Anti-Badiou, Part 1

Looking at my notes on Badiou, I'm realizing that this critique is likely to become a multi-page essay, not suitable to a single blog post. So I'm going to break it into pieces, and intersperse the postings with other topics. This leads to an administrative question: Anyone know of a resource for free, anonymous posting of PDF files?

Badiou and “Communism”: Ideas Masquerading as Hypotheses

Why should we care about Alain Badiou?

From a narrow perspective of political tendency, it would be hard to make a case. For nearly twenty years now, he has been associated with a practice of “politics without parties,” based on a syllogism that directly links the Bolshevik Party to the Stalinist party-state. As with any strict syllogism, the premise must be accepted to for the conclusions to follow. From a perspective that traces Stalinist rule to the annihilation of the Bolshevik Party, however unpopular such a view may conjuncturally be, then either the conclusions are false, or must be derived from different premises.

The reason to care about Alain Badiou is that, after decades of functioning as a (post-)Maoist militant and a metaphysician, he has discovered his true talent, his real calling, as a marketing genius. The juxtaposition of an adjective and a substantive, or a subject and a predicate, in a deliberately provocative manner may have been an ur-technique of the surrealists ("conquently the lion is a diamond"), but it was raised to the level of conscious artifice by the profession of advertisers and image-makers. So to the ranks of “revolutionary whitening systems,” “unforgettable mascara,” and “the children of Karl Marx and Coca-Cola,”—Godard, his fellow ex-“mao,” was also a bit of a publicist—we can now add “the communist hypothesis.”

Which is not to say that the phrase is innately false. As it happens, communism is a hypothesis. Or, more precisely, a nexus of interlinked hypotheses. But a hypothesis is not what Badiou presents it as, and neither is communism, at least not if it is to be understood as a hypothesis. He could have just as easily, and more precisely, said “the Idea of Transcendence,” as we will demonstrate. But that sounds like what it is, the stock in trade of metaphysicians and theologians for 2,500 years. It certainly isn’t provocative; it doesn’t sound like the sort of thing that would be put forward by someone whose thoughts on matters as timely as Sarkozy or the Tunisian revolution, or historical matters like the Paris Commune or the Chinese Cultural Revolution, would be of interest. But “the Communist Hypothesis:” Well, that we can sell!

I do not mean to suggest that such crass, commercial considerations were foremost, or even consciously present, in Badiou’s mind when he conceived the phrase. But in the capitalist world we have yet to transcend, ideas have power to the extent either that they inspire mass movements, or are assimilated to the commodity form. Badiou matters because his ideas have power, but not the sort of power needed to put the communist hypothesis to the test.

(For the purposes of this critique, I refer solely to the materials collected in the book The Communist Hypothesis, (London: Verso, 2010). Though Badiou makes repeated references to his earlier philosophical works, such as Being and Event and Logic of Worlds, for fuller expositions of his basic concepts, he at least has the decency to attempt brief definitions of them in the course of the book. That is good, because I firmly believe, regardless of whether of not Badiou would agree with me, that books should stand on their own; in the finitude of human lifetimes, no one should be expected to review a full corpus before confronting a thesis.)

Hypotheses and Conjectures

On pages 6-7, Badiou gives an illustrative example of a hypothesis, that is perhaps more illustrative than he intends. I will quote it at length, and do him the favor of correcting the presentation of Fermat's Last Theorem (which seems to have fallen victim to bad translation and typographical errors):

Take a scientific problem, which may well take the form of a hypothesis until such time as it is resolved. It could be, for example, that 'Fermat's theorem' is a hypothesis if we formulate it as: 'For [integer values of n>2], I assume that the equation xⁿ + yⁿ = zⁿ has no [positive integer] solutions (solutions in which x, y and z are [positive integers]).' Countless attempts were made to prove this, from Fermat, who formulated the hypothesis (and claimed to have proved it, but that need not concern us here), to Wiles, the English mathematician, who really did prove it a few years ago. Many of these atempts became the starting point for mathematical developments of great import, even though they did not succeed in solving the problem itself. It was therefore vital not to abandon the hypothesis for the three hundred years during which it was impossible to prove it. The lessons of all the failures, and the process of examining them and their implications, were the lifeblood of mathematics. In that sense, failure is nothing more than the history of the proof of the hypothesis, provided that the hypothesis is not abandoned.

For anyone familiar with the histories and terminologies of science and mathematics, this begs the question of why he chose an example from the history of mathematics, rather than an example from the physical sciences (e.g., the Theory of General Relativity). The answer cannot simply be Badiou's (in)famous love of mathematical illustrations. The example leads to some immediate objections:

1. Where scientists usually speak of hypotheses, mathematicians speak of conjectures. Anyone who has ever tried to prove a mathematical statement with an adequate degree of rigor knows the frustrating experience of being able to formulate a statement and say, "I think it's true, it seems like it's true, but I cannot yet devise a proof that establishes its truth, step by step, from what we already know to be true." If the statement is of a high enough level of significance, and one has a high enough degree of certainty, one can publish it as a conjecture and thus set to work an army of interested mathematicians to fill in the missing steps. (If one is a frustrated undergraduate, grappling with something one's professors consider "trivial," one considers changing one's major to philosophy.) If proven true, a conjecture becomes a theorem. This begs the question, however, of whether the statement is thus retrospectively determined to have already true when it was first formulated as a conjecture, a question that would receive conflicting answers. Philosophers of mathematical realist, formalist or structuralist schools, and probably most working mathematicians, would say "yes," George Lakoff and others would say "no," while I, borrowing arguments from Poincaré and Lakatos would say, "yes, but...". Arguing for that would take us far afield of the immediate point, but it's a topic worth researching/pursuing. The point for now is that the example does not demonstrate what it purports to. Rebranding a conjecture as a hypothesis obscures more than it elucidates.

