Source: http://www.cosmosandhistory.org/index.php/journal/article/view/229/341
Timestamp: 2019-04-22 16:40:16+00:00

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Abstract: This article addresses the relationship of contingency to necessity as developed by Quentin Meillassoux and G.W.F. Hegel. Meillassoux criticizes the restriction of possibility by modern philosophy to the conditions of the transcendental subject, which he calls ‘correlationism’, and opposes to this correlationism, mathematics as an absolute form of thought. The arch-figure of a metaphysical version of correlationism for Meillassoux is Hegel. This article argues that, while Meillassoux is right to criticize a version of correlationism for restricting the range of contingency, he overlooks Hegel’s unique contribution to this issue. Hegel provides us a version of necessity modeled on the mathematical proof which answers Meillassoux’s concerns about correlationist versions of necessity but does not altogether jettison the concept of the subject. Instead, the subject in Hegel is a contingent interruption which emerges from the breaks in the kinds of necessity we posit about the world. Hegel offers us a way of tying these two concepts together in what I call ‘contingent necessity’.
‘The antidote to a post-Kantian catastrophe threatens to be a neo-Hegelian reverie’.
Quentin Meillassoux’s After Finitude (2008) brings about another intervention into philosophy by what Francois Laruelle calls ‘non-philosophy’. In the arche-fossil statements of contemporary scientific discourse, e.g. dating the origin of the universe at 13.5 billion years ago, Meillassoux sees a rejoinder to the post-critical philosophical environment which, since the Copernican revolution in philosophy, has instituted the subjective conditions for the presentation of objects over the objects presented, elevated relations over related terms, and maintained the modes of presentation (transcendental) against what is presented (objective). This shift is what Meillassoux calls ‘correlationism’. To interpret the kinds of ancestral statements presented by the arche-fossil, the correlationist irremediably commits a twofold retrojection and doubling of their meaning: the correlationist will first retroject the conditions active for a subject now onto an ancestral past such that any conceivable event—past, present, or future—must conform to the modes of subjective representation; and second, the correlationist interprets the content of an ancestral statement as objectively true (yes, the evidence indicates that y event happened x years ago) with the addition of a formal ‘codicil’, that the ancestral statement is true only ‘for humans’ (AF 13/30). Thus the world for the correlationist is ‘what is’ for the subject; indeed, it must be. This conditioning of the world through a subjective armature simply reflects the nature of the a priori transcendental—all objectively true statements are true for us, objects thinkable by us, as given to the epistemic conditions of human cognition as such.
While philosophy since Kant has labored under correlationist assumptions, according to Meillassoux, ancestral statements interdict this ‘correlationist two-step’ by shifting the very conditions which support the correlationist circle onto an ex-centric, asubjective discourse (mathematics). In ancestral statements it is no longer a question of securing the necessary conditions by which something can be presented to the subject, but a question of the emergence of the transcendental as such, ‘the emergence of the conditions of taking place of the transcendental’. (AF 25). The modern mathematicization of nature thus instituted ‘the decentering [excentrement] of thought relative to the world within the process of knowledge’. (AF 115/160). Following Badiou, Meillassoux views mathematics as a uniquely transparent, non-metaphysical discourse which simultaneously allows us to absolutize statements about the world but which nevertheless remains irreducible to the correlationist circle. The upshot of Meillassoux’s account is that in mathematics we have the means at our disposal for decentering the correlationist circle, for which all necessity is necessary for the subject, in a form of contingency for which contingency alone is necessary, the thesis Meillassoux calls the ‘necessity of contingency’. Thus, according to Meillassoux, once we recognize that nothing is necessary except that no-thing is necessary, it is possible to track truly asubjective, diachronic referents, such as, those concerning ancestrality.
This account, however, leaves us with at least one important unanswered question about the correlationist subject: What has become of the correlationist subject if it is has been permanently displaced by mathematical discourse? Has the place of the subject simply been evacuated by the decentering discourse of mathematics, or did it never exist at all? And who is the subject of the enunciation of ancestral statements? This question concerning the correlationist subject immediately invokes the figure of Hegel as the post-Kantian figure who, like Meillassoux, attempted to think the ‘absolute’ by overcoming the correlationist subject, while also bringing contingency into the center of his system. But Hegel went a step further by explicitly maintaining a doctrine of the subject produced from within the process of overcoming correlationism. What is less obvious, however, is that in Hegel we also discover an alternative approach to the form of mathematical necessity formulated by Meillassoux. Hegel provides an alternative conception of the force of mathematical necessity, based on the notion of the ‘proof’, within which we encounter the formal limit of mathematics, a limit not set a priori either in the transcendental foundation of mathematics (Kant) or in a Badiouian meta-ontological thesis concerning the capacity of mathematics to speak for being.
Focusing on the Jena lectures on ‘Logic and Metaphysics’ (1804-5), I will develop Hegel’s conception of this alternative logic, macrological in its implication but mircological in its use, as an alternative to Meillassoux’s thesis of the ‘necessity of contingency’. The consequence of this logic is nothing other than the breakdown of the correlationist circle on correlationism’s own terms (pace Meillassoux). However, the breakdown of correlationism also amounts to the inscription of a new subject without simultaneously reinscribing another form of necessity into the heart of contingency. This new subject is not another reintroduction of absolute possibility, for which Hume’s problem would inevitably resurface, but finally the name of its ultimate failure. I will call this failure ‘contingent necessity’.
