The reproach of abstraction
This is a paper about abstraction, in particular, but by no means exclusively – and this ʻby no means exclusivelyʼ is a large part of its point – philosophical abstraction.* It is concerned at the outset with what might be called the reproach of abstraction: the commonly held view, across a wide variety of theoretical standpoints, more or less explicit, that there is some inadequacy inherent to abstraction per se, which is both cognitive and practical (ethico-political) in character. I aim to cast doubt on this reproach, in its exclusive form at least, in order to clear the way for a thinking of the idea of ʻactual abstractionsʼ as the medium of social experience in capitalist modernities. I take ʻglobal capitalist modernityʼ to be the transdisciplinary object unifying inquiries in the humanities and social sciences, if only implicitly – the idea of global capitalist modernity is the transcendental horizon of their possible uniﬁcation. I therefore take the notion of actual abstractions to be a methodological key to a philosophically reﬂective form of transdisciplinarity. It is only a transdisciplinarity such as this, I believe, that can rescue the idea of philosophy as a discourse of universal mediation from the corrosive critiques of its claims to an absolute universality, familiar in recent years in various pragmatist, historicist, contextualist and deconstructive forms. As Ricoeur once put it:
Philosophical discourse achieves universality only by passing through the contingence of cultures … its rigour is dependent upon equivocal languages … its coherence must traverse the war between hermeneutics. 
What is wrong with abstraction?
The epistemological version of what I am calling the reproach of abstraction derives mainly from Humean empiricism, with its psychological conception of abstract ideas as the product of ʻcustomary conjunctionsʼ of particular ideas, based on resemblances, annexed to ʻgeneral namesʼ.  This is essentially a psychologistic updating of medieval nominalism. The practical-political version of the reproach is perhaps most commonly associated with the Lukácsian trajectory of Western Marxism, although it is also found in various sociologies of modernity, such as Simmelʼs, and it appears in a more literary-philosophical form in the complexly entwined traditions of French Heideggerianism and French Nietzscheanism. It is epitomized in its Marxist variant by Moishe Postoneʼs concept of ʻabstract dominationʼ, set out in Time, Labour, and Social Domination (1993). Abstract domination is ʻthe domination of people by abstract, quasi-independent structures of social relations, mediated by commodity determined labour … the impersonal, nonconscious, nonmotivational, mediate form of necessity characteristic of capitalism.ʼ  Abstract domination, in others words, is domination by abstractions.
These two critical tendencies – epistemological and practical-political – often converge within Marxism, as in Derek Sayersʼs The Violence of Abstraction (1987).4 But their combination is by no means restricted to the Marxist tradition. Indeed, there is a paradoxical position, more or less explicit in a great deal of contemporary theory (it is shared, for example, by deconstruction and Adornoʼs version of critical theory), which holds that, not merely despite but precisely because of the necessity of abstraction to thought (the character of the necessity, that is), there is something both cognitively and politically inadequate about knowledge itself: not only existing knowledge, but all possible knowledges. For Feyerabend, for example, the history of Western thought could be told as ʻA Tale of Abstraction versus the Richness of Beingʼ.  Increasingly, it seems, from a variety of different standpoints, abstraction – understood here as conceptual abstraction – is accompanied by both a certain melancholy (loss of the real object) and a certain shame (complicity in the domination of the concept and hence repression of other, more vibrant, more creative aspects of existence).
This can be seen, I think, in the growing reverence and enthusiasm for ʻsingularitiesʼ of various sorts: * This is a lightly revised version of a paper delivered to the conference ʻContinental Drift? Modern European Philosophy in Britain Todayʼ organized by the Centre for Research in Modern European Philosophy, Middlesex University, London, at UCL, 14–15 May 2004. An earlier draft beneﬁted from discussion at a Social Theory and Historical Studies Workshop in the Department of East Asian Studies, New York University, March 2003.reverence in the spirit of the construal of alterity in the Levinas–Nancy tradition, that religious ʻdream of a purely heterological thoughtʼ otherwise called ʻpure empiricismʼ;6 enthusiasm on the model of Žižekʼs embrace of Badiouʼs ʻact as eventʼ. It is also visible in the turn within literary studies away from ʻtheoryʼ, strictly construed, towards a historicist particularism, on the one hand, and a revival of interest in ʻaestheticsʼ (in its nineteenth-century disciplinary sense – quite different from Kantʼs philosophical sense of aesthetic as critique), on the other. This movement has a correlate in studies in the visual arts, in which the Anglo-American reception of Deleuze has become entangled. Indeed, in this context, certain theoretical terminologies have themselves become primarily aesthetic means. However, things are complicated in matters of aesthetics – and the problem of abstraction is rendered ironic – by the proximity of a visual paradigm in which ʻabstractionʼ (in the sense of abstract painting, for example) appears as the privileged non-conceptual term: the object of the intuition of sensuously concrete form. This is, in part, a misrecognition (formalist modernismʼs mislocation of meaning in pure aesthesis), but it is also a sign of often neglected complexities in the concept of abstraction which the notion of ʻactual abstractionsʼ seeks to address: both the force and the ʻfeelingʼ of abstraction itself.
