Final Year at Vincennes

We are going to be involved for a short while in a series on Leibniz. My goal is very simple: for those who don't know him at all, I want to present this author and to have you love him, to incite in you a sort of desire to read his works.
To begin reading Leibniz, there is an incomparable working instrument. It is the life work, a very modest work, but a very profound one. It is by a lady, Madame Prenant, who had long ago published selected excerpts by Leibniz. Usually a collection of excerpts is of doubtful value, but this one is a work of art, for a very simple reason: Leibniz had writing techniques which no doubt were rather frequent during his era (beginning 18th century), but that he pushed to an extraordinary extent. Of course, like all philosophers, he wrote huge books. But one might almost be tempted to say that these huge books did not constitute the essential part of his works, since what was essential was in the correspondence and in quite tiny memoirs. Leibniz's great texts often ran 4 or 5, 10 pages, or were in letters. He wrote to some extent in all languages and in some ways was the first great German philosopher. He constitutes the arrival in Europe of German philosophy. His influence was immediate on the German Romantic philosophers in the 19th century, then continues particularly with Nietzsche. Leibniz is a philosopher who best helps us understand a possible answer to this question: what is philosophy? What does a philosopher do? What does philosophy grapple with?
If you think that definitions like search for the true or search for wisdom are not adequate, is there a philosophical activity? I want to say very quickly how I recognize a philosopher in his activity. One can only confront these activities as a function of what they create and of their mode of creation. One must ask, what does a woodworker create? What does a musician create? For me, a philosopher is someone who creates concepts. This implies many things: that the concept is something to be created, that the concept is the product of a creation.
I see no possibility of defining science if one does not indicate something that is created by and in science. And, it happens that what is created by and in science, I'm not completely sure what it is, but not concepts properly speaking. The concept of creation has been much more linked to art than to science or to philosophy. What does a painter create? He creates lines and colors. That suggests that lines and colors are not givens, but are the product of a creation. What is given, quite possibly, one could always call a flow. It's flows that are given, and creation consists in dividing , organizing, connecting flows in such a way that a creation is drawn or made around certain singularities extracted from flows.
A concept is not at all something that is a given. Moreover, a concept is not the same thing as thought: one can very well think without concepts, and everyone who does not do philosophy still thinks, I believe, but does not think through concepts. If you accept the idea of a concept as the product of an activity or an original creation.
I would say that the concept is a system of singularities appropriated from a thought flow. A philosopher is someone who invents concepts. Is he an intellectual? No, in my opinion. For a concept as system of singularities appropriated from a thought flow... Imagine the universal thought flow as a kind of interior monologue, the interior monologue of everyone who thinks. Philosophy arises with the action that consists of creating concepts. For me, there are as many creations in the invention of a concept as in the creation by a great painter or musician. One can also conceive of a continuous acoustic flow (perhaps that is only an idea, but it matters little if this idea is justified) that traverses the world and that even encompasses silence. A musician is someone who appropriates something from this flow: notes? Aggregates of notes? No? What will we call the new sound from a musician? You sense then that it is not simply a question of the system of notes. It's the same thing for a philosopher, it is simply a question of creating concepts rather than sounds. It is not a question of defining philosophy by some sort of search for the truth, for a very simple reason: this is that truth is always subordinate to the system of concepts at one's disposal. What is the importance of philosophers for non-philosophers? It is that although non-philosophers don't know it, or pretend not to be interested, whether they like it or not they think through concepts which have proper names.
I recognize the name of Kant not in his life, but in a certain type of concept signed Kant. Henceforth, one can very well conceive of being the disciple of a philosopher. If you are situated so that you say that such and such a philosopher signed the concepts for which you feel a need, then you become Kantian, Leibnizian, etc.
It is quite necessary that two great philosophers not agree with each other to the extent that each creates a system of concepts that serves as his point of reference. Thus that is not all to be judged. One can very well only be a disciple locally, only on one point or another, philosophy is detachable. You can be a disciple of a philosopher to the extent that you consider that you personally need this type of [concept]. Concepts are spiritual signatures, but that does not mean it's in one's head because concepts are also ways of living. And this is not through choice or reflections, the philosopher reflects no more than does the painter or musician. Activities are defined by a creative activity and not by a reflexive dimension. Henceforth, what does it mean to say: to need this or that concept? In some ways, I tell myself that concepts are such living things, that they really are things with four paws, that move, really. It's like a color, like a sound. Concepts really are so living that they are not unrelated to something that would, however, appear the furthest from the concept, notably the scream .
In some ways, the philosopher is not someone who sings, but someone who screams. Each time that you need to scream, I think that you are not far from a kind of call of philosophy. What would it mean for the concept to be a kind of scream or a kind of form of scream? That's what it means to need a concept, to have something to scream! We must find the concept of that scream. One can scream thousands of things. Imagine something that screams: "Well really, all that must have some kind of reason to be." It's a very simple scream. In my definition, the concept is the form of the scream, we immediately see a series of philosophers who would say, "yes, yes"! These are philosophers of passion, of pathos, distinct from philosophers of logos. For example, Kierkegaard based his entire philosophy on fundamental screams.