One of the more provocative claims in After Finitude is that Kant’s Copernican revolution in philosophy is the philosophical equivalent to a return to classical cosmology, some sort of ‘Ptolemaic revenge’. At least since Kant, Meillassoux argues, philosophy has become fundamentally correlationist, which is to say, in addressing the perennial philosophical question ‘what is it to be?’ the correlationism will answer: ‘to be is to be a correlate’ of the subjective conditions of possible experience (AF 28/39). What makes this thesis so provocative is that against the explicit goal of the first Critique—to ground scientific laws on the firm foundation of synthetic a priori judgments—the post-critical philosopheme that Kant helps to install in the form of the correlationist circle absolutely restricts the capacity of science to make any absolute claims whatsoever. In fact, under the weight of correlationism, philosophy must abandon all pretense to thinking the absolute and console itself by thinking absolutely what is only for us. This sets the noumenal realm, the region of the thing-considered-in-itself, outside the subject as the realm of absolute possibility, the place in which anything could happen, so long as it is not for us, at which point it would have to conform to the necessary epistemic conditions of the transcendental subject.
Against this foreclosure of our ability to think the absolute, Meillassoux indicates that the mathematical-scientific basis of ancestral statements shows us a way out of this correlationist circle on its own terms by showing that the circle is committed to its own unraveling. There are two sides to Meillassoux’s argument worth reiterating here. The first is the ‘principle of unreason’, Meillassoux’s answer to what he calls ‘Hume’s problem’. The kernel of this problem can be stated simply: ‘we must think an absolute necessity without thinking anything that is absolutely necessary’. (AF 34/47). That is to say, what Hume discovered in the famous billiard ball example was the problem of whether past events give us sufficient reason to believe that future events will happen according to the same causal sequence. In a word, it is a question of how necessary natural causal sequences are. The principle of unreason states in answer to this line of questioning that there is no reason that legitimates the continued existence of anything, and that anything has the potential to be otherwise without reason. This ‘anything’ is the ‘faultline’ of contingency at which we reach the limit of the correlationist circle. If anything could be otherwise than it is without some justifying reason, then the foundation of the correlationist circle, that everything we experience is necessary for us or given to human scale, is pulled out from under the correlationist subject. The absolute possibility that stands outside the correlationist subject, providing it the conceptual frame within which necessity appears, is the very displacement of the subject in an absolute possibility within which the correlationist can only allege that anything, even the unthinkable, could happen. The subject thus stripped of its transcendental armature is forced to face the ancestrality of the ‘Great Outdoors’ (Grand Dehors), the time radically prior to the subject.
This line of reasoning leads Meillassoux to the second implication of the principle of unreason, the principle of factiality (factualité). If, as Meillassoux alleges, the correlationist is committed to the absolute possibility that something could be different (in-itself) at any time, then the correlationist is also bound to ‘the absolute necessity of everything’s non-necessity’. (AF 62/84). That is to say, if in the unthinkable absolute anything could be different than it is for us, then it is this condition of being unconditioned, of being ‘absolute’, that allows the in-itself to be otherwise. The strength of Meillassoux’s argument for contingency rests on the correlationist’s assertion that any ‘unreason in-itself’ (irraison en soi)—the fact that things could change in the future without reason—is just a form of ‘unreason for-us’ (irraison pour nous) the inability to identify a principle in us that would grant to anything a necessary reason for its being this way and not another (AF 54/74). If we are able to show the absoluteness of this contingency, says Meillassoux, then contingency itself becomes ‘immunized’ against the procedure of correlationism to subsume contingency in-itself under contingency for-us (AF 55/75). So long as we maintain the distinction between for-us and in-itself, contingency is absolute; everything (in-itself) could be otherwise in the future, except for the fact that everything could be otherwise. As Peter Hallward puts it: ‘Nothing is necessary, apart from the necessity that nothing be necessary’. Thus, Meillassoux asserts, ‘contingency alone is necessary’ (AF 80/108), which amounts to the claim that we should consider ‘contingency the absolute property of every being, laws as well as things’.
