Lecture: Flesch: Fiction and Evolutionary Biology

NCTU Graduate Practical Philosophy

Comeuppance

Billy Flesch

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This book is the most complex and ambitious attempt I know of to try to reconcile contemporary claims of evolutionary theory with the often august claims for literature (and art in general, and by implication culture in general, although Flesch remains focused on literature in its narrative aspect).



Classically, the greatest account of the existence of literature, narrative, and art in general is Aristotle’s Poetics, from which nearly all thinking about literature and art derived for several centuries (up through Freud and Stephen Pinker). In that account Aristotle simply takes as a natural given that human beings take pleasure in the representation of reality—any reality, even terrible reality like cadavers—because it is by imitating that we humans learn anything at all, and learning for Aristotle is always pleasant. Tragedy, especially the tragedy of Oedipus which is Aristotle’s supreme exemplar, is no different. We enjoy the play because it is, firstly, a representation, and the particular intensity of our enjoyment for tragedy revolves around two specific emotions: pity and terror. In some notoriously dense passages, Aristotle specifies the tragic effect on the audience as the “purgation” of these two emotions. But he does not clarify this, and there is an enormous body of literary criticism devoted to trying to understand what Aristotle meant. I will only note this: the two emotions move in contrary directions, but each produces the same pragmatic effect. In terror we tend toward stiffening and freezing; in pity we tend to weaken and melt. It may be implied that for Aristotle all our emotions tend toward one of these two poles which appear opposed to each other but which have something in common. In each case our will to do or perform some act (including rational thought) is temporarily incapacitated; we are impotent. The “purgation” of these emotions would then be salubrious; we would be purified of our natural tendency toward becoming incapacitated in cases of strong emotion, thus reuniting our mental life with our natural faculties to do and to think. It is a sort of intellectual ritual. This would be one possible explanation of what Aristotle was thinking.



In light of modern evolutionary theory, the ultimate claims of Aristotle seem to have been abandoned or would need to be greatly modified. It remains to be explained in contemporary terms why we take such intense pleasure in narratives, in representations, in non-actualities like fictions. In the Introduction Flesch rejects two possible evolutionary theories as not fully explicatory of literary experience and adopts a third. He rejects what he calls (following S.J. Gould) “Darwinian fundamentalism” in which the leading character is the gene (2-5) which whishes to reproduce its form, or its information. The thinking which underlies this view is Hobbesian: at the genetic level there is a “genetic war of gene against gene”. We ourselves (as individuals or as groups) are minor characters who remain servants of our genes and act, in the last instance, on their behalf. Within this line of thinking there can be no genuine altruism; what may seem to be self-sacrifice at one level (of the person for his or her kin) is actually selfishness at the level of the gene (or of its information). This view has been attractive for some time since there seemed to be no evolutionary account for the existence of genuine altruism. Darwin himself, however, tried to account for survival at the level of the group and tried to show that groups who include altruists tend to survive better (again, as a group) than groups that do not. But this line of thinking could not be sustained since the group would be too porous and vulnerable to non-altruists to insure that the group would survive over and above either the individual or the gene. The third theoretical approach—provided in this book by combining the works of Frank, Sober and Wilson, Fehr, Miller, and the Zahavis—does bear out the possibility of genuine altruism, cooperation, and costly signaling which for Flesch are “central to our understanding of the human capacity for and delight in narrative” (5). This last group of biologists does not specify the basic unit of survival—the gene, the individual, the group, or whatever—because the focus is on cooperation among the units. Flesch does not deny that a capacity may be adaptively useful (a capacity for altruism, for example), but he says that this does not necessarily explain why it evolved in the first place (2). Flesch’s account of literature in general departs from the Aristotelian view; for Flesch: “An innate capacity for and tendency toward altruistic punishment seems to me the central human psychological phenomenon in one aspect of our interest in narrative: our desire to see the good rewarded and the evil punished, whether they exist or not.” Oedipus the King would then be a test case for Flesch, which he does not explicitly take up. How might the Flesh model explain the play by Sophocles since Oedipus is both good (he saves the city) and evil (he has killed his father and married his mother); both innocent (he killed and married in ignorance of his true identity) and guilty (he in fact did kill a relative and commit incest); and both punisher and punished on one individual (he gouges out his own eyes)?



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Beginning at Chapter 1, Flesch again rejects what I will call the “strong utilitarian” view which I think characterizes Dan’s presentation last week: that we are attentive to fictional narrations in order to “practice for the game of life” (8) as is argued both by Samuel Johnson and A.D. Nuttall. In each case, the literary experience is practice for how we would or could respond if we were in similar circumstances. We learn from our attentiveness to fictions. Flesch works at the level of the actual: why do we actually feel anxiety, grief, rage, embarrassment, etc. on behalf of or in response to what happens to characters which we know to be fictional, which we know very well could not actually be happening (because we are staring at a piece of paper, or at a screen)? And he reverses the logic: We are able to learn at all because of the dramatic illusion and our capacity to be impressed by—delighted by—the non-actual. Johnson, Nuttall, and also Sugiyama explain how literature instructs, but not how it enthralls (8-9). For Flesch the delight precedes, explains and is indispensable for the learning. While Flesch accepts that fiction may function as pedagogical, he objects that this does not fully explain the demand readers may have for solutions to anxious narrated problems that are improbable or magical and thus counterproductive to what we would, could, or should do in a similar situation. Flesch is arguing that there is an evolution of anxious attentiveness that cannot be reduced to sheer pedagogy (but that is necessary for any pedagogy to occur).



Flesch then considers the possibility that we attend so closely to narratives as part of an innate need to known whom to trust and so exercise our ability to sort out trustworthy information from untrustworthy information. But he again claims that this cannot explain the specificity of fictional enthrallment: “It may be beneficial to know whether we can trust someone, but it doesn’t help to know whether we can trust Roger Thornton or Eve Kendall (or Cary Grant or Eva Marie Saint)” (11). Further, why would the exercise, if it were purely pedagogical, be so passionate—as is literary passion? Would we not be better learners if we were to learn dispassionately? He goes on to consider the question of Freudian identification, as Dan dealt with last week. This too cannot adequately explain literary passion.



All these possible explanations rest on the Aristotelian notion that we are innately interested in representations per se through an emotional economy that hinges on pleasure/pedagogy. But this only gets us back to the original question: why should we care about the representations themselves (and not what or who—not the reality—they more or less refer to, or may possibly, in the future, refer to)? From Plato to Aristotle to Freud to Stephen Pinker the pleasure the audience (the end-user, the consumer) takes in the imitation of reality is the key. But this is too broad a conceptualization—it explains all imitations of reality. Flesch wants to shift to a different framework to get at especially fictional or narrated representations. The framework is the evolution of cooperation (13 ff). He is going to pursue his argument at a level that conceptually precedes imitation/identification: “tracking or monitoring the agent or thing to be imitated […] We humans are so good at learning because we’re so good at imitating others and we’re so good at imitating because we’re good at tracking” (17). Flesch is aiming to show that tracking (or monitoring or simply following, as we following a plot unfold) is weaker than but may explain more than the stronger notions of imitation (including its strongest form, identification). Tracking is immediate; imitation, identification, and pleasure derive from it. The capacity for tracking leads to “attitudes towards fictional as well as real people” which is part of a process by which we, in Strawson’s words “recover from the facts as we know them a sense of what they mean, i.e. of what we all mean, when, speaking the language of morals, we speak of desert, responsibility, guilt, condemnation, and justice” (21). This leads Flesch into altruistic punishment which forms the core of his non-Aristotelian views on fiction. He argues specifically “that we have explicitly evolved the ability and desire to track others and to learn their stories precisely in order to punish the guilty (and somewhat secondarily to reward the virtuous); we have specifically evolved an innate tendency toward what evolutionary theorists call ‘strong reciprocity’ [which means] that the strong reciprocator punishes and rewards others for their behavior toward any members of the social group and not just or primarily for their individual interactions with the reciprocator. Strong reciprocators mind everybody’s business, and in doing so […] they insure social cohesion” (21-22) [latter italics mine].



The capacity for tracking to the innate capacity for being “strong reciprocators” is still speculative evolutionary biology; there is no general and systematic account, Flesch admits (22) but such an account would explain the native capacity to become involved with business that is of no direct concern to us—which would include even business that cannot possibly be of any concern to us: fictional characters and their fates. This account will depend on the existence of true altruism, that is, altruism that would be irrational since the outcome of an agent’s act would not be what is optimally beneficial for that agent. Altruistic punishment (also irrational), Flesch says, “is the form of altruism most necessary for the maintenance of cooperation with a society made up largely of non-kin, that is, most human societies” (22). How does nature select for irrational altruism?



Flesch begins with the famous ‘Prisoner’s dilemma’ which begins what we might call a cultivation of irrationality such that long-term gain may be led to for a group. The prisoner’s dilemma game depends on the fact that others’ do have a disposition to act irrationally and that I know or believe that they can and may act irrationally and that others may count on me to act irrationally. The Prisoner’s dilemma raises the question of (irrational) social cooperation vs. genetic survival. From the gene’s point of view, defection in the Prisoner’s Dilemma game is the most advantageous. However, nature has made it pleasurable to cooperate, to be genuinely altruistic. Why has this pleasure evolved as it has for eating and reproduction (which fortify the survival of the genetic information)? Self-sacrifice on behalf of kin has been observed in social insects and can be inferred in humans where it would be genetically rational of me to sacrifice my own life (and genes) for two or more siblings, or eight or more first cousins, and so on. Apparent self-sacrifice on behalf of kin is not altruism at all, from the point of view of the genes. “In fact, so deeply ingrained is our tendency to make sacrifices on behalf of kin that we don’t need the incentive to do so. [It is] more of a reflex than a pleasure” (30). Kin altruism is thus deeply ingrained and does not require the “bait” of pleasure. However, this leads to the question as to where the “bait” of pleasure in non-kin altruistic behavior does arise from in forms of behavior that are more recent and harder to sustain. Flesch then moves on to another theory than accounts for apparently altruistic behavior which sees it a dual reciprocity (each side, when acting reciprocally, benefit) and then says that this explain a lot of human behavior but not all, and he appends a long footnote (214 n.45) in which he criticizes literary/philosophical critics of Pinker and Dawkins and the like for reducing human behavior strictly to maximized gene survivalism. The last quarter century has shown that genuine altruism (as counter to the individual’s (or gene’s) optimal strategy) indeed exists. He then discusses two cases (31 ff) in which a generalized sense of fairness, rather “trumps” an individual’s optimizing of personal success. Thus there is an expectation of the irrational which is direct, immediate, and not calculated. It is a form of vicariousness, or an irreducible sociality that precedes any calculation. We can go through these pages in detail if you wish (32-33).



If I understand these pages correctly, the games show that there is a deeply ingrained expectation of vicariousness for which I am willing even to deprive myself of rewards in order to signal to another that he or she is in violation of. I communicate my displeasure in a violator by spurning an offer I consider unfair (35). (An interesting point Flesch follows up on is that altruists like Gates, Buffett, Turner pay a lot in order to get the reputation for being altruists, and for taking pleasure in altruistic (35), since the cost of being known as altruistic is not rewarded with increased wealth.) Flesch then turns to the possible argument that altruistic punishment is actually a form of spite—that I intend to eliminate rivals as a way to increase my (or the genes in me) chances of survival, and hence is ultimately a selfish (or selfish gene) strategy. But the statistics don’t bear it out; altruistic behavior is differently motivated.



At this point we enter into the most tricky part of Flesch’s argument in which he will defend the view that we ourselves (a sociality not limited to kinship) and our genes enter into cooperation which is good for both “in the long run” (a phrase Flesch repeats several times through this lengthy and complex chapter). The underlying thinking derives from, not Hobbes, but David Hume on the issue of the co-compatibility of free will and selfish motivation. The point of the pages that end this section is that human behavior cannot be fully explained as a simple instantiation of genetic drive anymore than behavior can be fully explained by Freudian drive theory. Flesch goes so far as to say that those genes that cooperate with “us” stand, in the long run, to survive better than purely selfish genes—in short, even at the genetic level Flesch finds altruism: “We and our genes are partners in a Prisoner’s dilemma too” (42). Our genes provide us with the pleasures of vengeance, spite, and vanity, we like these behaviors even to the point of taking pleasure in anxiously anticipating them, a pleasure that literature recruits. This pleasure then becomes relatively independent and shows that we are not purely selfish (42-43).



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The argument then moves to the evolution of non-kinship cooperation. In these pages (45-52), based on the recursive models of Henrich and Boyd humans evolve n-orders of punishers not only of defectors (non-altruists) but of “second order defectors” or “second order free riders”: those who could altruistically punish but who do not (because of course it is costly to punish). Thus a society can be stabilized through n orders of trackers tracking other trackers tracking free riders and so on and so on. It is a kind of generalized policing. We have developed an incentive to monitor in the intensity of our emotional responses to non-actual wrongs, because punishment is always punishment for a past event in the present, and anticipation of vengeance is a present emotional state that looks forward to a future. We have evolved an extreme attentiveness to what has happened and what might happen later (i.e. whether what will happen is what should happen). A strong part of this emotional involvement is our tendency to have strong feelings of admiration for altruistic punishers and strong feelings of sympathy for victims.

