Emiliano Trizio Séminaire Philosophie & Mathématiques, ENS, Paris 2005
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Recorded at Séminaire Philosophie & Mathématiques, ENS, Paris (2005), featuring Emiliano Trizio. From the Michael Wright Collection, held by the Archive Trust for Research in Mathematical Sciences & Philosophy.

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This transcript was generated by speech-recognition software from an archival recording and has not been hand-corrected. It will contain recognition errors — particularly for proper names and technical terminology — so please verify against the audio before quoting. Timestamps play the recording from that moment.

0:00 The reverse, auto-reverse on this tape does not appear to have worked, and the last ten minutes or so of the seminar appear to have gone unrecorded. I'm going to re-record from the digital audio recording the whole of the question and answer session and then following that the first five minutes of the seminar so as to go up to the 4.47 seconds, 4 minutes, 47 seconds, break in the recording on the other side. So what you hear now is the last half an hour of the seminar recorded again, and then the first five minutes. It is necessary to formulate judgments on the world through the adoption of classes of objective objects. The whole measure of measures allows the objective determination of the world, its presentification beyond the perceptive field, and its present in common beyond the co-presence factually of different subjects. The disobjectivation of the world of life requires, as a result, a sort of a collective commitment of subjectivity qui, à partir de l'introduction des premières règles ou à progressivement accrue, sont enracinements dans la sphère matérielle et pratique. Alors, certes, la dépendance vis-à-vis de la sphère matérielle change de nature lors du passage de l'art de la mesure à la physique. Par exemple, les physiciens définissent les unités de mesure sous la base des concepts fournis par la théorie physique elle-même. So, we could think that we could do this, in the case of math physics. It's not as simple as that. First of all, we can say that it does not eliminate the dependence of the physics

2:30 in terms of the technical tradition, because every function function of physics and mathematics and all concepts belonging to the fundamental theory that presuppose the existence of techniques and procedures for their employment. It is not because you use the light of the lumière as an unit of measure that you can determine the world directly with the light of the lumière. It is a tradition of the appareils which are calibrated in a certain way to do this. And it is a tradition technique. So, according to Husserl, the geometry, as a tradition, is possible in virtue of the use in common, related to the language and to the writing. The mathematics of nature, for her part, also exige also the sedimentation collective of the knowledge of the practical, which is also liable to the tradition of production and the methodical method of artifacts, the tradition of the practical. It is to say that, well, we should say a lot more about it, but it is to say that when we understood that the application of the ideas of the world, the ideas of the mathematics in the world, that is the practical activity of the subject. Well, the science as a tradition, we see why, let's say, unlike the geometry, the tradition of physics, in particular the science empiric in general, is not only a tradition of language. So if you take the origin of the geometry, of Husserl and all that, in the case of physics, there is still something to change. something. This idea that the possibilities of the tradition, we find it in the language, in the case of the physics, it does not work. Well, obviously, there is a language, it is necessary, but there is also this tradition practical and a tradition of savoir-faire, which, again, in conclusion, I have my limit, simply, to say that from that, we could try to try to see how the concept of Husserlien and the history of science, which is always fondated by the continuity, here, finds some difficulties. Because it's clear that a technical tradition and a practical knowledge is obviously even more transparent, and even more transparent, than a language. And this brings us to the fact that I just mentioned that the mathematical ideologies applied to the world are the characteristics of an arrangement in the physical world.

