Exactitude in Science

[9]

Chapter 1

On the opposition between the arts and the sciences

1.1 The uncertainty of the concept of science.

In the Spring of 1964, the Press and Radio of France made public a joint declaration between the Dean of the Faculty of Medicine and the Dean of the Faculty of Sciences of the University of Paris. These two great dignitaries of thought were declaring the necessity of future students of medicine to provide themselves with a collection of indispensable mathematical prerequisites. Medicine, henceforth, is a science; no one can claim to be initiated therein if they are not geometers, if they do not possess such basic notions like those of function, logarithm, derivative ... Medical education, they claimed, presupposes an additional level of schooling which passes over the final classes of high-school science and mathematics. And the honourable Deans warned those students interested in medicine and their families of the deplorable waste of time and intelligence that an enrolment in a philosophy class would represent.

By chance, a broadcast journalist then went to ask some students of medicine what it was that they thought of this announcement. It was understood from their responses that the announcement appeared to them a little thoughtless. Knowledge of logarithms could perhaps be useful in medicine, but knowledge of humans and the human condition is essential; it is deplorable, they continued, that it is not taken into account in medical training. The students were a hundred times right to denounce this particularly noxious form of contemporary obscurantism which holds sway amongst the powers of the university just as it does the people on the streets. Overly technical and scientistic obsession is a sign of the times, the repercussions of which are felt in the organisation, or rather the disorganisation, of the education system at each of its levels. The literary disciplines are stricken with suspicion, and efforts are made to channel the greatest number of students to the courses of study in which physics and the acquisition of technical competence predominates. There has never been enough science classes, nor teachers of science, and the inadequacies of our pedagogical equipment [9 - 10] in this regard are the object of severe comments from all conscious and organized citizens.

Science exerts a sort of magistracy around the world. A government worthy of the name has a duty to honour science and to favour scientific research. The mediocre condition of scientists who, poor but as honest as they are brilliant, end up establishing themselves in the United States where they are better paid, is a theme of journalistic folklore in France. The sanction of our decay is the Nobel Prize, so numerous in France in the order of Literature that we are henceforth refused them in the domain of science.

Moreover, the authority recognised in scientists is such that we address ourselves to them whenever it comes to questions that do not concern them any more than anyone of their contemporaries. The moral and political stance of a Langevin or a Joliot-Curie, just as those of an Einstein or an Oppenheimer, are taken to have an exemplary value, as though the fact of being a good calculator or a good experimenter itself conferred a particular aptitude to judge the future of human reality, and to play, therefore, the role that was long ago reserved for the Sages of ancient Greece.

Science, however, has not always had the privileged position that it occupies today—far from it. This privilege is more or less a characteristic phenomenon of the last century of humanity, or perhaps even the last half a century.^*^* Gusdorf was writing in the 1960s. Hence the privileged position of science dates from around the mid nineteenth century. Moreover, the concept “sciences”, or “the sciences”, is not as evident by itself as what might be imagined by the school-child who goes to their science classes or the university student who frequents the Faculty of Sciences. The recourse to the history of Western Culture alone is able to shed light here, and dissipate the established prejudices and misunderstandings which abound.

It can be observed, firstly, that the signification of the word “science” is much more extensive than the epistemological domain of the Faculty of Sciences. These faculties, initially created by Napoleon the First as part of the framework of the Imperial University in 1808 and organised later in 1809, corresponded, moreover, to an unprecedented initiative at the time of their founding; there had previously never been anything like it before. The Napoleonic institutions were designed firstly to carry out the service of examinations and the collection of grades, and secondly for the teaching and learning of certain disciplines. The new institution was one of considerable importance in the history of higher education and in the history of ideas. “For the first time,” notes an historian, “scientists became university professors.”¹^1. CH. H. POUTHAS, “L’Université de Paris depuis la Révolution,” in: Aspects de l’Université de Paris, A. Michel, 1949, p. 216.

In the same stroke, a new division of knowledge would find itself consecrated through an administrative use, the Faculty of Science became the proper place for a certain intellectual discipline, ranking among the Faculty of Arts, the Faculty of Law, the Faculty of Theology, and the Faculty of Medicine. [10 - 11] It was not until a century and a half after the foundation of the Imperial University that its sister faculties began to protest and change their official designations. The existence, today, of both the “Faculty of Arts and Human Sciences”, and the “Faculty of Law and Economic Sciences”,^*^* The Facultés des Lettres et des Sciences humaines and the Facultés de Droit et des Sciences Économiques, respectively. clearly attests to the reclaiming of their identity against the abuse of linguistic trust which conferred on mathematicians, physicists, biologists and others, a monopoly of the scientific mind [l’esprit scientifique].

If things are considered at a certain distance, it appears that the word science which for a long time designated knowledge in general has ended up instead designating only a particular and privileged mode of knowledge. The Dictionary of Littré furnishes us with numerous examples of the classical use of the term, according to which science signified the “knowledge that one has of something”. It would be absurd to imagine, in the original Paradise, the tree of the knowledge of good and evil as a Christmas tree decorated with mathematical equations and chemical formulas.^*^* This comment is based off the fact that in French translations of the book of Genesis the “tree of the knowledge of good and evil” is rendered as “l’arbre de la science du bien et du mal,” which is itself a more direct translation of the Latin Vulgate ligno scientiae boni et mali (Gen 2:17). This is the kind of knowledge that can only be perfected by close reading and meditation, or exercised through the practice of life. Recalling some famous lines of the poet Malherbe:

 		Vouloir ce que Dieu veut, est la seule science
   	 		Qui nous met en repos.

 		To want what God wants, is the only knowledge
   	 		which places us at rest.

There is a “science of the world” which, cited by Littré, d’Alembert defined as “the art of conduct among humans that results in obtaining the greatest advantage possible from their commerce without however deviating from the obligations that the world imposes in that regard.”

But, originating in the epistemological revolution of the seventeenth century, this kind of knowledge is also able to take on a more precise meaning. Authentic science, when established as a concern for method and rigour, is that which is justified in itself, and is coordinated and systematised. In this sense, Littré cites some characteristic texts borrowed from Pascal, in particular a phrase from the Fragment d’un traité du Vide: “All the sciences which are submitted to experience and to reason must be augmented so as to become perfect; the ancients found them only roughly sketched out, and we will leave them to those who will come after us in a more accomplished state than we have received them.” The new mechanistic mind [novel esprit mécaniste] was making itself felt here; science is conceptualised as a search, susceptible of an increasing development in precisely the Baconian perspective of an indefinite progression of knowledge. Thus is announced, in the collective usage of the word, the prospect of the divergence which, through the intermediary of the Napoleonic reform of education, would lead up to the current restriction of the meaning of the word “science”.

Pascal never wrote in French however, and to do so would itself be a sign of the new times in which national languages in France as well as in Italy and England affirmed their capacity to compete with [11 - 12] Latin for the expression of philosophical and scientific ideas. It happens, however, that a serious study of the concept of science must also encompass the traditional language of the scholastics and the university. On this point, the Vocabulaire de la Philosophie of Lalande furnishes a substantial documentation. Lalande notes that the word science, which in Greek was épistèmè, and in Latin scientia, “for a long time presented a ‘deeper meaning’ [sens fort] which has almost disappeared in our time with the development of the natural sciences.” Certain modern authors, the Vocabulaire concludes, “can see in science only a system of permitted notation for the classification and prediction of phenomena.”

