7

THE FRACTAL MODELING OF PHILOSOPHY

THE PHILOSOPHICAL CLUTTER AND ITS SELF-ERASURE

AS a certain regulated—regulated as much as deregulated—use of natural language, philosophy quickly appears as a clutter, a manifold of motifs and objectives, objects and themes, syntaxes and structures (more or less mismatched or poorly assembled), a deformable tissue of aporias, of unmasterable neighborhoods, a particularly irregular curve. Postmodern thought is the exploitation of this irregularity, which, as we have already said, is only semifractal and weak; it is the exploitation of this fragmentation, which is not without rules, but is without rules that would not be themselves mismatched and hesitant.

Nonetheless, it is only a matter of a semifractality and of a curve. Let’s recall some results of philosophy’s dimensional description. This description brackets philosophy’s objects or contents in order to confine itself to its syntax of decision and position; on the other hand, it does not trace the dimensionality of a system of the number of philosophy’s terms or of its empirical “dimensions.” It can be said of any philosophical decision that it possesses either (a) essentially two “principles” (One and Dyad); (b) 2/3 terms (the two opposites of the Dyad and the One that is partially identical to one of them); or (c) precisely a dimension—in the scientific sense of the term—equal to 2/1 or 3/2, depending on the analysis, but an intrinsically fractionary or (semi)fractal dimension that tracks the empirico-transcendental distinction; this distinction is not found in this form within scientific knowledge. Now if we vary the degree of resolution of our gaze on the philosophical decision, either plunging by “magnification” into the details of structures and objects or, on the contrary, generalizing and extracting invariants by distancing and overhanging, then very different properties of philosophical thought emerge, seemingly heterogeneous organizations and logics until—depending on the case—the complete erasure of the structures in the details or the erasure of the details in the invariant structures. And yet it is remarkable that, from one end to the other of their path, these scale-changes or decision-changes leave nothing intact: no absolutely invariant structure, no inequality that would be strictly repeated. They modify or affect all possible layers of philosophy. Even what we called the philosophical semifractality, the empirico-transcendental fraction, or the value of its dimension, tends to be effaced or is at least constantly scrambled. Even the “philosophical decision” can be identified as the structure of a philosophy only at a certain degree of stable resolution. It can no longer be identified when we move to another philosophy; at that moment it requires a supplementary interpretation in order to be identified. In a regime of sufficient philosophy, any philosophy is and must be interpreted by another, whether this other is explicit and elaborated or whether it is a question of implicit and poorly elucidated philosophical “positions.” And yet this procedure of auto-/hetero-interpretation erases not only the singularity that philosophers speak of but also the singularities that philosophies themselves are. The interpretation of one decision by another, thus by Tradition—every philosophical decision represents the Whole of the history of philosophy for another decision—produces the global effect of inserting decisions into a reserve for which they work and that draws a surplus value from this labor of differences.

This is why the concept of “philosophical decision” and its descriptive value have to be relativized: they have a very limited scientific or fractal value, as we said; they are only pertinent from the perspective of another particular philosophy and according to the degree of resolution it represents with respect to and “on” the others. This weakness, this limited consistency of philosophical semifractality, its lack of reality—which makes it dissolve in scale-and-decision variations—obviously means that the auto-/hetero-interpretation, the reciprocal reading of philosophical systems, is caught within the circle of a Tradition that divests it of virtually any scientific value. “Decision” and the affiliated concepts (“multiplicities,” “differences,” “différance,” “language games,” etc.) have no theoretical stability or invariance; they are dragged along in a general circularity: of the structure and the detail, of the scale and the structure, of the tradition and a decision, of one decision and another, and so forth. Furthermore, the idea of scale-and-decision variation has to be, as we saw, critiqued and differentiated—we will say “dualyzed”—from the standpoint of science.

As we just appealed to it, this idea still expresses a philosophical decision or position. It cannot extract genuine invariants, a stable fractality with a theoretical value, insofar as it is affected in some sense by itself, insofar as it modifies its concepts or its essence as it is exercised. Put differently—this is a confirmation of what we already know—philosophy’s auto-/hetero-reflection is stripped of every scientific value and cannot found any theory of philosophy, any mathesis of thought. It is a semitheory, a practice that has theoretical aspects, but always accompanies theory with its limitation or its division.

FROM PHILOSOPHICAL MULTIPLICITIES TO THE FRACTALITY OF PHILOSOPHY: FROM DECONSTRUCTIONS TO ARTIFICIAL PHILOSOPHY

Scientific knowledges’ fundamental complication and chaos and, in this way, those of philosophy escape every philosophical enterprise, which only thinks of totalizing, systematizing, and capitalizing knowledges in an encyclopedia instead of knowing them and proposing a theory of their multiplicity. How can we emancipate the “labor force” at work in singularities, language games, disseminations…from this Tradition, from Philosophy itself [LA philosophie]? Only a science can conserve them without capitalizing them; it safeguards them in their identity, i.e., in their fractal constancy. It is obvious—this is a rule of every possible theory; philosophy is opposed to it—that thought must seek the most radical reason for the greatest fractality, that which can serve as a measure for philosophy itself, instead of letting itself be swept away by philosophy’s objectives and its precipitation. Only a science can propose the rigorous theory of a real fractality or chaos and impose it on the philosophical decision without reconstituting the illusory project of a metaphilosophy. A theory in the scientific sense is never a metaphilosophy; it is only the means by which the real determines knowledge in-the-last-instance. It alone can salvage the concept of fractal dimension from its subsumption by the philosophies of singularities, multiplicities, catastrophes, and so on. And it can thus let be the chaos of sciences without philosophically reinterpreting it once again, as “anarchism,” for example.

