by Daniel Smith
THE PRINCIPLE OF IDENTITY
We begin with the simplest statement of the principle of identity. The classical formula of the identity principle is “A is A”: “blue is blue,” “a triangle is a triangle,” “God is God.” But such formulae, says Leibniz, “seem to do nothing but repeat the same thing without telling us anything.”5 They are certain but empty; they do not force us to think. A more popular formulation of the principle of identity would be: “A thing is what it is.” This formula goes further than the formula “A is A” because it shows us the ontological region governed by the principle of identity: identity consists in manifesting the identity between the thing and what the thing is, what classical philosophy termed the “essence” of a thing. In Leibniz, every principle is a ratio, a “reason,” and the principle of identity can be said to be the ratio or rule of essences, the ratio essendi. It corresponds to the question, “Why is there something rather than nothing?” If there were no identity (an identity conceived as the identity of the thing and what the thing is), then there would be nothing. But Leibniz also provides us with a more technical formulation of the principle of identity, derived from logic: “every analytic proposition is true.” What is an analytic proposition? It is a proposition in which the subject and the predicate are identical. “A is A” is an analytical proposition: the predicate A is contained in the subject A, and therefore “A is A” is true. But to complete the detail of Leibniz's formula, we would have to distinguish between two types of identical propositions: an analytic proposition is true either by reciprocity or by inclusion. An example of a proposition of reciprocity is “a triangle has three angles.” This is an identical proposition because the predicate (“three angles”) is the same as the subject (“triangle”) and reciprocates with the subject. The second case, a proposition of inclusion, is slightly more complex. In the proposition “a triangle has three sides” there is no identity between the subject and the predicate, yet there is a supposed logical necessity; one cannot conceptualize a single figure having three angles without this figure also having three sides. There is no reciprocity here, but there is a demonstrable inclusion or inherence of the predicate in the subject. One could say that analytic propositions of reciprocity are objects of intuition, whereas analytic propositions of inclusion are the objects of a demonstration. What Leibniz calls analysis is the operation that discovers a predicate in a notion taken as a subject. If I show that a given predicate is contained in a notion, then I have done an analysis. All this is basic logic; up to this point, the Leibniz's greatness as a thinker has not yet appeared.
THE PRINCIPLE OF SUFFICIENT REASON
Leibniz's originality, Deleuze suggests, first emerges with his second great principle, the principle of sufficient reason, which no longer refers to the domain of essences but the domain of existences: that is, the domain of things that actually exist. The corresponding ratio is no longer the ratio essendi but the ratio existendi, the reason for existing. The corresponding question is no longer, “Why something rather than nothing?” but rather, “Why this rather than that?” The popular expression of this principle would be: “everything has a reason.” This is the great cry of rationalism, which Leibniz will attempt to push to its limit. Why does Leibniz need this second principle? Because existing things appear to be outside the principle of identity. The principle of identity concerns the identity of the thing and what the thing is, even if the thing itself does not exist; I know that unicorns do not exist, but I can still say what a unicorn is. So Leibniz needs a second principle to make us think existing beings. Yet how can a principle as seemingly vague as “everything has a reason” make us think existing beings?
Leibniz explains how in his philosophical formulation of the principle of sufficient reason, which reads: “all predication has a foundation in the nature of things.”6 What this means is that everything that is truly predicated of a thing is necessarily included or contained in the concept of the thing. What is said or predicated of a thing? First of all, its essence, and at this level there is no difference between the principle of identity and the principle of sufficient reason, which takes up and presumes everything acquired with the principle of identity. But what is said or predicated of a thing is not only the essence of the thing, but also the totality of the affections and events that happen to or are related to or belong to the thing. For example: Caesar crossed the Rubicon. Since this is a true proposition, Leibniz will say that the predicate “crossed the Rubicon” must be contained in the concept of Caesar (not in Caesar himself, but in the concept of Caesar). “Everything has a reason” means that everything that happens to something—all its “differences”—must be contained or included for all eternity in the individual notion of a thing.
