Hegel, Badiou, Žižek: Dislocations of the Dialectic and the Parallaxes of Worlds

• “…we must uncover an absolute necessity that does not reinstate any form of absolutely necessary entity” — Quentin Meillassoux, After Finitude, 34

• “it is unthinkable that the unthinkable be impossible” — Quentin Meillassoux, After Finitude, 41

The present essay aims to lay out the contemporary state of the philosophical Idea and the system of philosophy. I will be restricting myself to the works of three philosophers: G.W.F. Hegel, Alain Badiou, and Slavoj Žižek. For starters, Hegel is a common point to the more contemporary philosophy of Badiou and Žižek. A couple of previous posts may provide a decent place to start with Hegel and the groundwork problems to what I will be contending with here, here are some links to them: Absolute Antigone, The Last Philosopher, and How do you know what you think you know?Secondly, the philosophical importance I see in Badiou and Žižek amounts to the reactivation and remodeling of the philosophical Idea through its displacement; and they do this in a way that is still congruent with Hegel’s preoccupation over the inquiry into the system of philosophy as it pertains absolute knowing. Rather than preambling further, I will be jumping right into it unpacking this as it is best that we get further acquainted with Hegel’s outlook of philosophy so we can get just what got dislocated in the contemporary scene of philosophy.

The central point that I am advancing is that Hegel adequately set out an investigation into the system of philosophy and philosophical knowing —as far as Hegel is concerned, the philosophical Idea or knowledge of the truth can be known as the Logic, the Philosophy of Nature, and the Philosophy of Mind. I will be restricting myself over to the Encyclopedia Logic and the outline of Encyclopedia of Philosophy, with some passing interjections from the Phenomenology of Spirit.

The central questions that start any of these texts are simply: what is philosophy? What does philosophy know, or rather, how is it that philosophy is a science? Furthermore, what makes philosophical knowing different than specialized empirico-scientific forms of knowing or religion? This topic is the central preoccupation of the introduction to the Logic, Hegel is able to give us some insights to these questions. To start with settling some distinctions, Hegel notes that unlike the practice of empirical sciences, philosophy cannot the admission of givens and operative presuppositions for granted (Logic, 3) — furthermore, Hegel outlines two ways in which the empirical sciences fall short: for one, empirical sciences make do with a reductive satisfaction constrained by an appeal to probability rather than necessity; and the other concern that empirical sciences miss due to their finite demarcations are the objects characteristic to philosophical concern such as Freedom, Spirit, and the Absolute as infinite (Logic, 12 and 13). In this respect, Hegel notes that the objects of philosophy are very much the same as those of religion where the truth of the finite and determinate is treated in accordance to the Absolute. However, as opposed to religion, philosophy has taken a critical turn that is suspect of falling back into unfounded metaphysical dogmatism stuck at mere religious iconographies that do not rise to the level of the Notion; in short, while Hegel sees the truth and the Absolute in religion, it is not yet in the true form of the truth (Logic, 3; Encyclopedia of Philosophy, 70). That is to say, the Notion highlights that philosophy is concerned with a thinking study of things.

So, under these preliminary considerations, again, what is philosophy? If thinking characterizes the criteria of philosophy or what makes philosophy itself, then the essence of philosophy is immanent to philosophy itself — as much as we can determine or define philosophy through extrinsic means or inflexible first principles, for example, these ways of holding fast to philosophy become superfluous in the very questioning which is excessively integral to philosophy. For instance, this highlights a curious predicament about inquiry and the very terms of questioning, whereby when we ask a question, the terms of the question may overdetermine the kinds of conceivable answers sought out in the questioning — Hegel’s point remains that philosophy is this encircling movement that understands that as much as it presupposes the kinds of things the questioning thinks as answers, it is also positing these very presuppositions; that is to say, what guides the thinking activity is not merely determined, but determining of itself. In short, as philosophy is sorting itself out, it is working through a Notion of itself and while also being confronted with the actuality of the Notion. At the core, the rise of philosophy is due to these cravings of thought; that is to say that what empirical sciences and religious are unable to satisfy by themselves, philosophy still pursues AND actualizes as absolute knowing (Logic, 16). However, we still need to flesh out what thought properly means for Hegel — and this is crucial for when we turn towards Badiou and Žižek.

Indeed, philosophy is a thinking study of things. But just any type of thinking will not do by itself, as Hegel stresses that we are concerned with a peculiar mode of thinking in which thinking becomes knowledge, namely knowledge through notions (Logic, 4). As Hegel writes:

• And this difference connects itself with the fact that the strictly human and thought-induced phenomena of consciousness do not originally appear in the form of a thought, but as a feeling, a perception, or mental image — all of which aspects must be distinguished from the form of thought proper… The several modes of feeling, perception, desire, and will, so far as we are aware of them, are in general called ideas (mental representation): and it may roughly said that philosophy puts thoughts, categories, or, in more precise language, adequate notions, in the place of the generalized images we ordinarily call ideas. Mental impressions such as these may be regarded as metaphors of thoughts and notions. But to have these figurate conceptions does not imply that we appreciate their intellectual significance, the thoughts and rational notions to which they correspond. Conversely, it is one thing to have thoughts and intelligent notions, and another to know what impressions, perceptions, and feelings correspond to them (Logic, 4 and 6).

This last difference that Hegel establishes helps understand why the thought that concerns philosophy oscillates between abstract thinking and popular modes of thought — we can see how the spiritual torch of the philosophical Idea got passed on to Žižek who can explore a Hegelian notion as it corresponds with something as contemporary as Kung Fu Panda. The point is that, on the one hand, abstract, pure thinking cannot tell where in the world it is and thus comes across as unintelligible to the familiar mental representations; on the other hand, in clinging to the mental representations we are at home with does not quite realize the blend of thoughts sipping into feelings, percepts, and mental images such that we cannot see past the world. When we charge thought of being hard or narrow, we cannot make this claim about thought in general but rather the mode of thought that exercises the Understanding and the categories it deploys to make cognitions intelligible — maybe Kung Fu Panda or Shrek is all it takes to nodge someone towards the Absolute; though we have to remember that we are looking for an Absolute that calls for itself and is not just dependent on Shrek, or Shrek 2, or Shrek the Third, or Shrek Forever After… maybe we are just only thinking too late and the Absolute makes its claim in the last determination in the form of Shrek 5 as a figure of the future. Thus, the thinking proper to philosophy (Reason rather than Understanding) oscillates between different modes of thought and level of cognition as a science of comprehension, which is self-engendering movement of thinking sorting itself out (Encyclopedia of Philosophy, 69–71).

