There is a continuous insistence in philosophy on the illusion that the problem of the relationship between theory and practice can be thought of in terms of an original disjunction and a possible synthesis (the differential positions remain, but are constantly both traversed or synthesized). The monistic-plural thinking of a laruelle, on the other hand – thinking not of the one, but in the one – no longer wants to configure the seemingly opposing pair of theory and practice with the concepts of disjunction and synthesis, but rather to construct them anew in the last instance through the axiomatic demand of their identity. Theory and practice are superposed in a milieu of interference, a milieu made possible by the algebraic property of idempotence, a specific fusion of terms. The problem of philosophy for Laruelle is simply that it insists on a rather sneaky non-coincidence of theory and practice. (Gangle 2014: 45/Laruelle 2013a: 115) Non-philosophy tries to avoid this aporia, not by means of a hasty action of synthesizing the performative and static or descriptive aspects of practical discourse, but by the radical suspension of synthesis, in order to introduce itself a specifically axiomatic procedure of defining concepts, which defines its own practical methods and the syntactic operators that follow them: Determination-in-the-Last Instance (DLI), Sehen-in-Einem, Dualysis, Cloning and the Non-Philosophically Generic. The rigor of the non-philosophical thinking of the immanence of the One serves to create a discourse leading to the “oraxiom” in which the philosophical distinction between the theoretical and practical aspects of thinking, between the performative and the static functions of language is no longer operative.2 (Laruelle 2012: 51f.)
Laruelle makes a radical distinction between the Greek theoreticism of philosophy and the non-philosophical power of theory, which corresponds more to unlearned knowledge or to seeing-in-one. (Laruelle 2013e: 57) In place of the addictive agonistics of philosophy, which often enough can hardly be distinguished from its agony, there is a special theoretical practice, which for laruelle is that of unilateral duality. The non-philosophical theory and practice are thought sui generis in one, or as identical in the last instance (i.e., from the point of view that they are related to the real). It is, as we will see later, Laruelle’s special use of the axiomatic method to break with the philosophical logic of exchange, reversibility and circularity between concept and reality.3 Laruelle’s seemingly obscure axioms would therefore initially be to clarify in-one, in-the-last-last instance, in-the-last-last identity, -without-living the lived-without-life. These axioms or syntactic operators Laruelle also calls axiomatized abstractions, or in other words, they represent essential elements of the general formalization of first names.
But let us first come back to what Laruelle calls “the principle of sufficient philosophy,” the general coincidence and interaction between theory and practice that endlessly guarantees the sufficiency of philosophy, so that it can articulate itself again and again saturated by saying what it does when it says what it says. (Cf. the following presentation: Gangle 2014: 48f.)
In the mathematical category theory (metatheory of structure and its relations and constellations) and the figures of the arrow and the illustration, first clues can be found for the representation of the philosophical relation “practice and theory”, in which the conceptual worlds, the semantic registers of philosophy and its practices are included. Category theory is considered the general mathematical theory for the explication of the structures/systems of relations – categories – a theory in which objects are determined solely on the basis of their relations with other objects of the same abstract kind. These relations can be represented as graphs (set of points representing an object) and arrows between them (morphisms between one point and the other). However, certain conditions must be met: All arrows (“Head to tail” method) must be able to be combined in a uniform and determined way. If there is a morphism (the morphism determines the object) from A to B, and another from B to C, then there is necessarily a morphism/arrow from A to C that connects the two figures (transitivity). This combining arrow from A to C, which passes Bglues or sews the two arrows by transforming the discrete functions into the continuity of the One. (Cf. Gangle 2015)
Robert Brandom, to whom Rocco Gangle refers here (Gangle 2014: 49), has created a diagrammatic method with the help of category theory to represent the relevant relations between philosophical practice and the theoretical world as well as the relations and ideas contained in the latter. (Brandom 2008: 7ff.) In a diagram, Rocco Gangle follows Brandom by depicting language and concepts in an oval form – this stands for saying. Capacities or practices are represented in rectangular forms with rounded corners: they express the power of doing. One can now introduce the arrow from the rectangular instance equipped with observer capacity (for example, three given types of red) to the oval area containing the terms Magenta, Scarlet and Maroon. (Gangle 2014: 49) This arrow is called PB-sufficient-(practice term) when it indicates that the relation between the two instances is such that a given set of practices (color discrimination capacity) is sufficient to produce a correct set of terms. An arrow pointing in the opposite direction is called a BP sufficiency (term practice) if the given term vocabulary is rich and consistent enough to express and distinguish a given set of practices. It is therefore primarily a matter of the relations and systems of compositions they contain (morphism governs the objects). The details and contents of the two instances are completely unspecified, i.e. instances are only to be understood as indexes or designators. The relations reflect definite pragmatic and semantic modal conditions and are thus sufficient for the further use of practices and concepts.
