DELEUZE AND THE INFINITE: pluralism, immanence, the absolute, subjectivation

In my philosophical writing (readily available here on my blog AGENT SWARM and on my page) I discuss the ideas of a number of contemporary thinkers who work in the domain of epistemological and ontological pluralism. My analyses are based on the idea that one can better understand a philosophy by considering it not in isolation as a closed static system, but as a research programme evolving in the context of other programmes of the same type, and in (explicit or implicit) dialogue with them. I employ this expression of “research programme” in the wide sense that Karl Popper gives it in the Metaphysical Epilogue to the third volume of The Postscript to the Logic of Scientific Discovery. In Popper’s account a “metaphysical research programme” is a general conceptual framework comprising both non-testable speculative elements and testable empirical elements..

The theoretical projects which interest me are all « pluralist », in the sense that they escape the hegemony of the One, and give speculative priority to the multiple. In my work I seek to analyse these projects, to compare them, and to put them in conversation with each other in terms of a set of shared criteria.

In particular, one can examine a pluralist research programme in terms of its pluralism, its relation to the infinite, its relation to an Absolute, its testability, as well as its type and degree of immanence. Concerning the first mentioned criterion, that of pluralism, both Badiou’s and Deleuze’s metaphysical research programmes are based on a very general hypothesis that expresses their commitment to pluralist thought. This hypothesis can be formulated as follows:

Hypothesis1 – it is possible to speak in a meaningful and illuminating manner about our world and our lives in terms of the multiple outside the primacy of the One.

This pluralist hypothesis is shared not only by Deleuze and Guattari and Badiou but also by Lyotard, Derrida, and (in Deleuze’s reading) Foucault. According to these authors pluralist language allows us both to speak of our existential possibilities and to remain conceptually precise.

For Deleuze and Guattari in WHAT IS PHILOSOPHY? and for Badiou in THE IMMANENCE OF TRUTHS the principal mode of operation of contemporary oppression is to enclose us in the figure of relativism. Both works are written in opposition the contemporary “postmodern” ideology of democratic relativism. Contrary to postmodern appropriations of their work, there is an Absolute for Deleuze and Guattari, a One-All, that subtends and sustains the non-philosophical sensibility that we must maintain with regard to our concepts to avoid them falling into abstractions: “In any event, philosophy posits as pre-philosophical, or even as non-philosophical, the power of a One-All like a moving desert that concepts come to populate” (40-41). This Absolute is the guiding awareness in the Introduction, where Deleuze and Guattari move easily between philosophy, art, and science, before descending into the distinctions and demarcations that constitute the bulk of the book, and that are relativised in the conclusion. This can be formulated as a second, more specific hypothesis:

Hypothesis 2 – it is possible to speak in a meaningful and illuminating manner about our world and our lives in terms of an absolute horizon outside the relativity of language games and forms of life.

This hypothesis of an absolute is a part of these thinkers’ realism, and crystallises their rejection of postmodern democratic relativism. In its place they elaborate, each in their own way, a pluralist realism.

In this section I will compare the different types of infinity described and analyzed by Badiou with Deleuze and Guattari’s treatment of this theme in WHAT IS PHILOSOPHY? Both Badiou’s and Deleuze’s metaphysical research programmes are based on a third hypothesis that expresses their commitment to pluralist thought in its relation to a language of the infinite:

Hypothesis 3 – it is possible to speak in a meaningful and illuminating manner about our world and our lives in terms of a language of the infinite.

The infinite plays an important role in Deleuze’s thought, but it has not been the object of much discussion. Badiou’s set theoretic conceptual creations can provide us with a useful point of comparison. Contrary to Badiou, Deleuze does not make use of set theory, but prefers an intuitive and qualitative approach to the infinite. Despite this difference, there are important points of convergence between the two theoretical projects. In particular, Deleuze and Guattari’s WHAT IS PHILOSOPHY? is to a large extent occupied with the ontology of infinity.

In French the book contains 168 occurrences of the word “infinite”. If we add to this the book’s various synonyms for the infinite (”absolute”, “horizon”, “plan of immanence”, “outside”, “chaos”), we attain 540 explicit occurrences of the concept of the infinite in a book of only 200 pages. These words for the concept of infinity are to be found on nearly every page, often in multiple occurrences. Thus, contrary to a popular image of Deleuze as the thinker of becomings, the final word of Deleuze’s thought is not becoming, but the infinite.