Again, if we consider how the activity of questioning is not just determined but also determining of the kinds of things that thought can say about the question, we can say that in the process of realizing this double-ended predicament of thought, thought turns towards a negative, critical attitude towards the point from which it started with questioning (Logic, 16). For example, if our starting point is the phenomena of sense that we may take as the most immediate and given ground for thought, Hegel notes that “Through this state of antagonism to the phenomena of sense its first satisfaction found in itself”(Logic, 16). This immanent tension of thought notes a few things for us: 1) that the foundations of thought can be ungrounded in such a manner that this immediate moment of cognition has its root in something else, that is to say, it is actuality turning thought towards mediation; 2) through this critical, negative activity of thought, its claim to things as such gets restlessly suspended insofar as everything is mediated to thought; and 3) the only resolution that these contradictions immanent to thought find can only be resolved by thought itself, insofar as thought itself was determining (or mediating the mediations) of the contradiction and its actual restlessness — that is to say, 4) the positive comprehension of these contradictions is the speculative thought characteristic to philosophy; that rather than a negative suspension of the Absolute, this tension moves philosophy which realizes that the dialectic is in motion and it has moved us from dogmatic metaphysical presumptions to a critical suspension of judgment over to its speculative affirmation.

But let us linger further on this term “dialectics.” Hegel stresses that the dialectical principle is a common element appropriated by the Understanding and Reason, albeit in different ways. When the dialectical principle is appropriated by the Understanding, we see dialectics as a merely negative skepticism. And when the dialectical principle is appropriated by Reason, dialectics pertain the positive task of speculative treatment (Logic116). The crucial difference is that when the dialectical principle is appropriated by the Understanding, it ends up in a one-sided, limited activity — the Understanding only holds the contradictions in an irreconcilable manner as the Understanding by itself is not able to question the categorical schematic that makes the cognition intelligible and comprehended; this is the work of Reason which is affirmatively and decisively moved by the contradictions rather than restlessly falling back to undecidability over how to comprehend the contradiction, that the categories are not just determining of the Understanding, but determined by Reason. The contradiction, at the level of positive speculative Reason, is disintegrating and vanishing in the result of its dialectical activity — in this respect, speculative statements such as “the yet is contained in the already,” “ the rational is real and the real is rational,” and “the Spirit is a bone” are described by Hegel in this manner:

• Speculative truth, it may also be noted, means very much the same as what, in special connection with religious experience and doctrines, used to be called Mysticism… On which we first of all remark that there is mystery in the mystical, only however for the understanding which is ruled by the abstract principle of identity; whereas the mystical as synonymous with the speculative, is the concrete unity of those propositions which understanding only accepts in their separation and opposition… Reasonableness, on the contrary [from Mysticism that renounces thought for the sake of mystery], just consists in embracing with itself these opposites as unsubstantial elements. Thus the reason-world may be equally styled mystical — not however because thought cannot both reach and comprehend it, but merely because it lies beyond the compass of understanding (Logic, 121).

Hegel’s reason-world, thus, is an implicit form of Spirit as such, where it patiently has assumed the forms of consciousness for World-Spirit to arrive at a knowledge of itself (Phenomenology of Spirit, 458). Through thought as the dialectics of speculative reason, philosophy is the the thinking study of things in such as manner that thinking is sorting itself out rather than collapsing into its contradictions.

For instance, when we turn to the history of philosophy gives us a sense of the origin and development of the philosophical Idea as it sorts itself out in irreconcilable and inconsummerable systems, for instance a strife between Platonists and Aristotelians or between Rationalists and Empiricists. The irreconcilable tension between these systems remains to be a tension for the Understanding, as for Reason in philosophy, we observe the actuality of the Idea insofar as “the latest birth of time is the result of all systems that have preceded it, and it must include their principles” (Logic, 19). That is to say, even though there are multiple kinds of philosophy and none of them are the philosophy, we should not stop at the limitations of particular philosophical systems but rather rise to their own respective claims to the universality of the Absolute.

Another instance to consider, then, is the System of Philosophy itself as the movement of thought in thought itself, as the history of philosophy is only an external expression of the immanent development of the philosophical Idea. Thus, when we note that this active development of the philosophical Idea is happening through thought, it must be stressed that as a Science of the Idea it must form a system to comprehend the incongruity of its movements beyond the bounds of mere understanding. Without this systematization of contradictions, philosophy has no scientific productions and it is yet to comprehend how each of these movements of philosophy are expressions of the Idea (Logic, 20).

Now, according to Hegel, philosophy is subdivided into three subdivisions: Logic, the science of the Idea in and for itself; the Philosophy of Nature, the science of the Idea in its otherness or yet to be sorting itself out; and the Philosophy of Mind, the science of the Idea come back to itself back out of that otherness.

Hegel’s system of science, via Hegel.net

We will focus on the Logic insofar as it provides a ground work for Alain Badiou’s intervention on the System of Philosophy. In addition and in allusion to Badiou’s work, although Hegel has made significant strides in developing the Science of the Idea, the world of Reason and of Spirit remains quite tied to the One Absolute and not quite able to think something like the fundamental ontological approach for the logics of worlds. In reading the early section on Being as a subdivision of the Logic, we will highlight that the Hegel’s ontology at most translates to the one world that it can think.

The Science of Logic, via Hegel.net

Logic’s subdivision into Being, via Hegel.net

In looking at the Logic’s doctrine of Being, our focus on the movement to a determinate concrete understanding of Being from the indeterminate immediacy of pure Being.

Indeterminate Being and Determinateness in the Logic, via Hegel.net

At their most algorithmic, the movements that we see in these different subdivisions of the logic entail a movement from immediate indeterminacy over to mediating determinations which are later comprehended in the determining of determinations. To give an example out of the Logic, the dialectic of Indeterminate Being has us turn to pure Being as it is the most immediate, indeterminate way of breaching the question of Being. However, of course, pure Being is quite abstract to breach due to its indeterminacy — so much so, in fact, that pure Being in its abstraction is no different than pure Nothing due to both of their undifferentiated states (Logic, 127). It is this early on that thought contends with the dialectical principle, for insofar as Becoming comprehends pure Being and pure Nothing, thought now expects itself to work itself through the paradoxes implied therein the non-relationship between strictly pure Being and strictly pure Nothing. For example, in Book Gamma of the metaphysics, Aristotle contended against the paradoxes of Becoming that its resolution would arrive only by a decision over sense and by non-contradiction — however, for Hegel (as for Badiou and Žižek) there is a non-relation between being and sense, as Hegel stress that since the distinction between pure Being and pure Nothing remains indeterminate and without assuming determinate form at this time, so what we mean by Being here remains unutterable (Logic, 129). In addition, the Becoming is the first concrete thought and notion that we develop in the Logic insofar as it comprehends the abstractions of pure Being and pure Nothing — furthermore, Hegel stresses that Becoming is the first adequate vehicle of truth (Logic, 132). However, Becoming must grow in depth and weight of meaning, it must gain a sense of itself, a force of life and beyond mere logical Becoming; thus, we arrive to the question of Determinate Being, Being-There, or Da-sein.