Using GF, a science of philosophy will not of course struggle directly against this clutter, this hesitation, or this wavering, against these balanced amphibologies. It is not a matter of returning to a geometry or a topology of philosophy; of proceeding through repeated approximations and idealizations, through the outline of more regular curves, through procedures of regularization and smoothing, which could be gradually substituted for the doctrines’ poorly controllable details and would not perfectly track their contour. Such increasingly simple curves belong to the philosophical decision, and the history of philosophy itself does not fail to draw and trace these long chains that, without necessarily having a reason, form a tradition all the same. It is also not a matter of cutting or of differentiating these lines in an increasingly tight way, of crisscrossing these chains, of interpolating a manifold of decisions, of approaching the philosophical complexity of details: this procedure too belongs to philosophy; philosophy exploits and can describe it. Philosophy itself has already realized the “passage to the limit” (cf. the idea of an unlimited becoming-philosophy), either in the infinitely small or in the infinitely large of its objects. Regularization and uniformization, standardization and idealization, are procedures of philosophical possibilization, means of its realization; they are not at all real ingredients of this philosophy.

From the philosophical perspective itself, or from the perspective of autointerpretation, there is in general what may be called a variation of the manifold, of the content in approximate diversity of a philosophy. It is not so much this content that we are aiming for; or, if it is, then we are aiming for it from the perspective in which it is the material of a fractal constant of philosophy in such a way that this property is represented by an independent structure of the chosen method of approximation. The problem concerns the dimension of the real or fractal content (cf. the introduction) “of” philosophy. This content cannot be reduced to “multiplicity” or “partiality” as intraphilosophical concepts; to the thematic or other (signifying, textual, informational, etc.) content of systems. It cannot be appropriated and is not negotiable in the (hermeneutic, dialectical, analytical, etc.) autointerpretation that philosophy spontaneously gives of it. The problem is in fact double: to identify, if not to measure, the reality (not possibility) content and the theory content of a philosophy and of philosophy itself; an identification that is immediately the fractal practice of synthetic statements.

GF’s theoretical importance lies in its displacement of the weakened or continuous forms of identity, but also of the différe(a)nces or singularities that form a system with them; at the same time, it leaves intact the Identity-of-the-last-instance, the reality it obtains from it, and this reality prevents it from dissolving in philosophy. Its importance vis-à-vis the philosophical themes of irregularity, interruption, or else catastrophe resides in its capacity to afford them a radical indelibility—their nonconservative conservation—against every “founding generality,” every “full body,” every “tradition,” and so on.

It is well-known that the most innovative contemporary philosophies, those that defined a new postrationalist and postmetaphysical epoch of thought, are founded on the primacy of the Other instead of Being, a primacy exerted through numerous variations that do not concern us here. These philosophies have the following in common with their predecessors: they move within the forgetting of the One qua One, within the refusal to think Identity qua Identity. The more the Identity-of-the-Other is forgotten, the more philosophers overbid on this Other. They confuse this identity, which never strays from itself, with what constrains or enslaves the Other. They do not see that the Other’s ultratranscendent position is just as arbitrary as any ontological decision and that it avails itself of metaphysics’ old and most fundamental procedures. By contrast, GF is the discovery of the Identity-of-the-last-instance of the Other itself. It is a theoretical discovery rather than a decision or an affirmation: an immanent discovery, which concerns the essence of knowing rather than an object that can be located in the World. It is thus possible, in accordance with science’s procedures, to use this new theoretical tool for other fields of knowledge, to require it as a theoretical criterion for philosophy itself, in order to produce knowledges that will fractalize philosophical continuity. We are obviously led to treat philosophy—in its specific universality—as a new class of theoretical objects, at least a new class of materials.

Accordingly, if A Phi must have some points in common with deconstructions, as GF does with restrained fractality, it is a matter of an appearance—an objective appearance, of course, but to which we will not give any reality. A Phi is a scientific and positive project whose sole program is philosophical innovation rather than anamnesis. It contains a critique of philosophy only in the second and not the first state, as is the case with deconstructions. GF was not the philosophical transposition and interiorization of geometry, any more than the non-philosophical synthesis of statements can be the philosophical extension of the synthesis of images or the extension of the computer’s informatic possibilities. Here we will elaborate theoretical tools and research programs rather than new “positions.” “Non-philosophy” is such a program, and GF is what allows its realization by rendering an authentic A Phi possible. A Phi does not result from a philosophical extension of AI—we ruled out this solution; it is a relatively autonomous concept that ultimately should be written as “artificial non-philosophy.” But this would be a pleonasm, and, for reasons of strategy and of economy, it is better to speak of A Phi.

GF’S REAL ALGORITHMS

With GF, we have, in some sense, described knowledge’s essential a prioris. The next and final problem is to “realize” or fix the conditions of the “empirical” use of this fractal a priori in philosophy. As we saw, the most “natural” or immanent application of generalized fractals concerns the artificial synthesis of statements, which at once simulate philosophical decisions and dogmas and absolutely exceed their norms of admissibility.

