Conjectural Existence of the Categorial Complex Branes for Generalized Calabi-Yau.

Geometric Langlands Duality can be formulated as follows: Let C be a Riemann surface (compact, without boundary), G be a compact reductive Lie group, GC be its complexification, and Mflat(G, C) be the moduli space of stable flat GC-connections on C. The Langlands dual of G is another compact reductive Lie group LG defined by the condition that its weight and coweight lattices are exchanged relative to G. Let Bun(LG, C) be the moduli stack of holomorphic LG-bundles on C. One of the statements of Geometric Langlands Duality is that the derived category of coherent sheaves on Mflat(G, C) is equivalent to the derived category of D-modules over Bun(LG, C).

Mflat(G, C) is mirror to another moduli space which, roughly speaking, can be described as the cotangent bundle to Bun(LG, C). The category of A-branes on T Bun(LG, C) (with the canonical symplectic form) is equivalent to the category of B-branes on a noncommutative deformation of T Bun(LG, C). The latter is the same as the category of (analytic) D-modules on Bun(LG, C).

So, what exactly is, the relationship between A-branes and noncommutative B-branes. This relationship arises whenever the target space X is the total space of the cotangent bundle to a complex manifold Y. It is understood that the  symplectic form ω is proportional to the canonical symplectic form on T Y. With the B-field vanishing, and Y as a complex, we regard ω as the real part of a holomorphic symplectic form Ω. If qi are holomorphic coordinates on Y, and pi are dual coordinates on the fibers of T Y,  Ω can be written as

Ω = 1/ħdpi ∧ dqi = dΘ

Since ω (as well as Ω) is exact, the closed A-model of X is rather trivial: there are no nontrivial instantons, and the quantum cohomology ring is isomorphic to the classical one.

We would like to understand the category of A-branes on X = T Y. The key observation is that ∃ a natural coisotropic A-brane on X well-defined up to tensoring with a flat line bundle on X. Its curvature 2-form is exact and given by

F = Im Ω

If we denote by I the natural almost complex structure on X coming from the complex structure on Y , we have F = ωI, and therefore the endomorphism ω−1F = I squares to −1. Therefore any unitary connection on a trivial line bundle over X whose curvature is F defines a coisotropic A-brane. 

Now, what about the endomorphisms of the canonical coisotropic A-brane, i.e., the algebra of BRST-closed open string vertex operators? This is easy if Y is an affine space. If one covers Y with charts each of which is an open subset of Cn, and then argues that the computation can be performed locally on each chart and the results “glued together”, one gets closer to the fact that the algebra in question is the cohomology of a certain sheaf of algebras, whose local structure is the same as for Y = Cn. In general, the path integral defining the correlators of vertex operators does not have any locality properties in the target space. Each term in perturbation theory depends only on the infinitesimal neighbourhood of a point. This shows that the algebra of open-string vertex operators, regarded as a formal power series in ħ, is the cohomology of a sheaf of algebras, which is locally isomorphic to a similar sheaf for X = Cn × Cn.

Let us apply these observations to the canonical coisotropic A-brane on X = T Y. Locally, we can identify Y with a region in Cn by means of holomorphic coordinate functions q1, . . . , qn. Up to BRST-exact terms, the action of the A-model on a disc Σ 􏰠takes the form

S = 1/ħ ∫∂Σ φ (pidqi)

where φ is a map from Σ to X. This action is identical to the action of a particle on Y with zero Hamiltonian, except that qi are holomorphic coordinates on Y rather than ordinary coordinates. The BRST-invariant open-string vertex operators can be taken to be holomorphic functions of p, q. Therefore quantization is locally straightforward and gives a noncommutative deformation of the algebra of holomorphic functions on T Y corresponding to a holomorphic Poisson bivector

P = ħ∂/∂pi ∧ ∂/∂qi

One can write an explicit formula for the deformed product:

􏰋(f ⋆ g)(p, q) = exp(􏰋ħ/2(∂2/∂pi∂q̃i  −  ∂2/∂qi∂p̃i )) f(p, q) g (p̃, q̃)|p̃ = p, q̃ = q

This product is known as the Moyal-Wigner product, which is a formal power series in ħ that may have zero radius of convergence. To rectify the situation, one can restrict to functions which are polynomial in the fiber coordinates pi. Such locally-defined functions on T Y can be thought of as symbols of differential operators; the Moyal-Wigner product in this case reduces to the product of symbols and is a polynomial in ħ. Thus locally the sheaf of open-string vertex operators is modelled on the sheaf of holomorphic differential operators on Y (provided we restrict to operators polynomial in pi).