This leads Flesch into the discussion of costly signaling which Dan covered very well last week and which further supports the theory of an evolution of cooperation. Relying on the work of the Zahavi’s and Grafen, the cooperation thesis is able to contradict Dawkins selfish gene thesis. Dawkins wanted to show the possibility of faking, lying, and cheating in signaling which would inevitably infiltrate any social system including kinship, destabilizing it and reasserting the primacy of purely genetic selection. One of his examples were the nestlings who signal their hunger with (ideally) proportional cries. Dawkins has to insist that some of them are cheating their siblings, but Grafen instead sees them as cooperating with their mothers by signally their surplus strength, not their hunger. (In a note (224-25 n.78) Dawkins has since acknowledged his error and has praised the work of the Zahavi’s in light of which his assumption that signalers will be inclined to manipulate signaling in order to cheat is being reassessed.) Much of the remainder of the chapter is a continual reminder of the genuineness of altruism as opposed to disguised hypocritical selfishness.



“To summarize this argument briefly: We admire altruists because they can afford to be altruists. We might admire any embodiment of genetic privilege and wealth, but we have survived because we have admired those embodiments of genetic fitness who have signaled their capacity through altruism rather than selfishness. Therefore an admiration for altruism has been selected for—an admiration that also has an altruistic component. But altruism could not sustain an evolutionarily stable system without the contribution of altruistic punishers to punish the free-riders who would flourish in a society of purely benevolent altruists. We therefore admire a certain kind of altruist—the altruistic punisher” (66).







Lastly, returning to the question of literary passion, Flesch rejects the identification/utilitarian model by which we develop and hone our emotional life so as to be ready for various contingencies of life. Instead Flesch adopts the arguments of Adam Smith and Hume of the later Enquiries. On this model we “volunteer” an affect for someone who cannot feel that affect. He returns to this in a later chapter (117 ff). The classic cases are the anxiety we feel for a man napping in a meadow while a cart is about to trample him. The anxiety we feel is not for what he is himself feeling—he is asleep—but for what he will feel if someone, or we ourselves, do not intervene. We may even volunteer an affect for another audience member who may seem emotionally dense. Or there is the poignant case cited by Smith of the mother who volunteers anxiety on behalf of her young child who is suffering from an ailment but who is yet incapable of the emotion of fear. The child merely responds to the present discomfort; the mother offers anxiety for the child’s future; what is more we ourselves, in reading this account, “volunteer sympathy for the mother, first because we are like her, whereas she is not like her child. The child doesn’t know how to be afraid, but we do, and we pity her grief for the child because we too pity the child. We also pity her, feel for her something like the way she feels—although not the way she feels for herself. Still we feel for her what she is not explicitly aware of feeling for herself: her helplessness and terror and misery and distress” (122).These are instances of vicarious—volunteered affect—in which all the principles participate naturally, cooperatively. The instance that clinches the case for Adam Smith is when we mourn the dead, that is, when we volunteer for another what it is impossible one should ever feel for oneself.

On the whole, the book is an argument for a non-restrictive, or generalized tracking and monitoring, generalized passionate volunteering of affect, and a generalized sense of fairness.

Lecture: Ranciere

NCTU Graduate Practical Philosophy

Jacques Rancière

Dis-agreement

(The French title is La Mésentente: Politique et philosophie which does not mean disagreement but misunderstanding. Disagreement implies that we are looking at a common object in a common way but come to different conclusions about it. Misunderstanding implies different or incommensurable regimes of discourse each of which posses different ‘objects’, or each of which conceives of a common object differently.)



Chapter 1: “The Beginning of Politics”



This book was published the same year as Agamben’s Homo Sacer and both books begin with the same passage from Aristotle’s Politics yet each derives a quite distinct new understanding of the political from the same beginning. Each finds in the same passage from Aristotle—a passage which is perhaps the most quoted of all Greek Philosophy—an obscurity. Rancière makes a nice phenomenological point right from the start around which the entire demonstration of the book revolves [1-2]: humans and animals both have a voice to indicate a particularity, a sensation (which is always empirical and singular) such as pain, hurt. This is the aisthêtic (from which we get the word aesthetics) which is singular. Kant was the philosopher who showed from this that there can be no science of the beautiful; aesthetics is always empirical and singular; it is always subjective but from which we derive judgments which claim universality (but cannot scientifically or methodically show universality). And what is this but the schema of politics, or the image of politics: the claim that this singularity of hurt is universally wrong, but there is no science of wrong. Ontologically dependent on aisthêsis are claims (logos or theoria) which are the general, the shared, perhaps the universal. The former are deictic (indicative: they point to something, call attention to something, while leaving the something relatively indeterminate), the latter are expressive of something shared. Ranciêre asks “where exactly do we draw the line between the unpleasant feeling of having received a blow and the feeling of having received an “injury” [in the sense of a “wrong”] through the same blow” unless there is a feeling of the difference itself? That other feeling—the feeling of the difference between the blow and the subject’s having been wronged—is a shared aisthêsis which defines the political: the sphere in which right and wrong are distinguishable from raw sensation. This is highly paradoxical since aisthêsis is classically understood as singular. The notion of a “shared aisthêsis” is, like his notion of the “sentence-image” confounding. It is a “mediation of opposites” [3] and this “mediation of opposites” is politics (and also Kantian aesthetics). Rancière is describing a threshold between the singular event and the generally expressible; the threshold where the phenomenological becomes political. The fate of this “shared aisthêsis” is the fate of the political as such.



The feelings pleasant/unpleasant are relative and subjective; the feeling just/unjust is felt as objective and common; likewise the difference between the two, the “line” that articulates the two is felt as common. Utilitarian political philosophy tends to obliterate or dis-articualte the difference by placing weight on the teleology of a common good that is immanent to the feeling of harm, wrong, or injustice and the goal of a state is simply to maximize or optimize the useful while reducing the harmful. Hence no line need be drawn; the specifically political never appears as such. In practical terms, the optimized utilitarianism of a state is as commonly as good as is realistically possible; it would be virtually on a par with an Ideal Good. The useful is on a par with the just. But there is still no clear logical connection between the two. Rancière examines the terms employed by both Plato and Aristotle in their obliteration of the political: sumpheron and blaberon.



Blaberon connotes the actual damage suffered by an individual at the hands of another individual. In this way the feeling of having been wronged and the feeling of the difference between pleasant/unpleasant—just/unjust would remain in play. Sumpheron, on the other hand connotes a relationship to oneself, as in the utilitarian state where the state relates only to itself in maximizing its own common utility. The two terms are heterogenous, not opposites. It is possible to conceive of the state as a reciprocal zero-sum game, as does Thrasymachus [4]. The loss of one party is compensated for by the gain of another party, thus the two zero each other out, a common harm never appears, and the state is as it were Good by default. The goal of such a state is the parceling out of rights and wrongs; the just is deduced from, or is a consequence of, the partitioning of rights and wrongs among individuals. At the individual level, it is an arithmetic; what remains then is the common and proportional parceling out of advantages and disadvantages across the state as a whole: a geometry of “parts” or axiaï, from which a distribution of advantages is based upon what each “part” contributes to a community.



There are three parts in Aristotle: the oligarchy of the rich, the aristocracy of the good, and the freedom of the people (demos). These parts are said to contribute to a harmony. Keeping in mind that the “in common” is that all are speaking beings able to differentiate harm from wrong, how is it that the qualities wealth, goodness, and freedom—which are heterogeneous—can be harmonized? The basic problem is that freedom is not a positive quality, thus the free, the people, have noting to contribute, nothing to speak of—except in exceptional circumstances when genuine politics emerges. They have no name—they are the ‘they’, the ‘people’. The free are free only by default—they simply happened to have been born in Greece after slavery was abolished. The main point is that the poor are made to exist as that part of the whole that has no part, that has nothing to contribute to the whole except for its speech which is reduced to pleasure/displeasure. They (the demos, the ‘people’) are both nothing positive in themselves but at the same time they are the whole of the state. Thus the wrong disappears, or, the poor themselves are the wrong itself, political “stuff” itself. The virtuous aristocrats, Aristotle is compelled to admit [11] are in fact coextensive with the oligarchical rich. Hence there are really only two parts: the rich and those whose part amounts to nothing. There is then a struggle between rich and poor which constitutes politics, but the struggle is rigged since the poor are forced to exist as a party which is then compelled to represent the whole of the community even though they have nothing, have nothing to contribute to the community except for their bare existence itself and their empty freedom. So, there is no real opposition of rich versus poor. The State is the obliteration of the threshold of difference between harm and wrong and at the same time the institutionalization of wrong. It is a magnificent sleight of hand that covers over the sheer contingency of the entire set-up. Some are by happenstance born into wealth/virtue. These are those who possess wealth, intellect, logos. Others, the remainder, are by happenstance born into Athens after the abolition of slavery—they are not even slaves. They are the poor whom the law has brought into existence. They have nothing to say for themselves; each is nameless, that is, purely contingently equal to each other, interchangeable with each other. (This is what Hobbes will rechristen the equality which amounts to” the war of all against all”.) [15-17]



It does not matter that the poor may, for example, revolt and redistribute the wealth equally among all. The problem is deeper [14]. The poor are those who are without position; that is the fundamental wrong which they (the poor themselves) embody. They are politics itself which is, again, the threshold between indication and expression, animal and human, the relativity of pleasure/pain and the commonality of just/unjust. Now, in the prior order, the slave was at this threshold. The slave could understand logos but can not possess it [17]. This does not entitle the slave then to become equally included in the community. The slave remains part of the “natural pecking order”. In granting freedom to the slaves and converting them into the demos an interruption of the natural order is introduced. The demos unlike the slave-class is not a true part of the community, as we have seen. They are the same threshold as the slave but now “twisted”, introducing a “torsion” because they are given a property—freedom—which is actually nothing but impoverishment. Hence, instead of a competition of classes such as a slave revolt might engender, we have instead incommensuability and misunderstanding. The people are a class that is not even equal to itself, as was the slave class; the people are both the anonymous equality of anybody with everybody and also the communal whole. They are radically improper, caught between the arithmetical and the geometric orders and a confusion of both, as Plato dreaded, so that he devised his famous “one man, one art” principle, among others, in order to keep a veneer of naturalism to what threatened the State with coming apart at the seams.



Chapter 6: “Politics in Its Nihilistic Age”



In this chapter Rancière moves from “a democratic stage to humanitarian stage”. He recapitulates that there is politics when a party that is/has noting nonetheless “purports to be the whole of the community.” The party of these people who have nothing are themselves the nothing that separates the community from itself. They are themselves the threshold between the herd of animals who only indicate pleasure/pain/danger and on the other hand the community of humans who articulate the just from the unjust. “Politics ceases whenever this gap no longer has any place” and when the community is the sum of all its parts and nothing (not even the nothing of “the people”) remains. The consensus state is the attempt to eradicate the threshold. It operates on the need for “real parties” that have their own specific properties which in turn are a part of the whole. This strict coextensivity of the whole and the sum of its parts was to be called “humanity”. It was hoped that the world would be entirely comprised of individuals and groups that show a belonging to a common humanity. But “this is where the trouble starts”. [123-24]



Having been victorious over totalitarianism, the consensus state called Europe saw itself confronted not with a “landscape of humanity” but with “a landscape of fundamentalisms of identity”. And even within its boarders it finds the population of immigrants. The consensus state witnesses ethnic warfare, religious warfare, and in fact the very parody of the consensus state itself: state, regions, tribes which wish to eradicate “surplus identity”. What the consensus apologists overlooked was that between the individual and humanity (the whole) there is a threshold. Either the consensus state counts a part of those who have no part but who purport to be the whole; or the consensus state eliminates that part and geometrically arranges and distributes real identities (identical to themselves) wishing to play and capable of playing a part in the whole. What Europe discovered was a “new political figure”, a “non-political figure of the all identical to nothing […] everywhere under attack […] [and also] from now on called humanity” who/which may be defined as man born human yet everywhere existing as the inhuman. [125]



The epithet “humanity” is no longer polemically applied to women, blacks, the “damned of the earth”—who can identify and speak of themselves from out of their own identities. Thus “humanity” is only applied to the wordless victim, the man deprived of logos. Humanity has no mode of enunciation. This had a parallel in May ’68 when one well known student slogan was “We are all German Jews”. This is now no longer possible. “German Jew” today signifies the universal victim, the violence against whom (massacre, extermination) is said to be unthinkable and unpoliticizeable. But this then leads to the possibility of denials such as Holocaust deniers, which Rancière then analyzes [128-34]. Part of the analysis turns on the problem that the unthinkable would be the impossible and so, if we do really characterize the destruction of the European Jews as an unthinkable crime against humanity then we will be confronted by the denier who will say that the “crime against humanity” never took place. Rancière dispenses with this argument. The Holocaust is entirely thinkable; its logic was the logic of the incorporation of the demos into an ethnos and there was certainly sufficient will, hatred, technology, cruelty and cowardice to carry out the job. [133]



Rancière then examines Arendt but especially Lyotard for whom the “reason for the crime” was the attempt to eliminate the “philosophical” victim, the witness/hostage—the “jews” (as Lyotard names them)—to/of the Greco-Roman West. The “philosophical” thinking of the extermination becomes an Ethics. Briefly put, ethics becomes the other to which philosophy (the philosophy of freedom, mastery, and self-possession and any political philosophy based on them) must submit itself in mourning. The question of the human, sub-human, and super-human is an ethical one, not a political or philosophical one. And indeed, philosophy and politics have, since WW II taken on a new “modesty” (perhaps with the exception of Badiou). The state is more or less a group of managers of wealth, led by experts who delineate the possible from the impossible—“realists”. It takes as much as possible a distance from politics. Nowadays, the last thing a state needs is a political event to occur, since this would ruin the myth that politics is dead and buried. (Likewise, philosophy is no longer the philosophy of over-arching systems of thought. Philosophy has become a ‘minor’ form of discourse, we could say after Deleuze.) Rancière, of course, is leery of the political modesty of consensus wealth management. In a way, politics can free itself of political-philosophy and take up an “immodest stand” against managerialism. Politics can and should recommence political impropriety—the count of the super-numeric, the part of those who have no part; and it should retreat from a definition of a sense of the world that is a “community of humanity based on the victim” which is achieved in a body count of groups, locations, bonds, and identities.



