Ontological status of math. objects in Descartes / Le statut d'imagination dans les ecrit math. de Descartes (contd.)

0:00 In fact, a more thorough analysis of these two texts shows that on the one hand, the regulars did not give the primate to the imagination, and on the other hand, geometry did not try to eliminate it. In both cases, the purpose of the cards was to find a well-regulated use of imagination, that is, disciplined by intellectual operations, which benefited from the competition. What do the following texts show us in which the drawing is drawn on the horizon of the Cartesian square? I would like to point out that the idea of geometry is of course a lie, but in reality the classic reproach made to Descartes is in contrast to the fact that he submitted to the idea of geometry as an imagination. That is to say, to have considered the idea of geometry as something imaginable. This is the presumption. I assume that when we have the The map is precisely, it is exclusively used for what it does. So it's in that sense that we can understand a kind of

2:30 All the people who try to search in texts that are perhaps less important, the people who try to travel in the kitchen, write in the kitchen and not leave it in the living room, we are confronted with these texts all the time. It's stupid, it's stupid, it's not... We don't pursue mathematical texts, but they are useful elements for passages that are not mathematical, but in reference to the role of our imagination. There is a kind of separation between interpreters who really try to explain geometry, neglecting other texts, people who are attentive to the whole corpus and who, I don't know why, don't try to face these interpretations, who are sedimented and who fight against these interpreters. Maybe it's good to take them in because they are not specialists in mathematics and there is not much to learn from them. So, on the contrary, I would say that for the mathematicians, the questions on which Descartes would have to write the imagination of geometry, Descartes is not wrong, he is wrong. On the contrary, he is wrong, but it's not a good question. But if you think about it, There is a concept that appears with Descartes in the journal Écritique, that appears with Husserl, and it is the concept of projectivism. Previously, before Descartes, people met courses on the field, there was Emy, there was Jissoui, etc., but Descartes has two moments in his life when he talks about all imaginable courses. So, once we write the mechanical imagination, all the courses that I imagine being able to be written are not all imaginable courses. All the courses that I imagine being able to be written, and there it is a matter of proceeding according to the rules and principles, so it's me, but it's all the courses that are written.

5:00 The machine is a medium that allows you to imagine, not only to demonstrate, but there is in front of it a complete horizon of virtual courses, possibly imaginable. Maybe more complicated, it is the second part of algebra in which it is a strategic animation. It is when we talk about all algebraic courses. In all algebraic courses, it is mainly what we have to do in order to imagine them and to be written. These are the concepts of all the courses, the replacement of the concepts of the courses, we put our flowers in a room and then we look at what we have, and there all the courses are projected, we have to analyze them in a way that suits us. And so, unfortunately, the imagination works on the one hand in the mechanical register, which is the first register of Descartes, from which it begins, and on the other, in the register that is less familiar, with which it will be more likely to be less inspired, but nevertheless more intelligent, to all the couples obtained as an evolutionary equation. But, again, what seemed to me... well, these are imaginary truths. Our distinction between imaginary and imaginary appears to be very important, because here we find ourselves with the term of the world. In any case, for a mathematician to understand what he is conserving, the jacuzzi is a collection full of imaginations, in the sense that it is the creation of a multitude of things, of the universe, of the world, of the universe, of the universe. Geogeogeogeogeogeogeogeogeoge Imagination was simply the choice of the system to take advantage of it. Well, when we talk about imagination... Is it not in mathematics? No, not in mathematics. But we say it's often in Cartesian.

7:30 It's... I don't know. But what amazes me is that Espen Eckart did not know the geometric representation of the world before. So, the imaginary. No, not at all. Because it's the same. It's the same. It's all the same. No, no, but maybe... Maybe I... I'm more interested in the development of the idea of distinction between mechanical and symbolic imagination in terms of geometry. For me, perhaps due to a lack of solid knowledge of mathematics, I will always be in favor of the use of symbolic machines. I don't have the theoretical, mathematical tool to do it. Because we can discuss it, but in our dialogue it's not... To be precise, I would like to ask you another question, I would like to use the word. You said that Descartes criticized the ancients for the excessive use of imagination in geometry. But what does he mean by that? Because imagination, for example, in the geometry of Quine, it does not speak. It has never been the same as imagination. So what does he mean? Who does he mean? For example, do they say that mathematical objects are in the imaginary? Is that what they're saying? I have a question. I think it's related to the idea that demonstrations are done by chance. When I saw the precise notion of objects, This is not the case here, but simply, every time there is an interruption in the protocol, either in a deduction or in a definition of the procedure, the case is dehumanization, without which it is a negative concept of the imagination that intervenes here.

10:00 The difficult thing is to articulate in the second part of the thematic what is related to imagination and what is contrary to it. We must bear in mind that the use of imagination is of course exclusive to the practice of quantum physics, and that a kind of supplementation by imagination is not a substitution or an interposition, but rather a situation in which we have to find a solution. I think that in any field of object, imagination, mathematics, mathematics, physics, and science... I think that Descartes has only one faculty of Connes, so he may still be missing, or he may still have a degree of imagination, but I think that's what divides the analogy between us. There are two faculties, and I think that there is never an autonomous employment of a degree of imagination. No, it was just relative. In the question of symbolic imagination, we also have the letter of Descartes to Mersenne in 1743, where he speaks of touching grandeur, this time we will be in an unimaginable and inexplicable path of Mr Vitry de la Ville, Descartes says, I do not understand what he means by that, because in any case, all grandeur can be expressed by an equation, otherwise... He commented this passage in the new edition of 643 and he has no problem with this kind of thing because he says that any equation can be expressed by an equation and otherwise he quotes the casus ridicubilis in the two-card rule by saying that including non-imaginary equations can be expressed by an equation even if we can not extract them badly.

12:30 I do not imagine them being written. There is this relationship with Albert Girard that deserves to be studied.