Locally, there is no difference between the sheaf of holomorphic differential operators D(Y ) and the sheaf of holomorphic differential operatorsD(Y, L) on a holomorphic line bundle L over Y. Thus the sheaf of open-string vertex operators could be any of the sheaves D(Y, L). Moreover, the classical problem is symmetric under pi → −pi combined with the orientation reversal of Σ; if we require that quantization preserve this symmetry, then the algebra of open-string vertex operators must be isomorphic to its opposite algebra. It is known that the opposite of the sheaf D(Y, L) is the sheaf D(Y, L−1 ⊗ KY), so symmetry under pi → −pi requires L to be a square root of the canonical line bundle KY. It does not matter which square root one takes, since they all differ by flat line bundles on Y, and tensoring L by a flat line bundle does not affect the sheaf D(Y, L). The conclusion is that the sheaf of open-string vertex operators for the canonical coisotropic A-brane α on X = T Y is isomorphic to the sheaf of noncommutative algebras D(Y, K1/2). One can use this fact to associate Y to any A-brane β on X a twisted D-module, i.e., a sheaf of modules over D(Y, K1/2). Consider the A-model with target X on a strip Σ = I × R, where I is a unit interval, and impose boundary conditions corresponding to branes α and β on the two boundaries of Σ. Upon quantization of this model, one gets a sheaf on vector spaces on Y which is a module over the sheaf of open-string vertex operators inserted at the α boundary. A simple example is to take β to be the zero section of T Y with a trivial line bundle. Then the corresponding sheaf is simply the sheaf of sections of KY1/2, with a tautological action of D(Y, KY1/2).

One can argue that the map from A-branes to (complexes of) D-modules can be extended to an equivalence of categories of A-branes on X and the derived category of D-modules on Y. The argument relies on the conjectural existence of the category of generalized complex branes for any generalized Calabi-Yau. One can regard the Geometric Langlands Duality as a nonabelian generalization. 

Hegel and Topos Theory. Thought of the Day 46.0


The intellectual feat of Lawvere is as important as Gödel’s formal undecidability theorem, perhaps even more. But there is a difference between both results: whereas Gödel led to a blind alley, Lawvere has displayed a new and fascinating panorama to be explored by mathematicians and philosophers. Referring to the positive results of topos theory, Lawvere says:

A science student naively enrolling in a course styled “Foundations of Mathematics” is more likely to receive sermons about unknowability… than to receive the needed philosophical guide to a systematic understanding of the concrete richness of pure and applied mathematics as it has been and will be developed. (Categories of space and quantity)

One of the major philosophical results of elementary topos theory, is that the way Hegel looked at logic was, after all, in the good track. According to Hegel, formal mathematical logic was but a superficial tautologous script. True logic was dialectical, and this logic ruled the gigantic process of the development of the Idea. Inasmuch as the Idea was autorealizing itself through the opposition of theses and antitheses, logic was changing but not in an arbitrary change of inferential rules. Briefly, in the dialectical system of Hegel logic was content-dependent.

Now, the fact that every topos has a corresponding internal logic shows that logic is, in quite a precise way, content-dependent; it depends on the structure of the topos. Every topos has its own internal logic, and this logic is materially dependent on the characterization of the topos. This correspondence throws new light on the relation of logic to ontology. Classically, logic was considered as ontologically aseptic. There could be a multitude of different ontologies, but there was only one logic: the classical. Of course, there were some mathematicians that proposed a different logic: the intuitionists. But this proposal was due to not very clear speculative epistemic reasons: they said they could not understand the meaning of the attributive expression “actual infinite”. These mathematicians integrated a minority within the professional mathematical community. They were seen as outsiders that had queer ideas about the exact sciences. However, as soon as intuitionistic logic was recognized as the universal internal logic of topoi, its importance became astronomical. Because it provided, for the first time, a new vision of the interplay of logic with mathematics. Something had definitively changed in the philosophical panorama.

Brassier/Meillassoux and the Problematic of Representation


As Kant claimed in his Critique of Pure Reason that it is not uniformity that is a necessary criteria of ‘in-itself’ or ‘things-in-themselves’, but the possibility of consciousness and representation that require the constancy of phenomena in nature leading in and out of the tautological presupposition of the constancy of phenomena on the one hand and constancy of nature on the other. This representation or as Brassier says the problematic of representation has been accepted by the continental tradition without putting up any challenge that has encouraged relinquishing epistemological considerations into the theoretical investigations of nature and conditions of cognition. Meillassoux, on the other hand identifies the ‘frequentialist implication’ argument in Kant that proves the impossibility of representation as due not to the contingency of laws. Having identified it, he proceeds to expound his ‘anti-frequentialist’ argument that demonstrates that the contingency of the laws of nature need not entail their frequent transformation and thereby the impossibility of their representation, as his principle concern is to show what he calls the principle of unreason is to be in perfect compatibility with the stability of appearances and the scientific representation of nature.

Meillassoux wants to challenge modern philosophy’s appropriation of facticity as a limit to revealing knowledge of the absolute. Facticity tells us about the nature of the absolute. If all we can know is the contingency of facticity, then there is no reason for things to remain so rather than otherwise. Yet saying ‘everything is equally possible’ is an absolute claim, thus metaphysical. The only claim that can be made is based upon our facticity, not as limit but as absolute: the absolute is the absolute impossibility of a necessary being. This is the absolute truth of the principle of unreason: this is an hypothetical principle, which is a proposition that could bot be deduced from another proposition, but could be proved by argument.

