Logic

Logic: Alas, it is Badiou’s unquestionable merit to have established that pure logic is the “transcendental of appearing.” I directly acknowledged (as I said, I am everything but an ingrate) the most prominent outcome of this real conceptual conquest in Ontologique: in appearing, there is neither absolute difference, nor absolute identity, only infinite asymptotic degrees of differential identities. But what Badiou did not notice, because he refuses even to recognize the existence of the techno-ecological problem, is that this means: the transcendental of Nature. In fact, in physis in the Greek sense, what blooms by itself, there is no absolute identity between two beings [étants], never. This identity is produced, much later, in and by technology, and technology alone.

The error of mathematics (see below), which is the cost of archaic technomimetic appropriation itself, probably consists in maximizing the infinite and asymptotic identitarian approximations of Logic. In logic, identity remains what it is: a utilitarian fiction, which is never absolutized. This absolutization only takes place with the imperceptible mathematical transfer. As this great philosopher called Dupin said (but through which Poe, who knew everything, and always more than we think, perhaps copied The Phenomenology’s Hegel, who says more or less the same thing):

I dispute the availability, and thus the value, of that reason which is cultivated in any especial form other than the abstractly logical. I dispute, in particular, the reason educed by mathematical study. Mathematics is the science of form and quantity; mathematical reasoning is merely logic applied to observation upon form and quantity. The great error lies in supposing that even the truths of what is called pure algebra are abstract or general truths. And this error is so egregious that I am counfounded at the universality with which it has been received. Mathematical axioms are not axioms of general truth. What is true of relation—of form and quantity—is often grossly false in regard to morals, for example. In this latter science it is very usually untrue that the aggregated parts are equal to the whole. In chemistry also the axiom fails. In the consideration of motive it fails; for two motives, each of a given value, have not, necessarily, a value when united, equal to the sum of their values apart. There are numerous other mathematical truths which are only truths within the limits of relation. But the mathematician argues from his finite truths, through habit, as if they were of an absolutely general applicability—as the world indeed imagines them to be.1

The root itself of the mathematical transcendental illusion is first and foremost the very sign of equality. We can say that originary transcendentalization, which is written x=x, never comes up in Nature. In the originary envoi of being as physis, the fact is that there is absolutely no ontological identity anywhere. No man is ontologically “equal” to another man, no pear to another pear, etc., up to the tiniest constituents of Nature. As I wrote at the time of the Esthétique du chaos,2 the twentieth century added to the Kantian transcendentals of space and time (save for the absolute transcendental that is being itself) the transcendental of difference. It then seemed that we would never have to get back to it, and that the philosophy of our century could henceforth never change track again. But then Badiou entered the scene, giving the stunning impression of bailing out all the most hackneyed prerogatives of metaphysics … and this, with the brilliance of laying all purloined letters on the table, that is, by recasting metaphysics on its rear bases themselves: the logico-mathematical.

What about the fate of the transcendental of difference, of Heidegger’s as well as Derrida’s, Wittgenstein’s as well as Deleuze’s? This transcendental meant that even two “identical” letters or glasses are different because of their respective locations in space and time. Here the Badiouian square mind would tell me: “But no! You are bringing in these inexistent transcendentals where they have nothing to do. That two beings [étants] are ontologically identical does not change the fact, as the Master has shown in Logics of Worlds, that they are ‘different’ in the simple sense of being localized in a world; it is a difference of topological localization, where time and space have nothing to do with it. You yourself, Mehdi, do you not pay tribute to the point that in appearing, there is neither identity nor absolute difference? It is at the level of being (mathematical intelligibility, whose essential “syntactic” component is the sign =) that we can talk, if need be, of absolute identity. Take the example of two glasses made in the same factory. They are absolutely identical in their ontological composition. But it is their simple localization that differentiates them; what you weakly call ‘transcendentalization by space and time’ is just a difference of topological marking. Ontologically, in their respective elementary compositions, it is self-evident: they are perfectly identical.”