If we call an “event” what happens to a thing, whether it submits to it or undertakes it, we will say that sufficient reason is what comprehends the event as one of its predicates: the concept of the thing, or its notion. “Predicates or events,” says Leibniz.7
How does Leibniz arrive at this remarkable claim? He does so, Deleuze suggests, following Couturat, by reconsidering reciprocity. The principle of identity gives us a model of truth that is certain and absolute—an analytical proposition is necessarily a true proposition—but it does not make us think anything. So Leibniz reverses the formulation of the principle of identity using the principle of reciprocity: a true proposition is necessarily an analytic proposition. The principle of sufficient reason is the reciprocal of the principle of identity, and it allows Leibniz to conquer a radically new domain, the domain of existing things.8 By means of this reversal, the principle of identity forces us to think something. The formal formula of the principle of identity (“A is A”) is true because the predicate reciprocates with the subject, and Leibniz therefore applies this principle of reciprocity to the principle of identity itself. In its first formulation, however, the reciprocal of “A is A” is simply “A is A,” and in this sense, the formal formulation prevents the reversal of the identity principle. The principle of sufficient reason is produced only through a reversal of the logical formulation of the principle of identity, but this latter reversal is clearly of a different order; it does not go without saying. Justifying this reversal is the task Leibniz pursues as a philosopher, and it launches him into an infinite—and perhaps impossible—undertaking. The principle of sufficient reason says not only that the notion of a subject contains everything that happens to the subject—that is, everything that is truly predicated of the subject—but also that we should be able to demonstrate that this is the case.
Once Leibniz launches himself into the domain of the concept in this way, however, he cannot stop. At one point in the Metaphysics, Aristotle—who exerted a strong influence on Leibniz—proposes an exquisite formula: at a certain point in the analysis of concepts, it is necessary to stop (anankstenai).9 This is because, for Aristotle, concepts are general, not individual. Classical logic distinguishes between the order of the concept, which refers to a generality, and the order of the individual, which refers to a singularity. By nature, a concept was seen to be something that comprehends a plurality of individuals; it went without saying that the individual as such was not comprehensible by concepts. Put differently, philosophers have always considered that proper names are not concepts. At a certain point, then, the process of conceptual specification must stop; one reaches the final species (infima species), which groups together a plurality of individuals. Leibniz, however, does not heed Aristotle's warning; he does not stop. Instead, he attempts to push the concept to the level of the individual itself; in Leibniz, “Adam” and “Caesar” are concepts, and not simply proper names. The cry of sufficient reason—“Everything must have a reason”—is the problem that will propel Leibniz into an almost hallucinatory conceptual creation. “Leibniz pushes the presuppositions of classical philosophy as far as he can, down the paths of genius and delirium” (20 May 1980). It is not much use to raise objections or to argue against Leibniz, says Dele
uze; one first has to let oneself go, and follow Leibniz in his production of concepts. What, then, is the delirious chasm into which Leibniz plunges?
If everything I attribute with truth to a subject must be contained in the concept of the subject, then I am forced to include in the notion of the subject not only the thing I attribute to it with truth, but also the totality of the world. Why is this the case? By virtue of a principle that is very different from the principle of sufficient reason: namely, the principle of causality. The principle of sufficient reason (“everything has a reason”) is not the same thing as the principle of causality (“everything has a cause”). “Everything has a cause” means that A is caused by B, B is caused by C, and so on—a series of causes and effects that stretches to infinity. “Everything has a reason,” by contrast, means that one has to give a reason for causality itself: namely, that the relation A maintains with B must in some manner be included or comprised in the concept of A.10 This is how the principle of sufficient reason goes beyond the principle of causality: the principle of causality states the necessary cause of a thing but not its sufficient reason. Sufficient reason expresses the relation of the thing with its own notion, whereas causality simply expresses the relations of the thing with something else. Sufficient reason can be stated in the following manner: for every thing, there is a concept that gives an account both of the thing and of its relations with other things, including its causes and its effects. Thus, once Leibniz says that the predicate “crossing the Rubicon” is included in the notion of Caesar, he cannot stop; he is forced to include the totality of the world in Caesar's concept. This is because “crossing the Rubicon” has multiple causes and multiple effects, such as the establishment of the Roman Empire and the death of Jesus; it stretches to infinity backward and forward by the double play of causes and effects. We therefore cannot say that “crossing the Rubicon” is included in the notion of Caesar without saying that the causes and effects of this event are also included in the notion of Caesar. This is no longer the concept of inherence or inclusion, but the fantastic Leibnizian concept of expression: the notion of the subject expresses the totality of the world. Each of us, in our concept, expresses or contains the entirety of the world. This is the first hallucinatory Leibnizian concept that follows from the principle of sufficient reason.
