INTRODUCTION

SCIENCE, IDENTITY, FRACTALITY

THE ERA OF MULTIPLICITIES AND THE FORGETTING OF IDENTITIES

CONTEMPORARY philosophy has put an end to Hegelianism, Marxism, and structuralism by drawing our attention to new objects of a special type. Although very heterogeneous, these objects are globally foreign to “metaphysics,” “presence,” and “representation”: partial, fragmented, irregular, or fuzzy objects; badly assembled, mismatched, or dehiscent apparatuses; multiplicities and disseminations; games; differences and differends, in-betweens, and so forth. Since Friedrich Nietzsche, philosophy has been mobilized in a struggle against “logos,” understood as unity (“system,” “representation,” “hierarchy,” “closure,” etc.). This struggle has been the source of an inflation, a bidding up [surenchère] that has lead to the intensification of “multiplicities,” “inconsistent multiple,” “language games,” “catastrophes,” “turns,” “effects,” and “singularities.” These objects engender affiliated theories. Competing with one another, they compete even more, all together, with the equivalent scientific forms (critical points, bifurcations, catastrophes, fractals, and so on) to which they correspond and of which they are perhaps, simultaneously, the philosophical aftereffect and rival.

Nevertheless, those philosophies—and perhaps all philosophies without exception—quickly came up against typical difficulties. They sought in the invention of the new objects a “postmetaphysical” practice. But in several ways they merely extended through them a certain metaphysical impotence of philosophy and repeated on them their most traditional errancies. We shall return to these difficulties, which testify to the unreality of the aforementioned objects, to their merely possible character. But here they are, in short:

1. Those objects are not real or consistent objects as defined by sciences, but created or imagined artifacts, “decided” at will; mixed, half-given half-decided entities. Their degree of reality outside philosophical practice is and has remained entirely problematic.

2. They are of multiple types or genres at the whim of competing philosophical decisions. Their sole reality is that of philosophy itself, and philosophy behaves toward them as a tradition or a “reserve” of thought to the teleology of which they are ordained. It puts them to work for the benefit of its own goals or objectives, extracting from them a surplus value of sense, of truth, and of value.

3. They have no stable identity. More precisely, they are directed against every identity. Here identity is mistakenly conflated with a homogeneous and transcendent unity that would circumscribe them. They are caught in becomings, lines, textual or other interminable processes, in which they are exhausted. Their reality as points, terms, or individuals is drowned in tendencies, continuums, and infinite teleologies.

Our general thesis on this point is the following: “singularities,” “multiplicities,” “differences,” etc., 1/ exploit transcendence exclusively, profit from Being and exteriority, are the avatars of ontology and its power of autodissolution, which is at last manifested as such; 2/ project in their turn a transcendent or ontological (thus negative) image of the One or Identity in the form of Unity, with which they conflate it; 3/ requisition Identity, i.e., the One as One, without having elucidated its essence, its nature as a Given, which they negate by confusing the One with the Unity-for…; Identity with the Identification-of…, etc.; 4/ are mixtures of Identity and of Division or Scission; of false Identities and of true generalities, partially indeterminate and transcendent, which deny the real’s authentic “singularity,” conflating it with conceptual singularities, blending it with philosophical representation. Their element is dissolution, dissemination, deconstruction…the weakened forms of the negative. They are the excess of transcendence over itself, a product of its autocritique rather than the recognition—positive and for itself—of the identity (of) the real. So much so that, since every singularity is always too weak and presupposes another singularity, this thought culminates in a hermeneutics of philosophical texts and in a homage to Tradition. They are what remains of the traditional, unitary metaphysics when it undertakes to critique itself and continues to impose its oldest prejudices.

To be sure, contemporary philosophy has partially understood that, in order to ensure their reality, it had to cease recapturing singularities in a foundation, inscribing them in a representative generality, and had to ascribe them to the Other-of…or the Other-than…But it merely completed half the path, the less interesting half, the one it could complete by remaining “philosophy.” It transferred its old habits of self-sufficiency to the Other; it even accentuated them, by assuming this time Exteriority itself, Transcendence, the Other, as an Absolute in a state of “autoposition” or “auto-affirmation,” certainly attenuated but always arbitrary as well. It associated singularities yet again with a kind of universal and all-consuming Reserve (Episteme, Full body, Plane of immanence, Place-for-the-Other, Clearing, Tradition, and Destiny, etc.), a reserve that has exploited them with the good faith peculiar to cynicism. Philosophy counts on the infinite unlimitedness of time to save the singularities. It refuses to acknowledge that this infinity of philosophical time is a “bear’s service” [le pavé de l’ours], that it is thought-as-Reserve determined to exploit these singularities. It cannot help but “possibilize” them, turn them into semieffective, semipossible, semivirtual, semiactual mixtures, divide them, and destroy their identity. This identity is lost with all hands because it is a priori or by right “mixed” with that of which it is the identity. So much so that these singularities’ transcendent mode of existence (worldly, social and historical, textual and linguistic, desiring and political existence) drags their identity in an endless turnstile and their reality in unlimited games of the most decisory [décisoire] and arbitrary possibility. It is not surprising that these supposedly “non-negotiable,” “incompossible”…objects have been used to negotiate the maintenance of the oldest myths of the philosophies of history. They have served as an ultimate caution to philosophical sufficiency, a new mask for its claims over the real.

Clearly the revival of the problem of “singularities” and of “multiplicities” requires us to change our foundation—but what does this formula mean?—and to turn toward the original problem of Identity so as to give it an other-than-philosophical form, capable of affording singularities a reality that philosophy has contrived to strip from them.

PHILOSOPHICAL RESISTANCE TO IDENTITIES

Let Difference and Identity be “transcendentals” in the contemporary sense, absolutely general “metaphilosophical” categories that allow us to condense a philosophy or philosophy itself into a formula, for example: “Identity of Difference and of Identity.” Their circle, co-belonging, or reciprocal determination distributes the two terms unequally: Identity appears dominant since it intervenes twice: once as a simple term, another as a unity of the system of the two; as party and as judge, as productive and as contemplative. Difference only intervenes a single time, as an operative term of the whole.

But this is just an appearance that can mislead us as to philosophy’s sense and goals. In reality, the formula means that philosophy’s primary and dominant element is Difference. Let’s say the “Dyad”: Difference is not the Dyad; it is an already specified mode of the Dyad, which is a more indeterminate matrix. Difference is Dyad and One, at any rate, a particular philosophical system. But it can also represent the dyad side of every philosophy, and it is possible at a certain level of generality to assimilate the two. Philosophical thought begins with difference—with the multiple, experience, decision, etc.—and moves within this element when it thinks Identity. Identity is divided into several species or modes, so much so that its double intervention is the mark of its weakness; its final overvaluation is the effect of its initial undervaluation. Philosophy exploits Identity as a keystone of systems, but does not think according to Identity. Having divided it, philosophy resorts to palliatives or substitutes: analogy, univocity, and so forth. Identity thus forms two circles: the small circle that opposes it to Difference, to the Dyad, but that nevertheless enters with the Dyad into a superior Dyad; and the great circle through which it surpasses itself and reenvelops Difference or the Dyad it constitutes with Difference.