These indications show how useful a history of the idea of science would be, the only thing capable of bringing to light the vicissitudes hidden by the apparent permanence of the word. In the present situation, and for the uninitiated, it seems that science still preserves a “deeper meaning,” the only one capable of accrediting its social authority. And yet, in its classical usage, this deeper meaning of science referred to the highest degree of knowledge possible: “Science concerns the necessary and the eternal,” affirmed Aristotle in the Nicomachean Ethics (VI, 3). The Scholastics made science the absolute possession of the Truth. As the supreme Truth in the medieval world was religious order “science,” says Lalande “in theological language, was the most common term to designate the knowledge that God has of the world.”

No knowledge can be more perfect than that which the Creator has of his creation. The thinker finds virtue in the highest intellectual possession of the object of their thought. In the eighteenth century, Christian Wolff, successor of the scholastic tradition, defined science in the preface of his Logic as, “the demonstration of what it is that one affirms, that is to say, the deducing of certain and immutable principles by way of legitimate consequences.”

Only under its traditional meaning does this last definition consecrate in reality a major transformation of the idea of science. Amongst the Scholastics, heirs of Hellenic thought, the dignity of science recognised itself in the value of its object. The highest knowledge was that of supreme reality; it was therefore a part of the ontological and theological order. The human mind was content to receive the revelation of a truth which transcended itself. Modern thought, however, seems to be characterised by a displacement of the idea of science which, more and more, concerns the form and no longer the matter of knowledge. The definition of Christian Wolff emphasises this displacement in the interest of metaphysics towards the theory of knowledge. Since the mechanistic revolution, the attention of theoreticians has been directed towards the procedures of thought, towards the rules and methods of the constitution of thought, independently of the particular domains in which they are called to be worked. It is not by chance that Wolff himself was the inventor of a new ordering of knowledge, in which a “general metaphysics”, which was a science of principles, preceded the particular study of objects of knowledge, [12 - 13] that is to say, theology, cosmology, and psychology. We know that all Kantian thought would later be deployed in the interior of this new framework.

From this moment in history, perfected science would no longer define itself through reference to a divine knowledge, nor by hypotheses inaccessible to human thought. Science disconnected itself from all ontology, and acknowledged in its own account, without scandal, that death of God in epistemology which was one of the essential phenomena of the European eighteenth century. All of this was accomplished well before the celebrated day when Laplace revealed to Bonaparte his system of the world, confirming to him that the explication of reality can be made without resorting to the “hypothesis” of God. The positivism which was affirmed in the eighteenth century only drew out the consequences of the development of experimental science, which was closely associated with the implementation of mathematical expression. Christian Wolff himself recommended the introduction of number and magnitude in psychological research. In 1742 he composed the preface of one of the first German treaties on demography, and underscored the role played by mathematical intelligibility, under the form of the calculus of probabilities, in bringing order and reason to the what appeared to be the most irregular of social phenomena.²^2. Preface to J. P. SÜSSMILCH, Die göttliche Ordnung in den Veränderungen des menschlichen Geschlechts, Berlin, 1742.

Thus, from this moment on, science was defined by the manner of knowing much more than by the object of knowledge. New sciences would be able to appear only insofar as the scientific procedure was applied to unsuspected or neglected areas of knowledge. The character of such a logical ordering would become ingrained, and has remained so up to our times. In the Encyclopedia Britannica (edition 1961), Charles Singer defines science as “a study of judgments capable of obtaining universal assent,” and he clarifies, “universal, that is to say, for those who are capable of understanding the judgements and their foundations.” It appears, therefore, that the word science applies to the entire ensemble of knowledge insofar as it can assume the form of a system whose model is given by an axiomatic structure. Karl Jaspers gives, for his part, an analogous definition: “science is methodical knowledge which, in a binding manner, has a content that is at once certain and universally valid.”³^3. KARL JASPERS and KURT ROSSMANN, Die Idee der Universität, Berlin, Springer, 1961, p. 41.

These definitions express a conception of science which refuse to enclose it within the mental space of mathematics or physics alone. In fact, most theologians have always presented their discipline as a science. For John Henry Newman, for example, theology is “the science of God, that is, the systematic shaping of our truths concerning God; exactly as we have a science of stars which we call astronomy, [13 - 14] or a science of the terrestrial crust which we call geology.”⁴^4. JOHN H. NEWMAN, The Idea of a University, II, 7, Image Books, New York, Doubleday, 1959, p. 96. The Faculty of Theology can therefore claim the privilege of being a Faculty of science. The reformed theologian Karl Barth vigorously supports the claims of his catholic colleague. “No science possesses the exclusive rights over the word ‘science’; and there does not exist any theory of science which could grant or deny this title in the final instance. The conventions which intervene in all general concepts of science cannot claim our unwavering respect. Theology does not therefore have to allow itself to be denied the name of science.”⁵^5. KARL BARTH, Dogmatique, French translation, t. I, 1, Genève, Labor et Fides, 1953, p. 8-9.

And the author of Dogmatique clarifies: “When theology is made to be called a science, and gives itself as such, it affirms three things: (1) That it is, as in all other sciences, a human effort for grasping a definite object of knowledge. (2) That it follows, as in all other sciences, a precise and logical method. (3) That it is, as in all other sciences, capable of justifying this method in its own eyes and in the eyes of anyone (provided they possess a mind capable of applying itself to grasping this object and of following this method).”⁶^6. KARL BARTH, Dogmatique, French translation, t. I, 1, Genève, Labor et Fides, 1953, p. 6.

Nothing objectionable can be found in the affirmations of the theologian, even if they appear somewhat contrary to passively accepted mental habits. What designates science is the search for an objective intelligibility, capable of gaining the assent of all minds without prejudice. And so, it is impossible to claim that the Faculty of Sciences is the exclusive place where such forms of knowledge can be acquired. The Faculties of Napoleon were interested only in a very specific group of disciplines, yet their number since then has multiplied and does not cease expanding. At the beginning of the nineteenth century, for example, traditional natural history, both descriptive and empirical, had to make room for the new idea of a natural science, characterised by the appearance of the word biology, this natural science has not ceased multiplying into individual sub-disciplines even today. At the same time, however, Western culture came to attach an ever-greater importance to a new form of knowledge, which had been designated from the eighteenth century on by such expressions as the “moral sciences” or the “moral and political sciences”, and which later would be called les sciences sociales in France but Geisteswissenschaften in Germany. These human sciences fell outside the purview of the Faculty of Sciences at the University of Paris, even though they claimed a name which nobody then seemed to seriously consider disputing. [14 - 15]

These remarks suffice to make it clear that the concept of science is not so evident by itself. It would be absurd to project into the past the present meaning of the word, which is not at all so certain, just as it is absurd to imagine that science has always had a place of honour and a decisive importance in the ensemble of culture which it is generally recognised to have today. The idea of science is a historical variable. In the eyes of the historian, this is the name that from age to age was applied to a mode of knowledge, characterised by a system of discursive intelligibility. Astrology and alchemy, which cannot today lay claim to the dignity of science, were for a very long time recognised and practiced as such. According to the times, certain disciplines have, in this sense, taken on an exemplary value. Theology, which now must protest in order to safeguard its qualification, once had in the Middle Ages an incontestable reign over all the sciences. In the present moment, this pre-eminence seems to instead accrue to mathematics and experimental physics. Similarly, the idea of science once involved an unveiling of essences; under the pressure of inductive methodologies and positivism, it has now turned away from this towards the ordering of phenomena. Physicalist philosophy, which extends the neo-positivism of the Vienna Circle, corresponds to a systematic extrapolation of the methodology of the experimental sciences; the only affirmations which have any real meaning are those corresponding to protocols of experience, capable of verification according to the ways and means of the laboratory. In the eyes of the most recent supporters of scientism, the formulas of the theologian or metaphysician have no more validity than those of the poet.

