In a previous post (Virtual Ideas– Problems and Multiplicities) I suggested that Deleuze’s account of problematic ideas or the virtual shares far more in common with Plato’s conception of the forms or Ideas (eidos) than the empiricist conception of ideas as mental entities. The point here was not to claim that for Deleuze Ideas are forms after the fashion of Plato, but to underline that Ideas must not be conceived as mental entities, but as an ontological category presiding over the actualization of entities. Although Deleuze will later give up his language of “Ideas”, this concept will nonetheless persist under the title of “multiplicity” until the end of his work. However, with that said, it becomes necessary to distinguish Deleuze’s account of Ideas from Ideas of the Platonic variety and explain what philosophical or ontological work they’re doing.

In book six of The Republic, Plato remarks,

Let me remind you of the distinction we drew earlier and have often drawn on other occasions, between the multiplicity of things that we call good or beautiful or whatever it may be and, on the other hand, Goodness itself or Beauty itself and so on. Corresponding to each of these sets of many things, we postulate a single Form or real essence, as we call it… Further, the many things, we say, can be seen, but are not objects of rational thought; whereas the Forms are objects of thought, but invisible. (507a-c)

Plato’s motivation for positing the existence of Forms or Ideas is clear enough: On the one hand, the world that we see about us consists of objects that are constantly changing. Things come to be and pass away. If the criteria for rationality and truth lies in identity, then this entails that physical objects cannot be the objects of truth as they are unable to meet this criteria. On the other hand, to know is not to know this particular object, but the pattern or structure that underlies that object. Suppose that there were a form for gravity. I do not know what gravity is when I know that this or that object falls, but rather have a knowledge of gravity when I know the law governing all instances of gravity. From the standpoint of ordinary perceptual experience, phenomena such as a falling feather, a shooting cannonball, the manner in which I stay tied to the ground, and the movement of the planets all might appear highly unrelated to one another. After all, what could the graceful descent of a feather or a leaf have to do with the movement of the planets, and doesn’t the flight of an airplane or bird violate the principle of gravity? It is only when I move beyond the appearances that I am able to discern the common essence shared by all of these phenomena. The first step in any science is a step back from appearances and perception. Plato is making a similar claim with regard to phenomena such as justice. To know justice is to know that pattern or form common to all instances of justice. Like gravity, there might be examples of justice that seem to share nothing in common with other instances of justice. It is only when I know the form, that I am able to discern these relationships.

Unfortunately, Plato is unable to explain what individual entities contribute to being, if, indeed, they contribute anything at all. For Plato the true beings and objects of knowledge are the forms, not objects or entities in the world. The aim of philosophy, argues Plato, is to turn away to the world of the forms altogether, to purify our souls, so that we might re-unite with the forms themselves, as appearances or physical objects are not the true objects of our desire, but lures for our desire. For instance, in The Symposium Plato will argue that what I desire in the beloved is not the beloved himself, but rather the form of beauty itself. The beloved awakens me to the form of beauty, but if I am wise I will recognize that what I desire is this form, not the person. For Plato there is thus a strong separation between forms and objects. Objects participate in forms, but forms exist independently of objects. Even if all human beings ceased to exist in the world of appearances, the form “Humanity itself” would continue to exist and what is most important would not have been lost (as the form of humanity was the true reality anyway).

In addition to this peculiar separation between form and reality, the doctrine of the forms seems to lead to paradox as well. Plato examines this paradox, which appears to be an early version of Russell’s paradox, in the Parmenides, and it’s been suggested that he later abandons the theory of the forms altogether (for instance, the forms do not appear in Plato’s late work The Laws). A form is basically defined as those features that is common to a set of entities of a particular type. In an argument popularly known as the “third man argument“, we can posit for the set of all entities characterized as “human”, there corresponds a form defined as the “Human itself”. Now, once we posit the existence of this form we can ask whether this form has the characteristic of being human or not. If we answer yes, then we must say that there is an additional form known as “Human-2” that would be the form corresponding to the set of all entities that are humans and the form of that set. But now we need to ask whether the form “Human-2” has the characteristic of being human. If we say yes, we must posit a third form entitled “Human-3”, and so on. That is, the doctrine of the forms seems to lead us into an infinite regress. By contrast, if we say that the form of “human” doesn’t have the characteristic of being human, then it is difficult to see how it relates to the set of entities characterized as human, and the explanatory power of the doctrine of the forms collapses.