5:00 I thank you. Thank you very much. Non, c'est pour l'écrit, hein, c'est pas pour être plus... I think we go more and more towards the materialization. You have said the mess, but the mess is the most, of course. Yes, exactly. That's what I said at the end. Yes, of course. You did just at the end. It's a tendency that goes towards the materialization of the talons. The talons are the most important. You know, one of the practical problems is that for the mass, we are still at this level of demonstration. It's to say that for the mass, the only definition of an objective of a unit of mass is a certain chord which has for mass 1 kg. Well, that the mètre has been materialized for a long time. And there are projects, the meteorologists have been materialized for a minimum of 1 kg. Well, what I want to say is that it could be... Yes, of course, it's that. In fact, in the measure of the determination of the talons, there is always a reference to the reality. For example, if we take the temperature, which was one of the most difficult things to measure, that is not, I mean, I mean, I don't know what it is, what is the temperature. We give a procedure. We give a procedure that allows, from there, to find an objectivation of the temperature. Well, then, after, we can incarnate in objects, in thermometers, and the last form of thermometers are not necessarily thermometers digitized

7:30 or simply there is a complex phenomenon that affiche something. So, what it is, is that the relationship... Of course, there is a relationship with reality. And this relationship can be extremely different. It is to say that, as you said earlier, you have responded to your conclusion, but I would like to explain your conclusion, in saying that one measure is what, in fact, we can say that when an object is conducted to tell measures of temperature, of length, etc., it means that the quantity that we assign to tell, to tell grandeur, to tell circumstances is the one who respect the law. In fact, the measure itself is dependent on the physical law. and I think it is necessary to emphasize that there is a displacement, the problem is that there is a displacement of an object material which can be shown and which should be shown. And there are things that cannot be other than that. For example, the orientation to the left, the transmission, if you want to transmit someone very far away, this is my left and this is my left, it is extremely difficult. There are ways to envisage this. It's a science fiction. It's true that it's the last refuge of the monstration pure. But in fact, the measure of more and more becomes not an object, an act, but it's that there are a number of different measures that must be coherent with the laws that we have. And that change in the world. C'est toujours un rapport à la réalité. Un rapport non pas d'une idéalité, peut-être que le maître, avec un objet, peut-être celui-ci, mais en fait la cohérence d'un système d'idéalité, toute une structure, toute une construction de la réalité, avec un ensemble de faits. It's much more delicate. It's interesting to say three things. First, the materialization that you mentioned, and also motivated by the existence of objectivity. So it's an attempt to also idealize the talons. Just what I want to say,

10:00 if we go to the direction of using the constant Planck, the speed of light, etc., as a fundamental unit of measure, fundamental, we can do it because there is a series of experiment practices that are sedimented. That's right. The matérialization of the definition of the grandeur is not a detachment of the material matter. I think you are right. In addition, you just said that it is a procedure because, effectively, the instrument and as an object objectivant, it should be used. So each measure involves a procedure. And in conclusion, it's very important, it's the problem of the law, which is the definition of an operation of a measure. What's interesting is, the first thing that I've said, is that when we decide to determine the world A partir d'un objet qui est intermédiaire, on determine le monde à partir d'un morceau de monde. Et c'est ça qui est la base de ce problème, disons, de charge théorique de l'expérience en physique. C'est parce que j'utilise quelque chose pour déterminer quelque chose d'autre, je dois préjuger, au fond, l'objet que j'utilise. And at the end of the scale of Dumaitre, which I said simply that he is rigid if you want, all the objects objectives that we have introduced in the history of science are more and more charged with theories. The last remark is that on the history of the measure, it would be interesting to make a historical table and to see how, during the period of time, we gained the control of the measures. Very, very schematically, the length, it's hard to chiffre, and every civilization has a lack of lack of lack of lack of lack of lack of lack of lack of lack. The duration is much more difficult. It's the 17th century that the horloges begin, the horloges really précises, It's an egregious, but the horloges that appear in the 18th century. The sounds, Euler, from 1740, with the theory of music, has quantified for the first time, in a way vigoureux,

