Mathematiques et individuation (contd.)

0:00 because we have the occurrence, and we have to be modified by the concept. When it comes to an occurrence of barriers, it's there that we pose the question that we have. I said that Frege has not been proposed to the interpretation of the book. The substance of the position of Frege is implicitly the same, which is not a rhetorical text, which is not contradictory, which is a symbolic interpretation of the book. This is an interpretation of the position of Frege, which is therefore the constant of a certain difference between the language and the language of nature. The language of the symbol is not the reflection of the language of nature. De l'ordre de cette époque, se reconnut comme mathématicien celui-là seulement qui a prévu et jusqu'à l'ouvert, vous allez comprendre pourquoi j'ai dit jusqu'à l'ouvert, accepta de se reconnaître dans ce faisceau de conventions éminemment convergentes inscrites dans les cultures symboliques. Éminemment convergentes, c'est parce qu'il est possible de refuser de s'inscrire dans la convention de Dieu, tout simplement qu'il ne peut pas faire le calcul. So the calculus doesn't have to be limited to what he was or not. He can refuse. He can refuse to refuse a figure of geometry. Right, you can see the figure of geometry. And I repeat, I have one of the experiments that have shown that it was an obstacle to some of the students who say that there is a figure, there is a figure. I have to say, I have to say, I have to say, I have to say, you know, you know, you know, you know, you know, you know, you know, and the physicality of the example, that is not the same thing. It's a point of view constructivist which is perfectly acceptable to pass the point of view constructivism to achieve an idealistic and issue with idealism, demand at least an analysis, and then it's all what I want to say. So, it's a comment on the contingent. Faire de la géométrie pure avait also demandé l'acceptation d'une convention idéalisante contradictoire, in the language of nature. And it's the consideration of the geometry which gave the assumption of contradiction. That is, that there is already a geometry arbitraire and fixer. That there is also in the algebra algebra of the arbitraire and fixer which is also a convention rhetorically familiar with this, where the acceptation should be engaged by the literature symbolically. That the two garants should be extended to the natural language is a condition which appears as necessary, and that the history has proven, which I just want to say,

2:30 that it has been, in the two cases, chosen enough. I will conclude now, with an ensemble, that these two episodes describe the moments, the 16th and 19th centuries, fondamentaux, the passages fondamentaux in the history of mathematics, that we could call, for each choice, the exclusion of the subject, the subject mondain, the avalement of the subject abstract and the subject symbolical, the emancipation of the mathematics, or in other words, the avalement of the formal and the formal form. In fact, the subject mathematician real, concrets, we are, in certain circumstances, in certain circumstances, confronts against the problem of choice which is the symbolization of the determinants are, in fact, incapable of discernment between certain objects, simply because they are indiscernible in the sense of Leibniz. Aucun predicament ne les distingue. Pretend to be able to distinguish on such a tendency to determine an ambiguity native indissoluble or a non-sens in the case of the choice. Now, there are two episodes that show that for a good advance of the mathematics, that the mathematics doesn't remain where they are, it is imposed the necessity to surpass a certain conception of the subject. This was first the assumption of the contradiction inaudible from the 16th century, then, at the beginning of the 20th century, the moment where the plurality chose, in a way, chose, in a way, in a way, and at the end of the choice, it was, at this point, a paradoxical episode, among others, as you know, this period was rich in paradoxes of various sorts. But, I remember that this paradoxical episode, and philosophy, is crucial, because it is centered on the question of the individual, the annulation of the object of the show. What happened then? The solution, well known, which was imposed against two others, constructivism and logicism, was to postulate a subject mathématician ideal, abstract, abstract and creative, susceptible to assume some contradictions patentes while they were gagging, beyond the natural language, by a picture symbolical. This bifurcation, soutenu en un premier lieu par Hilbert, pris le nom de méthode axiomatique et de formalisme. Et son principe épistémologique était ad hoc.

5:00 Le retour à l'interprétation mondaine étant impossible sur certains points cruciaux, on se dispensa tout simplement de l'interprétation. Dans un tel nouveau système où les contraintes provenaient du seul registre logico-formel, l'existence des objets mathématiques ne tenait non plus of the world, the proprieties of the non-contradiction, independence, saturation of the scriptures axiomaltic, which have a vocation to be constituted in a system formative. These books are absolutely absolute. The sign is not the interpretation, the sign is the essence of the thing, do not search any interpretation. And the acceptation, which have a vocation to be constituted in a system formative. And the acceptance by the subject of the world, the existence of a subject symbolical, which is in order to support the conventions, the arbitraire is fixed, or the existence of a function choice in the domain of the same thing, is today the pire of all the recognition of a mathematician as a member of the community. The mathematician is the one who consent, who adheres, who consent. So I said that the fear of touching the recognition of a mathematician as a member of the community, in the same time as a racine of the creation of a mathematical modern, is also the source of a formidable development of mathematics today. The existence, the development of a subject symbolically which allowed to dispense the subject of the world of contradictions and nonsense in which they could be confronted with us, by balance in the sense inverse, has allowed an extraordinary development creator of mathematics. For those who know what's the meaning of mathematics today, there is no production of mathematics today, today, in one year, than in 30 years, than in 20 years. The development is properly exponential, with an exponential, with an exponential, and the question of the question of the mathematician, the question of the pleasure that they experience, is in general in two words. There is one that comes in all the time, which is the freedom. the freedom of being released to a sense of the fear that I wanted to analyze and circumcise