In short, this portion of the doctrine has helped us understand the fourfold movement that we see in Hegel’s dialectics: 1) the positive indeterminate immediacy which only gains a sense of its abstraction through 2) the negative movement comprehended at 3) the concrete determination which doubles over to 4) a concrete determination that is not merely logical. In this way, the questioning of Being has encircled itself in trying to comprehend itself:

Though Hegel’s movements should cautiously be referred to as Thesis, Antithesis, and Synthesis as they are better understood as expressions of the paradox of infinite judgment moving from Positing Reflection to External Reflection to Determinate Reflection doubled over to a Reflexive Determination; this diagram still comprehends the encircling spiral characteristic to the System of Philosophy as expressed by Hegel.

Therefore, since Hegel has noted that there are multiple starting points for philosophy and the development of its object, these initial moves highlight an Absolute that one feels around in a tipsy-turvy dance of thought sorting itself out, where “philosophy can be developed only out of its own generating problem” (Encyclopedia of Philosophy, 69). At this time, its own generating problem that expands over to the reason-world and World-Spirit is exactly the point of the Hegelian dialectic that calls for a non-dialectical dislocation. Indeed, Hegel has been able to approach philosophy as a scientific system working itself out through speculative thought (as dialectics) and, by turning to the work of Alain Badiou, we can preserve the endeavor of the philosophical sciences and the philosophical Idea, albeit in a manner that dislocates the point from which philosophy develops out of its auto-generic tarrying with the negative.

In an essay in Being and Event dedicated to his distance from Hegel’s Science of Logic, Alain Badiou writes the following: “The Hegelian ontological impasse ultimately rests upon maintaining that there is a being of the One; or more precisely: that presentation generates structure, that the pure multiple holds in itself the ‘counting as one’” (Being and Event, 161). This gives us a sense of where Badiou’s intervention of the System of Philosophy is situated: that it is a question of an ontological impasse, and that this impasse rests on Hegel’s upholding of the One as the auto-generic structure of philosophical development which serves as the developmentalism spoused in the mode of presentation of the Phenomenology of Spirit — or, in other words, that the structure and its presentation hold a common identity in tarrying with the negativity at the heart of the Absolute (Being and Event,162).

The way in which things are counted-as-one in the generic structure of Hegelian dialectical thought oscillates the passage from pure limit (as the stationary result of a determinate being as marking the other of its being) to the limitation (as the thing as such being other than itself) — this is what characterizes the infinity that Hegel’s point of being calls for in thought, what we have explored so far the overcoming of determinations of thought/being insofar as being/thought is determining of them. As Badiou writes: “Its being is accomplished by the crossing of non-being, which is to say by passing through the frontier. The profound root of this movement is that the one, if it marks being in itself, is surpassed by the being that it marks” (Being and Event, 163).

It will be noted that though the being of the one consists in the structure of counting-as-one as an ontological imperative, or a law of being, to supersede the limitation for Hegel; for Badiou, God, the One, or the Absolute in-consists in such a way that it disrupts the Hegelian endeavor to hold the dialectical continuity, since, for it, it is impossible to engage with pure disjunction. That is to say, “What Hegel cannot think is that the difference between the same and the same, that is, the pure position of two letters” (Being and Event, 34); or in the terms of the logics of worlds, “Two worlds with the same things can be absolutely different from each other, because their transcendentals are different. That is to say: the identities between elements of the same multiplicity can radically differ at the level of their being-there, from one world to another world” (“Toward a New Concept of Existence”). Badiou’s criticism of Hegel, in this respect, stems from the Hegelian system upholding a law of generative ontology that normatively calls for the reassurance that the Other occurs through the repetitions of its worldly law being further affirmed as the rational is actual and the actual is rational — Žižek similarly notes that “For Hegel, there is truth, but it is immanent to the symbolic process — the truth is measured not by an external standard, but the ‘pragmatic contradictions,’ the inner (in)consistency of the discursive process, the gap between the enunciated content and its position of enunciation” (Less Than Nothing, 78). This point by Žižek only stresses the point that in considering the limits of Hegel, Hegel can only think the pure disjunction of the Real that dislocates the dialectic in mere imaginary immediacies and symbolic mediations in the determinations and determining of law; or in short, Hegel cannot think less than nothing (or, more than the determinate Something of its world), he cannot think the indivisible remainder of the dialectical form as it is an excess of the Real overlooked by dialectical mediation, and the only comprehension it finds is only as the product of this mediation which oversees it (Less Than Nothing, 455, 480, and 495).

The subtlety of the dislocation of the dialectic insofar as it carries out the consequences set out by the Lacanian Real is expressed by Žižek in the following way: “The difference that separates Lacan from Hegel is thus a minimal difference, a tiny, barely perceptible feature which changes everything… minimal difference is pure repetition… its status is purely virtual, it is a difference which takes place at its purest when nothing changes in actuality, when, in actuality, the same thing repeats itself” (Less Than Nothing, 481 and 482). This minimal difference can further stressed that the Hegelian dialectical thought can barely register it insofar as it is overdetermined itself, that it is only locally defined by the “yet” of the “already” which is determinant of its world (Being and Event, 165). Thus, the normative generative ontology that Hegel advances assures itself of the One only insofar as it is in its locality that one term is counted or discerned into Hegel’s overdetermined transcendental horizon for the determination of being. Furthermore, the crucial difference between Badiou and Hegel here pertains the capacity to maintain a subtractive ontology that is able to think the discontinuity of the dialectic, meaning that this thought itself has to be non-dialectical and thus rethinking the locality of the dialectic of the reason-world to thinking the conceivability of multi-local worlds to the level of the global. What we see in Hegel as a law spiraling out of its own self-generative locality, for Badiou we have a decision prior to the locality of truth generic proceedures and the determinate worlds of their being. Or as Badiou writes in Being and Event: “the essence of the Hegelian thesis on infinity is the following: the point of being, since it is always intrinsically discernible, generates out of itself the operator of infinity; that is, the surpassing, which combines, as does any operator of this genre, the step-further (the still-more) — here, the frontier — and the automatism of repetition — here, the having-to-be” (Being and Event, 163).