12:30 the intervalles musica, the intervalles sonor. It's Alambert and Euler who have done the interviews. There are some of the work of musicologists who have established, in a way rigorous, what is it that is, an intervent musical, with a extremely direct measure. Well, the temperature, it's an echo of the 19th century. The temperature, it's an echo of the 19th century, with the standardization, we have really a control. Jusque-là, the temperature is very approximative. The thermomètres a little sharp, it's the one that came in, for example, but it's still there's a mirror at the end of the 18th century. There's a mirror at the end of the 18th century. And when the colors, I mean, it's before the oscillatory theory of the mirror, there's no objectivation. at the moment where we associate, the same that Humer or d'Alembert had associated the idea of sound, the idea of sound with the idea of frequency, which is an enormous part of scientific, that is only in the 19th century that we have associated with the theory of the mirror, the notion of a frequency that is lumineux. So, I think that history shows something about the difficulty. Today, we are surrounded by different measures, and they are all digital, and we don't even know what there is behind it, we don't even know what there is behind it. But it has been extremely long. Thank you. Merci. Jean ? Oui, je ne peux pas mal travailler sur ces réflexions précédentes du CERN. Je crois qu'elles sont essentiellement justes, enfin très profondes, et qu'en même temps, il y a quelque part une erreur. Alors, bon, elles sont justes. Bon, j'ai relevé là trois exemples, enfin, que vous avez cités dans votre exposé, qui sont des problèmes fascinants, enfin, et monumentaux. the difference between idealisation and abstraction. It's true that Husserl is the philosopher who knows what he's the most thématized.

15:00 This idea that the idealisation, as a process limit, port to the exactitude, while the abstraction port to the genericity and that the exactitude has nothing to do with the genericity conceptional. In fact, it's not a fundamental. all the way he represents the transcendental of Kant, on the problem of the fragmentation of space, on the fact that space is not just a concept, all the problem of the space that is pure intuition, after opposition, extensives, extensives, etc. And then the third example, that Cartier just said, C'est, à partir de Galilée, cette extraordinaire idée qu'on peut faire sur la physique, ce qu'on a fait sur la géométrie. Mais la géométrie, c'est les qualités premières, et la physique, c'est les qualités secondes. Et donc, en fait, Nusserl est aussi un de ceux qui a le mieux mathématisé ce qui est devenu une banalité dans la physique contemporaine, mais qui n'est pas une banalité, c'est la géométrisation. because for geometry, we have to be able to describe the second qualities like structures that can also be able to fill the space-temps. It's the problem of the remplacement. So, there are fields, there are shapes, there are different shapes, etc. So, it's an enormous part of the physics, this operation galilea. But, indeed, there is still an error. And a error, I can't say that it's a fault, but there is still a limitation of reasoning which is spectacular. You have said, I have said, I have said, that it is to fill the gap between perception and determination mathématiques and perceived with an edification graded of determination quantitative. It's all right. There is a gap between perception and scientific, let's say, physique. Rousser does the hypothesis, apparently evident, which is an evolutionist, almost an evolution culture, that as well as the evolution culture and the apprenticeship, we start with the world of life, and we start with math. mathématiques. Que, donc, on doit pouvoir comprendre comment la physique mathématique se construit à partir

17:30 du monde de la vie. Et c'est ce que vous nous avez exposé très brillant. Mais on pourrait pousser plus loin et dire de façon tout aussi évidente que la nature physique précède la nature biologique et la nature mentale, et que, donc, on peut complètement inverser le problème. is that this inversion has been made by some of the most great phenomenologists. Let's take an example of the relationship between Merleau-Pompier and Netto-Philosophie, it's a complete inversion of Husserl about that. But the one that we never talk about, which for me is the most great phenomenologist French with Merleau-Pompier, which is Chambon, Chambon in his book Perception-Réalité, I don't know if you have read it, a extraordinarily bien posé le problème en disant qu'il faut partir du concept de la nature. Ce concept de nature, au départ, sera la nature physique. Mais que doit contenir le concept de nature pour que puisse émerger ce concept qui ressemble au monde de la vie ? Donc vous pouvez complètement inverser et dire qu'il faut comprendre, qu'il faut compléter le lien, mais en comprenant comment du macroscopique peut émerger du microscopique, comment du qualitatif peut émerger du quantitatif, comment, etc., comment du perçu peut émerger du physique. Et moi je me suis essayé de faire ça parce que il y a 20 ans je travaillais énormément sur les liens entre Thom et Husser. Moi ce que fait Thom, c'est, c'était une version mathématique du programme phénoménologique de Husser. the very high math, the very high physics math, there was a problem. So I've worked hard on these texts, all of these ideas, all of them in 1972, in 1974, on the geometry exact, which will never be a morphological theory, there will never be a morphological theory, there will never be a morphological theory. It's good that there are. So what is fascinating is that if we reformulate the phenomenological problems that you have talked about, but in completely reverse the evolution of the evolution, Well, in fact, we obtain a description of an enormous part of the contemporary science,