These contradictory claims attest to the extreme difficulty of finding a definition of science that satisfies at the same time the mathematician and archaeologist, the historian and the jurist, the doctor or the theologian, who all claim to be considered learned and scholarly [savants] without any restriction. If one abstracts from all presuppositions, one is obliged to admit that the existence of “science” represents that there is a commonality between all the disciplines which present themselves as such, that is to say, a certain attitude of humanity in regard to the universe. Science corresponds to a perspective on reality, which, for example, is not that of the faithful in the church, the worker in the factory, the artist in their workshop, or the everyday person on the street. The scientist searches for an objective and intelligible knowledge, according to the paths of discursive communication. A scientific procedure must take account of each of its steps in accordance with specifications strictly defined at the start, and, thanks to procedures founded in reason, universally controllable.

If one keeps to this very general definition, which seems the only one outside of all bias, it appears that the division of intellectual work, consecrated in France through the organisation of the Imperial University, has caused a very regrettable ambiguity to prevail. It was originally the university, in its unity, which was the proper place [15 - 16] of science, hence, moreover, the medieval language gave the university a meaning according to which the universitas magistrorum et scholarium was at the same time universitas scientarum.^*^*"combination of teacher and student" and "combination of knowledge" respectively. The dichotomy introduced by Napoleon had never existed in British universities; and, for all of the nineteenth century, the Faculty of Philosophy in Germany, brought together the forms of education which had found themselves separated in France, and which had been split between the faculties of “Arts” and the “Sciences”. It is not here a mere question of words or of administrative convenience. It was the very destiny of thought which had found itself engaged in this disjunction.

In other words, the present meaning of the word “Sciences” is strongly marked by an opposition, passed on to it from our historical intellectual climate, between the Sciences and the Arts. The Vocabulaire of Lalande takes note of this nuance, and deplores it in judicious terms. The “sciences” he writes, “designate the disciplines of mathematics, astronomy, physics, chemistry, and all the so-called natural sciences, through opposition to the Arts (and to philosophy considered as discipline within the arts) as well as to Law and Medicine. This opposition which was consecrated in France by the organisation of the university faculties, does not appear to rest on theoretically justifiable reasons.” And Lalande gives an account from the great mind of Louis Couturat who, commenting on the edition of the complete works of Leibniz which had classified his opera philosophica and the opera mathematica in separate sections, said: “The absurd and deplorable schism between the arts and the sciences, compromises not only the future of philosophy; in isolating it from scientific speculations where it has always taken root, it falsifies its history and makes its past unintelligible.”⁷^7. LOUIS COUTURAT, La Logique de Leibniz, Alcan, 1901, Preface, p. viii.

This fracture between the arts and the sciences dominates all contemporary culture. All of our pedagogical system is built on this alternative, considered to be exclusive, between incompatible vocations. It is important, therefore, to bring to light the fact that this irreducibility, quite far from being well-founded in the nature of things, is only a phenomenon of recent date, and is most certainly pernicious to our health.

The Dictionary of Littré lists in the article for the French word lettre, twenty significations, of which the first is “each character of the alphabet.” The twentieth, which in the plural, les lettres, agrees with the English word for the arts, designates “knowledge that is produced from the study of books.” This last meaning is the one that interests us; it corresponds, in sum, to the very general idea of a culture which can be acquired by reading and interpreting. In the classical languages, a man “without letters” was someone who had not received the usual school and university education. Littré cites a passage from l’Eloge de Hartsoeker, by Bernard Le Bovier de Fontenelle, according to which “Huddle, a great mathematician, once said that it was astonishing that such a discovery had escaped the attention of all those who were [16 - 17] geometers and philosophers, and had been reserved instead for a man without letters such as Leeuwenhoek.” Leeuwenhoek, of course, was that common Dutch cloth-merchant who, without any previous education, had put the microscope to systematic use in the investigation of natural objects. This autodidact had the ability therefore to make many careful observation, accumulating a great amount of essential data for physics, botany, and biology.

As such, at the beginning of the seventeenth century, the word “arts” still retained without restriction the entire domain of knowledge. This global sense of the word is clearly shown by the famous autobiography of René Descartes, which constitutes the first part of the Discours de la Méthode. “I have been nourished on the arts since my infancy; and I had an extreme desire to learn all those disciplines which were able to persuade me that, by such means I could acquire a clear and certain knowledge of all that is useful in life.” The context shows that Descartes meant by this the complete program of the College de la Flèche, that is to say, “all those courses of study at the end of which one is usually accustomed of being received to the rank of doctor.”⁸^8. RENÉ DESCARTES, Discourse de la Méthode I, edited by Gilson, Vrin, 1930, p. 4. A more detailed examination follows, which lists, in no particular order, eloquence, poetry, mathematics, theology, “jurisprudence, medicine, and the other sciences.”⁹^9. ibid., p. 4. In fact, in this passage, it even seems that in the eyes of Descartes the words arts and sciences are equivalents, since he writes that “not being content with the sciences that were taught to us, I read through all the books which were able to fall between my hands, especially those which were esteemed the most curious and the most rare.”¹⁰^10. ibid., p. 10.

The commentary of Gilson on this particular passage interprets firstly the word “arts” as designating the litierae humaniores, or, what is called in French, and in English, the humanities. In reference to the Ratio Siudiorum of the Jesuits, Gilson then observes that “the word therefore designates grammar, history, poetry, and rhetoric.”¹¹^11. ibid., p. 101. But on the same page of his commentary and still concerning the passage in question, Gilson emphasises that “it is not at all a question of science in the text of Descartes itself, but of the arts. However, this expression designates, as we have seen, firstly the humanities; then, during the last three years, the sciences in the scholastic sense of the word.”¹²^12. ibid., p. 101. Even this hesitation of Gilson is significant. At the beginning of the seventeenth century, the pedagogical humanism of the Jesuits perpetuated a reviewed and corrected scholastic schema. And the word “arts” was applied indifferently to the totality of their program of studies. But it could have already been applied in a particular manner to only a part of their program. Regardless, in this last case, we will prefer to speak of the “humanistic arts” [lettres d’humanité], or even [17 - 18] “literature” [belles lettres], where today we would speak of the arts simply in opposition to the sciences. In 1683, Father Bernard Lamy, of the Oratorie, published his Entretiens sur les Sciences, “in which, in addition to the method of studying, one learns how one must use the sciences so as to make the mind just and the heart right, and so as to make oneself useful to the Church.” This celebrated work, twelve times re-edited in eighty years, treats, under the name of sciences, all the disciplines which can be objects of teaching and learning. A century after the age when Descartes completed his studies at La Flèche, Fontenelle, in the passage on Leeeuwnhoek, still maintained the general meaning of the word “arts.” But already in 1754, Duclos, in a text cited by Littré, observed that “the taste for the humanistic arts, sciences, and the fine arts have imperceptibly increased, and it has come to the point that those who do not have it affect it.”¹³^13. DUCLOS, Considérations sur les Mœurs de ce siècle, 1754, ch. XI. This time, the multiple meanings of the disciplines of the arts found separate meanings, and according to which usage it has since been maintained.

1.2 The role of the sciences in culture.

With the passing of Leeuwenhoek, whose funeral oration was given by Fontenelle in 1723, one can think that the distinction between the arts and the sciences entered into use in the French domain in the course of the second third of the eighteenth century. This fact, which may appear surprising to ill-informed minds, consecrated the deterioration of a one thousand year old tradition, a true displacement of the centre of gravity of Western culture.