The “other” humanity that threads its way throughout the essay is that of an interesse or a between and among of any number of identities, such as in the case of Blanqui [137-38]. The political is a dividing of a condition from itself. Rancière makes the point that the massacres in Bosnia did not create a bond that congealed around an identification with the victims as the persecution of Algerians by the French congealed around a dis-identification with the France responsible for the crimes. The political is not a bonding over a common wrong but instead an art of mixing identities and warping deductions; “It is local and singular cases of universality.” Consensus is the denial of humanity and it is not yet foreseeable how this circle can be shattered. But Rancière sees hope in that the logic of consensus will always run aground on the on the necessity that there be a part that counts for nothing but that represents the whole.

Lecture: Badiou

NCTU Graduate Practical Philosophy



MAY 1968 PARIS




March 22: Leftist groups, including poets, musicians and students seize an administration building at Nanterre University



May 2: Students protest at the University of Paris at Nanterre, leading authorities to shut down the university.



May 3: Students at the legendary Sorbonne in Paris, led by the Situationist International, meet to protest the closure at Nanterre and the threatened expulsion of some students. The police invade the Sorbonne.



May 6: 20,000 students protest the invasion of the Sorbonne. Police respond with tear gas; hundreds of students are arrested. The country is shocked by the virulence of the police response.



May 8: High school students and young workers march to the Arc de Triomphe to protest the police response and list certain demands.



May 10: A huge crowd gathers on the Rive Gauche and is met by riot police. Negotiations break down at 2:15 in the morning. Hundreds of arrests and injuries result from the melee. The events are broadcast live on radio and televised the next day.



May 13: A wave of sympathy results from the police’s heavy-handed actions. Anarchists, the French Communist Party, and Union Federations declare themselves in sympathy with the student protesters. Result: One million march on Paris. The police remain largely out of sight.

The Sorbonne is reopened and the students declare it a “people’s university”. “Action committees” are set up to voice grievances.



May 14: Workers now begin to occupy factories beginning with a sit-down strike in Nantes, followed by a strike at the Renault plant.



May 16: Strikes spread and by this day nearly 50 factories are occupied by workers.



May 17: An estimated 200,000 workers are on strike.



May 18: On this day the figure unexpectedly snowballs to 2,000,000 striking workers: Roughly 2/3 of the entire French work force!



May 25-27: Concessions are made to workers including pay raises. Meantime on the 27th , 30,000-50,000 protest in Paris to demand the overthrown of the de Gaulle government. De Gaulle himself has fled the country to an Air force base in Germany.



May 30: 400,000-500,000 march through Paris chanting “Adieu, de Gaulle!”





May 31: Assured that he has sufficient military behind him, de Gaulle announces the dissolution of the National Assembly and orders all workers back to work under threat of a national state of emergency.





Early June : The “Revolution” ends. Workers go back to work. Students call off proposed demonstrations. On June 16, police retake the Sorbonne. At the legislative elections later in June, de Gaulle triumphs. The entire crisis ends with De Gaulle more powerful than before.











Bretton-Woods



In the midst of the social chaos of 1968, President Charles de Gaulle of France asked the US to back France’s dollar holdings with gold, as per the Bretton-Woods arrangements which, with the Marshall Plan and the Truman Doctrine, had assured steady economic growth in the West after World War Two. But by the mid 1960’s, inflation and state debts had accumulated. By 1968 there was not nearly enough gold in Fort Know to back the dollar. International Keynesianism was coming unraveled. In 1973 the Gold Standard was abandoned and gold ceased any longer to represent anything besides itself; it became a commodity like any other commodity.





The Prague Spring



The Prague Spring began in 1967 with attacks on Czechoslovak president Antonin Novotny. Student demonstrations then escalated leading to the replacing of the Czech president with Alexander Dubcek. Dubcek initiated a series of reforms both economic and political, which worried the Soviet Union. Enthusiasm for change in Czechoslovakia resulted from the greater political freedoms. Dubcek was experimenting with what was called ‘Communism with a human face’, but the Soviets worried and in August Soviet troops invaded the country. Unlike the suppression of Hungary in 1956, the Czechs offered no resistance to the Soviets. Dubcek told them to stay at home and they did.





Analysis



What happened in that month of May in 1968 was completely unexpected. There had been relative prosperity in Europe and there was the unmistakable sense that, as Alexandre Kojève had predicted in the 1930’s, history had ended. The era of revolution was over. Fascism had failed. Communism was doomed to crumble under its own weight. What would remain would be liberal-democracies and generally Enlightenment principles of justice. Kojève, after having delivered his “Introduction to the Reading of Hegel” in which he outlined the ‘end of history’ scenario with unparalleled rigor, retired from philosophy and was influential as an advisor to European political leaders and remained actively involved in NATO policy. On his death bed, during May ’68, he was asked to comment on the events. He replied that the events were trivial because no blood had been shed.

That great student of Kojève’s, famous psychoanalytical theorist Jacques Lacan, responded to the events by declaring the students as mere “hysterics” and once telling them that, like any hysteric, what they truly want is a master to organize their desires for them. And he said “YOU SHALL HAVE ONE!” Indeed they did get one since de Gaulle not only survived the May insurrection, but strengthened his command on power in France.

On the other hand, political philosopher and activist Guy Debord, co-founder of Situationist International (which I will come back to) and author of the still influential Society of the Spectacle, remains an adherent of the protests, actions, and ideas of ’68. Moreover, possibly Europe’s best living philosopher, Alain Badiou, remains faithful to what happened in May 68 to this day. (“Fidelity and Love” being one of his philosophical categories (along with science, and art)). He is an avowed Maoist who says that in the streets of Paris he saw that history is multiples and is Events without knowledges of them. The Being of history is not unified, in short: History is a multiplicity without a one; history is not one and so History cannot be said to have “ended” because there is no One History. Instead of a one: the void and a militant truth procedure which develops step by step out of the potentialities of what he calls a “situation”. May ’68 was a situation.



Did something happen in Paris in ‘68 or not? A great historian at the time, Edgar Morin, said “We will need years and years to really understand what has happened” and he christened the revolt: une revolution sans visage. Meaning, revolution without a face, or, a revolution we cannot read (as we can read a face). How did it happen? How is it that a quite affluent country was paralyzed for a month. And Why? In my view: there was in 1967-68-69 a global desire to “get out”, to “escape”. And this desire was authentic, political and even ontological. May ’68 was a revolution of escape, even of the escape from revolution as previously conceived (i.e. as the master project to seize power. Instead of being seized, May ’68 showed that power can be arrested, paralyzed, and that this can have unexpected results), and even an escape from being itself as may be implied in one of the slogans of the time: All power to the imagination. (Badiou would abject to my view as an illegitimately unified characterization of that whose whole Truth is inconsistent, uncharacterizeable, Real.) The Czechs and other East Europeans wanted out of the Soviet system, Mao wanted bourgeois values out of his Communist China, American students wanted the US out of Vietnam, American and French students wanted traditional morality out of their private lives, French students wanted out of the highly restrictive French higher education system, Blacks in American wanted out of a two-tiered social cultural system that degraded them, workers wanted out of the bureaucratic administration of labor (“Fordism”) that restricted their labor to roboticism and restricted their salaries as well. And so on and so on. Right up until Spring 1968, all these “evils” had been passively submitted to until the idea of escape was conceived and once conceive, the idea spread. Alexis de Tocqueville, writing of the French 1789 revolution:



“The evil, which was suffered patiently as inevitable, seems unendurable as soon as the idea of escaping from it is conceived. All the abuses which are removed…seem only to throw into even greater relief those which still remain, so that their feeling is more painful…”



This revolt which consumed the whole population of France in one way or another, and which forced President de Gaulle to flee the country began with unhappy students. That’s all! Unhappy students! A book was published entitled On the Poverty of Student Life which dealt which such commonplace complaints as cramped unpleasant dormitories, too few books in the library, too few comfortable places to eat or coffee shops to study in, too few carrels in the libraries, etc. Owing to post war prosperity, the populations at French universities had grown much faster than the institutions could comfortably handle. (In 10 years the population of students at university grew from 170,000 to 600,000) Up until this year, the student population of France, had been traditionally quiescent. But, perhaps fuelled by the image of American student anti-war protesters broadcast on TV screens every evening, the idea grew that they need not be passive. Even Time magazine in America wrote:



“Thus French students often project an image of despair. They constitute a hard-pressed band of impecunious, hungry scholars restlessly roving the Latin Quarter, looking for a warm place in the winter or even a café with enough light to study by.”



To protest such conditions is hardly what would spark what became the conflagration to come. The point is, the students protested this in public by seizing an administration building and presenting specific demands. This was previously unimaginable, unthinkable in conservative, Catholic France. De Tocqueville again writing about the revolution of 1789 says:



“Imagination, taking hold in advance of this approaching and unheard-of felicity, made men insensible to the blessings they already enjoyed and hurried them forward to novelties of every kind…”



Indeed, novelties of every kind began to be demanded by students. Within weeks every possible demand was being made of universities and of society in general. One slogan of May ’68 was “All power to the Imagination”. This endless palette of demands is what led Lacan to dismiss them as hysterics (hysterics are always demanding of Power something impossible) and also alienated the students from the French Communist party which would be interested in more focused and strategic demands because it was still under the sway of Lenin-Stalinist thinking. Maoism was, however, already beginning to take hold of thinkers like Badiou, and the film maker Jean-Luc Godard.



In short, what began as specific complaints was transcended, expanded, multiplied, or allegorized and became a true movement. This was true in Paris, San Francisco, and Warsaw Poland. It is not difficult to understand how plant workers at Renault could get the idea that if students can seize university buildings and ask that their demand be met, why can’t we seize plant buildings and demand our rights too? Once the unthinkable happens, it becomes a contagion, it becomes a new norm. And here, contrary to Badiou, I think it possible to think the events of May as spreading by way of analogy, by way of human beings’ being-in-language (thought Badiou would of course deny this).



Once the contagion blossoms into a norm, into something that can happen, a new subjectivity is born. No longer passive acceptance of the given state of things no matter how affluent, but instead an active subjectivity that will demand the new, even if it does not know what that might be. Self-control transforms into self-assertion, a self-asserting subject is conscious of itself as fully in command of its desires and demands. (And indeed, many critics of May ’68 say that the students were just plain selfish, self-interested.) But this new subjectivity is truly revolutionary when it wishes to seize and transform the world, and that it must do so now, and that must include the revolutionizing of everything. This is where Mao’s “Little Red Book” seizes the imagination of the French. Mao writes:



“Progress is born in chaos. And originality comes from destruction.”



French Communist Party grudgingly and reluctantly saw the revolutionary possibly of chaotic revolt and eventually supported the students and workers. Anarchists began to make their presence felt, often feuding with communists, but themselves becoming part of a turn toward Maoism.



By May 26 these unprecedented events, which remained unpredictable from day to day, hour to hour, were enough to alarm even the conservative London Observer:



“[…]the events of the past three weeks are of historic importance. For they have crystallized longstanding, nagging doubts not only about France but about the nature of government in all advanced industrial societies—capitalist and communist alike. Something clearly is stirring under the surface of our inherited assumptions and conventional wisdom about the nature of our societies.”



In short, what was happening in France could happen anywhere: it was potentially global. A global political unconscious that could be stirred at any time.





The ins and outs of what happen in the final days, why this massive convulsion ended as quickly as it began, I will leave to historians of the epoch. There are too many details and theories for me to keep track of. De Gaulle retook power but in fact French society and culture was transformed. The old, traditional Catholic morality disappeared, new cinema was born, and the new novel was born. French higher education reformed somewhat. Workers made more money. Things changed, things didn’t change. A contradiction. An impossible revolution.



I will speak instead of two enduring “philosophies” that emerged from May ’68: the thinking of Guy Debord of the Situationist International, and Maoism.



Guy Debord and the Situationist International



The role of SI in the events of May was to create “situations”. It was this group that was part of the Sorbonne occupation committee. The definition of a “situation” is:



“A movement of life concretely and deliberately constructed by the collective organization of a unitary ambiance and a game of events.”