But Leibniz is from the great rationalist tradition. Imagine Leibniz, there is something frightening there. He is the philosopher of order, even more, of order and policing, in every sense of the word "policing." In the first sense of the word especially, that is, regulated organization of the city. He only thinks in terms of order. But very oddly in this taste for order and to establish this order, he yields to the most insane concept creation that we have ever witnessed in philosophy. Disheveled concepts, the most exuberant concepts, the most disordered, the most complex in order to justify what is. Each thing must have a reason. In fact, there are two kinds of philosopher, if you accept the definition by which philosophy is the activity consisting of creating concepts. But there are perhaps two poles: there are those who engage in a very sober creation of concepts; they create concepts on the level of a particular singularity well distinguished from another, and I dream finally of a kind of quantification of philosophers in which they would be quantified according to the number of concepts they have signed or invented. If I say: Descartes! That's the type of philosopher with a very sober concept creation. The history of the cogito, historically one can always find an entire tradition, precursors, but there is nonetheless something signed Descartes in the cogito concept, notably (a proposition can express a concept) the proposition: "I think therefore I am," a veritable new concept. It's the discovery of subjectivity, of thinking subjectivity. It's signed Descartes.
Of course, we could always look in St. Augustine's works, to see if it wasn't already in preparation. There is certainly a history of concepts, but it's signed Descartes. Haven't we made rather quick work of Descartes though? We could assign to him five or six concepts, an enormous feat to have invented six concepts, but it's a very sober creation. And then there are exasperated philosophers. For them, each concept covers an aggregate of singularities, and then they always need to have other, always other concepts. One witnesses a mad creation of concepts. The typical example is Leibniz. He never finished creating something new.
That's all I wanted to explain.
He is the first philosopher to reflect on the power of the German language as a concept, as German being an eminently conceptual language, and it's not by chance that it can also be a great language of the scream. Multiple activities, he attends to all, a very great mathematician, great physics scholar, very good jurist, many political activities, always in the service of order. He does not stop, he is very shady . There is a Leibniz-Spinoza visit (he who was the anti-Leibniz): Leibniz has him read manuscripts, and one imagines Spinoza very exasperated, wondering what this guy wants. Following that when Spinoza was attacked, Leibniz said that he never went to see him, he said it was to monitor him... Abominable, Leibniz is abominable. His dates: 1646-1716. It's a long life, straddling plenty of things.
Finally he had a kind of diabolical humor. I'd say that his system is rather like a pyramid. Leibniz's great system has several levels. None of these levels is false, these levels symbolize each other, and Leibniz is the first great philosopher to conceive of activity and thought as a vast symbolization.
Thus, all these levels symbolize, but they are all more or less close to what we could provisionally call the absolute. And that belongs to his very body of work. Depending on Leibniz's correspondent or on the public to which he addressed himself, he presented his whole system at a particular level. Imagine that his system is made of levels more or less contracted or more or less relaxed; in order to explain something to someone, he goes to situate himself on a particular level of his system. Let us assume that the someone in question was suspected by Leibniz of having a mediocre intelligence: very well, he is delighted, he situates himself on one of the lowest levels of his system, and if he addresses someone of higher intelligence, he jumps to a higher level. As these levels belong implicitly to Leibniz's own texts, that creates a great problem of commentary. It's complicated because, in my opinion, one can never rely on a Leibniz text if one has not first discerned the system level to which this text corresponds.
For example, there are texts in which Leibniz explains what, according to him, is the union of soul and body, right, and it's to one particular correspondent or another; to another correspondent, he will explain that there is no problem in the union of soul and body since the real problem is that of the relation of souls to one another. The two things are not at all contradictory, it's two levels of the system. The result is that if one does not evaluate the level of a Leibniz text, then one will get the impression that he constantly contradicts himself, when in fact, he does not contradict himself at all.
Leibniz is a very difficult philosopher. I would like to give titles to each part of what I have to propose to you. The principal #1 I would call "a funny thought" . Why do I call it "a funny thought"?, Well, because among Leibniz's texts, there is a small one that Leibniz himself calls "funny thought." Thus I am authorized by the author himself. Leibniz dreamed a lot, he has a whole science-fiction side that is absolutely amazing, all the time he imagined institutions. In this little "funny thought" text, he imagined a very disturbing institution that would be as follows: an academy of games would be necessary. In that era, as well with Pascal, certain other mathematicians, and Leibniz himself, there developed a great theory of games and probabilities. Leibniz is one of the great founders of game theory. He was impassioned by mathematical game problems, he must have been quite a games player himself. He imagined this academy of games as necessarily being at once - why at once? Because depending on the point of view in which one is situated to see this institution, or to participate in it - this would be at once a section of the academy of sciences, a zoological and botanical garden, a universal exposition, a casino where one gambled, and an enterprise of police control. That's not bad. He called that "a funny thought."
Assume that I'm telling you a story. This story consists in taking up one of the central points of Leibniz's philosophy, and I tell it to you as if it were the description of another world, and there I also number the principal propositions that go into forming a funny thought.