There are, then, importantly, both conceptual and non-conceptual versions of abstraction. Yet the very opposition between them appears to conﬁrm the onesidedness, and hence inadequacy, of both types, and hence of abstraction itself. (Dialectically construed, abstract painting appears as the ʻother sideʼ of conceptual abstraction, the melancholy mimetic mark of the excluded.  Yet in registering what is lost by abstract thinking, it reproduces its one-sidedness in an ontologically inverted form.) In terms of Kantʼs famous dictum, ʻConcepts without intuitions are empty, intuitions without concepts are blindʼ, both are merely abstracted ʻelementsʼ of a unitary process of cognition. In its root form, the Latin abstrahere, to abstract means ʻto draw away or remove (something from something else)ʼ; hence its inherent epistemological negativity, at least in so far as ʻoriginal unityʼ is the implicit measure of authentic knowledge and experience. But this is, of course, the very problem. The dominant discourse of abstraction is infused not only with empiricism but with a Romanticism of origins. It is this combination of empiricism and Romanticism that imparts to it its distinctive cultural tone. This is the contradictory philosophical common sense of bourgeois culture, this mixture of empiricism and Romanticism, narrowminded realism and unfulﬁllable desire.
However, let us not forget the other, ʻgoodʼ side of conceptual abstraction. For abstraction is, historically, philosophically double-coded: it is an epistemological virtue as well as a vice. While abstraction may, in its modern psychological form, be associated with a withdrawal from the reality (or particularity) of the object of experience, and hence a certain epistemological inadequacy, its deeper philosophical history is that of a focusing in on the essence of an object (a separation out of the contingent and inessential) as a condition of the possibility of knowledge. Abstraction is a condition of knowledge, of thinking the object; and abstraction is, apparently, a loss of the sensuous particularity of the object. Hence the melancholy, which at times takes on tragic tones. For Simmel, for example, ʻthe fact that the higher concept, which through its breadth embraces a growing number of details, must count upon increasing loss of contentʼ is ʻthe tragedy of human concept formationʼ.  The problem of abstraction is the problem of how to deal with this contradictory double-coding, beyond the simple declaration of an impasse: that brute declaration of the ʻnecessity but impossibilityʼ of knowledge to be found in both Adorno and Derrida, for example, which ﬂattens out the tragic aspect of Kantianism into a generalized epistemological melancholia. 
Prior to the late eighteenth century, the contradictory double-coding of abstraction tended to be distributed between two competing positions: a nominalism about universals, to which modern empiricism is the successor, and a realism about universals, retained by modern rationalism. With Kant, however, the problem was famously transformed in a way that opened up the conceptual space that would subsequently itself be transformed by Marxʼs concept of ʻreal abstractionʼ, the broader signiﬁcance of which remains to be thought. This change in the structure of the problem of abstraction was the result of Kantʼs transformation of the understanding of objectivity. In transforming the concept of objectivity Kantʼs philosophy opened it up to precisely those issues about normativity and disciplinarity that so trouble the humanities and social sciences today. We are still in certain crucial respects, both in philosophy and, especially, in other disciplines in the humanities and social sciences, within a Kantian ﬁeld. (Gillian Rose was largely right about that.  ) A brief recapitulation of the structure of this ﬁeld will serve as a prelude to some remarks about the dialectical redemption of abstraction as experience performed by the concept of actual abstractions.
