Ayache’s approach, following the philosophical positions of Quentin Meillassoux, inheres a thinking of what exists in the real independently of human beings and their thinking, indeed an attempt not to want to think being, since (absolute) contingency remains eternally prior to being and the human, quite in contrast to so-called correlationism, which quite roughly assumes that things are only relevant in relation to human subjects and their thinking. (Cf. Meillassoux 2008: 25) And there is also no ultimate reason that things are the way they are, and this also contrary to Leibniz’s assumption that everything in the world has its sufficient reason. Ayache distinguishes at this point between a conception that understands future states purely as possible states of the current state, and a position that understands both future and current states precisely as what they are in reality (and precisely not as realized possibilities), whereby each state could always also be not at all or differently. While the first position corresponds to a transcendental fabrication (Bergson), the second position affirms the status of the absolute, which, however, is laid out in Meillassoux as a double absolute, as the absolute of extra-logical reality and as the absolute of speculative reason. (Cf. Toscano 2013: 66f.) Consequently, Meillassoux posits contingency a priori and considers what the “thing-in-itself” might mean before we speak of being, for instance. In his conception of the absolute, Meillassoux does not limit himself to pointing to an extra-logical reality that exists separately from human thought, but in the course of rejecting the correlationist thesis, he virtually demands a speculative logic of the absolute. However, Meillassoux ends up placing speculative logic congruent with being again, conceiving of being without reference to the material, be it experience or capitalist structures. For Meillassoux, the (logical) absolute of speculation is absolutely necessary in order to attain the negative absolute (the absolute from speculation), so that one is finally able to consistently break the correlationist circle. (In doing so, however, Meillassoux continues to refer to chronological time in order to separate cosmological time from anthropomorphic time). If philosophical implication is taken as a position akin to modern science, then for Meillassoux there is a category of the absolute that we can know about, which he calls factuality. (Meillassoux 2008: 75f. ) Accordingly, contingency is stylized into absolute necessity, precisely because thought is incapable of proving the principle of sufficient reason for anything and everything and now, in fact, only factuality remains as an incontrovertible certainty, with which thought has access to the absolute, which in turn means nothing other than that the structure of thought is capable of thinking the structure of reality: it is the way it is, but it could also have been different and it can become different at any time; for Deleuze, this would be, so to speak, the virtual side of the real object. The way Meillassoux denies the existence of the contradiction in reality then gives final information about this position: contradictory entities are impossible and at the same time it is absolutely necessary that contingent entities exist. According to Meillassoux, contradictory being could never become another being purely for logical reasons. For if a contradictory entity existed, then it would contain contradictory properties, it would be what it is not at the same time, and thus there would be no properties, for example, that it could not have today but could have in the future. But it must be possible that an entity gains properties, which it does not possess up to now, and it must also be able to lose properties. Accordingly, this is a matter of purely logical reasons for rejecting the contradiction, so that Meillassoux’s conception of the Absolute leads back to an identity of being and thinking after all. (Ibid.) Moreover, he cannot think existence as properties, since this would imply that the (fluid) entity exists and does not exist at the same time (it has potentials that may or may not actualize). In Meillassoux, in addition to the problem of the logification of the absolute leading back to being, the question of the ontologization of reality qua mathematics consequently emerges at this point, since his notion of contingency, with its reference to Badiou’s interpretation of set theory, is that of a rational proof (in mathematics). We are again dealing with an ontological claim based on a hidden pragmatics, on a pragmatics that is still transcendent, and not far from an ontotheology of contingency, because Meillassoux does not relate the notion of contingency to anything else, such as plurality or the deterritorialization of concepts that come (logically) before space/mathematics. (Meillassoux is in a fix, so to speak, when on the one hand he pays homage to Deleuze with his conception of super-chaos, and on the other hand he pays homage to Badiou with his equation of mathematics and ontology. While the concept of super-chaos heralds the negation of the eternal validity of logic and mathematics, conversely logic and mathematics are to be understood as the negation of every form of super-chaos. Thus Meillassoux remains torn between two forms of the absolute, each of which is the negation of the other). According to Deleuze or Feyerabend, priority should always be given to that term which has the highest degree of plurality, so that contingency in the crystallized stage is always relative, as absolute only in the decrystallized continuum (chaos). Luhmann also speaks of relative contingency, which itself does not possess any necessity, it does not denote “the possible at all, but that which is otherwise possible as seen from reality.” (Luhmann 1984: 152) On the other hand, (absolute) contingency is written into a logical mysticism by Meillassoux, which finally also revises the gain in knowledge achieved up to that point in relation to probability theory.