We already described the conditions of a de jure “application” of GF to natural language, which is grasped not in an arbitrary use but within the philosophical regime. More than an application: a determination, as non-philosophical or artificial, of statements whose only material is philosophical. They are the rules that stem from science’s aprioric dimensions (cf. part 1), and these a priori rules are the rules of fractality: GF is in effect an a priori structure.

From this point of view, what we called elsewhere (in Philosophy and Non-philosophy) the rules of non-philosophical practices are obviously nothing more than fractal (albeit a priori) algorithms; they implement GF and can serve to describe philosophy’s reality content. As obviously nonmathematical, real algorithms that use natural language, they allow the “non-philosophical” description of the structure of scientific knowledge and the recourse to philosophical statements.

Why “real” and not logico-mathematical? A computer synthesizes images on the basis of a description, of a prior fractal modeling—one that can be dominated by algorithms. We should thus distinguish the operation’s theoretical aspect and its technological aspect. On the other hand, theory in the full sense we give to it (for example: non-philosophy in the case of first science) can no longer draw this distinction since it is “Identity” in-the-last-instance. It is at once, in an undivided way, the theoretical fractal modeling of philosophy and its “synthetic” image, at once the scientific explanation and the production of an “image” of philosophy whose internal structure cannot be discovered within philosophy. It is “synthetic” par excellence in the sense that its last reason is strict Identity and in the sense that it absolutely exceeds the philosophical givens or materials with which it is produced (it is therefore vis-à-vis philosophy alone and from its perspective that it is characterized in this way).

TRANSCENDENTAL DEDUCTION OF THE FRACTAL A PRIORI: FRACTAL DETERMINATION OF PHILOSOPHY AND PHILOSOPHICAL OVERDETERMINATION OF FRACTALITY

What is GF’s field of validity? It is no longer the geometric and physical regions, the regions of so-called natural objects, but thought itself in its most universal form. First, science, as representation or knowledge; second, the “application” of science to philosophy, i.e., “non-philosophy.” GF is a theory that stems from a particular science, the “first” science of Identities, but it holds for the essence of sciences, then for philosophy.

GF directly addresses the philosophical continuum, which enjoys a powerful universality; it shows in this way the simplicity, the diversity, or the scope of its “applications.”

To be sure, in GF’s relation to philosophy, which serves as its support and material, it is not a question of an application. A science does not apply to its object: it is a genuine a priori determination of this material as object, in this case as fractal object (i.e., object of knowledge).

We elucidated in the foregoing, though hastily, the reasons why GF was an a priori susceptible to a genuine transcendental deduction on the basis of the dual, the “relation” of Identity-of-the-last-instance to the philosophical material. The causality of the last-instance means precisely that the cause—the immanent real, the transcendental instance—cannot act directly on the data of experience, that it must necessarily pass through an a priori structure, in this case GF, which is de jure fractality-for…the philosophical or animated by a nonobjectivating intentionality (to) the philosophical. This transcendental deduction is obviously the key or the solution to the theoretical problem of A Phi.

The reason is that GF is the sole immanent fractality; it is more than a property: the immanent criterion of thought. All the others (geometric or philosophical) are transcendent and legible in the figure of the World. GF is immanent by its “transcendental” cause; it is located in itself rather than in the World and its geometry. It does not have a “home” within philosophy, but is exercised and manifested on the occasion of the World and its geometry and for them.

This a priori constant thus obtains from the Identity-of-the-last-instance its nonmathematical reality, which makes it touch on the essence of knowledge instead of being an ontic and regional knowledge. This does not mean that it is not a knowledge, but it belongs to first science and bears on science’s essence. Its cause thus relates it immanentally to philosophy and gives philosophy the fractal dimension it lacked. But it does not give it this dimension in order to fill the gap and fulfill it as philosophy; rather, it is a “grace” that lifts it outside itself and from itself. A philosophical decision is never fractal on its own, nor does it become fractal from its own depth. It becomes so from the very cause of fractality, ultimately from fractality as cause. Everything that forms an edge, a border, an angle…within a philosophy becomes really fractal only outside itself: within the element of knowledge. Philosophy is not fractal; it is fractalized heteronomously.

Imposing on philosophy and its system a static and a dynamic—chaotic rather than simply differential or deconstructive—is first of all a question of right or of deductive rigor…Philosophy is GF’s condition-of-object or of-material (it is thus philosophy and philosophy alone that is fractalized, and the other phenomena are fractalized as a result or inasmuch as they are virtually philosophizable). Other reasons are possible, other benefits can motivate the enterprise; but they are consequences of this deduction whose sense or “possibility” remains transcendental. For instance: the chaos languages are, by definition, extremely plastic and free as much as an axiomatic can be; they tolerate unstable environments and unforeseeable events—like the arbitrariness of the philosophical decision, since generalized chaos is (nonobjectivating) intentionality (of) philosophy. These reasons can become goals; they remain secondary and cannot legitimate A Phi.

A methodical consequence that clarifies A Phi’s meaning: instead of presupposing givens of natural phenomena, even of philosophy, in order to discover within them traces or regions of chaos and to expose them to a presumed and arbitrarily defined normality and dysfunctioning, we treat immanent generalized chaos as a guiding thread, no longer of a reading but of another practice of philosophy. It is the produced statements that matter as fractal rather than the elaborated statements. GF thus makes it possible to “describe” the philosophical phenomena nonspecularily, in a non-philosophical and noncircular way. To break at once with their “interpretation,” their “functioning,” and their “deconstruction,” procedures that collectively respond to a supplementary decision, which dooms the game to a zero sum. This clearly does not amount to “superimposing” on or “applying” to them a “grid” that is allegedly other than philosophy. On the contrary, it amounts to transforming philosophy into a simple overdetermination or mode of existence of the fractal structure.