In his “Immanence of Truths” project Badiou, following the contemporary mathematics of infinite sets, distinguishes four types of infinite, two defined in negative terms and two in positive terms:

(1) inaccessible infinites (2) compact infinites – infinites by resistance to division or partition (3) infinites by immanent power and (4) infinites by increasing proximity to the absolute.

Similarly, in Deleuze’s work (in particular in WHAT IS PHILOSOPHY? and FOUCAULT) we can find four concepts of the infinite that correspond approximately to Badiou’s list:

(1) inaccessible outside – the outside further than any exteriority

(2) resistance to stratification and segmentation – resistance is prior to power

(3) immanent affirmative outside – composed of distributions of powers, affects, singularities, and intensities

(4) increasing proximity to the “absolute horizon” – approaching the non-totalisable plane of immanence, by way of absolute deterritorialisation.

On the one hand one could argue from a Badiousian perspective that Deleuze’s concepts of infinity are too qualitative, too vague and imprecise, and that lacking mathematical formalisation they remain too intuitive and insufficiently theorised, staying too close to the “poetic” end of the spectrum.

On the other hand one could invert the arrow of comparison and argue from a Deleuzian point of view that Badiou’s concepts, which are based on the mathematical hierarchy of infinite cardinals, are insufficiently philosophical. While still “poetic” they are much closer to the mathematical (referential) end of the spectrum, and so represent a slowing down of the plane of consistency, belonging rather to the plane of reference.

However, Badiou could always retort that this Deleuzian critical term of “slowing down” is itself intuitive, qualitative and poetic.

Despite the fact that WHAT IS PHILOSOPHY? Is the book where Deleuze and Guattari speak the most about the infinite, we can observe a lack of clarity in their use of this word, compared to Badiou’s extreme precision. In this sense we could affirm that Deleuze’s work lacks the equivalent of the central, mathematical, part of Badiou’s THE IMMANENCE OF TRUTHS. Without this equivalent, the different terms of Deleuze’s philosophy that serve to designate the infinite (the outside, primary resistance, the plane of immanence, and the absolute horizon) tend to run together and become indistinguishable.

The question of testability is a crucial problem for a philosophy that claims to be more than an academic exercise and to talk about our concrete lives, both individual and collective. Despite his talking in terms of “hypotheses” (e.g. the communist hypothesis) Badiou often uses situations and experiences taken from the empirical world seemingly merely as a source of examples and illustrations, not of tests. However, his placing his philosophy under the condition of the truth procedures is a way of guaranteeing its indirect testability.

This conception of philosophy as submitted to conditions redefines the role of examples in Badiou’s text. Direct empirical tests are not the only possible form of validation. Badiou can consider that his configuration of a space of compossibility for the four truth procedures that are themselves testable is “test enough”. Badiou’s method of verifying a hypothesis proposed initially with reference to one truth procedure by searching for confirming examples in each of the other truth procedures insures a high degree of indirect testability.

It may be that Badiou in following this method considers that the network of correspondences he finds between the productions of different truth procedures is test enough. Privileging “Truths” over “facts” can be seen as the application of a hypothetico-deductive method (as against an inductive method).

The problem is not that of Badiou’s proceeding hypothetico-deductively (how could that be a problem?) but of whether Badiou makes use of this method to stimulate critical discussion or to close it off. Badiou’s books on theoretical rivals, such as Deleuze and Heidegger, have shown that he is capable of opening a discussion where previously it seemed impossible.

Contrary to Badiou, Deleuze and Guattari explicitly state that “science renounces the infinite”, which is left to philosophy. This renunciation (which can be extended to art, in the terms of WHAT IS PHILOSOPHY?) leads by way of the absolutisation of philosophy to a relativisation or finitisation of science and art. Thus in Deleuze and Guattari’s final system philosophical concepts are non-referential, so that direct testing is not possible. Moreover art and science exist on different planes to philosophy’s plane of consistence, and so cannot provide its concepts with indirect testability.