As against Kant’s dictum of the contingency of the laws of nature implying a frequency of transformation that render the impossibility of representation, Meillassoux concludes that the absolute contingency of the world’s physical structure is in perfect compatibility with the stability of the phenomena and thus the possibility of representation. Brassier discovers a fundamental flaw in Meillassoux’s invoking the anti-frequentialist argument. The flaw is in terms of leaving the ontological status of this stability unattended, despite the latter showing that that the ‘frequentialist implication’ argument unable to prove the reality as totalizable and that contingency is not necessarily incompatible with the appearance of stability, as the former thinks the ontological status of stability to be a cardinal issue in latter’s project of accounting for the ancestral claims to the conditions of possibility of science. Meillassoux is quite aware of this fact that reality in-itself is a non-totalizable multiplicity and as he says:

“We have not established the effectivity of this un-totalization – we have merely supposed it and drawn the consequences of the fact that such a supposition is possible.”

Thus he concedes to the fact of speculative argument, although subtle in his discourse, that would found the stability of appearances upon non-totalizability of absolute time.

Complexity Theory and Philosophy: A Peace Accord


Complexity has impacted fields diverse from the one it originated in, i.e. science. It has touched the sociological domains, and organizational sciences, but sadly, it has not had much of a say in mainstream academic philosophy. In sociology, John Urry (2003) examines the ideas of chaos and complexity in carrying out analyses of global processes. He does this, because he believes that systems are balanced between order and chaos, and that, there is no teleological move towards any state of equilibrium, as the events that pilot the system are not only unpredictable, but also irreversible at the same time. Such events rupture the space-time regularity with their dimension of unpredictability that was thought of as characterizing hitherto known sociological discursive practices. A highly significant contribution that comes along with such an analyses is the distinguishing between what Urry aptly calls “global networks” and “global fluids”. Global fluids are a topographical space used to describe the de-territorialized movement of people, information, objects, finances in an undirected, nonlinear mode, and in a way are characteristic of emergentism and hybridization. The topographies of global networks and global fluids interact in complex manner to give rise to emergent properties that define systems as always on the edge of chaos, pregnant with unpredictability.


Cognitive science and evolutionary theory have been inspirational for a lot of philosophical investigations and have also benefited largely from complexity theory. If such is the case, the perplexing thing is complexity theory’s impact in philosophy, which has not had major inroads to make. Why could this be so? Let us ponder this over.

Analytical philosophy has always been concerned with analysis, and logical constructs that are to be stringently followed. These rules and regulations take the domain of philosophical investigations falling under the rubric of analytical tradition away from holism, uncertainty, unpredictability and subjectivity that are characteristics of complexity. The reason why this could be case is attributable to complexity theory as developed on the base of mathematics and computational theories, which, somehow is not the domain of academic philosophy dealing with social sciences and cultural studies in present days, but is confined to discussions and debates amongst philosophers of science (biology is an important branch here), mathematics and technology. Moreover, the debates and deliberations have concerned themselves with the unpredictable and uncertain implications as derived from the vestiges of chaos theory and not complexity theory per se. This is symptomatic of the fact that a lot of confusion rests upon viewing these two path-breaking theories as synonymous, which, incidentally is a mistake, as the former happens at best to be a mere subset of the latter. An ironical fate encountered philosophy, since it dealt with complex notions of language, without actually admitting to the jargon, and technical parlance of complexity theory. If philosophy lets complexity make a meaningful intercourse into its discursive practices, then it could be beneficial to the alliance. And the branch of philosophy that is making use of this intervention and alliance at present is post-modern philosophy ++++

The works of Freud and Saussure as furthered by Lacan and Derrida, not only accorded fecundity for a critique of modernity, but, also opened up avenues for a meaningful interaction with complexity. French theory at large was quite antagonistic to modernist claims of reducing the diverse world to essential features for better comprehensibility, and this essentially lent for its affinity to complexity. Even if Derrida never explicitly used the complexity parlance in his corpus, there appears to be a strong sympathy towards the phenomenon via his take on post-structuralism. On the other hand, Lyotard, in setting his arguments for post-modern conditions of knowledge was ecstatic about paralogy as a defining feature, which is no different from the way complexity, connectionism and distributed systems would harbor.


Even Deleuze and Guattari are closer to the complex approach through their notions of rhizomes, which are non-reductive, non-hierarchical, and multiplicities oriented connections in data representations and interpretations, and are characterized by horizontal connectivities, as contrasted with arborescent models that find their characterizations in vertical and linear determinations. The ideas are further developed by De Landa (2006), where the attempt is to define a new ontology that could be utilized by social scientists. Components that make up the assemblages are characterized along two axes viz, material, explicating on the variable roles components might undergo, and territorializng/deterritorializing, explicating on processes components might be involved with.