There are thus three questions on the table: 1) How is it possible to overcome the transcendence of the forms, which renders the value of all objects null and void (this Platonic heritage will culminate in Kant who argues that “being is not a real predicate”), 2) what do individuals contribute to being, and 3) how is it possible to overcome the third man argument? Deleuze’s strategy is to treat objects as symptoms and Ideas not as essences or forms guaranteeing the identity of objects, but rather as generative matrices or problems presiding over the actualization of objects. Regarding the first point, Deleuze will say, in Nietzsche and Philosophy, that:

We will never find the sense of something (of a human, a biological or even a physical phenomenon) if we do not know the force which appropriates the thing, which exploits it, which takes possession of it or is expressed in it. A phenomenon is not an appearance or even an apparition but a sign, a symptom which finds its meaning in an existing force. The whole of philosophy is a symptomology, and a semeiology. (3)

All individuals that exist are, for Deleuze, symptoms. Symptoms of what? Of the forces that take possession of them. But what are these forces? These forces are what Deleuze will refer to in Difference and Repetition as “Ideas”, “Multiplicities”, “Problems”, or differentials. As Deleuze will write in Nietzsche and Philosophy,

Forces in relation reflect a simultaneous double genesis: the reciprocal genesis of their difference in quantity and the absolute genesis of their respective qualities. The will to power is thus added to force, but as the differential and genetic element, as the internal element of production. It is in no way anthropomorphic. More precisely, it is added to force as the internal principle of the determination of its quality in a relation (x + dx) and as the internal principle of the quantitative determination of this relation itself (dy/dx). (51)

Now, it’s worth pausing here for a moment and noting that the sign of difference– dy/dx –derives from differential calculus (a point that will be confirmed explicitly in Difference and Repetition). This is incredibly significant with regard to Plato. As I observed above, Plato argues that the world of physical objects is irrational and unthinkable because it is constantly changing and therefore fails to obey the law of identity required for something to be thinkable. However, with the emergence of calculus, everything changes, for what we have in differential calculus is the mathamatics of instantaneous rates of change of quantities with respect to other quantities. This, I think, is one of the most significant contributions of Deleuze’s account of the virtual. Where historically it has been impossible to think change, with the invention of calculus, change now becomes thinkable. On the basis of this move, it is no longer necessary to posit an identity transcendent to the ever changing object (a substance underlying changing predicates such as we find in Descartes’ famous wax example from the second meditation, or Kant’s first analogy in The Critique of Pure Reason), but rather the continuous differing of the object from itself becomes thinkable as a unity of difference. Elsewhere, in his book on Leibniz, Deleuze will refer to the object as “objectile”, which is a sort of portmanteau word combining “object” and “projectile”, inviting us to think the individual not as a substance that underlies change, but as an unfolding event tracing a trajectory through the world. The object is now thought as identical to its becoming. All objects become events or happenings.

Nor need we presuppose a prior identity to beings at all, but it now becomes possible to see them as emerging from difference itself and of being differentiated as a result of a process of integrating a solution to the differentials of which they are a symptom. This allows us to be done with the concept of models which objects are understood to more or less approximate, once and for all. For instance, in Aristotle all objects are measured against how closely they actualize their formal-final cause, such that he must formulate the category of “monster” to cover those entities that seem to approximate no formal-natural cause (such as deformed animals). In Deleuze, by contrast, these entities are a solution to a particular differential field. It is in this regard that Deleuze refers to objects as solutions to a problem.

However, as Deleuze is careful to point out in Difference and Repetition, problems are neither negative, nor do they disappear with their solutions. For every object that we encounter we are invited to ask “what problem is this object a symptom of? or what set of genetic conditions generate an object in this way?” In this regard, individuals are to be thought as inhabiting a differential field to which they share no resemblance, of which they are the integration and solution. In this way, Deleuze is able to claim that his ontology captures the singularity of existence itself, of this thing here, now, in this place. Existence is a real predicate and is always a unique creation within being. Deleuze provides a beautiful example of this in Difference and Repetition. Early in the text, Deleuze remarks that,

