Euclid & Aristotle (contd.) / discussion

0:00 The subject is not in the context of the subject. It is a subject grammatical subject, if you have to understand, but do not need to, because after you are in the text, you have to use aristocratism, because it is not the first paragraph to determine what is the subject for him, and not only between parenthesis. Yes, of course. Yes, of course. It is to say that you use it systematically. Yes, of course. Because of course, of course, it is a different paragraph, but it is a different thing. So the subject is the substance. Yes, it is. It is to say that the subject and the substance. When it goes well, it is the same thing. Yes, that's right. And the substance. When everything goes well, it's the same thing. But there it's the same thing. But it's the same thing. What you just said before, because there you go directly into the difficulties, but before the fact that there is a theory for Aristotle, and in the same time, he recognizes the generalities which excèdent his theory, and he expose and he has some words to say this difficulty. and that is why all of this is very complex and that there are 2 million comments that are in the end of the 25th century. That's what I'm saying, but I'm saying it's too late. It's too late. Yeah, it's too late. Yeah, it's too late. All of a sudden, it's not an introduction. Yeah, it's not an introduction. So in the introduction, it's also possible that you're going to talk about some of the assumptions rationales of the grid, because we discover it in the course of route, that it's the main theme. that you critique certain reconstructions who have absolutely wanted to have a theory in general in the sense of unifying behind Euclide and that you say that these reconstructions Adil triture at every time a malheureux passage of Aristotle and that when we say the general context it understands other things I have a problem in the presentation because because what makes the context, the context, particularly in the end, it's the fact that the critique of these ancient interpretations takes a lot of space and difficulties to understand. And when we arrive at the end, we propose our own interpretation.

2:30 We are already fatigued. Well, I don't know why it's a question, it's a question, it's a question, it's a question, it's a question, it's a question, it's a question, it's a question, it's a question, est-ce qu'il ne faudrait pas que tant d'interprétations à quoi passent avant la critique des interprétations reçues, ou au moins, est-ce qu'il ne devrait pas avoir, à l'intérieur de l'introduction, un résumé de ta propre interprétation, qui soit déjà un peu, c'est évidemment intelligent, disons, pour qu'on n'arrive pas à ce niveau-là, seulement on va être épuisé à la fin d'article. He started to make a resume for the review. Yes, I think that what I'm going to do is... There are two things, when we do it in isolation, and we want to retro-projeter an idea of a science completely unified for the Grecs. So we take Aristotle and Euclid, and when we superpose the two, we see that there are the same complex of articulations. So I'm absolutely conscious of that. It's to say that what we need is an introduction. Yes, yes, yes. Yes, yes, yes. I promise an introduction. I don't have the time to do it. Because in fact, what you do is to do, if you don't talk about it, if you don't talk about it, it's against the principle of the reconciliation which would be a total unification. What you want to say is that there is a problem of the generalization. I was not a priori. A posteriori, it seems to be a lot more things in the will of the commentators than in their objects. What you just said is that Aristotle has a problem of generality, a problem explicity. Yes, the chapter 5, it's called the difficulties. It's not the difficulties for the philosophers who attack the wrong arguments by their adversaries. It's the difficulties that they recognize in their own theory. Ah, no, it's the difficulties that people have the people, it's not them. I think it's a type that is reconstituted. It's not the same. No, but it starts like that. We don't want to take a look at the view that often it happens to us and that is not in fact first and universal, in the sense that I think I would show you the first and universal. I have not had an edition bilingue.

5:00 So you can't do the first one? No, because the first one is still a mess, if you want. It's to say that you can, in every genre, you can, and that would be a lot to do with Karim, you can isolate a representative who represents better than others, It's the first subject. I'm not going to go into it because I'm not going to go into it. In fact, it's interesting that behind a very rigid character, it's a bit what I've tried to make sense, when we look at the examples, we see that he's trying to understand a certain number of examples. And he has some difficulties. He has some difficulties. So, for him, in an ideal structure, ideal, there should be something like a first subject, which is something like the triangle. In fact, it's not obvious. It's not obvious that in all the genres, there is a sort of object like this that we can exhibit and that we gather all the generalities. So I think that's the example that they give, with the triangle, compared to all these species. So that's a first subject, it's great, if we have that, everything works well. Just to tell you what I found, it's on the ground It's not to be dissimulated but often the reaction that what is proven does not belong to the first one as the first one It's not at all the same thing It's not at all but not at all It's also at all It's not at all but what I thought I'm sorry Aristote, it's terrible. It's terrible. I didn't want to go into the details. Maybe more. but then this idea of a little to approach the grandeur and the number at the base of the theory for science it's very clear to this database it's an error it's what we don't have to do except that there also for no longer arranger the last phrase of the paragraph on the database it's the passage of Jean Rallot so it's interdit

