For the love of the world

Kolakowski tried to claim that “truth as a value different from effective applicability is … a part of a myth which refers the conditional empirical realities to an unconditioned universe”. What Kolakowski calls the “myth of Reason” we might instead call a sort of eidetic intuition of a world (what Dante called God in the Paradiso and what Borges described as the Aleph where we see, chiastically, the Aleph in the earth and the earth in the Aleph). In these intuitions we “encounter” the One but of course we know that there is no such One. There is no “myth of Reason”* simply because the impossibility of providing consistent expression to this intuition is the condition of possibility for thought to occur; the impossibility of the coincidence of completeness and consistency constitutes the infinitude of thought, i.e., that there is thought at all. Thought does not ground itself because such a “pure” thought is always radically impure in its transcendence, embedded in ambiguities, contradictions, contexts, situations, and interests. The task of reflection is thus to do justice to the concrete infinitude of thought in and of a world.

*There is, however, a myth of the world.

One and nothing: free variations (continued)

4. The distinction between Greek mathematics and modern mathematical analysis allegedly turns on certain discoveries of properties of infinite series. What this characterization obscures, however, is that we need not think of the problem of number as one of enumeration or, more generally, that the problem of multiplicity be confused with that of a series. The work from Bolzano to Cantor recognized the latter fact with the well-known consequence that there are perfectly good ways to speak of actual infinities. But the mortgage that set theory had to pay—and here the original problem returns—is, broadly speaking, an account of the structure of multiplicity, toward which we cannot remain indifferent and which has both logical and ontological consequences (the former, for example, being an effect of the reflexive problem exposed by Löwenheim-Skolem and the latter simply a consequence of the trivial fact that there is no reflection arrow for the empty set).

The turn toward intuitionism in mathematics, viewed in a certain light, is a return to the problem of Platonism not only in the ontological (Brouwer) but also the epistemological sense, which is the explicit difference in the treatment of number between, for example, Plotinus and Proclus (but which remains a difference in aspect only). The question of number takes place not at the level of unity and multiplicity (one and many) in the order of being(s) but, rather, in the passage from being to non-being where the latter is understood not as the negation of being already counted as one under the category of quantity but as a transcendence of being (i.e., the non-being of the One, for example, is already a double negation: a negation of the first negation of being as nothing). The typical theological mistake has been to conflate Platonic cosmogony/ology with ontology.*

*Here Heidegger’s account of onto-theology has severely limited our capacity to understand the terms of anti-Aristotelian metaphysics.

Proclus’ ideal (eidetikos) number or Plotinus’ substantial (ousiodes) number are principles of the intellect understood as the ontological expression of what is prior to being and nothing other than the activity (energeia) of being. Proclus in a sense ‘domesticates’ Plotinus’ account of substantial number in the intelligible by locating it as a sort of category in the soul; but this account nevertheless is supposed to explain how mathematical number is possible within the Platonic account of number as substance against the Aristotelians. The significance of the monad in Platonic metaphysics is that it is the principle not only of the unity but also the limit in being: the monad is not itself (counted-as-)one, which explains how the dyad participates in the monad in different ways (i.e., how the dyad is both clearly discrete and continuous). The persistent mistake of Aristotelianism has been to insist that the difference between number and monad be quantitative and to fails to understand that substantial number does not count substance.

5. The ambiguity of the substantial and the mathematical one is, however, necessary insofar as it expresses the duality of thought and being; or that thought and being are expressions of substance considered under different attributes à la Spinoza; or that thought is the reverse of being and vice versa. Modern mathematics has simply given rigorous formulation to the perennial Pythagorean proposition: not only that being is number but that being is number as structure. The absence of structure has been nominated variously as One (Plotinus), as zero (Peirce), or as void (Badiou). Everything turns, however, on how we interpret the nature of this absence and that we should not be misled neither by the nomination of the transcendental,** the confusion of number with enumeration, nor the conflation of the One with the “all” (as universe, the whole, the set of all sets, etc).

**Badiou is exemplary here: “I say ‘void’ rather than ‘nothing’, because the ‘nothing’ is the name of the void correlative to the global effect of structure. … The name I have chosen, the void, indicates precisely that nothing is presented [emphasis added], no term, and also that the designation of that nothing occurs ‘emptily’, it does not locate it structurally”.

6. The symbol of the monad is the circle since it “preserves the specific identity of any number with which it is conjoined” (Iamblichus), just as the void can be added to (and/or subtracted from) any set. For the Pythagoreans, the monad was also the intellect insofar as it was seminally (“potentially”) all beings; the circle has therefore long been the geometric expression or symbol of infinity.***

***See, for example, Augustine’s famous image of God or, more interestingly, Spinoza’s curious remark that “number is not applicable to the nature of the space between two non-concentric circles. Therefore if anyone sought to express all those inequalities by a definite number, he would also have to being it about that a circle should not be a circle”.

While the monad is often characterized as stability (monad is derived from “menein”, “to be stable”), stability is distinguished from nothingness as nascence (or, as before, harmony is only possible by forgetting a fundamental disharmony):

“[T]his incessant movement and progression which all things partake could never become sensible to us but by contrast to some principle of fixture or stability in the soul. Whilst the eternal generation of circles proceeds, the eternal generator abides. That central life is somewhat superior to creation … and contains all its circles. For ever it labors to create a life and thought as large and excellent as itself; but in vain; for that which is made instructs how to make a better.” (Emerson, emphasis added)

This is the real (ethical) meaning of transcendence or the “moral fact of the Universe”: that the given is never sufficient and that “every ultimate fact is only the first of a new series”. The very condition of possibility for thought is its inadequacy to being, which thus constitutes its fundamental imperative: to recognize this deficiency not in itself but in what is given to it. “Beware when the great God lets loose a thinker on this planet. Then all things are at risk.” The weakness of thought—its inadequacy—calls not for its mystical renunciation but a persistent refusal of that temptation toward cessation, whether in its annihilation or defeat by the overwhelming burden of totality or its pacification by the illusory satisfaction of identity—“I’m just me” or “I’m only human, after all”. The Pythagorean monad is the limit of being only as a self-limitation (which is the only way to account for the priority of the monad with respect to the dyad) and in a certain sense thought is nothing other than the (reflexive) expression of this “self”. This expression, however, betrays itself only through negation: just as the Pythagoreans called the One “Apollo” (from a-pollon, “not many”) and harmony requires the impossibility of complete unity, “the one thing which we seek with insatiable desire is to forget ourselves, to be surprised out of our propriety, to lose our sempiternal memory, and to do something without knowing how or why; in short, to draw a new circle” (emphasis added). Thought fulfills its destiny not only when it ventures into the unknown but takes the leap into what, in principle, it can never know.

[Cf. the previous post from March 2010 “Dialectics at a standstill”.]

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!).

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).

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.