What Is Philosophy?

Under these conditions, the first difference between science and philosophy is their respective attitudes toward chaos. Chaos is defined not so much by its disorder as by the infinite speed with which every form taking shape in it vanishes. It is a void that is not a nothingness but a virtual, containing all possible particles and drawing out all possible forms, which spring up only to disappear immediately, without consistency or reference, without consequence.1 Chaos is an infinite speed of birth and disappearance. Now philosophy wants to know how to retain infinite speeds while gaining consistency, by giving the virtual a consistency specific to it. The philosophical sieve, as plane of immanence that cuts through the chaos, selects infinite movements of thought and is filled with concepts formed like consistent particles going as fast as thought. Science approaches chaos in a completely different, almost opposite way: it relinquishes the infinite, infinite speed, in order to gain a reference able to actualize the virtual. By retaining the infinite, philosophy gives consistency to the virtual through concepts; by relinquishing the infinite, science gives a reference to the virtual, which actualizes it through functions. Philosophy proceeds with a plane of immanence or consistency; science with a plane of reference. In the case of science it is like a freeze-frame. It is a fantastic slowing down, and it is by slowing down that matter, as well as the scientific thought able to penetrate it with propositions, is actualized. A function is a Slow-motion. Of course, science constantly advances accelerations, not only in catalysis but in particle accelerators and expansions that move galaxies apart. However, the primordial slowing down is not for these phenomena a zero-instant with which they break but rather a condition coextensive with their whole development. To slow down is to set a limit in chaos to which all speeds are subject, so that they form a variable determined as abscissa, at the same time as the limit forms a universal constant that cannot be gone beyond (for example, a maximum degree of contraction). The first functives are therefore the limit and the variable, and reference is a relationship between values of the variable or, more profoundly, the relationship of the variable, as abscissa of speeds, with the limit.

Sometimes the constant-limit itself appears as a relationship in the whole of the universe to which all the parts are subject under a finite condition (quantity of movement, force, energy). Again, there must be systems of coordinates to which the terms of the relationship refer: this, then, is a second sense of limit, an external framing or exoreference. For these protolimits, outside all coordinates, initially generate speed abscissas on which axes will be set up that can be coordinated. A particle will have a position, an energy, a mass, and a spin value but on condition that it receives a physical existence or actuality, or that it “touches down” in trajectories that can be grasped by systems of coordinates. It is these first limits that constitute slowing down in the chaos or the threshold of suspension of the infinite, which serve as endoreference and carry out a counting: they are not relations but numbers, and the entire theory of functions depends on numbers. We refer to the speed of light, absolute zero, the quantum of action, the Big Bang: the absolute zero of temperature is minus 273.15 degrees Centigrade, the speed of light, 299,796 kilometers per second, where lengths contract to zero and clocks stop. Such limits do not apply through the empirical value that they take on solely within systems of coordinates, they act primarily as the condition of primordial slowing down that, in relation to infinity, extends over the whole scale of corresponding speeds, over their conditioned accelerations or slowing-downs. It is not only the diversity of these limits that entitles us to doubt the unitary vocation of science. In fact, each limit on its own account generates irreducible, heterogeneous systems of coordinates and imposes thresholds of discontinuity depending on the proximity or distance of the variable (for example, the distance of the galaxies). Science is haunted not by its own unity but by the plane of reference constituted by all the limits or borders through which it confronts chaos. It is these borders that give the plane its references. As for the systems of coordinates, they populate or fill out the plane of reference itself.