a) The thought flow, eternally, brings with it a famous principle that has a very special characteristic because it is one of the only principles about which one can be certain, and at the same time one can not see at all what it offers to us. It is certain, but it is empty. This famous principle is the principle of identity. The principle of identity has a classical formula, A is A. That is certain. If I say blue is blue or God [is] God, I am not saying with this that God exists, in a sense I am in certainty. Only there it is, do I think something when I say A is A, or am I not thinking? Let us nonetheless try to say what results from this principle of identity. It is presented in the form of a reciprocal proposition. A is A means: subject A, verb to be, A attribute or predicate. There is a reciprocity of subject and predicate. Blue is blue, a triangle is a triangle, these are empty and certain propositions. Is that all? An identical proposition is a proposition such that the attribute or the predicate is the same as the subject and reciprocates with the subject. There is a second case just a bit more complex, notably that the principle of identity can determine propositions which are not simply reciprocal propositions. There is no longer simply reciprocity of the predicate with the subject and subject with the predicate. Suppose that I say: "The triangle has tree sides," this is not the same thing as saying, "The triangle has three angles." "The triangle has three angles" is an identical proposition because it is reciprocal. "The triangle has three sides" is a little different, it is not reciprocal. There is no identity of subject and predicate. In fact, "three sides" is not the same thing as "three angles". And nonetheless, there is a supposed logical necessity. This logical necessity is that you cannot conceptualize three angles composing a single figure without this figure also having three sides. There is no reciprocity, but there is inclusion. Three sides are included in the triangle. Inherence or inclusion.
Likewise, if I say that matter is matter, matter and matter is an identical proposition in the form of a reciprocal proposition. The subject is identical to the predicate. If I say that matter is in extension <étendue>, this is again an identical proposition because I cannot think of the concept matter without already introducing extension. Extension is in matter. This is all the more a reciprocal proposition since, inversely, perhaps I really can think of extension without anything filling it in, that is, without matter. This is therefore not a reciprocal proposition, but it is a proposition of inclusion; when I say "matter is in extension," this is an identical proposition by inclusion.
I would say therefore that there are two kinds of identical propositions: there are reciprocal propositions in which the subject and predicate are one and the same, and propositions of inherence or inclusion in which the predicate is contained in the concept of the subject. If I say "this page has a front side and a back side," OK, let's leave that, I withdraw my example. If I am looking for a more interesting statement of the identity principle, I would say in Leibnizian fashion that the identity principle is stated as follows: every analytical proposition is true.
What does analytical mean? According to the example we have just seen, an analytical proposition is one in which either the predicate or the attribute is identical with the subject, for example, "the triangle is triangular," reciprocal proposition, or proposition of inclusion such as "the triangle has three sides." The predicate is contained in the subject to the point that when you have conceived of the subject, the predicate was already there. It suffices therefore to have an analysis in order to find the predicate in the subject. Up to this point, Leibniz as original thinker has yet to emerge.

b) Leibniz emerges. He arises in the form of this very bizarre scream . I am going to give it a more complex expression than I did earlier. Everything that we're saying is not philosophy, but pre-philosophy. This is the terrain on which a very prodigious philosophy will be built. Leibniz arrives and says: OK, the identity principle gives us a certain model. Why a certain model? In its very statement <énoncé>, an analytical proposition is true, if you attribute to a subject something that constitutes a unity with the subject itself, or that is mixed up with or is already contained in the subject. You risk nothing in being wrong. Thus, every analytical proposition is true.
Leibniz's stroke of pre-philosophical genius is to say: Let's consider reciprocity! Something absolutely new and nonetheless very simple starts there, since this had to be thought through. And what does it mean to say, "it had to be thought through"? It means that one had to have need of that, that had to relate to something quite urgent for him. What is the reciprocity of the identity principle in its complex statement, "every analytical proposition is true"? Reciprocity poses many more problems. Leibniz emerges and says: every true proposition is analytical.
If it is true that the identity principle gives us a model of truth, why are we stumped by the following difficulty, notably: it is true, it doesn't make us think anything. The identity principle will force us to think something; it is going to be reversed, turned around. You will tell me that turning A is A around yields A is A. Yes and no. That yields A is A in the formal formulation which prevents the reversal of the principle. But in the philosophical formulation, which still amounts to exactly the same thing, "every analytical proposition is a true proposition", if you reverse the principle: "every true proposition is necessarily analytical," what does that mean? Each time that you formulate a true proposition, it must be analytical (and this is where there is the scream!), whether you want it or not, that is, it is reducible to a proposition of attribution or of predication, and not only is it reducible to a judgment of predication or attribution (the sky is blue), but it is analytical, that is the predicate is either reciprocal with the subject or contained in the concept of the subject? Does that go without saying? He throws himself into a strange undertaking , and it is not from preference that he says that, rather he needs it. But he undertakes an impossible task, in fact he needs some entirely crazy concepts in order to reach this task that he is in the process of giving himself. If every analytical proposition is true, every true proposition certainly must be analytical. It does not go without saying at all that every judgment is reducible to a judgment of attribution. It's not going to be easy to show. He throws himself into a combinatory analysis, as he himself says, that is fantastic.