We will say of these synthetic statements of non-philosophy that they have, as their structure, science or fractality, which is determinant of their production and as their existence or conditions of existence, the philosophical, which is strictly overdeterminant. They are now philosophical only in their appearance or their occasion and through the channel of their material alone, which is also what overdetermines them.

GF is an a priori that is essentially indifferent to philosophical decisions or differences, which it nevertheless determines. They now play only an occasional role as materials or conditions of existence for this non-philosophical fractality. They no longer coconstitute it, and it can determine them as a fractal manifold endowed with a stability, an objectivity, and, above all else, an identity that they do not immerse in an interminable becoming. The very notion of “object,” as we saw, loses in this way its vulgar and perceived sense, which extends into the philosophical idea of objectivation. But also the vague intuitive sense it has within the concept of the fractal geometric object. It is a matter of an objectivity that is immanent by its essence, manifest through and through and with a more than “objectivating” or “intentional” fractal structure or again intentional, but absolutely not positing. The scale-variation is relativized and transformed into an occasional condition in general, as we already explained, a condition that is necessary only for the philosophical existence of fractality, but is contingent for the essence of fractality. With this shift in status, it ceases to affect fractality itself, while allowing it to “be realized.” Or, rather, it allows it to exist no longer under purely “philosophical” conditions, but under conditions that have a philosophical origin, and to exist as fractality for philosophy. Thus, as we have already repeated, GF is the theoretical instrument that should allow us to concretely implement the science of philosophy we are looking for.

FRACTAL MODELING OF PHILOSOPHY

In first science the transcendental Deduction of the a priori is also the right of philosophy’s fractal modeling. The fractal a priori determination of philosophy is also what we were able to call—always under the aforementioned reservations or transformations—not only a scientific operation of modeling, but a modeling of philosophy by science as such. The philosophical objects, accompanied by their mixture-form, from which they are inseparable, can be modeled by the essence of science itself. They are not idealized and interiorized or else deconstructed, but “reduced” into “materials” for knowledges. Science does not represent an abstract fractality, but a fractality for them or a fractality with a transcendental origin.

GF therefore presupposes a transcendental (but not philosophical) concept of the model as model-for… (an object to be known)—a modeling intentionality, if you want—and thus presupposes that it is not an ontic knowledge, but the very essence of science, that can be this model-for…philosophy.

Modeling, as we will incessantly see, is not a specular double, a simple image that reproduces a given object in a “theoretical” mode. It is a knowledge that, in a sense, is without “common measure,” without a third and transcendent or “common form” with its object. It is an absolute or absolutely mirrorless reflection. It proceeds through phenomenalization in the theoretical mode; it manifests the philosophical and, in a sense, the philosophical itself—but, from now on, in theoretical forms. This manifestation in the mode of knowledge takes the form of a phenomenal state-of-affairs that shows itself absolutely (theory is a nonpositional reflection (of) self…). Thus this reproduction, the very reproduction of knowledge, does not reproduce philosophy in a specular double; it reproduces it, but without its fractalization, which gives to it a scientific universality. This is, moreover, why GF is a model rather than an interpretation. Whereas the restrained, geometric, fractal modeling ceaselessly risks turning in an epistemological circle of the object and of its mathematical image, as a representation that reproduces an object and risks ceasing to be a model, GF is what “separates” science from philosophy, that through which science separates itself from philosophy, discharges it while summoning it, and dissolves the amphibologies.

It is, moreover, not a matter of a geometric, philosophical, or mixed idealization. The theory contains an ideal dimension, but an ideality devoid of every transcendent object it would have reproduced. GF manifests precisely philosophy’s transcendent figure. From this point of view, it deidealizes philosophy at the same time that it dematerializes and definalizes it and, having suspended every teleology, delivers it to chaos.

Given this function and this essence of the model, we will only say that GF models irregularities of philosophy, situations of fragmentation, or the bristling, the angularity peculiar to the details of the philosophical Tradition as a curve of metaphysical differences or decisions. For philosophy is enough to interpret such situations; and they define its essence. GF models philosophy only by producing knowledge from it, but without any originary continuity with it. We can see here how much the idea that “science studies an object’s properties” is problematic and poorly formulated. It is a matter of a property of scientific knowledge, which is thus in its turn a knowledge produced by and in the theory of science, in first science.

PHILOSOPHY’S CHAOTICIZATION; PHILOSOPHICAL SYSTEM AND SCIENTIFIC CHAOS; NON-PHILOSOPHY’S CHAOS-LANGUAGES

We typically examine philosophy with procedures of magnification or of enlargement, with scale-and-decision variations. But these procedures become fertile and are distinguished from the Greek and average gaze with which philosophy tends to be confused only when they are placed in the service of a fractal experience that, in itself, does not depend on them. The science of philosophy is not a variation in “resolution” or even in decision, which are only an occasional condition of fractalization and not its essence. In principle, we see the philosophical under non-philosophical conditions and “in-fractality”; we describe the images that fill this fractal vision and that are detached—by transforming themselves—from philosophy’s inert body. These images are more irregular, more disordered, than the philosophical clutter or fuzziness. But this is a difference in nature and not in degree. At the very scale of philosophy, of its autoreflection, all that can oscillate from the most continuous to the most dispersed, from the most regular to the most aleatory, is grasped at the heart of theory as a fractal chaos of non-philosophical knowledges. It is more than a magnification of details and a variation in the optic field; it is a mutation in the very conditions of thought’s “optics.”