EXAMPLE 10

It is difficult to see how the limit immediately cuts into the infinite, the unlimited. Yet it is not the limited thing that sets a limit to the infinite but the limit that makes possible a limited thing. Pythagoras, Anaximander, and Plato himself understood this: the limit and the infinite clasped together in an embrace from which things will come. Every limit is illusory and every determination is negation, if determination is not in an immediate relation with the undetermined. The theory of science and of functions depends on this. Later, Cantor provides this theory with its mathematical formulas from a double—intrinsic and extrinsic—point of view. According to the first, a set is said to be infinite if it presents a term-by-term correspondence with one of its parts or subsets, the set and the subset having the same power or the same number of elements that can be designated by “aleph o,” as with the set of whole numbers. According to the second determination, the set of subsets of a given set is necessarily larger than the original set: the set of aleph o subsets therefore refers to a different transfinite number, aleph I, which possesses the power of the continuum or corresponds to the set of real numbers (we then continue with aleph 2, etc.). It is odd that this conception has so often been seen as reintroducing infinity into mathematics: it is, rather, the extreme consequence of the definition of the limit by a number, this being the first whole number that follows all the finite whole numbers none of which is maximum. What the theory of sets does is inscribe the limit within the infinite itself, without which there could be no limit: in its strict hierarchization it installs a slowing-down, or rather, as Cantor himself says, a stop)—a “principle of stopping” whereby a new whole number is created only “if the rounding up of all the preceding numbers has the power of a class of definite numbers, already given in its whole extension.”2 Without this principle of stopping or of slowing down, there would be a set of all sets that Cantor already rejects and which, as Russell demonstrates, could only be chaos. Set theory is the constitution of a plane of reference, which includes not only an endoreference (intrinsic determination of an infinite set) but also an exoreference (extrinsic determination). In spite of the explicit attempt by Cantor to unite philosophical concept and scientific function, the characteristic difference remains, since the former unfolds on a plane of immanence or consistency without reference, but the other on a plane of reference devoid of consistency (Gödel).

When the limit generates an abscissa of speeds by slowing down, the virtual forms of chaos tend to be actualized in accordance with an ordinate. And certainly the plane of reference already carries out a preselection that matches forms to the limits or even to the regions of particular abscissas. But the forms nonetheless constitute variables independent of those that move by abscissa. This is very different from the philosophical concept: intensive ordinates no longer designate inseparable components condensed in the concept as absolute survey (variations) but rather distinct determinations that must be matched in a discursive formation with other determinations taken in extension (variables). Intensive ordinates of forms must be coordinated with extensive abscissas of speed in such a way that speeds of development and the actualization of forms relate to each other as distinct, extrinsic determinations.3 It is from this second point of view that the limit is now the origin of a system of coordinates made up of at least two independent variables; but these enter into a relation on which a third variable depends as state of affairs or formed matter in the system (such states of affairs may be mathematical, physical, biological). This is indeed the new meaning of reference as form of the proposition, the relation of a state of affairs to the system. The state of affairs is a function: it is a complex variable that depends on a relation between at least two independent variables.

The respective independence of variables appears in mathematics when one of them is at a higher power than the first. That is why Hegel shows that variability in the function is not confined to values that can be changed (²/₃ and ⁴/₆) or are left undetermined (a = 2b) but requires one of the variables to be at a higher power (y²/x = P). For it is then that a relation can be directly determined as differential relation dy/dx, in which the only determination of the value of the variables is that of disappearing or being born, even though it is wrested from infinite speeds. A state of affairs or “derivative” function depends on such a relation: an operation of depotentialization has been carried out that makes possible the comparison of distinct powers starting from which a thing or a body may well develop (integration).4 In general, a state of affairs does not actualize a chaotic virtual without taking from it a potential that is distributed in the system of coordinates. From the virtual that it actualizes it draws a potential that it appropriates. The most closed system still has a thread that rises toward the virtual, and down which the spider descends. But knowing whether the potential can be re-created in the actual, whether it can be renewed and enlarged, allows us to distinguish states of affairs, things, and bodies more precisely. When we go from the state of affairs to the thing itself, we see that a thing is always related to several axes at once according to variables that are functions of each other, even if the internal unity remains undetermined. But, when the thing itself undergoes changes of coordinates, strictly speaking it becomes a body, and instead of the function taking the limit and the variable as reference, it takes an invariant and a group of transformations (the Euclidean body of geometry, for example, is constituted by invariants in relation to the group of movements). The “body,” in fact, is not here the special field of biology, and it finds a mathematical determination on the basis of an absolute minimum represented by the rational numbers by carrying out independent extensions of this basic body that increasingly limit possible substitutions until there is a perfect individuation. The difference between body and state of affairs (or thing) pertains to the individuation of the body, which proceeds by a cascade of actualizations. With bodies, the relationship between independent variables becomes fully worked out, even if it means providing itself with a potential or power that renews its individuation. Particularly when the body is a living being, which proceeds by differentiation and no longer by extension or addition, a new type of variable arises, internal variables determining specifically biological functions in relation to internal milieus (endoreference) but also entering into probabilistic functions with external variables of the outside milieu (exoreference).⁵