The origins of this culture go back to classical antiquity. Its educational program was defined in a precise manner through the perspective opened by sophist educators, the first affirmers of the function of education, and intellectuals who today are unjustly discredited by the accusations carried against their fellow members by the most illustrious of them, Socrates. The humanism of the Sophists developed throughout the Hellenistic age and all along the millennium of antiquity, right up to Saint Augustine and beyond. Their systems and methods of education and learning gravitated around a common program, which the Latin masters received without the ruptures of their Greek predecessors. This educational program corresponded to the pedagogical theme of the enkuklios paideia, which is poorly transcribed by the modern expression encyclopaedia. It concerned, in fact, not an accumulation of different kinds of knowledge, distinct and incompatible amongst themselves, but a panorama of knowledge and culture, both general, systematic, and harmonious. The Romans rendered enkuklios paideia as orbis doctrinae: for the Ancients, the form of a circle was always a perfect form and a symbol of Divinity.

General culture, organised and codified in the century which preceded the era of Christianity, grouped together the literary disciplines: grammar, rhetoric, dialectic (logic); and the scientific disciplines: arithmetic, [18 - 19] geometry, astronomy, and music. There could be no question, however, of separating these diverse disciplines. Each had its own value in itself; but it acquired a supplementary value by the fact of its conjunction with the other domains of knowledge in a combined order. “The mathematical sciences,” states the historian Henri-Irénée Marrou, “never ceased to figure as the equal of the literary disciplines in the ideal education program of the general culture of the Greeks.”¹⁴^14. H. I. MARROU, Histoire de l’Éducation dans l’Antiquité, éditions du Seuil, 1948, p. 244. Cf. also WERNER JAEGER, Paideia, Berlin 1936. Even from beyond such diverse educational degrees, one can observe that the highest intellectual accomplishments of classical genius presupposed the complete refusal of all disassociation between what we now call the literary order and the scientific order of knowledge. The philosophical works of Plato are entirely pervaded by a type of mathematical exemplarism. Aristotle, a brilliant biologist, still thinks as a biologist when it is a question of understanding either the universe or divinity. One can observe, finally, that the Museum of Alexandria’s extraordinary grouping of institutions of higher culture, was, in the West, the common centre from which all the traditions of literary research (philology, critique) as well as those of scientific research (astronomy, mathematics, etc.) proceeded.

Despite of the vicissitudes of history and the discontinuities in the military, political, and religious order, the intellectual structures of classical antiquity continued throughout the difficult beginnings of the Western Middle Ages and were still asserting themselves in its sumptuous efflorescence. The program of the enkuklios paideia, preserved in its entirety, entered into the schema of the medieval university as the universitas scientiarum. The harmonious cycle of studies required the initiation into the seven liberal arts, so named because the general culture of which they defined the indispensable moments, was the necessary apprenticeship that lead to the liberation of the mind.

In the edifice of the University, such as it was constituted in the thirteenth century, the liberal arts constituted the domain of the Faculty of Arts, considered as the “inferior faculty”, that is to say, as a propaedeutic, a necessary passage for all those who intended to enter into the “superior” faculties, that of Theology, the proper place for higher speculations, and those of Law and Medicine, those faculties which were intended to train the practitioners indispensable to the city. But, even at the superior level, knowledge formed a totality. It was not impossible for the same person to successively travel through the cycles of study of all the faculties, finally consummating within themself the unity of full knowledge and perfect wisdom.

Nevertheless, from the twelfth century onward, the consciousness of an intrinsic diversity within the very program of the liberal arts emerged. The contemporary opposition between the arts and the sciences found perhaps its more distant origin in the scholastic distinction between the two groups of disciplines. On the one side, grammar, rhetoric, [19 - 20] and dialectic (logic), all of them arts of discourse, artes sermocinales,^*^* arts of conversation. comprised the trivium. On the other, the quadrivium brought together arithmetic, music, geometry, and astronomy. Certain theoreticians had an awareness of a characteristic peculiar to each of the two groups. The ensemble of the seven liberal arts was together sometimes called philosophia; but it also happened that this appellation applied only to that of the quadrivium, considered as furnishing the knowledge of things and external realities, while the trivium, which gave mastery to discourse, received the name eloquentia.¹⁵^15. For more details cf. PARÉ, BRUNEY, TREMBLAY, La Renaissance du XIIe siècle, Ottawa, Paris, Vrin, 1933, p. 195.

We must even give credit to the celebrated school of Chartres for having granted a particular importance to the study of that which today we call the sciences—in the restricted sense of the word. “Of all the schools of the twelfth century, Chartres was the home of the quadrivium, that is, the home for the cycle of arts which, in short, dealt with what we call the more mathematically precise scientific culture.”¹⁶^16. ibid., p. 30. There existed at Chartres, therefore, a premier Faculty of Sciences, even before the time of the universities, before the time, moreover, when the reputation of Chartres would no longer be more than a memory. But we must not let ourselves be taken by appearances. Christian “science” was of Platonic inspiration; it was nourished on the metaphysical and mystical speculations of Plato’s Timaeus, which were blended together with Christian theology. There was no similarity at all with our desacralized and autonomous sciences which are of axiomatic or experimental form. For the middle ages in its entirety, the autonomy of any kind of epistemological territory was out of the question. The same procedures of scholastic thought—where the rites of disputation and the commentary of texts predominated, and where one did not cease to gloss and improve the works of incontestable authorities—hardly permit speaking of the scientific mind in the same sense in which it is used for the eighteenth century without risk of a grave anachronism. One could glorify such-and-such a mathematician or physician of the Middle Ages only by arbitrarily isolating certain passages of their works, and by abstracting it from the immense theologico-metaphysical context from which those texts were inextricably unified.

The Renaissance emerged as a reinvention of human values, aroused by a radical transformation of educational programs and methods of study. This mutation of the pedagogical ideal was closely linked to that which was called the “restoration of literature”, that is to say, the return to the sources of Western culture such as it was presented in the texts preserved from classical antiquity. The phenomenon of renaissance par excellence corresponded to the inspiration linked to the rediscovery of the ancient spiritual World at the very moment when new maritime and colonial Worlds were opening themselves up to the adventurers of power, gold, and faith. A large [20 - 21] number of the great ancient texts had been lost, and, moreover, the entirety of medieval culture had deployed itself in the form of commentaries on Aristotle and Plato. But the Renaissance denounced scholasticism as a flourishing of abusive superstructures; they claimed instead to follow philology, which was the study and the honouring of ancient texts such as they were in themselves, both in their letter and spirit. Medieval knowledge had incorporated all the ancient elements of thought into Christian revelation without concern for the incoherence it created; henceforth, it would constitute a sort of profane revelation, worthy too of the highest reverence, and which the labour of scholars would never cease to increase in its extent and in its depth.

The phenomenon of renaissance is situated, therefore, in essence, in the order of the human arts, or the humanities. It is interested only secondarily in our “scientific” disciplines. The science par excellence was that of philology which, thanks to the knowledge of classical Latin, Greek, and Hebrew, allowed access to a treasure of new cultural value through the meticulous study of the vocabulary, grammar, customs, and institutions of Antiquity. Even insofar as the educational program of the liberal arts was only a reprisal of the enkuklios paideia, the traditional framework remained valid for the new times, under the sole reserve of a systematic appeal to ancient texts, and the dismissal of scholastic rituals that were replaced by a contemporary methodology. The ratio studiorum of the Jesuits, which systematised at the end of the sixteenth century the practical pedagogy used in the colleges of the Society of the Friends of Jesus, had already recognised the course of study of grammar and the humanities which would be perpetuated in French teaching and learning right up to the edge of the twentieth century. Johannes Sturm, who, at the request of the municipal authorities, created in 1538 the Gymnase or High School of Strasbourg, cradle of the future University of Strasbourg, summarised the intention of his enterprise with the motto sapiens et eloquens pietas, which replaced the formula of the Latin rhetoricians who had set out to form their students under the model of the vir bonus dicendi peritus. Christian piety had come to impregnate or reward a liberal and rhetorical education; and after having served for two thousand years as the regulating principle for studies in the West, it has since been effaced, without being substituted with another prototype so as to replace the void now present in modern pedagogy.