7:30 at the end of the paragraph it says Sauf si les grandeurs sont des noms. Alors là, c'est pareil, des générations de commentateurs se sont étridées. Autant te dire que tout le monde ne traduit pas comme tu fais. Oui, sauf que la phrase de la grecque, pour le coup, elle dit... Excuse-moi, je suis juste là. Il y a cinq mots, quoi, elle veut dire, sauf si les grandeurs sont des noms, quoi. Mais on peut l'interpréter de deux façons, c'est... ou bien c'est une erreur. Ça, fastoche. Donc, c'est-à-dire, les gens font le passage parce qu'ils se sont... Non, pas une erreur d'Aristote, ça serait, ils stigmatiseraient. Sauf si on conçoit les grandeurs comme des noms, ça ne serait pas bien. Ou alors il y aurait une première ligne d'interprétation qui est assez dominante d'ailleurs. Ils sont bien obligés d'ailleurs, sinon il y aura des exceptions à la méthode. Mais si tu prends cette lème d'Eclipse, je ne vois pas que c'est absolument nécessaire cette idée de généralité. Parce que quand même tu peux bien sûr dire qu'il y a le concept de nombre qui intervient dedans. So it's already implicit in the definition of what is possible, etc. But it remains, I don't know, at the same time. Yes, there is no problem there-dessus. The problem, if you want, is really the proposition 5.5. It's to say that it has strictly no sense to put in the same proportion the rapport between grandeur and the rapport between noms for a very simple reason. It's not the same definition. Yes, but... Go ahead. Go ahead, go ahead. And it's really in the... Ah, yes, it's in the same... Yes, it's in the same way. When I saw that, you know, at this time, when I saw that, when I saw that, when I saw that, at the beginning of the 7th, that in fact, the way, of course vague, so they define the unit, etc. And then after they talk about the measure by the unit or the unit, etc. We have the impression that implicitly they consider the unit as a grander. So we are in a particular case of the theory which precedes the grander. And so we have an operation of concatenation of the unit which is the same as the concatenation of the grander, etc. Sauf qu'on a évidemment, comme c'est le cas où on a une grandeur unité plus spécifique, on a toutes sortes de constructions qu'on peut faire, qui n'existent pas dans le cas général des grandes, mais en tout cas on en reste globalement dans la même théorie et donc il n'est absolument pas tout étonnant que sans aucune explication, au chapitre 7, on a des propositions qui mènent les deux notions.

10:00 And in the demonstration 10, in the demonstration, when you look at the demonstration, you see that they are practically explicit. they are completely on the same pieds. But in Don Canary, there is absolutely nothing to surprise. The only thing is that we need to understand that the definition of legality of the reports, the definition of the obscenity of the obscenity, and the definition that we have of the number of numbers in the corporate world is incompatible. And it's not that they are incompatible. Because in reality, we have to do a particular case with the units, and a particular case with the vendeur. So, the units are the grandeur, which are floating. Conventionally, we have to choose the one that has to do with the unit. Well, that, I'm talking about it. I'm sure on some points, and then on some more. Because of the fact that the lecture is a little bit naive, which means to say that there is not much difficulty in the proposal of 15, which is exactly what says Vitrak, I am rather agree. It is an argument of Vitra that is quite interesting, that we have traces, we have a lot of comments, and also traces of some who are perdus, etc. Can you tell me what it is? It is the grander commensurable which is the ones who have a rapport of non and non. And we have not... It is also on the Livre V, We have no evidence that there was a big debate, etc. That's coming after, with the Arabs, with the Mediolans, etc. So, visible, it passed relatively easily. After, the reason for which it passed relatively easily, it's a bit more complicated to explain because to say that the numbers are a sort of domain of the grandeur, it doesn't work. We can't say it like that. I tried to show you that it doesn't work exactly like that. and especially if they wanted to... but there are reasons quite profondes,