20:00 which, they-mêmes, think of a post-physical science. All this is about the emergence of morphology matroscopic in the natural world, the emergence of forms, it's not only Tom, there are many people who have worked on it. On a maintenant des magnifiques théories mathématiques de l'émergence des formes biologiques, des coquillages, des feuilles, etc. Tout ce qui se fait sur la physique macroscopique, tout ce qui se fait sur des qualités sensibles. There are people like Eugène and all that who explain why the col-col. Well, they recover the qualitatif and the macroscopic, the second qualités, from the physics of the fundamental, in explaining the interface, the fractals of the interface, and what are they? And then I don't talk about the science cognitive, of the cognitive neuroscience, which explains the emergence of the perception from the process of fundamental processes, which are all of the type of physical. So you can completely reverse the problem. What is interesting is that Husserl, he-même, envisage this, and he calls it a scientific counterpart of the phenomenology, dans des sciences à venir qui n'existent pas encore, mais qui pourraient éventuellement exister un jour. Et je pense que ces sciences existent maintenant. Et que donc l'opposition entre scientificité et phénoménologie, actuellement, dans notre actualité scientifique, est pour moi absolument caduque. C'est la remarque. Yes, I have a response, in the sense that I believe, I will know what I want to answer. You have right, and maybe you have right when you say that today, l'insertion réelle du sujet dans le monde est objet d'étude scientifique mais que tout cela

22:30 va arriver après dans la démarche transcendantale c'est à dire que comme vous avez dit pour Husser il n'y a pas de contraste dans le sens que Husser tout d'abord ne fait pas d'explication il y a So, if you want to change that, it's true that the project of Husserl can be reversed, but it's true that Husserl says always, as you say, that the subjects are also constituted. They also perceive it. They perceive it. They perceive it as a choice of the world. Well, it's a bit of that, I agree with you. Finally, Hussap never went against science. He never did that. He wanted to explain the conditions and possibilities of science which, they are explicative. And so... mathématiques de façon Hilbert-ciel. Hilbert était un très grand ami et donc c'est vraiment la conception axiomatique hilbertienne qui pour lui était la clé de cette idéalisation qui porte les concepts à l'exactitude etc. Et plusieurs fois il dit on ne peut pas imaginer une axiomatique des formes naturelles. C'est totalement impossible qu'il y ait quelques axiomes dont on dériverait all the forms, the profusion of forms, for example, biologiques, like that. Apparently, he's right, but in the same time, actually, I think we can say that this affirmation is totally false. So it's something very formalistic, which we don't find at people like Poincaré, and the fact that the thesis that there cannot be a physicality and a geometry qualitative