In developing the principle of factiality, Meillassoux distinguishes his standpoint of the ‘necessity of contingency’ from a standpoint which would subsume contingency into a wider metaphysical framework, thus immunizing the decentering power of being’s capacity-to-be-other in metaphysical necessity. Here the spectre of Hegel emerges as the primary figure of the metaphysical alternative to Meillassoux’s post-metaphysical ‘necessity of contingency’. Meillassoux notes that by itself the thesis that ‘contingency is necessary’ is ‘entirely compatible with metaphysics’ (AF 80/108), and thus needs to be distinguished speculatively from metaphysics. According to Meillassoux, Hegel’s notion of contingency subsumes contingency into a Whole (Tout) ontologically superior to contingency itself, and thus reinscribes contingency into an overriding framework of necessity. For this reason, says Meillassoux, ‘in Hegel, the necessity of contingency is not derived from contingency as such and contingency alone’, to which he adds the qualification, ‘This is precisely what separates the factial from the dialectical’, ‘the speculative from the metaphysical’ (AF 80/108-9). While the Hegelian approach subsumes contingency under a rational totality ‘to which nothing can remain external’ (n’avoir rien en lui d’extérieur), even nature (the basis of ancestral statements) and the irrational (AF 80/108), the speculative approach makes absolute claims to knowledge of the thing itself without simultaneously making them necessary. The necessary movement of the Hegelian Whole, on Meillassoux’s account, must include the peripheral contingency of a moment of ‘pure irrationality’ (pure irrationalité), so that in the end nothing is left out, even contingency. However, if the Hegelian position were based on ‘contingency as such and contingency alone’, then there might be grounds for a more favorable comparison of the two approaches. Indeed, the minimal line of separation between Hegelian and Meillassouxian versions of the thesis of the necessity of contingency is worth investigating further.
Meillassoux’s choice of Hegelian language here (‘external’ (extérieur), the ‘Whole’ (Tout), ‘totality’ (totalité)) is interesting as it reveals a marked prejudice toward certain suspicious readings of Hegel, especially when Hegel is considered to be the ‘metaphysical’ thinker closest to the ‘necessity of contingency’ thesis. For instance, Hegel credits critical philosophy with having transformed classical metaphysics into a logic. Hegel even explicitly states his intention of following this transformation by substituting metaphysics for a logic in the General Division of Logic of the introduction of the Science of Logic. But aside from the question of an ‘authentic’ reading of Hegel, there is a more compelling reason to read these two versions of the contingency of necessity thesis together. For Meillassoux, at stake in the distinction between speculative and metaphysical, factial and dialectical, is the possibility of transitioning smoothly from a Kantian in-itself to a pure mathematical Cartesian in-itself, with the goal of ‘resolving the problem of ancestrality by an absolutization [absolutisation] of mathematical discourse’ (AF 80/109). Thus, Meillassoux also ties this transition from the correlationist circle with the absoluteness of mathematics. We can read in this desire the goal not only of absolutizing mathematical discourse but also of overcoming the subject as such. Insofar as the subject fails to live up to the absolutization of mathematical discourse, insofar as the subject reinscribes absolute possibility in the capacity-to-be-other on the terrain of the thing-in-itself, it leaves open the space for fanaticism and the ‘religionizing [enreligement] of reason’ (AF 47/64). It is only by the eclipse of the subject, then, of the subject’s persistent failure to overcome its own drive to understand the world according to its representations, to not face up to the hyper-chaos of contingency for which nothing is necessary except everything’s non-necessity, that the absoluteness of contingency can be instituted. Hegel however represents the ultimate failure of this goal.
Before turning to the discussion of the role the constructed proof played in the Jena ‘Logic and Metaphysics’ (1804-5) lectures, let’s take a detour by way of the more commonly known statement a few years later in the preface to the Phenomenology (1807), the famous passage on the ‘defectiveness’ (Mangelhaftigkeit) of mathematical cognition. A lot has been made of Hegel’s statement as to the ‘defectiveness’ of mathematical cognition; far less attention, however, has been paid as to what precisely it is about mathematical cognition (Erkennen)—and not mathematics per se—that leads Hegel to classify these cognitions as ‘defective’. Hegel indicates that the defect in mathematical cognition stems from the fact that an ‘external purpose’ (äußerer Zweck) governs the movement of the proof, but it is not immediately clear what this necessity consists of. The proof follows a path that ‘begins somewhere or other’ (irgendwo anfängt) which appears contingently, without indication as to the purpose of the proof or what the proof is supposed to show about the world (PS §44 25/3.44). Without an indication as to the direction the proof will follow, we are left having to supply another reason (or set of reasons) as to why and what the proof demonstrates. This does not limit the importance of the proof for Hegel, however, as the proof provides a conceptual orthography which discloses what it is to be for thinking, and thus opens the space for philosophical scrutiny. And philosophical reflection supplies the additional essence or moments that constitute thinking (the task of philosophical cognition). As Hegel makes clear, ‘mathematical cognition sets forth only the genesis of the existence (Daseins), i.e. the being (Seins) of the nature of the thing in cognition as such’ (PS §42 24/3.42), which still belongs to a wider cognitive process of which the completed proof is a result. ‘The whole production of the result is a way and a means of cognition’, and the course followed by the proof only exposes the limits of ordinary thinking, that is, ‘its relation to the knowing subject’ (PS §42 24/3.42). Just as the progress toward knowledge will find ‘no satisfaction’ (Befiedigung) in ‘the stations on the way’ (PS §80 51/3.74), so too the result of the proof can only be reached if we have followed the necessary course internal to the proof. But even with that mathematical result in hand, we are left wondering about the result’s significance for the world it interprets. How does mathematics pass into interpretation? Said another way, there is a gap between the mathematical proof as a micrological engagement and what that proof shows about the world (for instance, in an ancestral statement)—a gap between the necessity internal to the proof and its relation (necessary or contingent) to the world, which is the basis for a macrological engagement. This gap, says Hegel, ‘only proves how great is the need of proof for cognition’ (PS §46 26/3.45), the limit at which the thinking subject emerges.