Thus we find ourselves confronting a new string of functives, systems of coordinates, potentials, states of affairs, things, and bodies. States of affairs are ordered mixtures, of very different types, which may even only concern trajectories. But things are interactions, and bodies are communications. States of affairs refer to geometrical coordinates of supposedly closed systems, things refer to energetic coordinates of coupled systems, and bodies refer to the informational coordinates of separated, unconnected systems. The history of the sciences is inseparable from the construction, nature, dimensions, and proliferation of axes. Science does not carry out any unification of the Referent but produces all kinds of bifurcations on a plane of reference that does not preexist its detours or its layout. It is as if the bifurcation were searching the infinite chaos of the virtual for new forms to actualize by carrying out a sort of potentialization of matter: carbon introduces a bifurcation into Mendeleyev’s table, which, through its plastic properties, produces the state of organic matter. The problem of a unity or multiplicity of science, therefore, must not be posed as a function of a system of coordinates that is possibly unique at a given moment. As with the plane of immanence in philosophy, we must ask what status before and after assume, simultaneously, on a plane of reference with temporal dimension and evolution. Is there just one or several planes of reference? The answer will not be the same as the one given for the philosophical plane of immanence with its strata or superimposed layers. This is because reference, implying a renunciation of the infinite, can only connect up chains of functives that necessarily break at some point. The bifurcations, slowing-downs, and accelerations produce holes, breaks, and ruptures that refer back to other variables, other relations, and other references. According to some basic examples, it is said that the fractional number breaks with the whole number, irrational with rational numbers, Riemannian with Euclidean geometry. But in the other simultaneous direction, from after to before, the whole number appears as a particular case of the fractional number, or the rational as a particular case of a “break” in a linear set of points. It is true that this unifying process that works in the retroactive direction necessarily brings in other references, the variables of which are subject not only to restrictive conditions for giving the particular case but, in themselves, to new ruptures and bifurcations that will change their own references. This is what happens when Newton is derived from Einstein, or real numbers from the break, or Euclidean geometry from an abstract metrical geometry—which amounts to saying with Kuhn that science is paradigmatic, whereas philosophy is syntagmatic.

Science is not confined to a linear temporal succession any more than philosophy is. But, instead of a stratigraphic time, which expresses before and after in an order of superimpositions, science displays a peculiarly serial, ramified time, in which the before (the previous) always designates bifurcations and ruptures to come, and the after designates retroactive reconnections. This results in a completely different pace of scientific progress. Scientists’ proper names are written in this other time, this other element, marking points of rupture and points of reconnection. Of course, it is always possible, and sometimes fruitful, to interpret the history of philosophy according to this scientific rhythm. But to say that Kant breaks with Descartes, and that the Cartesian cogito becomes a particular case of the Kantian cogito, is not entirely satisfying since this is, precisely, to turn philosophy into a science (conversely, it would be no more satisfying to establish an order of superimposition between Newton and Einstein). Far from forcing us to pass through the same components again, the function of the scientist’s proper name is to spare us from doing this and to persuade us that there is no reason to go down the same path again: we do not work through a named equation, we use it. Far from distributing cardinal points that organize syntagms on a plane of immanence, the scientist’s proper name draws up paradigms that are projected into necessarily oriented systems of reference. Finally, the relationship of science with philosophy is less of a problem than that of its even more passionate relationship with religion, as can be seen in all the attempts at scientific uniformization and universalization in the search for a single law, a single force, or a single interaction. What brings science and religion together is that functives are not concepts but figures defined by a spiritual tension rather than by a spatial intuition. There is something figural in functives that forms an ideography peculiar to science and that already makes vision a reading. But what constantly reaffirms the opposition of science to all religion and, at the same time, happily makes the unification of science impossible is the substitution of reference for all transcendence. It is the functional correspondence of the paradigm with a system of reference that, by determining an exclusively scientific way in which the figure must be constructed, seen, and read through functives, prohibits any infinite religious utilization of the figure.6