abstraction, objectivity, normativity
As is well known, Kant redeﬁned knowledge in terms of an essentially subjective conception of ʻobjectivityʼ (Objektivität), rejecting the metaphysical conception of knowledge, shared in their different ways by rationalism and empiricism, as a correspondence of ideas to the properties of independent objects or things (Dinge) in favour of a transcendental-logical or essential ʻsubjectiveʼ conception of the objectivity of knowledge. The independent reality of the thing ceased to be the measure of knowledge – that notion is incoherent. It was replaced by an ontologically ambiguous notion of the ʻobjectʼ of knowledge, the ʻobjectiveʼ character of which depends on the demonstration of the universality and necessity of its various subjective ʻelementsʼ, along with that of the process of their uniﬁcation or synthesis. (There is a strong conceptual and terminological opposition here of ʻobjectʼ (Objekt) to ʻthingʼ (Ding). For Kant, ʻobjectivityʼ is not about things; it is about the conditions under which the given yields ʻobjectsʼ – that is, becomes conceptually apprehendable and hence ʻknowableʼ.)The conceptual aspect of this process of object-formation is presented in Kantʼs Logic as the product of a sequence of three ʻlogical actsʼ, of which abstraction is the third. Following comparison and reﬂection – ʻthe likening of presentations to one another in relation to the unity of consciousnessʼ and ʻthe going back over different presentations … in one consciousnessʼ – abstraction is ʻthe segregation of everything else by which presentations differʼ.  This is described by Kant as a ʻnegativeʼ act, whereas the other two are termed ʻpositiveʼ. There is a residue here of the psychological process of Humean empiricism – the separation out of resemblances – but its epistemological function is rendered transcendentally ideal and, in the process, constitutive of the object. In its formative role in the generation of concepts, abstraction thus has a positive epistemological signiﬁcance, not merely despite, but precisely by virtue of its ʻnegativeʼ role in distancing certain presentations from others, within the manifold of intuition through which the given appears.
Kant was the ﬁrst philosopher to give an unequivocally positive epistemological value to abstraction as constitutive of the object of knowledge, while nonetheless retaining its negative connotation of leaving out of consideration certain presentations given to the senses. (It is important to note here that just as the object of knowledge (Objekt) is ontologically distinct from the thing-in-itself (Ding an sich) so, no less importantly, is the object of knowledge to be distinguished from the object as mere appearance (Gegenstand) given to consciousness by sensibility – the unknowing appearance of the thing – which will become ʻknownʼ only through its transformation into an object of knowledge, by the concepts of the understanding. So there are three levels of analysis here.) This is an internally complex transformation in the concept of objectivity, from ʻthinghoodʼ to ʻobject-constitutionʼ, but it does not (contra someone like Rorty) wholly leave ʻthingsʼ behind, since it is the realm of thinghood that appears, although it is not known ʻin itselfʼ. No amount of pragmatist epistemology can eradicate the existential dimension of the thingness of appearing; indeed, ultimately, pragmatism requires it in order to make sense of its own central concept of ʻpurpose for lifeʼ (Hume), as Peirce saw so clearly. It is, after all, the common ontological substrate of subject and object that makes human subjects mortal. As conditions of the possibility of knowledge, mortality and natality are of transcendental-epistemological, as well as existential, signiﬁcance.
This shift in the measure of knowledge from the idea of the thing (which is unknowable in its independence) to the ʻobjectivityʼ, that is, universality and necessity, of objects of knowledge – a shift from self-evidence, quasi-mathematical proofs and laws of association to a discursive logic of justiﬁcation – brought to the fore the normative dimension of the concept of knowledge. This is manifest in Kantʼs text in the famous metaphorics of its legal terminology – most explicitly, in its legal understanding of the terms ʻdeductionʼ and ʻproofʼ, the transcoding of which (from logic and mathematics to law) was the semiotic condition of Kantʼs critical philosophy taking over the mantle of rationalist metaphysics. It needed to appropriate and transform the old terminology. Methodologically, Kantian philosophy reduces the laws of science to the status of the decisions of an eighteenth-century court of law. For some, this leads to the impasse and anxiety of ʻundecideabilityʼ, and the thrill of the decision; for others it is, more deeply, the belated philosophical recognition that the human is the social. And if the human is the social, the human is the historical, since the historical is the temporality of the globally social. All questions of the universally human thus become questions of history, in the collective singular. This is the decisive (Hegelian) result of Kantian philosophy. To the extent that recent revivals of mathematics as the model for philosophy fail to engage with this problematic, they risk the fate of all neo-classicisms.
Kantʼs notion of objectivity is bound up with normativity not in the sense that it requires ʻdisinterestʼ or ʻaltruismʼ as its condition (for such notions derive from a pre-Kantian conception of objectivity as undistorted access to the thing), but in the sense that it requires demonstration, in the form of the discursive redemption of a universality of interest. Nietzsche and later pragmatisms are in this respect the legitimate, albeit rebellious, heirs to Kantʼs concept of objectivity. What is misrecognized as ʻscepticism about objectivityʼ in contemporary thought in the humanities is, rather, from this standpoint better understood as an exploitation of the possibilities for plurality – different forms of object-constitution – inherent within Kantʼs transcendental concept of objectivity. This is neither scepticism nor relativism but a play internal to the universality of a discursively based concept of objectivity. The practical-political critique of abstraction as conceptual domination is located within this discursive space. It depends upon the historical character and variability of object-constitution, and hence upon the possibility of alternative forms of the subject–object relation, alternative forms of human existence.