A second concept follows immediately, since there is a danger lurking here for Leibniz: if each notion of the subject expresses the totality of the world, that could seem to indicate that there is only a single subject, and that individuals are mere appearances of this universal subject (a single substance à la Spinoza, or absolute Spirit à la Hegel). But Leibniz cannot follow such a path without repudiating himself, since his entire philosophy remains fixed on the individual, and the reconciliation of the concept with the individual. To avoid this danger, Leibniz creates another new concept: each individual notion comprehends or includes the totality of the world, he says, but from a certain point of view. This marks the beginning of “perspectivist” philosophy, which would be taken up by later philosophers such as Nietzsche (who none the less understood perspectivism in a very different manner than Leibniz). Point of view, however, is such a common notion that one easily risks trivializing Leibniz's conception of perspectivism. Leibniz does not say that everything is “relative” to the viewpoint of the subject; this is what Deleuze calls an “idiotic” or “banal” notion of perspectivism. It would imply that the subject is prior to the point of view, whereas in Leibniz it is precisely the opposite. In Leibniz, the point of view is not constituted by the subject; rather, the subject is constituted by the point of view. Points of view, in other words, are the sufficient reason of subjects. The individual notion is the point of view through which the individual expresses the totality of the world.
But here again, Leibniz cannot stop. For what is it, then, that determines this point of view? Each of us may express the totality of the world, Leibniz tells us, but we express most of the world in an obscure and confused manner, as if it were a mere clamor, a background noise, which we perceive in the form of infinitely small perceptions. These minute perceptions are like the “differentials” of consciousness (Maimon), which are not given as such to conscious perception (apperception). However, there is a small, reduced, finite portion of the world that I express clearly and distinctly, and this is precisely that portion of the world that affects my body. Leibniz in this manner provides a deduction of the necessity of the body as that which occupies the point of view. I do not express clearly and distinctly the crossing of the Rubicon, since that concerns Caesar's body; but there are other things that concern my body—such as my writing of this essay—which I do express clearly. This is how Leibniz defines a point of view: it is the portion or the region of the world expressed clearly by an individual in relation to the totality of the world, which it expresses obscurely in the form of minute perceptions. No two individual substances occupy the same point of view on the world because none has the same clear or distinct zone of expression on the world.
The problem posed by the principle of sufficient reason thus leads Leibniz to create an entire sequence of concepts: expression, point of view, minute perceptions, and so on. “In the majority of great philosophers,” writes Deleuze, “the concepts they create are inseparable, and are taken in veritable sequences. If you do not understand the sequence of which a concept is a part, you cannot understand the concept” (26 Nov 1980). But the notion of point of view will lead Leibniz into a final set of problems. For the world, Leibniz continues, has no existence outside the points of view that express it. The world is the “expressed” thing common to all individual substances, but what is expressed (the world) has no existence apart from what expresses it (individuals). In other words, there is no world in itself. The difficulty Leibniz faces here is this: each of these individual notions must none the less express the same world. Why is this a problem? The principle of identity allows us to determine what is contradictory: that is, what is impossible. A square circle is a circle that is not a circle; it contravenes the principle of identity. But at the level of sufficient reason, things are more complicated; Caesar not crossing the Rubicon and Adam not sinning are neither contradictory nor impossible. Caesar could have not crossed the Rubicon, and Adam could have not sinned, whereas a circle cannot be square. The truths governed by the principle of sufficient reason are thus not of the same type as the truths governed by the principle of identity. But how, then, can Leibniz at the same time hold that everything Adam did is contained for all time in his individual concept, and that Adam the non-sinner was none the less possible? Leibniz's famous response to this problem is this: Adam the non-sinner was possible in itself, but it was incompossible with the rest of the actualized world. Leibniz here creates an entirely new logical relation of incompossibility, a concept that is unique to Leibniz's philosophy, and which is irreducible to impossibility or contradiction. At the level of existing things, it is not enough to say that a thing is possible in order to exist; it is also necessary to know with what it is compossible. The conclusion Leibniz draws from this notion is perhaps his most famous doctrine, one which was ridiculed by Voltaire in Candide and by the eighteenth century in general: among the infinity of incompossible worlds, God makes a calculation and chooses the “Best” of all possible worlds to pass into existence, a world governed by a harmony that is “pre-established” by God. But this rational optimism seems to imply an infinite cruelty, since the best world is not necessarily the world in which suffering is the least.