   By contrast to a conjecture, a hypothesis in the physical sciences is never proven true in the mathematical sense. At most, it is plausible, based on the available evidence and received theory. As evidence accumulates in its favor, it can be regarded as a theory, meaning that it still has a provisional, hypothetical nature, but can be regarded as "true enough" for the purposes of serving as a basis for continuing investigation. If superseded by another theory, this does not wholly negate the evidence that the original theory was true, but reveals it to have been "true enough" within a defined sphere. A canonical example of this is the theory of gravitation: Newton's laws were readily testable on a terrestrial scale, even on the scale of the solar system, and demonstrably "true enough" in that sphere. Einstein's theory of general relativity began with a mathematical demonstration of the consequences of applying special relativity within a gravitational frame of reference, and showed slight divergences from Newton's equations. Einstein himself proposed several phenomena that could be observed to detect phenomena that would differ between Newton's model and his own. The first such observation came within a few years, with Arthur Eddington's observation of evidence of the deflection of light from a distant star by the sun, during a solar eclipse. In a certain sense, despite the compelling nature of Einstein's derivations of the Theory of General Relativity, up until that point it was more an ingenious hypothesis than a theory.

   While mathematical demonstration was important for both Newton and Einstein, neither of their sets of equations can be taken to be "true" in the way that Fermat's Last Theorem is. They are not true with reference to a given mathematical formalism, but true with reference to an observable phenomenon.

2. It is inaccurate to refer to the history of the proof of Fermat's Last Theorem simply as a history of "failures". It is true that until Wiles connected it to elliptic curves, no prior attempt was successful. But there were several partial successes. Had Fermat himself not already demonstrated the theorem for the case of n=4, it is likely that, despite his reputation as a brilliant mathematician, his conjecture would not have been taken as seriously as it was. The next major steps forward were by Leonhard Euler, who proved it for n=3 (and thereby, indirectly, for all even multiples of 3), then Sophie Germain and Adrien-Marie Legendre, etc. Wiles' proof ended up using strikingly different methods, using mathematical concepts that could hardly be said to have existed 100 years before. Ironically, it was Legendre who originated several of the branches of mathematics that ultimately contributed to Wiles' proof, while working on problems that to him seemed unrelated to the task of proving Fermat. Special cases do not prove a general rule--every mathematician knows this. Yet mathematicians are human, and human psychology, with our mental tendencies to generalize (and over-generalize), can trick us into thinking that the proof of a special case is a sign of progress toward the general rule, or at least a hopeful sign that the general rule may be provable. Without the incremental progress on special cases--and sometimes transformative progress, as with Ernst Kummer's proof for all regular primes--it is more likely that Fermat's conjecture would have been set aside as uninteresting, implausible, or both.

   Again, Badiou's example does not demonstrate what it seeks to, namely that failures do not matter, so long as you hold on to the misnamed "hypothesis". Failures do matter, but in human endeavors, of which mathematics is just one, they are given their meaning by the incomplete successes they enable.

So what is Badiou on about? That became clear to me as soon as I turned the page, to page 8, and found the following statements: "Universality, which is the real attribute of any corpus of truths, will have nothing to do with predicates. A real politics knows nothing of identities, even the identity - so tenuous, so variable - of 'communists'. It knows only fragments of the real, and an Idea of the real is testimony to the fact that the work of its truth is ongoing."

My marginal note there was "Platonism." I thought I was pretty smart, until I got to page 229, the first page of his concluding essay "The Idea of Communism," where he frankly acknowledges it, in main text and footnote, and gives citations of his past and forthcoming work on Plato. At least he admits it. By the end of that essay, he admits, though in an evasive manner, that the entire book is misnamed: "We can give new life to the communist hypothesis, or rather to the Idea of communism." (260) What we are dealing with, then, is not a hypothesis, which emerges in time, has a history, is never absolutely demonstrated and can, if necessary, be abandoned, but an "Idea" with a big, fat capital-I, which is more real than this icky, contingent, historical mess, and is true whether proven or not. In that respect, it is not even a conjecture in the mathematical sense. Either Badiou does not know what a hypothesis is, or he used it as a kind of disguise, smuggling the old, dusty heritage of metaphysical idealism in under a modern, scientific-sounding guise (like Lenin slipping out of Petrograd clean-shaven and wearing a toupée).

It is still necessary for me to clarify what it means to speak of a hypothesis in the realm of history. After all, I've already pointed to the example of the physical sciences, where the guiding ideological assumption of its practitioners (to the extent that they think about such things, and as opposed to how things actually work) tends to be falsificationism, the creation of Karl Popper, who explicitly used it to deny the applicability of scientific methods to history. And I will do that.

But first I need to finish dealing with Badiou, who, if he did not exist, would have to have been invented by a Popperian, as a living example of a cartoon communist in the post-Soviet world. One for whom "History does not exist," (243) or who speaks of "the non-factual element in a truth." (244)

Alas, as a historical materialist, before I write I need to think, and before I think I need to eat, and before I eat I need to cook. So the next portion will wait until later. Next installment (not necessarily the next post): Ideas without History, Truth without Facts.