithmetic); one that is open in principle (indefinitely stratified signifier). II a) The ideological re-presentation of this existence as the trans-mathematical norm of completely controllable rationality (the ideological destratification of the mathematical signifier). II b) The posing of a question to mathematics about its conformity to this ideological norm, in the form of the axiomatic and formalist intention, whose goal is to display a founded transparency (this is the ideological motivation of Frege and Russell). Ill) Break: the mathematical treatment of this ideological representation of mathematics via the actual construction of formal systems that "represent" historical arithmetic (Principia Mathematica). IV a) The ideological re-presentation of this break: formal systems conceived as trans-mathematical norms of rational closure via the idea of a nomological system (Husserl). IV b) The posing of a question to mathematics about its absolute conformity to the ideological norm of closure: this is the metamathematical intention, relative to the internal demonstration of a system's consistency (Hilbert). 67

ALAIN BADIOU: KEY CONCEPTS V) Break: the mathematical treatment of ideological representation via the actual construction of a mathematical metamathematics (the arithmetization of syntax). Godel's Theorem: the structural stratification of the mathematical signifier does not answer the "question" of closure. VI) Ideological re-presentation of this break: Godel's Theorem is experienced as a limitation relative to the normative expectation. Ideological exegesis of this "limitation" as: - openness of speech and concealment of being (Ladriere); - finitude; - splitting, suture; VII) Break: the general theory of the limitation-effect, positively conceived as a structural instance of certain mathematical objects (Smullyan's epistemological truth). The epistemological upshot of this convoluted adventure reminds us that mathematics operates upon its own existence such as it is designated in ideology; but that 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. (ML 172) The dialectic between scientific production and its ideological representation is one in which science responds to the questions put to it by philosophy by forging differences that subvert the pertinence of the categories presupposed by those questions. Science works with its own ideological representation (the philosophical de-stratification of what science has stratified), with which it then breaks by deploying a new layer of stratification (producing a difference for which no category yet exists). Ideology, understood as philosophical categorization, is not extrinsic to science; but scientific productivity requires constantly breaking with its own ideological self-representation. 3. In what way is this production of "stratified differences" an index of "materiality"? But in what sense is science's production of difference "material"? Clearly, the "materiality" of mathematical practice is not to be understood as an analogue of the specious philosophical category of "matter", 68

SCIENCE whether physically, biologically, or even economically construed, but rather as an index of the scriptural production of difference. What Badiou means by "scriptural materiality" is somewhat opaque. As Zachary Luke Fraser has pointed out, the materiality Badiou has in mind here cannot be understood in terms of the substance of graphic marks, whether they consist of chalk, graphite, or ink ("Introduction", in CM xxxvi). The materiality at issue can only be understood as incorporeal. Badiou persistently reiterates the Marxian link between productivity and materiality, with the former providing the veritable index of the latter. What renders formal systems productive is their stratification, understood as the differential network through which mathematical symbols and operators are assigned a signifying function and variously combined to produce distinct statements. Thus materiality is to be conceived in terms of this formal capacity for producing intelligible differences independently of the categories of representation. Logicomathematical inscription circumvents the metaphysical primacy of the linguistic signifier via a "stratified multiplicity" of differential traces such that "no signifying order can envelop the strata of its discourse" (ML 163). Scientific stratification subverts the representational categories of designation and reference - "Neither thing nor object have any chance here of acceding to any existence beyond their remainderless exclusion" (ML 156) - and dispenses with the need for the activity of a constituting subject: "[T]here is no subject of science. Infinitely stratified, regulating its passages, science is pure space, without inverse or mark or place of what it excludes ... Science is an Outside without a blind-spot" (ML 161-2). Here we encounter all the essential features of Badiou's Platonist materialism: scientific thought is "outside", that is beyond the enclosure of ideological representation, not because the subject of science is endowed with a faculty of intellectual intuition that would grant her intuitive access to a transcendent realm of intelligible objects, but, on the contrary, because the remorselessly mechanical "rule governed transparency" of logico-mathematical inscription results in a cognitive practice for which the categories of subject and object are completely superfluous. The non-representational character of scientific discourse is a consequence of its machinic nature, since "[a] formal system is a mathematical machine, a machine for mathematical production, positioned within that production" (CM 43, trans, mod.). But the means of mathematical production are themselves produced; the mathematical machine or instrument is also a mathematical product, a result: there would be no formal systems without recursive arithmetic, and no rigorous experimental protocols for such systems without set theory. 69

ALAIN BADI0U: KEY CONCEPTS Yet it is because this scientific reproduction of the means of production harbours a constitutive historicity that science's self-reproduction is inherently differential. Or rather, it is the inherently differential (dialectical) nature of scientific reproduction that generates its historicity. Scientific re-production is self-differentiating because of the way in which science itself intervenes within a determinate epistemological conjuncture by means of formal experimentation. Thus, for example, by proving the consistency of a model of axiomatic set theory with the axiom of choice and the continuum hypothesis, Godel demonstrates that these two axioms can be integrated into the formal theory without compromising its coherence. He thereby provides a conceptual sanction for mathematical practice: "In doing so, [Godel's experimentation] transforms, not the theory, but the status of the theory within the historical process of the production of knowledges" (CM 51). Given a mathematical configuration inscribed within the history of this science, to treat it as a model of a formal system is to situate its specificity by transposing it beyond the narrow ambit of the illusions engendered by its ideological recapture and into the wider mathematical space constituted by the various models of the system. In the history of a science, the experimental transformation of practice via a determinate formal apparatus retrospectively assigns the status of model to those antecedent instances of scientific practice. For Badiou, then, the materialist category of model designates formalism's retrospective causality upon its own scientific history. The historicity of formalism consists in the "anticipatory intelligibility" of what it retrospectively constitutes as its own model. Ultimately, for Badiou, the fundamental epistemological problem is not that of the nature of the representative relation between the model and the concrete, or between the formal and the model; rather "[t]he problem is that of the history of formalization" (CM 54). The materialist category of model proposed by Badiou designates "the network traversed by the retroactions and anticipations that weave this history; whether it be designated in anticipation as a break or in retrospect as a reconfiguration" (ibid.). More importantly, Badiou's account of the epistemological dialectic of break and reconfiguration provides a rationalist rejoinder to the anti-rationalist invocation of empirically arbitrary "paradigm shifts" in order to account for the structural discontinuities that punctuate scientific history. The discontinuity of science is not an objection to its rationality since discontinuity is already inherent in the immanent conceptual mechanisms of scientific practice - for "science is precisely that which is ceaselessly cutting itself loose from its own indication in re-presentational space [i.e. ideology]" (ML 165). This is why, for 70