However, as indicated by Kantʼs retention of the horizon of the thing as a negativeor limit-concept, there is an absolute limit to such play (which is nonetheless inﬁnite in scope), detectable in practice, at the limits of the subject, as the limits of experience. But this is not something that can be speciﬁed in advance. It is technologically elastic, for example, especially biotechnologically: hence the essentially experimental character of knowledge. The post-Kantian transcendentalism common to neo-Nietzschean and non-Peircean pragmatisms alike tends to discount this limit, theoretically, in favour of a pure practicism, precisely because it cannot be speciﬁed in advance. Yet it is the existence of the limit that determines the meaning and existential signiﬁcance of ʻknowledgeʼ. This is not a matter of ʻcriteriaʼ, or the epistemological ʻindistinguishabilityʼ of this position from its opposite, anti-metaphysical one at the level of individual claims to knowledge, as a philosopher like Rorty supposes. Abstraction is constitutive of the object of knowledge, which is nonetheless actual for that.
This problem of the limit reappears, theoretically, as the problem of ʻthe wholeʼ (Kantʼs ʻtotality of conditions and hence the unconditionedʼ) consequent upon the interconnectedness of objects of knowledge within the transcendental unity of experience – the realm of Kantian ideas. This continued necessity of a thinking of the unconditioned, as a thinking of the whole, gave rise, after Kant, to the requirement for an ontological concept of truth, beyond the subject–object relations of an epistemological conception – a demand to which both Hegelʼs and Heideggerʼs thought were explicit responses. In this respect, the problems internal to Kantʼs concept of objectivity determine the unity of the problematic of nineteenthand twentieth-century European philosophy as a whole. For his part, Hegel attempted to develop an ontological concept of truth critically (in the Kantian sense), in its identity with the totality of possible knowledge, and hence as a speculative system. It is from this context that Hegelʼs reformulation of the problem of abstraction in terms of a ʻdialectic of the abstract and concreteʼ derives both its philosophical meaning and its continuing signiﬁcance for a transdisciplinary thinking of universality.
abstraction, systematicity, disciplinarity
In logic, Hegel wrote in his Science of Logic (ʻthe absolute culture and discipline of consciousnessʼ), thought ʻbecomes at home in abstractionʼ (Er wind dem Abstrakten … einheimisch).  This was, no doubt, in polemical response to Novalisʼs Romantic deﬁnition of philosophy as ʻhomesickness, an urge to be at home everywhereʼ – a position that was revived early in the twentieth century by both Lukács and Heidegger, and which continues to lie behind much of the contemporary melancholy about abstraction;13 although Lukácsʼs conception of modernity as ʻtranscendental homelessnessʼ may also be taken in another, more positive direction by an afﬁrmative conception of non-place.  Being at home in abstraction, Hegel believed, philosophical thought (that is, dialectical logic) is peculiarly suited to the comprehension of the modern world. For Hegelʼs understanding of modernity is already that of a culture of abstraction – of the ʻabstract individualʼ with its ʻabstract rightsʼ engaging in monetary exchanges determined by ʻthe abstract value of goodsʼ. (These are all phrases of Hegelʼs.) In modernity there is a paradoxical concreteness to certain abstractions. Yet, despite this paradoxical concreteness possessed by some abstractions – in the sense that they have a kind of empirical ʻrealityʼ (holding open the hope of philosophical thought becoming a genuine medium of knowledge of the actual, rather than the merely second-order activity which it was largely to be in the neo-Kantian and analytical wakes of Hegelʼs system) – the type of concreteness possessed by these abstractions belongs, for Hegel, to only the ﬁrst stage in knowledge of the actual. It is an abstract type of pseudo-concreteness, familiar from his critique of empiricism. It is neither a true concreteness of thought nor an expression of the deeper truth-function of the abstract. Only the concrete concept, the concrete universal, Hegelʼs version of the ʻideaʼ, or what, more methodologically (following Marx), we might call the ʻconcrete in thoughtʼ, can achieve that. In its adjectival form ʻabstractʼ (abstrakt) thus remained a predominantly derogatory term in Hegelʼs lexicon. It denotes the one-sidedness and ﬁnitude of the concepts of the understanding (Verstand) in distinction from reasonʼs (Vernunft) dialectically comprehensive conceptual grasp of the whole.
