 Next talk of our morning session is by Gerhard Heinzmann from career from a philosophical point of view. Thank you very much. So first I will thank the scientific committee for this invitation. Then it's good sir, okay. Then my talk overlaps with several remarks done by Professor Fein and Professor Greil. And finally learning is by imitation and reputation. So perhaps you can grasp better some points on Poincare's philosophy. Now the summary of my points is first I will give introduction as Professor Fein is Poincare a philosopher. Then some general elements of Poincare's philosophy and these elements will be declined in different respects in arithmetic, geometry, mechanics, physics and a conclusion. So first of all Poincare is Poincare a philosopher. Now to see what is going on we should perhaps first determine what is distinguished to a philosopher from a scientist. Until the 19th century there are terminological connections. For example Newton's theoretical mechanics is entitled Philosophia Naturales. Liné wrote the Philosophia Botanica, La Mach, Philosophie Zolochique. But there are not only, there are more. Since Aristotle there is not only a terminological but even a systematical connection between philosophy and science. Both philosophy and science give justification of our actions. But the mode of consideration of philosophy is Cattolu general and the mode of the special science is Cata Miros particular. Now what means general? The philosopher tries to justify the conceptual framework of scientific knowledge. He has to invent the conceptual presupposition useful for scientific knowledge and to clear up the scientific activity in a symbolic form. So philosophy is not after science. The Spenster cabinet not before science but involved in science and here naturally we find Poincare. Now if you have such a position there are two perspectives. One perspective is to say that philosophy have a normative approach fixing conditions for what must be criteria of science. Naturally scientists don't like it because if you should make revisions of your science you will not be happy about this and I think philosophy says nothing. That's the metaphysicist task. In contrast a purely descriptive approach limits itself to describing science in action. Nach Schwetzerei. So philosophy reduced to history. This is a positive word but philosophers don't like it. You know that the most since the old times the biggest difference is between history and philosophy. This is completely different as perspectives. Now one solution is moderate naturalism. Philosophy cannot articulate reality independently of the conceptual schemes used in science and the epistemological justification of beliefs and proposition has its origins in scientific practice. This perspective can now be considered in a dispute, in a classical dispute and Professor Fine who spoke about this dispute about between realists and anti-realists. This can be, you can consider this dispute under different perspectives, under semantic perspectives, that means the realist says scientific proposition are true and false independently of us. I'm making red, what's this Poincare's position? Yes, for logic he says this. Logic he is not an intuitionist in logic. He accept the principle of bevelance that means not a tersex, not that, but the principle of bevelance which means every proposition is false or true, he accepted. And you can be anti-realist, that's truth is an epistemic notion. And all rules there are in mathematics, the constructivists will say there are rules and rules have no truth values. And Poincare for some domain he is an anti-realist too. So from an ontological point of view, naturally we Professor Fine told it, Poincare says the relation are the only objective reality. So maybe they exist. But there are terms described only apparently theoretic entities, he said these two because singular terms in effect, objects are not existing for Poincare. So in one sense he said this is in different hypothesis. In another sense is anti-realist too. Concerning the continuity problem, he is clearly realist because he says there is the invariance between all the structure and the history, between all the theory and the history is the structure, we heard it. And then naturally it is the distinction between extern and intern and there he is reality is independent of our mind and our knowledge, no, here Poincare is clearly idealist. So is Poincare a philosopher? Or is Poincare's position in current position? Realist and anti-realist? No, I think rather the alternative between realists and anti-realists is obsolete, naturally this is Noah Professor Fine's position. But I will go more in a pragmatic direction. Poincare finds a pragmatic way out between Kant's idealism and Thale-Moll's empiricism preparing Nelson Goodman's approach for a specialist and he is between anti-rem and in-ray structuralism. What means this? Anti-rem structuralism means if you say a structuralist, now there is the structure and is the structure a mathematical object? If you are a structuralist, the structure should be itself a position in the structure. So you have a regress. And if you are in a re-structuralist, you say the structure is an abstraction of positions, but these positions should be done in, there should be available a background theory and the background theory should be, because you see a structuralist should be half a structure. So you have there a regress on the other side. And in both, position seems not to be a current. But, so I will show you that Poincare is between these two perspectives and he is a great philosopher and more non-philosophist science has one of its origins in Poincare's approach. Now, what is Poincare's philosophical approach in accordance with the empirical maxim, the construction of reality must be guided by experience in accordance with the idealist viewpoint. Experience is not sufficient. It is only the occasion to become aware of certain mathematical categories of the mind with which we must accord our experience with decision or convention. And in accordance with moderate naturalism, scientific development and