Difference is therefore the essence or motor of philosophy, Identity its existence and objective appearance. This hierarchy is complex. It separates the functions, distributes the roles, and decides the share of each. In effect, philosophy is a reunification only because it is and remains a transcendental partition. It is in a dominant way an activity of decision and determinant division from which thought never exits. Even when it aims for Identity, philosophy still thinks it in the last resort in the mode of its division. Even when it assumes Identity in an elementary way, as the principle of identity, it is never A, but A=A. There is no philosophy that does not maintain a double, even multiple discourse on Identity: that of the numerical unit-of-account, the atomic unit, an ingredient of arithmetic or of the sensible multiple, but also that of transcendental Unity as an ingredient of Being and convertible with it (or with the Other in contemporary deconstructions).

This savage will to the “forgetting”—the denial—of Identity takes several forms on the basis of its preliminary division. The most noteworthy is the form of its convertibility at times with the numerical one of arithmetic, at others with dominant Totality or systematic closure—in all cases, ultimately, with…Unification. In each case, its convertibility replaces its real essence and devotes it to “technological” works that buttress the ontological decision. Unable to rid themselves completely of the One (which is necessary for arithmetic, but more profoundly for the relation of the multiple to the One itself), some philosophers fantasize its murder. They fantasize the liquidation of the “Greek god of the One” and believe they “make the decision” by deciding to invert the old hierarchy: into In reality, they merely “decide,” i.e., fantasize a murder that has already occurred a long time ago, a murder tethered to philosophy’s very existence rather than to their own decision and which, if it testifies to a redoubtable, murderous will on the part of philosophy, is a murder for laughs with regard to Identity itself. These philosophers claim to have finished devaluing the One as a simple unit-of-account and to have overturned its old metaphysical empire in the name of an uncountable multiple. Such a division allows them, on one hand, to reduce it to the secondary functions of unifying the Dyad or consistently closing Difference; on the other, to accuse it of all possible evils (closing, systematic closure, domination, totality, etc.). In these accusations, philosophers are manipulated by philosophy, which is nothing more than the unity of this double gesture of devaluation and overvaluation. Those who claim to put the One to death continue to secretly overvalue it, for they think inside a system that desires these two gestures at once. No philosopher can do without the One and its unifying functions, which are always surreptitiously presupposed. No philosopher can avoid limiting its efficacy. For philosophy, Identity is a necessary evil. We cannot believe that it is or has ever been philosophy’s main object. It is Being that is its primary object, and this is why philosophy overvalues the One: because it seeks its ruin. The idea of overvaluing and devaluing the One, i.e., the real, is absurd. It is, nevertheless, the foundation of philosophy.

Difference can only be understood as a form of amphibology, of forced unity between heterogeneous terms, of apparent identity between terms whose own nature or real identity renders them foreign to each other. Conversely, the amphibology claims only to divide the real identity of these terms. But it is the whole of philosophy—pervaded by Difference of which it is the development—that is the activity that puts Difference where Identity is and Identity where the true “difference of nature” lies, the heterogeneity of Identities. Difference supplies the purest philosophical, i.e., amphibological satisfactions: two becomes one at the same time that one becomes two. Philosophy is not only Difference’s priority; it is its primacy or its domination. When Difference is primary and when one begins by deciding, dividing, partitioning, or simply distancing, this gesture engenders universal hierarchy and domination as the essence of thought. Even when it apparently cedes its place to Identity, this place continues to be that of domination. Contemporary philosophy, at least the philosophy of “deconstructions” (Ludwig Wittgenstein, Martin Heidegger, Jacques Derrida), has not eliminated this primacy of difference; instead, it has intensified it, injecting a supplement of alterity into Difference so as to prevent its perfect or remainderless interiorization into Identity. Plugged into an Other, which is doubtless not the form of an Identity’s scission but the power of the scission, Difference was “opened” or quartered. It has become an irreducible distance, an irreducible tension. For this reason, deconstructions have not destroyed philosophy; they merely reinforced its dominant internal tendency: the dislocation of Identity. They took this destruction of the One to its limit, which obviously proved to be a limit of impossibility. There is (always) some One—and not only as a unit-of-account—even and especially when the One is presumed to be expelled from the “real.”

On the basis of this description, the following hypothesis can be proposed: philosophy as a whole is “opposed” to Identity, since it divides it and fails to think it as Identity. The entire philosophical activity of differentiation and identification (dialectic, synthesis, system, arithmetic, etc.) relies on this global rejection. That of which philosophy speaks and which it assembles with Difference (with Being, the Other, the Multiple, etc.) is merely an image or an appearance of Identity (under conditions foreign to the latter), but is not Identity as such. Philosophy can in no way think Identity and only gains access to it by dividing it, reducing it to secondary, even “vulgar” and “empirical” functions (arithmetic) and simultaneously raising it to the state of a transcendent absolute beyond Being and in positions of domination it immediately proposes to “critique,” “overturn,” or “deconstruct.” This explains a fundamental trait of philosophical activity: Identity qua Identity—and the science of Identity—is a formula that we can discover in ontology; but it is never fulfilled, no more than any formula of this kind. Philosophy is not a science of the One but primarily of Being, a science that tries to find its bearings, fails and elevates its failure to the state of success, an aporetic science that establishes itself as a “science” of the aporia, a sought-after science that becomes a “science” of the search.

Once the extent of this repression (and, in the first place, the depth of the problem of Identity) has been grasped, it would not be an exaggeration to say that philosophy only lives off its resistance to Identity, its denial of the One for the benefit of Being, that it starts to “speculate” about a transcendent, ontological One or, weary, reduces it to the unit-of-account. Philosophy’s global failure “before” the real stems from the fact that it thinks in the mode of the decision and, more generally, of transcendence, already beyond and against Identity, and that it only seeks the reality of singularities in singularities themselves, thus in the transcendence that effaces them, in the exteriority that dissolves their essence. Philosophy has only ever possessed a superficial, transcendent concept of Identity. In the One, it discovered a kind of rarefied double of Being. It is the system of a superficial experience and of a naive critique of Identity.

The balance sheet of the philosophies of “difference,” of “multiplicities,” of the “multiple,” and finally of “deconstructions,” is what we could call a semidiscovery, an incomplete discovery of singularities, or more than incomplete: falsified and symptomatic from the start. “Continuous multiplicities” fated to the erasure of their identity, a mixed semisingular semiuniversal real, and possible inasmuch as it is real: such is in effect the meaning of this ubiquitous appeal to difference, to the differend, to the inconsistent multiple, to language games and to catastrophes. The science of singularities, in the same way as philosophy and for the same reasons, remains a “sought-after science” and will eternally remain so as long as the very problem of science (to begin with and in its relation to the One rather than to Being), not to mention that of multiplicities, is posed under the philosophical horizon.

CHANGING THE TERRAIN: SCIENCE AND SINGULARITIES

The events that haunt the World’s surface may be objectively narcissistic. Perhaps they themselves appreciate this labor of division and envelopment to which they are subjected—care and attention of philosophers. Nonetheless, it is not clear that those who engender events or manifest them (artists, engineers, scientists, or any man insofar as he creates, believes, imagines, legislates, writes, crosses space, saves, or kills) equally appreciate this labor of assimilation and recuperation. Events have no shortage of all kinds of philosophies and interpretations; in fact, they have too many of them. There is an objective excess of philosophy or of mediatization, which ends up concealing singularities’ virulence and fulguration.