Badiou identifies the root of the problem in that Hegel is unable to intervene in number; that is to say, that in favoring a qualitative treatment of the question being and infinity, Hegel is unable to provide a proper treatment of a mathematical ontology and quantitative infinite. Hegel goes as far as to look down at mathematics and the quantitative as a poor and devoid form of thought, hardly capable to rise to the level of Spirit without working itself through the significance of the qualitative — however, Badiou’s plea is that we should not discard the significance of the minimal form of the thought of being that mathematics are able to offer, as even by Hegel’s own terms, this is still thought nonetheless; furthermore, a difference however minimal can make all the radical a difference. While in the generative ontology, everything is intrinsic; the subtractive ontology tolerates and even requires some exteriority, some extrinsicness, since the mode of presentation of count-as-one is not inferred from inconsistent presentation (Being and Event, 163). What concerns Badiou is the exhaustion of the integral interiority to the Hegelian generative ontology, namely “his frenetic desire exhaustion, the impatient passion of the encyclopedist, the desire to show that we are already — or at least he is already — at the point of acceding to the totality of all possible shapes of consciousness” (German Philosophy, 23 and 24). This concern by Badiou echoes Jacques Lacan’s critique of pure desire as a dislocation of the integrated Cartesian subject over to its extimate point through the unconscious; as he writes in Being and Event: “Lacan introduces us into the intricacies of this place by means of disturbing statements, in which he supposes ‘I am not, there where I am the plaything of my thought; I think of what I am, there where I do not think I am thinking’” (Being and Event, 431). In this respect, Badiou holds as much as we are concerned with philosophy, its role has to take into account different non-philosophical /non-dialectical conditions of philosophy through which, by virtue of truth generic proceedures, philosophy is able to subtract their products in a systematized manner (Manifesto for Philosophy, 33–39).

At this point, rather than focusing on Badiou’s account of Hegel, I want to turn our attention over to the same question, now pertaining Badiou: what is philosophy? Philosophy is concerned with thinking, which he defines as “the non-dialectical or inseparable unity of a theory and a practice” (Infinite Thought, 79). In other words and as we will see, Badiou is interested with thinking as a zero-degree point between concepts and engagements, a moment when these lock onto one another as a moment of Truth, which he calls Event — when something happens, concepts and engagements have to reconfigure themselves to be faithful to the Event and whatever the element it was that concepts and engagements overlooked before the Event (Being and Event, 232 and 233). Furthermore, for Badiou, thought is only of being (Being and Event, 282).

For Badiou, Philosophy is not an isolated affair, as it has conditions where the binding of theory and practice occurs. Badiou challenges the notion that immanence is strictly for philosophy conditioned by immanence alone, but rather he argues that immanence is in the conditions of philosophy as politics, art, science, and love. There is Truth that binds the immanence of philosophy to the subjectivation of its subject, as it always returns to the Truth. Other forms of thinking for Badiou are science, love, politics, and art.

Let’s exemplify these truth generic procedures: science has moments of truth such as scientific revolutions, i.e. that Physics as a whole had to reframe itself in the transition from the Newtonian paradigm to comprehend the Einsteinian Event; when we fall in love, we cannot pretend as if nothing happened, as our ideas of the loved one change in the face of love and our engagements attest to the Event (In Praise of Love, 33); in politics, a revolution brings to the forefront of the social a tension that it witnesses, such that the way of being in the city (the polis) is reframed (Metapolitics, 141 to 152); and in art, new techniques, mediums, mindsets, and circumstances transform the possibilities of what art can be (The Age of Poetry, 4 and 5). In each of instances where thought happens, the philosophical Idea is reactivated and remodeled in accordance to dislocation of its conditions — as Badiou writes of the Idea of Communism: “The Idea is an historical anchoring of everything elusive, slippery and evanescent in the becoming of a truth. But it can only be so if it admits as its own real this aleatory, elusive, slippery, evanescent dimension” (“The Idea of Communism,” 8).

When thinking happens, Philosophy is in touch with its conditions in such a way that thinking engages in what Badiou calls a truth generic procedure(Being and Event, 327 and 331 to 343) — in other words, for Badiou, Philosophy pertains Truth, and it is in the face of the Event that thought happens as the faithful inscription of what is new into being. Rendering this slightly differently, Badiou is interested in localizing the void, what was missing from our constructive knowledge, as in the Event we are trying to figure out what is the proper place of what once was void (Being and Event, 175). Philosophy not only arises from its conditions, but it also changes the moment of constructible knowledge in a moment of truth. And insofar as thinking is the thought of being as well as ontology being mathematics for Badiou, it is worth stressing that: “The mathematical occurs here as discontinuity within the dialectic. It is this lesson that Hegel wishes to mask by suturing under the same term — infinity — two disjoint discursive orders” (Being and Event, 169). For Badiou, the One is not, as Badiou’s notion of the Event entails that the Two of breaching Being and the void of the Event, and the One is only functional as the philosophical function of thought counting-in-one through which the inconsistent multiplicity are turned into consistent ones. To this extent and as opposed to Hegel, the universal as formulated by Badiou is arrived at in accordance to the chance of an aleatory excess, not a matter of determination, but a radical contingency for dialectical consequences (Philosophy in the Present, 47). Or, following Badiou, in After Finitude Quentin Meillassoux notes Badiou’s accomplishment for the prospects of philosophy through his subtractive mathematical ontology:

• … we have no grounds for maintaining that the conceivability is necessarilytotalizable. For one of the fundamental components of this revolution was the detotalization of number, a detotalization also known as ‘the transfinite’… Among Badiou’s fundamental theses the mathematical conceivability of the detotalization of being-qua-being… it uses mathematics itself to effect a liberation from the limits of calculatory reason, a gesture altogether more powerful than any external critique of calculation in the name of some supposedly superior register of philosophical thought. (After Finitude, 103)

In the Logics of Worlds, Badiou furthers his remarks on Hegel which can further flesh out with an understanding of Badiou’s system. Whereas Badiou theory of transcendental horizons postulates there is no Whole, Hegel maintains there is nothing but the Whole. The crucial distinction is how thought is distributed in these two positions. In Hegel’s dialectical thought, the Whole distributes thought between purely abstract universality and absolutely intensive concreteness; between the Whole as a form and the Whole as content. Or in the language of the Logic, the threefold distribution of dialectical thought occurs as the immediate, mediation, and the overcoming of mediation all which are in reference to the Whole sorting itself out. In Badiou’s non-dialectical thought, the theorem of the non-Whole distributes things in a threefold manner: “the thinking of the multiple (mathematical ontology), the thinking of appearing (logic of worlds), and true-thinking (post-evental procedures borne by the subject-body)… the triple of the non-Whole, we advocate, is as follows: indifferent multiplicities, or ontological unbinding; worlds of appearing, or the logical link; truth-proceedures, or subjective eternity” (Logics of Worlds, 144). While for Hegel the cause of thought is the Whole, Badiou’s aleatory chance as the cause of thought is a vanishing cause or an abolished flash called the Event.

