English translation of the French transcript, made with AI and not yet proofread — click a paragraph to jump to it. Show the French original
Euclid, geometry, and the universal against opinion 3:00 perfectly defined terms, but as a result we're no longer in everyday language with its metaphorical richness and the purposes that it more or less consciously conveys. What am I saying here, following directly from the answer to your question? I'm saying that there's a split in culture starting with Euclid, right up to today. One can be rigorous, objective, whatever the skeptics may say, those who believe there are really only opinions—here we have something universal.
3:31 If Peter is Paul's brother, then Paul is Peter's brother. There you go, that's logical. If A equals B, B equals A. What am I telling you here? It holds for everyone, it's universal. That's where we are, in geometry. So you're asking me how to do that in philosophy, when philosophy adds... I'll answer right away: yes, one must be geometrical in philosophy, but above all not settle for that. It's necessary but not sufficient. I have another mathematical reference, precisely. It's necessary in order to break with opinion.
4:02 With the proliferation of singularities of opinion in which today's capitalism tries to enclose us. Let's not forget that it's not only man who was attacked under Deleuze and Foucault, etc.—it's the universal. It's one of the most discredited notions. You say you're for the universal, and you'll be told you're ethnocentric, that the universal is a Western notion, etc. Yet when you talk with Africans, they want their children to be raised in good health, to be well educated. And they too, the Africans, if you tell them that if Kwaku is Akissi's son, then Akissi is Kwaku's mother—that's universal, whether we like it or not.
4:33 So, to defend the universal, in this period when this notion is perhaps the most vilified, when each of us is locked into our own culture, our own religion, our own ethnicity, our own identity—I come back to the rigid one-sidedness of earlier, which leads to war—this detour was necessary. And that's why Plato puts it there—and here I really need to see whether it was Plato—to show that it's necessary but not sufficient, that let no one enter here who is not a geometer.
Plato: geometry as propaedeutic, the table and the circle 5:04 But what does that mean, at the entrance? It means we're not going to do mathematics inside. It means it's an excellent preparatory training to have practiced, before doing philosophy, contemplating intelligible realities first. For Plato, that's no small thing. Because in everyday life, you see a table, you never see the idea of table. Try that with students. What is a table? Come on, you think philosophy means talking about God, the soul, eternity, we're going to do interesting things, interesting people. No, no, no, I'm much more prosaic than that—what is a table?
5:35 So they'll say, a table is a thing that's square, that has four legs, that's made of wood. I've never seen a round table. Oh right, damn, a round table, yes. With a single leg, a bistro table, yes. A gold table at a minister's house, why not? Glass, paper, a multiplication table. And in the end, damn, it's not the matter, it's not the form, there's no more table. Philosophers are a pain. You understand why Socrates had to be put to death, because if it starts like this with the table, imagine what it'll be like with the notions that concern us. So then, what exactly is the universal, starting from this one table, which by itself does not embody, does it, the immense potential of the concept of table.
6:11 So one had to go through geometry. And not confuse circles with round shapes, for example. You make ripples in water, but it took mathematics for the notion of circle to appear. Which exists nowhere empirically. Nowhere will you see a perfect circle. When you draw with a compass, when you magnify under a microscope, not to mention an electron microscope, however perfect a laser compass you might have, it will always be infinitely too large compared to the geometric definition of the circle. A point, a line—these are things that have neither thickness nor dimension, and yet. Afterward, it's extraordinary, this freedom of man who decrees.
6:42 I call it circle, the way God calls. I bring forth a reality that did not exist before me. I call. The master of logos, I call. So one had to go through that. Now, if we stay there, we get a discourse that allows us, as Descartes would say, to render man master and possessor of nature. Since by knowing the laws governing nature through mathematics, we can act upon them. It's possible, to our benefit. When I take notes there, I feel it as universal as possible.
From the laws of nature to the human field of determinability 7:12 But I am at a loss when it comes to human beings. That's why the human sciences find themselves in this state of misery today, in this chaos. There's a body of knowledge in the natural sciences. The human sciences should always deserve their scare quotes—are they sciences? Indeed, the discussion now is about the human sciences, we have social sciences to try to evade the difficulty. But it always comes back to the same thing. Well, precisely, because either you approach it in a positivist mode, believing that geometry—mathematical geometry, I'm generalizing—will suffice to explain human complexity.
7:49 And we fail completely. Or else we abstract from it into irrationalist doctrines, Nietzsche-style, regarding the moral and human world. To send both back to back, one must take into account the objective, external universality brought by logico-mathematics, which inspired the philosopher Plato, who comes right after Euclid. It's the bio-concept, going from examples to essence—let's move quickly. But in parallel, one must model another universal besides the geometric, mathematical universal, precisely, for relations between human beings.
8:29 What am I saying here? I'm saying that when Marx says we are determined by economic factors, etc.—you see, Marx's account there has nothing to do with freedom, on the contrary, it's the implacability of the terms. Ah no, no, no, there's a misunderstanding, and it goes back to Rousseau, that's why I mention him. What does Marx mean? We are influenced by the infrastructure, to go very quickly. But that is not at all the same kind of determination as the one that obliges the Moon to revolve around the Earth. Because as I was saying earlier, the Moon has no choice.
9:00 There is no reversibility of the law. The Moon cannot say to itself, I'm a bit bored going around the Earth, I'll go around Venus instead, that'll be a nice change. No, it has no choice. The Earth being greater in mass, it's the stronger one, we come back to force prevailing. There is no reversibility. Just as I cannot live without eating, instead of saying I must eat in order to live, as if I had a choice. That too is deceiving myself. I cannot—it's a matter of can, not must—live without eating. On the other hand, I can run a red light. I can transgress the law of monogamy, have a mistress, or covet another man's wife.
9:32 I must not, but I can. The difference in the human domain is that the opposite is possible, which is not the case in the order of nature. So when Marx brings economic determinations to light, he presents us with a battery, or rather a field of determinability, to be precise, which is much more advantageous than the natural determinism against which I can do nothing. For, and here I come back to Rousseau, as Rousseau says so strikingly in Emile, everything that men have made, they can undo.
10:02 There is no ineffaceable character, to continue with Rousseau, except those imprinted by nature, and nature makes no one rich, no prince, no great lord. So there you have it—geometry is necessary to raise us to the universal, but quite insufficient to reach the concrete universal, as Hegel would say, the one that governs peoples, where one must appeal to the notion of freedom, as you'll come to know. We appeal to the contract as the founder of freedom, which has nothing to do with geometry, the realm of law. There you go.