What Brandom calls a “meaning-use-diagram” applies to every particular system of instances and fields in which PB and BP sufficiencies and the necessary relations between them can be connected in a compellingly categorical way. For example, a BP-sufficient relation that starts from terms B/1 and should lead to a set of practices P can be combined with a PB-sufficient relation that in turn leads from a set of practices to further terms B/2, to finally establish a meta-conceptual relation between B/1 and B/2 – a new relation formed exclusively from the given BP and PB sufficiency relations, a relation which identifies B/1 as sufficient enough to say what needs to be done to achieve the relation of the concepts B/2. (Ibid: 50)
So there is a set of terms and a set of practices, both of which together contain three explicit relations: 1) The B-sufficient relation, a relation in which the terms have sufficient expressive resources to specify a given set of practices. 2) The P-sufficient relation sufficient to develop a set of terms. 3) A third arrow representing the BB-sufficient relation, a relation of concepts to themselves that says what it does when it says what it says. (it specifies itself in its own medium). In category theory, the third relation is called the composition of the two primary representations. The BB-sufficient relation is ultimately identical to the composition of the BP-sufficiency relation and the PB-sufficiency relation. (ibid.: 51)
What is of particular interest here is the reciprocal relation of the first two sufficient relations. The PB-sufficient relation indicates (qua hermeneutics, deductions, induction, etc.) that it is sufficient as a set of practices to develop a consistent philosophical conceptual vocabulary that enables philosophical statements. The BP-sufficient relation indicates that philosophy, through its conceptual acrobatics, is able to provide necessary specifications for a set of practices that is itself sufficient for philosophy. And there is a meta-conceptual BB-relation about the composition of the relations, which leads from concepts to concepts, whatever the contents of the internal structures of the concepts may be – and these three relations taken together document for Laruelle the principle of sufficient philosophy, which in turn is applied auto-referentially by philosophy to philosophy. Or, to put it another way, philosophy here adequately says what it does when it says what it says. (ibid.: 45) It supplies itself with its pragmatic metavocabulary. For Laruelle, the practical-theoretical sufficiency of Hegelianizing philosophy is evident, since it creates an operative unity with regard to the active-productive and reflexive-thematic moments of philosophical thought.
One would now have to discuss the various conceptual levels at Hegel on which this circular figure appears in each case. And then one cannot avoid assuming, in the movement from being on oneself to being for oneself and finally to being on and for oneself, precisely the terms and practices that Brandom calls the “expressive-pragmatic bootstrapping” (quoted after: ibid.: 51) depicted here. In Hegel’s dialectical concept, action (practice; as-is) systematically precedes saying (theory; for oneself), and this on all levels traversed up to the boundary and up to the conclusion in the absolute mind, with which the otherness of the object outside itself is dissolved in a knowledge that is aware that it “is with itself in its otherness as such”. (Hegel 1970: 575). Although Hegel does not eliminate the ontable, everything that exists is permeated by the spirit that comes to itself in absolute knowledge. Reality remains as it is, and it is taken back into philosophy through an essentially Christian reconciliation. No matter how one wants to relate Brandom’s diagram to Hegel, it represents the circularly composing and composed system of categories and concepts (objects and relations) as the basic form of philosophy, which Laruelle finally identifies with the digital – one divides into two – or with the fraction 1/2, the systematic unity of a dualism, whose prime example is the transcendental-empirical duplicate. 4
This criticism of Hegel is now a commonplace in continental philosophy. As early as the mid-20th century, a posthegelian and postkantian philosophy was formed around authors such as Badiou, Derrida and Levinas, which with its critique of dialectics relies on concepts such as event, the finally real, the other, etc., i.e., continues critique by means of the stratagems of supplement or adjunction. (Cf. Gangle 2013: 51f.) These theories all operate with a structure of philosophy that Laruelle designates with the fraction 3/2. Difference philosophy continues to insist on duality, which, however, is interrupted and puttied again by a supposedly third term (real, event, other). Distinguished from the 1/2 system of the empirical-transcendental doublet, the 3/2 system formulates the more complex doublet of the transcendental and the real.
The unity and symmetry of the dialectical model, which contains a two-tiered circle, stands in a certain contrast to the recourse to an external third term, which seems to be beyond philosophical sufficiency. Laruelle nevertheless wants to use the methods of non-philosophy to show a constitutive relationship between dialectic and philosophy of difference. Both models should be superimposed, so that it can be shown how both philosophies mutually fertilise and develop each other by partout not ceasing to end their mutual alternation. This mediating function is carried out in contemporary continental philosophy with the help of the figure of open chiasm. For Jean Luc Nancy and Catherine Malabou, Hegel’s absolute knowledge is completely misinterpreted if one does not simultaneously think of closure as openness to difference. In Alan Badiou or Jacques Derrída, however different their philosophical conceptions may be, we find a philosophical sufficiency of the second order, an undecidable oscillation between auto-sufficiency and hetero-supplementation.