Why doesn't it go without saying? "The box of matches is on the table," I'd say that this is a judgment, you know? "On the table" is a spatial determination. I could say that the matchbox is "here." "Here," what's that? I'd say that it's a judgment of localization. Again I repeat very simple things, but they always have been fundamental problems of logic. It's only to suggest that in appearance, all judgments do not have as form predication or attribution. When I say, "the sky is blue," I have a subject, sky, and an attribute, blue. When I say "the sky is up there" or "I am here," is "here" - spatial localization - assimilable to a predicate? Can I formally link the judgment "I am here" to a judgment of the kind "I am blond"? It's not certain that spatial localization is a quality. And "2+2=4" is a judgment that we ordinarily call a relational judgment. Or if I say, "Pierre is smaller than Paul," this is a relation between two terms, Pierre and Paul. No doubt I orient this relation upon Pierre: if I say "Pierre is smaller than Paul," I can say "Paul is larger than Pierre." Where is the subject, where is the predicate? That is exactly the problem that has disturbed philosophy since its beginnings; ever since there was logic they have wondered to what extent the judgment of attribution could be considered as the universal form of any possible judgment, or rather one case of judgment among others. Can I treat "smaller than Paul" like an attribute of Pierre? It's not certain, not at all obvious. Perhaps we have to distinguish very different types of judgment from each other, notably: relational judgment, judgment of spatio-temporal localization, judgment of attribution, and still many more: judgment of existence. If I say "God exists," can I formally translate it into the form of "God is existent," existent being an attribute? Can I say that "God exists" is a judgment of the same form as "God is all-powerful"? Undoubtedly not, since I can only say "God is all-powerful" by adding "yes, if he exists". Does God exist? Is existence an attribute? Not certain.
So you see that by proposing the idea that every true proposition must be in one way or another an analytical proposition, that is identical, Leibniz already gives himself a very hard task; he commits himself to showing in what way all propositions can be linked to the judgment of attribution, notably propositions that state relations, that state existences, that state localizations, and that, at the outside, exist, are in relation with, can be translated as the equivalent of the attribute of the subject.
In your mind there must arise the idea of an infinite task.
Let us assume that Leibniz reached it: what world is going to emerge from it? What very bizarre world? What kind of world is it in which I can say "every true proposition is analytical"? You recall certainly that ANALYTICAL is a proposition in which the predicate is identical to the subject or else is included in the subject. That kind of world is going to be pretty strange.
What is the reciprocity of the identity principle? The identity principle is thus any true proposition is analytical; not the reverse, any analytical proposition is true. Leibniz said that another principle is necessary, reciprocity: every true proposition is necessarily analytical. He will give to it a very beautiful name: the principle of sufficient reason. Why sufficient reason? Why does he believe himself fully immersed in his very own scream? EVERYTHING MUST SURELY HAVE A REASON. The principle of sufficient reason can be expressed as follows: whatever happens to a subject, be it determinations of space and time, of relation, event, whatever happens to a subject, what happens, that is what one says of it with truth, everything that is said of a subject must be contained in the notion of the subject.
Everything that happens to a subject must already be contained in the notion of the subject. The notion of "notion" is going to be essential. It is necessary for "blue" to be contained in the notion of sky. Why is this the principle of sufficient reason ? Because if it is this way, each thing with a reason, reason is precisely the notion itself in so far as it contains all that happens to the corresponding subject . Henceforth everything has a reason.
Reason = the notion of the subject in so far as this notion contains everything said with truth about this subject. That is the principle of sufficient reason which is therefore justly the reciprocal of the identity principle. Rather than looking for abstract justifications I wonder what bizarre world is going to be born from all that? A world with very strange colors if I return to my metaphor of painting. A painting signed Leibniz. Every true proposition must be analytical or still more, everything that you say with truth about a subject must be contained in the notion of the subject. You sense that this is getting crazy, he's got a lifetime of work ahead of him.
What does "notion" mean? It's signed Leibniz. Just as there is a Hegelian conception of the concept, there is a Leibnizian conception of the concept.

c) Again, my problem is what world is going to emerge, and in this sub-category c), I would like to begin to show that, from this point, Leibniz is going to create truly hallucinatory concepts. It's truly a hallucinatory world. If you want to think about relations between philosophy and madness, for example, there are some very weak pages by Freud on the intimate relation of metaphysics with delirium . One can only grasp the positivity of these relations through a theory of the concept, and the direction that I would like to take would be the relationship of the concept with the scream. I would like to make you feel this presence of a kind of conceptual madness in Leibniz's universe as we are going to see it be born. It is a gentle violence, let yourself go. It is not a question of arguing. Understand the stupidity of objections.
I will add a parenthesis to complicate things. You know that there is a philosopher following Leibniz who said that truth is one of synthetic judgments. He is opposed to Leibniz. OK! How does that concern us? It's Kant. This is not to say that they do not agree with each other. When I say that, I credit Kant with a new concept which is synthetic judgment. This concept had to be invented, and it was Kant who did so. To say that philosophers contradict one another is a feeble formula, it's like saying that Velasquez did not agree with Giotto, right! It's not even true, it's nonsensical.
Every true proposition must be analytical, that is such that it attributes something to a subject and that the attribute must be contained in the notion of the subject. Let us consider an example. I do not wonder if it is true, I wonder what it means. Let us take an example of a true proposition. A true proposition can be an elementary one concerning an event that took place. Let's take Leibniz's own example: "CAESAR CROSSED THE RUBICON". It's a proposition. It is true or we have strong reasons to assume it's true. Another proposition: "ADAM SINNED".
There is a highly true proposition. What do you mean by that? You see that all these propositions chosen by Leibniz as fundamental examples are event-ual propositions , so he does not give himself an easy task. He is going to tell us this: since this proposition is true, it is necessary, whether you want it or not, that the predicate "crossed the Rubicon," if the proposition is true, but it is true, this predicate must be contained in the notion of Caesar. Not in Caesar himself, but in the notion of Caesar. The notion of the subject contains everything that happens to a subject, that is, everything that is said about the subject with truth. In "Adam sinned," sin at a particular moment belongs to the notion of Adam. Crossing the Rubicon belongs to the notion of Caesar. I would say that here, Leibniz proposes one of his greatest concepts, the concept of inherence. Everything that is said with truth about something is inherent in the notion of this something.