As Hegel put in his early feuilleton, ʻWho Thinks Abstractly?ʼ, it is thinking abstractly ʻto see nothing in the murderer except the abstract fact that he is a murderer, and to annul all other human essence [Wesen] in him with this simple qualityʼ (or indeed, in her – since abstract right should abstract from gender in the formality of the law).  This is the historico-philosophical basis of the critique of abstraction as conceptual domination: abstract domination is a practical effect of conceptual one-sidedness. And it can take on ferocious forms. The paradigmatic instance in Hegel is, of course, the famous section on ʻAbsolute Freedom and Terrorʼ in the Phenomenology of Spirit. There the division within the concept of universal freedom between the ʻequally abstract extremesʼ of ʻa simple, inﬂexible cold universalityʼ and ʻthe discrete, absolute hard rigidity and self-willed atomism of actual self-consciousness[es]ʼ leads to the preparation by representatives of the former of ʻthe coldest and meanest of all deathsʼ for the latter, ʻwith no more signiﬁcance than cutting off a head of cabbage or swallowing a mouthful of waterʼ. There can be few sentences in Hegelʼs oeuvre of such chilling current signiﬁcance as the one that reads: ʻThe sole work and deed of universal freedom [that is, abstractly universal freedom] is … death.ʼ 
We ﬁnd in Hegel a systematic set of distinctions between different types of abstraction – good, bad and indifferent – derived from the relationship between the oneness of truth and the variety of logical forms. Brieﬂy, for Hegel, ʻbadʼ abstractions are the one-sided, oppositional abstractions of the understanding, considered as if they are true forms of knowledge. (They are bad because they are forms of misrecognition.) ʻGoodʼ abstraction is the concrete abstraction of the absolute idea, containing within itself the systematic relations between the abstractions of the understanding (ʻall determinatenessʼ, in Hegelʼs expression17); or, alternatively, it is an abstraction of the understanding viewed from the standpoint of its place within the whole, as a merely partial manifestation of the absolute idea. ʻIndifferentʼ abstractions are abstractions of the understanding viewed independently from the question of truth, from the standpoint of their limited, partial function within the process of knowledge as a whole. One need not adopt a strictly Hegelian position in order to borrow this structure of distinctions so as to develop them analogically, in a transposed form; or at least, in order to problematize certain prevailing critiques of abstraction, some of which themselves have an implicit, quasi-Hegelian form. In fact, they are largely universalizations Hegelʼs conception of ʻbadʼ abstraction into the sole form.
Hegelʼs attempt to actualize an ontological concept of truth in the immediate unity of the totality of knowledge was inevitably a failure, since, given the radical openness of the temporal horizon, systematicity can only take the form of an ongoing, inﬁnitely revisable, inherently partial, speculative achievement – which was not Hegelʼs own ultimately Christian, neo-Platonic idea of speculative experience. As a result, Kantʼs subjective requirement for a continued thinking of the unconditioned was displaced from being the postulated ground of knowledge to its speculative historical horizon. (Once knowledge is historicized, totality becomes historically, as well as metaphysically, speculative.) With this, the idea of the systematic interconnectedness of knowledges takes on the new function of negatively determining the limitations of speciﬁc knowledges – something which became integral to the early Horkheimerʼs conception of Critical Theory. Systematic orientation (rather than system as a form of presentation) became, in part, a reﬂexive means to overcome the illusory selfsufﬁciency of speciﬁc knowledges, immanently and speculatively, via reference to the absent whole. (There is an afﬁnity here between Horkheimerʼs Kantian Hegelianism and Benjaminʼs Romanticism.) Hence the revival of philosophical Romanticism after Hegelianism as a model of thought, in Adorno among others – although, in Adorno, outside of art theory, the positive content of interconnectedness became increasingly attenuated. This post-Hegelian problematic involves a change in the philosophical conditions and meaning of disciplinarity.
There is a common historical narrative of the relationship between philosophy and other disciplines that tells the tale of modern philosophy as a tale of incremental depletion. It runs something like this. Following the foundation of modern empirical science in the seventeenth century, philosophy lost progressively more and more of the empirical totality of objects of knowledge to the various emergent sciences, until by the early twentieth century nothing remained outside of science. Philosophy was left with either the purely formal sphere of the various types of logical universality alone (this is the story of logical positivism) or some separate ontological domain (Bergsonʼs duration or Heideggerʼs Being, for example). Henceforth philosophy would therefore have to conﬁne itself to these domains alone. From this point of view, any attempt to know the world through philosophical concepts involves regression to a pre-critical type of pseudo-science based on empirically arbitrary and hence scientiﬁcally (rather than philosophically) ʻbadʼ abstractions. This is still a widely prevalent view among professional philosophers. Indeed, holding it is, in most places, a condition of entry into philosophy as a discipline.