As, for Hegel, the cause of thought is the Whole, in the existent rising over the realm of laws in the reason-world and the World-Spirit, where the evanescent existent and the phenomenal world see their endurance in their changing. However, this is not the case for Badiou’s formulation of existence, for “Existence stems solely from the contingent logic of a world which nothing sublates, and in which — in the guise of the reverse — negation appears as pure exteriority” (Logics of Worlds, 152). In his lecture “Towards a New Concept of Existence,” Badiou helps to elaborate on this distinction between mathematical ontology and the logics of worlds in order to develop his concept of existence without a reference to something like consciousness, experience, or human-being as Hegel does (“Towards a New Concept of Existence”). Badiou’s proposal is set in three parts: 1) ontologically, we ask, what is our concept of being-qua-being? It is multiple, a multiplicity of multiplicities insofar as the One is not which is pursues a theory of things without qualities. 2) As far as a concept of localization of Determinate Being, we ask, what is being-there? A transcendental field without [Absolute] subject, a complex network of multiplicities, not multiplicities of multiplicities, but multiplicities of differences, identities, qualities, intensities, and other modulations of ontological Things appearing as objects of logical worlds. 3) Existentially, of course, we ask what is existence? Badiou proceeds from the question in declaring that the degree of some Thing’s identity to itself in a world is its existence in the world.

Whereas the logic of Things is mathematically composed of sets of sets in a purely extensional quantitative infinity, and the logic of Worlds is more like a Hegelian logical phenomenology of the distribution of intensities in the transcendental field where multiplicities not only are, but also appear as an object in a world. Prior to looking at Badiou’s complete logic of objectivity, we may state the difference between Thing and object in this manner: if a pure multiplicity is a Thing, a multiplicity with its discerning identity function is an object in the world. There are two points to stress here: the technical structural orders where we are studying the form of the transcendental field of degrees of identity of an object in the world in its worldly structuring, and the relationship between Things and objects where we study the identity function between multiplicities (indiscernible and discernible) and the transcendental. On the first point, there are many types of orders, therefore many possibilities for the logical organization of the world such that two worlds with the same things can be absolutely different from one another. And on the other point, the identity function oscillates between two limits where two elements in a world are neither absolutely identical nor absolutely different. We note three expressions of the identity in three different ways: 1) if, in a world and for a couple of elements, the two elements are absolutely identical in this world (have the same appearance/determinate being), then the identity function takes the maximal degree of identity; 2) if, in a world and for a couple of elements, the two elements are absolutely different from each other in this world, then the identity function takes a minimal degree of identity; and 3) if, in a world and for a couple of elements, the two elements are are identical to some extent, an extent which is measured by intermediate transcendental degree, then the identity function takes an intermediate value (“Towards a New Concept of Existence”). In this respect, the appearing multiplicity must be understood as a very complex network of degrees of identity between its elements — in other words, we are not just concerned with the mathematics of ontological extension, but also we are looking after the logic of its qualities such that we are moving beyond its pure being to its existential intensity.

At this point, we can say that existence is the name for the value of the identity function when it is applied to one and the same element, as the measure of the identity of a Thing to itself or the transcendental degree which a Thing assigns to the identity of its own being. In this respect, existence is not a category of being (in mathematics), but it is a category of appearing (in logic). By itself, existence is senseless, and it can only be said to have sense in relation to its localization in a world. In looking at existence qua the transcendental field of degrees of identity, we can meaningfully speak of existence in two extreme ways: 1) if the degree of identity of a Thing to itself is the maximal degree, then we can say that the thing exists in a world without any limitation — the multiplicity, in this world, completely affirms its own identity. And 2), if the degree of identity of a Thing to itself is the minimal degree, then we can say that this Thing does not exist in the world — the Thing is in the world, but with an intensity which is equal to zero; its existence is a non-existence, or better: it is (ontologically) inexistent(phenomeno-logically) which helps up stark the contrast between being and existence as different. This being said, the existence of a multiplicity in a world is often neither maximal nor minimal, as the multiplicity exists to some extent — such that, when Badiou remarks on a philosophy of death that takes this concept of existence into consideration, he declares: “Do not be afraid by the logic of a world, or by the games of existence. We are living and dying in many different world” (“Towards a New Concept of Existence”).

To provide a summary of Badiou’s intervention of philosophy. On the one hand, you have Badiou take on Ontology as mathematics as a logic of Things — this pertains indifferent, indiscernible being as such. On the other, a (Hegelian) Logical Phenomenology of determinate beings as a logic of Worlds. So far this is all mirrors Hegel’s Logic, except for Badiou’s study of indifferent pure being as such through mathematics, which Hegel looked as an impoverished form of thought — and yet, Badiou is able to remind us that it is thought however minimal it is. Badiou even grants that mathematical ontology by itself don’t grant us other forms of philosophical knowing, like those of the phenomeno-logical logics of worlds — in this much, he agrees with Hegel that philosophy does not end at ontology. Now, what Badiou has dislocated from Hegel I think amounts to this: whereas Hegelian thought as dialectical can grant us the logic of World-Spirit; Badiou’s thought as non-dialectical dislocates the dialectic to the conceivability of worlds. The coordinates of the Hegelian spiral have been dislocated, and now we can think worlds! And more so, the qualitative developmentalism of Hegel can be preserved in a manner that it is also radically transformed from the dialectical necessity of overdetermined shapes of consciousness!

On this much, Slavoj Žižek is in agreement with Badiou: philosophy is axiomatic, and asks how the true philosophy could actually be known; in addition, Žižek adds another agreement:

• To point out that the alternatives we collectively face form a disjunctive synthesis, that is, that they are false alternatives, has to be the first gesture of the philosopher here: he must change the very concepts of the debate — which in my opinion represents precisely the negative of that which Badiou calls a ‘radical choice’. (Philosophy in the Present, 49–51)

And indeed, this is what we saw Badiou do with his concept of existence as well as with the mathematization of the fundamental ontological question. Much in the same dislocative spirit, Žižek will seek to do a similar activity in working towards a new foundation of dialectical materialism and a Hegelian overcoming of Hegel’s inability to think the Real — furthermore, I will be turning my attention towards Žižek’s notion of the parallax view to see how these dislocations have their actuality in the phenomeno-logical worlds that Badiou’s philosophical intervention has opened up. Most crucially, it is worth noting that Badiou and Žižek are both contending with sorting out the philosophical significance of Lacan’s the Real — in this respect, their projects are minimally common as they pertain the Science of the Real.

Thus, in proceeding along, it will service us to discuss Jacques Lacan and the Real. To give a short-hand to Lacan’s work, Lacan’s work has three major sections: his early, middle, and late period. In addition, Lacan’s the Real is explored through Lacan’s modelling of the three structural levels of subjectivity.

Lacan’s early period highlights the Mirror Stage and the Imaginary as their key topic. In short, the relationship between an ego and its object in “I want this” supposes the phenomenological insight that consciousness is apparently transparent to itself.

Lacan’s middle period highlights the Big Other and the Symbolic as their key topic. In short, consciousness is apparent to itself only through an-other — for instance, the formation of an ego and desire is only under the condition of a language through which it articulates itself, or a culture that makes its sense of self intelligible, or a religion or belief system through which the ego gains worldly orientation. Or for instance, in the terms of psychoanalytic transference, there is an observation that when desire in accordance with the desire of the Other, we turn to particular others to see in them these injunctive demands of desire in wondering just “what the hell does the Other want?” Furthermore, transference is mobilized as this relationship of the drive to desire is dislocated as the drive seeks satisfaction and produces desire in lack thereof satisfaction in each object of desire it turns to — it slips over from parents to teachers to partners and even to the analyst, who uses this space as the active motor of psychoanalysis.