prediction serve as supplementary arbitrators of the servility of the chosen conventions. Now, in this talk, I don't emphasize the historical context nor the historical stringency of Poincare's argumentation. I'm interested in the question, if Poincare's writings give the conceptual possibility to classify him today belonging to the philosophical tradition, that is, he is a big philosopher for our philosophers. So some general elements of Poincare's philosophy. There are two traditions to interpret Poincare. One is he is, he's an intuitionist, he has an intuitionist tendency and at the same time he considers the pre-spolemics against logicism and formalism, so against Russell and Hilbert and so on. On the other side, one opts for a conventional and linguistic aspect of his work. And my thesis is that the intuitive and the formal aspects are two sides to the same coin. Poincare always supports the same philosophy. It consists in a reconstruction program of the process of understanding theories, of understanding theories. And here, it is not yet appeared but Jeremy Gray's scientific biography of Poincare that will appear I think in one month by Princeton. If you read this, then you understand what means Poincare by understanding theories. So I think it is the best work on Poincare. He gave me a copy to do the exposition. Thanks Jeremy. So now the construction of scientific objects is simultaneously conceived with a construction of language. Or more exactly, the empirical basis is the occasion of the process of language learning. This is what Poincare is doing with us. And but not language learning at all. As Descartes or something like this. No, we are already able to understand but from time to time the understanding is interrupted and he will know why, why, why it is so and not in the other way. Perhaps we discussed Hilbert and Hilbert gives a very beautiful axiomatic systems of geometry. Poincare says, wonderful, but I cannot understand what geometry is by this, by his axiomatic system. I cannot understand why they are, constant curvature is important, for example. So now second basis, the interface between language factors and experience is the term hypothesis. It's a valuable indicator of the difference and the analogies of different sciences, mathematical sciences and physics and its semantic function is declined by Poincare with respect to the link between the liberty of creativity and the guidance by experience. Now the problem Poincare is concerned with is the achievement of an equilibrium between the very traditional problem of the relation between objectivity and subjectivity. That concerns in fact the relation if now I take the vocabulary of Milovitschlich between knowledge and intuition or acquaintance or labeness or if you take the Russell terminology between knowledge by description, objective description and subjective acquaintance. We have seen it already, the relations should be common to many minds, transmissible by discourse could not be concerned outside of a mind and there are sensation actions on the other side. It is in transmissible pure quality, but one point is especially important for me. He wrote in the introduction of value of science, the only real objective reality, the veritable reality is the internal harmony of the world. So there is a static component, I will say later what it means. Now like many philosophers at the end of the 19th century, Poincare emphasizes the genetic point of view. What distinguished Poincare from other authors is a systematic but not historical interpretation of the genesis resembling was a logical empiricists called a reconstruction program. This is what he makes the same, it's a reconstruction program, but the difference consists in the fact that it includes an aesthetic element and this is excluded by the logical empiricist. Now I come to the core of this talk, the local forms of how you can decline it in different sciences. Poincare distinguishes a priori principle, for example a complete induction, principle of reference in arithmetic, from conventions as apparent hypothesis, for example the parallel axiom and geometry, and from hypothesis as generalization, for example the hypothesis phosphorus melts at 44 degree. Placed side by side, all of these notions express local forms specific to the different fields considered of Poincare's philosophical problem, whose principle subject is, and I emphasize this, the epistemological questions of the relational form of scientific knowledge and its exact formulation with respect to our subjective acquaintance. Now, how it works in arithmetic. That is one of the most interesting questions, the justification of the principle of recurrence. I give here, you will understand later why, second order formulation, if you know this, and now how to justify the principle of recurrence. If you think perhaps that Poincare, he was not sort of old mathematics and today it is no problem, you can pour for example one way to define the natural number by explicit definitions. This is the explicit definition, a natural number who is, an inductive number. So, this is the definition given by data kind and tracel and you have immediately the induction principle. Now, what is with this? One condition, it is clear what you should do here, is if you say it's analytic, there is, you see there, is this analytic? There's more than logic, right? There is set theory, very important for philosophers, because logic, you can, this is Denis Bonet here from Paris, he showed it for five years in this very brilliant dissertation, that if you take the normal consideration of logic as general and you can substitute and all these things, you come to arithmetic. I already met with logic. So, the formal, what you call the formal logic, it's not, the consideration, what is logic is naturally a difficult question, it's not simply, but we can say, okay, let's go, first all logic is logic, okay. It's not, in fact, it's not so easy to say that Jean-Pierre, he's right too. It's not so easy. So, now, the justification, we are here, so there are, it's just by the explicit definition in a dedicated Russell