Turning now to the lectures on ‘Logic and Metaphysics’, Hegel presents basically the same form of the argument. In the section headed ‘Proportion’, Hegel considers the classic Euclidean proof of the Pythagorean theorem. First, Hegel says we begin with an indifferent unity, the figure of the right-angled triangle as a whole; but after we distinguish its parts, we are able to produce a set of determinate relations and an equality among them, which are not themselves equal to the whole. ‘The result of the proof is that the indifferent relation of the whole and the parts is the same time a differentiated relation of the moments. The proof fastens both relations together for the first time […] an equivalence of opposed moments’. (LM 121/7.115). The proof allows us to explicate a set of determinate relations which were not apparent from the outset. But what this further exposes about thinking is the most interesting function of the proof. Hegel entertains this thought explicitly: ‘This transition from the positive to the negative [unity] and from the parts into moments, is what constitutes the nature of cognition and of real definition’. (LM 121/7.115). Thus, the movement from thinking an intelligible entity, such as a right triangle, and exposing the differentiated unity that constitutes it as moments is cognition, ‘cognition displays the unity of both relations’. (LM 121/7.116). Hegel then goes on to state, ‘cognition displays what has previously taken place, the transformation of the undifferentiated relation into the differentiated one, and the equivalence of both’. (LM 121/7.116, emphasis added). There are two ways we can read this statement. The first way, is that what ‘has previously taken place’ is precisely the steps that make up the proof, the moments that return to the differentiated unity as a result. The second way of reading this statement is that it is only after a cognitive sequence ‘has previously taken place’ that cognition itself can be exposed through the analysis of the result of this differentiated unity. The first, superficial reading would say nothing more than that thinking can be separated into discrete steps, and that our discursive understanding of these steps is only displayed afterwards. The second reading helps to explain why it is that for Hegel ‘philosophy always comes too late’ or that the Owl of Minerva only flies at dusk. It is only after something has transpired for thinking that we can begin to think about the moments which constitute that something for thinking.
The wonder of mathematical proofs is this remaining lack of satisfaction [zurükbliebende Nichtbefriedigung], which indeed passes over from what appears to be contingent in the construction to the necessity of the proof, but which does not grasp that construction through itself [nicht durch sich selbst begreifft] because it is not a concept, not something differentiated, and therefore also not the transition. (LM 123/7.117-18).
The wonder here is that we can go through the rigor of a mathematical proof without exposing the function of our cognition in its construction. What this shows about cognition is that cognition readily acts without reflection, inducing us to think under objective presuppositions, and it is only afterward, after we have reflected back on the sequence, that we can retroactively distill the moments that constitute cognition. Thus, as Hegel states in the Phenomenology, it as though necessity operates ‘behind the back of consciousness’ (hinter seinem Rücken) (PS §87 56/3.80).
At first it can appear as though there are two circuits of contingency running here, one circulating objectively in the mathematical proof, and one subjectively in the fortuitous appearance of philosophical reflection. However, upon a closer inspection of the mathematical proof, the steps of the proof show that the first is a micrological contingency. The individual steps in the proof are necessary within the proof to produce the result, however, that these steps were posited correctly (or at all) to arrive at the result is itself contingent. There is a barrier of contingency separating the necessity of the proof from its appearance in the world and the necessity which allows it to say something about the world, a ‘middle term’ or mediation through which cognition passes outside itself, ‘becoming an other than it is itself’ (wird ein anderes als er selbst ist) (LM 126/7.120). Once we have a completed proof, we can refer back onto the proof’s necessity, but not before; ‘before’, the proof itself is utterly contingent. For this reason, any engagement with mathematical necessity will be a microlocial engagement—it depends on someone engaging in a proof, completing it, and then making use of it to interpret the world. For Badiou to claim, for instance, that mathematics is ontology requires a meta-ontological decision, and only after the decision has taken place can we decide what that claim reveals about being and thinking, the absoluteness of mathematical discourse as an ontology. This inability to show beforehand, a priori or otherwise, the ultimate significance of a proof—what Hegel calls the ‘lack of satisfaction’ (Nichtbefriedigung) of the proof—shows further that even the most rigorous form of necessity contains the kernel of its own failure to produce another order of necessity at the macrological level. That, ultimately, it is only by thinking through the form of the proof that necessity appears at all. The strongest implication is, moreover, in its effect on thinking. It reveals that necessity is always contingent on a subject for which it appears, but even this fortuitous appearance of the subject is itself contingent. Thus, on the Hegelian model of the proof, necessity is contingent and even this fact is not necessary in any a priori, deductive sense, as alleged by Meillassoux. Necessity only appears contingently and need never have appeared at all. If there was no disruption in cognition that lead consciousness to ‘turn around’ to reflect on what’s going on ‘behind its back’, then there need never have been a thinking subject at all. The ‘subject’ only names the breakdown that lead to philosophical reflection—contingency was the doorway through which the subject stepped. When we fill this picture out historically (and not only logically), it means that in the most radical sense things could have been otherwise, because they could have not been at all.