Thus we must see in Deleuze’s idea of the infinite an ambiguity concerning the immanence of the infinite. Deleuze reserves the infinite for philosophy, and affirms that “science renounces the infinite”. Implicitly the lesson, of renouncing the infinite, is the same for art. thus Deleuze finitises science and art, he relativises them, he cuts them off from the infinite. There follows from this absolutisation of philosophy to the detriment of science and art a lack of testability of Deleuze’s later philosophy, compared to the testability that the truth procedures provide for Badiou.

From this relative lack of testability there results the proximity of Deleuze’s pluralism to democratic relativism. The danger that haunts his thought is the fall into relativism. Deleuze attempts to protect his thought from this danger with the Idea of the infinite, but this idea is vague, abstract and confused, due to its lack of formal precision.

Consequently, Deleuze’s concept of the infinite is potentially too weak to protect his pluralism from the threat of relativism and to guarantee the freedom necessary to be able to create.

In contrast, Badiou infinitises and absolutises science, art, love, and politics. However, despite their divergences there is a commonality to their thought: the Idea of the infinite as a means of protection against relativism, and also as a resource for emancipatory creation. Nonetheless, we feel that there exists inside us something deeper that is in relation to the infinite, and that Deleuze and Badiou respond to this feeling.

This feeling of something deeper which subtends the common ground between Deleuze and Badiou concerns the subjectivation of the infinite. What is the use of comparing disjointed, divergent thoughts, such as those of Deleuze and Badiou? What is important for us is not such and such an author but the encounter of the infinite intensities that are incommensurable with our mental and social constructions. Without an irreducible infinite the multiplicities and becomings, even enormous and dynamic, constitute impasses. Therefore, we must seek a primary infinite, we must speak the language of infinities.

However, it is not only a question of language. We need to resort to the infinite to respond to a blocked situation, where even the death of God (of the One) has not liberated us. In our everyday lives, we are still enclosed in finitude, only covered over by a supplementary layer of false infinity that redoubles and reinforces the blockage. The whole is submitted to the quasi-transcendence of the inaccessible infinite of Capital. That is our actuality. Against the hegemony of democratic relativism, Deleuze and Badiou reply that we are capable of experiences of more or less greater proximity to the absolute, but that under the conditions of finitude, under the reign of democratic relativism, we do not know that this capacity exists.

Badiou’s final evaluation of Deleuze’s solution is that it is torn between the absolutism of philosophy and of its great inorganic life close to chaos on the one hand, and on the other the relativism of bodies and languages. From Badiou’s perspective, Deleuze’s absolute, or plane of immanence is too fragile, as Deleuze’s idea of the infinite is too vague, through lack of formalisation.

Finally, Deleuze’s subjectivation is too empirical, one must not begin by subjectivating. Subjectivation comes after formalisation. Badiou’s solution is to begin with a formal elaboration of the dialectic between finite and infinite in mathematical terms. His maxim is: formalise first and only then subjectivate. However, Deleuze considers that modes of subjectivation, as another name for deterritorialisation, are primary. His maxim is: first subjectivate, then formalise.

The concrete conditions for subjectivation, or subjective appropriation, exist, they are the object and the stake of all living philosophy. According to both Deleuze and Badiou, infinite subjective intensities reside in reserve in the unconscious, both as an immanent infinite resource of energy and concepts and also as an inchoate perception, informed by the Absolute, of new possibilities of which one is as yet unaware that one is capable. One can always, within the wanderings of a life lived without an Idea, fall by chance on an infinite intensity incommensurable with our conscious expectations. However, in this case it is improbable that we recognise the new intensity if we don’t already have within us the idea of such an infinity. This is the paradox of Plato’s MENO. We must already have the idea of the infinites within us, as immanent intensities, in order to perceive the infinities we encounter in the world.

Badiou agrees with Deleuze in positing the primacy of « deterritorialisation », which according to Deleuze, and despite its negative prefix, “comes first”. According to Deleuze, if there is no absolute deterritorialisation we are condemned to the relativism of assemblages of bodies and languages, and at best to relative deterritorialisation. On this relativist hypothesis, against oppression we are limited to mere resistance (a reactive, negative, and relative concept) instead of being able to accede to creation (an active, affirmative and « absolute » concept). Badiou et Deleuze want more than to resist finitude, they want to create something that partakes of the absolute, and to accomplish this each relies on the concept of the infinite.

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