With the science of the One, we can cast on philosophy another gaze than History’s, Tradition’s, Sending’s, or Destiny’s. We can see philosophy in-Identity, that is to say, “in-”fractality and no longer as a more or less continuous curve. Non-philosophy no longer consists in drawing lines, but in fractalizing the lines, even when they are already affected by folds or points of retrogression and dispersion, by critical points or catastrophic breaks. Philosophy is not itself (from its own viewpoint) fractal, but we see it in this way within the element of another discourse that makes use of it without obeying it any longer. For theory is “vision-in-science” and is filled with philosophical materials only by imposing on them a new “chaotic” distribution. This distribution does not lack rules, as we suggested, but is the fractalization of philosophical rules by rules of a whole other type. There is an a priori intuition (of) fractality; it “surpasses” the “transcendental imagination” (philosophy’s resource), not metaphysically but “chaotically.” By means of knowledge, it is capable of receiving not only the structure of lacunary clusters but more profoundly the structure of chaos that orders these clusters themselves.

Here and there (Plato, Descartes, Kant, Husserl, and Nietzsche), philosophy has sufficiently brandished the menace of chaos—in order to propagate the rules of the philosophical Decision it imposes through this violence—that one should finally take it seriously, respond to the challenge and put an end to the blackmail. There is really a chaos, but it is the chaos of the real and of the knowing of the real, which philosophy has never mastered. Philosophy simply called on this chaos as a scarecrow, which, when it is exposed and manifested according to its own laws, is capable of subsuming philosophy itself. We limit philosophy as a simple disorder in view of a transcendent order, as a fear of chaos so as to make way for science as the sole theoretically valid chaos. This chaos is founded on the minimal order of Unilaterality and is capable of containing the philosophical Decision’s rules or half-rules.

Any philosophy whatever is a system and not a chaos; it is therefore a circular structure. But more profoundly and in the full phenomenal sense of the term, it is a “linear” system (with lines, vectors, or directions, with continuous trajectories and curves). Generalized chaos is a static and a dynamic that are delinearized, absolutely fractal through and through; fractality is no longer sustained by the support or the object, but by Identity-of-the-last-instance. It is not, in fact, a marginal or an atypical angularity, which can be partially compensated for and negotiated, rectified and idealized: ideality and objectivity themselves are intrinsically fractal; they are as “multiple” or individuated as the Identities-of-the-last-instance. Hence A Phi ceases to trace lines and to recognize the chains of a Tradition, to identify the signs of a consignment and the critical points of a process. It describes ever new fractal dispersions, radically diachronic, in which it is chaos as the originary space-time of fractality that occurs, forever outside every teleology and philosophical closure that should be passed through, circumvented, leapt over, etc.

Non-philosophy multiplies—through the play of realizations of the simplest fractal structures—more than an unfolded surface, more than the flattening and effacement of a fold that reverts to a surface: a structure that is, if we may phrase it this way, the very intermediary of all the possible differences, a unilaterality more powerful than every in-between. At the same time that it voids this dimension of every object that is supposed to be given in the World or in philosophy, at the same time that it absolutely unlimits it, non-philosophy fills it with local yet fractally dispersed clusters and fills it without saturating it: these are the chaos-languages. Non-philosophy is a practice of chaos-languages. Its material is philosophy-language (or language-in-philosophy); its theoretical means, generalized fractality; its product, language-in-philosophy, distributed in the mode of chaos. This distribution is more than a dis-persion, which remains a unitary concept close to difference. It is the dimension of an opening-without-open, of a space-time that occurs without being able to fold or close on itself.

It then becomes possible, with very little philosophy, with a very poor material, to produce an extreme variety and an extreme complexity of statements that make one last reference to philosophy, call it up one last time without being able to localize it. GF makes it possible to stretch out, infinitely and absolutely, outside every pregiven surface or horizon, philosophy’s little stain, to stretch it out according to an ongoing, absolutely spatiotemporal dimension, but not according to a line or toward a horizon. Chaos neither is nor becomes [devient]; it absolutely occurs [ad-vient] each-time-one-time. The horizon (goal, telos, end) is merely the material of fractal chaos. What we previously called philofiction or hyperspeculation is none other than this fractal practice of language-in-philosophy or of virtually philosophizable language.

The non-philosophical statements produced in this way enjoy a special property that the classical philosophical statements, as differentiated as they may be, lack. The statements fabricated more or less artificially with procedures that remain in a dominant way those of the philosophical continuum (the statements of deconstruction or of language games) also do not enjoy this property. On the contrary, every change in the degree of resolution on these statements or in the decision that serves as their material, every new production of statements, allows an inequality or unilaterality to subsist. This inequality does not cease to occur, under variable conditions of existence, but it is lived and received not as identical through these variations, but as the Identity (of) their unilaterality or their strangeness. New details are uncovered. More exactly: new statements are produced or occur (the equivalent of the interpolation to infinity). But they have this radical fractality they cannot eradicate, which is inalienable in its conditions of existence. The unforeseeable is here more than aleatory; it is lived “in itself,” as fractality in the flesh rather than as a simple fluctuating and vanishing property in its material.