Learning takes place not in the relation between a representation and an action (reproduction of the Same) but in the relation between a sign and a response (encounter with the Other). Signs involve heterogeneity in at least three ways: first, in the object which bears or emits them, and is necessarily on a different level, as though there were two orders of size or disparate realities between which the sign flashes; secondly, in themselves, since a sign envelops another ‘object’ within the limits of the object which bears it, and incarnates a natural or spiritual power (an Idea); finally, in the response they elicit, since the movement of the response does not ‘resemble’ that of the sign. The movement of a swimmer does not resemble that of the wave, in particular, the movemens of the swuimming instructor which we reproduce on the sand bear no relation to the movements of the wave, which we learn to deal with only by grasping the former in the practice as signs. That is why it is so difficult to say how someone learns: there is an innate or acquired practical familiarity with signs, which means that there is something amorous– but also something fatal –about all education. (22-23)

By sign, Deleuze appears to be referring to the systems-theoretical concept of irritation, whereas by “signal” he appears to be referring to the concept of information whereby an irritation is transformed into information for a particular system. Expanding on this idea much later, Deleuze goes on to say,

In fact, the Idea is not the element of knowledge but that of an infinite ‘learning’, which is of a different nature of knowledge. For learning evolves entirely in the comprehension of problems as such, in the apprehension and condensation of singularities and in the composition of ideal events and bodies. Learning to swim or learning a foreign language means composing the singular points of one’s own body or one’s own language with those of another shape or element, which tears us apart but also propels us into a hitherto unknown and unheard-of world of problems. (192)

There is a profound theory of pedagogy or learning to be found throughout all of Deleuze’s work, that he sets in opposition to the tradition of epistemology or knowledge. I wish American legislators would take this theory of learning into account in designing curriculum in the United States, as it’s clear that they take learning to be “memorization of the same”. All knowledge, for Deleuze, is a solution to a particular problematic or differential field. The problem, multiplicity, Idea, or “differentiation”, in this example consists in the differential relations among singular points between the body and the waves. It is this that Deleuze refers to as the “virtual”. It will be observed that these are literally “no-thing”. Nor do the singular points of the waves or the
body resemble the actualized, differenCiated activity of swimming. Finally, there is nothing negative in this “problem” that disappears once the problem is “solved”, but rather the problem persists each time the person swims as the positive genetic condition of these movements. Solving is an ongoing and endless activity, such that the problem never disappears once and for all (Deleuze draws profound inspiration from Kant’s account of “regulative ideas” in formulating this positive conception of problems). My grandfather, for instance, has a very peculiar walk. If I did not adopt Deleuze’s theory of actualization or individualization, then I might seek to examine his body to see what is wrong with him physiologically after he’s dead, just as a neuropsychologist seeks to look at the brain or genetics of a person alone to understand something like depression, ignoring ecological considerations. However, being aware that my grandfather spent a good deal of his life at sea, I discover that his form of movement is a solution to the virtual differential field defined by the relation of the singular points pertaining to the body and the rocking of a ship from waves. His movement solves this problem and allows him to stand upright as he walks to and fro on the deck of his ships, while I am cast about left and right and sometimes fall down when I walk about on these ships. Similarly, in the case of swimming, one’s style of swimming (the actualized individual) will differ depending on the field or environment in which one learns how to swim. The individual style that integrates the relation of the body to the flows of the water in a swimming pool will be different from the individual style of a California surfer who has to deal with heavy ocean currents and crashing waves. Deleuze is thus able to show how Ideas are the genetic conditions of certain actualized individuals and how the actualized individual is the only possible actualization of this particular problematic field. In short, we dispense with all models saying how an individual should do things, and instead look at the problematic field to which an actualization responds. The individual is no longer secondary or something to be gotten beyond. Nor, finally, is Deleuze’s account of actualization restricted to cognition. Just as the particular movements I employ in swimming refer back to a problematic field or Idea to which they are a solution, the rock outside, the clouds, the trees, the earth, are all integrations of a set of differentials that “solve” a problem that persists. Insofar as each solution generates further differential relations, it follows that there are always new problems to be solved and integrated, and thus new actualizations. We must integrate even our own actualizations. All of this brings about significant transformations in how we study the world, pose ethical questions, pose political questions, and understand the relationship between aesthetics and ontology.

I had hoped to give a more precise account of differentiation and how it differs from differencitation, but hopefully this is a good start.

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