The consequence of all this is that, far from creating a metaphysical framework of pure necessary deductions that subsume contingency into an ontological Whole, Hegel meets Meillassoux’s goal of decentering the correlationist circle via the absolutization of mathematical discourse. The mathematical proof presents to thinking the ultimate limit of necessity which leads to another form of necessity predicated on this limitation. However, what Hegel’s shows, contrary to Meillassoux’s necessity of contingency, is that mathematics does not produce a system of propositions for which only contingency is necessary, but that necessity itself is dependent on contingent micrological engagements. At the macrological level, what we are able to venture about logic in general, is that even this result could have been otherwise; that is, if there hadn’t been the kind of preliminary disruption in our thinking which propelled us into philosophical reflection, there might not have been the appearance of a micrological engagement (the proof) at all. Thus, there is no necessity of contingency. Only contingent, micrological necessities: contingent necessity.
As a concluding note, returning to the problem of correlationism, we could interpret Kant’s commitment to correlationism in a slightly modified way, in which it is not the absolute possibility outside of the subject which is absolute (as the principle of factiality supposes), but that all necessity is only necessary on the hypothesis that there is a subject for which it is necessary. Necessity itself would then be a relation absolutely dependent on there being a subject, even if that subject itself were contingent. Thus, facing the ‘Great Outdoors’ outside of the subject, we have nothing but the contingency of the ‘capacity-to-be-other’ before us; however, in order to make this ‘outside’ meaningful, we must engage in a process of attempting to think it, that is, to understand it, if we are to discover any ‘necessity’ within it at all, even the necessity of everything’s non-necessity. Necessity itself would then be contingent upon the fortuitous appearance of the conditions that allow for a thinking subject—a subject, we might add, that would be compatible with the hyper-Chaos implied by Meillassoux’s necessity of contingency. Seen through this modified Kantian lens, we could present a Hegelian (and Fichtean) variation on the theme of Hume’s problem. There is a displacement within thinking between an ordinary consciousness which does not ‘feel’ any force of necessity, because the world seems to be going well according to its representations (intuitions, feelings, beliefs), and for which there is no ‘need’ for philosophy, and a consciousness whose representations have been ‘disrupted’ (Absonderung), and through this disruption begins to analyze what something means for it. The first consciousness would have no problem assimilating ancestral statements of the arche-fossil kind, as ordinary thinking often sits comfortably with a common-sensical realism concerning natural science. Indeed, the ‘religionizing of reason’ that Meillassoux sees as a byproduct of correlationism could be as much a byproduct of the profound ‘faith’ that the layman places in scientific discourse for producing truths. It is in the second form of consciousness, however, the one infected with reflection and which depends for its very being on the fact that philosophical reflection ‘takes place’, that we begin to think the necessity or contingency of anything, much less the necessity of contingency. Our thinking must in some sense fail to represent the world adequately in order to employ the micrological engagements which produce necessity, and in this failure the subject of cognition, the thinking subject, appears (but it didn’t have to).
As Slavoj Žižek, always the good Hegelian, frequently points out, the subject is the very form of this displacement, the ‘subject “as such” is a subjectivized predicate; subject is not only always already displaced, etc., it is this displacement’. The subject appears only in ruptures, in its inability to stabilize its relationship to the world according to an overarching necessity, in the ‘lack of satisfaction’ that accompanies even the most rigorous mathematical proof—in a word, in its failures. Meillassoux’s identification of mathematics as an asubjective logic capable of expressing being qua being without representing or repeating this failure is an attempt to overcome the persistence of the subject, even in its non-correlationist form. Here another problem emerges. The presupposition of ache-fossil statements rests on a commitment to a non-correlationist, metacritcal world: one world, a world of speculative mathematical-scientific statements, a world without subjects. In this way, mathematical-scientific statements appear as surrogates for objectivizing effects—the opposite of Badiou’s ‘subjectiving effect’—which destabilize and undermine the position of subjects qua subjects. Arche-fossils in this sense are traces of radically de-subjectivized worlds that push forward the originary failure of the correlationist subject to remain centered as a self-subsistent and transparent substance, even if only as a correlate of appearance (apperception or co-presentation) stripped of any substantial attributes. The question, however, remains whether this general collapse of the correlationist subject is not indicative of yet another failure out of which we glimpse another subject. That is to say, one can wonder whether the reinsertion of necessity in the thesis of the ‘necessity of contingency’ does not, in the final analysis, return as a surrogate ‘subject’ of non-correlationist (non-subjective) worlds. Is it a speculative ‘subject’ of the mathematical statement, which has no place in the factial but nevertheless can speak in it, that remains?