And Lacan’s later period highlights the famous phrase “There is no sexual relationship” and the Real as their key topic. In short, because consciousness is apparent to itself only through an other, consciousness is not transparent to itself. However, this does not mean that the Imaginary and the Symbolic are nulled as a result, for arriving at truth took semblance, obscuration, and forgetting — the tension of the Real is only possible in so far as the Imaginary and the Symbolic are also in operation.

Badiou’s central concern concerning Lacan’s psychoanalysis is whether or not psychoanalysis is thinking, a non-dialectical unity of theory and praxis, and therefore a condition of philosophy. For one, he points out that there is psychoanalytic theory and there is psychoanalytic practice in the clinic, and in the specific case of Lacan’s work, Badiou claims that psychoanalysis has thought in providing mathemes — in other words, formal, logical statements that constitute a zero-degree point between concepts and practices. To give an example, Jacques Lacan has summarized the structure of metaphor as:

Formula of Metaphor

What this means in the psychoanalytic experience is that, in the relationship of speech, the analysand is at knots with what they may mean in talking to the analyst between what can be spoken out (S) in the act of speaking ($) — in other words, the subject of psychoanalysis is split between what it can say about itself and what it fails to say, because what is explicitly spoken out can obscure what is happening in the act of speaking. Lacan once worded this in a playful restaging of Descartes in essentially saying: I think where I am not, therefore I am where I do not think. I am not whenever I am the plaything of my thought; I think of what I am where I do not think to think (Écrits, 429 and 430). Of course, I must digress with a word of warning that Lacan’s matheme of metaphor cannot be reduced to just this formula or its extensions.

However, for Badiou, this is an instance in which psychoanalysis has inscribed itself as thought in Lacan providing such a formulation of the psychoanalytic experience. In the Lacanian matheme, Badiou stresses that mathematics is the main border that philosophy and psychoanalysis share — because, unlike other conditions of philosophy, psychoanalysis touches on other conditions, as heating debates over what science is, examining politics and civilization, in the interpretation of art and in our relationship to aesthetic experiences, and in talking about love and sex.

We must mind that Badiou calls himself a philosopher, and in the light of this, it is a curious thing that he stresses that psychoanalysis is only ofinterest to the philosopher if and when it is thought. This implies that philosophy is only interested on psychoanalysis when it is in a minimal relationship with philosophy when psychoanalysis takes the form of a mathematical formalization — and if mathematics is the common border of philosophy and psychoanalysis, as a point of minimal relationship, we could also argue that mathematics performs the role of a mirror through which recognition happens. When philosophy is interested on psychoanalysis, we could say that philosophy is interested on psychoanalysis only when it is a mirror of philosophy — in other words, philosophy looks for itself as thought in psychoanalysis. But the curious thing here is that philosophy always finds more and/or less than itself in the psychoanalytic mirror — for example, psychoanalysis seems like it could be a condition of philosophy, and yet it seems to do more than just a condition. When we highlight the question of “interest” on the philosopher’s part, we are looking to highlight that psychoanalysis has a relationship with philosophy, except when it does not.

The consequences are as follows: the minimal relationship between philosophy and psychoanalysis entails a minimal point of communication between philosophical thought and whatever (is) besides thought. Why “(is)”? Because, according to Badiou, thought is only of being (Being and Event, 282) — therefore, besides thought is besides being. Psychoanalysis highlights the limits of philosophy by bringing to the fore the problem of ontological incompleteness in that philosophy is lacking something besides it — as in the case of the old definition of philosophy as “the love of wisdom” wherefore the love entails that wisdom is not in one’s possession. Something different than being only comes into a relationship with it as a minimal relationship — in other words, a relationship lacking, as it is related only in non-relation, which means that philosophy is lacking something other than itself in an abysmal gap of difference. Therefore, when psychoanalysis has a relationship with philosophy, except when it does not, there is a non-relationship where the relational mirror breaks highlighting the blindspot of the philosopher that thinks less than nothing — catching the philosopher implicated in their desire and enjoyment, or why Lacan was able to draw out that the Ethics of Kant and Sade were formally one and the same. Perhaps it is then that we can turn towards psychoanalytic intervention of philosophy in the need to think what Žižek terms a “dentology” (Absolute Recoil, 5) — this is Žižek’s Hegelian move beyond Hegel, a materialist foundation that can tarry a fundamentally restless negativity, that we are back to the Thing as such which is less than nothing.

While Badiou is very deliberate to provide definitions and formalizations of his arguments, Žižek is not. Perhaps the best example of Žižek’s approach is the case of a dispute where Žižek teased Badiou:

Žižek: Nobody wants to be philosopher

Badiou: Except me!

Žižek: Exactly! (“Is Lacan an Anti-Philosopher?”).

Žižek’s approach is very subtle and manifests the other side of psychoanalysis that Badiou has glossed over — it even mirrors Žižek’s dear joke by the Groucho Marx joke: “He may look like an idiot and talk like an idiot but don’t let that fool you. He really is an idiot”. Now, the key operator of the exchange here is “want” — and the question is: How is it that desire and enjoyment are intercepted in this philosophical debate that may come across as mere rambling or name-calling? As I have already done some of the preliminary work to make Žižek’s position more clear, Badiou wants to be a philosopher and his identification as point of enjoyment and desire is very telling — we may properly ask under psychoanalysis, did a Freudian slip occur when Badiou said “Except me!”? Or in other words, did the unconscious speak in such a way that the blindspot of the philosopher is his want-to-be-a-philosopher? Badiou perhaps said more than he intended, and if the topic is that enjoyment and desire playing the role of a fundamental stumbling block to philosophical thinking, this perhaps is a weighted perhaps. The psychoanalyst would argue that the impotency of philosophy rests in this blindspot that demarcates and inaugurates what falls under the sight of the philosopher, as the philosopher cannot recognize what they cannot see — and the philosopher, as Badiou has defined it, works from a decision that inaugurates how the System of Philosophy dislocates itself to new parameters; yet nevertheless, we risk another closure of philosophy insofar as it remains merely ontologically refounded.