For Cantor and following him Badiou the thinkable as well as the contingent independent of the observer is not totalizable. The power set axiom of Zermelo-Fraenkel allows to form the set of all subsets of an original set [for every set (A) there is a set (P) whose elements are subsets of (A)]. If we have a set of elements (a, b, c), the power set can be written as follows: [(a), (b), (c), (a, b), (a, c), (b, c), (a, b, c)]. For purely formal reasons, the power set axiom ruins any form of closed whole or totality, since the power set is always larger than the original set, even if the latter were infinite. Therefore, it also seems possible to form an infinite series of infinite sets, which in turn means that a set determined as a totality (Z) cannot contain the quantity that can be formed starting from the set of the totality (Z). (Meillassoux 2008: 140f.) Russell already proved the logical inconsistency of a set of all sets. Namely, it is not possible to construct a set of all objects without including this total set itself as an object, which in turn requires another total set to integrate that object and so on. Therefore, the power set can be used to recursively generate a set that is always larger than the previous set. However, the question arises whether Cantor’s transfinite, which points to the importance of the (necessary) contingency of every law, which can change rapidly or also rarely with respect to its frequency, whether this kind of transfinite is really amenable to ontologization, as Badiou or Meillassoux following him certainly assume. But by making it possible in principle to think the incalculable surplus, the ontological foundation of mathematics is to affirm the thinking of the contingency of social relations, which can always be put together and structured differently, within an economy of the same as manifolds of being itself. Assuming that the number of possibilities is not totalizable, it can then also be assumed that anything can happen in derivatives markets, at any time and in any place; the market would then virtually contain (virtually inscribed in it) the prices of all derivatives of an untradeable set n, which in turn would exhibit the error of the statistical model n-1. This implies the definition of an absolutely contingent market as a radical alternative to statistics, wherein a kind of continuous unfolding of an incalculable event à la Badiou is implied: the place of a continuous revolution, which, according to Elie Ayache, exceeds the effectiveness of the algorithm and requires the subject. (Cf. Ayache 2010a)
Finally, the extensional composition of the set refers to the fact that the elements of the set are, on the one hand, independent objects, and on the other hand, parts of larger objects or sets from which one can subtract them. Thus, the elements are not defined solely by relations within a set, but also exist as independent elements which can be detached from their participations and relations, without which, however, they cannot exist at all. If extensional sets do not include any specific order of relations between the elements, then it follows that there are no “ultimate” relations between the elements, which means that the relations are external to the elements. In contrast to classical structuralism, which thinks the relations between the elements strictly as internal relations, from which follows that the elements have no independent existence outside of the relations, the ontology of inconsistent manifolds (the excess is the incomparable of a reality trimmed to comparability) wants to attach itself to the figure of the externality of the relations, so that it seems possible that elements (here understood as the properties of synthetic securities like time, price, cashflow, risk etc.) are only temporarily consistent. ) enter into only temporarily consistent connections with each other, and these connections are necessarily contingent and could be otherwise. Badiou’s mereological way of thinking would insofar make it possible to think the break and the change in the (social) relations, but on the other hand with the philosophical decision to present an ontology of mathematics/set, this possibility is closed again. It is not only with Deleuze’s critique of the royalist, axiomatic deductions of a mathematics oriented purely to set theory that doubts about Badiou’s ontology can be unfolded; the post-Fordist answer to Badiou and Meillassoux here would probably be that mathematics today can no longer be contextualized ahistorically, even if in the past there were sufficient reasons with which to contextualize mathematical regions such as geometry, symbolic logic, analysis, algorithms, set theory, etc. could be hived off from ontic history to be located entirely outside the history of institutions, social relations, and modes of being (but not necessarily outside the history of substances). In contrast, mathematics as calculus (formalized computer languages and algorithms) is currently at the core of the capitalist mode of production itself, i.e., mathematics bpossesses its function in driving capitalist growth and its productivity as an integrative and integrating part of the economy, so that there is no longer any reason to historicize mathematics per se; rather, the analysis of the contemporary capitalist mode of production forces mathematics and its object-oriented formal languages and algorithms to be thought of as part of capitalization itself. And last but not least, in the future, the use of algorithms in, for example. And last but not least, in the future the use of algorithms, e.g. in high-frequency trading on the stock exchanges, will become cheaper than the remuneration of brokers or managers, perhaps even more efficient, because, after all, human intuition requires a time-consuming handling of mathematical problems – and thus, for the first time in the internal history of capital, a group that can be counted among the social elites would be threatened in its existence by the use of technical innovations and, in the short term future, would become part of a new lumpenproletariat, whereby exactly what Paolo Virno prophesied would come to pass: The so-called knowledge society tends to degrade the entire social labor potential to a post-industrial reserve army. (Cf. Virno 2008: 153f.) In all areas of production, there is already an algorithm-based conversion of business processes, which could lead in the medium term to even management consultants, marketing specialists and designers having to fear for their jobs.
It is not entirely by chance that probability theory inverts some of the basic assumptions of physical chaos theory, such as those formulated by Ilya Prigogine and Isabelle Stengers. While Prigogine/Stengers distinguish between a microscopic and a macroscopic level, the difference between which is that, for example, turbulence and vortices occur as irregular tendencies on the macroscopic level, while they are highly organized on the microscopic level, the distinction macro (stable order) and micro (random events, which, however, lead to order in the long run) is used by stochastics in order to develop the so-called prognostic probability theory, which corresponds here to the micro level, from the balancing statistics, which corresponds to the macro level. (Cf. Reichert 2008: 39) Especially in stochastics, the formalization indicates less a mathematical abstraction than a normalizing scale that parallels deviations from the mean (Gaussian curve) with a deviation from normality. (Cf. Esposito 2007: 43) At this point, Nicholas Taleb calls the Gaussian normal distribution parsimonious (parsimonious) because it has only two parameters and thus must necessarily negate that with the addition of “layers of possible jumps” that bring more and more probabilities into play, infinite combinations and recombinations of cases are possible. (Taleb 2010: 77)