For Badiou, “situation” is also a category, as we shall see. Importantly, however, the situation for Badiou has no relation to “life concretely and deliberately constructed”. For Badiou, the situation merely and purely “is”. It is not lived or consciously constructed. The constituents of the situation are outside either imagination or intuition. The situation for Debord refers to a dialectical unification of art and life in a most general political sense of these terms. It was intended to be a political advance over the “happenings” of the Beats in San Francisco. A situation could be the take over of a university building, the establishment of a theoretical committee, a sit in teach in; or it could take more sever forms such as the Watts riots in Los Angeles. The goal was total revolution, which meant the revolutionizing of everyday life, the reconstruction of all public spaces, or even the abolition of the distinction between public and private, and so on.



The chief theorist for the Situationist was Guy Debord who argued in his book that social life (right down to its minute details) in modern capitalist western societies had been transformed into a sheer spectacle. He says in his Society of the Spectacle:



“The spectacle is capital to such a degree of accumulation that it becomes an image.”



His thinking is greatly influenced by media theorist Marshall Macluhan. They should be studied together. Each was able to see before anyone else the new influence of media and the new creation of what we call globalism. The difference is that everything Macluhan celebrates and enthuses over horrifies Debord. Debord is arguing by spectacle and image that we modern westerners are merely quiescent viewers of our own existences. Capitalist society itself had reified itself and separated itself from the very people who inhabit it and who now only watch it and themselves as if from an implacable distance, as if from behind a glass wall. The whole point of situationism was to show that a group of people, a society, can do, make, construct, invent something themselves, for themselves, in complete consciousness of what they are doing. Essentially, Debord is arguing that capitalism in its final phase expropriates human life from any experience of itself as human and social and its own. Human life is that which observes and contemplates everything—everything in the world—without ever experiencing anything or making anything: as if society—the spectacle—had become autonomous. The logic is borrowed from Marx’s famous “fetishism of commodities” from Capital. Debord simply broadens it to say that today Capitalism itself has become fetishized, separated from its own organic production and history, and now occupies a zone “above” all of us who inhabit it.



The problem is, it is difficult to construct a situation without that situation itself becoming part of the spectacle. Slavoj Žižek has accused the situationsits of creating fantasies of transgression rather than really altering the social spectacle, because nowadays everything feed the spectacle. What appears is good, what is good appears. That’s all there is to it.







Maoism



Partly as a long term result of the Soviet suppression of Hungary in 1956 and more directly as result of the Soviet crushing of the Prague Spring, Eurocommunism began to study the thoughts of Mao Zedong.



Mao was critical of Soviet Lenin-Stalinist communism and proposed a new ‘form’ of communist practices. Principally, he was critical of Stalin who, he said, did not fully understand dialectics and ended up in metaphysics. He could not distinguish between different kinds of contradictions. Further, Soviet imperialism transformed communism into something not in principle different from Western imperialism.



Mao’s principal advances over Stalinism are:



1. Guerrilla warfare/People’s War: essentially the army is ‘the people’ and ‘the people’ is the army. They are not distinct.



2. The concept of a ‘Third World’: those nations outside of, and exploited by, the First two worlds of The USA and the USSR



3. In backwards nations, the material conditions of the masses must be improved prior to any thought of revolution.



4. Contradictions are the essential feature of society: the contradictions are wide ranging and in fact constitute society, rather than any sort of something-in-common. (This thought has led Alain Badiou to say that governments exist precisely to prohibit the unbinding that these wide-ranging contradictions consistently make possible.) Taken collectively, these wide-ranging contradictions are humanity pure and simple.



5. Cultural revolution is required after political revolution had erased the bourgeois power structures because bourgeois thinking remains, class struggle is on going.



6. Revolution begins with the masses and in the countryside in backwards countries when their basic economic situation is stabilized. Revolution does not begin with an avant garde. Revolution continues even after the country has been transformed into a People’s State. Division of labor ceases and everyone learns to be a soldier, a farmer, a thinker, etc. so that every citizen is truly well-rounded. In short, Maoism resonates with Spinoza and univocity of Being in that, for Mao every person is (should be) the complete expression of the State (of China) and the State immanates from the people.

DOCTRINE of the UNIVOCITY OF BEING: SPINOZA/DELEUZE

Spinoza takes over the concepts of ‘substance’ and ‘attribute’ from the western metaphysical tradition of Aristotle through Descartes, but he gives it a radically new, some would say “bizarre”, inflection. In Aristotelian logic every proposition contains a subject and a predicate which reflect a fundamental division in reality: substances and predicates or attributes of substances which inhere in substances. The attributes of substances can change: Dr. Wall weighs more or less 67 kg now; he weighed 3 or 4 kg at some time; about 30 kg as a youngster, etc.. The substance named ‘Dr. Wall’ must somehow endure through all the changes of attributes, otherwise there would no coherence whatsoever in the universe. That substances somehow endure change gives rise to the medieval thought that substances can be neither created nor destroyed. (Spinoza clearly adheres to this line of thinking.) In any case, from Aristotle through Descartes and beyond, substances count as the ultimate constituents of reality. Since there is a division in the universe between substances and attributes, it must then be possible—at least intellectually—to separate them and thus to determine what are substances pure and simple, substances prior to any attribution: or, what essentially are the substances with the attributes becoming then “accidents” which are dependent on that in which they inhere, and are in that sense inferior. (Spinoza clearly rejects this line of thinking.)

For Aristotle, substances are many and countable. They are divided into genera and species. But this led to many problems. Some substances were countable, others were not, and some were ambiguous. ‘Man’, for example, can refer both to an individual man (and other individual men) and also the class in which he is (or they are) included. What of ‘snow’ and ‘water’? These are “mass” nouns or mass substances: Do we say that all of water is in this bottle of water, or do we deny that water is substantial? (Spinoza was clearly alert to the issue since he will affirm the uncountability of substance altogether. Spinoza/Deleuze will say that, yes, this bottle of water, that drop of water, etc. completely express ‘water’, or completely actualize ‘water’. In order to count, you have to begin: substance does not begin; it is eternal.)

Medieval theologians became enamored of the idea of a substance that may exist necessarily; that is, a substance whose essence entails existence. The “ontological argument” of St. Anselm became the most famous of all attempts at deducing that God as prime substance must exist necessarily. The argument runs something like this:

We have a clear (if only hypothetical) idea of a being which possess all perfection—every positive attribute: God. No greater Being than this can be thought. If this Being were to exist only in our minds and not in reality, then it would yield to an even greater Being whose perfections do include real existence. But this violates the hypothesis. Therefore the idea of God as possessing existence necessarily must correspond to reality.

Both Descartes and Spinoza take over versions of this argument. St. Thomas Aquinas rejected it on the basis of Christian doctrine. Kant refuted it summarily by denying that existence is a real attribute. But the idea of a God who exists necessarily, is omnipotent, all-knowing, etc. became a powerful claim which then had to be reconciled with ideas of human freedom, agency. And, it was essential to show that at least one being, one substance must exist necessarily. Otherwise, there is only meaningless contingency which cannot explain, for one thing, the existence of language which presupposes meaning. But, on the other hand, basically, the concept of such an omniscient, all knowing God banishes all contingency from the world, and human agency or human subjectivity becomes illusion. So, western thinking is caught in an impasse.

By far, the most decisive philosophical event after Aristotle was René Descartes and the force of his thinking was immediately apparent, especially to Spinoza (and also Leibniz). Descartes simply refused to accept as true any proposition that could not be clearly proven. All science must be founded on metaphysics and metaphysics is the system of self-evident truths: truths that need no further proof than that which is contained in their premises and conclusions. Unless there are self-evident truths, nothing at all is clearly knowable. Descartes’ famous self-evident truth is the ego cogito: ‘I think therefore I am’ from the Discourse on Method. This he considered to be indubitable, and his Meditations set out to demonstrate its indubitability and the consequences thereof. For Descartes, the ego cogito was as self-evident as the truths of geometry. These truths Descartes labeled as “clear and distinct” ideas. A clear idea is one I can comprehend without the assistance of the senses, one I comprehend purely through reason; a distinct idea is an idea unmixed with any other idea. Like Descartes, Spinoza believed that knowledge must begin with fundamentally indubitable premises, not experience. In a letter to Simon de Vries he writes, “You ask me whether we need experience to know whether the Definition of any Attribute is true. To this I reply that we need experience only for those things which cannot be inferred from the definition of the thing…” [L 10]. Descartes, however, famously ended up with only the one first principle, the ego cogito ego sum; and he ended up with two radically distinct substances: res cogitans (clear and distinct) and res extensa (obscure, but “guaranteed” reality by God who would not fundamentally deceive the senses) which could have no possible interaction. (Likewise, in Spinoza, different attributes would have no relation to each other (a very important point [P2]).) As with the ontological proof, Descartes showed that there is at least one self-evident truth.

Spinoza will retain the ambitions of rationalism but radically ontologize them via the path of immanence (and of course this is what will have a major an impact on Deleuze). And, Spinoza will retain Descartes’ geometric method. His Ethics is built on axioms and definitions and then proceeds to proofs. Spinoza’s geometric method is also a response to the warnings of Moses Maimondes’ Guide to the Perplexed, in which he complains of the misleading languages of man which tend to be imaginative. For example, men tend to speak of God as perfect, all-powerful, all-knowing, but these are anthropomorphisms, as if God is Super-Man. In Letter 9 to de Vries Spinoza says that human language can get access to essences but only if there are “real” definitions at the start. And we see that the Ethics begins with the famous and notoriously obscure definition of “substance”. If there are “real” definitions at the outset, then the reader will able to grasp that which the deductions express, or, that which is immanent to the deductions.

Spinoza

The colossal and rational conclusion Spinoza draws from both St. Anselm’s ontological argument and Descartes’ self evident ego cogito is simplicity itself: There is at most, or only, one substance:

P14 Except God no substance can be or be conceived

P15 Whatever is, is in God, and nothing can exist or be conceived without God

Axiom 4 The knowledge of an effect depends on, and involves, the knowledge of its cause

If A causes B then B is dependent on A for the very idea of B involves the idea of A which caused it. The truth of B will always refer to A, and A explains B. All conclusions are dependent on premises. Only if the properties of something follow from its own idea is it independent. To be dependent is to be ‘in’ something. Suppose we form a philosophy club, each of us contributes some money, and then we rent out a room on a monthly basis in order to meet and discuss things. We say that our club rents out the room each month; none of us individually rents out the room. It seems as if the club rents out the room; but in fact it is only because some or each of us did this or that thing—donated some cash, discussed the issue, made phone calls, signed some agreements, etc.—that the room now available for us. Thus, for Spinoza, it is not that we are in the club (he is not a set theorist), but that the club is ‘in’ us; is immanent to us, or in Deleuze’s word, the club “imminates” from/in us (and not emanates from out of us, or we from out of it: Spinoza, Deleuze are also not neo-Platonists).

D1 By cause of itself [causa sui] I understand that whose essence involves existence, or that whose nature cannot be conceived except as existing.

This is the entire content of the world. For Spinoza, that which is conceptually independent is also ontologically independent. Substance depends on nothing outside itself, and, as there is only the one substance in Spinoza, there is only the one world and nothing outside, nothing beyond, no transcendence. To the question ‘why is there something and not rather nothing?’ Spinoza answers ‘because substance necessarily exists; its very concept entails existence’. This is now no longer Aristotelian substances which can be enumerated and categorized. Scholastic and Cartesian philosophers assumed substances to be the basic constituents of the world and to be self-dependent. Spinoza merely draws the conclusion that if self-dependent then obviously self-caused and as self-caused necessarily existing (for, a cause cannot cause nothing to be; a cause always, by definition, causes something, if only itself and thus itself must exist—if anything at all exists) and, as self-existing, always existing in some mode. The mode or modification is dependent for its existence on substance for a mode can be conceived of as existing or not existing. You and I can conceivably not exist; thus we are modes of, and are dependent on, divine substance: Spinoza’s God. If we exist, we do so because of some power outside us which explains our existence.

Different from mode is attribute. Attribute constitutes the essence of substance, as thought constitutes the essence of mind. This is also how Descartes understands attribute in his Principles of Philosophy. But Spinoza adds intellectual perception to the definition:

D4 By attribute I understand what the intellect perceives of a substance, as constituting its essence.

This is not just a subjective “point of view” of substance but actually constitutes the essence of substance. The attributes are incommensurable with each other, however. Yet, each constitutes substance essentially. Thus, we can know reality, substance, the world completely in utterly incommensurable ways. Spinoza’s God is substance consisting of infinite attributes each of which express eternal essence.

That there is only one substance is not numerical data. He says somewhere (I can’t find the reference) that it is not that we begin counting up the substances in the universe and stop at one. The “oneness” of substance does not belong to the essence of substance. ‘One’ is not an attribute and the infinity of attributes is not in any way numerical. Numbers belong to the languages of man. Spinoza takes this from Moses Maimonides’ Guide to the Perplexed. For Spinoza, number is imaginative and is not a feature of reality.