If philosophy is the mistress of this enterprise of drowning determination under the triple veil of sense, truth, and value (the three dimensions of space it folds onto the real), we maintain, in contrast, that artists—but this is true first and foremost of scientists—have already won their majority, that they have escaped the state of minority in which philosophy held them captive. We no longer believe that philosophy represents the “majority” for man. Rather, precisely because it is merely a majority of the understanding or of reason, it constitutes the reign of the imposed minority. It often holds artists in a state of dependency, even though scientists have already broken with this servitude. To be sure, when artists cease in their turn to be the minors of philosophy, it is then that they enter into the community of true “minoritarians.” The authentic minorities, those who no longer let themselves be identified and determined by philosophical Authorities: this is what the very “experimental” research undertaken here will try to discern.

The old problem of “determination” and the most contemporary problem of singularities constitute a possible entry point into this new way of thinking. A historically dated entry point, no doubt, and required by the urgency of situation. But it is the global work of scientists, artists, and technologists that we should take as our object and not only that of avant-garde philosophers, at the risk of losing the generality of the paradigm we call “nonphilosophical” and covertly returning once more to a shameful philosophical decision. That the events, objects, and procedures of the hour appeal to us more than others, that they become a symptom for us, is perfectly reasonable, provided we distill each time the scope and radicality of the new paradigm, inasmuch as it can be measured against philosophy’s paradigm and, more than measured against it, become a measure for it.

In effect, it may be more interesting to understand the work of artists as a set of procedures designed to demediatize the event. Demediatization of the real rather than deconstruction of interpretation; production of a naked singularity from clothed singularities; subsumption of envelopes associated with the event into the materiality of the event. Still, the expression demediatization betrays what is at stake and must be “corrected” and made possible. Instead of suspending interpretation in order to reascend toward a supposedly pure real, toward a disrobed singularity—the old and circular philosophical schema of suspension or reduction—we would start from the already-Determined in order to move toward philosophy’s folded singularities. We would treat these singularities as a simple contingent material on the basis of rules or procedures that express the real’s unreciprocated precession on philosophy, singularity on its interpretation, the Determined on Determination. We would thus circumvent not only the philosophical gesture of retrocession or ascent toward the real, which is illusorily presupposed outside philosophy or on its margin, but also the trap of a primary empiricism or of a materialism of materiality.

What conditions produce a radical singularity, not enveloped or leveled by philosophy’s transcendent spaces? To this question, contemporaries responded with the prodigious recourse to the Other in increasingly heterogeneous and undecidable forms. This solution is conservative; it does nothing more than register what is in question. By displacing the philosophical operation toward the nonspace (of) the Other, it simply confirms the supposed necessity of the mixed or philosophical state of singularity instead of positing its contingency and its unreality. Hence the invasion of thought by these effects-(of)-the-Other: the symptom, trauma, heterogeneity, the fold, fragments or fractures, catastrophe…all that constitutes the multifarious content of the “postmodern” (understood more or less rigorously). Isn’t it instead the question itself that is conservative and that already programs the division and doubling of singularity? How can we claim to produce determination ex nihilo or even from what is not already the Determined and what contains some indetermination in itself? This impossible task is that of philosophy. The real work of scientists and artists is elaborated according to a whole other axis. What is at stake—if we treat the already-Determined as a guiding thread of the description, but also of the real operation that scientists and artists carry out, which is neither an interpretation nor a deconstruction—is: 1. extracting from enveloped singularities their real or phenomenal content, i.e., a singularity stripped of every decisional and positional environment; 2. overdetermining it, but from now on without dividing it—by means of mixed singularities that are interpreted, enveloped with decisions and positions. Two simultaneous operations, whose sum is the transformation of these clothed singularities in accordance with the Determined, not the production, which is at any rate impossible, of the Determined itself. It would be naive to claim to negate the systems of interpretation that accompany the real of the World, of Art, of History, and of Politics in the name of an allegedly purer real. Our project does more than reverse this path: instead of allowing philosophies to exploit the reality of singularities, we make use of them as resources in the service of this reality. What we reject is the autoposition of these interpretations, which claim to occupy the entire space of thought.

It is at this nonphilosophical level that the problem of a more radical apprehension of singularities must be posed, not at a socio-semio-etc.-logical level, which is merely a disguised philosophical position. Philosophy is an enterprise of idealization and of composition—a technology—of singularities, but this expression contains a paradox. Can’t we imagine another paradigm of thought that would no longer associate the ideal or universal side of singularities and their empirical side, but would elaborate them according to wholly new nontechnological relations, outside every causality of division/doubling and with a greater respect for their specificity? The philosophical conception does not only lack the empiricist sense of what is given as such, contingently or “in excess,” the sense of the World’s unlimited horizontality or its “flattening” (the empirical is necessary to philosophy, yet it is also intolerable to it; it “inter-venes” [“inter-vient”/inter-comes] in it). It also lacks the sense of ideality and of functionality. It is neither quite Humean nor quite Platonic, but carries out a blending above all. What is singularity in the philosophical sense? The blending of the empirical manifold and the ideal unity, their co-belonging, with the movement that animates this blending. Thus: their interimpediment or interinhibition. Can we imagine another way of thinking for which singularity, which certainly always constitutes a complex edifice, would no longer have the internal structure of the interinhibitive mixture or circularity? A double attention, perhaps a double donation, is required to do justice to singularities: the sense of the absolutely contingent and nonstandard given, treated as such and not transformed, the sense of the theoretical ideality that is independent of every empirical content. If these two dimensions are no longer associated in a mixture, what will be the law of their new relation? Perhaps it is necessary to defy the spirit of blending to the point of positing a duality—radical, unheard-of, precisely without blending—of the real and ideality and, on this basis, to discern how both can still, if not “compose,” at least produce a singularity of a new type. To singularity’s mixed and auto-effacing state, we will oppose its double donation where D is the radical Determined (Identity), d the mixed determination or singularity, and u the universal or the space associated with the singularity. A nonphilosophical, perhaps scientific redistribution—founded directly in the real itself—of the Determined, of Determination, and of the Determinable: this is where we hope to locate the new resources for a more faithful and rigorous description of the materiality of the World, of History, of Science, and of Art. These various fields contain an ingredient-of-reality that must be described and that can only be described if the phenomena they offer stop legislating on themselves and self-interpreting and are treated as a pure inert determinable ready to receive the procedures of determination that flow from the real or from the Determined itself. To elaborate this new concept of singularity, we have to return to the old problem that serves as its framework: the Principle of Sufficient Determination.