These few indications suffice to illustrate the preponderance of literary meaning in the humanist culture of the Renaissance. The most representative individuals of that time are the great Italian men of letters, an Erasmus, a Guillaume Budé, whose interests were generally quite foreign to the exact sciences. Medieval culture had been deployed in the order of scholasticism, that is, the order of spoken disputation. Renaissance culture was a written culture, linked to the appearance of printing, and centred under the interpretation of ancient texts. The study of poets and orators, of historians, philosophers and Antiquity, sometimes completed by the study of sacred texts, was called for in the first place; the rigorous sciences, which [21 - 22] although they had appeared in the program of the enkuklios paideia, remained in second place. In his De Studiis et Litteris, the great humanist Leonardo Bruni declared that many domains of knowledge do not merit the same attention. There are disciplines in which it would be little-honourable to be completely ignorant; but for which it would be vain and inglorious to pretend to have climbed to their summits. One would waste one’s time attempting to unravel all their subtleties. So it was with geometry, arithmetic, and even astrology.¹⁷^17. LEONARDO BRUNI ARETINO, “De Studiis et Litteris” (1422-1429), in Humanistische Schriften, published by Hans Baron, Leipzig, Teubner, 1928, p. 11.

Up to the end of the Ancien Régime, the teaching of schools would remain, with rare exceptions, faithful to these principles. It was study and the practice of Latin that occupied the majority of a student’s time. Our sciences hardly had any place in the successive classes of grammar, humanity, rhetoric, and philosophy. Elements of geometry intervened only in the final classes; while physics and cosmology were the subject of a few lectures of the professor of philosophy, who would perpetuate in Latin the most traditional of views. The literary trivium concentrated the near-totality of pedagogical attention, to the detriment of the scientific quadrivium. It would be such almost everywhere in Europe, and for example at the University of Aberdeen, where the Scottish thinker Thomas Reid taught philosophy from 1752 to 1763. “The burden that Reid had to carry as professor of philosophy,” writes Victor Cousin, “was enormous. In the college of the University of Aberdeen, as formerly in those of the University of Paris, the course of philosophy included mathematics, physics, and philosophy proper so-called today, with all its different parts.”¹⁸^18. VICTOR COUSIN, Philosophie Ecossaise, 4th edition, 1864, p. 245.

But, in the eighteenth century, the persistent indifference of the traditional university in regard to the exact sciences was the expression of a sort of pedagogical sclerosis, since modern mathematics, experi¬mental physics, and natural history had already been firmly established. In the fifteenth and sixteenth centuries, however, these disciplines still found themselves in a nascent state. And yet, they had already acquired a certain awareness of themselves, for the great en¬terprise of the discovery of the earth could not have been possible without the implementation not only of new technical equipment, but of an appropriate set of mental tools: geography, astronomy, cartography constituted the essential elements of the art of navigation. Economic expansion, the first capitalist financier, are both equally tied up in the implementation of accounting techniques and rigorous planning. Thus a new mental space was affirmed, which was an experimental space, attested by the great anatomists and the contemporary naturalists. Henri the Navigator and Christopher Columbus, Copernicus, Vesalius, Mercator, Gesner, were all, in their diverse works, the proponents of that new affinity with the world, which resolutely confronted reality so as to conquer it through exact knowledge and action.[22 - 23]

At the juncture of the Renaissance with modern times, Francis Bacon would be the prophet of this dextrous knowledge of traditional passivities, devoted to the possession of the exterior world. But before him, the French contemporary of philological humanism, Pierre de la Ramée (1515-1572), had attested to the necessity of giving to the exact sciences that place which is usually refused them in studies. Ramus was a great, generally misunderstood figure of the University of Paris. His entire life was a fight for the renewal and the modernisation of knowledge. According to a recent historian, it is he who “has the honour of not having hesitated to attribute to mathematics the same role in the preparation of the mind as that which the other humanities had already accorded to ‘eloquence.’ In the works of Ramus, we see accomplished the transition which drove philological and literary humanism to the mathematical and natural sciences of the Renaissance.”¹⁹^19. R. HOOYKAS, Humanisme, Science et Réforme : Pierre de la Ramée, Leyde, Brill, 1958, p. 30 ; see also CH. WADDINTON, Ramus, 1855.

The enterprise of Ramus was deployed firstly on the theoretical plane; he published numerous works of mathematics and physics, whose reeditions would perpetuate his influence well after his death. He appeared as one of the pioneers of algebra, and, in the words of a specialist, “his arithmetic and geometry are truly scientific.”²⁰^20. J. O. FLECKENSTEIN, “Petrus Ramus et l’Humanisme bâlois”, in La Science au XVIe siècle, Hermann, 1960, p. 121. But his ambition was greater, because Ramus was first of all a fierce adversary of the pseudo-Aristotelianism of degenerate Scholasticism. He tried hard to bring out the principles of a new logic, that which presupposed a reform of understanding, that is, a reform of teaching and learning, extended to all areas of knowledge, including even botany and medicine. He tirelessly insisted for the importance of technical procedures. Science, he conceived, was that which had an end of concrete application in the workshops of artisans and the boutiques of merchants. The mindset of empiricism and experimental rationalism which, through the intermediary of Bacon, would be transmitted to the encyclopaedists of France, was here already announced. In his 1562 project of university reform, Ramus called for the creation of the teaching and learning of both mathematics and physics in the Faculty of Arts. From 1531, before hostilities with the universities, François I had instituted a post of royal lecturer in mathematics which was attributed to Oronce Finé; without doubt the first master of this discipline in France. This initiative from on high did not have many followers, and Ramus took it upon himself to combat all those who resisted it—all of who, moreover, would end up getting the better of him, since Ramus would be killed during the massacre of Saint Bartholomew for his views on reform.

But the case of Ramus is exemplary insofar as that great spirit which dominated his time remained a spirit of his time. While one of his commentators observed that “Ramus represents the [23 - 24] high point of the transition from the philological Renaissance to the mathematical Renaissance,”²¹^21. ibid., p. 20. the formula risks creating an illusion. Because the mathematical Renaissance was not distinct from the philological Renaissance. The mathematical Renaissance was a philological Renaissance, what the same historian recognised implicitly in praising Ramus for being “the master of mathematical erudition of his time.”²²^22. ibid., p. 20. Ramist mathematics was closely associated with erudition, that is to say, it was presented both as the celebration and the commentary of the great scientific texts of classical Antiquity. Thought had not yet developed to take leave of the foundations which it possessed; it still recognised the authority of former masters.