An attribute is an essential; it is not an accident. Dr. Wall weighs 67 kg accidentally: he could conceivably weigh 68 kg tomorrow. Dr. Wall is animal: if this is changed he ceases to exist. But, still, attributing animality to Dr Wall does not constitute his essence. There is more involved, and it is very difficult to understand because God has infinity of attributes of which we know only two: thought and extension, or ideas and physical objects. Thought, on the one hand, and extension (the objects of the world) on the other are both essentially substantial and each completely explains or expresses God. Nothing else is required. The problem of the incommensurability of mind and matter (res cogitans and res extensa) does not arise for Spinoza as it does for Descartes because mind and extension are two attributes of the same substance. However, this involves Spinoza in some grave difficulties. God’s attributes are infinite. The infinite is conceived of by Spinoza as an ontological category, not a number. But there are at least two attributes we humans know of: mind and extension. Somehow, ‘infinite’ and ‘at least two’ must be compatible. I think this is at the crux of the Badiou-Deleuze debate. Deleuze, as Badiou states in his chapter on Deleuze, remains at the level of the two, while Badiou, adopting set theory accepts the infinite as actual.

Deleuze’s Spinoza: Expressionism In Philosophy

Chs. 2 & 3: Attributes, Substance, Names, Words Each attribute completely expresses substance which has no existence outside of its expressions, outside of its attributes. There is one substance and many attributes, that is to say, many essences. This is completely foreign to Aristotelian/Medieval metaphysics. Essentially, for Spinoza/Deleuze (and Negri/Hardt): essence (and not Being—not Badiou!) is multiple. Or, essence is multitudes of existences. Substance has no existence outside its attributes, just as the philosophy club I mention above has no existence outside its members, is completely co-extensive with its members, but is not, for all that, numerically identical with its members. The club could have any number of members; no number of members could possible exhaust the club, could cause the club to be greater or lesser, better or worse, because the club is not a quantity but instead a quality. The club is potentially any number of members; it does not matter how many. Each member of the club is an expression of the club in essence, and all the members and any portion of members express the club essentially. From Expressionism in Philosophy: Spinoza:

What is it that exists through itself, in such a way that its existence follows from its essence? This is clearly substance, the correlate of essence, rather than the attribute in which essence has existence solely as essence. [EP 43]

In the club each member’s existence is necessary, and all or any portion of members are necessary; but the necessity does not exist in each (all, some portion) member him or herself (because this or that member (or some or all) can be replaced by another.) Also, the club is “expressed” completely in the bodies (rei extensa) of the members; and also expressed completely in the idea of, or ideas for, the club (res cogito).

Deleuze then discusses the problem of divine names, Words, and propria and says that attributes are truly Words. (He is thinking here of the Word(s) of God: “Let there be Light, and there was Light.” Does the Word create Light? Mean Light? Describe Light? No, the Word actualizes and expresses Light.). Suppose we try to understand this by shifting our example from the philosophy club to language (Anyways, this is the analogy I am using to try to understand EP 44-51). All words completely express language (but do not exhaust language) and each word completely expresses language. But, “all words” do not mean or describe language; and no word—not this word not that word—means or describes language. Neither “explains” language. All the words, and each word, are Word: the Name of language; Scripture; the voice of Language; because language is uni-vocal. (French, English, Chinese etc. would be “modes” of language in this analogy.) No matter how many words or how “well’ or “badly” we speak, the ‘nature’ of language is not exhausted and we—via words themselves except insofar as we use them, practice language, speak or write, or make signs—do not substantially approach or understand the “nature” of language. Because it is of the nature of language that its essence includes its existence which, in the case of language, entails usage because language is not something lying around (in dictionaries or grammar books) awaiting activation. Likewise, no creature of God (of substance) is an emanation of or from out of God: God is already “in” each creature just as language is “in” each word, and the philosophy club is “in” each member.

Now, “all the words” and “each word” expresses, actualizes, formalizes language but neither “all the words” nor “each word” means language and thus the outlines for a ‘negative theology’ are revealed: language is, eminently, what “all the words” and “each word” are not. Likewise, according to a long tradition: God is not everything and anything we can say of Him. Nothing in Spinoza’s thought logically prevents such a reading yet nothing is further from the whole force of Spinoza’s thought which is, as Deleuze tirelessly asserts, nothing but affirmative. There can be no negation of univocal Being just as language always affirms univocal existence: I may say “there is no elephant in this room” but I cannot say this, cannot negate the presence of the elephant without a prior affirmation: there is.

In reality (but not in thought or imagination) “all the words” or “each” or “any word” and language are identical just as (and I think this is not completely clarified in Deleuze) attribute and substance are in reality (but not in thought) identical. They are cross-referenced at every point:

L2 By attribute I understand whatever is conceived through itself and in itself, so that its concept does not involve the concept of another thing.

L4 By substance I understand what is conceived through itself and in itself, i.e., that whose concept does not involve the concept of another thing.

Attributes do not represent substance; they are not predicates of substance; or names for substance. Spinoza has managed to liberate what in Aristotle remained a relation of predication. This means that the relation Spinoza is aiming at is not an intellectual one; it is a real unity, not a relation nor even a necessary relation. Attribute is in substance and at the same time substance is in attribute but without any dependence. They are co-independent. They cooperate independently, or, by way of being independent Their real unity bypasses intellect. Attribute and substance share the same definitive identity univocally. That there may be more than one attribute (at least two: extension and thought) is not numerically “more than” the single identity of attribute and substance. Let us be clear, for this is something Hegel refused to read in Spinoza: there is first substance, and then modes; but there is not first substance, and then attributes. Attributes and substance are the same definition: I no sooner define substance than I concretely define attribute, and I no sooner define attribute than I concretely define substance. Hegel’s misreading from Lectures On the History of Philosophy: “What comes second, after substance, is the attributes” [259]. Hegel is attempting to confine Spinoza to classical Aristotelian predication (above) when in fact, precisely by defining attributes in the same way as substance, Spinoza “liberates” the attributes from dependence. This attempt has profound consequences of which Deleuze, Althusser, Negri and Hardt are aware.

(On this point I myself cannot conceive of this ambivalence of singularity of Being/multiplicity of Attributes without thinking of Gustave Le Bon’s La psychology des foules [The Crowd: A Study of the Popular Mind]. The argument of that study hinges on the precise constitutional ambivalence of the “crowd” [foule: throng, mob, mass] as an undecideable singularity and multiplicity. Within the crowd everyone identifies with everyone else and thus every one at the same time every one dis-identifies with everyone else (because everyone else’s identity is not his or her own identity). The identity of the crowd is precisely its dissolving of any “one” identity. The crowd is the concrete refutation of mathematics. Le Bon’s “crowd” is the always potentially nightmare version of the club from my example above example. A crowd is another example of a nonnumeric but still distinct concrete unified reality. This unity is not a number but a condensed plethora, or ‘body’.)

Although substance and attribute are concretely identical; attributes themselves are formally (that is to say, intellectually, conceptually) distinct [EP 65-66]. Attributes are ontologically singular—they are all and each substantial—but formally distinguished from each other. Deleuze’s next step is to show that this real univocity to which formal differentiation concretely refers is not inertia and indifference but is productive. For this he relies on the basic definition that opens the Ethics which includes the causa sui: There is always a dynamic causality: substance, in causing itself, is necessarily the cause of all things which Deleuze will get to in the second part of his treatise on Spinoza:

God is said to be cause of all things in the very sense (eo sensu) that he is said to be cause of himself.

[EP 67].

Ch. 4 Absolute, Infinite, Virtual I’m going to bypass most of this chapter because I’m not familiar with Leibniz’s arguments on these points. I’ll only comment on the striking conclusion to the chapter: Deleuze’s assertion that the opening propositions of the Ethics are “not hypothetical but genetic” [EP 79-80]. By this he/Spinoza want to get around the standard objection made to the ontological argument of Anselm and to Descartes’ version of it; namely, that only a hypothetical God has been proven to exist because no necessity can be demonstrated of His possibility. For Deleuze/Spinoza: since God is by definition an infinity of attributes and since each attribute is independent of any other attribute then nothing whatsoever prevents their “compatibility”: thus God is necessarily possible unless something prevents His existing in actuality; but then God would not be God, because nothing can prevent God from anything; thus God necessarily exists. You may accept that argument or not, but what is important for Deleuze is the concept of “necessary possibility” which, I believe, in his later writings becomes the kernel conception of the ‘virtual’. The virtual is that which is necessarily possible, but not actual. This is exactly like death in Blanchot and Heidegger which can never be actualized in the first person and, in that way, is eternally possible (…even, in a certain way, after I die!) It is that “in” the actual which necessarily escapes; nothing prevents its escaping by virtue of its inactualizability, or, its “ability” to be not-actualized. For Deleuze the virtual (or virtue) is power. (But it is nothing more than a power to escape power, is it not? Deleuze is so often talking about escape and ‘lines of flight’ is he not?) For Badiou, this is the aspect of Deleuze that inadvertently describes transcendence.

The attributes, which are independent and infinite, are a virtual “composition” Spinoza calls God, the Absolute, “in which there is nothing physical” [EP 79]. We begin to see here the nascent politics which will prove so attractive to Deleuze, Negri and Hardt: each attribute must remain independent, free, and thus increase strength/power and also increase the infinite virtual multitudes which forever escape totalization.

Here, let us speak of it at last: are not ‘escape’, ‘lines of light’, and even ‘radical passivity’ just various forms of messianism, or of a perpetually “incomplete” messianic redemption? (This is the issue that Giorgio Agamben continually wrestles with.) Keep in mind that Deleuze famously called Spinoza the ‘Christ’ of philosophy and he himself was attracted to ‘philosophical orphans’: Spinoza, Nietzsche, Bergson, Hume. I.e., those who left no “tradition” behind them as did Plato, Aristotle, Descartes, Kant, Hegel… “Bachelors”, in short…

Ch. 5 Power Power is the capacity to exist; a capacity that is necessarily possible (or eternally virtual, or—same thing—eternally escaping). I think it comes down to this: Substance is that which exists to the extent that it is affected by the attributes. To be affected is a power to exist necessarily, not a power to do this or that necessarily. The power to be affected by attributes is also a power to preserve itself in existence. Substance, which causes itself, is a power to exist insofar as it is affected by its attributes and insofar as its preserves itself.

Attributes are the constituting power of substance which is the power to exist or to be affected and constituted by/in any number of modes which come after substance and which are constituted and which are actual. That which is preserved is not, ultimately, this or that mode (which may change) but the ability (capacity, power) to be constituted—which, for Spinoza, is existence. Do not be mislead by certain Leibnizian critics of Deleuze and Spinoza:

Reducing things to modes of a single substance is not a way of making them mere appearances, phantoms, as Leibniz believed or pretended to believe, but is rather the only way, according to Spinoza, to make them “natural” beings, endowed with force or power. [EP 92]

TOTALITY AND INFINITIES

Attempts to formalize mathematics have often met with paradoxical results. Russell’s paradox is perhaps the most well known: Does the set of all sets that are not an element of themselves include itself as a member? (For example, the set of all dogs is not a dog (a set is not a dog) and thus does not include itself as a member while the set of all words is a set of words and does include itself as a member.) If it does, it shouldn’t; if it doesn’t, it should—both by definition. Another famous paradox is the Liar’s paradox: “I met a man who told me he is a liar. Was he telling me the truth?” Russell and Whitehead constructed a “theory of types” which addressed and in fact solved the problem but this theory (although in its own way eloquent) made mathematics extremely unwieldy. Different “ways” of conceiving of mathematics have evolved to address the potential problems. I will examine the intuitionist approach which is then radicalized by Wittgenstein, and is then rejected by Cantor.

Intuitionism. Originating in the work of L.E.J. Brouwer, intuitionists reject the notion that infinite sets can be treated as mathematical objects. They claim that there is no warrant for making any claims about infinite sets from the behavior of finite sets. Mathematics is built in the mind and does not correspond to any Platonic reality. Any mathematical object that can be defined but not constructed is considered illegitimate. Brouwer, for example, denies that that it makes any sense to say that it is either true or not true that the infinite expansion of  has an infinite number of paired repeating digits, because there is no infinite expansion of. For the intuitionist, infinite sets cannot be treated as totalities; infinity is the name of a potential endlessness, not an actual totality. (This approach has a correspondence in the work of Emmanuel Lèvinas for whom the totality (an ethics based on identities, the other—small ‘o’, the other person in and as his person, his race, ethnicity, gender, etc.) is a repression of the infinite (an ethics inflated by endless responsibility to the other as Other)).

For the intuitionist, only those mathematical objects which can be constructed count as objects at all. True, the intuitionist will say that one can always add 1 to the greatest number one can think and so derive a greater number, but they will deny that this describes an actual totality; they deny that we can talk about natural numbers in general, or about the indenumerable infinite, which Cantor postulates. Only that which can be constructed in a finite series of steps is admitted into intuitionist objectivity.

This derives from the ideas of Poincaré which is a return to the synthetic a priori of Kant. Poincaré noted that mathematics ultimately derives from the simplest of axioms: A=A and yet develops into the most complex and far reaching of all scientific ventures. He asked, “Are we then to admit that the enunciations of all the theorems with which so many volumes are filled are only indirect ways of saying that A is A?”.

But mathematics wishes to promulgate general laws, general theorems, general results. The problem is the same as for Hume who wished to understand how we go from masses of particulars to a general claim, how we go from atomized perceptions to generational knowing. Poincaré solved the problem with induction: To prove something true of all natural numbers you can prove two things which in combination provide a general claim. First, if something is true for some arbitrary number n, then it would be true for n + 1. Since the number n is arbitrary, n + 1 can substitute for n, so, what is true for n + 1 would be true for (arbitrary number n + 1) + 1, and would be true for (arbitrary number (arbitrary number n + 1) + 1) +1, and so on, up to and including any natural number whatsoever. Then you prove that the theorem is in fact true for n, and you consequently have an induction that will have shown it to be true for 2, 3, 4, 5, … This method does not make any claims about natural numbers as a set, it merely shows how to move inexorably and infallibly from one number to the next in the series.