We will therefore attempt to elucidate—on the basis of the symptom-problem of determination, of singularity, and of fractality—the absolutely primitive and minimal structures of every thought. These structures will be reduced and simpler than those of the philosophical decision. Far from representing a new “return” to things themselves and to a metaphysical “simplicity,” or a simplicity of the retrocession-beyond-metaphysics, this attempt realizes an antedecisional-and-positional simplicity and minimality. It is science that possesses these incompressible structures of every thought, and not philosophy, which merely lays claim to the “inescapability” of its own existence. It is from this essentially indestructible or irreducible (because real) given that we set out to describe sciences, arts, and even philosophical “complexity.” Philosophy’s infinite and wily developments, its overcomplexity, not to mention the “theories of complexity” that are its ultimate extension, create the illusion that philosophy is capable of representing and describing a “real” deemed to be increasingly “complex.” Yet, since philosophy itself starts with complexifying the real by investing and projecting itself specularily in it, we find here an eminently vicious illusion and a vicious solution that conflate the real with “reality.” Perhaps complexity is only accessible to a thought that will not have retroceded once more to a “simple” metaphysics or to a metaphysics of “withdrawal,” a thought that will have assumed the means of starting from philosophically unheard-of simplicity and minimality: those of the scientific posture rather than those of the philosophical position. So as to summarily extend this type of distinction, we could oppose the revolutions of the complex or the philosophical and the mutations of the simple or the minimal; the philosophical’s internally closed openings and the scientific’s radical openings; the increasing philosophical complexifications and the scientific transformations-mutations of the complex (representations or knowledges) under the law of the scientific posture “in” the real. We have to develop these aspects of the “scientific” or “nonphilosophical paradigm” and elucidate it in terms of the crucial problems of determination and singularity.

Singularities must stop being a “question” in order to become a theoretical “problem” posed on the terrain of science. But science must also become a problem posed on the terrain of thought. It is a matter of discovering a rigorous form of thought, with the traits of science rather than of philosophy, capable of affording the philosophical half-discovery of multiplicities its true theoretical sense and the plenitude of its reality. To save singularities from their philosophical effacement through their theoretical implementation: such is the “watchword” that we baptize with the term nonphilosophical. But the paradox is that, for this operation, we must agree to give the appearance (in the eyes of the philosopher alone) of a kind of “flashback” toward the problem of Identity, which is particularly repudiated by contemporary philosophies as well as poorly understood or repressed by them.

GLOBAL REEVALUATION OF THE RELATIONS BETWEEN SCIENCE AND PHILOSOPHY: STARTING FROM “SCIENCES THEMSELVES”

Measured against the obsessions of our time, against its objects and criteria, what we call “nonphilosophy” is a theory of identities rather than a philosophy of singularities. All the same, we do not believe that it marks the return to a metaphysical state of thought. Rather, what is stake is its displacement, its mise en place [establishment], on the terrain of science. Not the terrain of any (philosophical) image of science whatsoever: the fundamental task of the solution on which everything will depend consists in knotting (and more than knotting: identifying) Identity qua Identity, finally restored to itself, and the essence of science. We will have to describe this radical imbrication of Identity and of thought-science.

Sciences are everywhere triumphant, to the point where they are undisputed in their sphere and are rejected solely out of “ideological” or philosophical distaste on account of “culture.” They triumph as the sole incumbent body of theoretical knowledge, in possession of the conditions of historical change. An observation: philosophy itself recognizes that it has lost the great battle of theory. A paradox: science in no way has the thought it merits; it is left up to its philosophical consumption.

On one hand, philosophy has lost in fact—and recognizes this loss through its avoidance and cultural consumption of science—the great combat it always waged against science for the control of theoretical knowledge. Always: even when science did not exist, it already occupied the future battlefield. But philosophy renounced theory and explicitly took refuge in unending side tasks or secondary ends: everyday practice and the maxims of prudence; the “resistance” that determines the choices amid sciences and powers; the quest for happiness and the new “honest,” i.e. mediatic, culture. New consensus where everyone must be recognized: companies, educated men, educational and academic institutions, scientists who are asked to expound their “philosophy.” Philosophy returns to a life of misery by visiting the scene where it is summoned as a “noble” force of conservation and “resistance”; reduced to the functions of self-defense and security; in charge of expressing the distaste of “intellectuals” against the real labor of sciences, against theoretical dignity. It is true that it never thought in order to think, but in order to live or survive: as an aid to life and the decision. Philosophy is in its essence a practice of prudence with aspects of thought; it is not a practice of thought, but a desire for thought that gradually recognizes, in this respect, that it is merely an aborted dream within the dream. If it is also something else, it obtains this extension from science.

On the other hand, despite their triumph—or because of it?—the sciences are awaiting a thought adequate to theoretical knowledge. Instead of this thought of science, we have the rearguard battles that end in the “returns-to…” (to Immanuel Kant, to Leibniz, to Aristotle, etc.) and the epistemological self-defense groups. We have the obsessional return of the old solutions—those that were forged in response to prior states of theory and knowledge. We have the epistemological consumption of knowledges, isolated and abstracted from their process of production. We have the “philosophies of science” or those founded on an old scientific theory and that, by definition, lag doubly behind: behind the “current state” of knowledges in the field and because philosophy is late de jure, displaced in relation to science, in a “reactive” position. We have ideologies that scientists project through their work. More generally, we have the globally specular image that philosophy cannot help but ascribe to Science [la science], the unitary confusion it cannot but introduce between the two of them, the exchange it requires between “knowledge-without-thought” and “thought-without-knowledge.” The founding confusion of our time, immemorial like philosophy itself, is not that of Being and being; it is the confusion of science and philosophy in the name of philosophy against science.

This will be one of the tasks of the future historians of spontaneous philosophical representations (let’s try to imagine them): to describe the forms of this extremely protracted repression, the strange strategies through which philosophy will have passed itself off for so long as the authentic thought of science when it merely reflected or expressed itself, without restraint, in the distinct, ever transcendent images it created of science. It will have incessantly imposed limitations on science, endowing it with foreign objects and external goals, derealizing it in order to set itself up as science’s real foundation. In general, philosophy will not have allowed science to think on its own; it will have put itself in science’s place in order to speak “in its stead” and to expel it from itself, to alienate it.

The first task is thus to set out from what we will call “sciences themselves.” This will be our “watchword” and no doubt a whole other thing than an imperative or an injunction. Our axiom, from which we deduce science’s essence, scope and autonomy vis-à-vis philosophy, is science thinks; it thinks without philosophers and despite all the apparent counterexamples. Instead of understanding by “science” a particular and complete knowledge that philosophy abstracts from its element, appropriates and “autoposits” as a fact (faktum) or an “object,” we will understand “science itself,” its identity, which can think itself in its philosophically unprecedented way. Everything will then mutate in the specular economy of philosophy’s relations to itself: the “philosophy of sciences,” epistemology, and scientific ideologies will reveal their nature as activities of cultural self-defense.

“Nonphilosophy” is the attempt to elaborate a thought that responds to the most general scientific criteria (internal or “transcendental” determination, rigorous coherence, exclusion of circularity in favor of deducibility and experimentation, etc.). It is thus the attempt to elaborate a thought adequate to the theory and immanent practice of sciences. It is a theory of the essence of theory. Yet the theory at issue not only excludes positivism but also idealism and theoreticism, the philosophical normalizations of science. Theoreticism in particular would arise if, in isolating a theory, we assumed that it autoposits and autolegitimates itself and “gives” the real, as philosophy assumes. Here theory is determined in-the-last-instance in or by the immanence of real-Identity. This cause-of-the-last-instance of theory shatters every theoreticism and liberates all the more the theoretical dimension from its (philosophical) confusion with the material or the object.