25:00 radicalizes its alternative. And the alternative is the phenomenon. But I think that the position that he is concerned about phénoménology is liable to a kind of limit intrinsically seen in his science of his time, and that there he is still a little bit tromping, because he is liable to a formal position. You said that he is not tromping. Well, yes, because Poincaré, Poincaré was a contemporary, and Poincaré was completely in the same way. He said that the geometry is liable to the perception, but there is not necessarily this kind of genese phenomenon. I don't know, but it's obvious that and that we can object and observe that these philosophies are a little dated from the point of view of the science. And he was also not too aware of what happened at his time, in some cases. That's what we always say, perhaps, but it's not true. Regardez les appendices de la crisis sur la mécanique quantique, ils sont super bien. Alors, il n'a pas l'air de quelqu'un qui comprend vraiment ce qui se passe. Pour un philosophe, il se passe. Moi, je n'ai pas eu l'impression que ça comprenait vraiment ce qui s'est passé. Il a fait des remarques qui sont très générales. But the big problem, it's that what's first interest Husserl, it's the order of the Constitution, it's that. It's this hierarchy. And so, when you say that we can reverse Husserl, Well, in the end, we have to decide, we have to decide whether we remain transcendental, whether we remain transcendental or not. If we start from a transcendental philosophy, then everything changes.

27:30 I'm completely agree with you. At this moment, everything changes. But if we remain in a transcendental philosophy, a philosophy which is first interrogated on what is first, what is first, what is first, First of all, this itinéraire of the perception towards the idealism seems to be justified. I don't think it could be reversed. Maybe I'm wrong. Another question, another format, or the interviewer? It's a little bit naive, a little bit more. You talked about the things that are issues, for example, and also issues. Maybe you had talked about it at the beginning. I was not there. I read somewhere. It's a sort of a question that I pose. Longueur, mass, change. Longueur, the mètre. Well, we define it as the middle part of the case of the earth, where the length of the length of the train, or the portion of the Bretagne, etc. But it seems, after my lectures, which are not as pushed as the others, that in the history of the years, the maître is at about a length of my arm, or my arms, or my arms, and then the size of the man. I think it's 1,75 m. So it's an angle of the size of a bit. Because of the angle of the size of a large size, or it's an angle of the size of a large size of a mathematical size. You can use the logarithm of a... Well, in a sense. The second, I once had read, I have read it, I'm not sure how to write it, but it was about the time of a human heart. About. The mass is perhaps a bit more difficult, but when the Egyptians would be able to do with water, or I don't know what, or a bowl, or an urn, not an urn, but a jar, the Greeks, etc., it was perhaps not 1 l, 1 kg, but it was about to this order. Well, I say about it, it's between and between and between the grandeur.

30:00 So, there are three things. Is it totally idiot to say that it's still more or less attached to something of our living life, that's to say the length of our arms, or the length of our arms, etc. and what he does every day, even the mass, for a man, it's between 50 and 100 kilos, we can talk about it. I don't know what we can say there-dessus. Yes, I think yes. It was an object of... Yes, I agree with you, in the sense that, In fact, what I've tried to show is that we are in the same way because we need to determine things all of the same way, all of the world can determine things all of the same way. That's one of the reasons. It's one of the elements that we treat our objectivity. And so that's why we chose those who were there, those who were close, those who were accessible to everyone. That's the idea. I agree with you. There is a march towards a dématérialization of things like Pierre Cartier, at least it doesn't matter. I don't know. I don't know. I don't know. It's in the sense of the objectivization. It's more precise. It's clear. It's clear. It's clear. It's clear. It's clear. It's clear. It's clear. the precision of the measures that we have today, the erosion of nature, the talons, the part that we have is not stable at the level that we want to acquire today for the measures. The part that we have deposited is about a thousand millionth, we know, a thousand millionth, we know, it's very sufficient to define the number and the number and the number. So there is a x plus that, but less liable to the aléas material, so in the sense of objectivation. It's a little bit more in the sense of objectivation of objectivation. But I would like to tell you, I would like to tell you,

32:30 or the procedure that we can improve, and if we think in a physician, there will always be a little error, maybe it will be zero, but it will never be null. Is this a nonsense or is it that you are almost all right? I am now going to re-record the first five minutes of the talk. So first of all, throw a lead to see whether that gives better sound quality. Good evening. First of all, I would like to present very quickly calca-reflection husserlienne, D. Husserl lui-même, et j'espère pouvoir aller plutôt rapidement. Et après je vais essayer de développer. Je voudrais tout d'abord dire que, au fond, le problème à la base de ces considérations est celui de la mathématisation de la nature. Alors, il faut tout d'abord être très attentif à la signification de cette expression mathématisation de la nature. Parce que, comme tout le monde sait, Husserl est passé par les grands critiques de la mathématisation de la nature. C'est-à-dire que lorsqu'on lit la Crésis, on trouve des critiques à cette conception que Husserl attribuit à Galilée. It is to say that nature is the same, a multiplicity mathematique, a structure mathematique.

