Pythagoric snares

Those interested in Badiou should note the currently (and temporarily) available material online at Critical Inquiry, whose summer 2011 issue featured an article by David and Ricardo Nirenberg: "Badiou’s Number: A Critique of Mathematics as Ontology." In Critical Inquiry's forthcoming winter issue (which, when it comes out, will render the links here dead), the Nirenbergs' critique is responded to by A.J. Bartlett and Justin Clemens, whose article is prefaced with some brief remarks by Badiou, the gist of which is (I quote) "What a disappointment!"

Bartlett and Clemens' description, which I read first, led me to expect some truly dismal thinking when I turned to the Nirenberg's original essay. The claim is, over and over, that not only have the Nirenbergs (who they, um, "cleverly" re-name Nini, with a nod to Derrida's Limited Inc, in a move that seems just depressingly nyah-nyah by the third instance) misread Badiou, but that they have done so willfully, or stupidly, or both—unless, that is, the Nirenbergs have not read him at all, which Bartlett and Clemens do not hesitate to insinuate may well be.

Suffice it to say that upon turning to the Nirenbergs' essay, this claim does not hold up. But their point that the Nirenbergs have read Badiou against his own express declarations certainly stands. This is not, to my mind, a coup de grace. One may well say, after all, that if the Nirenbergs can argue that Badiou's formulations can be put to serve positions which contradict other of his own explicit statements, so much the worse for Badiou. The real question is not whether the Nirenbergs have read from (or even into) Badiou statements which are contradicted by some of Badiou's own intentions (or, God help us, the secondary literature), but whether or not their readings are defensible philosophically. Certainly they arrive at conclusions about Badiou which I cannot share, but the condescending dismissal of their argument seems to me to be woefully beside the point.

To be sure, I am not of their position, nor of Badiou's, when it comes to the nature of philosophy nor of what they call "pythagoric snares." Their central contention—that, as they put it in their rejoinder to Bartlett and Clemens,

Badiou's thesis deliberately blurs essential distinctions between realms of discourse

—could be put as well to Plato (a point they concede in advance); but this is, I maintain, a constituent practice of philosophy, not a regrettable lapse of good philosophical discrimination but one half of philosophical praxis. The other half, of course, is knowing what one is doing, and continuing to make the "essential distinctions" which are nonetheless blurred. It must be said that Badiou reiterates these distinctions with a rare degree of articulation. If I think he lapses, it not in blurring the distinctions, for which the Nirenbergs fault him, but in doing so with too guilty of a conscience.

This is because I maintain that the Whole, with which Badiou is overtly willing to dispense, is a sine qua non of philosophy. The "blurring" for which the Nirenbergs reproach Badiou is, to my mind, the unavoidable (albeit deniable) practice of the "flip side" of articulation. The closest we come to this in language is poetic trope. Obviously, this thesis is close to unacceptable to Badiou, for whom it could (depending on just what we mean by "language" here) amount to conceding that poetry is a form of silence (as he puts it in his study of Wittgenstein), or—more tendentiously—a form of non-thought. On the other hand it is also unacceptable to the Nirenbergs, since for them it would license the "pythagoric snares" to which they object so strongly, mistakes (as they see it),

in which contingent aspects of mathematical models are used to reach cosmological or ontological conclusions.

They point, e.g., to Glaucon's discussion of the "nuptial number" at Republic 545 &c. I on the other hand hold that the account of political justice, or cosmogenesis, or the relation between word and object, in terms of mathematics or cookery or what have you is an echo of an archaic-&-perennial consciousness whose critique and defense are the twin sides of the proper vocation of philosophy. I therefore do not regard the "snares" in the symptomatic a priori objectionable terms used by the Nirenbergs; indeed I do not see such moves as "reaching conclusions" at all; I see them as being suggestive and pointing beyond the articulable realm. (Their example is a case in point, as would be obvious if they paused to consider—among other things—that it is Glaucon not Socrates who makes this argument)

A final word about the Nirenbergs' own tone. While hardly as persnickety as Bartlett and Clemens', there is something a little troubling about it. The conclusion of their essay states:

insofar as [Badiou's] mathematical ontology disguises the contingent in robes of necessity, it can only diminish our freedom. We can embrace the politics if we so wish. But we should not confuse this choice with mathematics, nor can we call it philosophy.

I have my doubts about this whole formulation, and Bartlett and Clemens do a fair job of explaining why one might be forgiven for thinking the first sentence naïve. I am not concerned with the naïveté, but with the tendentiousness. The implication is that Badiou has either deceived himself or hopes to deceive us into "confusing" politics with mathematics. Confusion is not the same as "blurring," or, to have recourse to an over-used but still pertinent word, problematizing, a discursive boundary. As I have elsewhere argued, it may be permissible to question Badiou's philosophy's claim to the title platonism. But it is pretty staggering to suggest that his platonism does not deserve the title of philosophy.