This is the first aspect or development of sufficient reason.

d) When we say that, we can no longer stop. When one has started into the domain of the concept, one cannot stop. In the domain of screams, there is a famous scream from Aristotle. The great Aristotle -- who, let us note, exerted an extremely strong influence on Leibniz -- at one point proposed in the Metaphysics a very beautiful formula: it is indeed necessary to stop (anankstenai). This is a great scream. This is the philosopher in front of the chasm of the interconnection of concepts. Leibniz could care less, he does not stop. Why? If you refer to proposition c): everything that you attribute to a subject must be contained in the notion of this subject. But what you attribute with truth to any subject whatsoever in the world, if were it Caesar, it is sufficient for you to attribute to it a single thing with truth in order for you to notice with fright that, from that moment on, you are forced to cram into the notion of the subject not only the thing that you attribute to it with truth, but the totality of the world. Why? By virtue of a well-known principle that is not at all the same as that of sufficient reason. This is the simple principle of causality. For in the end, the causality principle stretches to infinity, that's it's very characteristic. And this is a very special infinite since, in fact, it stretches to the indefinite . Specifically, the causality principle states that everything has a cause, which is very different from every thing has a reason. But the cause is a thing, and in its turn, it has a cause, etc. etc. I can do the same thing, notably that every cause has an effect and this effect is in its turn the cause of effects. This is therefore an indefinite series of causes and effects.
What difference is there between sufficient reason and cause? We understand very well. Cause is never sufficient. One must say that the causality principle poses a necessary cause, but never a sufficient one. We must distinguish between necessary cause and sufficient reason. What distinguishes them evidently is that the cause of a thing is always something else. The cause of A is B, the cause of B is C, etc..... An indefinite series of causes. Sufficient reason is not at all something other than the thing. The sufficient reason of a thing is the notion of the thing. Thus, sufficient reason expresses the relation of the thing with its own notion whereas cause expresses the relations of the thing with something else. It's limpid.

e) If you say that a particular event is encompassed in the notion of Caesar, "crossing the Rubicon" is encompassed in the notion of Caesar . You can't stop yourself in which sense? From cause to cause and effect to effect, it's at that moment the totality of the world that must be encompassed in the notion of a particular subject. That becomes very odd, there's the world passing by inside each subject, or each notion of subject. In fact, crossing the Rubicon has a cause, this cause itself has multiple causes, from cause to cause, into cause from cause and into cause from cause of cause. It's the whole series of the world that passes there, at least the antecedent series. And moreover, crossing the Rubicon has effects. If I limit myself to the largest ones: commencement of a Roman empire. The Roman empire in its turn has effects, we follow directly from the Roman empire. From cause to cause and effect to effect, you cannot say a particular event is encompassed in the notion of a particular subject without saying that, henceforth, the entire world is encompassed in the notion of a particular subject.
There is indeed a trans-historical characteristic of philosophy. What does it mean to be Leibnizian in 1980? They exist, or at least it's possible that they exist.
If you said, conforming to the principle of sufficient reason, that what happens to a particular subject, and which personally concerns it, then what you attribute it with truth, having blue eyes, crossing the Rubicon, etc. ... belongs to the notion of the subject, that is encompassed in this notion of the subject; you cannot stop, one must say that this subject contains the whole world. It is no longer the concept of inherence or inclusion, it's the concept of expression which, in Leibniz's work, is a fantastic concept. Leibniz expresses himself in this form: the notion of the subject expresses the totality of the world.
His own "crossing the Rubicon" stretches to infinity backward and forward by the double play of causes and effects. But then, it is time to speak for ourselves, little matter what happens to us and the importance of what happens to us. We must say that it is each notion of subject that contains or expresses the totality of the world. That is, each of you, me, expresses or contains the totality of the world. Just like Caesar, no more, no less. That gets complicated, why? A great danger: if each individual notion, if each notion of the subject expresses the totality of the world, that means that there is only a single subject, a universal subject, and the you, me, Caesar, would only be appearances of this universal subject. It would be quite possible to say: there would be a single subject that would express the world.
Why couldn't Leibniz say that? He had no choice. It would mean repudiating himself. All that he had done before that with the principle of sufficient reason would then make what sense? In my opinion, this was the first great reconciliation of the concept and the individual. Leibniz was in the process of constructing a concept of the concept such that the concept and the individual were finally becoming adequate to one another. Why?
That the concept might extend into the individual, why is this new? Never had anyone dared that. The concept, what is it? It is defined by the order of generality. There is a concept when there is a representation which is applied to several things. But identifying the concept and the individual with each other, never had that been done. Never had a voice reverberated in the domain of thought to say that the concept and the individual were the same thing.
What had always been distinguished was an order of the concept that referred to a generality and an order of the individual that referred to a singularity. Even more, it was always considered as going without saying that the individual as such was not comprehensible via the concept.
It was always understood that the proper name was not a concept. Indeed, "dog" is certainly a concept, but "Fido" is not a concept. There is certainly a dogness about all dogs, as certain logicians say in a splendid language, but there is no Fido-ness about all Fidos. Leibniz is the first to say that concepts are proper names, that is, that concepts are individual notions.