manner. But, now, philosophical objection, naturally, Poincare's first says that set theory is not logic. And secondly, but this definition is imperative. This definition one here is naturally imperative, because this natural number is defined between a totality and it is itself, it is a part of the totality. So, this is called by him an impredicative procedure. And now, why we should not, maybe we should avoid the impredicative procedure because the realist approach behind this implies a contradiction. It is responsible for the unrestricted application of the action of comprehension, which leads to a famous type of logical antinomies. Platonism is here drawn up as a methodical fallacy. If it is a platonist to accept the postulate, does there exist a Y and Y is the X with the AX, as for every propositional function, that follows together with the definition of the element relation. This one, the action of comprehension. And if you take, there exists a Y, Y you take E and A to X, X is not an element of X, you have naturally the contradiction. So, this contradiction is interpreted by Poincare as a fault, a philosophical error, a philosophical error. It is realist to be realist in philosophy. Now, Poincare's solution. He says, we have the faculty of conceiving that the unit might be added to a collection of units. Thanks to experience, we have had the occasion of exercising this faculty and our conscious. So, the indefinite repetition is occasioned by experience without being itself empirical and constitutes as such a theoretical part of our knowledge. And complete induction, he says, is nothing but the affirmation of the power of the mind, which now is itself capable of conceiving the indefinite repetition of the same act when this act is once possible. The mind has of this power direct intuition and experience comes for it to nothing but an occasion to make use of it. And by this, to become aware of it. So, in fact, experience is the ratio cognoscendi of the affirmation of the fact that either domain can be constructed through an act of indefinite repetition. A property is valid for all elements. It is valid for the success of any elements. So, in fact, in arithmetic, we seem to use native hypothesis, no convention, but an operative intuition a priori. Now, this operative intuition a priori should be very, very strong because, naturally, for Poincaré and this is why I formulated in the second order version, the principle of recurrence, it should exclude non-standard models. And, in fact, naturally, if you say you repeat iteration, the iteration is completely different from the affirmation that you can repeat it because his formulation, the affirmation is nothing other than the final clause. All numbers can constructed in this manner. And the final clauses, if you have the both together, you have the deduction principle. And this is, naturally, this is now a very strong intuition that we cannot... against Wittgenstein. This here is... we have a capacity about entities and Wittgenstein says, no, this is too intuitive. There is too a strong intuition. And here, Poincaré as a mathematician, it is necessary to do mathematics and we have to accept it. Do it. Okay, now, we compare... the principle of complete... Poincaré compares the principle of complete induction as a necessary tool of mathematics with the understanding of the principle of empirical induction. The later is a natural hypothesis, he said, or a practical rule in the sense of a necessary tool of physics without this empirical induction principle you cannot do physics. It exists. That's the nature you have to place you both as an order in some principle of causality. Now, the stridding analogy of complete induction with the usual process of induction lies in the function to be both tools in order to structure different domains. These tools are suggested by experience for the mathematical induction and for the other induction, but are themselves inaccessible to experience. So, Poincaré intends to confront a mathematical theory with the experience from a systematic point of view every time the result is a hypothesis. In arithmetic, given the analogy with the physical induction principle, the difficulty of indefinite repetition could be called a natural hypothesis which is inaccessible to experience but suggested by it. It made good sense to say that the synthetic a priori element constrains the natural hypothesis. So, in fact, Poincaré uses here apparently completely Kantian formulation but what he's doing is to say so we have concrete repetition and the concrete repetition is not enough. We cannot add one thing to another but I have not this what is necessary in mathematics. This is only the Razzio Cognoscendi to have this faculty of indefinite repetition and he calls this synthetic a priori but in fact it is a status because he says this is conventional thus the concrete repetition should be adapted to this mathematical intuition and you can call this a natural hypothesis without this faculty of indefinite repetition you cannot do mathematics and mathematics should always be together with the objective and the subjective element so it is synthetic a priori right, Poincaré said it but in a systematic manner you can say it is a natural hypothesis. So, what is in analysis? In analysis the indefinite repetition with respect to the symbolism is a conventional adoption of our theoretical experience. He says if I have a square and a circle in a square and then the diagonal the intersection point cannot be rational naturally and so he gives a lot of example and says this is the experimental part now the experiment is naturally a mathematical experience the experimental part of mathematics is to show that we should have the continuum the real numbers he says it is a bad argumentation because naturally if he says that it is the indefinite repetition he is explicitly thinking about edigins cuts but this suppose a total infinity so he cannot accept it and so he is in this point is not very clear and he says it is an intuitive capacity but he is not able contrary to the induction principle to design exactly to determine exactly the