A final Hegelian remark here would be that insofar as the problem of ‘necessity’ reemerges, we have not yet fully overcome the problem of correlation. We are left wondering where (if at all) does necessity inhabit the world? Necessary to whom and necessary for what? The correlationist answer was relatively simple: necessity exists according to the forms of the subjects that exist. The Hegelian modification, however, is that these subjects only exist in the failure of thinking to duplicate necessity at all levels of thinking. Even if mixing the kinds of necessity that operate on the micrological and macrological levels is a category mistake, it is a category mistake that thinking actually makes; it is indigenous to thinking to try to make sense of what it thinks, to put ‘two and two’ together, so to speak. If the arche-fossil statement introduces a break in the correlationist circle, as Meillassoux alleges, this fact should lead us not to introduce another sort of necessity, the necessity of contingency, but a full-fledged contingency—the contingency of worlds prior to any subjects as such, worlds in which no necessity at all operates. However, the idea of a necessity-less world is predicated on the fact that we have an idea of necessity from somewhere, that is, according to the kinds of worlds that exist for some subject.
The truly profound Kantian insight here is that even if such necessity is purely illusory in-itself, as long as it appears to a subject such that a subject can think it, that thinking happens according to the form of possibility—the obverse side of the coin of subjective necessity. Just as in judgments of beauty Kant indicates that despite the contingency of our feeling pleasure, we nevertheless act as though the pleasure induced by the experience of the beautiful (possibility) was fitted to our faculties (necessity). What is peculiar to these experiences of pleasure is that we can’t help but feel as though there was a purpose behind our faculties for which the feeling of pleasure was meant. Likewise, necessity operates on us simply because it is as though it were necessary for us. If the world closed the correlationist circle absolutely, there would not even be the semblance or trace of an other, the possibility of something radically different than what appears to the subject (whether the thing-considered-in-itself or the arche-fossil). Even if necessity at the level of the subject is actually illusory, the fact that it appears to a subject at all renders it possible for the subject to conceive otherwise than what is necessary for it. The Hegelian point here is that even this failure itself says something about the subject. It tells us that reflected possibility is ‘not nothing’, ‘it is illusory being insofar as in it the absolute illusion-s [scheint]’. (SL 532/6.190). If we continue down this line—that the subject marks the place of this not-nothing, the empty space created by the failure to reinscribe necessity in thinking—then, while Meillassoux’s arche-fossils interrupt the self-possessive movement of the correlationist circle, the arche-fossil only does half the task. The sheer possibility of other worlds is only conceivable via the failure of correlationism to close the circle. But insofar as the circle fails to close, we are faced again with the empty place of the subject, the subject of mircological engagements, the subject of contingent necessity. But we must wait here for another failure before that subject appears, and for that, we could wait forever (though I doubt it).
. From the transcript of a talk given by Alberto Toscano at the UWE Bristol ‘Speculative Realism/Speculative Materialism’ conference, 24 April 2009: http://www.cinestatic.com/infinitethought/2009/05/alberto-toscano-against-speculation-or.asp.
. For instance, Laruelle states that ‘Every non-philosophical break discovers its element in the oldest duality of philosophy and the Real, a duality each time articulated by a certain type of foreclosure’, François Laruelle, Dictionary of Non-Philosophy, trans. Taylor Adkins, accessed online: http://speculativeheresy.wordpress.com/resources/, p. 5; originally published François Laruelle, Dictionnaire de la Non-Philosophie, Paris, Editions Kime, 1998. Meillassoux’s use of the arche-fossil can be seen as just such a reevaluation of an ‘old duality of philosophy and the Real’ by which a deep-time relation without subject intervenes into the circle of correlationism. Through the surrogacy of mathematical discourse, arche-fossil statements produce an alternative relation to being or the Real of ancestrality than the correlationist relation of the ‘givenness’ of being under subjective conditions allows.
. Along with Kant, Meillassoux heaps together under the banner of ‘correlationism’ Husserl and Heidegger, and any philosopher who ‘hypostatizes some mental, sentient, or vital term’. This list includes: ‘representation in the Leibnizian monad; Schelling’s Nature, or the objective subject-object; Hegelian Mind; Schopenhauer’s Will; the Will (or Wills) to Power in Nietzsche; perception loaded with memory in Bergson; Deleuze’s Life, etc’. (AF 37/51). The first page number refers to the English, Quentin Meillassoux, After Finitude: An Essay on the Necessity of Contingency, trans. Ray Brassier, London, Continuum, 2008, hereafter AF. The second number refers to the French, Après la finitude, Pars, Editions du Seuil, 2006.
. Alain Badiou introduces his ‘meta-ontological’ thesis that mathematics = ontology in the introduction of Being and Event, trans. Oliver Feltham, London, Continuum, 2005. While Meillassoux applauds Badiou’s ‘singular project’ of mathematicizing the detotalization of ontology, ‘it is thanks to his singular project that we have been able to discover the means through which to extricate ourselves from the ontological conditions inherent in the necessitarian inference’. (AF 103), Badiou makes this project an explicit extension of his hypothesis in Theory of the Subject, ‘that there “was some” subjectivization’. (Badiou, Being and Event, p. 4). In Theory of the Subject, Badiou was concerned with the fact that ‘in reality we can only arrive at the subject. This is what marks the time of Marx and of Freud, namely, that the subject is not given but must be found’. Badiou, Theory of the Subject, trans. Bruno Bosteels, London, Continuum, 2009, p. 279. By the time of Being and Event, the problem becomes explicitly mathematically focused, a more robust attempt to think the subject according to pure mathematics in answer to the question: ‘pure mathematics being the science of being, how is a subject possible?’ (Badiou, Being and Event, p. 6).