These are particularly nonintuitive statements; they are foreign and unacceptable to every philosophical logic. And yet they are deployed in their own dimension, the dimension of an unreflected and opaque intelligibility. GF is said of statements whose form, the form of their sense, is irreducible to any philosophical syntax. These statements are almost meaningless according to philosophy and pure grammar (cf. Husserl), and yet they are not contradictory; they are produced with coherence and rigor according to the criteria of a real intelligibility (even if it is philosophically blind). Philosophical but not scientific “monsters,” they are useful for opening to theory new, already existing fields (Technology, Ethics, Aesthetics, etc.) that up to now have been subject to and exploited by philosophy alone. They can be directly used for deciphering the reality of science, technology, and philosophy; for rendering them intuitive in another mode; and for rendering Transcendence accessible in a mode that is no longer itself given as transcendent. Philosophical intuitivity (so dependent on natural, perceptive, and topological intuitivity for example) is replaced by another that is less external or contingent: a pure theoretical intuitivity, which is the element of this real and no longer logical, fractal axiomatization.

THE REALITY-EFFECT OR SEMBLANCE-WITHOUT-IMAGE OF GF; SPECULAR REALISM AND REALISM OF-THE-LAST-INSTANCE; SCIENTIFIC MODEL AND PHILOSOPHICAL MODEL

A realist appearance of a special type accompanies GF; it has to be described and should not be confused with the fully specular realism of an object-image.

There is a very intimate connection between the self-similarity of geometric fractals and their power to simulate the real. The connection is even more intimate between GF’s Identity-of-the-last-instance and the realist appearance it creates. A few clarifications have to be introduced with respect to scientific representation, to its power of manifestation of the real, of its cause-of-the-last-instance. As we understand it, science, on one hand, does not manifest its data or the theorico-experimental phenomena that serve as its material; it manifests the real—its cause—by means (“occasion”) of these data and the objects of knowledge of which they are the ingredients. It knows the real by means of the production of objects-of-knowledge; it does not know these objects. And, on the other hand, it is a nonpositional reflection, a description, (of) the real, a theoretical representation inasmuch as, in itself and by its global or undivided existence, it is the manifestation-in-theoretical-mode (of) the real as it is, i.e., inalienable precisely in its representation. The non-philosophical or artificial statements created by means of GF do not represent an “object,” the material, in a specular mode; they are the nonspecular, albeit purely descriptive, representation of Identity-of-the-last-instance, their cause. This is an absolute manifestation, without reference or aim; it manifests the real of-the-final-instance as it is, although only by its existence as reflection and not by an image that would biunivocally correspond to an object or that would represent in the manner of a tableau. There is indeed a reality-effect given by scientific representation, but it is intrinsic, absolute in its order, not locally motivated by reference to a transcendent object. It is a reality affect, an invincible and nonlocalizable, nonidentifiable feeling of reality—what we should call a realism of-the-last-instance. In-the-last-instance alone, and despite everything, despite the absence of every relation of resemblance or of “tableau” to an object, science presents itself globally as an index of reality, of undivided “realist” representation.

To better understand this apparent paradox, let’s start again from philosophy. It carries an objective realist appearance, which is necessarily divided or separated, half-realist, half-imaginary. It gives itself in the mode of Tradition, of Metaphysics [LA métaphysique] and of its History, of a Memory and a Reserve—of a philosophical Great Body that insists and subsists, watches over the work of philosophers and necessarily accompanies them. Philosophy [LA philosophie] is a half-invariant, half-variant process. The identity according to which it is reproduced is not given as simple and inalienable, as identity-of-the-last-instance; it is alienated and returns to itself in the form of a Same, a Great Appearance—an “objective” appearance, i.e., binding, but divided, lived as partially real and partially ideal. The philosophical landscape is at once stable and mobile—metastable; at once “real” and an “image”—surreal; modified by every new decision or every scale-variation. Hence its uncertainties and its objectively doubtful or problematic nature: philosophy is an insufficient Identity; its nature as lack-of-the-real [manque-au-réel], its visceral nihilism, its limited consistency, plagued by the simulacrum; its ultimate loathing of every “realism”; the extensive impregnating of its thought with artifact and imagination; its tissue of transcendent and intuitive images or metaphors (circle, whirlpool, band, ground, horizon, cone, ribbon, surface, plateau, etc.).

Science’s realism has a whole other nature. In a sense, it is without division: one can only say that science as a real appearance or a semblance-without-image is equally imaginary by one of its sides. In fact, it does not have two sides; it is uniface or unilateral. Undivided through and through, it is an integral (re)semblance (to) the real. But (to) a real of-the-last-instance alone: its realism is an undivided effect; it is not founded in the reproduction or even in the simulation of a transcendent object that would divide or nuance its reality-effect. Science, thanks to its fractal nature, emancipates thought from every ideal of specular resemblance—which is sometimes more or less deferred—to supposedly given objects and to their horizon: the World, History, Power, Philosophy. The remainderless destruction of the philosophical theory of “truth tableau” or of “common form,” of transcendent mimesis, is included de jure in the scientific practice and in the nonpositional-Reflection (of) the real.