What is the illusion of the Platonic fiduciarism and sophism here that hides behind the always peremptory challenge of the Badiouian square mind?

Here as everywhere else, since Rousseau our only access to the concept of Nature is negatively mediated, and precisely by what supplements it: technics itself which, having been sublimated, becomes “pure Logic” only belatedly, and mathematics, even more belatedly.

What is techne since Aristotle? It is that which is produced by the hand of man, and not that which blooms by itself. This is exactly why no one—except for the artificial, i.e. the technologically produced, paradise of mathematics—will ever be able to find the slightest example of absolute ontological identity—only “localized” differentially in the topological distribution of appearing—anywhere else than in what is technically, therefore anthropologically, produced. This is why Logic wins over mathematics in ontological dignity: it keeps closest to the essence of scientific appropriation, which is mimesis-techne. Here as elsewhere, the bad image philosophy has made of mimesis must be overturned: Logic is a discourse which continues to keep, mimetically, as close as possible to the being [l’étant] such as it gives itself “naturally,” in the absolute absence of identity between two literally “given” beings; whereas mathematics goes astray, for hypostasizing the acquisitions of transcendental-logical appropriation as identitarian isomorphism, extended so as to include all that is, i.e. exists.

Logic is a mimesis that is faithful to what it transcendentalizes by the void; mathematics is a deceptive mimesis of the being’s [l’étant] “egalitarian” putting in equivalence. The eidetic conception of the being begins with mathematics; a conception which would be Plato’s and would be renewed with the Kantian doctrine of the in-itself—a doubling of the being which is the more or less the darling original sin of philosophers. This empty “essentiation” of things, merely enabled by logic, is “consecrated” by mathematics.

In Plato, the hatred of mimesis conceals the profound truth of a mimetic essence of thought that is much more perverted, precisely because it is mathematized. Because nothing spiritually rhymes better with mimesis than mathesis—and it is above all not artistic catharsis that can rival it in this respect, not more than any other. Only mathematics suppresses what it subsumes without preserving anything of it. Hence the calamitous ethical consequences, as Dupin would say, drawn therefrom by the metaphysician who places his paid work under this paradigm.

The critique of metaphysics which we owe so much to Heidegger does not indemnify him from having carried on the philosophical absurdity par excellence, which is the hatred of mimesis. Kant inaugurates the philosophizing by the critique of metaphysics; he would fail to cross out definitively the essence of the latter, which is the secretly pleonectic propensity to “double from the bottom” [dédoubler par le fond] the being [l’étant] with his doctrine of the in-itself and the noumenal, which Badiou takes up again as it is, all the while inveighing against Kant. The SoN “puts things back on their feet”: it shows that the operation of doubling is indeed fundamental, and fundamentally metaphysical: but this doubling in fact never leaves the surface of things. In this respect, like in Deleuze, there is something profoundly “Stoic” in the aggressively anti-Platonic strategy of the SoN; and it is the anti-metaphysicist envoi advocated by Nietzsche, rather than Kant, that continues here, in fidelity as well (long-time critical, but fidelity nevertheless), the tremendous French moment of the “philosophies of difference,” which was almost made null and void by Badiou’s impact on contemporary philosophy.

Against these proclamations, to mark firmly the primacy of Logic over mathematics is also to reaffirm the archi-ethical primacy of difference over Identity. But the SoN’s move is even more radical: if Logic is the transcendental of things that remains “at the surface,” without doubling them into a truncated identitarian “in-itself” (pleonasm, because pleonectic), as in the case of mathematical drifting, it is still necessary, in the Derridean mode, to inquire into the conditions of this transcendentalization: the technomimetic. The techne-mimesis-catharsis-aufhebung complex is a philosophically more fundamental Logic than the entire formal Logic dissected by analytic philosophers or Badiou. Its archaeological “empiricity,” in the Derridean mode then, is the transcendental of the logical transcendental (of the empirical, modeled on infinite asymptotic approximations of differential identities, and never on the absolute identity of mathematics, not more than on its aberrant doctrine of indiscernibles [maintained by Leibniz as well as Badiou], or the theorem of the point of excess [see Mathematics], etc.).

