The concept of immanence is ultimately very simple, yet it proves very difficult to accept in its implications. To affirm immanence is to affirm that the world is sufficient unto itself, that we need not refer to anything outside of the world to explain the world such as forms, essences, or God, that the world contains its own principles of genesis. As Laplace responded to Napoleon when asked about the role of God in the new physics, “Je n’ai pas besoin de cette hypothèse”. “I have no need of this hypothesis.” What could be more beautiful and affirmative than this simple quip? To affirm immanence is to affirm the world as it gives itself and to deny any transcendent terms that might shackle the world to what a putrifying and decaying subject believes the world ought to be. Those who affirm immanence affirm the existent and its potentialities.

The immediate corollary of immanence is the consequence that “the whole is not” or that there is no whole. This is an ontological rather than epistemological thesis. Suppose we claim that the whole is. What are the conditions under which the whole would be possible? In order that there be a whole, it would be necessary that there be some point outside the whole through which the whole could be surveyed like an astronaut might survey the planet earth. But such a point of survey would be transcendent to the whole or world. Yet we have already affirmed that the world is immanent. Therefore such a point of transcendence does not exist.

Such is the rejoinder to Descartes’ proof for the existence of God.

It is not clear that we can demonstrate that the world is immanent. Rather, immanence is a thesis that can only be declared and followed through, as rigorously as possible, in its consequences. Perhaps the closest we come to a demonstration that the whole is not is to be found in Badiou’s appropriation of Cantor’s paradox. Cantor’s paradox states that there cannot be a set of all sets because the axiom of the power set stipulates that the subset of a set is always “greater” than the initial set from which we begin. Suppose we take a set a composed of elements {x, y, z}. The power-set of a would consist of the set of all subsets of a or {{x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}, {0}}. That is, the power-set of a is a to the 3rd power, just as the power set of the power set of a would be P(a) to the 8th power. In short, the power-set or subset axiom leads to an infinite proliferation of being such that any totalization of a set can only be provisional.

As Badiou argues in Being and Event, the consequence that follows from the thesis that the whole is not is that being consists only of situations without any global, overarching situation (contra any holistic conception of being such as we find in Hegel or Whitehead). That is, it follows as a consequence that all logics are local. Despite Badiou’s mutilated reading of Deleuze in Deleuze: The Clamor of Being, where Badiou contends that Deleuze is a thinker of the One-All, the thesis of the primacy of situations, of the locality of being, had already been affirmed by Deleuze in his account of incompossible worlds (in contrast to Leibniz’ thesis that all modes are compossible or that this is the best of all possible worlds) and divergent series.

It is sometimes suggested that Deleuze rejects logic, but this thesis is poorly understood so long as we are unclear as to what Deleuze is rejecting in rejecting logic. If Deleuze rejects logic– and here I am skeptical as I have not found such passages in his work –then what Deleuze rejects is not logics, but rather logic, the law of identity and non-contradiction, as the normative measure of situations or worlds. Here, I think, Badiou expresses the issue with the greatest clarity. If Logic is to be reject (I capitalize the term to denote logic as a norm governing all situations), then this is because the thesis of a logos governing all situations returns us to the standpoint of transcendence requiring a point of survey outside the world (thereby undermining immanence). However, the rejection of Logic does not entail the rejection of logics. It is this move that motivates Badiou’s recent turn to category theory in Logiques des mondes. As Badiou describes it in Briefings on Existence: A Short Treatise on Transitory Ontology, “What topos theory offers is a description of possible mathematical universes. Its method employs definitions and schemas, and a geometric synopsis of its resources. It is tantamount to an inspection of Leibniz’s God: a categorical journey through thinkable worlds, their kinds and distinctive features. It ascertains that each universe bear its own internal logic. The theory establishes the general correlations between ontological features of these universes and the characterization of their logic. But it does not decide on a particular universe. Unlike Leibniz’s God, we do not have any reason to consider some such mathematical universe as the best of all possible universes” (Badiou 2006, 119). In short, what topos theory or category theory offers is a way of mapping the internal or immanent logic (logos) of a situation, or of describing the structure, system, or norms that govern the situation itself, rather than binding a situation to a norm extrinsic to that situation.

