DELEUZE /// The two Architectures of the Infinite Possible Worlds: Leibniz's Pyramid & Borges' Garden of Forking Paths


In his class at the Universite de Vincennes in 1983-84, Gilles Deleuze approaches cinema by what he calls la puissance du faux (power of the false) which intermingles (and not confuses) imaginary and reality to create the false and by extension, fiction. The notion of truth is therefore fundamental for his class and in his December 6th 1983 session, he exposes two visions of the world  of truths of existence (in opposition to truths of essence) affiliated with each other. The first one comes from 17th century philosopher Gottfried Leibniz who imagined an infinite pyramid composed by the infinite possible worlds in which, each variations of circumstances brings each world to be what it is (see excerpt 1 after this text). To end up with a truth of existence, Leibniz has to bring in the notion of moral -and even of theology- for that he states that at the top of the pyramid, stands the world that God has chosen as it is unmistakably the best one.
The second vision, born from Leibniz’s narrative, occurs two centuries and half later, in 1941 with the short story El Jardin de Senderos que se Bifurcan (The Garden of Forking Path) written by Jorge Luis Borges. In this story, Borges introduces a book in which all the possible world are contained, simultaneous and equally real (see excerpt 2).

To this two visions brought-up by Deleuze, I would like to add the one proposed by Philip K. Dick in 1977 for the Metz’s (France) Science-Fiction Festival in a lecture entitled If you find this World bad, you should see some of the others. In fact, this vision has less to do with architecture and more with fashion design (!) as he suggests that each world is a coat owned by God who decides “in the morning” which one to wear. One obvious novel in which he developed this theory is The Man in the High Castle (1962) in which P.K. Dick introduces a parallel world (one might say an uchronia) that saw the Axis Powers (Germany, Japan and Italy) won the second world war three decades before the plot.

The following excerpts are not extracted from Deleuze’s class about the Power of the False (1983) as I could not find an English translation, but from the 1980 class about Leibniz which gathered a shorter yet very similar comparison:

Leibniz (excerpt from Webdeleuze):

I just exposed already a first difference between truths of essence and truths of existence. In truths of essence, the analysis is finite, in truths of existence, the analysis is infinite. That is not the only one, for there is a second difference: according to Leibniz, a truth of essence is such that its contradictory is impossible, that is, it is impossible for 2 and 2 not to make 4. Why? For the simple reason that I can prove the identity of 4 and of 2+2 through a series of finite procedures. Thus 2+2=5 can be proven to be contradictory and impossible. Adam non sinner, Adam who might not have sinned, I therefore seize the contradictory of sinner. It’s possible. The proof is that, following the great criterion of classical logic — and from this perspective Leibniz remains within classical logic — I can think nothing when I say 2+2=5, I cannot think the impossible, no more than I think whatever it might be according to this logic when I say squared circle. But I can very well think of an Adam who might not have sinned.Truths of existence are called contingent truths.

Caesar could have not crossed the Rubicon. Leibniz’s answer is admirable: certainly, Adam could have not sinned, Caesar could have not crossed the Rubicon. Only here it is: this was not compossible with the existing world. An Adam non sinner enveloped another world. This world was possible in itself, a world in which the first man might not have sinned is a logically possible world, only it is not compossible with our world. That is, God chose a world such that Adam sinned. Adam non sinner implied another world, this world was possible, but it was not compossible with ours.

Why did God choose this world? Leibniz goes on to explain it. Understand that at this level, the notion of compossibility becomes very strange: what is going to make me say that two things are compossible and that two other things are incompossible? Adam non sinner belongs to another world than ours, but suddenly Caesar might not have crossed the Rubicon either, that would have been another possible world. What is this very unusual relation of compossibility? Understand that perhaps this is the same question as what is infinite analysis, but it does not have the same outline. So we can draw a dream out of it, we can have this dream on several levels. You dream, and a kind of wizard is there who makes you enter a palace; this palace… it’s the dream of Apollodorus told by Leibniz. Apollodorus is going to see a goddess, and this goddess leads him into the palace, and this palace is composed of several palaces. Leibniz loved that, boxes containing boxes. He explained, in a text that we will examine, he explained that in the water, there are many fish and that in the fish, there is water, and in the water of these fish, there are fish of fish. It’s infinite analysis. The image of the labyrinth hounds him. He never stops talking about the labyrinth of continuity. This palace is in the form of a pyramid. Then, I look closer and, in the highest section of my pyramid, closest to the point, I see a character who is doing something. Right underneath, I see the same character who is doing something else in another location. Again underneath the same character is there in another situation, as if all sorts of theatrical productions were playing simultaneously, completely different, in each of the palaces, with characters that have common segments. It’s a huge book by Leibniz called Theodicy , specifically divine justice.

You understand, what he means is that at each level is a possible world. God chose to bring into existence the extreme world closest to the point of the pyramid. How was he guided in making that choice? We shall see, we must not hurry since this will be a tough problem, what the criteria are for God’s choice. But once we’ve said that he chose a particular world, this world implicated Adam sinner; in another world, obviously all that is simultaneous, these are variants, one can conceive of something else, and each time, it’s a world. Each of them is possible. They are incompossible with one another, only one can pass into existence. And all of them attempt with all their strength to pass into existence. The vision that Leibniz proposes of the creation of the world by God becomes very stimulating. There are all these worlds that are in God’s understanding, and each of which on its own presses forward pretending to pass from the possible into the existent. They have a weight of reality, as a function of their essences. As a function of the essences they contain, they tend to pass into existence. And this is not possible for they are not compossible with each other: existence is like a dam. A single combination will pass through. Which one? You already sense Leibniz’s splendid response: it will be the best one!

And not the best one by virtue of a moral theory, but by virtue of a theory of games. And it’s not by chance that Leibniz is one of the founders of statistics and of the calculus of games. And all that will get more complicated…

Borges (excerpt from Webdeleuze):

In Ficciones, there is a short story, “The Garden of Forking Paths.” As I summarize the story, keep in mind the famous dream of the Theodicy.
“The Garden of Forking Paths,” what is it? It’s the infinite book, the world of compossibilities. The idea of the Chinese philosopher being involved with the labyrinth is an idea of Leibniz’s contemporaries, appearing in mid-17th century. There is a famous text by Malebranche that is a discussion with the Chinese philosopher, with some very odd things in it. Leibniz is fascinated by the Orient, and he often cites Confucius. Borges made a kind of copy that conformed to Leibniz’s thought with an essential difference: for Leibniz, all the different worlds that might encompass an Adam sinning in a particular way, an Adam sinning in some other way, or an Adam not sinning at all, he excludes all this infinity of worlds from each other, they are incompossible with each other, such that he conserves a very classical principle of disjunction: it’s either this world or some other one. Whereas Borges places all these incompossible series in the same world, allowing a multiplication of effects. Leibniz would never have allowed incompossibles to belong to a single world. Why? I only state our two difficulties: the first is, what is an infinite analysis? and second, what is this relationship of incompossibility? The labyrinth of infinite analysis and the labyrinth of compossibility.