What troubles philosophical common sense is that nonphilosophy is simultaneously, in its practice and not only through its object (philosophy), a science and a thought; that it has scientific rather than philosophical operations, and yet they are a priori and transcendental; that the two traditional, opposed images of so-called positive science and philosophy are no longer valid, that these old partitions are abolished for the benefit of the identity of science and of thought. An identity that rejects both the positivist image of science and the reflexive (autopositional, redoubled, or folded…) image of thought; that rejects them not merely for its own good, but for the good of science as well. On the whole, this schema is closer to the spirit of “sciences themselves” than to philosophy, i.e., to the unitary or hierarchical opposition between sciences and philosophy. Our constant image of the sciences has a philosophical origin and must be eradicated by sciences “themselves.”

We no longer believe that what—perhaps for all eternity—is dubbed “philosophy” could still claim to supply thought’s ultimate structures. Philosophical Authorities decide and legislate; they manifest a vigor and an insistence that forbids any “decision” on their inexistence. On the other hand, beyond their effective existence, they do not cease struggling against, not a mere suspicion, but an absolute rejection that is opposed to them everywhere and which, in order to defend themselves, they mistakenly reduce to a positivist bad will or an empiricist obstinacy, to a scientific barbarism or an anticulture that besieges them from all sides. The real situation is simpler, or else more complex. Perhaps philosophy is the one that has not ceased repressing and resisting another way of thinking that is now emerging, that has already emerged and claimed the plenitude of its rights without the slightest awareness on philosophy’s part. What philosophy takes for an external crisis, an assault on “free thought” and “reflection,” what it seeks to turn into the deconstruction of the most metaphysical forms, are perhaps the cracks in its edifice, the fissures in its own resistance. A certain becoming of thought is delineated, a history is discerned, but it is less the emergence of another thought inside and outside philosophy’s limits than the autodissolution, the autocritique by which philosophy reacts to its basic impotence in the face of what has always been there “before” it and what emerges a little more distinctly through the invalidation of its claims. As old as it is, philosophy arrived too late in relation to another way of thinking, which can be primarily identified as that of science, then as the one that acts, for instance, in the work of artists. That there is an authentic and consistent thought in science, that it does not depend on external and, in particular, positivist and empiricist philosophical decisions, is precisely what we call the scientific or “nonphilosophical” paradigm.

The new problem is then no longer the fulfillment of philosophy, its minor positivist death through sciences or its major death through auto-completion, through “thought” or “deconstruction.” It is the problem of its global measure and determination through another experience of thought, which never had anything to do with it, and now less than ever. Any serious practice of philosophy is enough to show that the current North American slogans of “after-philosophy” and the “end-of-philosophy” have absolutely no conceivable sense: neither philosophical (especially when they are attributed to “deconstruction”…) nor even scientific. There is no effective end to philosophy. Neither can philosophy program its own destruction without reaffirming itself, nor can science envisage anything of the kind, since its goal is at most to rigorously know philosophy, but certainly not to replace it. Only positivist philosophical decisions that lack self-awareness can share, for a moment, the illusion of an effective suppression of philosophy. But if these decisions have some significance for thought, they have none for the real. Instead, with regard to philosophy’s claim to provide the essence of thought, to legislate over science itself, we can say at once that it continues as before with the effectivity peculiar to it and, moreover, that it is already invalidated, displaced outside itself, restored to its place outside of and by science.

Our goal is to elucidate the new paradigm as well as to demonstrate the well-known insufficiency of every philosophy (not only of “metaphysics”) to sufficiently fulfill the tasks of a simple, slightly rigorous description of scientific, artistic, technological…work. We are thus not concerned with the “postmodernist” or “deconstructivist” rescue attempts. It is always possible to believe that the work of sciences and of arts has been “covered” with the old apparatuses of philosophy, once they are brought up to date—philosophers are among the last handymen, those who do not yet know that their tool has been irremediably deficient since its birth and was cobbled together—but it is increasingly less possible to attribute the enterprise’s inefficacy to the “height” and dignity of “thought”…

FROM THE IDENTITY OF SCIENCES TO THE SCIENCE OF IDENTITIES

Difference and Identity serve here as our guiding motifs for a reflection on the ultimate foundations of science and of philosophy and on the possibility of a scientific reform of the philosophical understanding. At first glance, Difference and Identity do not introduce us to science, but merely to philosophy. Yet the destiny of these “categories” is tied to the continuous expansion of their signification within philosophy, an expansion we now try to shift toward science itself and its ultimate foundations. Difference and Identity were at first simple predicables in a list of notions with reflexive yet secondary functions (cf. Porphyry, Isagoge). At the very most, we can admit that Identity communicated implicitly with the thematic of the One. But this thematic, as we know, is subject to the greatest uncertainties and to illusions whose solution—precisely with respect to Identity and its relation to Difference—would have to touch on the future of philosophy. With Kant, they acquired the superior, always “reflexive” status of concepts that regulate the “amphibological” use of the understanding and that bear on the whole of philosophy. With contemporary thought since Nietzsche and Heidegger, Differe(a)nce and in turn Identity acquired a still higher dimension as “transcendentals” of a new kind, as principial [principielle] categories. Identity is capable of summing up the entire metaphysical or representative thought, differe(a)nce the thought that seeks to critique, delimit, or deconstruct it.

But in all these cases Differe(a)nce and the correlative Identity in no way express a theory of philosophy as such.¹ They express the perspective of a singular philosophy, a gaze on the tradition as a whole, which nevertheless remains trapped within it. We will attempt to impose an ultimate extension—in the form of a scientific thought of philosophy rather than a new philosophy—on these “categories” and thereby to destroy their uses as “overcategories” of the old ontology or as “transcendentals” of the deconstructions of this ontology. Difference must be able to describe (without any remainder) philosophy in its most enveloping concept, and Identity the theory of philosophy, i.e., a science that can problematize philosophy and that has at least its “power.”

We note that this new use—first for science and its theory, then for the relation of science to philosophy—implies a “reversal” of the priority between the two. In philosophy and on its margins, Difference overrides Identity. This is even how we will define philosophy, in its telos at least: by the primacy of Difference over Identity and by what this primacy implies, their system or their correlation, one being inseparable from the other, the two reciprocally determining each other, Difference itself presupposing Identity. On the other hand, in the new theory of science, which can be established by treating these notions, and especially Identity, as a guiding thread, Identity overrides Difference (i.e., philosophy), although now it is no longer a matter of domination or primacy but of simple priority or order. It is still necessary—we will undertake this—to emancipate Identity from Difference’s traditional authority, to emancipate it more exactly from their system or their correlation, which sustains the primacy of Difference. We must be able to render them heterogeneous to each other, in such a way, nonetheless, that their system (philosophy itself) is not simply fractured or deconstructed (according to Difference), but no longer serves as the foundation of their relation. It is no longer but a “term”—Difference itself—coming after Identity and its priority. The new problem is thus the following: how to think Identity outside-Difference, i.e., as such? How to rectify its concepts and its ontological statements so as to render “thinkable in itself” and plausible the existence of such a thought, which no longer moves within Difference—within the Two as much as within the One—but within and through the One alone, maintaining with the Two a new and freer relation? If Difference and Identity are inseparable in philosophy, reciprocally determinable from the standpoint of their knowledge and their reality, they are so in science only unilaterally and only from the standpoint of Identity’s representation, not from the standpoint of its reality. Difference is necessary only to the knowledge of Identity and not to its essence. This is to say that Identity and knowledge, the real and science, are not reciprocal or convertible. What destroys convertibility is “determination-in-the-last-instance.”