There are two main problems with this scenario.
The ﬁrst is that it conﬂates a transcendental (constitutive) with an empirical (given) conception of scientiﬁc object-domains. The second is that it leaves out of account altogether the problem of the whole. In the ﬁrst case, the idea that the empirical totality of objects of possible knowledge could be exhaustively divided up between different sciences presupposes that this totality is empirically given and as such ʻdivisibleʼ. Yet, on the post-Kantian conception, such objects must be theoretically constituted as ʻobjects of knowledgeʼ, as varying means of knowing what is given. And such constitutions must be discursively redeemed. The conceptual arbitrariness in the historical formation of actual disciplines – hardly a model of ʻempirical methodʼ – provides rich materials here for philosophical reconstruction and critique of object-constitution. From this point of view, the so-called ʻepistemological crisis of the humanitiesʼ is not a crisis about ʻrealism, scepticism and relativismʼ (this is the misunderstanding that perpetuates it); it is a crisis of changing and overlapping object-formations, and hence of interdisciplinarity. It is also, of course, a crisis of genres (of how different practices of writing ﬁgure, and cross, particular object-domains) and of the social relations of intellectual production – the institutional sustainability of different forms of collaboration. (Serious interor trans-disciplinarity can only be a collective project, but the social form of intellectual work in the humanities remains, importantly, predominantly individual.) This is a philosophical issue because it concerns the interconnection of knowledges and their functions within the whole. This is the second problem: the problem of the whole.
Disciplinarity only makes sense against an implicit speculative background of interand transdisciplinarity of various sorts, which requires more than a merely methodological thinking of the whole. Hence the importance of certain general transdisciplinary concepts in historical, social and cultural theory – production/reproduction, modernity/tradition, desire/gender (to name but a few) – as the point of mediation between different disciplinary discourses in the humanities and social sciences, as historicophilosophical forms of object-constitution mediating the relations between different forms of inquiry; and also the importance, ultimately, of ontological concepts of natural history, mediating the ʻnaturalʼ and ʻhistoricalʼ domains.  This transdisciplinary domain is the point of mediation with experience and social practice since what is given in experience is never less than an aspect of the whole. The question thus arises as to the precise logical, ontological and phenomenological characteristics of those mediating forms constituting ʻglobal capitalist modernityʼ and, indeed, their historical content. 
From a Hegelian point of view, such forms will be grasped in thought as ʻgoodʼ – that is, logically and hence ontologically ʻconcreteʼ, and therefore actual – abstractions. However, once we divest ourselves of Hegelʼs notion of an achieved absolute, the theoretical and practical sides of Hegelʼs theory of abstraction begin to come apart. Since subjectivity can no longer be wholly assimilated to the subjective aspect of the absolute, the analytical virtue of ʻgoodʼ (that is, concrete) abstraction is no longer at one with the practical virtue hitherto associated with it: namely freedom, in Hegelʼs sense of a recognized necessity. Analytically ʻgoodʼ abstraction, ʻconcrete fullness of abstractionʼ, or the unity of the categorial forms of a systematic dialectic, may now correspond to practically ʻbadʼ abstraction: paradigmatically, in Marxʼs analysis, domination by the abstractions of the value-form. For if there is a ʻsubstance which is subjectʼ in Marxʼs analysis of capitalism, it is capital, not the collective worker. (Adorno had a more accurate reading of the logic of Capital than the Lukács of History and Class Consciousness on this point, let alone Negri, for all his late Frankfurtean stress on the universalization of ʻreal subsumptionʼ.) In terms of the logical form of Marxʼs analysis in Capital, it is self-valorizing capital – not the proletariat – that corresponds to Hegelʼs ʻideaʼ.  Indeed, in so far as analytically ʻgoodʼ abstraction (Marxʼs ʻconcrete in thoughtʼ) takes the ultimate form of a self-sufﬁcient totality of interconnected abstractions, it will presumably always correspond to practically ʻbadʼ abstractions that stand over and against individual subjects, in so far as there are a plurality of social subjects. However, and this is my main point here, this kind of practically ʻbadʼ abstraction has a different logical form to the ʻone-sidedʼ bad abstractions of the understanding, from which the discourse of good and bad abstraction derives.