12:30 for example, if... There is no product interne, it's true, so there is a notion of unity which is quite important, because the product of unity by unity should be unity in a certain way, and so... There is that on the one side, there is the fact that, inversement, for the grandeur, there are all sorts of things that are... there is the problem of taking the ennemi part of a grandeur which is something that we can't do with the non. Well, I give you examples like that, it's to say that... Yes, I'm sorry. I'm sorry, I'm sorry. There are things where it's not easy to put grandeur in place. There is a problem much deeper. If they really thought that it was a sub-domain, the question is to ask why they would have repeated a second theory of proportion for the number, such that, on a lot of points, it's what we do. It's because it existed already before. Yes, I don't know. It's there-dessus that people are engaged. and when they started to have one as a domain of the other, they started to say that if she is there, it's a sort of surveillance, etc. And I don't think that it works exactly like that. There is a lot of separation between the two domains. We can explain the reports, in other words, when it comes to a specificity, in the case of the entiers, we can't do it for the vendeurs. So it's interesting to explain things differently. Yes, I'm pretty sure. But the separation between the two domains makes problematic the fact that for him, it's always a problem when we put it to his place, that would be a domain of the other, I don't know. I don't know. I forgot the details, the precise difficulties that you point, but I was convinced by your analysis that if we take the period of the 7th, we have a problem with the demonstration. If we take the period of the 5th, we have a problem with the 5th. I found it convaincant, but I have the impression that in your conclusion, you came back to the idea that the 5th could still be what Aristotle thought. I will explain that, because it's really the end of the deal. It's what I've tried to explain. The idea is to concilier a little bit, not naïve, but perhaps perhaps more reconstructive with all these hypotheses, in saying that there is no problem with Dyssey. And then after, there is to explain why they have no problem with Dyssey.

15:00 What I've tried to show is that in the version of Aristotle, we can get out of it because there is no more these issues of domain and sub-domain, because it is interdit, it is absolutely clear, that the non cannot be a sub-domain of grandeur, but there are expressions of generality, which are expressions that we can't express in a separate, autonomic, with a subject, a subject, an object identified, and from this point of view, it is true that the theory of the V is universe, because it has a certain number of traits that are more general than those of the 7th. And how do we not have difficulty 2? The difficulty 2? Well, we have a demonstration. We have a difficulty 2. We have difficulty 2, but there is no problem. I remind you that the difficulty 2, I remind you that it is just those who did the demonstration in case by case. I don't know. But it's worse than that. It's just the proportions. If you want, I don't understand I don't know how this solution to the difficulty of 2 is still a solution. That's what I've even understood. I'm trying to explain. I'm trying to explain. I'm trying to explain that in the definition 5.5, because it works for the granders commensurables which are comparable to the granders commensurables and that the granders commensurables are comparable to number to number, she has a generalised virtue that makes it work both for the grand and for the number, but not for the domain of objects. You see what I want to say? And that's why that 15 is possible. That's why we can say that the grand eur commensurate are the same with the number of numbers. I can tell you this point-là. You will see my marge. I said, but how do you do it? But how do you do it? I don't know if the others want to make this difficult... I remember a certain number of texts that I cite in Mu, Mu 2 and 3. Yes, entre parenthèses, Mu, for you it's absolutely obvious that it's a metaphysic or alpha, beta, I don't know what. For people who are not... Well, at a moment, there's a one. I told you one, it's good, but of which one? Okay, okay. So in the passage of Metaphysique Mu 2 and 3, it takes an example of note 33.