The anti-Aristotelian Ramus developed his physics in the margins of Aristotle. For him, as for Aristotle, physics was a philosophy of nature. In 1566, at the occasion of a nomination to the chair of mathematics at the Collège Royal, Ramus rose up violently against the candidature of his colleague and enemy Charpentier because he did not know Greek. It was necessary, Ramus protested, that “the professor of mathematics, especially the professor royal, have formerly studied and practiced all the arts of the Latins and Greeks, both rhetoric and logic; not the vain logic of sophists, but a logic which is solid and practical.” Indeed, a mastery of mathematics presupposed a philological education, so that the professor would be able “not only to interpret, but even correct and improve upon the works of Euclid, Archimedes, Ptolemy, and all the other princes and heroes of mathematical sciences.”²³^23. “Petri Rami actio secunda pro regia mathematicae professionis cathedra”, 1566, in P. Rami and A. Talaei Collectaneae, p. 541.

As such, the most resolutely modern of the great minds of the sixteenth century could envision the future of science only through the perspective of the Renaissance of the arts. Ramus himself taught both the literary trivium and the scientific quadrivium alternately, without the least awareness of a possible separation in the unity of knowledge. And so, when Copernicus opened the way to a transformation of the image of the world, it was not done according to the ways and the means of positive observation and experimentation; it proceeded from the meditation of ancient authors who had defended the theses of heliocentrism, and Copernicus’ work is replete with a kind of solar mysticism inspired by Neoplatonism.

The line of demarcation beyond which autonomous scientific disciplines were affirmed, independent of literary studies, and if necessary hostile to them, is situated at the beginning of the seventeenth century. For Ramus, killed in 1572, the cause of mathematics was bound together by that of philology. Descartes, born in 1596, had been the happy student of the Jesuits of the Counter-Reformation, continuers of classical humanism. But in the eyes of the founder of mathematical analysis (Descartes), [24 - 25] philology and the arts of the trivium were the prerogative of pedants and scholastic disputations.

Better still than Descartes, his elder, Francis Bacon, incarnated the passing of a traditional mentality, dominated by reverence towards the past, to a mentality of opposition and rupture. Free intellectual enterprise made the conquest of the present and the construction of the future its educational program. The men of the West felt sure enough of themselves to venture outside of the Judeo-Hellenic mental space, and the mechanist revolution of the seventeenth century begun to correspond to a new affirmation of man in the universe. Medieval knowledge had centred on God; it found in theology the superior form of Knowledge. The humanism of the Renaissance discovered in humanity the principle of the exultation of man; knowledge was organised according to a new awareness of self, on the basis of aesthetic and moral norms. The sciences of early-modernity, however, asserted the predominance of a relationship to the world which, from then on, was more authoritative and more decisive than the relationship to God or the relationship to oneself. The essential task was to discover in the order of things, a revelation which was more difficult to obtain than that of the order of God or the order of values. Reason ceased to be a gift passively received, and appeared as that which was at stake in a permanent conquest, carried out by a man, finally matured and aware of his responsibilities. Henceforth, scholars were the guardians of this natural and rational “magic”, very different from the supernatural and illusory magic of former times because the “natural magic” was identified, in the words of Bacon, with “operative science”, capable of transforming the world for the benefit of man.

Since this age, a dividing line seems to take shape between the order of the arts and the order of the sciences, in the modern sense of the term. But this dissociation was affirmed only slowly in the realm of pedagogy. More or less everywhere, and especially in France, the system of education refused to take action on the new structure of knowledge, perhaps because all systems of education are in essence conservative. Masters were always behind the actuality of knowledge by a whole spiritual generation, and enforced the perpetuation of an already outdated system.

It could be that this is the reason for which the seventeenth century was the century of the Academies, a new phenomenon in Western culture. Since the fifteenth century, the first societies which this title stemmed from were devoted to philosophical and literary activities, such as the Platonic Academy of Florence, or the Accademia Pontaniana of Naples, both of which were associations of humanists. But the seventeenth century would see the appearance of specialist academies for the service of purely scientific research, which Bacon had sketched an outline of in the form of a utopia in his New Atlantis, his last work published in 1627, in the year which followed his death. Already, during the first thirty years of the century, there existed in Rome the Accademia dei Lincei whose members, on the example of their colleague Galileo, [25 - 26] endeavoured to uncover the secrets of nature. From 1657, and for about ten years after, the disciples of Galileo, patronised by the grand duke of Tuscany, constituted in Florence the Accademia del Cimento, whose research of experimental physics was followed with attention by all the scholars of Europe.

It was in England, and in the Baconian tradition, that the first permanent institution would finally be imposed, the Royal Society of London for the Advancement of the Knowledge of Nature, consecrated in 1662 by a Royal Charter, whose activities concerned the natural, physical, and mathematical sciences as well as their technical applications. Since the development of the Royal Society, which has remained up until our time a privileged space of scientific culture, its gradual constitution has consecrated the appearance of the scientist in the modern sense of the term, by opposition to the medieval clerk and the renaissance man of letters. The scientist, as it was affirmed in the group of British virtuosi, would be illiterate and godless. But the activity of scientists in the domain of mathematics, in the domain of physics and chemistry, from Boyle to Newton, in the domain of natural history, with Ray and Tyson, or in medicine, with Sydenham, have all been decoupled from philological obedience. The new science recognised the external authority only of that rigorous method and facts appropriately ascertained.

In France, the movement of the Academies had commenced quite significantly in 1635 with the foundation of the Académie Française. It was not at all here a question of an Academy of Arts or of Literature, in the humanist sense of the term. The Académie Française^*^* French Academy. affirmed, in Paris, the awareness, which was also expressed elsewhere, the dignity of national languages. Richelieu felt that the French language was an inheritance which had to be managed by way of authority. French, which was not the language of the University, found a new illustration in the Académie, thanks to a powerful backing. As for the sciences, they would still have to wait for a generation so as to enjoy a central institution of communication and of study in the French domain. From the first half of the seventeenth century, there was a small group of scholars in Paris, mathematicians and physicists, a number of whom can be counted Mersenne, Roberval, Gassendi, Pascal, and some others, French counterparts to the English virtuosi, with whom they found a correspondence, thanks to Huygens for example. The vigilance of Colbert would recognise the importance of scientific activity. The creation in 1666 of the Académie Royale des Sciences^*^* Royal Academy of Sciences. officially consecrated the dignity of scientists who, subsidised and honoured by the State, were charged with the permanent mission of the advancement of the sciences and the progress of technology.

France had therefore been endowed by royal will with two distinct academies, one for the sciences and one for literature, in the same way as in the Napoleonic reorganisation, it would be the first nation to possess distinct faculties for the Sciences and the Arts. The Royal Society of London was especially designed for [26 - 27] the enrichment of the sciences of nature; but it had no pretensions in the domain of language. In regard to Germany, it was only after the Treaty of Westphalia (1648), which gave in the end the terrible devastations of the Thirty Years War, that it would know the possibility of cultural activity. Among the first projects, the most curious was one that was developed by the grand Elector Frederic Guillaume of Brandebourg in 1667. Inspired by his minister, the great jurist Pufendorf, he made the plan of a “university of the people for the sciences and the arts”, a sort of international and interfaith learned society, open to all friends of Truth and all who were persecuted. A true learned city, another New Atlantis, had to be created in Brandebourg, where higher education and research in all the domains of science and technology were combined together. The project would never be realised however, but, under the reign of the Elector Frederic, first king of Prussia, the unrelenting activity of Leibniz would allow for a less ambitious creation. In 1700 the Royal Society of Sciences was founded, that Academy of Berlin which would play an important role in the intellectual life of the eighteenth century. The name “Sciences”, however, covered at the same time the arts, philosophy, and the disciplines which are properly scientific. In the realm of Hanover, the Royal Society of Sciences of Göttingen, founded in 1751, would have a similar range of many different activities. Here the word “Sciences” still designates the totality of knowledge.