Relations of exteriority define components, implying that components are self-subsistent, or that there is never a loss of identity for them, during the process of being unplugged from one assemblage to be plugged into another. This relationship between the assemblages and components is nonlinearly and complexly defined, since assemblages are affected by lower level ones, but could also potentially act on to these components affecting adaptations in them. This is so similar to the way distributed systems are principally modeled. Then why has philosophy at large not shown much impact from complexity despite the French theoretical affinities with the latter?

Chaos theory is partly to blame here, for it has twisted the way a structure of a complex system is understood. The systems have a non-linear operational tendencies, and this has obfuscated the notion of meaning as lying squarely on relativism. The robustness of these systems, when looked at in an illuminating manner from the French theoretical perspective could be advantageous to get rid of ideas about complex systems as based on a knife’s edge, despite being nonlinearly determinable. If the structure of the system were a problematic, then defining limits and boundaries was no easy job. What is the boundary between the system and the environment? Is it rigorously drawn and followed, or is it a mere theoretical choice and construct? These are valid question, which philosophy found it difficult to come to terms with. These questions gained intensity with the introduction of self-organizational systems and/or autopoietic ones. Classical and modern philosophies either had to dismiss these ideas as chimerical, or it had to close off its own analyzing methods in dealing with these issues, and both of these approaches had a detrimental effect of isolating the discipline of philosophy from the cultural domains in which such notions were making positive interventions and inroads. It could safely be said that French theory, in a way tried its rescue mission, and picked up momentum in success. The major contribution from continental philosophy post-60s was framing solutions. Framing, as a schema of interpretation helped comprehending and responding to events and enabled systems and contexts to constitute one another, thus positing a resolution on the boundaries and limits issues that had plagued hitherto known philosophical doctrines.

The notion of difference, so central to modernism was a problematic that needed to be resolved. Such was never a problem within French theory, but was a tonic to be consumed along side complexity, to address socio-economic and political issues. Deleuze (1994), for example, in his metaphysical treatise, sought a critique of representation, and a systematic inversion of the traditional metaphysical notions of identity and difference. Identities were not metaphysically or logically prior to differences, and identities in whatever categories, are pronounced by their derivation from differences. In other words, forms, categories, apperception, and resemblances fail to attain their differences in themselves. And, as Deleuze (2003: 32) says,

If philosophy has a positive and direct relation to things, it is only insofar as philosophy claims to grasp the thing itself, according to what it is, in its difference from everything it is not, in other words, in its internal difference.

But Deleuzean thesis on metaphysics does make a political intervention, like when he says,

The more our daily life appears standardized, stereotyped, and subject to an accelerated reproduction of objects of consumption, the more art must be injected into it in order to extract from it that little difference which plays simultaneously between other levels of repetition, and even in order to make the two extremes resonate — namely, the habitual series of consumption and the instinctual series of destruction and death. (Deleuze 1994: 293).(1)

Tackling the complexity within the social realm head-on does not lie in extrapolating convenient generalities, and thereafter trying to fathom how finely they fit together, but, rather in apprehending the relational schema of the network, within which, individuals emerge as subjects, objects and systems that are capable of grasping the real things.(2) 

One major criticism leveled against complexity is that it is sympathetic to relativism, just like most of the French theoretical thought is. Whether, this accusation has any substance to it could be measured by the likes of circular meaningless debates like the Sokal hoax. The hoax was platitudinous to say the least, and vague at best. And why would this be so? Sokal in his article, “Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity”, incorporated the vocabulary of his specialized discipline to unearth the waywardness of usage by the French theorists. This, for Sokal was fashionable nonsense, or an act of making noise. He takes the French theorists to task for a liberal use of terms like chaos, complexity, quantum, relativity, gender, difference, topology, and deconstruction, without any proper insight. Who would be vague in the Sokal affair? The physicist, or the bunch of French theorists? Such an issue could be tackled on an intelligibility concern. Intelligibility is a result of differentiation and not a guarantee of truth-giving process (Cilliers 2005: 262).

Clearly communicated does not give any indisputable identity to a concept. The only way, (such a meaning can) be meaningful is through limitations being set on such communications, an ethical choice once again. These limitations enable knowledge to come into existence, and this must be accepted de facto. In a parallel metaphoric with complexity, these limitations or constraints are sine qua non for autopoiesis to make an entry. Cilliers (2005: 264) is quite on target, when he lays down the general schema for complexity, if it is, aligned with notions of chaos, randomness and noise, the accusations of relativism and vagueness will start to hold water. It is aligned with notions of structure as the result of contingent constraints, we can make claims about complex systems, which are clear and comprehensible, despite the fact that the claims themselves are historically contingent.