intuitive element of this capacity of this capacity to construct a continuity now in geometry the geometric space is obtained by choosing the language of group to serve as tool of reasoning about representation of muscular sensation I present four steps to the so-called result the so-called absolute space the space without metric by supposing that the geometry is only at constant curvature the first step similarly to Karnab's off-bau and I am sure that Karnab he was very well read the starting point is the definition of two-place relation Karnab is a two-place relation and here in Poincare 2 two-place relation what is this relation? here an external change A with X, A, Y for X change in Y without muscular sensation you see it as a car pass and the internal change with X as Y for X change in Y are combined by muscular sensation so you have a sphere and you turn the sphere you can compensate this rotation by going on the other side this is the first step then he introduced a classification of external change among external change some can be compensated by internal change others cannot and the first are called change of position and the second change of state naturally if you have a glass of water and you have a chain middle process you can turn the sphere nothing changed so third step modular and identity condition with respect to the compensation by internal change the identity condition are two external change equivalent if they can be cancelled by the same internal change approximately cancelled Poincare defines the equivalent glass of changes of position and it's called a displacement so displacement is the equivalent glass and so on it is reputable so we can recognize that two displacement are identical and finally the main result is that the set of displacement glasses external and internal together form a continuous group in the mathematical sense continuity is another difficult point as a group it should be continuous this is intuitive too now what's the conclusion of this the general concept of a group is a form of our understanding existing in our mind the group actions is a structure it is the natural hypothesis of if you prefer a synthetic material element the set of presuppose relation satisfying the group actions is exemplified and specified by the specific displacement structure which is a continuous transformation group which is the mathematical expression of relation between sensations and the psychological principle the mathematical expression of the psychological principle of free mobility now a big component of this group structure can be seen the fact that is exemplified exemplified mean has some characters in common in a big variety of systems element this is the element of harmony that means mathematics is harmonic is a harmony because you can see certain structures which you can use and naturally for Poincaré there are first groups and then topology topological intuition too geometry is replaced later by topology and aesthetic means nothing than us but this is a lot of thing because it means to see to see the characters in common this is the point what Steudoné always criticized by Poincaré because Poincaré if you go in the topological writings then he is acting and thinking about figures in a topological way and naturally if you have not the good perspective the reasoning is not correct this means aesthetic reasoning now there is an empirical under determination naturally I have not yet spoke about this the form of convention where exist a choice between different possibilities because naturally I think Poincaré convention is that there is agreement and with respect to this agreement we have different choice that they are equivalent and until now convention was only a sort of classification is only an adaption of not precise experience with its make precise by the mathematical structure and now this is a new a new comprehension of convention where when you study now this transformation group the property of this transformation group you study several subgroups and then you have the choice between this different geometries and non-negligent geometry and but now this empirical under determination of the groups has only a purely contrastive characters this term of state thought if the groups are isolated from the background beliefs about the world it means what Poincaré said okay I have the choice and this is with the air rotation is the same thing I have the choice between Copernic and Ptolemy in the mathematical sense I can do it but if I have a more holistic view if I take the consideration of commodity simplicity and geometry then the Euclidean geometry is to prefer now look Poincaré against Hilbert Poincaré is often quoted greater saying that in mathematics the word exist means exempt of contradiction must be seen under known Hilbertian light he never was interested to have a non-contradiction proof as Hilbert for reasons concerning the involvement of impredicative procedures Poincaré excludes mathematical real ability by consistency proof in the Hilbert world so the direct consistency proof because he says it is necessary to have an induction and the induction is known predictive and so on so how what he is doing the real ability of geometrical spaces for him given by his psychopsychological genesis using the tool of real actions with imagined sensation in fact this is a very complicated construction because Poincaré if you read it consciously he is not experimental he is not going to how it in a psychological way or in a the physiological way he makes no experiment it is in the state it is an imagined sensation what would happen if I will grasp an object as he says and he takes a structural position without disengaging completely meaning and knowledge from ostension his concept of structure constitutes a development of the traditional algebraic one that means naturally there are not the geometrical actions are not propositions but there are only conventions neither norfalls and the justification because you have no propositions by Hilbert is done by the consistency proof by Poincaré it is done by the exemplification and exemplification