For Poincaré, induction, or “reasoning by recurrence” is the very heart of mathematical thought and it is thus that mathematics “crosses the abyss” which any formalism cannot cross without succumbing to paradox. The mind has no direct intuition of the infinite, however, it does have a direct intuition of its power to perform the same act repetitively. This insight has resonance in psychoanalytic theory since, for Freud, repetition substitutes for the totality toward which it intends.

Keep in mind that Badiou rejects philosophical intuitionism; that philosophy begins with an intuition (that Being and existence are to be thought together against all previous metaphysics, e.g.) and works methodically towards a coherently discursive investigation of the possibility of the intuition (the existential analytic of Dasein) and tests its explanatory power against other philosophical intuitions and investigations (Heidegger’s rewriting of the history of western philosophy in terms of ontology).

Wittgenstein. Wittgenstein is an even more radical constructivist. For him, mathematics and numbers have a history; mathematics and numbers were invented by human beings as a way to get things done, a way to yield results, a way to accomplish things, and there is to be sure historical evidence to support this. Somewhere he says that we do mathematics, learn to count, etc. because it “pays off to do so”. Mathematics is a part of and not apart from human activities. This approach, Badiou says, we must learn to reject.

Wittgenstein begins his study of mathematics with the knotty issue of rule following and he will conclude that the performance of mathematics is a species of judgment or human practices that “pay off” and not a species of rule following. It is part of the grammar of social life. For the mathematician Hilbert ( a non-intuitionist contemporary of Poincaré) and now Badiou, this attitude is rigorously rejected. For Hilbert, Brower and Badiou, mathematics is a form of silent thought, non-linguistic thought in comparison to which, the languages of man are inappropriate, however noble, beautiful, and sincere the languages of man may be.

The central argument may be this: Humans are mathematical beings (indeed, for Badiou, ontology—including the ontology of man—is mathematics) and mathematics is rule governed, no matter how complex the rules. The history of mathematical theory is the increasingly complex formalization of rules. Wittgenstein wished to separate rules from mathematics and show instead that “practices” or judgments that “pay off” govern mathematical assertions. For Wittgenstein, humans are practical beings (and mathematics is one of our practices, among many, many others). The difference between the two attitudes is colossal and, in my opinion, may determine the fate of philosophy (and thought in general) to come. The question we may ask ourselves is this: what constitutes social liquidity: is it mathematics or is it language (or something else altogether)?

Wittgenstein asks a plangent question: what is that that allows us to continue a series correctly? A series that begins 2, 4, 6, 8, … or even a series that begins 2, 2, 2, 2, 2, …? Is it a rule, is it an intuitionist induction, is it a metaphysical apprehension of Platonic reality? Is schematized intuition—or any kind of knowledge at all—required to continue the series + 0 ? Wittgenstein will say that when asked to continue the series n + 2 he will not have any doubt that after writing 2006 he will write 2008 but this does not mean that the figure 2008 was determined in advance either Platonically or intuitively. He will say that sequencing numbers is itself a human activity and the series are continued by acts of decision that are ungrounded on anything, just as the alphabet and the rules of grammar are ungrounded on anything but are merely the way that we construct thoughts into sentences. Is there a rule that the series A, B, C, D, E,… will continue F, G, H, I, … and not E, D, C, B, A, Z, …? If intuition were needed to continue the series n + 2 then it would also be needed to continue the series n + 0, which seems absurd. That which enables one to continue a series is a way of acting which is learned in public as a language game. The apparent inexorability of mathematics is merely the consequence of lessons taught remorselessly. Mathematics belongs to human life and not to a metaphysical realm; the generality of mathematics that Poincaré wanted to secure with complete induction is for Wittgenstein a pragmatics of decisions which may at some time in the future change as human needs change. Complete induction is not “a vehicle that takes us to infinity”. What assurance do I have that the series n + 2 will continue inexorably even after the universe comes to an end?

The intuitionist officially denied the apprehension of infinity as any sort of totality; the infinite remained a potential, but Wittgenstein sees that they come close to treating the infinite like a totality with the notion of inexorable recurrences or schematized repetitions. Wittgenstein rejects this attitude and regards the infinite much in the manner of Kant for whom the infinite is the absolutely great and is not a name for a reality but instead a description of a state of mind which can conceive of the notion of the infinite at the point where both apprehension and comprehension break down and yield to a purely Reasoned Idea of the infinite; a supersensible; the mathematical sublime. It is a limit to legitimate thought which crosses over into a pathos (as does, for Wittgenstein, the post-Cartesian philosophical category of “certainty”).

From Paradoxes to Zermelo to Cantor to Cohen to Badiou. Cantor changed everything by regarding the infinite as an actuality, and he showed that to demonstrate this different orders of infinity were required to be thought and that, ultimately an infinity of different orders of infinity were required to be thought and that, finally, the infinity of different orders of infinity could not be determined to belong to any of the orders of infinity. The possibility that the orders of infinity formed a continuum (were sequential or coherent in some way as finite numbers can be shown to be coherent in many ways) was wrecked by Cohen in 1963. On Cantor’s demonstration it can be shown that, for example, the number of even integers is the same magnitude as the number of all integers (even and odd)!

Allow me to demonstrate…

This begins to ruin Kant’s notion of a mathematical sublime and also ruins the ambitions of intuitionism. The infinite as an absolutely great totality is hurled into an abyss, or, eventually, into multiple abysses. There are an infinite number of different infinities. Cantor resists the notion of a totalization just as Wittgenstein but in a wildly different way.

The difficulty of an “actual” infinite can be addressed and satisfactorily resolved even by non-experts if we have recourse to the old paradoxes of Zeno, for example, Achilles and the tortoise. In the paradox the tortoise is given a head start of some distance in a race against Achilles. In order to overtake the tortoise and win the race Achilles must first cover half the distance between the tortoise and himself, and also half of that distance, and also half of that distance, and so on to infinitely small distances. He must cover an infinite number of distance units and he must do this in real time. Yet, Achilles actually has an infinity of time to do the job since time is also infinitely divisible. In fact, Achilles can and does overtake the tortoise by actually accomplishing an infinity of distances over an infinity of time units. Hence, infinity must be actual. But this is trivial for it can be objected that we still do not know how Achilles can even begin the race to overtake the tortoise. For him to begin there must be a least interval of time and least interval of space; but this implies finitude. (Post Cantorian mathematics writes of an infinite interval that has no lowest nor highest as the set (0,1) which is indenumerable and infinitely dense (I will return to this). Its density is rendered orderly by way of the Dedekind “cut”, which Badiou discusses in his “Numbers” book.) Mathematics from Zeno up to Cantor tended to regard the notion of an actual infinite as noxious, while allowing for a virtual infinite to be conceivable (but never demonstrable in actuality).

Zermelo, in the early part of the 20th century, axiomatized set theory so as to avoid paradoxes like Russell’s. He axiomatizes that there is but one primitive element for set theory symbolized as  meaning “is an element of”, thus x  Y reads “x is an element of Y”. Importantly, this does not mean that there are two kinds of objects, namely, sets and elements, for elements are treated as sets such that sets are always sets of sets and the relation  is hence relative and not absolute. For example, a line which may be an element of a triangle is in fact a set of points; a point is a pair of (set of) real numbers (its coordinates); a real number is regarded as a sequence of rational numbers, and so on.

Zermelo was then able to dissolve paradoxes such as Russell’s by establishing the “axiom of choice” principle. He wrote:

Let A be a set, and let S(x) be a statement about x which is meaningful for every object x in A. There exists a set which consists of exactly those elements x in A which satisfy S(x).

This is customarily denoted symbolically by: {x  A  S(x)} or, “the set of all x in A such that S(x)”. This system does not allow us to form {x  S(x)} or “the set of all x which satisfy S(x)” but at best to form {x  A  S(x)}. Russell’s paradox turned on the words: “the set of all sets which are not elements of themselves” or {x  x  x}. But this cannot be formed in Zermelo’s system which only allows us to produce {x  A  x  x} where A is any set which can be shown to exist. Suppose S denotes {x  A  x  x}, then:

S  S is impossible since S  S implies S  S, a contradiction! More clumsily: {x  A  x  x}  {x  A  x  x} is impossible since {x  A  x  x}  {x  A  x  x}  {x  A  x  x}  {x  A  x  x}, a contradiction! It follows that S  A, for if S were in A then (because of S  S) we would obtain S  S, a contradiction. Hence Russell’s paradox is reduced to proving merely that if A is any set then {x  A  x  x} cannot be an element of A. (Or, more simply, x  A and x  A and A  x and A  not-x , thus A  x and A  not-x, for any existing A. Impossible.)

Zermelo was able to show that following the axioms of choice the creation of “excessively large” sets, such as Russell’s, is prohibited. Axiom of choice only allows the formation of subsets of actually existing sets. There are other systems which were created to avoid paradoxes such as those proposed and proven by Neumann, Bernays, and Gödel, but as Badiou relies on Zermelo I shall forego discussion of them. I will only note that they all rely on the primitive notion of “is an element of” in order to work. Sadly, for intuitionists and ordinary human beings sets of things like “apples”, “cats”, or “all the atoms in the universe” (i.e. sets that depend on properties of some or any kind) are not admitted into Zermelo’s system which only admits of sets that can be described with seven mathematical symbols:

 Is an element of

 Logical disjunction (as in A or B)

 Logical conjunction (as in A and B)

 Is not

 Material implication (if A is true then B is true; if A is false then nothing is said of B)

 For all, for any, for each

 There exists

x, y, z variables

Thus, only sets that arise naturally within a purely mathematical context counts as sets at all, giving the Zermelo axiomatization maximum flexibility (also called “expressivity”) but minimal applicability.

What little I understand about the discoveries of Cantor is this… In classical set theory a class A which contains everything in another class, B, and also some other things not in B, is said then to be greater than B. Say A is all Natural numbers (1, 2, 3, 4, …) and B is all even numbers (2, 4, 6, 8, …). A would seem to be greater than B, indeed, exactly twice as great. Galileo had noticed that is it possible to map the two class and show an equivalence of membership by the formula n  2n, or, for every 1 in class A there is a 2 in Class B; for every 2 in class A there is a 4 in class B, and so on. Thus, counter intuitively, the classes seem equally great. The mathematician Dedekind called these things reflexive classes and said that an infinite class will be a reflexive class or a class that is equally as great as any other of its sub classes. Cantor noted that we can map even other classes, n  4, n  6, n  8 and so on to create a sequence of classes any two of which can be mapped together and shown to be equally great. Cantor then asked if we can assign a Cardinal number to these classes. This seemed ludicrous since, as a result of the mapping exercise, one would have to assign the same Cardinal number to classes which are plainly differently defined, leading to confusion. Thus Cantor devised a name: the Transfinite number, or an uncountable number:  (Hebrew ‘aleph’) but which is now customarily written as N . This was the smallest transfinite number. Importantly Cantor saw that this number is classed not as a Cardinal but as an Ordinal: it the smallest, or the 1st of the transfinites. Differently defined infinite sets cannot rationally be discussed using Cardinals, but they perhaps could by using Ordinals.

Cantor then wanted to create an arithmetic of transfinite classes. Cantor showed that N + k (any finite number) = N .What he wanted to show was that there are orders or sequences or continua of transfinite numbers, just as there are of finite numbers (1, 2, 3, 4, 5, …)(1, 3, 5, 7, …)(1, 2, 4, 8, 16, …). Cantor showed that 2 > N . The former number 2 represents a class having N members and whose range is a class having just two members (as in the mapping exercise above). Suppose, Cantor said, there are as many classes of finite numbers as there are finite numbers. There would then be a one-to-one mapping from class to number. This procedure inadvertently creates a contradictory class x of all numbers that do not belong to their associated class (for example the number 1 of the class of all even numbers, the number 2 of the class of all odd numbers) and this class would have to be represented as a unique, or exceptional, number. Would this number have an associated class? This class x could only have an associated number if it does not have an associated number. The number would have to belong to a class neither finite nor infinite, which is impossible. Thus the number 2 is clearly different from N and, as it cannot be smaller, it must be greater.