Undoubtedly, complexity rides on modesty. But, the accusations against this position only succeed to level complexity as weak, a gross mistake in itself. Let us take Derrida here, as read by Sweetman (1999). Sweetman cites Derrida as an ideal post-modernist, and thereafter launches an attack on his works as confusing aesthetics with metaphysics, as mistakenly siding with assertions over arguments in philosophy, as holding Derrida for moral and epistemological relativism and, self-contradictory with a tinge of intellectual arrogance. Such accusations, though addressed by Derrida and his scholars at various times, nevertheless find parallels in complexity, where, the split is between proponents of mathematical certainty in dealing with complexity on the one hand, and proponents of metaphorical proclivities in dealing with the phenomenon on the other. So, how would relativism make an entry here? Being a relativist is as good as swimming in paradoxical intellectual currents, and such a position is embraced due to a lack of foundational basis for knowledge, if nothing more. The counter-argument against the relativistic stance of complexity could be framed in a simplistic manner, by citing the case of limited knowledge as not relativistic knowledge. If these forms of knowledge were equated in any manner, it would only help close doors on investigations.

A look at Luhmann’s use of autopoiesis in social theory is obligated here. This is necessitated by the fact of autopoiesis getting directly imported from biological sciences, to which, even Varela had objections, though intellectually changing tracks. Luhmann considers the leaving out of self-referentiality as a problematic in the work of Chileans (Maturana + Varela), since for Luhmann systems are characterized by general patterns which can just be described as making a distinction and crossing the boundary of the distinction [which] enables us to ask questions about society as a self-observing systems[s] (Hayles, K., Luhmann, N., Rasch, W., Knodt, E. & Wolfe, C., 1995 Autumn). Such a reaction from Luhmann is in his response to a cautious undertaking of any import directly from biological and psychological sciences to describe society and social theory. Reality is always distorted through the lens of perception and, this blinds humans from seeing things-in-themselves (the Kantian noumenon). One could visualize this within the analytical tradition of language as a problematic, involving oppositional thinking within the binary structure of linguistic terms themselves. What is required is an evolutionary explanation of how systems survive to the extent that they can learn to handle the inside/outside difference within the system, and within the context of their own operations, since they can never operate outside the system (Hayles, K., Luhmann, N., Rasch, W., Knodt, E. & Wolfe, C., 1995 Autumn). For the social theory to be effective, what requires deconstruction is the deconstruction of the grand tautological claim of autopoiesis, or the unity of the system as produced by the system itself. Luhmann tells us that a methodology that undertakes such a task must do this empirically by identifying the operations which produce and reproduce the unity of the system (Luhmann 1992). This is a crucial point, since the classical/traditional questions as regards the problem of reference as conditioning meaning and truth, are the distinctions between the subject and the object. Luhmann thinks of these questions as quasi-questions, and admonishes a replacement by self-reference/external-reference for any meaningful transformation to take effect. In his communications theory(3), he states flatly that as a system, it depends upon “introducing the difference between system and environment into the system” as the internal split within the system itself that allows it to make the distinction to begin its operative procedures to begin with (Luhmann 1992: 1420). The self-reference/external-reference distinction is a contingent process, and is open to temporal forms of difference. How to define the operation that differentiates the system and organizes the difference between system and environment while maintaining reciprocity between dependence and independence is a question that demands a resolution. The breakthrough for autopoietic systems is provided by the notion of structural coupling, since a renunciation of the idea of overarching causality on the one hand, and the retention of the idea of highly selective connections between systems and environments is effected here. Structural coupling maintains this reciprocity between dependence and independence. Moreover, autopoietic systems are defined by the way they are, by their mode of being in the world, and by the way they overcome or encounter entropy in the world. In other words, a self-perpetuating system performing operational closure continuously are autopoietic systems that organize dynamic stability.


Even if the concepts of complexity have not traveled far and wide into the discipline of philosophy, the trends are on the positive side. Developments in cognitive sciences and consciousness studies have a far reaching implications on philosophy of mind, as does in research in science that helps redefine the very notion of life. These researches are carried out within the spectrum of complexity theory, and therefore, there is a lot of scope for optimism. Complexity theory is still in the embryonic stage, for it is a theory of the widest possible extent for our understanding the world that we inhabit. Though, there are roadblocks along the way, it should in no way mean that it is the end of the road for complexity, but only a beginning in a new and novel manner.