means now not in a model theoretic manner exemplification it is not going in model theory and using using the set theory set theory you can use it is an informal way an informal way to exemplify exemplificate and this is the aesthetic element of mathematics naturally now this is not so the it's clear that Poincaré is more an artist in the sense as Hilbert was it's clear but you do remember all that Poincaré distinguished very well between mind of logician and the mind which is intuitive this is the intuitive character now the schema of generalization in mechanics experience provides complex phenomena which we reduced into a number of elementary phenomena this is interesting too there are complex phenomena and not a single phenomenon to physical induction we move from the phenomenon to the experimental fact and by means differential equation to Lowe's and verifiable hypothesis Lowe's can be elevated by decree to the status of conventional principle it's the same now the same thing as he made in arithmetic the same thing as it made in geometry he's going from a law or from something which is not completely correct to something which is correct by convention this is a principle long quotation I will not read all this and the better because also you can find it in the value of science one can a law if you is very well confirmed you say a law is now a principle and then it's out of the way to test to test this principle now what are the more interesting the methodological analogy between geometry and mechanics in geometry the conventions or definitions are chosen as a function of objects so lead bodies or rise that are not the use of geometry this is very important and we place it both the category of group the empirical under determination is restricted by consideration of commodity and simplicity now in mechanics the convention are convenient even with respect to mechanical objects and therefore this reason generalizations generalizations in the other in the other way this is a conventional and the other is a conventional decision it is not a generalization generalization is an empirical empirical procedure and the decision is a linguistic procedure and the empirical systematic non epistemic under determination we have no other way to formulate reality is restricted now by holistic consideration a physical theory is by so much the more true as it puts in evidence more true relations was by fine too now Poincare's big dissolution Poincare's model of explanation found that in a minimum of well-confirmed hypothesis directed by means of fictions and from which all meaningful proposition can be deduced is called into questions by Maxwell's approach the English scientist he says does not try to erect a definitive well arranged building this is Poincare should be well arranged all is philosophically he was a philosopher he seems to rise rather a large number of professional and independent constructions between which communication is difficult and sometimes impossible and he says the same thing about Einstein in his letter to Weiss he make a report on Einstein and he says oh pardon he is not attached to the classic principle and in the presence of a physical problem it takes to envisage all possibilities this is immediately translated into a spirit by the prediction of new phenomena susceptible to a day verified by the experiment I do not want to say that all these predictions resisted by control of the or this control will become possible that is to say this is an approach which is Poincare does not understand it he does not want to, no he understands well but he does not accept his philosophical position he does not accept because for him it is not to do postulates free subtleties it has to do a philosophical classification of subtleties and does not intervene the free subtleties so to say the first principle of relativity I want to come back to this difference in two minutes in order to render the physical principle of relativity with Galilei space time immune to revision Poincare consider this as a conventional principle promoted from law obtained by generalization by a confirmable hypothesis and this law of the Galilei relativity principle is neither postulate to test the hypothesis nor a convention in the sense of an apparent hypothesis characterized by the contrastive empirical underdetermination in date he says if a principle ceases to be factored experiment without contradicting it directly will nevertheless have condemned it that is naturally now a typically pragmatic construction I cannot I cannot because once I have erected it in a principle it cannot be contradicted by experience so it will be just put aside in the poubelle de la science and now it's not clear I think before the death of Poincare that's the principle of relativity with law and covariance was enough well confirmed to be unassailable by experience and to make this principle to make the Galilei principle unfruitful the situation is what there is clear is called transient underdetermination that is theories which are not empirically equivalent but equally or at least reasonably well confirmed so we have the Lorentz covariance and the Galilei covariance well confirmed both but are they equivalent it's not so sure they are not equivalent by our evidence we have to have in the head in the moment so we should wait as there is a better decision in phase of new results and I think this was this was the position of Poincare with respect to Einstein so naturally Poincare understand very well convinced Einstein if you read it you see very well he says this is a new convention but I cannot accept this new convention I mean Kowski in the fourth dimension was present in Poincare's dynamic electron in 1905 so he has the relativity but he was not able to say that this should be now the new theory this was Einstein he said it so conclusion in favor of Poincare as a philosopher in the analytic tradition I would say the actuality of Poincare's the philosophical explication of scientific thought is possible through a philosophical analysis a conventional adoption of objective relation the reality mathematical language