In the preface of For They Know Not What They Do, Žižek has argued that Badiou risks mistaking Lacan’s psychoanalysis for a formalism (For They Know Not What They Do, lxxxiv to lxxxviii). Badiou has regarded his approach as “forcing the Real” — the Lacanian approach to truth is one that still minds the tensions pertaining the Real Event, in that the Real is not symbolizable through-and-through, for symbolization understands its inadequacy to the Real through fantasy, and the Real is irreducible its causes. In other words, Badiou tries to contain the negativity of the Event and the Real into a consistent truth by fetishizing the matheme (For They Do Not Know What They Do, lxxxviii) than in Lacan arriving at the Real is also post-evental by traversing forgetfulness, obscuration, and mistakes, for arriving at the Real does not collapse the Imaginary and the Symbolic (“From Purification to Substraction,” 177). In other words, Badiou is not able to offer a discourse of the Real, because this discourse depends on fantasizing around the mathematical realist material — for the reductive account in Badiou cannot think the excess to the formula, save as a logic of worlds.

It is then the rhetorical force of Žižek’s psychoanalytic interjection to Badiou that points towards something very funny, ad hominem is just the point as far as desire and enjoyment is concerned — in this respect, the Sophist remains excessively integral to the Philosophical Idea in a curious way that it continues to restlessly mobilize however much the Sophist is played out as less than nothing to philosophical consideration; Aristotle goes as far as to call the sophist a plant as a snarky retort of his own (There is no Sexual Relation, 10 and 20; Less Than Nothing, 77). Badiou’s formalism is turned on its head in the face of a playful informal remark where the philosophy of psychoanalysis is turned into the psychoanalysis of philosophy — in other words, the question becomes: what is the depravity, obscenity, and perversion behind philosophy?

It will serve us to consider this term “den” in considering the role that it has played in the Ljubljanian School of psychoanalytic philosophy, as Alenka Zupančič and Mladen Dolar also discuss the den and dentology at length. The term is an appropriation of Democritus’ concept of atomic void in his aleatory materialism— as Žižek writes in Absolute Recoil:

• This brings us back to the notion of den, Democritus’ term for the particles the primordial Void is composed of and whose ontological status is that of “less than nothing.” It may seem that den signals a key limitation of Hegel’s thought, his inability to think the Real. One has to be very precise here since Hegel obviously can think the Real in the sense of “lack in the Other” or structural impossibility. This Real is most clearly discernible if we oppose it to the standard notion of the Real as the substantial Thing — recall how Lacan accomplishes a reversal which can be illuminated by the passage from the special to the general theory of relativity in Einstein. While the special theory already introduces the notion of curved space, it conceives of this curvature as the effect of matter: it is the presence of matter which curves space, i.e., only an empty space would be non-curved. With the passage to the general theory, the causality is reversed: far from causing the curvature of space, matter is its effect, and the presence of matter signals that space is curved. What does this have to do with psychoanalysis? Much more than it may appear: in a way exactly homologous to Einstein, for Lacan, the Real — the Thing — is not so much the inert presence that curves the symbolic space, introducing gaps and inconsistencies into it, but rather an effect of these gaps and inconsistencies. (Absolute Recoil, 380)

In this respect, Žižek is philosophically interested on the notion of broken symmetry, and how something can emerge out of nothing by way redefining nothingness itself — furthermore, we bare in mind the insight by Barbara Cassin that: “[the den] cannot be dialecticized precisely insofar as it is not an not an assumed and sublated negation of negation but a subtraction after negation and thereby a trick, a fiction, obtained by critical secondarity” (There is no Sexual Relationship, 35). Furthermore, in a footnote, Žižek redoubles the notion of the Event between its dentological status and its ontological status, as he writes:

• It is interesting to note the gap that separates the event as Fall (broken symmetry, disturbed balance) and the Badiouian event as a break in the normal flow of things (a love encounter, a scientific discovery, etc.). The key asymmetry between the two is that the Fall breaks with (disturbs) the Void and thereby creates the “normal run of life,” while the Badiouian Event breaks with this normal flow of things itself. One should nonetheless note that a love event is also a kind of Fall — falling in love — something that traumatically disturbs the emptiness of our previous existence. (Absolute Recoil, 390)

Thus, Žižek’s dislocation of the drive of philosophy and the cravings of thought that we see in Badiou and Hegel helps us reframe the status of materialist dialectics, as he discusses in Less than Nothing:

• It is true that one finds in Hegel a systematic drive to cover everything, to propose an account of all phenomena in the universe in their essential structure; but this drive does not mean that Hegel strives to locate every phenomenon within a harmonious global edifice; on the contrary, the point of dialectical analysis is to demonstrate how every phenomenon, everything that happens, fails in its own way, implies a crack, antagonism, imbalance, in its very heart. Hegel’s gaze upon reality is that of a Roentgen apparatus which sees in everything that is alive the traces of its future death. (Less than Nothing, 8)

Therefore, by taking into consideration this restless fundament of being in the den, we can proceed to discuss Žižek’s notion of the parallax view, a concept which Žižek adopts from Kojin Karatani’s Transcritique: On Kant and Marx (“The Parallax View,” 214). For Žižek the parallax gap is “the confrontation of two closely linked perspectives between which no neutral common ground is possible” (The Parallax View, 4). In both the short essay and the full-length book on the topic, Žižek begins his discussion of the topic by exploring Immanuel Kant’s antinomies of reason as presented in the Critique of Pure Reason. In short, through the Critique, Kant sets up a critical filter over what goes in philosophy and over what goes in claims about knowledge, either by the means of experience or by the means of reason — as the position of the Kantian Critical Philosophy places itself at the antinomy of modern philosophy in facing the tensions of rationalism and empiricism. As we operate under this Kantian critical filter, anything that falls under the determinations of the filter is actually knowable, whereas everything outside it remains radically inaccessible. By situating his Critical Philosophy at this gap and torsion in knowledge, Kant elaborates on the antinomies of reason like simultaneously holding that: “the world has a beginning in time, and is also limited in regard to space” and “the world has no beginning, and no limits in space, but is, in relation both to time and space, infinite”; or “causality according to the laws of nature is not the only causality operating to originate the phenomena of the world. A causality of freedom is also necessary to account fully for these phenomena” as opposed to “There is no such thing as freedom, but everything in the world happens solely according to the laws of nature”. Now, Žižek’s position is concerned with the question of radical critique rather than determinate critique, as he writes in the essay:

• …when confronted with an antinomy in the precise Kantian sense of the term, one should renounce all attempts to reduce one aspect to the other (or, for that matter, to enact a kind of ‘dialectical synthesis’ of the opposites). One should, on the contrary, assert the antinomy as irreducible, and conceive the point of radical critique not as a certain determinate position as opposed to another position, but as the irreducible gap between the positions themselves, the purely structural interstice between them. (“The Parallax View,” 214)

Furthermore, what is an epistemological antimony for Kant, Žižek furthers to the point of a dentological-ontological antimony, as he shortly remarks in the essay that this mirrors the Lacanian Real as a pure antagonism, as an impossible difference which precedes. The parallax view, thus, can be also elaborated through the question of sexual difference where non-relation is at the heart of every relation, which moves us from the ontological statement that “there is no relationship” to the dentological statement “there is a non-relation” (What is Sex?, 32). This is neither a mediation that stands in between relations nor a homogeneity in relations. What we are concerned with here is a radical heterogeneity that is implicatively found in differences in identity and antagonisms as they come to generate any sense of identity or relation —or as Alenka Zupančič writes in What is Sex? “it is the inherent (il)logic (a fundamental “antagonism”) of the relationships that are possible and existing” (What is Sex?, 24).