35:00 The world all entirely is idealized in itself. It is true that in this book, Husser developed a critical point of view because it is interested in the crisis of science, it is to be an oublier of the subjectivity transcendental in the scientific activities. But it is also true that we can criticise the idea that nature is an idealist mathematic, while accepting the effect, obviously incontournable, that the physics is mathematical. It's clear that when we talk about mathematics and nature, we have to distinguish, let's say, the issue ontological, and what is the nature itself or mathematics, as a certain point of view physicalist would be, from the issue methodological, which is applied to the application of mathematics to nature. Oh, that's a fact, we apply the mathematics to the nature, that's part of the physics, the physics is mathematics. And so, in this sense, the mathematics of the nature is a condition of possibility of the physics. And Husserl, of course, must always remember the fact that Husserl was very interested in finding science. Alors, pour lui, il était essentiel de rendre compte un principe de toute activité scientifique. Après, malheureusement, il n'a pas trop développé ce point de vue concernant les sciences empiriques en général. Mais la phénoménologie, un principe, doit donner un compte-rendu aussi de ce type particulier d'activité judicative which is the measure and which is the application of mathematics mathematics to nature. Or, this is what I'm going to try to do today. First, I've said something very quickly about what Husser has said about the operation of measures and its role in the construction of physics. And then I tried to propose a few developments from a point of view phenomenological perspective, trying to be more faithful to the methodology of the Husserl,

37:30 trying to provide an understanding of the phenomenological approach to the application of the mathematics to the nature, so, at the base, as a condition of the possibility, and the operation of the measures. Alors, du point de vue phénoménologique, ce problème fait partie du thème plus vaste, qui est celui de l'origine de la physique dans le monde de la vie. Alors, Husserl, dans la dernière partie de sa vie, essaye de montrer comment les savoirs, les sciences objectives, se développent à partir de ce sol universel et primitif qui est le monde de la vie. But we can give a very simple definition, which, for us, will suffice. The world of life is the world spatio-temporel of things such as we have experienced in our life, and as far as scientific. And beyond this experience, we know that they can be experienced. So the world of the current experience is possible in everyday life, so it's not... Well, first of all, we can say what it is not, and Husser said all of a sudden, very quickly, that the world of life is placed in contrast to the sphere of the mathematical ideas. Husser said, but here, in the world of life, we don't find anything from the geometries, nor the space geometrical, nor the time mathematical with all these forms, Ni pour nous ajouter les objets propres à la physique mathématique, à savoir énergies cinétiques, ondes, électromagnétiques, etc. Donc, pour ainsi dire, l'étoffe conceptuelle même est une dernière analyse mathématique. Donc, s'il est vrai que dans le monde de l'expérience ordinaire, on ne trouve pas des formes parfaites, on ne trouve pas des structures mathématiques, It is also true that we don't find these objects a little bizarre, which are the objects of physics. So what is an object of an electromagnetic field? Well, an object of electromagnetic field is... An object of electromagnetic field is a fluctuation in a same field vectorial. A field vectorial is a function to a vector vectorial defined in the same space. So it's an object completely ideal.

40:00 That's the problem. We don't find the world a function of vectorial defined in the real space to three or four dimensions. No one has ever seen an electromagnetic field in this sense, and no one will never see it. That's the problem of Husserl. So there is an dualism. That was six minutes and 25 seconds, the first six minutes and 25 seconds of this talk re-recorded.