17:30 Well, he says the following thing. He takes the example of the Catholou and Toys Mathematicals, so the universels in mathematics. It's like that it's called... It's like that it's called. I've supplied, but I've put it between crochets, propositions and demonstrations, because after, it's called propositions and demonstrations. And so, in these propositions universels in mathematics, We don't deal with something that exists separately, outside of the grandeur and the number, but with the grandeur and with the number, not in terms of grandeur and in terms of divisive. So if you want, it's absolutely clear that... We don't deal with it separately. It's the only solution. So that's where I say that there is no contradiction to the fact of traiter, in the grandeur, a proposition that is universal, from a point of view, aristotécian. He said that. He said that we can't do anything else if there is no expression. The error of all the reconstructors is to say that there is something that we have no trace, well, we have a little trace, but that is not coherent with what is written here. And that's just something very, very tardive. there would be a formal definition of the proportion which is between terms, and that is what Théon said. And when they want to reconstruct it, they have the choice between two versions. There is the mole, which consists of saying that a is a b, c is a d. That would be the definition of the proportion, general. And after, amuse-toi to demonstrate, in the sense euclidian, the permutation, the permutabilité. And then there is a more difficult version, which means to say that this property formelle would depend on a procedure that is the antifference. I explained that in a long, in a large. But what I explained is that we don't have at all need to invent this separate treatment, because Aristotle explained that precisely, he was not separate.

20:00 But how do you do with the proposal of the 5th book that you can't demonstrate for anyone? That's exactly what he says! This proposition uses something universel between grandeur and... That's what I tried to explain at the end, why it's universel? There are aspects of the Livre 5 that would be universel and not separate, and there are other aspects that would not be distinguished from the first, and that would be specific for the Grand Horde. That, in my opinion, if you want to add this phrase, because, if you want, you don't understand the difficulties that you oppose to the people who have read the author of the Livre V in general, you say, yes, but you have forgotten that, you have to do that. In my opinion, it is important. I'm not sure if it's what there was in the test of the film. that we don't know absolutely not we have a little impression that it's in his concept of unity which is a problem which is very vague but it's a concept of thought it's the fact that we can take conventionally what we want as an unit n'importe quel vendor and then for example we can take the number of 10 as an unit which will allow to define a product no but that's what is true it's that if he had that as an idea on the first definition it's quite enigmatic but in the same time interesting no I understand I understand, but what is interesting, for the coup, is the force of the reconstructions. If we try to creuse that, we have to see that the reconstructions proposed things that we gain. If we go to the parallel, especially in the antiféritical treatment, there we have really with the question of the unit. And there is something that we gain and that we lose, it is that when we do antiféritical with grandeur, we cannot use the number. So if we really thought that the unit was a concept flotting It would have been much easier to do what they propose. It is to say that we have a suite of quotients partiels. And so, he does not do that. And it becomes infernal. It is to say that he has to introduce a grandeur with a name at each quotient partiel. He does not say, I divide this grandeur by this, etc. Boom! I have a quotient. No, he does not say that. He says, Appelons this grandeur AG. He refait the truc, appelons cette grandeur, machin, et ça, ça a deux inconvénients.

22:30 D'abord, c'est très très lourd dans les démonstrations, c'est absolument infernal, et en plus c'est non manipulable. Alors qu'on a des exemples beaucoup plus tardifs justement chez des auteurs comme Heron, avec des algorithmes, là pour le coup, sur des grandeurs. Ils n'ont pas de problème là-dessus, où on fait un petit peu dans la veine de ce que tu as dit, c'est-à-dire unité est un concept opératoire, et donc on peut l'utiliser avec les deux sens, et on a des procédures opératoires qui sont à ce moment-là communes, because we can have an algorithm, for example, the approximation, we have this for the racine of 2, and it's absolutely obvious that, not only on the page of Euclide, but in the form where we have Euclide, we can't have it. But that he doesn't push his reflection to the parallelism at this level, it's not that it's not that it is. But the fact that the parallelism exists, I think, is that in the terminology, the way you employ the term, it's clear. Yes, I'm sure, I'm sure. Wait, what do you want to say about the measure? Because there is a thing that I didn't understand. What do you want to say about the measure? No, it talks about the first definitions. It talks about the measures exactly in a parallel way to the which comes in the definition of the number 5. In the number 5. No, but you just said that it's in contradiction with that, because you said that the measure... Because the measure is not defined in the number 5. But how do you define it? multiple? I don't know. I don't know. I don't know. I don't know. But the employment is quite analogue. We talk about the number which is measured by the unit, even if we talk about the vendor, which is measured by the vendor. There is a parallelism evident. There is also a notion... Yes, but what is interesting is that in a case, we have an explicitity, to be a part, to be a part, to be a part, etc., so we can explain it. You see, there is a measurement in the district. No, no. we can't get it, we can't get it, we can't get it, the term measure and the relationship of measure are universal, absolutely, even multiple, multiple is absolutely universal, the question is to know, the question is to divide the commentators, so there is the version deflationist which today reprend a little bit the dessus, which is where I place, which consists of saying, yes, it's all right, but attention, just, it's multiple and measure, it's not number, and we have a certain number of indices really strong, which shows that he didn't want to put numbers. Because if he had to put numbers... That's an argument that I had already thought about it.

