Badiou
One and nothing: free variations
1. Along the way toward expressing the thoughts of God before the creation of the world, Hegel's logic consumes the possibility of mathematics at the highest moment in the doctrine of being. Just before his explicit treatment of quantity, however, he includes a note on Leibniz' monadology and observes that "plurality remains as a fixed fundamental determination, so that the connection between [monads] falls only in the monad of monads, or in the philosopher who contemplates them". What Hegel has grasped only vaguely here is that for Leibniz mathematics and metaphysics express the same thought, i.e., that mathematics understands the world in the same way as the divine intellect (which is the real meaning of his remark at the determination of a maximum is the work of the divine mathematician who determines the greatest number of compossibles in a given world). Leibniz' "new mathematics", he says, "makes man commensurate with God".
The problem of plurality to which Hegel refers is Leibniz' notion that the infinite (number of) monads are representations of a single universe (Monadology §78) without thereby understanding this universe as substance.* Leibniz struggles to provide an adequate topological model of such a universe** and instead speaks of the "accommodation" or harmony of all things.
*One is tempted to say "Spinozist" substance were Spinoza's definition of substance as "one" not problematic from a mathematical point of view and which would require extensive work in disambiguation. Rather, we might safely say here "Aristotelian" substance up to and including Heidegger's interpretation of ousia.
**Elsewhere I have claimed that such a model would be something like a Klein bottle.
2. Yet we should remember that the essence of harmony is a fundamental gap or discontinuity in what the sensibility desires as unity. The law of the series that guarantees the immanence of the world in the monad (what Badiou calls the "absolute interiority" of the monad) allows us to speak of the monad as one in a strictly different sense than that of the universe.
Here we might benefit from recalling that this is the Platonic problem par excellence. Against the Aristotelian dictum that being is always a being (i.e., that unity follows immediately from being)—and Aristotle's well-known confusion of the Indefinite Dyad as two "counted-as-one"—Plotinus' account of substantial number accounts both for the ontogenetic differentiation of being (see, e.g., Enneads VI.6.15) and for the fact that the One is not enumerable. What is at stake, philosophically if not mathematically, in Platonist mathematics is precisely the capacity to distinguish the one in the order of intelligibility from the unity of any individual. Being, for Plotinus, exists only because it inherits unified number from the One and, conversely, multiplicity is not the division of the One but the intellect's contemplation of the One. We might say that substantial number is the "form" of the monad—as the immediate image of the One—combined with the "matter" of the Indefinite Dyad or, in perhaps more precise language, the Indefinite Dyad is nothing other than the limitation of unity as apostasis (and reciprocally, according to the Neopythagorean conception of monadic number, the monad is the limit of quantity: the monadic number is a progression to and a regression from mulitiplicity), the intellect is nothing other than substantial number, which is why being is not itself number but number is the principle of being.
3. What does it mean, then, to be a thinker of the One? Or, perhaps more modestly, what is at stake is the character of our ethics. For a thinker of the One, ethics is beyond being, in a sort of pagan transcendence of that which cannot be counted-as-one, as opposed to an ethics of the void, which must resist, perhaps violently, the capacity for being named and that must tear itself away from the very conditions of its survival. Our choice, however, is not that between excess and subtraction since the Plotinian One is nothing other than a series of negations: not to move away and not to progress "even a little" to the two. If there is not a symmetry between these two orientations, our choice seems to be in what direction this negation operates: whether the difference that counts is a negation of the given (multiplicity) or in the (im)possibility of negating what does not exist (a double negation!).
Posted in Badiou, Deleuze, Leibniz, mathematics, Plato
The fundamental decision of metaphysics
Ancient philosophy enforced a decision between speech and silence. When modern philosophy accused its predecessor of therefore confusing being and nothingness (since to say what "is not" cannot be said does not preclude the identity of the being of what is not), we were asked to choose between the unity or the difference of being and thought. Hence, for example, Badiou's characterization of the constructivist position in metaphysics declares that what is unnameable simply "is not", such that metaphysics finds itself in a position of absolute immanence that "maintains the entire dialectic of the event and intervention outside thought". Such a position, of course, simply begs the question as this is precisely the point for someone like Deleuze (see the plane of immanence as the image of thought). Rather, between the constructivist (Deleuzian) and generic (Badiousian) orientations of thought, beyond the difference between excess and subtraction, lies perhaps this fundamental choice: whether to address the genesis of thought through an account of the names of being or whether to name the indiscernible point at the chiasmus of thought and being (what Badiou nominates as the "void") but which therefore cannot be either. If Badiou right to insist that, for the constructivist, the event is prohibited from thought, we must decide if the vocation of philosophy is to culminate in the science of thinking (logic and metaphysics) or in the affections and passions of movement (physics).