For there is decisive transformation in the Hegelianinspired critique of abstraction as domination once it is extended beyond the merely empirical ʻrealityʼ (Realität) of the one-sided abstractions of the understanding in ʻthe abstract individualʼ, ʻabstract rightʼ and the like (an empiricism of everyday economic, legal and political life) to the more concretely abstract forms that unify dialectically structured totalities. In terms of Hegelʼs ontology, such forms are not merely ʻrealʼ (real) but ʻactualʼ (wirklich). They are actual abstractions; indeed, ultimately, aspects of self-actualizing abstraction. As such, they are constitutive of the unity of the totality as a self-developing whole, and so contain ʻsubjectivityʼ within themselves. This is a speciﬁc form of ʻconceptual dominationʼ in which the deep social structure of subjectivity is implicated. It is quite different from the ʻdominationʼ associated with the one-sidedness of abstract universals of the understanding, which is epitomized in the terror of absolute freedom and which, on Adornoʼs analysis, takes an everyday form in capitalist societies in the schematizations of the cultural industry. (Adornoʼs analysis is explicitly Kantian on that point.) Yet the practical-political critique of abstraction, as currently formulated, conﬂates the two forms. It operates with only one form. The whole set of relations between these different concepts of the abstract and the concrete, and of the real and the actual, thus needs to be rethought in order to take account of the ontological distinctiveness of the ʻactual abstractionsʼ at issue. For the ontology of the value form is that of an objective ideality which is nonetheless immanent to a social materialism. 
A number of questions arise. First, politically:
are ʻactual abstractionsʼ necessarily forms of social domination, qua abstractions, rather than relative to their historically speciﬁc forms and social contents? For if, for example, it is the very abstractness of the value form that is the condition of its universality as a social mediation, how are we to conceive of alternative forms of equally universal social mediation other than as being in some sense equally abstract? Are certain experiences of abstraction not the necessary condition of any global social interconnectedness in such a way that it makes no sense to criticize them for their abstraction per se? In which case a certain pervasive political discourse requires a new conception of the relationship between emancipation and actual abstraction – some conception of appropriation within abstraction, perhaps. But what form of subjectivity would that be – individual and collective? Or is the very metaphor of ʻappropriationʼ (derived from the theory of alienation) redundant at this point – a blockage to thinking new kinds of relations between subjectivity and abstract social forms? What new possibilities of the human are produced by the mediating force of actual abstractions? 
Hardt and Negri, for example, still seem bound to a Romanticism of origins – originary subjectivization – in this respect. Their social generalization of the concept of the collective worker into the ʻmultitudeʼ masks the fact that in terms of its social productivity in capitalist societies living labour is a moment in the self-mediation of capital. The generalization of the concept of real subsumption from the sphere of production to society as a whole registers the internality of labour to capital at one level, social form, but Negri insulates this level from the (fundamental) ontological level of living labour itself. Living labour is thus granted an ontological exemption from history, which is an exemption from abstraction itself. 
Second, epistemologically: how far can we legitimately extend the Hegelian notion of actual abstraction in the investigation of the status, the scope and the critical function of general, transdisciplinary concepts in the theory of global capitalist modernity? Crucially, does it have an application beyond the mediations of the value form? Can it be legitimately applied, as I have suggested elsewhere, to the most general temporal and spatial forms associated with modernity as a structure of historical experience – the temporal logic of the historically new and the spatial logic of ʻnon-placesʼ – since these, like value, are fundamental modes of unity of the total global social whole, although in other respects they are very different kinds of form?  And, if so, to what else? What is the productive range of this kind of concept? Alternatively, is there anything actual outside it?
1. ^ Paul Ricoeur, Freud and Philosophy: An Essay on Interpretation, trans. Denis Savage, Yale University Press,
New Haven and London, 1970, p. 47.
2. ^ David Hume, Treatise on Human Nature, Book 1, §7.
3. ^ Moishe Postone, Time, Labour, and Social Domination, Cambridge University Press, Cambridge, 1993, pp. 126, 127.
4. ^ Derek Sayers, The Violence of Abstraction, Blackwell,
5. ^ Paul Feyerabend, Conquest of Abundance: A Tale of Abstraction versus the Richness of Being, University of Chicago Press, Chicago and London, 1999.
6. ^ The phrase is Derridaʼs, from his early critique of Levinas. Jacques Derrida, ʻViolence and Metaphysicsʼ, in Writing and Difference, trans. Alan Bass, University of Chicago Press, Chicago, 1978, p. 151.