25:00 And so, after all the rest, on is agree. It's to say, there is a relationship universe with the measure, it's evident. There is a relationship... So, you have to repeat the phrase that you do on the measure, because I didn't understand that it was compatible with what you just said. Ah, really? At the moment, you say, we can't define the measure, or I don't know what... Well, we can't define it in a universal way. It's a relationship. It's interesting. There's no definition of the measure for the grandeur. And for a reason simple, it's not to define it with the same operator that for the noms, which is to be a part or a part. Why? Because if they're not mesurables, if they're not commensurables, we're going to be embêtised. And so, we don't want to do that. So, the strategy consists of passing by the equis multiple. I explain why, of course, it seems to be more universal. Because it's pretty mad. by the fact that it is stable and I think it's that it's a good idea it's a good idea it's really great and so it's really nice and so it's a good idea that the comparison between the numbers and the vendors does not operate directly on the measures it's not that I'm opposed to those who go from the antiferares because of the antiferares we have a procedure operator of the measures which we use for the numbers. We repose on all the parallels, but there is an area where we block. If we want it to go to the end, it will also work for the incommensurable. And if we want it to work for the incommensurable, we are obligated to define the difference between the grandeur and the comparison of the two reports as opposed to the infinity, the infinity, but it's a bit like when we define the parallel. When we define the parallel, there is no time to prolong it in the definition? I haven't read the definition. It's interesting that it's not the same thing. Because in the case of the incommensurable, the problem is to arrive at the end. You are obligated to go to say that they are really not commensurable with the antiferenes. It will never stop. You are obligated to do it. You have to be able to compare, term to term, so you have two quotients. you compare them, imagine they never differ except for a millionth and the problem is... but it's the same for the... it's the same for the world you are obligated to prolong you have to say... you have to say...

27:30 because I think with the criteria of the 50 you have a criteria I don't know if it's... it's a typical It's one of the examples typical in the definitions where you have the infinity of Euclide? To my knowledge, the only place where you have the infinity of Euclide... No, the 5th of Euclide. And the 2nd of Euclide also. 2nd of Euclide. Because you prolong? And the 5th of Euclide also, because you know how to form it? So it's a postulate. and so it's a postulate these lines are parallel which are not in the wrong plane and are produced indefinitely in the two directions but they are not in any direction but it's not a procedure I don't know how to say it it seems that it's quite different of the idea of comparing de suite infinie je t'ai mis dans les marges je pense quand même que tu peux pas sauter petit jour sur cette difficulté c'est marrant parce qu'en fait aucun des reconstructeurs n'a jamais mentionné cet exemple ça me surprend tout d'un coup parce qu'il ya évidemment tu imagines qu'il y a eu des discussions très très en fait les plupart des reconstructeurs pour pensent que c'est un problème dans leur propre solution le fait que c'est rien infini et donc il ya deux So they say, but now we can't do it. And in fact, they don't do it at all. It's pretty interesting. They're obligated to do a demonstration by option. It's just like that it works, of course. Because we have a problem with a number of steps, which is not the same thing. It's the same thing that we have to do with an action. Yes, of course, it's what I... Well, if you want, you have a definition that implies the infinite. Yes, of course, but what it means is not that we exclude the infinite in general. No, no, that's not my problem. In fact, if you want to insert a cordon sanitaire to say that we can do something between the two, but in my opinion, if you want to... Yeah, yeah, but it's interesting. You've got to adopt the postulate, you've got to do it with other presentations, you've got to do it again. Everyone, if you want to take care of it, you notice that the universe is finished by Aristotle and the fact that you have to do the right parallel to the right parallel, you have to prolong it for you to know if they are parallel or not.