The most banal slogans, the most basic statements like “the identity of a people,” of an individual, or of a phenomenon, are this science’s guiding formulas. Guiding because they are symptomatic or indicative of a problem: do identity and its object, that in which language says identity, co-belong or not? Do they reciprocally determine each other or not? A science of Identities sets out from the dissolution (without a protocol, absolutely given) of this bond between language and representation—philosophical representation or indeterminate generality in which, on one hand, Identity and, on the other hand, Being, being, or the Other are supposed to convert into one another, to co-belong and to form more or less reversible blends. It is not enough to suspend every structure of intentionality and of ekstasis (“identity-of… ,” in the style of “consciousness-of…”), if this suspension aims to maintain the simultaneity of the One and Being. We have to start by recognizing the autonomy of the One as real before Being and the Other, therefore before singularities themselves. Identity-of-the-last-instance opens then a new field of descriptive and theoretical possibilities. But on the condition that it is no longer considered directly legible on the surface of objects or logical forms, of Being or the Other, any more than concealed behind them and “withdrawn” from the World. Identity-of-the-last-instance is independent of that of which it seems to be said. It is a real essence, an essence that has never been an attribute, and, for this reason, since it is the Given anterior to every Donation, it does not constitute a back-ground like Being, for example. It is the World that is ultra-One; it is Being that it trans-unary.

If this problem can be resolved in all theoretical rigor and without the help of philosophical methods—but perhaps with the (henceforth secondary) help of philosophical statements—then it is indeed the future of thought before or after philosophy—outside it at any rate, but in a new relation to it—that will be implicated in this new bifurcation, which is no longer between Difference or Identity, but between the domination of Difference over Identity or the order that goes from Identity to Difference.

To this end, it is enough to show that the One qua One or qua emancipated from Being is the object of a science rather than of a philosophy, but also that this science of the One or of Identities allows us to describe the essence of sciences, the sense of scientific labor, in a nonepistemological description (or a description emancipated in its turn from philosophy). It is in this way that science (as nonepistemological) and the real or Identity (as nonontological) intersect: both are nonphilosophical. This task is accomplished in a new theory of science. The interest of this theory—we obviously do not describe it here—is that it combines, to the point of radically identifying them, the essence of Identity and the essence of science. On one hand, it affords science a real or transcendental dimension it lacks in epistemologies, which implies that science is not an abstraction, a formalism, a dialectic…but is directly related to the real itself, as philosophy claims to be, with the difference that it is actually related to the real. On the other hand, or in parallel, this real to which science relates its knowledges is no longer Being, but the One, which stands outside-Being, outside-presence or outside-representation: in itself alone, or, as we will say, it forms a “determination-in-the-last-instance.” In other words, it is inalienable in the theoretical representation that makes it possible and that is nevertheless its representation or the knowledge that determines it. Hence the double exclusion to which we referred and that is explained by this “real” or “transcendental,” nonempty character of science, which, in the form of the science of the One or of theory of Identities, can treat philosophy, its sense and its language as its objects, and can do so without contradiction. There is an affinity, even an identity, between the essence of every reality, the One-of-the-last-instance, and the essence of science. Only philosophy can desire to separate them, to separate science from what it can do and to refuse to acknowledge the existence of this original thought.

The elaboration of this new science—the science of Identity qua Identity and thereby the science of the essence of every science—amounts to formulating a kind of “general method” for posing and resolving problems. It calls science and philosophy to the same task, but in new relations. “General” no longer has here the sense of “unitary theory” (primacy, domination: of philosophy over science, of Difference over Identity), but the sense of “unified theory” (simple priority, without primacy, of science over philosophy, which is treated as a specific “object” of this science). It is a matter of extricating thought from the state of separation with what it can do, to which philosophy’s domination consigned it, and reforming the understanding in the nonpositivist direction of a scientific thought that continues to make use of philosophy, of philosophical statements about Being, although it is nevertheless not a philosophy and above all not a “philosophy-as-rigorous-science.” It is science that comes from the depths of itself “to” philosophy: to meet it. Not in the sense that it starts to philosophize and loses itself in the process, but that it institutes itself as nothing-but-science and thus maintains a new relation to philosophy.

We describe here and there some aspects of this general method, articulated on the priority of Identity, insisting above all on the new freedoms it gives thought. Precisely because it is massively a thought of and by Difference, philosophy treats nothing but amphibologies. This is what will in turn cause the science that mainly treats identities to appear. But it is a science of a new type: not extracted from philosophical mixtures, but globally “anterior” to them. Philosophy is the thought by and for blends (of orders, spheres, or instances). And it is not only the forms of classical representation that constitute an economy of differences and identities. On the other hand, the thought (of) science, thought-science, is the chance of an access to the real, to the identity of phenomena. There is little doubt now that this identity is no longer metaphysical or generally philosophical. We will say that it is the Identity-of-the-last-instance of phenomena. Any forgotten phenomenon of philosophy and often of already constituted sciences, from the most concrete (the book, photography, etc.) to the most abstract (the real, the ideal, the understanding, intuition, judgment, etc.), can now become the object of a science that relates it in a specific way—for which science alone is the key—to its identity. Science rediscovers the orders, spheres, or instances against philosophy, which, blending them systematically, can think none of them, but only “thinks” itself.

Under the name Theory of Identity, we propose to establish the principles and most of the techniques of this general method for the description of any phenomenon whatsoever (phenomenology should have been this method, but it failed because it exempted itself de facto from the description). This discipline does not claim to replace existing sciences, but rather to replace philosophy, which always excepts itself, not so much de jure as de facto, from its own theory and compensates for this failure of its theoretical project with the illusion of its hermeneutic omnipotence. All phenomena no doubt—but only from the perspective of their Identity-of-the-last-instance, and from the standpoint of the Identity through which they cease to simply belong to the World or to philosophy—can enter into the vision not of an already existing science (they are already the object of various sciences), but of this science in which we demonstrate and know what it means for them to be objects of science and to cease belonging as such to the World or to leave philosophy’s sphere of influence.

Unlike other rival theories (catastrophes, multiplicities, critical points, language games, complexity, self-organization, etc.), the theory of Identities is not obtained through a reflection on current scientific knowledges, isolated from their context; on particularly seductive or promising theoretical givens; or on longstanding theories, accepted as a kind of scientific common sense (axiomatic set theory, for example) and abstracted from the immanent scientific process. It is not a philosophical artifact engendered by the present state of sciences and doomed to imminent obsolescence, like the theories that only hold up because of philosophical inertia rather than scientific movement. It is elaborated by a science of the essence of science, of its status vis-à-vis philosophy (even when the theory of fractals is at issue), a theory of what it can do as science and so forth. Far from representing a simple effect produced by the impact of a determined theory on a fluid, indeterminate philosophy that is ready to immediately reorganize or rebalance itself, it represents an attempt at a global reevaluation of the relations between science and philosophy, a redistribution of their exchanges. A redistribution that is simply the description of their real distribution. This description does not merge with their philosophical image, which forms a system with the continuous production of ideological, half-scientific, half-philosophical artifacts, whose mixed nature ordains them in a privileged way to mediatic consumption. It originates in the “spirit” of science alone, in the thought of which science is capable and that has no need of philosophical support.