structures and experience and experience applies a double part it gives the occasion to be aware of the norm and it is an occasion to test the norm in its role as an aesthetic instrument for the conceptualization of reality you can see it very well so we have this sensation then we have the general group then we have subgroups and these subgroups should be equivalent so the rotation, translation and all you have to think about it the best writing from Poincare most precise is the foundations of geometry in English in the mind in 1898 and then you have to go so to experience and from experience you have to return as always this this move the analysis of this enterprise the only possible tool to access to objective reality and to understand it because Poincare is more to understand mathematics than to prove compared to logical empiricists due to touring tests I think logical tools are not sufficient for the understanding of ourselves thank you very much are there any questions or comments thanks for your conference I wanted to ask you if in your opinion Poincare would accept that theories could be objects of thought and objects of experience because naturally because if you accept theories as objects of experience you would have another way to prove the principle of induction yes naturally this is the main point of Poincare that intuition is not only the intuition of the Bergson intuition or something like the initial one but intuition is learned too this I can show I will just publish a book by Varin which shows this point of Poincare how to formulate intuition that it is scraps this element of the mathematical experience that can be intuition of several level of several level and how to formulate it as intuition and not conceptual this is all the proof you should go in an action theory you should consider take the category theory because there are arrows you should consider the arrows as action and then you can reflect about the arrows in an intuitive way but on arrows you can do this and in a very abstract theory there is nothing to do with sensible but it is in one sense sensible too because you have the structure of sensible science any more questions please first a remark that does not call no answer I think that there is no more inconvenience than an advantage to consider Poincare as a philosopher because it is easy to trap him to put him in contradiction on the other hand I would as Pascal a thinker now the question I have never seen Poincare about hypothesis would specifically refer to this tradition that comes from Newton which is taken back to the 19th century by Fourier and Emperor who says the advantage of making a description of mathematics of nature laws of nature is that we do not need to know if there is behind I do not make a hypothesis Fourier says that in a remarkable way we speak what is the question now what is the argument so it is an argument and historically I do not know Poincare is interested in the notion of hypothesis I have never seen reference to the canonical text of the 19th century French Poincare was not a historian everyone did not know now but he does not care in history as an argument he does not say it's like that because in history in the preface of Fourier everyone knew it but as an argument I try to reconstruct the philosophical argumentation of Poincare which is obviously always involved in mathematics and now I am less interested in the explicit argumentation of Poincare because it is always involved in a philosophical vocabulary we were not a professional philosopher I am going the opposite way that is to say I look what are the mathematical results so I understand them a little bit sometimes and see what are the how to make a philosophical argument that is what he says that is to say I do not have a historical approach to philosophy I wish Poincare his mind on this subject yes just on this subject it did not seem to me that Fourier was well known by Poincare after all the edition by Darbou it is simply Poincare was young and even in this edition the theme of Fourier that you address that is to say there is no need to know what does the heat consist of to study the propagation of the heat and it is more the comments around Fourier than Fourier itself to Fourier his word of order was that of nature is the source of mathematical discoveries and this is the Fourier comment the question on Poincare the work you did is magnificent because you are not content to look at the philosophical writings of Poincare but you looked at the scientific practice the mathematical practice of Poincare and its practice as a physicist you have mentioned several times the commodity and I would like to ask you if there is no evolution in the concept of the commodity according to Poincare between science and hypothesis the value of science and last thought yes yes it becomes more important the pragmatic aspects are reinforced clearly after 1905 1906 it is more conscious because there were discussions on logic with Couture with the philosophers and he is pressed by the king then in the value of science to be more precise and he he says that this commodity and the simplicity he makes reflections on this that's it you have to see Poincare in the value of science you have to make a distinction between the raw and the scientific and normally everyone knows but when you look at it he does not say that he says there is a difference between the eclipse of the moon and what I say I do not see the moon the raw the real raw it will only be the first but that is subjective and already to express that in language it is already a way a way to explain to explain to explain to articulate the world we do not arrive to reality in itself it is always by means of communication from there he understood the role of the language and also in a systematic way it is obviously it is correct you can not see a fact but still today sometimes people say that it is done we can see we can not see a hammer never seen a hammer you can not you see that but that it is a hammer all a conceptual device I think that we should postpone the future discussion let us thank the speaker again