Like so much of the “dialogue” between Deleuze and Badiou, it appears that we here encounter a productive mis-communication. Had not Deleuze already discovered the idea of topoi in his account of virtual multiplicities, where he seeks to unfold and elaborate the organization immanent to a particular actualization? It is sometimes suggested that Deleuze rejects all order, that he is the thinker of chaos, but to my thinking it seems much more productive to conceive Deleuze as the thinker of how order emerges out of chaos, of how being generates its own or orders out of the infinite differences composing being. Take, for instance, Deleuze’s analysis of Francis Bacon in Francis Bacon: The Logic of Sensation. If there is a distinguishing feature of Deleuze’s aesthetic studies, it is the manner in which he approaches these works immanently in terms of their own internal organization, topos, or logic. And if we look to mathematics, to Riemann and topology from which Deleuze draws his inspiration in formulating the concept of multiplicity, what do we discover if not the thesis that a topological space or multiplicity is studied in terms of its own intrinsic organization rather than the manner in which it relates to its embedding space. The analysis of virtual multiplicities is the analysis of topoi.

Despite the joyous and affirmative nature of the concept of immanence (both as a thesis about the world and about situations) there is nonetheless a horror of immanence that even the greatest champions of immanence experience. If immanence is horrifying, then this is because it undermines our ability to refer to a transcendent standard or order that would tell us how to be, how to think, how to desire, and so on. That is, the affirmation of immanence is also the affirmation that “the Other does not exist” (that there is no transcendent rule or standard), or that “there is no Other of the Other” (that there is no point of view from the outside), or that “there is no metalanguage”.

In a very fine “B” science fiction film entitled “Cube” and directed by Vincenzo Natali, we are confronted precisely with the thesis that the Other does not exist, that there is no Other of the Other, and that there is no metalanguage. The film “Cube” depicts a story in which seven people one day awake in an enormous metallic maze that they must traverse using their knowledge of mathematics. If they are unable to decipher the mathematical riddle underlying the relationship from one room of the cube to another, they die a horrible death by taking the wrong path. As the film progresses we learn that each person has worked on the project of constructing this maze, yet we also discover that the maze was not created for any particular purpose or with the guidance of any single leader, but rather emerged out of the blind collaboration of a series of bureaucratic government agencies each trying to spend their budgets, without anyone envisioning a project such as the cube in which the seven characters are trapped. Fortunately the characters manage to unlock the mathematical riddle of the maze and escape. Yet upon escaping they discover that the maze they just escaped is a part of a larger maze with a new logic all its own.

The film “Cube” provides one of the finest depictions of Lacan’s thesis that the Other does not exist and of the Deleuzian affirmation of immanence that we find in perhaps all of cinema. On the one hand, the film depicts the claims that there is no metalanguage and that there is no Other of the Other in that there is no one code that governs these mazes and that there is no point of view outside the bureaucracy overseeing the creation of these mazes. On the other hand, the film depicts the thesis that the Other does not exist insofar as it undermines the phantasy that there’s a position we could adopt outside our situation that would finally allow us to completely understand the situation or see what is common to all situations.

The practice of analysis affords one of the most direct and anxiety provoking encounters with immanence and the non-existence of the Other to be found. If transference and traversing the phantasy mean anything, they mean 1) the belief that there is some ultimate standard we can refer to in defining who we are, how we should live, what we should desire, and what is wrong with us, and 2) coming to discover that we are our own immanent topoi such that there is no ultimate law or logic we can refer to in defining our being and desire. As a Lacanian I am approached by a very particular group of people, who are already sophisticated in their knowledge of “theory”, in generally adopting a leftist and postmodern politics, and who already affirm immanence. Yet strangely, in my practice, the first thing I discover among these analysands is that they wish for me to tell them who they are and whether they are living their lives in the right way. That is, they transferentially refer to me as the Other who has the answers and who is capable of measuring them and guiding them in their lives. My job, as analyst, is to refuse this position of mastery, this position of insight into God, and to perpetually be where I am not expected, so that they might increasingly come to discover that there is no overarching Law or order by which they might measure themselves, but only the immanent topoi by which their own internal logic unfolds. As the second film in the “Matrix” series claims, the point is not to make a choice, but rather to understand why we made the choice that we already made.

My question, then, is not simply that of how we might assert immanence, but rather how we might affirm all of the anxiety provoking consequences that follow from our assertion of immanence, or the manner in which we come to be cast adrift in the ocean of immanence, without any ultimate compass. Or yet again, how we can endure affirming difference, divergence, and incompossibility so as to find a little order in the world and no longer look to authority, the father, or God as the guarantee of our being.