Complexity theory as imbibed within adaptive systems has a major role in evolutionary doctrines. To add to this, the phenomenon of French Theory has incited creative and innovative ways of looking at philosophy, where residues of dualism and reductionism still rest, and resist any challenges whatsoever. One of the ways through which complexity and philosophy could come closer is, when the latter starts withdrawing its investigations into the how- ness of something, and starts to seriously incorporate the why-ness of it. The how- ness still seems to be arrested within the walls of reductionism, mechanicism, modernism, and the pillars of Newtonian science. So, an ontological reduction of all phenomenon under the governance of deterministic laws is the indelible mark, even if epistemologically, a certain guideline of objectivity seems apparent. What really is missed out on in this process is the creativity, as world in particular and universe in general is describable as a mechanism following clockwork. Such a view held sway for most the modern era, but with the advent of scientific revolutions in the 20th century, things began to look awry. Relativity theory, quantum mechanics, chaos, complexity, and recently string/M-theory were powerful enough in their insights to clean off the hitherto promising and predictable scientific ventures. One view at quantum mechanics/uncertainty and chaos/non-linear dynamics was potent to dislodge predictability from science. This was followed in succession by systems theory and cybernetics, which were instrumental in highlighting the scientific basis for holism and emergence, and showing equally well that knowledge was intrinsically subjective. Not just that, autopoiesis clarified the picture of regularity and organization as not given, but, rather dependent on a dynamically emergent tangle of conflicting forces and random fluctuations, a process very rightly referred to by Prigogine and Stengers (1984) as “order out of chaos”. In very insightful language, Heylighen, Cilliers and Gershenson (2007) pin their hopes on these different approaches, which are now starting to become integrated under the heading of “complexity science”. It’s central paradigm is the multi-agent system: a collection of autonomous components whose local interactions give rise to a global order. Agents are intrinsically subjective and uncertain about the consequences of their actions, yet they generally manage to self-organize into an emergent, adaptive system. Thus uncertainty and subjectivity should no longer be viewed negatively, as the loss of the absolute order of mechanicism, but positively, as factors of creativity, adaptation and evolution….Although a number of (mostly post-modern) philosophers have expressed similar sentiments, the complexity paradigm still needs to be assimilated by academic philosophy.

Such a need is a requisite for complexity to become more aware about how modeling techniques could be made more robust, and for philosophy to understand and resolve some hitherto unaddressed, but perennial problems.


1  The political implications of such a thesis is rare, but forceful. To add to the quote above, there are other quotes as well, that deliberate on socio-political themes. Like,

“We claim that there are two ways to appeal to ‘necessary destructions’: that of the poet, who speaks in the name of a creative power, capable of overturning all orders and representations in order to affirm Difference in the state of permanent revolution which characterizes eternal return; and that of the politician, who is above all concerned to deny that which ‘differs,’ so as to conserve or prolong an established historical order.” (Deleuze 1994: 53).


“Real revolutions have the atmosphere of fétes. Contradiction is not the weapon of the proletariat but, rather, the manner in which the bourgeoisie defends and preserves itself, the shadow behind which it maintains its claim to decide what the problems are.” (Deleuze 1994: 268).

2 It should however be noted, that only immanent philosophies of the sort Deleuze propagates, the processes of individuation could be accounted for. Moreover, once such an aim is attained, regularities in the world are denied any eternal and universal validation.

3 He defines communication as “a kind of autopoetic network of operations which continually organizes what we seek, the coincidence of self-reference (utterance) and external reference (information)” (1992: 1424). He details this out saying,

“Communication comes about by splitting reality through a highly artificial distinction between utterance and information, both taken as contingent events within an ongoing process that recursively uses the results of previous steps and anticipates further ones”. (1992: 1424).


Ciliers, P. (2005) Complexity, Deconstruction and Relativism. In Theory, Culture & Society, Vol. 22 (5). pp. 255 – 267.

De Landa, M. (2006) New Philosophy of Society: Assemblage Theory and Social Complexity. London: Continuum.

Deleuze, G. (1994) Difference and Repetition. Translated by Patton, P. New York: Columbia University Press.

—————- (2003) Desert Islands and Other Texts (1953-1974). Translated by Taormina, M. Los Angeles: Semiotext(e).

Hayles, K., Luhmann, N., Rasch, W., Knodt, E. & Wolfe, C. (1995 Autumn) Theory of a Different Order: A Conversation with Katherine Hayles and Niklas Luhmann. In Cultural Critique, No. 31, The Politics of Systems and Environments, Part II. Minneapolis, MN: University of Minnesota Press.

Heylighen, F., Cilliers, P., and Gershenson, C. (2007) The Philosophy of Complexity. In Bogg, J. & Geyer, R. (eds), Complexity, Science and Society. Oxford: Radcliffe Publishing.

Luhmann, N (1992) Operational Closure and Structural Coupling: The Differentiation of the Legal System. Cardoza Law Review Vol. 13.

Lyotard, J-F. (1984) The Postmodern Condition: A Report on Knowledge. Translated by Bennington, G. & Massumi, B. Minneapolis, MN: University of Minnesota Press.
Prigogine, I. and Stengers, I. (1984) Order out of Chaos. New York: Bantam Books.

Sweetman, B. (1999) Postmodernism, Derrida and Différance: A Critique. In International Philosophical Quarterly XXXIX (1)/153. pp. 5 – 18.

Urry, J. (2003) Global Complexity. Cambridge: Polity Press.

Human Rights, (Badiou + Rancière)

“Human Rights are axioms. They can co-exist on the market with many other axioms, notably those concerning security or property, which are unaware of or suspend them even more than they contradict them: “the impure mixture or the impure side by side,” said Nietzsche. Who but the police and armed forces that co-exist with democracies can control and manage poverty and the deterritorialization-reterritorialization of shanty towns? What social democracy has not given the order to fire when the poor come out of their territory or ghetto? Rights save neither men nor a philosophy that is reterritorialized on the democratic State. Human rights will not make us bless capitalism. A great deal of innocence or cunning is needed by a philosophy of communication that claims to restore the society of “consensus” to moralize nations, States, and the market. Humans rights say nothing about the immanent modes of existence of people provided with rights.” 