From the seventeenth century, the creation of academies was complemented by that of the first scientific journals; the same year 1665 saw the appearance in France of the Journal des Savants and in England the Philosophical Transactions. And other institutions complemented the Academies: the observatory of Paris was founded in 1667, one in Greenwich, England in 1675. All these facts attest to the new political, administrative, and social landscape of the exact sciences. One can speak of a true event of scientific knowledge, consecrated in addition by the appearance of a literature of scientific popularisation. Fontenelle, who realised on his account the personal union of the Académie des Sciences and the Académie Française, gave in 1686 the first masterpiece of the new genre with his Entretiens sur la Pluralité des Mondes.

The central fact is that this incident in the history of thought, as well as the works which were its expression, were situated outside of the universities, which, in France at least, remained in a hostile stance towards it. In England then in Holland, chairs were created for the diffusion of new disciplines. But almost everywhere the teaching and learning of schools, which educated the intellectual elite, remained faithful to the norms of traditional humanism. Not only were mathematics and physics limited to the smallest portion, but the national language, if it gained any consideration, only came after Latin, which kept its place of prominence. The natural sciences were not taken into account any more that of national history.

For this reason, throughout the eighteenth century, the sentiment of discordance [27 - 28] between the real situation of knowledge, where the sciences occupied a greater and greater importance, and the official order of culture, which perpetuated the out-dated predominance of literature, grew. This discrepancy aroused the justified reaction of the best minds, who were thus lead to emphasise the opposition, and perhaps the incompatibility, between literary education, useless and regressive, and scientific education, the only one opened to reality and mastery of the future.

In the century-old polemic between the arts and the “sciences,” it was the sciences which took the offensive so as to force the recognition of its misunderstood validity. One of the major aspects of “experimental philosophy,” for which Francis Bacon was made the prophet, corresponded to the demand of a total reformation of teaching and learning so as to give prominence to those disciplines which would give to man a mastery over reality. Similarly, when he recounted his studies, the Descartes of the Discours de la Méthode declared for himself an overhaul of educational programs in which the master disciplines of the mechanistic age found themselves in a dominant position. The same idea of mechanism supposed an archetype of knowledge borrowed from the material world of technical intelligibility, and no longer from spiritual aesthetics.

Such was the meaning of the debate between Ancients and Moderns which had fascinated the enlightened opinion of Charles Perrault in the last years of the seventeenth century. Perrault opened the debate by the reading of his poem, Le Siècle de Louis-le-Grand, to the Académie Française in January 1687, which had begun to be published in the year following his Parallèle des Anciens et des Modernes. It is here, that the new mind took its distance from the past. It was the scientific mind. “Things have quite changed face,” observed Perrault. “The prideful desire to appear knowledgeable through quotations has given way to the wise desire to actually be knowledgeable through knowledge of nature.”²⁴^24. CHARLES PERRAULT, Parallèle des Anciens et des Modernes en ce qui concerne les Arts et les Sciences, new edition, Amsterdam, 1693, I, p. 65. Nature “has revealed an infinite number of mysteries which it has kept hidden from the wiser ancients. It is necessary only to read the Journals of France and England and to cast one’s eyes on the beautiful works of the Academies of these two great realms to be convinced that, in the past twenty or thirty years, there have been made more discoveries in the science of natural things than in all the extent of learned Antiquity.”²⁵^25. ibid., p. 66. Charles Perrault, the author of Contes, speaks here of the knowledge of causes. His brother Claude, a doctor and architect, presided over the publication of Mémoires pour servir à l’Histoire des Animaux, for the Académie des Sciences (1671-1676). This magnificent collection is one of the premier French monuments of natural history and of comparative anatomy.

The development of European culture in the eighteenth century would agree with the defenders of the Moderns who, having won in the domain of living knowledge, did not cease to demand a transference in the order of the system of teaching and learning, which had always been dominated by the tenants of traditional literature. Such was the opinion of Leibniz according to whom the pedagogical priority, hitherto recognised in poetry, scholasticism, and logic, must pass to the sciences of reality, to [28 - 29] mathematics, history, physics and geography. The polemic on this theme would continue to be renewed right up to our times, repeating tirelessly the same arguments. Without a doubt we must see in this dispute the principal source of the opposition recognised today between the Sciences and the Arts.

Voltaire, a fine mind if there ever was one, but resolutely modern, made the apology for scientific knowledge, incarnated in his eyes by Isaac Newton, for whose works he had been the principal introducer and presenter in France. Even in the domain of metaphysics, the only criterion was “experimental philosophy” in the manner of the English: “When we do not have the ability to help ourselves with the compass of mathematics nor the torch of experience and physics, it is certain that we do not have the ability to make a single step.”²⁶^25. VOLTAIRE, Traité de Métaphysique, ch. III, 1734; Œuvres, Édition Lahure, vol. XVII, p. 130. Voltairean scientism would go so far as to humiliate the Académie Française, the academy of rhetoric, in front of the Académie des Sciences, where one supposedly worked for all of humanity. “While it is a law in the Académie Française to print all these discourses by which it alone is known, it should be a law of not printing them.”²⁷^27. Lettres philosophique, lettre 24 : Sur les Académies (1734) : Œuvres, édition citée, L. XVII, p. 116. On the contrary, added Voltaire, “the Académie des Sciences, in its more difficult and more sensibly useful research, embraces the knowledge of nature and the perfection of the arts. It is to be believed that studies so profound and so followed by calculations so exact, of discoveries so fine, of views so grand, will finally produce something which will serve the good of the universe …”²⁸^28. ibid., p. 117.

One can date to the second third of the eighteenth century the generalisation in France of an intellectual sensibility in enlightened opinion which opposed the arts and the sciences; a sensibility which accorded to the sciences a priority which teaching and learning had refused them. The arts corresponded to a waste of time and intelligence; the sciences, thanks to their technical applications, allowed for the improvement of the conditions of existence of man on earth. The sciences and the technical arts would pair together, but the arts proper would continue to lose their prestige. The famous question set as a competition in 1749 by the Académie de Dijon: If the restoration of the sciences and the technical arts has contributed to corrupt or to purify our times, consecrated the decisive importance of both pure and applied science in civilisation. The Encyclopédie, although a “work of a society of men of letters,” was presented as an “orderly dictionary of the sciences, the technical arts, and the professions.” From 1751 onwards, the diffusion of this great work would realise a decisive piece of propaganda in favour of the new tendencies.

In the end, the great pedagogical reflection of the eighteenth century would place the emphasis on the sciences; and the theoreticians insisted on it because this importance remained misunderstood in the institutions. The arts appeared to have partial links with the ancient intellectual, political, and social regime. [30] They would figure, therefore, in the many victims of the Revolution. Among the significant accounts of this period of interesting intellectual fermentation, one can cite those of Condorcet, who expressed perfectly the state of mind of the first wave of the revolution, before himself being submerged by the second.

Condorcet passed on to the nineteenth century, the century of Comte and Jules Ferry, the tradition of the Encyclopédie. In his eyes, the pedagogical priority of the sciences was called for in a manner all the more decisive because they brought about an intellectual formation thanks to which traditional values found themselves definitively eliminated. The class of physics would allow for the cleansing of the void of outdated meanings. Of all the advantages of the sciences, Condorcet felt, “the most important perhaps was to have the prejudices of some sort of human intelligence—forced to submit to false directions which absurd belief had imprinted with the terrors of superstition and the fear of tyranny and passed down to childhood by each generation—destroyed and rectified. All political and moral errors have as their foundation philosophical errors, which themselves are linked to the errors of physics. There does not exist either a religious system, or a supernatural extravagance which cannot be founded on the ignorance of the laws of nature. The inventors and defenders of these absurdities could not foresee the successive improvement of the human mind … The progress of physical knowledge is still all the more often fatal to these errors than not, it destroys them without appearing to attack them by responding to those who persist in defending these errors for their ridiculous debasement of ignorance.”²⁹^29. CONDORCET, Esquisse d’un Tableau historique des progrès de l’esprit humain, 9th Epoque, Œuvres, Garat et Cabanis, 1801, p. 300-301.