SCIENCE Badiou, u[T]here are no crises within science, nor can there be, for science is the pure affirmation of difference" (ibid.). Representation, empiricism, naturalism Ultimately, those empiricist and idealist variants of epistemology rooted in the difference between fact and form are faced with the problem of characterizing the unity underlying this fundamental duality. For vulgar empiricism, the unity of the duality of fact and form is posed in terms of the question of the theoretical model's reproduction or functional simulation of reality. Thus an extrinsic relation of analogical resemblance is invoked in order to bridge the gap between the supposedly inert opacity of empirical fact on one hand, and the active construction of theoretical form on the other. Here, of course, the precise nature of the desired "resemblance", "simulation" or "reproduction" remains vague and ambiguous. For the brand of "naturalized epistemology" spearheaded by Quine, however, the unity of the difference can be unearthed by sealing the gap, by replacing congruence with reciprocal presupposition, by supplanting "resemblance" and "simulation" with isomorphy, and by ensuring the double articulation of fact and form. No longer inert and passive, the structure of the empirical itself generates the form of representation that will account for it. Here evolutionary epistemology and ultimately natural history provide the fulcrum for explaining the relation between empirical fact and theoretical form. Badiou's own epistemological stance in the period culminating in Concept of Model exhibits both surprising parallels and profound divergences with Quinean naturalism. Like Quine, Badiou insists on philosophy's dependence upon science and on the immanent autonomy of scientific thought. Like Quine, he refuses any recourse to a sciencetranscendent philosophical foundationalism: "One establishes oneself within science from the start. One does not reconstitute it from scratch. One does not found it" (CM 33, trans, mod.). But, unlike Quine, Badiou will have no truck with empiricism and hence refuses to reintegrate the sciences into a broader evolutionary and ultimately biological narrative about the development of human cognitive prowesses. For Badiou, the irreducible variety of scientific practices harbours discontinuous historicities that remain internal and immanent to each practice. These historicities cannot be reabsorbed into an all-encompassing bio-evolutionary narrative about the human organism's "science-forming" faculties. Badiou's conception of the autonomy of science rules out the possibility of naturalism. "Science" cannot be mistaken for its empiricist 71

ALAIN BADI0U: KEY CONCEPTS representation or conflated with an ambient scientific worldview, a diffuse ideological distillate synthesized from various scientific disciplines (this could serve as a more apt definition of "scientism"). It is rather an entirely autonomous, ceaselessly self-differentiating mode of theoretical practice invariably defined by a specific historical conjunction between conceptual demonstration and formal experimentation. The signal merit of Badiou's rationalist conception of science lies in the way in which it manages to reconcile a critical recognition of science's inevitable ideological envelopment - thereby abjuring positivism and empiricism - with an attentiveness to the way in which science is continually breaking away from its own ideological re-inscription. Indeed, for Badiou, scientific progress is fuelled by this constant dialectic between capture and escape, breaking and remaking. At the same time, Badiou's account is one in which there is nothing that science cannot know because, dispensing with every vestige of substance, Badiou's formalist ontology leaves no room for the inconceivable or unconceptualizable. Truth is the sole exception to the order of being, but science is one of the harbingers of truth. Notes 1. See, for example, Henry (2001), where science is roundly castigated for being one of the primary sources of "the ideology of barbarism". 2. Badiou is refreshingly scornful of reactionary jeremiads about the perils of technology: "We hold these meditations, reckonings, and diatribes concerning technology, however prevalent they may be, to be uniformly ridiculous" (MP 53, trans, mod.). 3. Oliver Feltham and Zachary Luke Fraser have both provided admirably detailed explanations of the role played by these decisive early texts in Badiou's ceuvre. See Feltham (2008: 12-31); and Fraser's "Introduction" to his translation of Concept ofModel (CM xiii-lxi). English versions of "Mark and Lack: On Zero" and "Infinitesimal Subversion" will appear in Concept and Form, the forthcoming volume edited by Peter Hallward. 4. Badiou gives three examples: the "Platonic" category of "ideal number" denotes an inexistent "adjustment" between arithmetical concepts and hierarchical moral-political notions; the Kantian categories of "space" and "time" combine Newtonian concepts with notions that are relative to human faculties; the Sartrean category of "History" combines Marxist concepts with metaphysicomoral notions such as temporality, freedom and so on. Regarding the second of these examples, it should go without saying that Badiou is here using the term "category" in a sense entirely distinct from Kant's and is perfectly well aware that for Kant space and time are "forms of intuition" rather than "categories". 5. Badiou's use of the term "presence" here is perhaps intended as an allusion to Derrida's work, with which he was certainly already familiar (cf. Badiou 1967: 445). One possible implication here may be that the deconstruction of logocentrism can be enlisted as part of the critique of empiricist epistemology. 72