There is a concept of the individual as such. Thus you see that Leibniz cannot fall back on the proposition since every true proposition is analytical, the world is thus contained in a single and same subject which would be a universal subject. He cannot since his principle of sufficient reason implied that what was contained in a subject -- thus what was true, what was attributable to a subject -- was contained in a subject as an individual subject. Thus he cannot give himself a kind of universal mind. He has to remain fixed on the singularity, on the individual as such. And in fact, this will be one of the truly original points for Leibniz, the perpetual formula in his works: substance (no difference between substance and subject for him) is individual.
It's the substance Caesar, it's the substance you, the substance me, etc. ... The urgent question in my sub-category d) since he forbids himself from invoking a universal mind in which the world will be included ... other philosophers will invoke a universal mind. There is even a very short text by Leibniz entitled "Considerations on universal mind," in which he goes on to show in what way there is indeed a universal mind, God, but that does not prevent substance from being individual. Thus irreducibility of individual substances.
Since each substance expresses the world, or rather each substantial notion, each notion of a subject, since each one expresses the world, you express the world, for all times. We notice that, in fact, he has a lifetime of work because he faces the objection that's made to him immediately: but then, what about freedom? If everything that happens to Caesar is encompassed in the individual notion of Caesar, if the entire world is encompassed in the universal notion of Caesar, then Caesar crossing the Rubicon only acts to unroll --odd word, devolvere, which comes up all the time in Leibniz's works -- or explicate (the same thing), that is to say, literally to unfold , like you unfold a rug. It's the same thing: explicate, unfold, unroll. Thus crossing the Rubicon as event only acts to unroll something that was encompassed for all times in the notion of Caesar. You see that it's quite a real problem.
Caesar crossed the Rubicon in a particular year, but even were he crossing the Rubicon in a particular year, it was encompassed for all time in his individual notion. Thus, where is this individual notion? It is eternal. There is an eternal truth of dated events. But then, how about freedom? Everyone jumps on him. Freedom is very dangerous under a Christian regime. So Leibniz will write a little work, "On freedom," in which he explains what freedom is. Freedom is going to be a pretty funny thing for him.
But leave that aside for the moment.
What distinguishes one subject from another? That, we can't leave aside for the moment, unless our flow were to be cut off. What is going to distinguish you from Caesar since just like him, you express the totality of the world, present, past, and future? It's odd, this concept of Expression. That's where he proposes a very rich notion.

f) What distinguishes an individual substance from another is not very difficult. In some way, it has to be irreducible.
Each one, each subject, for each individual notion, each notion of subject has to encompass this totality of the world, express this total world, but from a certain point of view. And there begins a perspectivist philosophy. And it's not inconsiderable. You will tell me: what is more banal than the expression "a point of view"? If philosophy means creating concepts, what does create concepts mean? Generally speaking, these are banal formulae. Great philosophers each have banal formulae that they wink at. A wink from a philosopher is, at the outside limit, taking a banal formula and having a ball , you have no idea what I'm going to put inside it. To create a theory of point of view, what does that imply? Could that be done at any time at all? Is it by chance that it's Leibniz who created the first great theory at a particular moment? At the moment in which the same Leibniz created a particularly fruitful chapter in geometry, called projective geometry. Is it by chance that it's out of an era in which are elaborated, in architecture as in painting, all sorts of techniques of perspective? We retain simply these two domains that symbolize that: architecture-painting and perspective in painting on one hand, and on the other hand, projective geometry. Understand what Leibniz wants to develop from them. He is going to say that each individual notion expresses the totality of the world, yes, but from a certain point of view.
What does that mean? Of so little import is it, banally, pre-philosophically, that it is henceforth as equally impossible for him to stop. That commits him to showing that what constitutes the individual notion as individual is point of view. And that therefore point of view is deeper that whosoever places himself there.
At the basis of each individual notion, it will indeed be necessary for there to be a point of view that defines the individual notion. If you prefer, the subject is second in relation to the point of view. And after all, to say that is not a piece of cake, it's not inconsiderable. He established a philosophy that will find its name in the works of another philosopher who stretches out his hand to Leibniz across the centuries, to wit Nietzsche. Nietzsche will say: my philosophy is a perspectivism. You understand that it becomes idiotic or banal to whine about whether perspectivism consists in saying that everything is relative to the subject; or simply that everything is relative. Everyone says it, it belongs to propositions that hurt no one since it is meaningless. So long as I take the formula as signifying everything depends on the subject, that means nothing, I caused, as one says ...

. . . What makes me = me is a point of view on the world. Leibniz cannot stop. He has to go all the way to a theory of point of view such that the subject is constituted by the point of view and not the point of view constituted by the subject. Fully into the nineteenth century, when Henry James renews the techniques of the novel through a perspectivism, through a mobilization of points of view, there too in James's works, it's not points of view that are explained by the subjects, it's the opposite, subjects that are explained through points of view. An analysis of points of view as sufficient reason of subjects, that's the sufficient reason of the subject. The individual notion is the point of view under which the individual expresses the world. It's beautiful and it's even poetic. James has sufficient techniques in order for there to be no subject; what becomes one subject or another is the one who is determined to be in a particular point of view. It's the point of view that explains the subject and not the opposite. For Leibniz, every individual substance is like an entire world and like a mirror of God or of the whole universe that each substance expresses in its own way: kind of like an entire city is diversely represented depending on the different situations of the one who looks at it. Thus, the universe is seemingly multiplied as many times as there are substances, and the glory of God is redoubled equally by as many completely different representations of his/her/its . He speaks like a cardinal. One can even say that every substance bears in some ways the characteristic of infinite wisdom and of all of God's power, and limits as much as it is able to.