The first difference between philosophy and science lies in the respective presuppositions of the concept and the function: in the one a plane of immanence or consistency, in the other a plane of reference. The plane of reference is both one and multiple, but in a different way from the plane of immanence. The second difference concerns the concept and the function more directly: the inseparability of variations is the distinctive characteristic of the unconditioned concept, while the independence of variables, in relationships that can be conditioned, is essential to the function. In one case we have a set of inseparable variations subject to “a contingent reason” that constitutes the concept from variations; and in the other case we have a set of independent variables subject to “a necessary reason” that constitutes the function from variables. That is why, from this point of view, the theory of functions presents two poles depending on whether, n variables being given, one can be considered as function of the n – 1 independent variables, with n – 1 partial derivatives and a differential total of the function, or, on the contrary, whether n – 1 magnitudes are functions of a single independent variable, without differential total of the composite function. In the same way, the problem of tangents (differentiation) summons as many variables as there are curves in which the derivative for each is any tangent whatever at any point whatever. But the inverse problem of tangents (integration) deals with only a single variable, which is the curve itself tangent to all the curves of the same order, on condition of a change of coordinates.7 An analogous duality concerns the dynamic description of a system of n independent particles: the instantaneous state can be represented by n points and n vectors of speed in a three-dimensional space but also by a single point in a phase space.

It could be said that science and philosophy take opposed paths, because philosophical concepts have events for consistency whereas scientific functions have states of affairs or mixtures for reference: through concepts, philosophy continually extracts a consistent event from the state of affairs—a smile without the cat, as it were—whereas through functions, science continually actualizes the event in a state of affairs, thing, or body that can be referred to. From this point of view, the pre-Socratics had already grasped the essential point for a determination of science, valid right up to our own time, when they made physics a theory of mixtures and their different types.8 And the Stoics carried to its highest point the fundamental distinction between, on the one hand, states of affairs or mixtures of bodies in which the event is actualized and, on the other, incorporeal events that rise like a vapor from states of affairs themselves. It is, therefore, through two linked characteristics that philosophical concept and scientific function are distinguished: inseparable variations and independent variables; events on a plane of immanence and states of affairs in a system of reference (the different status of intensive ordinates in each case derives from this since they are internal components of the concept, but only coordinates of extensive abscissas in functions, when variation is no more than a state of variable). Concepts and functions thus appear as two types of multiplicities or varieties whose natures are different. Although scientific types of multiplicity are themselves extremely diverse, they do not include the properly philosophical multiplicities for which Bergson claimed a particular status defined by duration, “multiplicity of fusion,” which expressed the inseparability of variations, in contrast to multiplicities of space, number, and time, which ordered mixtures and referred to the variable or to independent variables.⁹ It is true that this very opposition, between scientific and philosophical, discursive and intuitive, and extensional and intensive multiplicities, is also appropriate for judging the correspondence between science and philosophy, their possible collaboration, and the inspiration of one by the other.

