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December 17, 2004

Notes on Badiou, D&G, and the new antiliberation movement

Badiou declares the necessity of the 're-entangling' of philosophy and mathematics, and claims that philosophy (by which we later understand something like, philosophy after Hegel) has systematically excluded mathematics.

His savage purification gives no quarter to collaborators of any ilk. They are all guilty insofar as they perpetuate a romanticism of finitude, an image of life. It styles itself a neo-enlightenment, insisting on the cold, eternal truths of mathematics as the only corrective, the only weapon against universal superstition.

The disjunction of mathematics is seen as philosophically constitutive of Romanticism - so that romanticism (from Hegel) 'retroactively determines' the Classical age of philosophy as one in which philosophy was conditioned by Mathematics. And "what is ultimately at stake here [is] the following question...can we be delivered, finally delivered, from our subjection to romanticism?"

According to B, Positivism and Empiricism are mere inversions, made from 'within the completed disentanglement of philosophy and the sciences'. They fail to question the premises of this disentanglement. The respective purisms of Heidegger and Carnap merely draw out the dichotomy of the romantic gesture of schism between scientism and the retreat into poetry. Logical positivism and 'Anglo-American linguistic sophistry' (after wittgenstein) are likewise strategic retreats: unable to admit of mathematics as a 'type of thinking' rather than merely a 'language game': "Whatever the case may be, mathematics does not think". In fact they are merely keeping at a distance the fact that mathematics constitutes a reality and a discipline 'which it is impossible to be lazy in'.

What was primarily instrumental in these thinkers maintaining such a distance was the temporalization of the concept (historicism): "It was the newfound certainty that infinite or true being could only be apprehended through its own temporality that led the Romantics to depose mathematics from its localization as a condition for philosophy...Romantic speculation opposes time and life as temporal ecstasis to the abstract and empty eternity of mathematics." The second root of the 'disentanglement' is finitude; the thinking of the horizon and the theme of finitude that characterise german romanticism. So that the re-entanglement of philosophy and mathematics is also 'to have done with finitude'; a finitude which in persisting renders the death of god ineffectual. ("we do not possess the wherewithal to be atheists so long as the theme of finitude governs our thinking"; "Descartes was more of an atheist than we are, because eternity was not something he lacked")

Emerging here is a philosophical expression of the french reactionary anti-liberalism of the 80s and 90s (of which houellebecq is the most incisive and - to his credit - ambiguous interlocutor) ; and Badiou's critique of Deleuze is based on placing him within this romantic lineage (as a 68er and neo-Bergsonian vitalist), as having fudged the movement from one/multiple to multiplicity by totalising the infinity of the cosmos into a big One (BwO) in which consequently all beings are of necessity undifferentiated (ontological liberalism). Deleuze, he argues, still resides in a metaphorical thinking of the infinite as the Open, of beings-as-simulacra and truth as historicised (subject to time) etc...Thus there is a great deal of delight taken in 'exposing' deleuze (never D&G, because Badiou doesn't like to talk about CS, except as a sort of 'bad influence') as an nice but unfortunate fool who in attempting to overturn plato merely ended up with a comically unwitting platonism (whereas B is upholding a 'full-strength platonism'). For where plato would have banished poets and only allowed geometers access to philosophy, today the opposite is the case. The only way we can escape from neo-romanticism without lapsing into a neoclassicism is to re-examine these relationships (between maths, philosophy, poetry) since postmodernism is merely a confused expression of their irresolution.

To 'complete' the enlightenment project requires a renewed effort of desecration, dismantling of historicism, and demystification of the infinite ("the infinite must be submitted to the matheme's simple and transparent deductive chains, subtracted from all jurisdiction by the One...released from the metaphor of the open").

The suggestion is that mathematics (and specifically, the species of set theory that proceeds from Cohen) provides us with the best tools for an ontology of the multiple, or 'the infinite as indifferent multiplicity" (the post-Cantorian treatment of the infinite as plural and numeric that "renders the infinite banal"). "It is in this sense that I have invoked a 'Platonism of the multiple' as a program for philosophy today. The infinite untethered from the one (as indifferent multiplicity)."

The argument for the absolute sovereignty of mathematical thought rests on its violence, and the combined outlandishness and applicability of its results: What we discover, to take a simple example by way of the square root of -1 and the complex number plane, is an astonishing proof of the potency of mathematics. We discover a real entity whose basis lies entirely within number, but which displays none of the stereotypical qualities that those ignorant of mathematics would expect or propound in their folk-philosophies (which could be summarised as linearity, metric regularity, identity, etc.). In fact non-mathematicians would be forgiven, looking at something like the mandelbrot set, for suspecting some sleight of hand, that some empirical germ has been smuggled in somewhere in the process. But ultimately they would have to concede that these entities are real, that is, they consist, and that the pursuit of number offers us far more sophisticated, if outlandish, ways of understanding (for which read 'counting') reality, than could ever be provided by the putative 'thinking' of the philosopher.