. Meillassoux encapsulates this Ptolemaic revenge in Kant in the following way: ‘the condition for the conceivability of the Copernican decentering wrought by modern science is actually provided by a Ptolemaic re-centering of thought’. (AF 118/164). It was only by stabilizing the decentering effect of the mathematicization of nature in the transcendental a priori that Kant could ‘secure’ the foundations of knowledge for scientific discourse. Meillassoux calls this attempt to recover the stability of thought the ‘Ptolemaic counter-revolution in philosophy’. (AF 118/163).
. Meillassoux poses the question as an inverted form of Hume’s: ‘since Hume has convinced us that we could a priori (that is to say without contradiction) conceive a chaotic modification of natural laws, why not have confidence in the power of thought, which invites us to posit the contingency of the laws of nature, rather than in experience, in which alone the presentation of the apparent fixity of observable constants finds its source?’, Quentin Meillassoux, ‘Spectral Dilemma’, Collapse: Philosophical Research and Development, vol. IV, Robin Mackay (ed.), Falmouth, Urbanomic, 2008, pp. 261-275, p. 273.
. As Meillassoux states: ‘There is no reason for anything to be or to remain the way it is; everything must, without reason, be able not to be and/or be able to be other than it is’. (AF 60/82).
. In a note to his translation, Ray Brassier indicates that he coined the terms ‘factial’ and ‘factiality’ to preserve the distinctly philosophical meaning of Meillassoux’s neologisms ‘factual’ and ‘factualité’, from the ordinary French term ‘factuel’ and the philosophical ‘facticity’, which Meillassoux reserves for the Heideggerian ‘Faktizatät’, and which Meillassoux uses to distinguish the absolute contingency of factiality from the familiar correlationist meaning of facticity (AF 132-33).
. Peter Hallward, ‘Anything is Possible: Review of Quentin Meillassoux, After Finitude’, Radical Philosophy, vol. 152, 2008, pp. 51-57, p. 51.
. Meillassoux, ‘The Spectral Dilemma’, p. 273.
. Meillassoux makes this distinction between ‘speculative’ and ‘metaphysical’ approaches to the absolute in order to avoid allegations of returning to a naive pre-critical metaphysics: ‘Let us call “speculative” every type of thinking that claims to be able to access some form of absolute, and let us call “metaphysics” every type of thinking that claims to be able to access some form of absolute being, or access the absolute through the principle of sufficient reason’. (AF 34/47).
. Meillassoux himself invites this closer scrutiny. In asking what is the difference that separates Kant from Hegel, transcendental idealism from speculative idealism, Meillassoux couches the answer in the possibility of deducing the ‘a priori forms of knowledge’: ‘Kant maintains that we can only describe the a priori forms of knowledge (space and time as forms of intuition and the twelve categories of the understanding), whereas Hegel insists that it is possible to deduce them’. (AF 38/52). Meillassoux interprets this supposed deducibility of the categories as ‘an unconditional necessity that abolishes the possibility of there being an in-itself that could differ from them’. (AF 38/53). Thus, Hegel’s thesis of the necessity of contingency differs from Meillassoux’s in that where contingency alone is necessary for Meillassoux, for Hegel everything is necessary, including contingency. As I will show, this interpretation of Hegelian necessity overlooks an important dimension of Hegel’s conception of necessity and the role that mathematical proof plays in it.
. Hegel states: ‘The objective logic, then, takes the place rather of former metaphysics which was intended to be the scientific construction of the world in terms of thoughts alone. […] Objective logic is therefore the genuine critique of them’ (SL 63-64/5.61-62). All references to the Science of Logic will be to the English, G.W.F. Hegel, Hegel’s Science of Logic, trans. A.V. Miller, Amherst, NY, 1969, followed by the German, G.W.F. Hegel, Werke, vols. 5-6, E. Moldenhauer and K.M. Michel, Fankfurt am Main, Suhrkamp Verlag, 1969), hereafter SL.
. At §44 Hegel states, ‘what is really defective [Mangelhaftigkeit] in this kind of cognition concerns the cognitive process itself, as well as the material’ (PS 25/3.43). The first page number refers to the English translation of G.W.F. Hegel, Phenomenolgoy of Spirit, trans. A.V. Miller, Oxford, Oxford University Press, 1977. The second set of numbers refer to the volume and page number of the German, G.W.F. Hegel, Werke, vol. 3, E. Moldenhaurer and K.M. Michel (eds.), Fankfurt am Main, Suhrkamp Verlag, 1969. Hereafter abbreviated PS.
. ‘[…]das ganze Hervorbringen des Resultats ist ein Gang und Mittle des Erkennens’. (PS §42 24/3.42, translation modified).