Posted in Badiou, Deleuze, metaphysics
Politics and democracy
Recently, La Fabrique éditions asked a series of fashionable authors to comment on the sense of the word "democracy" and whether the word should today be abandoned. The collection (Démocratie, dans quel état?) is prefaced by invoking, as a provocation, the spirit of La Révolution surréaliste.*
*Posing the question in this way is only possible in Europe where the notion of "democracy" was both early and late to arrive. For this reason, none of the authors make the mistake predominant among their Anglo-American counterparts in political theory of assuming that the word "democracy" designates a particular type of constitution or state-form, which is axiomatic (in a non-technical sense) for so-called "democratic theory". The very (odd and ultimately disastrous) distinction between political theory and political philosophy is another symptom of the confusion of the Anglophone discourse on democracy, which is yet another problem entirely than the confusion addressed by the Fabrique volume and deserves separate polemical treatment. The internal discourse of political theory itself cannot refuse to address its nebulous status as neither political science nor political philosophy (the "neither" here in the pejorative sense of being "inadequate"). The particularly banal treatment of the "return of democracy" on Obama's election should be proof enough of this. Under the auspices of a naïve empiricism, democratic theory has ceased to understand what is at stake (dare we say, "metaphysically"?) in the very notion of "representation" which is not merely an epistemological nor even a metaphysical question that can be separated from its meaning as a political term (for Negri and Foucault, "representation" is an ontological question; for Badiou it is logical; for Deleuze it is both; etc). At best, "representation" becomes a procedural term for democratic theory and, consequently, is beholden to a problematic positivist methodology. Or, to put it another way, what calls itself "democratic theory" proceeds by assuming that there are democratic subjects—who are/not represented, who behave as political agents in ways that can be charted ("rational actors"), etc—who are constituted by "the citizen" considered as a purely legalistic entity, which leads us into an ultimately futile debate in legalism that ends in the sham proceduralism of so-called "legal process" in America or hermeneutics by another name. It is also noteworthy along these lines that Habermas—who is praised by the advocates of legalism—is not among the authors collected in the Fabrique volume.
The provocation of La Révolution surréaliste is not its overtly communistic program but rather in its professed allegiance to the "principle" of historical materialism, i.e., in Breton's words, the "sovereignty of thought". The question, in its most brutal form, is simply: what is the relation of thought to politics? Obviously, "thought" is not taken here in the abstract sense of so-called "rational choice theory" or even in the metaphysical sense of a res cogitans. But if thought is to be taken in its substantive or concrete sense, then the question is not how to relate thought to politics insofar as the conditions for thought are always already political. But to say this is still too abstract, since the liberal democrat would affirm the same thing: the end of politics is to establish the form but not the material of association (i.e., the "human being").
Rather, the question at hand is a Nietzschean question: what are the conditions under which thought is possible? This is, essentially, what Badiou posits in his reading of the Republic (in the Fabrique volume) in what he identifies as two fundamental theses:
1. The democratic world is not really a world.
2. The democratic subject is not constituted with respect to its pleasure [jouissance]. [My translations; "pleasure" is preferable to "enjoyment" here insofar as Badiou is responding to the usual treatment of hedonism in Plato.]
The first of these is readily recognizable as an extension of Logiques des Mondes. The second is (and this is now my reading of Badiou's reading of Plato) an intervention in the question of political education—that there are not political subjects but that we must become political subjects. The democrat tries to claim the transparency of the political subject (particularly to itself!) problematically both as the condition and the result of political education. But if there is anything we can learn from the democratic impulse it is just that the very site of politics is the disjunction between thought and its transparency.
This, it seems to me, is one step in avoiding two tendencies in continental political philosophy: 1) to reduce politics to democracy tout court (e.g., democracy is always deferred, impossible, etc);** 2) to reduce politics to the operations of the state or, conversely, 3) to reduce politics to the attempt to insert some distance between the subject and the state. Rather, I submit, politics is nothing other than the continuous construction of the state. The simultaneous separation of subject and state is what, following Abensour, might be called metapolitics.
**One possible exception to this charge is Lefort.
Posted in Badiou, Plato, politics