If scientific realism is an appearance that is real as appearance, in its order of representation, if there is a relative autonomy of the objective appearance of reality that science is, we should say that there is a fractal realism of the same nature, that GF communicates an undivided or in-the-last-instance reality-effect to statements whose synthesis it enables. This originary impression of reality (strictly without foundation, but not without cause) affects all knowledges produced under the “fractal” rules of science, but outside the codes that ground the resemblance to philosophy. There is indeed a self-resemblance or a realism proper to this philosophical material, but it remains secondary, included in an undivided impression of resemblance (—to…)—to nothing transcendent. An undivided semblance that is not founded on any reference, any object-image. It is a reflection-without-mirror or a (re-)semblance-without-image, “abstract” and a priori; but it completely penetrates all the artificial statements. The philosophical variations in scale and in decision, in material, do not cut into it: it is reproduced, or rather occurs, as fractality itself. It is nothing other than the objective appearance of the fractal structure, how it is manifested. And it is manifested as real without nevertheless reproducing for its part transcendent images of its material, without folding back on the fractal structure itself.

This fractal realism does not bear on the used and fractalized material, for it is not this material that is fractally reproduced. It bears on the fractal structure itself. It is, moreover, clear that there are phenomena of autosimulation peculiar to philosophy. But the fractal reality-effect does not prolong them; it does not therefore oscillate between transcendent and imaginary reality, between copy and model, between one simulacrum and another. The philosophical “family resemblance” of non-philosophy is one thing (it moreover varies according to the type of assumed decision); the fractal production of non-philosophy as representation (of) the real is another. It is now impossible to blend them unitarily. Science clarifies the uncertain and unstable realism of philosophy; it destroys philosophy’s amphibological nature (half-real, half-imaginary) and restores to the order of fractal appearances (of) the real its identity.

A Phi’s theoretical context, as we see, excludes the model/copy system (“model” in the Platonic-metaphysical sense, not in the scientific sense), but it equally excludes its inversion and displacement—its “Nietzschean” becoming—in the unlimited simulacrum, in the becoming-simulacrum. Just as GF is distinguished from philosophical semifractality, so the fractal modeling of or for philosophy is distinguished a priori from philosophical concepts of models and thus from simulacrum and simulation, since it fractalizes them in their turn. Identity-of-the-last-instance is the cause that maintains the order of the model, of modeling, as relatively autonomous. It does not blend once more with this order so as to generate the famous “simulacrum” of postmodern philosophies. This simulacrum results from the autodissolution of the circular “model/copy” system, of the decision of the model and the copy, instead of receiving its reality from an unbreachable Identity. Of course this dualysis, this uni-lateralization of the unitary and undetermined concepts of resemblance, realism, reflection, and model, is equivalent to their fractalization. Not only the reality-effect is essentially fractal, but its description also has this character.

GF’s rules or algorithms allow us to synthesize statements and texts that cannot be reduced to the codes of philosophical perception and intelligence. But these statements do not objectively appear to have any less of a striking reality (and validity), opening a prodigious non-philosophical heaven, an intelligible universe superior to every psychological and philosophical imaginary. In the domain of thought, first science—in the extension of effective sciences—produces an effect comparable to that of the artificial synthesis of images in the visual domain and in cinema, for example. It creates an “artificial” space and an “artificial” time, a nonontological opening that traverses the “Being” of philosophy, intellectual-and-sensible landscapes, simulations of scientific and philosophical behaviors, and so on. The equivalent of a visual and graphic informatics would, in this case, be an “automatic” and non-philosophical writing of philosophy, an entire scientific conception assisted by philosophy—at least by artificial philosophy or non-philosophy. These “quasi”-philosophical, synthetic, absolutely universal space-times also produce exploitable aesthetic effects or poetry-fiction.

First science thus opens a new “space-time” for the exercise of thought, unchained from the World or History, but not imaginary for all that. It opens a sphere of existence that can be called intelligible. Realism is inevitable; no thought can escape it, and it would be nonsense or absurdity to want to dispense with it, an effect of philosophy’s perverse realism. The problem is to liberate realism from the constraints of supposedly first Transcendence, from the ontico-ontological disorder. This disorder is not chaos, and its function is in fact to normalize science’s chaos and to bring it back into the philosophical order. Far from being imaginary or semi-imaginary, science is the real critique of philosophical appearances and effects of reality, the critique of the more or less idealized trompe l’oeil realism that is desired by all the philosophical decisions without exception. But this critique is an effect; it is not one of the objectives of first science.

“NATURAL” OR SPONTANEOUS PHILOSOPHY AND ARTIFICIAL PHILOSOPHY; SCIENCE OF SENSE; OF NON-PHILOSOPHY AS MONOGRAPHIA OF THE REAL AND OF THOUGHT

From the start—it is even there that they were invented—fractals were tied to problems of economy, meteorology, and linguistics, to natural phenomena that, as always, seemed to go beyond their then possible mathematical modeling. Once this step is taken and this law is summoned, it is up to us to note that science itself is, in a sense, a “natural” phenomenon that goes beyond the “modeling” (or rather the interpretation) carried out nowadays by philosophy and epistemology. We can also consider philosophy to some extent as a quasi-“natural” process or object. There is a spontaneous, in some sense ambient philosophy, a philosophical faith whose spontaneity feeds the elaborated system; it is never put into question by philosophers themselves, who do not cease confessing this faith. Despite their statements to the contrary (in order to mark the exceptional character of their discipline), philosophy’s existence is a mundane phenomenon, as frequent, as inscribed in the World as the topology of natural or linguistic geometric forms. This ambient philosophy can be autodescriptive, it can fold on itself or prolong itself more explicitly. But it cannot describe itself in a theoretically rigorous and grounded way; it cannot produce validated, rectifiable statements under conditions of scientific stability, and still less can it provide any explanation of itself.