— Deleuze and Guattari (1996, 107)

The quote from Deleuze and Guattari’s ‘What is Philosophy?’ nicely sums up the abstraction, pure, empty abstraction that Deleuze calls the party line for odious intellectuals. Deleuze does not pay much heed to the notion of human rights, but, instead broods over life rights.

My intention is not to delve into the Deleuzean version of Human/Life Rights, but to look at the conception of human rights from the point of view of two French philosophers who have made an impact in the English speaking world. The thinkers in question here are  Badiou and Rancière who with their delivery of political agencies are not only complexly similar on many grounds, but provide many insights into the differences between one another. Their writings  delve into human rights as a base for their versions of political agencies.

The time was February, 2008, when a group of the so called new philosophers signed a petition in Le Monde calling the practices of the United Nations as diametrically opposed to the ideals of human rights. It was further commented that there was a cause of concern with the institution becoming a caricature. Although we are ensconced in a multicultural world, the level of tolerance could be said to be reaching a nadir of sorts as was substantially proved in the petition detailing religious criticism as a form of racism, thus highlighting the tide against the basic ideas of Human Rights. The petition then called for the return to the Universal Ideals on Human Rights.

It would be far fetched, but still appropriate to call the new philosophers as sandwiched between viewing the ideals of 1948 as problematic with their emphasis on a return to ideals. That the new philosophers are sandwiched between the two poles is attributable to one pole being that of Arendt and Agamben with their insistence on Human Rights as infringing of the political into the private sphere and the other of Badiou and Rancière calling for a political agency critiquing both the view points. Arendt dismisses the idea of Human rights by calling it necessity based as action by the nation state to impose its control over the huge mass of refugees created in the aftermath of the second world war, when the refugees that had been rendered stateless had nothing left but their humanity. This way, for Arendt, the nation state gets to determining who gets the rights and who doesn’t or who is part of humanity and who is not, thus quashing the ideals meant to protecting rights. Despite the good intentions behind the formulation of the Universal Ideals, it is nothing but an apparatus through which, the state exercises its total power over the stateless by making the latter submissive to it and other allied organs of power. This indeed proves the thesis that an interventionist approach is taken up by the nation state into the private sphere.

Arendt’s thesis is pressed upon by Agamben, when he calls the peril of our present time as lying alongside an intercourse of the political power into the bare public life as omnipresent. Agamben links the notional intercourse as no different from what the refugees had to face in concentration camps. For him, the human rights act in a totalizing manner as now the most basic human existence is intricately surrendered to power structures thus making existence politicized. To quote Agamben,

“…until a completely new politics – that is, a politics no longer founded on the exception of bare life – is at hand, every theory and every praxis will remain imprisoned and immobile, and the “beautiful day” of life will be given citizenship only either through blood and death or in the perfect senselessness to which the society of the spectacle condemns it.”

Ernst Hemel reads the following quote in a dual way, viz. the seizure of private bare life by the structures of power and the deprivations of the individual in engaging with true emancipatory politics. The institutionalization of human rights is therefore seen as a part of the imprisoned and immobile life that somehow fails in its approach to reach the blunt political situation we are all faced up with. This reaches its aporetic limit in a way to invent a new political situation after criticizing the entire idea underlining human rights. So for both Arendt and Agamben, the codification of the Universal Declaration of Human Rights is fraught with a critique that runs counter to new philosopher’s insistence on attaining the ideal.

Badiou and Rancière both show their aversion to these readings and in their own ways of constructing the political agency exhibit displeasure in treating human rights as an ideal on the one hand and refusing to believe in the all encompassing political dominion on the other. Rancière brilliantly unearths the tautology in Arendt’s version of human rights by noting that the rights of man are the rights of the unpoliticized person, or they are the rights of those who have no rights, thus amounting to nothing and rights of man are the rights of the citizen, that is, they are being attached to the fact of being a citizen, thus connoting rights of man as rights of citizens. This in conflation amounts to a tautology. In effect, there is abandonment of human rights in Arendt according to Rancière since it is based on state power who has the discretion of providing rights to those who are excluded. This argument is taken forward to deal with Agamben, wherein it is noted that any kind of emancipatory political action is in retreat. Rancière quotes from his ‘The Politics of Aesthetics’,

“There was at least one point where ‘bare life’ proved to be ‘political’: there were women sentenced to death as enemies of the revolution. If they could lose their ‘bare life’ out of the public judgment based on political reasons, this meant that even their bare life – their life doomed to death – was political. If, under the guillotine, they were as equal, so to speak, as men, they had the right to the whole of equality, including equal participation to political life.”