And it is precisely because it creates teleologically (including Descartes and Galileo: “man as master and possessor,” etc.) the transcendental illusion of the identical that the technomimetic animal can then industrially manufacture the identical: two glasses, two clones … In nature, even the two most conjoined of twins can never be “ontologically” identical. The Leibnizian principle of indiscernibles is mathematically valid; philosophically, since Kant’s critical envoi, it is no longer worth anything. The following has been the mainspring of my theoretical thinking since its first autodidactic steps:3 I showed how the transcendentalization of difference by the best philosophy of the twentieth century proceeded from the celebration—in the history of philosophy—of the transcendental as such by Kant, in the instances of space and time. It took hardly a century for the—empty—universal transcendence of time and space to vouch for what metaphysics had disastrously ignored for twenty-three thousand years: it is difference itself, by the always singular conjunction of the time and space of a being [un étant], that constitues the third transcendental accompanying the former two, until Badiou arrived, and took advantage of the adjective “transcendental” in order to neutralize this apparently irrefutable triumvirate: For the Pol Potist, only just recovered from his erring, there was no longer any space, any time, and no longer any difference. I am not forcing here the trait of a philosophy I studied more than any other. This philosophy truly constitutes the “final solution” of difference, and as such, the most Titanesque contemporary attempt to make the metaphysical Phoenix rise again from its ashes.

This speaks volumes on the hypnotic trust we are supposed to put, without further examination, in the “ontological dignity of mathematics” in general. And, in the face of the essential international philosophical audience, it is this very principle that Badiou would celebrate with his literalized, i.e. “Wolffly” mathematized neo-Platonism.

In his (admirable) commentary on Hegel in Being and Event, Badiou says Hegel is incapable of thinking the simple difference between two letters. It is true, but with new consequences, of Badiou himself: two letters are “ontologically” identical, he will tell us; it is their topological localization, their being-there, their appearing that produces their simple, ontic difference of place. Ontologically, they are perfectly identical. But the two letters are still and always technological, anthropological examples; it is by the transcendental and illusory appropriation of identity (therefore: of mathematical equality =) that man produces, and only afterwards, the identical being [l’étant identique]. Once again, the metaphysical fraud, reactualized by Badiou with great pomp, consists in reversing the order of things, literally and in every sense, by putting the mimetically appropriated, pleonetically produced Principle “in the origin,” as it were, “in the posts of command”: the principle of identity, condoned by the very precarious event of technomimetic appropriation, from then on claims to “condone things,” to be at their origin.

Thus when you come up with an immense “phenomenology of appearing,” on the basis of Logic, in order to infer therefrom that, in the ontic being-there, there is never identity or absolute difference, you are not really talking of appearing, but of physis. Technology, which territorializes identity “ontologically” appropriated by man, makes appear absolute identity, differentiated only in the topological localization of two identical artifacts: two letters, two glasses, two clones … Then can we say that the doctrine of indiscernibles is applicable. But only then. Meaning, only in the technological appearing. The ontological in-itself of mathematics, and, for instance, of the scheme of indiscernibles, is nothing but a phantasm; here my refutation of Badiou is, after all, exactly the same as Kant’s which shattered the age of metaphysics, in its Leibniz-Wolffian embodiments, in his famous “Appendix on the Amphiboly of the Concepts of Reflection.” Only its phenomenalization takes place, first in mathematical writing, and then as technological production. Everything is at the surface; the in-itself has never existed.