. The first page numbers refer to the English translation from G.W.F. Hegel, The Jena System, 1804-5: Logic and Metaphysics, trans. John W. Burbidge and George di Giovanni, McGill-Queen’s University Press, 1986. The second refer to the volume and page number of the German, G.W.F. Hegel, Gesammelte Werke, vol. 7, Jenaer Systemtwürfe II, Rolf-P. Horstmann and Johann Heinrich Trede, Hamburg (eds.), Felix Meiner Verlag, 1971. Abbreviated LM.
. Both of these references refer to the preface to the Elements of the Philosophy of Right, trans. N.B. Nisbet, Cambridge, Cambridge University Press, 1991.
. Even proofs that demonstrate theorems of a foundational nature imply the internal relationship of necessity and contingency to produce the proof and require a second level of interpretation by which we decide the ultimate significance of the proof, that is, what the proof demonstrates. These two steps need to be distinguished in order to track the role of contingency in the mathematical proof as a total function of cognition.
. In fact, tying necessity to the fortuitous appearance of the subject (including the subject of the enunciation of mathematical statements) would help to explain the radical contingency of this chaos, that is, its supernumeracy: ‘the possibilities of which chaos—which is the only in-itself—is actually capable cannot be measured by any number, whether finite or infinite, that it is precisely this super-immensity of the chaotic virtual that allows the impeccable stability of the visible world’. (AF 111/153). Thus, we could say, that it is precisely that a subject appeared at all which is radically contingent, but nevertheless provides a relative stability to the ‘visible world’ qua visible, i.e. as perceiver.
. In the Science of Logic Hegel criticizes Fichte’s beginning with an abstract ego on the basis that no one experiences this ego directly. It is ‘something unknown to the ordinary consciousness, something it does not find therein’. (SL 76/5.76). Thus Hegel indicates: ‘Before the ego [Ich], this concrete Being, can be made the beginning and ground of philosophy, it must be disrupted [Absonderung]—this is the absolute act through which the ego purges itself of its content and becomes aware of itself as an abstract ego’ (SL 76/5.76).
. Slavoj Žižek, ‘Fichte’s Laughter’, Gabriel Markus and Slavoj Žižek, Mythology, Madness, and Laughter: Subjectivity in German Idealism, London, Continuum, 2009, p. 129.
. It is interesting to imagine how Meillassoux’s account of the necessity of contingency might have differed if rather than focusing on Cantor’s theorem, he instead focused on Gödel’s incompleteness proof: that for any well-defined system of propositions, another proposition can be added that neither follows from nor contradicts that well-defined system. While Meillassoux focuses primarily on Badiou’s interpretation of Cantor’s theorem in Being and Event to show that no complete series of sets can be collected as a set, or that ‘the (quantifiable) totality of the thinkable is unthinkable’ (AF 104/144), Badiou singles out Cohen as proof against the absolute constructability of set theory, whose theory of the ‘generic’ opens mathematics to its remainder, the subject, ‘the sole remainder left by mathematical ontology to whomever is struck by the desire to think, and for whom is reserved the name of Subject’. (Badiou, Being and Event, p. 285).
. Badiou expresses the ‘subjectivizing effect’ in the following way: ‘When the popular insurrection breaks out, it is never because the calculable moment of this insurrection has arrived. It is because it is no longer worth doing anything else except to insurrect. […] Our anecdote reveals that it is the interruption of an algorithm, and not its execution, that has a subjectivizing effect’. Badiou, Theory of the Subject, p. 257. In the interruption of the ‘algorithm’ the place of the subject emerges as an effect.
. If there wasn’t this failure (a failed adequacy, adequatio) Hegel’s position might be indiscernible from Spinozism, for which necessity is duplicated at all levels of thinking. The failure however is immanent to thinking as transition, or something that transpires in time. As Hegel indicates, cognition is the expression of a transition: ‘Cognition is itself just this transition; the content falls asunder; it is a series of indifferent [things] that enter as isolated, each on its own account. The unity is the differentiated unity of cognition’. (LM 128/7.122). Cognition brings together a series of isolated, indifferent things and attempts to make them into a meaningful unity. However, in this process of producing meaning out of indifference, thinking itself comes apart in this indifference, but never dissolves itself permanently; it never ceases thinking. ‘In this way cognition is realized infinity, which is thrown apart in the doubled relation and returned to itself’. (LM 130/7.124).
. ‘What is strange and anomalous’ about these judgments, Kant states, is that even though these experiences are not cognitive as they lack a concept, they display a kind of purposefulness as though the faculties were made for the judgment of the beautiful. In the judgment of taste, the feeling of pleasure operates like the transcendental object. We attempt to make the judgment objective in its form. It is ‘nevertheless to be expected of everyone and connected with its representation, just as if it were a predicate associated with the cognition of the object’. (5: 191). Immanuel Kant, Critique of the Power of Judgment, trans. Paul Guyer and Eric Matthews, Cambridge, Cambridge University Press, 2000, p. 77.
. ‘Der Schein ist nicht das Nichts, sondern er ist Reflexion, Beziehung auf das Absolute; oder er ist Schein, insofern das Absolute in ihm scheint’. Translation modified.

References: §44
 §42
 §42
 §80
 §46
 §87
 §44
 §42