Another way to show the existence of another infinity is to compare all Real numbers (numbers which measure something, such as a number line) to all Natural numbers {1, 2, 3, 4 …} . Suppose each class is infinite. Is it possible to map one class on to the other? It is not; hence there must be two orders of infinity! The set of all numbers between 0 and 1 includes 0 and 1, whereas the class of all Real numbers between 0 and 1 does not include either 0 or 1. This latter class, which does not have an upper limit nor a lower limit, is described as infinitely “dense” and “unbounded” rather than infinitely large; the infinitely dense cannot be mapped onto the infinitely large. Surprisingly, density is greater than the infinitely large. The set of all Real numbers between 0 and 1 is uncountable; i.e. unmappable. This is a different ‘kind’ of infinity. Essentially, Cantor had shown that there are infinitely more sub-sets of sets than there are members of that set. (This leads Badiou to see the importance of the difference between inclusion and membership or presentation and representation. (A member is included and represented as a ‘member’ of set A; while a sub-set is actually included but not represented as a ‘member of’ set A—it (they) merely present themselves outside any membership. An entire political thought unfolds from this…))

Allow me to demonstrate Cantor’s proof:

Now, is the class of all Real numbers (0,1) or 0  x  1 infinite? Following Dedekind’s definition above, it is infinite if a sub-class can be mapped on to a set and vice-versa. Can all Real numbers greater than 0 but less than 1 be mapped onto all Real numbers? It can! Thus it satisfies the definition of the infinite: one which remains uncountable but is theoretically mappable! Its Cardinality is transferred onto Ordinality; it is the next or 2nd Infinity, and if there are at least two, we can conjecture a 3rd…4th…5th…

I will demonstrate:

Having established that there are at least two different transfinite numbers whose relation can meaningfully be quantified by greater than, lesser than, Cantor went on to show an infinite number of different transfinite numbers and an infinite number of transfinite classes. The challenge was to ask if these numbers were or could be well-ordered. This led to the Continuum conjecture which Paul Cohen showed could not be satisfactorily resolved from within the logic of set theory itself. For Cantor there is no number “between” N and 2 , hence 2 is N . What is threatening here is that if not well ordered (continuous) the infinite realm of transfinite numbers is infinitely chaotic (but only from the point of view of univocity; from the point of view of working mathematicians, infinite chaos is perfectly quotidian and can be “managed” by means of axioms such as Zermelo’s). Basically, this is the vision of Lucretius but multiplied to infinity so that the “nature of things” becomes “unnaturally” multiple; the very unity of the concept ‘nature’ falls into the abyss. In short, the demonstration of Cohen showed that there is no organized knowledge of the behavior of infinites, no One consistency, no Law of the behavior of infinites, but these infinites are actual, in short they are; thus Badiou simply and rigorously can say that “mathematics is ontology”. In the realm of the infinite there is no continuity, no systematic unity or, being very strict about it, such continuity cannot be shown or represented from within the axioms of set theory itself. It has yet to be either provable or disprovable that there is or is not a number between N and 2 (or, if Cantor is right, N ). In the realm of the infinite there is only “unbinding”, thus Badiou once said the function of the state is to prevent the unbinding that is always presenting itself. Inconsistency and unbinding are merely the indifferent and normal state of affairs within set theory. What appears as exceptional from the standpoint of the finite is perfectly ordinary from within the infinite. Inconsistency is harmless and even banal. The realm of the political is, for example, a regional manifestation of non-relation, of the multiple; as is poetry, love, and science. (Lacan: There is no sexual relation.) Infinite mathematics presents itself within the abandonment of consistency and is completely untroubled by this. Infinite mathematics is a rigorous thought of the exception which has become the rule (or the count-as-rule). Badiou will say that mathematics is a presentation of itself, a presentation without representation, or is pure appearing, and as it is non-unified, it is a pure appearing within a “situation”, and not within a unity, a World, a Totality, a History, of any kind.

I believe that this is where the notion of ‘forcing’ arises for which Badiou so enthusiastic. This exercise is beyond my capacity to comprehend. As a correlate to this, Badiou begins philosophy with an axiom: there is no One, there is no Totality and with this forces philosophy to be identical in principle to mathematics as it is understood after Cantor and outside of any intuitionism.

Now, set theory presents itself to thought as actually existing and as a presentation at all it must be said to consist even if (after Cohen) it is impossible to think that of which it consists, or, if you like, that of which it consists is inconsistency. The realm of the infinite consists of inconsistent multiplicities (infinities) which, for Badiou, are not One, but instead ‘count-as-one’. The count-as-one of set theory is the theory of pure inconsistency, or the ‘void’. In standard set symbolization sets are defined such that the first element of any set is the void or empty set:

{1} = {  , {1}}

{1, 2} = {  , {1}, {2}, {1, 2}}

{1, 2, 3} = {  , {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

 

(Note that in very case there are more subsets than there are members in the set.)

Likewise, Badiou’s philosophy is itself purely inconsistent, but which counts-as-one, as the philosophy of a guy named Alain Badiou. We must not search for a consistency in this philosophy. It is a philosophy of what is. Being is inconsistency. It is not a presence but instead, a “subtraction”. It is outside of any experience, and hence the nostalgia of an Agamben or a Benjamin for the possibility of human experience of what is, of our ontological vocations is misplaced. If in fact ontological experience is dead, that is because there never was in fact anything ontological to experience, not even inconsistency itself. And here think of T. S. Eliot from The Wasteland: “These fragments I have shored against my ruin”. Eliot experiences modern inconsistency as ruin; so he piles up more and more fragments which only ruin him all the more… This pathos is entirely foreign to Badiou. Philosophy is henceforth foreign to any experience (including the experience of the loss of experience, or its absence) as well as to any coherence.

Here I will pose an objection to Badiou which is probably all too obvious, but I was trained in that atmosphere which Badiou resolutely rejects: phenomenology and its limit cases, language and its limit cases, ontological difference, and the necessity of Kantian Critique (owing to the very structure of thought itself and thought’s conflicting faculties). The objection is this: Is it not the case that post-Cantorian mathematics is like or similar to ontology? Or politics? Is it not possible that this analogizing (which I mentioned previously in regard to May ’68) shows that we remain within language, that being (inconsistent or not) is being-in-language; that what is most common is not pure inconsistency but our linguistic being? Thus the limit question for ontology concerns the being-language of language or, conversely, the otherwise-than-being of language (as in Blanchot: that which appears precisely when there is no being: literature and the economics of rumor, gossip).

One way out of the problem is Badiou’s assertion that mathematics is genuine thought; it is non-linguistic thought (something Wittgenstein denies; for Wittgenstein mathematics does not think). Here, Badiou can enlist psychoanalysis. Freud dreamed that one day his theories could be shown to be correct and efficiently reduced to chemistry, and the late Lacan began to think in “mathemes”—outside of any rhetoric, outside of the resources of language.

Badiou’s enormous throw of the dice begins by pointing out that mathematics continues to think outside of any coherence, and thus may we, indeed, we must! One of his favorite examples is Fermat’s Last Theorem which, for many years, was an insoluble problem, and which, if no solution could be found threatened to dissolve the edifices of mathematics altogether. The problem as now been solved. Badiou’s point is that mathematics continued to “think” in the interim perfectly well and with, we now see, enormously rewarding results. That is, fundamental (or apparently fundamental) theoretical crises do not trouble mathematicians. They are the norm. Mathematics is always becoming inconsistent.

With Badiou we begin with the infinite, not the finite. To begin with the finite is to confine ourselves to intuition and critique; and ultimately to hand philosophy over to poetic language, the poetic dwelling in language which the later Heidegger was working towards. To begin with the infinite is to begin with inconsistent situations as the most banal and ordinary of conditions whose Truth will have become apparent in the future just as Fermat’s Last theorem became mathematically intelligible long after he proposed it, while in the interval, mathematics continued to function spectacularly well. Likewise, psychoanalysis operates in the same way. The psychoanalyst does not know your problem, cannot solve it at once but operates in the unboundedness and inconsistency of your statements to him/her in the confidence that this is perfectly normal and, in time, the Truth will have become intelligible; when the analysand is placed in contact with that Truth, he or she emerges as a Subject (and is on the road to recovery, we presume). At any rate, for Badiou mathematics is the Master Discourse. That is the whole upshot of chapter 1 of the Theoretical Writings. Philosophy’s attempt to ‘confine’ mathematics to being an aspect of philosophy or to being merely of interest to philosophy is a mistake.

Chapter 2 of the Theoretical Writings is Badiou’s strenuous plea to reconstitute mathematics from its location somewhere in the suburbs of thought (thanks largely to Romanticism and the “sophistry” of Wittgenstein) to thought’s central point. Part of Badiou’s concern is that Philosophy is in danger either of being handed over to poetry (Heideggerianism) or, far worse!, sinking exhausted into the arms of religion. With regard to the first fear, I think it likely that should philosophy fall upon poetry and expect from poetic discourse its support, poetry would be purely and simply crushed; poetry could not bear the weight. Badiou enlists the famous ‘expulsion’ of the poets from Plato as part of his argument in this chapter. However, a careful reading of the Republic, such as was done by Phillippe Lacoue-Labarthe reveals that it was not poetry per se that disturbed Plato, it was the “mixed mode” [cf “Typography”, P L-L]: the “mixed mode” (as in Homer) where it becomes impossible to distinguish fact from fiction: the true statement resembles the fictive and the fictive the true thus unleashing within discourse of any kind whatsoever an unbounded, uncontrollable, and undetectable mimesis. The “expulsion” of the poets and the reconstitution of thought on the principles of mathematics was the only practical solution to the threat Plato could devise. The expulsion was makeshift, and indeed troubling.

In part this chapter is an argument for the sheer expressivity of mathematics and in this regard I am beginning to think that the proximity to and difference from Deleuze may be a red herring. The thinker perhaps in the greatest proximity to Badiou may be Emmanuel Lèvinas. I quote from Badiou: “…it is impossible to be lazy in mathematics. [Mathematics] is possibly the only kind of thinking in which the slightest lapse in concentration entails the disappearance, pure and simple, of what is being thought about.” First, note how far this attitude is from Agamben for whom distraction is a mode of being of which we ought to become capable (and no longer rely on the entertainment industry to accomplish for us)! Secondly, this quote is a paraphrase from Lèvinas who wrote “philosophy is philosophers engaged in an intersubjective intrigue where no one is allow a lapse in attention or a lack of rigor” and which in turn is paradigmatic of the infinity and rigor of the ethical rapport. In short, it is not possible to read Badiou’s ontology as an ethics of philosophy?

What is impressive about Lèvinas is the unprecedented expressivity of his ethical thought and its distance from any practicality. His thought does not allow a clear answer to the classical question “what ought I to do?” and he has been criticized for this. Starting from Lèvinas we never arrive at a program of action; we end in a radical passivity, and this is why I, in my book, say that his èthique is imaginary and then turn to Blanchot to investigate the (quasi-)ontology of the image. Likewise, Badiou’s favored version of set theory, the Zermelo-Fraenkel axioms, have been described by one mathematician (at the Stanford online philosophy site) as the “most expressive” of all set theories and also the “most difficult” to find any practical application for. Is it possible to critique both Badiou and Lèvinas as having become spellbound by the powers of sheer expressivity; to critique Badiou for a fetishizing of “rigor” and Lèvinas for rigorously de-ontologizing ethical discourse? Badiou pushes ontology to its “outside”, the empty set, and Lèvinas pushes ontology to its outside: the Face of the Other (who is no other, or no other than God—who is no one at all). For Badiou, mathematics (he says this) is paradigmatic for unflagging, infinite philosophical thought, and for Lèvinas, philosophical thought is paradigmatic of unflagging, infinite ethical responsibility.

Badiou and Kant: Event, Object, Non-Relation. The chapter on Kant, Chapter 11, is striking and I admit I have not yet gotten my mind around the notion of a “subtractive ontology” which relates in some way to Lacan’s notion that “there is no sexual relation”. If I understand set theory correctly then I understand that in the infinite Ordinals behave differently than they do in the finite realm. In the finite Ordinals form continua; in the infinite Ordinality does not purely and simply vanish (greater than and lesser than remain but only as indices of differences to which set theory as a whole is indifferent since these Ordinals cannot be shown, from within set theory itself, to constitute continua. Thus, in the infinite, Ordinals exist but in a relation of axiomatically sequential non-relation.) In the finite realm, continua have been shown, by Kant, to be constitutive of any event and thus I can begin to distinguish the radical difference between Badiou’s notion of Event and Kant’s.

Kant’s work is a response to the skepticism of Hume for whom there is no being but only Cardinality—an infinity of points which are habitually associated or anticipated as per our “second nature”. These habits then congeal into thoughts such as the thought of an object—a cat, for example—or the thought of causality. Hume seemed to show that these thoughts are illegitimate, that they are mere fictions. I do not perceive the cat per se, I perceive a myriad of perceptions, a myriad of points which I habitually associate with the object we name ‘cat’. Kant wished to show that these so called habits are in fact a priori synthetically unified by way of the faculties of intuition and understanding working in harmony. Kant was able to show that the notion of number, for example derives from the prior intuition of time. Badiou and Cantor of course reject this because they reject all intuitionism. For Kant, all time is one time because I cannot ever represent some object or some event from happening outside of time. Time is profoundly unified, is always already unified and from this inescapable intuition I derive the notion of number beginning with the number 1. Likewise, I cannot intuit anything as actually existing outside of space. Thus space too is profoundly unified, and as space is different from time I can conceive the idea of at least two numbers. (The combination of these two produces a third, and so on…)

Events are different from objects. We observe a boat floating down a river. For Hume, this is entirely fictional for the boat, the river, the motion itself are all habitual associations of an infinite Cardinality of perceptions which are perceived in it does not matter what order. But for Kant there is a necessity underneath our perceptions, not merely habituation:

[…]I see a ship move down stream. My perception of its lower position follows upon the perception of its position higher up in the stream, and it is impossible that in the apprehension of this appearance the ship should first be perceived lower down in the stream, and afterwards higher up. The order in which the perceptions succeed one another in apprehension is in this instance determined, and to this order apprehension is bound down. In the previous example of the house, my perceptions could begin with the apprehension of the roof and end with the basement, or it could begin from below and end above…

In this way Kant’s colossal achievement is to infer the necessity of the logical category of causality with regard to events (the ship floating down stream). Kant bypasses Cardinality and relies upon Ordinality (1st, 2nd, 3rd, …). Events are necessarily a priori Ordinarily arranged, sequenced.