Then Aristotle is right, and Plato is wrong: mathematical pleasure, before being epistemic, is first of all aesthetic; it is a matter of the childish happiness felt by the “natural metaphysician in us” for simplifying/dominating the influx of the diverse, through the purely noetic emulsion of an equivalence that is not really there. It is only in a second instance that this appropriation becomes “epistemic,” i.e. political: instrumental. The old Platonic wish to recover the erroneous general “ontological” equivalence plated on the diverse, and by the very means of this fictitious noetic equivalence, failed the first time and hence has no chance of better succeeding the “second” time. The political destination of the mathematical is not “communism,” which in its turn is purely noetico-programmatic, but capitalism, which realizes it in general equivalence.

In the kingdom of the “natural” being [l’étant], there is not one example of absolute ontological identity or equality. A rose is never absolutely identical to another rose, nor is any being which “blooms by itself” identical to another. The generalized relativism of identities and differences in the appearing is a rule of the pre-anthropological physis, and not of “the appearing” in general. Within this physis, there is one and one only region of being=event that transgresses this “Law of general relativity” of always differential identities, and always approximatively identical differences: it is the technomimetic region, belonging to Aristotelian production. The instrumental illusion introduced by anthropological noesis in the presumed “ontological” noumenon—“nature written in mathematical language”—that is based on the principle of identity and therefore equalization of the being, is precisely nothing but an instrumental-transcendental illusion. There is no in-itself and noumenon except as specifically produced; the essence of mathematics, even more than Logic, is technological. In Kantian terms, mathematics is the schwärmerei of Logic, and Logic the schwärmerei of techne, etc., etc.

Mathematics as the “in-itself” of things, as we have seen with the ontological differend, has historically proved to be nothing more than a fiction that is turning against us today, with the devastating violence we know too well. The mathematical fiction of equality and identity allows the production of afterwards, through technics, two in every respect identical artifacts, such as two glasses coming from the same factory. In 2001: A Space Odyssey, if the regular appearance of the monolith is frightening, it is because we know that nature, unlike what Galileo held, is not written in mathematical language. There are no “perfect” circles or squares in nature: geometrical forms and mathematical idealities constitute a simplification of natural forms, “just like” life was a simplification of matter.4 For instance, the planets are formally simplified by our geometrical spheres, which are not “at the bottom” [au fond] of things, their ontological in-itself being forbidden by Kant, and delivered turnkey by the equation ontology=mathematics; only technics makes appear, for instance in the regular angles of the buildings in which we almost universally live, the square and the rectangle in the heart of Nature, like hair on soup. The monolith’s appearance in 2001 is terrifying—and would be so, if it should happen in some extra-human reality—because we confusedly, but very profoundly, know that we are the only depositaries of the technological event; we also know with which terrifying prerogatives this fortune has corrupted/spoiled us in the heart of all being [l’étant]. And so we are scared that suddenly another being could, even virtually, attain the means to do to us what we have done to others: we are terrorized by the monolith in the same way we would be terrorized by monkeys if they started rubbing flints together, or producing sophisticated tools. This is why, once again following the metaphysical critique launched by Kant, and aggravated by Nietzsche-Heidegger, the distinction “being-appearing” has become absolutely worthless. Mathematics, more severely than Logic, remains at the surface of things. Its claim to ontological “depth” is the very heart of the ancestral metaphysical calamity. Logic is explicitly the art of the link between things, of the always asymptotic degrees of similarity and dissimilarity, of always relative identities and also always relative differences. This is why it is precisely more “profound” than mathematics, in the very sense that Nietzsche said the Greeks “were superficial … out of profundity.” Hegel calls his great ontological work, “The Science of Logic.” We cannot even imagine that he would call it “The Science of Mathematics”… When Spinoza, for instance, lays down more geometrico as philosophical Ideal, the fact still remains that he produces a general Logic of the Relation. As we saw, mathematics can constitute an absolutely admissible paradigm of philosophizing … provided that pure mathematics itself is not taken too seriously. The mathematics of the affect (see above), or the mathematics of play (see above), must be completely different from pure mathematics.