7. ^ See, for example, Jay Bernstein, ʻThe Death of Sensuous Particulars: Adorno and Abstract Expressionismʼ, Radical Philosophy 76, March–April 1996, pp. 7–16.
8. ^ Georg Simmel, The Philosophy of Money (1900; 1907), trans. Tom Bottomore and David Frisby, Routledge, London and New York, 1990, p. 221. For Simmel, this tragedy, which is the tragedy of ʻthe evolutionary process of the practical mindʼ, is quintessentially the tragedy – but also, importantly, the ʻinﬁnite possibilityʼ – of money.
9. ^ This ﬂattening out is more pronounced in Derrida than in Adorno, whose thought crucially retains a historical dimension. However, in so far as for him the contradiction within the idea of knowledge is structural, the historicity of its genesis is cancelled in its result.
10. ^ Gillian Rose, Hegel Contra Sociology, Athlone, London, 1981, ch. 1.
11. ^ Immanuel Kant, Logic (1800), trans. Robert S. Hartman and Wolfgang Schwarz, Dover, New York, 1974, p. 100.
12. ^ Hegelʼs Science of Logic, trans. A.V. Miller, Humanities Press, Atlantic Highlands, 1989, pp. 58–9; G.W.F. Hegel, Werke 5, Wissenschaft der Logik I, Suhrkamp, Frankfurt am Main, 1986, p. 55.
13. ^ Georg Lukács, Theory of the Novel: A HistoricoPhilosophical Essay on the Forms of Great Epic Literature (1920), trans. Anna Bostock, Merlin Press, London, 1971, pp. 29, 41; Martin Heidegger, The Fundamental Concepts of Metaphysics: World, Finitude, Solitude (1929/30), trans. William McNeill and Nicholas Walker,
Indiana University Press, Bloomington, 1995, pp. 5–7.
14. ^ See Peter Osborne, ʻNon-Places and the Spaces of Artʼ, The Journal of Architecture 6, Summer 2001, pp. 183–94.
15. ^ Hegel, ʻWho Thinks Abstractlyʼ (c.1808), in Walter Kaufmann, Hegel: Texts and Commentary, Anchor Books, Garden City NY, 1966, pp. 113–8, p. 116.
16. ^ Hegelʼs Phenomenology of Spirit (1807), trans. A.V.
Miller, Oxford University Press, Oxford, 1977, pp. 359–60.
17. ^ Hegelʼs Science of Logic, p. 824.
18. ^ Adornoʼs early essay ʻThe Idea of Natural Historyʼ (1932), trans. R. Hullot-Kentor, Telos 60, Summer 1984, pp. 111–24, remains one of the few attempts at such a thought.
19. ^ Cf. Peter Osborne, Philosophy in Cultural Theory, Routledge, London and New York, 2000, ch. 1.
20. ^ See Christopher J. Arthur, The New Dialectic and Marxʼs Capital, Brill, Leiden/Boston/Cologne, 2002, chs 1–8. 21 Cf. Christopher J. Arthur, ʻThe Spectral Ontology of Valueʼ, Radical Philosophy 107, May/June 2001, pp. 32–42.
22. ^ The familiar theoretical alternative to appropriation is afﬁrmation. See Gilles Deleuze, Nietzsche and Philosophy (1962), trans. Hugh Tomlinson, Athlone Press, London, 1983, ch.
5. ^ However, in its principled rejection of mediation this Nietzschean alternative remains, at least as yet, incapable of thinking the ontological distinctiveness of social form.
23. ^ Antonio Negri, Marx Beyond Marx: Lessons on the ʻGrundrisseʼ (1978), trans. Harry Cleaver, Michael Ryan and Maurizio Viano, Automedia/Pluto, New York/London, 1991, ʻLesson Six: Social Capital and World Marketʼ, pp. 105–26; Antonio Negri and Michael Hardt, Empire, Harvard University Press, Cambridge MA and London, 2000, pp. 254–6, 272; Antonio Negri, ʻKairòs,
Alma Venus, Multitudoʼ (2000), in Time for Revolution, trans. Matteo Mandarini, Continuum, New York and London, 2003, ʻLiving Labourʼ, pp. 235–48. The exemption of living labour from history is the price Negriʼs thought pays for its rejection of all concepts of mediation.
24. ^ Osborne, Philosophy in Cultural Theory, chs 1 and 3; ʻNon-Places and the Spaces of Artʼ. See also David Cunningham, ʻThe Phenomenology of Non-Dwelling:
Massimo Cacciari, Modernism and the Philosophy of the Metropolisʼ, Crossings 7, 2004.