30:00 In fact, the real problem is that it is the proposition 1.10 where you have to really need an infinite time, where you have to trace a perpendicular to a point at a right. The problem is that if it is not in the length of the right, you have to prolong it. And as you have no reason for that, in the text that we have, the right is infinite. So it's even more problematic, but it's a bit the same type of problem. But I think it's not the same problem, but I try to formulate it with the comparison of two reports. but I think that it is equal to be even to the license, I guess what is going on... I assume that the number abstracts, which is what you have in the arithmetic. I'm talking about the number abstract, and the number concrete, that you have, instead of that, a theory of the number concrete, with the units concrete, and that you restrain... the content of the arithmetic is only what works for the numbers concretes. At this moment there is absolutely no problem than what you have said. It is to pass from the 7th to the 10th. It is to pass the fusion between the theory of the vendors and the arithmetic becomes completely natural because the theory, the arithmetic and the theory is reduced to a theory of the vendors. So we suppose that we have an I have done an exposé here, on this question, because, justement, Aristotle talks about this. And what is interesting is that he talks about it as a other traitement. There is a certain number of passages on the distinction between the number, he doesn't call it abstract, he calls it monadic, but the number of mathematics, and the number, sometimes he calls it the number number,

32:30 Sometimes there is a number of numbers, a number of numbers, and sometimes there is a number of monadies that is a number of... Because we know that in fact there is a number of concrete, there is a number of concrete, there is a number of concrete. And, just like this example, this example is precisely in the text that I referenced earlier, which is the only exception, but in fact it is not mentioned by the reconstructors in general, so I don't know. mentionné. Il y a un texte dans l'éthique anicomaque où il explique et où il parle de l'analogia, mais là c'est plutôt l'insertion des moyennes proportionnelles que la proportion mais peu importe. Et il dit que ça a lieu entre des termes par rapport à un nombre qui est un nombre général. Voilà. Un nombre général. Je vais faire un exposé là-dessus. Il faut que tu l'écrises. Ouais. Et ce qui est intéressant, c'est que il est parfaitement au courant qu'on peut faire ça. Effectivement, visiblement, on le faisait. Ça permet de travailler concrètes et notamment visiblement dans plein de domaines là les exemples qu'il prend sont des exemples économiques des problèmes de répartition comment donner autant comment mesurer ce que le coordonnier a gagné par rapport à toque alors il faut rendre les grandeurs il dit comment sur a c'est vraiment intéressant c'est le même mot c'est sub-beta et donc j'ai fait tout un exposé là dessus mais ce qui est intéressant c'est qu'une fois qu'on a fait ce constat on se rend compte qu'il sépare précisément ce traitement qui existait visiblement de celui qu'il trouve dans I think that what you said is all right, it exists. But as you said, it's not in the clip, it's in the numbers. But it's not in the clip, it's in the numbers. It's not in the clip, it's not in the clip, but it's not in the clip. It's the fact that they treat at this moment the numbers, the renders, they treat at this point... But I think everyone is agree on the fact that it's in the prolongement, the question is to know how they thought about this prolongement, and visible, it's going to have to pose some problems, and we have all sorts of testimonies. So the idea that there is a continuity, I think everyone is aware. For me, the key problem is that the unity is invisible. It is a divisive unit, but it is conventional, because as we see in the way that the concept is used in the development of KIFI, we see that it is conventional, because you are going to take 10 units when you are going to divide the product. But I believe that at Euclide, it's absolutely impossible to have something like unit condition. It's a bit, if I understand, the idea is to give all these theories,