In all this, I maintain that the new concept of point of view is deeper than the concept of individual and individual substance. It is point of view which will define essence. Individual essence. One must believe that to each individual notion corresponds a point of view. But that gets complicated because this point of view would be in effect from birth to death for an individual. What would define us is a certain point of view on the world. I said that Nietzsche will rediscover this idea. He didn't like him , but that's what he took from him. The theory of point of view is an idea from the Renaissance. The Cardinal de Cuse , a very great Renaissance philosopher, referred to portraiture changing according to point of view. From the era of Italian fascism, one notices a very odd portrait almost everywhere: face on, it represented Mussolini, from the right side it represented his son-in-law, and if one stood to the left, it represented the king.
The analysis of points of view in mathematics -- and it's again Leibniz who caused this chapter of mathematics to make considerable progress under the name of analysis situs --, and it is evident that it is connected to projective geometry. There is a kind of essentiality, of objectity of the subject, and the objectity is the point of view. Concretely were everyone to express the world in his own point of view, what does that mean? Leibniz did not retreat from the strangest concepts. I can no longer say "from his own point of view." If I said "from his own point of view," I would make the point of view depend on a preceding subject , but it's the opposite. But what determines this point of view? Leibniz : understand, each of us expresses the totality of the world, only he expresses it in an obscure and confused way. Obscurely and confused means what in Leibniz's vocabulary? That means that the totality of the world is really in the individual, but in the form of minute perception. Minute perceptions. Is it by chance that Leibniz is one of the inventors of differential calculus? These are infinitely tiny perceptions, in other words, unconscious perceptions. I express everyone, but obscurely, confusedly, like a clamor.
Later we will see why this is linked to differential calculus, but notice that the minute perceptions of the unconscious are like differentials of consciousness, it's minute perceptions without consciousness. For conscious perceptions, Leibniz uses another word: apperception. Apperception, to perceive , is conscious perception, and minute perception is the differential of consciousness which is not given in consciousness. All individuals express the totality of the world obscurely and confusedly. So what distinguishes a point of view from another point of view? On the other hand, there is a small portion of the world that I express clearly and distinctly, and each subject, each individual has his/her own portion, but in what sense? In this very precise sense that this portion of the world that I express clearly and distinctly, all other subjects express it as well, but confusedly and obscurely.
What defines my point of view is like a kind of projector that, in the buzz of the obscure and confused world, keeps a limited zone of clear and distinct expression. However stupid you may be, however insignificant we all may be, we have our own little thing, even the pure vermin has its little world: it does not express much clearly and distinctly, but it has its little portion. Beckett's characters are individuals: everything is confused, an uproar , they understand nothing, they are in tatters ; there is the great uproar of the world. However pathetic they may be in their garbage can, they have their very own little zone. What the great Molloy calls "my properties." He no longer moves, he has his little hook and, in a strip of one meter, with his hook, he grabs things, his properties. It's a clear and distinct zone that he expresses. We are all the same. But our zone is more or less sizable, and even then it's not certain, but it is never the same. What is it that determines the point of view? It's the proportion of the region of the world expressed clearly and distinctly by an individual in relation to the totality of the world expressed obscurely and confusedly. That's what point of view is.
Leibniz has a metaphor that he likes: you are near the sea and you listen to waves. You listen to the sea and you hear the sound of a wave. I hear the sound of a wave, that is, I have an apperception: I distinguish a wave. And Leibniz says: you would not hear the wave if you did not have a minute unconscious perception of the sound of each drop of water that slides over and through another, and that makes up the object of minute perceptions. There is the roaring of all the drops of water, and you have your little zone of clarity, you clearly and distinctly grasp one partial result from this infinity of drops, from this infinity of roaring, and from it, you make your own little world, your own property.
Each individual notion has its point of view, that is from this point of view, it extracts from the aggregate of the world that it expresses a determined portion of clear and distinct expression. Given two individuals, you have two cases: either their zones do not communicate in the least, and create no symbols with one another -- there aren't merely direct communications, one can conceive of there being analogies -- and in that moment, they have nothing to say to each other; or it's like two circles that overlap: there is a little common zone, there we can do something together. Leibniz thus can say quite forcefully that no two individual substances have the same point of view or exactly the same clear and distinct zone of expression. And finally, Leibniz's stroke of genius: what will define the clear and distinct zone of expression that I have? I express the totality of the world, but I only express clearly and distinctly a reduced portion of it, a finite portion. What I express clearly and distinctly, Leibniz tells us, is what relates to my body. We will see what this body means, but what I express clearly and distinctly is that which affects my body.