The denounced artifacts are scientific yet local knowledges, abstracted from the process of scientific thought or from their scientific sense and associated with another type of thought (the philosophical) in order to compensate for their initial abstraction. They result from a dismemberment of theories. Philosophy cuts off theory from what it can do; it isolates the knowledges produced by science from their immanent theoretical-being and then substitutes itself for science, claiming to stand in for it or to fill in what it believes to be a void or an absence. It thus obliterates the identity of knowledge and of thought-theory; it appropriates the former and negates the latter. It then produces these strange beings, these half-scientific, half-philosophical chimeras: “multiplicities,” “catastrophes,” “singularities,” “inconsistent multiples,” and so forth.

A theory of Identities does not rest on this ground and rejects these traditional customs of philosophy. It merges with the autodescription of thought-science, of theoretical-being and of its cause. It positions itself precisely at the point of the Identity-of-the-last-instance of the real, of knowledge and of thought. A particularly ungraspable, opaque point, so barely illuminated in itself by the light of logos that this light makes it vanish without delay. Hence the indefinitely varied distinctions between knowledge and thought, theory and philosophy, metaphysics and thought—so varied that the efforts to surmount them only revive or reproduce them in the most symptomatic fashion, in the form of artifacts that represent nothing but themselves, the unreality of philosophy’s suture to science. Identities, as they are immanently postulated by science’s theoretical practice, are more primitive, simpler and more originary, if possible, than their philosophical equivalents, which are transcendent constructions, always labored and unstable, endangered by the elaboration of knowledges and the falsification of theories.

A theory of Identities has therefore a scientific and nonphilosophical origin. It rejects all these “negative” and transcendent traits of singularities. Instead of restarting with singularities as a “new” beginning, it starts out with the beginning, with Identity as such. Far from being a last mode of ontology’s autodissolution, it is founded on the immanence of real Identity (to) itself, on its absolute nonconvertibility with Being (philosophy of the Ancients) and with the Other (philosophy of the Contemporaries). Conceived in this sense, Identities do not sacrifice singularities, but only their exteriority and their folded nature as mixture or doublet, their transcendence in relation to the real, and, lastly, their generality and indetermination.

Identities’ radical description, that of their irrevocable precession on every representation (even the theoretical), gives a new impetus—at the same time that it alters their nature—to contemporary questions about philosophy, to its association with an Other-than-philosophy. Philosophy itself has only been able to contest its own claims (in a limited way) through practices of the relation to the Outside, the Other, the Margin, the Nonphilosophical, and so forth, insofar as they are “without-relation.” But it continues to presuppose the whole of its right, the essence of its validity, and admits, in the same style, an “Other” or an “Outside” it cannot found. This double presupposition breathes life into philosophy, but is theoretically arbitrary and cannot be accepted within a theory of Identities. At most, it can become an object, a “phenomenal given,” of this science that hence radicalizes the critique of philosophy, in other words, alters its nature. A critique that ceases to be entrusted to philosophy itself in order to be entrusted to a science.

FRACTALITY AND CHAOS: THE OBJECTIVES OF A GENERALIZED FRACTAL DESCRIPTION

The restoration of Identity’s essence (and thus of science’s) is the first step toward a more rigorous position of the problem of philosophy. Before reaching this threshold, we will cross a second stage that will form the transition between the science of singularities and the science of philosophy: the elaboration of the concepts of generalized fractality and chaos. Since we are prohibited by definition from proposing a philosophy of fractals, which would once again interiorize the geometric and physical fractals (Benoit B. Mandelbrot) into the concept and through the system of philosophical operations, we will use them as a simple indicative material in elaborating the generalized concept of fractality. This concept will rest on a mutation in the theoretical basis of fractality. And it will place us directly on the path of an Artificial Philosophy: a science of philosophy that proceeds by the “fractal” and nonphilosophical synthesis of statements.

The geometric theory of fractals belongs to the set of new objects (catastrophes, singularities, differences, games, turns, etc.) that contemporary thought has discovered and exploited against metaphysics. Yet it stands out for its scientific status, and we treat it here as our guide. It has undergone theoretical extensions (from one region of physics to the other or from physics to economics, etc.), but also aesthetic and sociological “interpretations.” The extensions and the interpretations do not respond to the same criteria and do not exhibit the same type of rigor. We propose to rework them here and to afford them more than a regional theoretical extension and more than a free and metaphoric interpretation or an aesthetic transfer, although it is for us a matter of realizing the identity of this double objective, rendering these two uses identical. This is what we call a theoretical recasting of fractality, a change in the theoretical element of fractal objects. It is a matter of elaborating the concept of a generalized fractal that could be quickly called (subject to precisions and nuances) non-Mandelbrotian. To be sure, this enterprise requires extremely precise conditions so that it does not founder in a simple “hermeneutic” requisition or a groundless transfer of Mandelbrot’s discovery. To give an initial idea of the difficulty in elaborating this theory:

•    it must be scientific, yet not geometric or a physical application of geometry; theoretical, yet not necessarily mathematizable;

•    it must be formulable in natural language and able, moreover, to define a fractality that affects this language, yet it must not remain philosophical.

This double exclusion—of geometry, but not of every science; of philosophy, but not of language—negatively defines the field to be explored. It is, in some sense, the “negative” of this undertaking. The enterprise obviously emerges as a paradox in the eyes of scientific common sense (for which there is no science other than mathematizable science) and of philosophy (for which there is no “possible” science of language and sense other than philosophy itself). The paradox of this type of generalization of fractals is clearly the same as the paradox outlined by one of our guiding formulas, one of the possible objectives of this research, the Idea of a science of philosophy. It does not go beyond this objective and is even inscribed in the program of a science or a theory in the strong sense. But a science that is not mathematizable (thus unacceptable according to the “spontaneous” ethos of the scientist) and that bears on an object of language and sense that has, up to now, always resisted its reduction to the state of a science’s object (thus unacceptable according to the ethos of the philosopher). Here the exclusion is fertile insofar as it is double and bears simultaneously on the geometric version of fractals and on their eventual philosophical version (whether it already exists or not is of little importance, it is entirely imaginable). But how is it possible, what concept of science, of a science that does not yet exist (that of the essence of science, thus of philosophy) must we develop—and could we?—to render credible or simply plausible this scientific break in the theory of fractals, this generalization, which can only be scientific and no longer philosophical?

In reality, we define the question in this way only because we already have at our disposal, not the formal and elaborated solution, but the problem’s givens and thus the possibility of the solution. This generalization of fractals, which is neither a “regional” extension nor an interiorization and an ideological capture, is one of the unexpected consequences of the nonepistemological theory of science. It founds itself on an older discovery: the “grounding” element or the cause of science is not Being; rather, the reality scientists speak of is much closer, albeit not identical, to what philosophers call the One. Provided we first emancipate the One or Identity from their philosophical use, from their forced companionship with Being. This is not yet the appropriate place to elaborate such a theory of science; we did so elsewhere (En tant qu’Un) and do so right here in the first chapter. But this sketch is enough to show that the paradox of a science of philosophy, and thus the paradox of a generalized fractality under the conditions of this science as this theory formulates it, and which are therefore neither mathematical nor philosophical conditions—that this paradox only exists in philosophy’s eyes. The path is open for the recasting of fractality. It is hardly necessary to say that this recasting contains no critique (philosophical or mathematical) of Mandelbrot’s fractality, whose generalization under these precise conditions is by no means its negation. It is not a matter of a rival theory, but of the only theory capable of safeguarding geometric fractals from their interiorization and philosophical capture, from what can only dull their virulence.