Finally, there is a third major difference, which no longer concerns the respective presuppositions or the element as concept or function but the mode of enunciation. To be sure, there is as much experimentation in the form of thought experiment in philosophy as there is in science, and, being close to chaos, the experience can be overwhelming in both. But there is also as much creation in science as there is in philosophy or the arts. There is no creation without experiment. Whatever the difference between scientific and philosophical languages and their relationship with so-called natural languages, functives (including axes of coordinates) do not preexist ready-made any more than concepts do. Granger has shown that in scientific systems “styles” associated with proper names have existed—not as an extrinsic determination but, at the least, as a dimension of their creation and in contact with an experience or a lived10 [un vécu]. Coordinates, functions and equations, laws, phenomena or effects, remain attached to proper names, just as an illness is called by the name of the physician who succeeded in isolating, putting together, and clustering its variable signs. Seeing, seeing what happens, has always had a more essential importance than demonstrations, even in pure mathematics, which can be called visual, figural, independently of its applications: many mathematicians nowadays think that a computer is more precious than an axiomatic, and the study of nonlinear functions passes through slownesses and accelerations in series of observable numbers. The fact that science is discursive in no way means that it is deductive. On the contrary, in its bifurcations it undergoes many catastrophes, ruptures, and reconnections marked by proper names. If there is a difference between science and philosophy that is impossible to overcome, it is because proper names mark in one case a juxtaposition of reference and in the other a superimposition of layer: they are opposed to each other through all the characteristics of reference and consistency. But on both sides, philosophy and science (like art itself with its third side) include an I do not know that has become positive and creative, the condition of creation itself, and that consists in determining by what one does not know—as Galois said, “indicating the course of calculations and anticipating the results without ever being able to bring them about.”¹¹

We are referred back to another aspect of enunciation that applies no longer to proper names of scientists or philosophers but to their ideal intercessors internal to the domains under consideration. We saw earlier the philosophical role of conceptual personae in relation to fragmentary concepts on a plane of immanence, but now science brings to light partial observers in relation to functions within systems of reference. The fact that there is no total observer that, like Laplace’s “demon,” is able to calculate the future and the past starting from a given state of affairs means only that God is no more a scientific observer than he is a philosophical persona. But “demon” is still excellent as a name for indicating, in philosophy as well as in science, not something that exceeds our possibilities but a common kind of these necessary intercessors as respective “subjects” of enunciation: the philosophical friend, the rival, the idiot, the overman are no less demons than Maxwell’s demon or than Einstein’s or Heisenberg’s observers. It is not a question of what they can or cannot do but of the way in which they are perfectly positive, from the point of view of concept or function, even in what they do not know and cannot do. In both cases there is immense variety, but not to the extent of forgetting the different natures of the two great types.

To understand the nature of these partial observers that swarm through all the sciences and systems of reference, we must avoid giving them the role of a limit of knowledge or of an enunciative subjectivity. It has been noted that Cartesian coordinates privilege the points situated close to the origin, whereas those of projective geometry gave “a finite image of all the values of the variable and the function.” But perspective fixes a partial observer, like an eye, at the summit of a cone and so grasps contours without grasping reliefs or the quality of the surface that refer to another observer position. As a general rule, the observer is neither inadequate nor subjective: even in quantum physics, Heisenberg’s demon does not express the impossibility of measuring both the speed and the position of a particle on the grounds of a subjective interference of the measure with the measured, but it measures exactly an objective state of affairs that leaves the respective position of two of its particles outside of the field of its actualization, the number of independent variables being reduced and the values of the coordinates having the same probability. Subjectivist interpretations of thermodynamics, relativity, and quantum physics manifest the same inadequacies. Perspectivism, or scientific relativism, is never relative to a subject: it constitutes not a relativity of truth but, on the contrary, a truth of the relative, that is to say, of variables whose cases it orders according to the values it extracts from them in its system of coordinates (here the order of conic sections is ordered according to sections of the cone whose summit is occupied by the eye). Of course, a well-defined observer extracts everything that it can, everything that can be extracted in the corresponding system. In short, the role of a partial observer is to perceive and to experience, although these perceptions and affections are not those of a man, in the currently accepted sense, but belong to the things studied. Man feels the effect of them nonetheless (what mathematician does not fully experience the effect of a section, an ablation, or an addition), but he obtains this effect only from the ideal observer that he himself has installed like a golem in the system of reference. These partial observers belong to the neighborhood of the singularities of a curve, of a physical system, of a living organism. Even animism, when it multiplies little immanent souls in organs and functions, is not so far removed from biological science as it is said to be, on condition that these immanent souls are withdrawn from any active or efficient role so as to become solely sources of molecular perception and affection. In this way, bodies are populated by an infinity of little monads. The region of a state of affairs or a body apprehended by a partial observer will be called a site. Partial observers are forces. Force, however, is not what acts but, as Leibniz and Nietzsche knew, what perceives and experiences.