Thus I obviously do not express clearly and distinctly the passage of the Rubicon, since that concerned Caesar's body. There is something that concerns my body and that only I express clearly and distinctly, in relation to this buzz that covers the entire universe.
f) In this story of the city, there is a problem. OK, there are different points of view. These points of view preexist the subject who is placed there, good. In this event, the secret of point of view is mathematical, geometrical, and not psychological. It's at the least psycho-geometrical. Leibniz is a man of notions, not a man of psychology. But everything urges me to say that the city exists outside points of view. But in my story of expressed world, in the way we started off, the world has no existence outside the point of view that expresses it; the world does not exist in itself. The world is uniquely the common expressed of all individual substances, but the expressed does not exist outside that which expresses it. The world does not exist in itself, the world is uniquely the expressed. The entire world is contained in each individual notion, but it exists only in this inclusion. It has no existence outside. It's in this sense that Leibniz will be, and not incorrectly, on the side of the idealists: there is no world in itself, the world exists only in the individual substances that express it. It's the common expressed of all individual substances. It's the expressed of all individual substances, but the expressed does not exist outside the substances that express it. It's a real problem!
What distinguishes these substances is that they all express the same world, but they don't express the same clear and distinct portion. It's like chess. The world does not exist. It's the complication of the concept of expression. Which is going to provide this final difficulty. Still it is necessary that all individual notions express the same world. So it's curious -- it's curious because by virtue of the principle of identity that permits us to determine what is contradictory, that is, what is impossible, it's A is not A. It's contradictory: example: the squared circle. A squared circle is a circle that is not a circle. So starting from the principle of identity, I can have a criterion of contradiction. According to Leibniz, I can demonstrate that 2 + 2 cannot make 5, I can demonstrate that a circle cannot be squared. Whereas, on the level of sufficient reason, it's much more complicated, why? Because Adam the non-sinner, Caesar not crossing the Rubicon, is not like the squared circle. Adam the non-sinner is not contradictory. Understand how he's going to try to save freedom, once he has placed himself in a bad situation for saving it. This is not at all impossible: Caesar could have not crossed the Rubicon, whereas a circle cannot be squared; here, there is no freedom.
So, again he's stuck, again Leibniz has to find another concept and, of all his crazy concepts, this will undoubtedly be the craziest. Adam could have not sinned, so in other words, the truths governed by the principle of sufficient reason are not the same type as the truths governed by the principle of identity, why? Because the truths governed by the principle of identity are such that their contradictory status is impossible, whereas the truths governed by the principle of sufficient reason have a contradictory status that is possible: Adam the non-sinner is possible.
It's even all that distinguishes, according to Leibniz, the truths called truths of essence and those called truths of existence. The truths of existence are such that their contradictory status is possible. How is Leibniz going to get out of this final difficulty? How is he going to be able to maintain at once that all that Adam did is contained forever in his individual notion, and nonetheless Adam the non-sinner was possible. He seems stuck, it's delicious because from this perspective, philosophers are somewhat like cats, it's when they are stuck that they get loose, or they're like fish, the concept becoming fish. He is going to tell us the following: that Adam the non-sinner is perfectly possible, like Caesar not having crossed the Rubicon, all that is possible, but it did not happen because, if it is possible in itself, it's incompossible. That's when he created the very strange logical concept of incompossibility. On the level of existences, it is not enough for a thing to be possible in order to exist, one must also know with what it is compossible. So Adam the non-sinner, though possible in himself, is incompossible with the world that exists. Adam could have not sinned, yes, but provided that there were another world. You see that the inclusion of the world in the individual notion, and the fact that something else is possible, he suddenly reconciles the notion of compossibility, Adam the non-sinner belongs to another world. Adam the non-sinner could have been possible, but this world was not chosen. It is incompossible with the existing world. It is only compossible with other possible worlds that have not passed into existence.
Why is it that world which passed into existence? Leibniz explains what is, for him, the creation of worlds by God, and we see well how this is a theory of games: God, in his understanding , conceives an infinity of possible worlds, only these possible worlds are not compossible with each other, and necessarily so since it's God who chooses the best. He chooses the best of possible worlds. And it happens that the best of possible worlds implies Adam as sinner. Why? That's going to be awful . What is interesting logically is the creation of a proper concept of compossiblity to designate a more limited logical sphere than that of logical possibility. In order to exist, it is not enough for something to be possible, this thing must also be compossible with others that constitute the real world. In a famous formula from the Monadology, Leibniz says that individual notions have neither doors nor windows. That arrives to correct the metaphor of the city. No doors or windows means that there is no opening. Why? Because there is no exterior. The world that individual notions express is interior, it is included in individual notions. Individual notions have no doors or windows, everything is included in each one, and yet there is a world common to all individual notions: for what each individual notion includes, to wit the totality of the world, the notion includes it necessarily as a form in which what it expresses is compossible with what the others express. It's a marvel. It's a world in which there is no direct communication between subjects. Between Caesar and you, between you and me, there is no direct communication, and as we'd say today, each individual notion is programmed in such a way that what it expresses forms a common world with what the other expresses. It's one of the last concepts from Leibniz: pre-established harmony. Pre-established, it's absolutely a programmed harmony. It's the idea of the spiritual automaton, and at the same time, it's the grand age of automatons at this end of the seventeenth century.
Each individual notion is like a spiritual automaton, that is what it expresses is interior to it, it's without doors or windows; it is programmed in such a way that what it expresses is in compossibility with what the other expresses.
What I have done today was solely a description of the world of Leibniz, and even so, only one part of this world. Thus, the following notions have been successively laid out: sufficient reason, inherence and inclusion, expression or point of view, incompossibility.