With regard to objects the issue is more complicated and relies, for Kant, ultimately upon the form of the object in general, the “object = x” and the form of the subject in general “subject = x”.

From my book (somewhat abbreviated):

With regard to empirical concepts, the schema "produce" or "pre-scribe" a non-thematic view, or, as Heidegger calls it, a schema-image such that any particular can appear as what it is without being confined to any actual particularities of appearance. Giorgio Agamben, quite appropriately, calls this an "example." I borrow an example from William Richardson to explanation of how the schema-image works:

Across the street is a house. I know it to be a house, for it is presented to me by an act of knowledge. By reason of this presentation, the house offers me a view of itself as an individual existing object encountered in my experience, but more than that, it offers a view of what a house (any house) looks like. This does not mean, of course, that the house has no individuality, but only that, in addition to its own individuality the house as presented offers a view of what a house can look like, sc. the "how" of any house at all. It opens up for me a sphere [Umkreis] of possible houses. To be sure, one of these possibilities has been actualized by the house that I see, but it need not have been so.

With Richardson, we must emphasize the "can" here for it indicates a potentia and an activity by which a thing is able to appear as what it is (i.e., to "reveal itself," in Heideggerian language). Importantly for Richardson, Kant, Heidegger, and Agamben, this pre-scription or "rule-for-a-house" is not a determinate catalogue of characteristics proper to a house. It is, in Richardson's words, a "full sketch [Auszeichen] of the totality of what is meant by such a thing as 'house' "[emphasis mine]. This "view" by which a thing can appear as what it is called is, in Agamben's analysis, "purely linguistic": "the name, insofar as it names a thing, is nothing but the thing, insofar as it is named by the name” [Coming Community 77]. Furthermore, Richardson adds, "the view of which we are speaking here is as such neither the immediate (empirical) intuition of an actual singular object (for it connotes a genuine plurality), nor a view of the concept itself in its unity. The view we are speaking of is not thematized at all."

By way of the schema the unity of the empirical concept (which is ultimately ‘a word’ (Agamben)) is referred to the intuited plurality of possibilities it unifies without, however, being restricted to any one or any set of them. In contrast to this, the pure intuition—time—is already unified. It is instead the pure concepts (the categories) that are many. The schematism of the categories must, therefore, require special kinds of schemata or schemata of a character different from those of empirical intuition. As the pure intuition of time is the presentation of any object-in-general, the schemata must unite the categories to time so that ontological predicates may be applicable to objects in general. That is, the profound unity of time must be vulnerable to various modes ("ways") of presentation while remaining one time (for, "all times are one time", as Kant says [CPR 75], or, we may say that all languages (Mandarin, English, French, …) are language (even though nobody speaks “language” itself)).

Richardson reminds us that this is the most difficult and ambiguous aspect of Heidegger's entire analysis of the Critique of Pure Reason. Does he want to say both that time is the root of the transcendental imagination and that the transcendental imagination is the root of time? Richardson explains it as follows: since time is already unified, the schema (the "power" to unify) have nothing to unify. But, as time is already unified, it is always already schematized, or is the (pure) image of any schema whatsoever. Time is the very pattern of the schema-image and as the schema are several, each is already temporalized. Thus the schema "determine time" (or, articulate it, formalize it) and time in-forms that which it is articulated by. Time, as unified, "makes possible" that which articulates it and time is only as articulated (i.e., fused with categories such that ontological predicates can be applied to any object whatever). That is to say, quite obviously, the terms form and content are inadequate to capturing this circuit of activity and passivity.

Now, if the transcendental schemata make possible the application of ontological categories to "any being whatever," then we must look into the ontological status of this "whatever" for it is precisely the ontologically known. In short, what is an object in general?

Kant's answer is simple and disarming. It isn't anything:

Now we are in a position to determine more adequately our concept of an object in general. All our representations have, as representations, their object, and can in turn become objects of other representations. Appearances are the sole objects which can be given to us immediately, and that in them which relates immediately to the object is called intuition. But these appearances are not things-in-themselves; they are only representations, which in turn have their object—an object which cannot itself be intuited by us, and which may, therefore, be named the non-empirical, that is, transcendental object=x.

The pure concept of this transcendental object, which in reality throughout all our knowledge is always one and the same, is what alone can confer upon all our empirical concepts in general relations to an object, that is, an objective reality" [CPR 137; latter emphasis mine].

Heidegger will say that the mysterious object=x is a "something of which we know nothing." As an object in general, the x is not any particular object and, like the Umkreis 'house', it is not determinable. It is the Umkreis of any possible object. It is the so-called object, or any object purely insofar as it is called an object. It is what all objects share, but it is in-itself a no-thing, non-being, non-object. It is, in Agamben's language again, "the pure being-in-language of the non-linguistic." (It is what would be the word for ‘word’, but there is no word for ‘word’) It is that which, in any object, objectifies it, formalizes it for experience, envisions it as such, as an object. The object-in-general is purely imaginary because it is schematized par excellence, yet it is that which is not presented in any presentation. Heidegger will call it a "pure horizon" within which any object can be rendered present-to-us. Kant will say it is a "pure correlate" to transcendental apperception insofar as it is a unity waiting for something to unify, a like that precedes anything to liken. In that sense it is more objective than any object, more being than any being so that Heidegger will be able to re-christen it as Being. In the "Brief über den Humanismus" he says (in my own translation which I leave crudely literal in order to emphasize the point): "Thus Being is being-er than any being [Gleichwohl ist das Sein seiender als jegliches seiende]” [Wegmarken 359].

The object=x is not a being, not an object, hence its relation to the knower will not be cognitive. It is not present. It is more than present, more present than any presentation. It is the sheer "can appear" of any appearance whatever. Not absolutely nothing at all, nor just anything at all, it is the disjunction of something and nothing. “This =x," Kant says, "is only the concept of absolute position, not itself a self-subsisting object but only an idea of relation, to posit an object corresponding to the form of intuition" [OP 172]. Alien to all substance (i.e., not "self-subsisting"), the object=x is fragility itself. Empty of all content, the x is the sheer "that there is" [il y a, es gibt] something rather than nothing, just as Da-sein, or the transcendental imagination, or, unified apperception, or the Kantian “I” is the sheer "there is" someone rather than no one. Infinitely fragile and transcendental, the x is arche-relation, arche-obligation that there be such a thing as imagination (forming, presentation) itself.

This presentation, needless to say, is ambiguous. Nothing, or the Nothing, is presented. Nothing is "beyond" the presentation; no thing-in-itself arises ghostlike beyond the objectively (phenomenologically) known. The x, the sheer presentation, is suspended, delayed, retarded, interrupted—coming but never arriving. The essential distance between the knower and what is preeminently ontologically known erodes in such a way that the two sides cannot but fuse together. Nothing definitive is presented. No figure, no outline, no border, nothing framed. What "happens" is (only) that the transcendental imagination feels itself obliged to (or constrained to) present. That is to say, it feels itself and thus submits to itself as if it came from outside itself--as if it was itself an exterior force. This auto/hetero-affection is profoundly temporal, moreover, in the sense of an extreme tens(e)-ion, or anticipation, not unlike Hume’s involuntary and naturally human association of ‘tick’ with ‘tock’. The "power" of Einbildungskraft is here fused with an essential impotence. The object=x shares with the Entstand the characteristic of unknowability, but, as a presentation in extremis, it turns away from God back toward objects, back toward its proper domain. The object=x is the irreparable consignment to things, to objects, to formalized profanity, but only via a detour through the Nothing, through non-being.

We do not then, suddenly and unexpectedly confront the thing-in-itself, the sacred thing, the Entstand as it is directly offered from out of the Most Ineffable [God]. To the contrary, we suddenly and unexpectedly confront nothing, non-being, that is to say, ourselves: ourselves as the no-thing itself: or, the Kantian transcendental ‘I’. That which all that is has in common is no-thing, that is to say ‘I’. We confront a limit without ever confronting it for the limit was nothing, was always already "in" things, erased in its approach and suspended en deçà du temps like a paralyzed and paralyzing force. For, that which is presented is the sheer "there," and this pure "there" is the pure position of the Kantian "subject" or, the knower, the transcendental imagination, the Da-sein.

The object=x is the very turning away from the sacred for it is the pre-presentation of things, of objects (i.e., of that which is never presented to God). If you like, the x "shows" the ungodliness of the world. It shows the irreparable profanity of the world. Via this paralyzed presentation the world is presented precisely such as it is: it (the world) is precisely phenomenal and nothing more. Appearances conceal (only the) nothing. That which seems is. No proper nature is revealed to us, no coming-from-out-of-Ineffability is unveiled. Only the irreducible "thusness" of things is revealed. Thought, then, before it thinks any thing, is able to think (or is not able not to think) pure profanity, or pure ordinariness, as its only extra-ontic thought.

This means then that (pure) thought is naïveté par excellence. Turning at once to objects, it has always already forgotten God. Irreducibly lost among things, thought--pure being-in-language--is abandoned, undestined, scrupulously (formally) thing-ish. Thought is constrained to think nothing beyond objects. This is its "extreme youth"—to have always already evacuated itself of any Platonic latency. Thought is originally purely exposed, purely presented, purely there, and it is "able" to hold itself in suspense just prior to its "work" of figuration. Thought, in short, before it is captured in the world, "thinks" the place of art, the space of poetry. It is "able" to think, before there is any thing, "relation in general" in the pure "there". This "ability" is a passivity. It is a pure passion. A passion, however, that is never present like a state-of-mind: It is not a psychology except in Kant’s purely rational sense. It is the pure finding-myself-there, or being-the-there. It cannot not be-the-there (without purely and simply ceasing to be). That is to say, for a paralyzed moment, purely exposed to all its possibilities (all its predicates) it is un-destined to any one or any set of them. But this paralyzed moment does not belong to a past, a "was." The Kantian "subject," is its there incessantly, without, however, being able to bring itself before itself.

We have seen that, for Kant, the transcendental apperception cannot grasp an object in particular. The sole “content” of its knowing is always the same: the object=x; a “something of which we know nothing” (Heidegger says). Deprived of any actual object, transcendental apperception can only think a pure ‘there’ or a “pure position”, which, in fact, it (the transcendental apperception) itself is. Deprived even of intellectual content (or intellectual intuition—something Kant declares strictly impossible), this “perfectly contentless representation [i.e. the transcendental apperception],” he says:

Cannot even be called a conception, but merely a consciousness which accompanies all conceptions. By this I, or It, who or which thinks, nothing more is represented that a transcendental subject of thought = x, which is cognized only by means of thoughts that are predicates, and of which, apart from these, we cannot form the least conception. Hence we are obliged to go round this representation in a perpetual circle, inasmuch as we must always employ it, in order to frame any judgment respecting it. And this inconvenience we find impossible to rid ourselves of, because consciousness is not so much a representation governing a particular object as a form of representation in general…

Like the object = x, the subject = x is inconceivable outside its predications. It is nothing other than its predications yet it is itself not purely and simply its predications. It resembles the object = x which is no thing, nothing. The I resembles nothing. It is pure resemblance, likeness itself, analogy. A mere x, this transcendental subject is not knowable or experienceable in itself. Per consciousness it is itself unconscious of itself. The transcendental subject is a nothing that can grasp nothing. It is that which accompanies all experience but is itself never experienced (confirming Hume). It is exactly a consciousness: I, He, She, or It makes no difference. That which unites all experience and makes any experience “mine” is anonymous: an interiority exterior to itself: it frames itself and hence at the same time eludes itself. And so on, and so on…The Kantian subject is an “inconvenience” we cannot do without, without falling purely and simply into Humean flux on the one hand or Cartesian solipsism on the other…

It is this line of thinking that Badiou rejects for he insists upon a subtraction, a non-relation of void (object = x) and void (subject = x). There is no arche-relation nor is one even desirable. He is hinting that, in Kant, we can see the outlines for a non-objective thought which is asymmetrical with the void of the subject. In this, I believe he is drawing heavily from Lacan. Instead of subject-object in representation underwritten by the imagination, there is instead “pure multiple presentation” which would not relapse into Humean skepticism. In short, Kant never was able to ontologically ground the universality of relations (imaginarily or logically). The very fact that there are discrepancies between the two editions of the Critique of Pure Reason is an attestation to non-relation, for Badiou. It was not an insoluble problem but a presentation of a multiple (at least two). In actuality, the very operations of ontology—unbinding—dissolve the critical operation of binding the object in general to the subject in general. In short, Badiou’s advice to Kant might be: Let unbinding be, for this is the characteristic of ontology, to subtract itself from all binding, from all relation, from all objectivity.

In the history of philosophy the thesis of the univocity of Being is taken over from the thinking, beginning with Aristotle, of Substance. When in this introduction I speak of Spinoza and substance, we can substitute Being. Put differently, it is now widely recognized that, while remaining with the vocabulary of Metaphysics (Substance, attribute, etc.) Spinoza was in fact defining a new mode of thinking which would come to dominate philosophical discourse: ontology.