7:30 the conditions that are liées to the existence of a subject in the world which would be contraint to affront these contradictions. So I would say that this point is also to say that that is a point where they are largely separated mathematicians and non-mathematicians which is not enough for this concept. And the distinguo, I'm going to go on that. The distinguo grammatical of Adama, which I talked about earlier, was perfect for the separation between the Je or even the O provenant, which you don't know, the Je or even the O provenant of one of the subjects modern, and the form passive, neutre, which is the subject of the subject. as simple as a technique for a presentation very rich and there is perhaps another time for a little bit of a question to have a little bit of a time yes, excuse me I have a question I have a question when we give this example we have an example of a an individuation different from the Greek, an ukrainian. If we take an example of the book, the 7th, 8th, 9th, is this really different? Because apparently the Greek is something like that. When AB, which is not just a line, but a number, and we can also say that these numbers are inputted in the limits of the specific data, which is a number of pairs, for example, but not just a number of pairs, etc. Is it still quite close to the time of the year when we have a sign? And then it's not something that is fixed, but it's more like a variable. Well, it's true, it's not the text, but it's true when it comes to the geometry,

10:00 because it's what I said, the geometry of the book of the Antiquity and the Renaissance uses the figures in which, in the transparent way, there is a mark A, there is a mark B, C. Mine was represented by A and B, C. And I tried to explain earlier that for a lecteur naive, it's A and it's B and it's C. And for a lecteur geomètre, it's A and everything that could be at its point. The arbitraire is fixed. I repeat, one thing can't be fixed, arbitraire is fixed. It can't be fixed, it can't be fixed, it can't be fixed. On a ici l'incarnation d'une contradiction. Alors, il faut demander, on va revenir au collecteur de la géométrie à l'ancienne, où il disait encore, ce que tu vois au tableau, le triangle que tu as là, c'est ce triangle-là, mais en fait, le raisonnement que tu vas faire est valable pour tous les films. Ce qu'il faut comprendre, c'est qu'il y a des gens qui veulent dire non. non non non une chose et une chose et c'est l'ensemble ses propriétés et c'est pas et c'est quoi alors demandez alors carré et je signale que quand j'ai fait cet éprouvé au séminaire j'ai des professeurs qui me dit qu'ils avaient une petite classe qui dit qu'il avait des élèves qui avaient refusé c'est un simple c'est premier niveau de refus mais ce refus est fondé se dire si dans la vie when I started to say that one thing is the same and it is the same from the other side, I would explain that, if I would accept it, he must adhere to a convention. And that if he... We are not so much in the discussion of the practice, with a student, but if he does not adhere to a convention, if he does not adhere to a convention, he does not adhere to it. He does not adhere to it. is the situation. But if you will, the arbitraire is fixed, and we have... There I expose the things clearly in epistemology, but of course it's not considered as cru. We say that this triangle is a triangle idéal that represents the whole of the triangles. Well, I don't want to say that, but if I do not, it's not.

12:30 So, I have a question, could you really talk about this model, Proclus, it's called Ectesis. Pardon? Proclus, in this commentaire, it uses the term Ectesis, it's something in French that's something that's something that's put in it. But, is it you can say that, let's say, in modern mathematics, modern ... or I don't know, I don't know, this model of the art that we use will change with a new culture symbolical, or it still remains the same model? I don't understand your question, because what I was trying to tell you, is that what was accepted in the book, because at the end, there was a tradition that was also accepted, that there were these figures, there were these ideas, that there were these ideas. The simple presence of the figures that we've written in a text in a context of the ideas that the editors, which the editors were supposed to be subscribed. Well, when it comes to the calculation, when it comes to the calculation, it's there that, in the 13th century, there was no convention in September that would allow it, because there, it would have been a bit of time. In the calculation, the grand air would not be at the time I, and the same. There are reasons that I can't explain here, but I'm going to ask you why I have to do this. It's a story a little bit complicated, it's a question of homogeneity, it's a question of homogeneity, it's a question of homogeneity, so he wanted to impose the homogeneity of the formule, and so the démarche of Viet has consisted in doing so, that in the calculation of this, the letter represents something which is arbitrary. Or, this is an element that we have to do with it. It is one, and it is eventually the other. So, we have to ask, at this moment, to the lecteur calculateur to adhere, of the same way, to a proportion, to a certain number of which we can't adhere. In order to see, you can continue the discussion. Thank you. Thank you.

15:00 Thank you.