35:00 which do not depend at something like choice, unit, etc. And in this sense, there is still a difference between these theories on the grandeur, geometric, and the number. So what I have to say is that you take the number in as a number, so if you cast it in two, in as a number, you have two. It's a concept completely special, but I think it's related to what we talked about. C'est tout ce qu'on peut considérer comme 1, il dit dans la définition. Alors évidemment, c'est qu'on peut mettre beaucoup de choses sous 1, c'est ça le problème. Mais moi je crois que le fond du problème, il est moins là que dans le fait qu'après, dans le résultat final, on a des théories qui ne communiquent absolument pas les unes avec les autres, et il y a vraiment quelque chose dont on doit rendre compte. Parce que visiblement, dans les témoignages qu'on a, on n'en a pas beaucoup, mais de ce type-là, c'est-à-dire traitement des grandeurs concrètes, ou alors les trucs un peu sur l'épithagoricien, on ne sait pas grand-chose, mais enfin on sait deux, trois trucs par Aristote. Visiblement, c'était justement, c'est ça qui est tout à fait étonnant, c'est que la tendance allait à ne pas séparer ces deux domaines, à les traiter comme communiquants l'un avec l'autre. Et ce qui est la chose qui, à mon avis, il faut prendre en compte, c'est un peu l'inverse de ce que tu dis, c'est-à-dire qu'en un sens, Euclide, lui, il rigidifie la frontière entre les deux. All the analogies, I've tried to show you. The demand, the antiférez, the unit, the measure, all of that. But what's interesting is that there is no communication between these two theories. And that's really a fact that there is no reason for it. Strictly, there is no... Well, on can... It's a multiplicity or a multiplicity, it's not a number, it's clear. And it doesn't say number. You know, I've never seen this thing, so I was really happy to... Well, that's a vitrack. Yes, I haven't seen the vitrack. It's your general debate. I haven't seen the vitrack, but I haven't seen this thing. I thought it was really... I can tell you something about the article, which is important. You know, there are plenty of details that you can see in the image, but there is a thing that is important for me, it is the way you want to talk about the antiferaise,

37:30 then you tell the difficulties that you see, and you say, now I'm going to propose another solution, and somehow it comes back to the antiferaise, and almost as if it could be a solution, and in fact, no, and in fact, how many of us, you know. Moi je trouve ça plus satisfaisant. Si tu me faisais un bon sort, une fois pour toutes quelques parts qu'ensuite tu t'occupais de ta solution et éventuellement dans les notes tu dis Là on pourrait peut-être penser que l'antiféresse n'est pas Là on pourrait penser qu'l'antiféresse Mais si tu veux j'étais gênée dans la lecture par le fait que ça revenait assignments dans ta partie Avec un statut qui était clair au bout de plusieurs lignes Em importante Enfin, tu … C'est marqué dans les marges I wanted to tell you a little bit about it. A little bit too. A little bit too. It's a problem that I've had myself in the class. With the order of the presentation. I think that the introduction can be arranged. If it is well done. It will be well done. I think there's really a lot of things. I think it's really a question of clarification. to determine where the text is, where the other commentators are, where you are. It's really a question of restructuration, of explicitation. The only thing I've heard about is explicite, explicite. I also have a certain number. I think you have some solutions to a relatively radical solution. I haven't recoured yet, but I'll be back at the end. But the English language is very good. Well, from the time in time, he is good, isn't it? Well, there are little errors, but not much. Sometimes in the traductions of Aristotle, you don't know who it is. I don't know if it was because you didn't know it, or if it was because it was completely wrong. Sometimes you say x modifié by moi. Yes, in general it's x modifié. Because I'm not able to use it.