The problem of meta-difference, the difference of differences, is only briefly presented here. If two terms A and B are given, which represent concepts, objects etc., then the difference itself (between A and B) is represented by A/B. The structure of the meta-difference now shows the following: The difference in itself between the two terms (the complex term A/B) is distinguished from one of the two terms (A) (which it already includes) and is identified with the other term (B). For the term B in the relation, the entire expression A/B is substituted, so that the difference (A/B) is different from the term A. The term A is then identified with the other term (B). The result can then be written down as follows: A/(A/B). Here term B remains relatively unanalyzed, or to put it another way, the process remains undecidable and leads to the bad infinity of A-B= A/(A/(A/B)). We are faced with the problem of self-inclusion, i.e. a one-sided doubling of difference, which itself is one of the terms. (ibid.)
The difference thus takes itself as its object and transcends at the same time its own Objectification. This can be described not only as meta-difference, but also as meta-relation: A-B. So what happens if one of the terms of the relation is the relation itself? One takes the relation A-B for the term B, substitutes it with B and gets the expression: A-(A-B). But what happens if the fixed term A also iterates? Then we get not only A=A/B, but also B=A/B (A ≠ B). (ibid.) We are obviously in a conflict here insofar as each of the two terms is the difference and the conflict itself. And nothing else represents the figure of thought of Chiasmus. Ultimately this means that the philosophy of difference cannot endure a real non-relation. On the one hand there is the tendency in difference philosophy to maximize differences (Nietzsche), insofar as difference promises a superiority that can be driven to infinity, on the other hand difference can also remain relatively obscure in order to lead to an original reason that is tautology (not nothing). With Nietzsche it can be asserted that the properties of a thing are only effects for other things. If one now eliminates the term “other thing”, then a thing has no properties at all, and the conclusion is that there is definitely no thing without other things, i. e. the relations absolutely dominate. In other words, the thinginess dissolves into the stream of differential events. Instead, the objective particularity of the relativity must be thought of as dependent on the real, from a non-objective transcendence that divides each relativity into two formally distinct sides, one side being assigned to the uncovering and concealment of the being of the existing, and the other side to the object that is indifferent to the other side. At this point, an essential and tautological subtraction in itself (the essence of being) is for the Kantian “thing in itself”. According to Derrida, Laruelle, on the other hand, carries out a complex mixture or chiasm of the Nietzschean and ianian models: He formulates the meta-difference between the two models. Difference, according to Laruelle’s summarizing critique, is a philosophical syntax sui generis and a reality or an experience of the real (cf. Laruelle 2010a: 2) and thus a principle that is to be assessed more real than formal and more transcendental than logical. Difference articulates in the representational mode a mixture as such by demanding “neither… nor”, and at the same time a kind of inclusive disjunction with which “neither… nor” is so minimally negative that it produces indivisibility as one (nothing as being).5
For Laruelle, both dialectic and philosophy of difference, both of which can be represented by diagrams, are correlative tendencies that are always present in philosophy and are weighted differently according to need and situation. It is the undecidable conjunction/disjunction of the two duplicates themselves – transcendental-empirical or transcendental-real – that characterizes philosophy at its most general level. Philosophy is thus neither completely sufficient nor completely insufficient, but it constantly enlivens its own semi-system of sufficiency/insufficiency, which presupposes and repeats itself by simultaneously criticizing and maintaining undecidability. For Laruelle, this instability follows from the warlike nature of philosophy.
1 In the history of philosophy, the real has been discussed a) as independence and b) as authenticity. It is independent, whether someone perceives it or not, thinks about it or translates it into a language related to a referent. This refers to the a priori transcendence of the real with respect to any ideality, a relative transcendence that Laruelle designates as the still attractive distinction between philosophical syntax and reality. Authenticity, on the other hand, permits certain gradations of reality, because the real can now be a more or less existing thing according to its essence, i.e. the essence itself is still gradual. Authenticity and independence are always understood in philosophy as qualifications of what exists.
2 The oraxiom (the combination of axiom and oracle) indicates the superposition of the mathematical axiom and the non-philosophical decision. The “axioms” of non-philosophy or generic science, and in particular DLI, conjugate two types of decision – the mathematical one to produce a formal field structure, and the non-philosophical one, i.e. the undecidable decision. The or axiom is radically immanent. Further nuances of the oraxiom such as cryptic, enigmati, the abyssal or the groundless, the delirious, etc. belong to philo-fiction and should be transformed according to the same conditions. The future is what is demanded and performed par excellence qua Oraxiom.
3 Axioms and theorems form the most important elements of Laruelles Method, cf. Laruelle 2012: 45ff.
4 What is given is divided, that is Hegel’s true principle. Hegel in some way uses both the digital (the One, divided into Two) and the analog (Two, synthesized in One) as elements of his dialectic: the moment of analysis in which the One is divided into Two, and the moment of synthesis in which the Two are combined in One. With synthesis, Hegel finally wants to overcome alienation. There are contradictions, but they must be reintegrated into the big whole, the absolute spirit.
5 Laruelle thinks against these different forms of difference the One, but possibly ends up introducing a fundamental logic himself again, according to one critique, and thus he only repeats the problems he is currently criticizing. The non-notion of “chora” may be an interface between Derrida and Laruelle. While for the former it is the last name of what is not, namely différance, for the latter it is the first name for what is expressed axiomatically.
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Translated with www.DeepL.com/Translator
Foto: Bernhard Weber