An example from a prior essay on “The Exploitation of Social Antagonisms” can help elucidate the problem:

• Even if we do the math (as if it were the purest discourse to determine the matter), fantasy distorts the fundamental impasse of capitalist being and its structuring. Perhaps example from the Office is due:

  Kevin: The pie shop is 13 miles away. So at 55 miles an hour, that just gives us 5 minutes to spare.

  Angela: So, wait, when pies are involved, you can suddenly do math in your head?

  Oscar: Hold on, Kevin, how much is 19,154 pies divided by 61 pies?

  Kevin: 314 pies.

  Oscar: What if it were salads?

  Kevin: Well, it’s the — carry the four and the — it doesn’t work (The Office, Season 9, Episode 4).

  Much like Kevin’s inability to do pure math and see past the little differences of pies and salads, the fundamental fantasy that sustains capitalism operates in a similar manner. The very structuring of Being itself is biased, cracked from within informing it of what it is — where fetishized objects, such as the commodified difference between pies and salads, seem as if they make a difference.

We can contrast this by looking at the Badiou-Meillassoux camp against the Žižek-Zupančič camp, we can articulate the difference as it pertains the question of ontology and dentology in the following way: Meillassoux asserts his response to the Leibnizian question “Why is there something rather than nothing?” the answer remains ontological: “it is necessary that there be something rather than nothing because it is necessarily contingent that there is something rather than something else” (After Finitude, 76). In other words, one cannot ask “why is there something rather nothing?” because it makes no difference as there is no difference; and the only way to reintegrate difference into the question is by restricting the right to make contradictory statements about an entity. Psychoanalytically and dentologically speaking, this means that the gravitational center of fantasy is inconsistent as such — for example, in masculine fantasies of Woman as an ideal object of desire, one finds fantasy plagued with images of Woman that cannot contain the excessive fact that this fantastical ideation of Woman is not; whereas on the feminine side of the antimony of sexuation, Woman is adorned in a masquerade covering over what is less than nothing to maintain the semblance that Woman exists. Zupančič puts this in psychoanalytic terms in that the satisfaction in speaking is the same as the satisfaction in the thing itself as the den (What is Sex?, 1–2) — Woman never existed to begin with, but in fantasy which is productive over the gap, she does not know she doesn’t exist.

Therefore, the antinomies of sexuation have an ontological implication insofar as they register the field of being-qua-being as inherently twisting itself around what is less than nothing, namely sex as such as impasse of being. And it is in the positions of sexuation like the masculine and the feminine that we can express the minimal form of this parallax view implicating not just being, but the logics of worlds — indeed, Badiou is correct to assert that we live and die in different worlds as part of the logics of worlds, but furthermore, there is a Žižekian twist that we must further affirm insofar as the logics of worlds see themselves disoriented around the destabilized structure of ontology.

To summarize, while G.W.F. Hegel was able to establish the System of Philosophy as a Science of the Philosophical Idea to the level of the reasonable being actual and the actual being reasonable as World-Spirit. However, the dislocative interventions by Alain Badiou and Slavoj Žižek have been crucial in two respects: 1) Badiou’s intervention has dislocated the Hegelian dialectical thought through a non-dialectical form of thought in mathematics enough for us to reframe the parametric coordinates of the Hegelian dialectical spirals such that we can think the mulitiplicity in the form of worlds rather than World-Spirit. Furthermore, the qualitative developmentalism of Hegel as a logic of appearance can be preserved in a manner that it is also radically transformed from the dialectical necessity of overdetermined shapes of consciousness or the presumption of sufficient movements in reason to arrive at the Absolute. 2) Žižek’s intervention dislocates Badiou’s ontological insight into the conceivability of worlds and stresses the radical significance of dentology and its symptomatisms as ontological antinomies such as those of sexuation and the parallax view. Therefore, what we mean by the titular “Parallax of Worlds” is the integration of both philosophical dislocations insofar as we are trying to comprehend what these interventions mean for the System of Philosophy as a Science of the Philosophical Idea in a manner that it can think the Real, which Hegel could barely scratch at by Symbolic means. The point is that from the Real not only can we think worlds, but we can also detect a radical excesses of those worlds implicating each other in the antinomic fashion of the parallax view — to think the non-dialectical core of the dialectic cannot just be accomplished at the level of ontology as both Hegel and Badiou have pursued, we must also tarry with the level of dentology. The thought that concerns philosophy has, thus, shifted from speculative dialectics, to a non-dialectical thought which is always of being, to a non-dialectical thought of less than nothing — something we will have to revisit in contemporary philosophy when the question rises again: What is thinking?

References and Citations

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— —(2007). Being and Event. Trans. Oliver Feltham. Great Britain: Continuum.

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— — (2006). Metapolitics. Trans. Jason Barker. New York: Verso.

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Badiou, Alain and Barbara Cassin. (2017). There’s No Such Thing as a Sexual Relationship Two Lessons on Lacan. Trans. Susan Spitzer and Kenneth Reinhard. New York: Columbia University Press.

Badiou, Alain, Jean-Luc Nancy, & Jan Völker. (2018). German Philosophy: A Dialogue. Trans. Richard Lambert. Cambridge: The MIT Press.

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Badiou, Alain, Slavoj Žižek, & Peter Engelmann. (2009). Philosophy in the present. Cambridge ; Malden, MA : Polity.

Hegel, G.W.F. (1959). Encyclopedia of Philosophy. Trans. Gustav Emil Mueller. New York: Wisdom Library.

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Lacan, Jacques. (2006). Ecrits. Trans. Bruce Fink. U.S.A.: W. W. Norton & Company Inc.

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Žižek, Slavoj. (2015). Absolute Recoil: Towards a New Foundation of Dialectical Materialism. New York: Verso.

— — (2008).For They Know Not What They Do: Enjoyment as a Political Factor. New York: Verso.

— — (2004). “From Purification to Subtraction: Badiou and the Real” in Think Again: Alain Badiou and the Future of Philosophy. Ed. Peter Hallward. Great Britain: Continuum.

— — (2013). Less Than Nothing: Hegel and the Shadow of Dialectical Materialism. London: Verso.

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Žižek, Slavoj and Alain Badiou. (2017). “Is Lacan an Anti-Philosopher?” Retrieved from: https://www.youtube.com/watch?v=Fv5VMf-RJx4

Zupančič, Alenka. (2017). What Is Sex? Cambridge, Mass: The MIT Press.

This essay originally appeared as Hegel 2 — Badiou and Žižek.