It is only in these situations that the totality is fissured in that there is a sense of inclusion but not belonging that is governed by exclusion that is only brought to light through acts of dissensions. This Rancièrean point is closely linked up with what Badiou has been maintaining with his ‘Event’. ‘Event’ is the coming into being of what was never thought of (accidental) in the conceptual structuring of the present scenario. To explicate on the coming into existence of the ‘Event’, one needs to change the conceptuality and his idea behind this is borrowed from Cantorian set theory of placing the element inside the set, but at the same time not belonging to the set. This is philosophically pertinent to the distinction between the political inclusion but non-belonging, in that, inclusion shares the possibilities in the world, whereas belonging-ness presents a systemic snapshot congruent with the given world view. In the moment of the ‘Event’, a person is faced with an ethical choice, by either denying what happened as new and trying to fit it in the existing template or by accepting it and building upon new consequences. To draw on these consequences is brought about by the act of naming. For Badiou, the notion of human rights is incapable of accommodating truth and is an attempt on the part of the dominant structure to be be able to account for all elements of the set. As he writes,

“The refrain of “human rights” is nothing other than the ideology of modern liberal capitalism: We won’t massacre you, we won’t torture you in caves, so keep quiet and worship the golden calf. As for those, who don’t want to worship it, or who don’t believe in our superiority, there’s always the American army and its European minions to make them be quiet.”

For Badiou, the only universality is that which resists structuring and becomes tangible in the notion of an ‘Event’. If Universality be equated with Truth, then according to his thesis in Manifesto of Philosophy, ‘Truth makes a hole in knowledge‘ and therefore it could now be inferred why for Badiou human rights as a kind of universality in equality, in freedom is anything but a form of dominant western ideology. To quote him again,

“The latest violence, the presumptuous arrogance inherent in the currently prevalent conception of human rights derives from the fact that these are actually the rights of the finitude […]. By way of contrast, the eventual conception of universal singularities requires that human rights be thought of as the rights of the infinite.”

So for Badiou, codification of the situations along the prefixed lines of universality results in redundancy alone and little wonder why he admonishes the case for human rights to be thought of as that which is included but not belonging. He takes a similar viewpoint towards justice by claiming the irrelevance of justice in the creation of anything new and thereby is more concerned with the conditions of possibilities of new politics rather than improving the sphere of juridicalness. In a way, what Badiou is looking for is very similar to what Rancière aims at and that being looking at human rights as an affirmative action. For both the thinkers, it is the exclusive situation where the insight into the human rights is to be taken up, to be formulated in a reconstructive manner. The exclusive situation is normed as disruption by the thinkers and this disruption is then the affirmation for the coming into being of affirmative changes in the socio-political aspect. Since, this aspect of coming into existence is missing in the universal declaration, it becomes non-political in its conception as far as gauging the totality of the situation is concerned. Rancière sees this as the inability of the logic that dictates who is part of the situation, who has the right to voice claims and who forms the basis of political agency. For Badiou, it is the false totality altogether as it is impossible to envisage anything new or radical getting to the surface concretely. Since, there is absence of anything radically new, it is doomed to repeat the dominant power based ideology.

Although there are similarities in the ways the thinkers look at human rights, there are some differences that are stark in nature. For Rancière, it is the un-belongingness that counts cardinally despite the fact of the subject being inclusive in the system under consideration, whereas for Badiou, it is the subject getting called onto witnessing the ‘Event’ and thereby faced up with the radical choice that is ethical in nature. Badiou’s invoking of mathematics to first name the ‘Event’ and thereafter follow it up to rewrite the radicality of the situation differs from reinterpreting human rights as suggested by Rancière. Most importantly, Rancière uses disruption as a singular revelation in that he is constrained in the expansionary vision/force of the dissensus. Badiou on the other hand emphasizes on the extensibility of the ‘Event’. Rancière works within the existing system and is not concerned much with restructuring and vacillates between dissensus and consensus thereby giving it a more democratic feel of basing itself on negotiation, where Badiou aims at a revolutionary agency that he calls militant in nature.

The only universal human right that Badiou and Rancière envision is the right to intervene in the name of infinite universality, and they remain far from any institutionalization of universal human rights. Instead their theories  are geared towards a critical evaluation of the underlying presuppositions  of doing politics, and providing rights. This critical evaluation is done in  preparation of ‘truthful’ politics,   which entails for both Rancière and  Badiou a radical break with notions of politics that are defined in terms  such as citizenship, freedom of speech or a return to ideal enlightenment values. Politics aim at a constant possibility.

Agamben, G. (1998) Homo Sacer: Sovereign Power and Bare Life. Stanford: Stanford University Press.

Arendt, H. (1973) The Origins of Totalitarianism. New York: Harcourt Brace Jovanovich Inc.

Badiou, A. (2004) ‘Huit Thèses sur l’Universel’.

    – (2001/2002) ‘On Evil : An Interview with Alain Badiou’. Cabinet Magizine Online, 5,

Deleuze, G and Guattari, F (1996) ‘What is Philosophy?’. New York: Columbia University Press.

Hemel, Ernst van den. (2008) Krisis:  Journal for Contemporary Philosophy.

Rancière, J. (2004) The Politics of Aesthetics. New York: Continuum.