A generalized fractal description responds, then, to several interconnected objectives:

• The first is to extend the geometric concepts of dimension and of fractality, first from objects to science, to scientific thought itself, then to philosophy. Put differently: from nature to thought, from so-called natural and regional phenomena (turbulences, economy, meteorology, theory of aggregates and interfaces, etc.) to those of the representation of these phenomena, to the absolutely universal sphere of knowing. This generalization is thus not “ontic” from one region to the other; nor even “axiomatic” (a “non-Mandelbrotian” fractality, although we will re-use this term); but from being [l’étant] to Identity, to science as the thought of the One. A transcendental yet nonphilosophical extension, required by science itself, which uncovers its authentic sense. If so-called natural properties are merely reified knowledges, it becomes possible to carry out this extension from “ontic sciences” to “first science.” In this way, the fractal modeling of philosophy itself—instead of a philosophy of fractals—becomes possible in the form of a “philosophy-of-synthesis” or an “artificial philosophy,” which is nothing other than “nonphilosophy” (in the sense in which this word designates the final product of our undertaking). We also have to first remodel and generalize the concepts of fractality and chaos under nongeometric conditions, the conditions of the essence of science itself, without thereby producing a philosophical generalization that could only subdue “scientific” fractality once again.

• The second objective is to detect, to give consistency and above all a clear formulation, to a new problem overlooked by philosophies, whether they are philosophies “of” sciences or…“of” philosophy itself: the problem of a definition and a measure of the reality-content of knowing. Here it is a matter of a new property or determination of knowings, of knowledges or of thoughts, which would have to liberate them from philosophical authority. If philosophy merely examines knowings themselves, the idealized knowledge-contents it appropriates, what is at stake then, with the problem of the content-in-reality of these knowings, is an absolutely new problem, a theoretical discovery, which alone suffices to justify this research that goes from Identities to Artificial Philosophy. This is a discovery as crucial for the nonepistemological theory of science and of philosophy as the discovery of the content-in-fractality of phenomena that have seemed, up to now, to pertain exclusively to continuous physico-chemical or geometric processes. It is a matter of a “structural” property that touches on science in its essence and thereby on philosophy, but which cannot be explained by continuous processes like those that philosophy and its epistemological images can exploit. It is the problem of the dimensional nature of knowing in general, and in particular its dimension of reality, which cannot be reduced to the dimensions of possibility and of effectivity. It is a matter of measuring, qualitatively, of course, this property—new in relation to their idealized knowing-contents—of philosophical decisions and bodies of knowledge. This property is their fractal dimension. We will show that it maintains the closest links to real Identity. The dimensional description of philosophy, of ontic sciences and of first science is what allows us to distinguish them, to extricate them at last from their unending philosophical confusion and to inaugurate new, more fertile intersections. Among these dimensions, the fractal will be the most complete and the most decisive; it will allow us to measure the qualitative degree of reality of the figures of thought, for example: “singularities,” “multiplicities,” “differences,” “language games,” etc.

• The third objective is to make use of this generalization of fractality as the long-awaited solution to an old, unresolved problem: the possibility of an “artificial Philosophy” whose concept is not uniquely informatic and restricted to this technology.² Even though the principle of the solution has been discovered with the scientific position of the very problem of artificial philosophy, the theoretical tool of generalized fractality will be necessary to make the idea of such a synthesis of philosophical statements plausible and noncontradictory. As generalized, fractality has to allow us to pass from the aporias of an artificial philosophy via informatics—which would now represent only a local means—to the concept of statements of synthesis that rely on fractal procedures. We must not forget, in fact, that the main upshot of this generalization is the extension of images-of-synthesis to phenomena of natural language and sense, the extension of sense and of thought itself.

Once this theoretical threshold—a fractality of identity and no longer of difference—is crossed and once the unraveling or unwinding of philosophical resistance is realized, the formula “science of philosophy” returns to the scene and takes on a new sense. Not only is this guiding formula intrinsically grounded and legitimated through the idea of a generalized fractality, but it also develops concretely as a fractal theory of philosophy itself. It is science or theory that is fractal and that fractalizes. On its own, philosophy is not and refuses to be fractal. Instead, it represents the condition of continuity, the continuous curve that tolerates a minimum of—if any—fractality. It can and must be fractalized in its turn. And in a way all the less external and “artificial” because it is par excellence the object fractalized by the science of the One, the support or material that receives the fractal structure. Philosophy is one of the internal conditions of this structure, but in such a way that it does not constitute it and that this structure comes to it from the outside.

We establish in this way the theoretical basis for a fractal description or modeling of philosophy. The theoretical, yet transcendental and nonmathematical generalization was needed in order to extend this theoretical tool to philosophy, a grounded extension despite the resistance of philosophy, which rejects this new science and tries to interiorize it anew. In its geometric state, fractality is hardly useful for phenomena of sense or of philosophy, i.e., of language-in-philosophy, of logos. It is probably useful for linguistic phenomena, signifier and signification, but not for logos. We now have the theoretical bases that allow us to potentialize it and to afford it the transcendental dimension that its new object (philosophy) requires. The bases to force philosophy to cease capturing singularities, critical points, catastrophes, and scientific fractals, and instead to fractalize logos itself in a radically heteronomous way (this heteronomy is fractality itself, its transcendental and nonempirical or given-in-the-World sense).

But this triple objective refers to practice. The preliminary task will be to found the new concept of fractality on a renewed theory of Identities; this concept will be valid for natural language and no longer uniquely for physico-geometric nature. Philosophy has two complementary concepts of Identity at its disposal, which it divides as follows: Principle of Identity (logical) and the Same (logico-real), plus all their intermediary modes (unity, subject, bond, synthesis, difference, etc.). Neither concept can constitute the terrain of this fractality; it must be real and not simply a possibility dissolved for the benefit of philosophical generalities, which are partially indeterminate and “efface” fractal rigor, which cannot even grant a right, an unconditional right, to geometric fractality, a fortiori, to the fractality that can be generalized to scientific thought itself or as such. The theoretical elaboration of a radical concept of Identities corresponds to the opening of a new space of thought. It is in this space that fractality can be reformulated as an “internal” or “transcendental” property of knowing itself and not only of some of its objects; it is in this space that it finally allows us to resolve the otherwise impossible problem of an artificial philosophy.

The first and second parts of this research supply what should be termed the “conceptual” (rather than mathematical) “formalisms” necessary for the establishment of a science of philosophy. They make what philosophy would have called “concepts” or “categories” manipulable; they transform them into exportable tools, which can be transferred to other regions of knowing. This is not to say that the last part is the most important and that this essay “culminates” or “concludes” in a theory of the philosophical decision. Scientific knowing does not recognize such philosophical hierarchies and teleologies, and the theory of Identities is as crucial as that of fractal Identities and that of philosophy. Because it is a question of the same “irregularity,” the same “fractality” from one end of these inquiries to the other. Their “self-similarity”…