Wherever purely functional properties of recognition or selection appear, without direct action, there are observers: hence this is so throughout molecular biology, in immunology, or with allosteric enzymes.12 Maxwell already presupposed a demon capable of distinguishing between rapid and slow molecules, between those with high and weak energy, within a mixture. It is true that in a system in a state of equilibrium, this demon of Maxwell’s linked to the gas will necessarily be affected by vertigo; nonetheless it can spend a long time in a metastable state close to an enzyme. Particle physics needs countless infinitely subtle observers. We can conceive of partial observers whose site is smaller the more the state of affairs undergoes changes of coordinates. Finally, ideal partial observers are the perceptions or sensory affections of functives themselves. Even geometrical figures have affections and perceptions (pathemes and symptoms, said Proclus) without which the simplest problems would remain unintelligible. Partial observers are sensibilia that are doubles of the functives. Rather than oppose sensory knowledge and scientific knowledge, we should identify the sensibilia that populate systems of coordinates and are peculiar to science. This is what Russell did when he evoked those qualities devoid of all subjectivity, sense data distinct from all sensation, sites established in states of affairs, empty perspectives belonging to things themselves, contracted bits of space-time that correspond to the whole or to parts of a function. He assimilated them to apparatus and instruments like Michelson’s interferometer or, more simply, the photographic plate, camera, or mirror that captures what no one is there to see and make these unsensed sensibilia blaze.¹³ Far from these sensibilia being defined by instruments, since the latter are waiting for a real observer to come and see, it is instruments that presuppose the ideal partial observer situated at a good vantage point in things: the nonsubjective observer is precisely the sensory that qualifies (sometimes in a thousand ways) a scientifically determined state of affairs, thing, or body.

For their part, conceptual personae are philosophical sensibilia, the perceptions and affections of fragmentary concepts themselves: through them concepts are not only thought but perceived and felt. However, it is not enough to say that they are distinguished from scientific observers in the same way that concepts are distinguished from functives, since they would then contribute no further determination: both agents of enunciation must be distinguished not only by the perceived but by the mode of perception (nonnatural in both cases). It is not enough to assimilate the scientific observer (for example, the cannonball traveler of relativity) to a simple symbol that would mark states of variables, as Bergson does, while the philosophical persona would have the privilege of the lived (a being that endures) because he will undergo the variations themselves.14 The philosophical persona is no more lived experience than the scientific observer is symbolic. There is ideal perception and affection in both, but they are very different from each other. Conceptual personae are always already on the horizon and function on the basis of infinite speed, nonenergetic differences between the rapid and the slow coming only from the surfaces they survey or from the components through which they pass in a single instant. Thus, perception does not transmit any information here, but circumscribes a (sympathetic or antipathetic) affect. Scientific observers, on the other hand, are points of view in things themselves that presuppose a calibration of horizons and a succession of framings on the basis of slowing-downs and accelerations: affects here become energetic relationships, and perception itself becomes a quantity of information. We cannot really develop these determinations because the status of pure percepts and affects, referring to the existence of the arts, has not yet been grasped. But, the fact that there are specifically philosophical perceptions and affections and specifically scientific ones—in short, sensibilia of the concept and sensibilia of the function—already indicates the basis of a relationship between science and philosophy, science and art, and philosophy and art, such that we can say that a function is beautiful and a concept is beautiful. The special perceptions and affections of science or philosophy necessarily connect up with the percepts and affects of art, those of science just as much as those of philosophy.