40:00 For example, in the top of the note 35... It's just one. Yes, once I put it in, I'll put it in. It's possible. In the top of the note 35, it's always Ross. But I can't put it here. I would like to ask you a question. What do you think in general, for people who are specialized in history, in production of Barnes? Well, it's just to know. Because I saw that you used everyone except him. I think, if you want, it's the same problem that Pellegrin. Trico is very, very bad. But Trico is much easier to read. It's to say that in the recent traductions, I sometimes don't understand anything. as well as Tricot he did his things we have trouble because of all the way the font is complicated there is not to worry about the second analytics but we see a little I think the recent traductions have this difficult because they are often illisible and I have the same problem with Barnes but just they have authority there is a note by line, it is infernal before I found out Yes, yes, there are. I haven't seen the entries. Just because I didn't understand the entries. I didn't understand the entries. I didn't understand the entries. But, of all, I have modified them. In general, I have modified them a lot. Just because I have perceived them with the type of English language. I have modified them a lot, in general, because I don't think they're satisfied. You see, all these passages on the common principles and the propres principles at the beginning of the year, if you read it in Greek, it's quite clear. Because there are two categories, there are the koina and the zidia. Simplement, it's traduisible. There are the common and the propres. And so, like that embêtent the traductors, they don't want to finish. They add principles, common principles, proper principles. But sometimes, it's not the principles. because there are only common principles, so we don't know that there is no common principles. You can use the traditional German language. It's the best way you can. Yes, it's possible. So I've always tried to come back to this type of language. I have the impression that there was a kind of vocabulary...

42:30 It's not a joke. It's not a joke. It's not a joke. It's not a joke. It's not a joke. It's not a joke. It's not a joke. It's not a joke. It's not a joke. I would like to ask a question about 33, the note 33, on page 17, the last thing. The one is indivisible just because the first thing is indivisible. And it's not the same way that each one is indivisible, for example, one foot is limited. The latter is indivisible, while the former must be placed among the things that are invisible for perception. Why is it indivisible to perception? It's exactly what we talked about. It's an expression. It's divisible by convention. Indivisible by convention. Because it's a grandeur. It's indivisible by convention. Indivisible by convention, it's visible to indivisible by convention. I think it is necessary to explain it. Yes, I can. Yes, I can. Yes, I can. Because the line of after, only to the perception, because without doubt, each thing continues to be divisible. However, this last phrase, I have to remove it, she is terrible, and there are even people who say that she is not Aristotele. Yes, we don't understand it. Yes, I thought it was the most clear It's just because it's more tardive. No, because in fact, it doesn't say that in Greek. I will find it. Yes, I was agree with the chrono. Just the one I understood, but I thought it was just the one I understood. Well, because if that means that by convention, there's no contradiction. Except that this phrase, it doesn't say that in Greek. It says something else. I can find it in the same way. In any case, I said I don't understand, so it's a drama of who?

45:00 I'll put a note. The thing that's curious is that he says, indivisible for perception. But he uses it several times. The context is clearly that it refers to all the individual, because for what we call it by convention. It's divisible, but we do it as if it was indivisible. Because there are three, it's an allusion to the original. No, no, it's related to his theory ontological theory. It's the first, in the sense... Yes, it's not the way to get there. It's an interesting passage. It's the same, I'll comment it long ago, but not in this article. In fact, he explains that all this theory of units, etc. has served as a model for the philosophy. in fact and so this idea of being measured by a unit etc etc had served as a model ontology and so there was the first one in each one it's funny what you just said in the numbers we are not measured by an unit in the numbers we are not measured by an unit no we are measured by another one we are not measured by an unit yes yes yes then he said that's a frapper there is a number which measure in another moment, but 1... He said, he said, in fact, the phrase... What is he? 1, but not a number. 1, but not a number. He said, the number is measured by the unit. He said, it's not a number, but by the unit. I don't know how he said, but 1... That's a very good idea practically in the proposition 5. Aristote, he dit... La proposition 5 du livre... C'est la définition, un nombre, c'est ce qui est mesuré par l'unité. Non, c'est une multiplicité d'unité. Non, oui, c'est une multiplicité d'unité, mais non, c'est pas... La question était là, est-ce que c'est prêt ? Non, je t'assure. Oui, ça je sais. Lui est d'accord avec ça. Tiens. Mais Aristote, il dit, lui, que... En fait, c'est un passage qui est un passage sur la métaphysique are equivocations. They are equivocations. Equivoque, univoque. Ah, really? Equivoque, it means that it's just in different senses. It's just in different senses. Is it a couple equivoque-univoque?

47:30 Ah, yes. Equivoque, it's univoque. It's either the one or the other. In fact, Aristote, he uses the word It's to say in different senses. I prefer this expression. Is it true?