This is where first science and its fractal tool intervene: to scientifically describe this ambient and natural, quasi-vital philosophy, to provide an essentially theoretical description of this set of invariant gestures (the “philosophical decision”). It is possible only if, far from unmarking or untracing the philosophical in a metaphilosophy, the description takes a detour through the generalized fractal and is practiced as a modeling of philosophy.

Philosophy will have only delivered thought from its interior and most representative images—and only for the benefit of movement, becoming, and the Other. It will have crammed it with more idealized, more interiorized images, but these images presuppose some continuity with perception, with common sense, with the topology of natural forms, and with the intuition of the World. The paradox is that it is science and not philosophy that has at its disposal the least transcendent realism, the least imaginary reality-effect, the effect that is best grounded in the most irrefutable real. Thus science alone can reform the philosophical understanding and lead it to a freer form of operation, a form that is less entangled in the insistence of the World’s objects. Thought of synthesis (in the non-philosophical sense of the word, not in its informatic and cognitivist sense), which is also a unified and not unitary thought of science and philosophy, is the thought that receives its true “spirituality,” its dimension of free transcendence in relation to the philosophical Tradition, the philosophical Reserve. Its nature as GF allows it to create new research dimensions: politics-fiction, poetry-fiction, simulation of thought’s behavior, etc.

The solution to the problem of a plausible, philosophically and scientifically noncontradictory A Phi resides in the discovery of a fractality that concerns knowing rather than nature. It thus concerns the (philosophical) sense through knowing, even if it is devoid of sense and of any reflexive dimension. The solved problem is that of a science of sense, which is de jure impossible for philosophy itself as well as for the science that is used and understood in a positivist way. Obviously the problem for us is no longer to subsume new objects under philosophy, not even its old objects, which escape “mechanistic” science (catastrophes, differences, metaphors, and metastability of forms), to subsume them under a renewed regional-ontic science, subtler and more impregnated with philosophy (cf. the mathematical Theory of Catastrophes and its spontaneous neo-Aristotelian philosophy). Instead, the problem is to subsume, under science, philosophy itself, i.e., the object that resists it par excellence, more than a simple regional object that is still inaccessible to a current science. With philosophy, we are dealing with a supraregional, ontological, or “fundamental” object, and it is true that none of the existing ontic sciences, which are adapted to being, can assert its rights next to Being. We needed the discovery of a science of the One to discern the possibility of treating philosophy at last, and without contradiction, as the object of a theory, i.e., as a set of phenomena or data that would no longer arise from their autointerpretation and its phantasms, that would arise from a rigorous theorization. Paradoxically, it was necessary to show that science is unintelligible for the procedures of the philosophical continuum in order to uncover within it, in return, the power to fractally model the most elaborated phenomena of sense, the highest semantic and discursive layers—those of the philosophical use of language.

Artificial Philosophy is thus not a philosophy of artifice, the interiorization of foreign artifices into philosophy (aesthetic, informatic, etc.). Nor is it the contemporary philosophical implosion of simulation and of the simulacrum—it is a matter of breaking with this spontaneous, repetitious, and naively idealist philosophism. Nor, as we said, the simple transfer of criteria and practices from AI or cognition to thought. From our point of view, we have assumed the means of a conceptual and theoretical mutation capable of giving philosophy a new impetus—an impetus that does not come from its own depths, but from elsewhere. The principle or motor of this break in the theory of thought is the theoretical and unphilosophical discovery that the thought of the One qua One is, on one hand, of the order of a science and, on the other, is fractal or irreducible to every philosophical logic. This discovery, which was initiated here and there in some philosophies, did not receive its full sense until now. It cannot in fact leave philosophy’s claims intact and has to contest its most global status within thought and the works of man. This contestation entails the renunciation—at least the de jure renunciation—of the narcissistic practice and procedures of the philosophical continuum; it entails the elaboration of a new nonepistemological theory of science and the thematizing of the fractalization of philosophy.

The majority of philosophies have therapeutic goals (therapeutic of the soul, the body, thought, language, logic, perception, etc.). But there is also a universal pathology of philosophy (fetishization, excess of memory and repetition, loss of variability, decline of differentiation, sedimentation, smoothing, or regularization, insofar as philosophy refuses to abandon their principle and identifies with their autoaffirmation). We find at once an arbitrariness of the decision, of the possible, and of the lack of reality, and what balances them (repetition) in the vain hope of providing, through this procedure, a lacking reality. We find not only the nihilist senescence: the internal decline of philosophy, but also congenital wisdom and old age: philosophy is born fatigued. Its fractalization by science, by the chaotic dynamic proper to theory, changes its practice and grants it the unexpected gift of a vigor that we may have believed to be lost.

What is non-philosophy? It is the monographia of the real and, thereby, of the World, as Identity-of-the-last-instance-of-the-Other. It is still a matter of Clouds, the Ocean, the Heaven and the Earth, but insofar as, far from being left to themselves, i.e., to the hubris of unbridled philosophy, to spontaneous autoposition, they are now described from the perspective of their cause, from this Identity-of-the-last-instance.

So it is the monographia of thought, its rigorous description, or its unified theory, that invalidates the hierarchical distribution of philosophy and of science. And a monographia should have good reasons, which have been theoretically tested (in the One itself), so that it does not appear as the return of metaphysics against the contemporary digraphia, the ever unitary digraphic decision…