It is the strength of mathematics, says Badiou, that, in taking its lead from the order apparent in empirical realities, it can extend them to finally uncover explanatory schema that comprehend not only those empirical realities, but others; a second step to this is to say that in doing so it is found that these realms of number, monstrous efflorescences from the point of view of phenomenologically-led folk-wisdom, often turn out to describe with extreme precision the results of physical experiments; which, in turn, allow us paradoxical insights into the nature of reality which phenomenology could not hope to achieve. Mathematics is the only way to pursue an inquiry about what is true of reality _as such_ with the _guarantee_ of jettisoning phenomenological or other preconceptions. Thus, the sign above the door to philosophy should once again read 'only geometers my enter' . Whether, given the rest of Badiou's ponderous writings, this also implies 'abandon your desiring machines...' is another matter. What is for certain is that under Badiou's conditions, philosophy-mathematics absolutely renounces any ability to say anything about 'beings', that is actually existing contingent material assemblages.

[[For DG, are not the singularities of matter constitutive of the abstract machine as much as mathematics (metallurgy and numerology are instances of tracking processes, just as philosophy should be. Isn't the hardness of rock just as irrecusable as the reality of the complex plane? Is it simply a prejudice against phenomenological data that obscures this?).
- their strength is to present empirically instances as they occur in life, in a multitude of forms
- the problem at the level at which it proposes itself – which may be as double bind, as calculus, or sets.
- But for B, this is all so much ‘phenomenological pottering’.

Badiou only wants to concentrate on the quality of mathematical truths
-He exalts maths as that which allows us to become immortal, to lift us up from this 'scurrying on the earth', that which removes us from life

Why are D&G described as 'vitalist'? Is there anything in D&G that suggests the imputation of some transcendental principle beyond pure machinism? If not, what exactly is the content of the charge of 'vitalism'?
]]

My question then is : what is the relation of onto-mathematics to "mechanomics" (that is, the practice of numerical signs as directly-effective real entities)? Given that Badiou's argument would not allow for an argument on historical-materialist grounds (something like a 'proletarian' popular numeracy, or engineering vs geometry, royal vs vagabond sciences) since it would lead back into historicism and thus romanticism, how are the authority of mathematics, as a masterly discipline to philosophically tame the world with its explanatory power, and the sheer machinic potency of number as reality in its rawest state to be distinguished on purely abstract, numeric grounds? And in what way does the former 'depotentiate' the latter?

As I understand it, something like the complex plane would belong, in D&G terms, in the abstract machine, as (the closest we can get to) the pure grain of the real as nummoid difference (here we might return to the idea of vagabond/metallurgical science which would affine to numerological mysticism), or attractors immanent to all matter, activated as contents and forms are zipped together through stratification processes. Badiou takes away any possibility of understanding number as materially effective.

It does seem to me that there is something real at issue here, in terms of this multiversal tendency to react against the multiplicitous undecidable nummoid processes that libidinal materialism unleashes with a masterful discourse of a 'return to rationalism'.

It makes sense to take issue with Badiou from the position of Capitalism and Schizophrenia, because he (and Zizek) consider this to be the worst efflorescence of 'bad' Deleuzism, productive of the ‘vitalist terrorism’ of his ‘disciples’ and constitutive of his ludic complicity with the feverish multiplication of cultural product lines constituted by ‘digital capitalism’, something from which Deleuze must be rescued before any attempt is made to salvage 'true' (=platonic, even if an inferior platonism) deleuzian thought.

[Alliez's argument] Badiou’s reading of Deleuze operates first of all by a strategy of assimilation, allowing him to bring Deleuze into closer proximity with himself by asserting that the carnivalesque parade of ‘cases’ in fact conceals a monotonous indifference. By thus indicating that the two parties are as one in this indifference, Badiou neutralises any differend on the basis of pragmatics (that is, on the very basis that was the driving force of CS) to take up instead an apparently simple choice, presented entirely in his own terms (those of an irrecusable and universal fundamental ontology), between a rigorous mathematical conception of multiplicity and a failed or deluded conception of the multiple-in-one.

CS is a dangerous machine, it was a dangerous path for Deleuze to take.

It is profoundly ambivalent – the profound ambivalence of the BwO to the organs, and the profound ambivalence of the capitalism, in its conjoint movements of liberation and reterritorialization. So it should be no surprise that it can be, and has been, employed wittingly or unwittingly as a prop to the ‘ideology of digital capitalism’ (zizek's phrase); since this ideology, insofar as it exists, must partake precisely of the same ambivalence. But the strength of CS is that it only takes sides on the level of Desiring-production, which is already double, a double-movement of the BwO and the organs, of construction and flux.

There is no denying that now more than ever we are in need of a reinvigoration of thinking. But it is a machinic thought that will constitute the new enlightenment, not a rationalism made poor by purification. It’s a matter of the cold or the hot; the clean and the dirty.

I wonder why, in his survey of how philosophy has wrenched itself away from the mythopoetic continuum by entangling itself with mathematics, Badiou treats in sequence: Parmenides, where the matheme breaks the surface of the poem but ultimately cohabits with it; Plato, where the matheme finally subjects myth to its cold discipline (but Derrida had something to say about the way that myth always has a way of twisting out of the grip of rationality); but not Heraclitus, thinker of fire-myth, exchange and the paradoxical reversibility of sign-systems.

Posted by undercurrent at December 17, 2004 12:45 PM

Comments

Posted by: northanger at December 26, 2004 02:39 AM

Posted by: undercurrent at December 26, 2004 01:16 PM

Posted by: northanger at December 26, 2004 07:41 PM