In the perspective of the great revolutionary overture, the scientific disciplines seemed therefore to offer the most appropriate means for “écraser l’infâme”,^*^* To crush the despicable. according to the watchword of Voltaire. This was why Condorcet would be one of the education experts for the first Assembly of the Revolution. To the traditional primacy of Latin in an irrational system, destined above all for the formation of “theologians and preachers”, Condorcet opposed the primacy of scientific disciplines. “One can without doubt acquire justice, method, a sane and profound logic … through the application of literature and grammar, history, politics, philosophy in general. But how much more easily does one acquire all of these virtues through the study of sciences? In addition, this study is within the range of a large number of minds.” The sciences are therefore democratic by vocation. “Those who follow the trends,” Condorcet believed, “see the time approaching when the practical utility of their endeavours will occupy an extent to which one would not have formerly dared to have carried their hopes, where the progress of the physical sciences will produce a happy revolution in the practical arts; and the surest way of accelerating this revolution is to spread this knowledge [30 - 31] throughout all classes of society, to facilitate their means of acquiring them.”³⁰^30. CONDORCET, Rapport et Projet de décret sur l’organisation général de l’Instruction Publique, presented at the Legislative Assembly 20-21 April 1792; cited in JOSEPH FAYET, la Révolution Française et la Science, Marcel Rivière, 1960, p. 361.

Henceforth, before the tribunal of revolutionary knowledge, the arts figured in the position of the accused. All projects gave to the sciences an incontestable pre-eminence, from the central schools which, replacing the ancient Colleges, for the first time counted amongst their ranks professors of the sciences, to the Institut National des Sciences et des Arts,^*^* National Institute for the Sciences and Practical Arts. which was substituted for ancient academies. The National Institute, organised by the law of Public Instruction in the year IV, under the influence of the idéologues for whom the spokesperson was Lakanal, comprised three “classes”. The first, the most numerous, was devoted to the mathematical and physical sciences; the second devoted itself to the moral and political sciences; and the third, finally, brought together literature and the fine arts. This structure made the National Institute into a sort of living extension of the Encylopédie, an encyclopaedia made of humans. The creation of the Conservatory of Practical Arts and Professions, from 1794 to 1799, completed the National Institute in the domain of technology. The École Polytechnique, the Museum, other revolutionary creations which have brilliantly survived up to the present, attest too, in their way, that from this moment on the solicitude of public power is not carried towards literature, but towards scientists and engineers. Without a doubt the Terror destroyed Lavoisier and Condorcet; but the Convention itself before dividing, manifested openly that in its eyes the Republic had a great need for chemists.

The ambiguous genius that Napoleon, the executor of the will, seems to betray in many domains of this Revolution, was also manifested in the intellectual and pedagogical order. Henceforth, the orthodox thinkers of the revolution [bien-pensants] had a tendency to see the sciences as natural allies of the detested Jacobinism. A certain form of propaganda spread the opinion that “all mathematicians are atheists, and all naturalists are materialists.”³¹^31. Cited in GEORGES WEILL, Histoire de l’Enseignement Secondaire en France (1802-1902), Payot, 1921, p. 35. But Napoleonic pragmatism, the prodigious expansion of the Empire, always required more officers, artillery, military and civil engineers, administrators of all types, in the spirit of which the concern for rigorous standards overcame the respect of aesthetic values. The organisation of secondary schools would be inspired by a search for an equilibrium between Latin and mathematics. The sciences took their place, in a definitive manner, in secondary teaching and learning; they also obtained a recognition which had been refused to them heretofore. High government official of teaching and learning, the naturalist Cuvier, recorded in 1807 that “each secondary school has teachers for mathematics, physics, and natural history, in equal numbers as there are for the languages and literature, and it is ordered [31 - 32] that students be equally instructed in the two fields.”³²^32. CUVIER, De la part à faire aux Sciences et aux Lettres dans l’Instruction publique, Moniteur universel, 3 Novembre 1807, reproduced in : Revue Internationale de l’Enseignement, X, 1885, pp. 385-386. This pedagogical revolution was also an epistemological revolution. Despite the inevitable nature of trial and error as well as the modifications which followed, it was here a question of an irreversible phenomenon. There existed from this moment on a teaching and learning professional, and one sees the appearance of a literature of manuals and treatises on the operation of classes concerning diverse scientific disciplines.

These here were all aspects of a renewal of cultural values in the favour of which a new civilisation was announced. The political and social revolution lead to an apparent failure, however, consecrated by the European phenomenon of Restauration. But the industrial revolution which followed cannot be placed in question. Economic and technological necessity condemned, even at the level of institutions, the ancient educational regime, of which the survival appeared from then on inadmissible. The attitude of Cuvier was quite significant: “There was an argument some time ago,” he wrote, “over the pre-eminence of the Sciences and the Arts … it would have been worth as much arguing over the pre-eminence of the Spring and the Autumn or of the sun and the rain. In addition, nobody agreed, either on the meaning of the word pre-eminence, which some people took for utility and others for difficulty, or the meaning of the word arts, under which the partisans of the arts included everything that was not physics and mathematics, and which their adversaries restricted to the art of writing.”³³^33. ibid., p. 380. Cuvier felt that it was here a matter of a false problem, or, rather, an outdated problem: “We always reason as if science excluded literature, or even as though it were possible that a scientist were not literate. An absurd proposition! Because that which is today named a scientist is only a man of letters who, in addition to the languages and the general laws of reasoning, has studied something still more determinate, and the forms of knowledge generally named literature are a necessary condition of all real progress in the Sciences.”³⁴^34. ibid., p. 383.

The baccalaureate in sciences made a timid appearance in the context of the Napoleonic reorganisation, and as an initially little sought after complement of the baccalaureate in arts, the only one that was required by everyone. From 1809 to 1818, the collection of the Faculties of the Sciences conferred 143 bachelor of sciences degrees. But this examination would continue to gain in importance throughout the nineteenth century up until the moment where it would see its full autonomy recognised by the reforms of the Second Empire. In April 1852, Minister Fortoul consecrated this autonomy by a decree, the statement of intention of which was perfectly explicit: “The baccalaureate in sciences will henceforth be the sanction of secondary scientific studies just as the baccalaureate in arts is the sanction of literary studies of the same degree; it is a proof, analogous, but independent of the latter; because if it [32 - 33] is given to some elite individual natures to excel in both the sciences and the arts at the same time, it would be fanciful to want to impose on ordinary minds, which make up the majority, the obligation to juggle both scientific and literary studies.”³⁵^35. Cited in J. B. PIOBETTA, Le Baccalauréat de l’Enseignement secondaire, J. B. Baillière, 1937, p. 392. One will find in this work numerous instances concerning the evolution of the ideas and regulations on the subject which interests us here.

From Cuvier to Fortoul, the evolution is significant. While Cuvier affirmed the necessary unity of the two disciplinary orders, Fortoul legitimated between them an indispensable bodily separation, and also conformed to the Saint-Simonian and technocratic spirit of the Second Empire at its beginning. It is clear that the primacy of the Arts had found itself placed in check; the social prestige of science would not cease to increase. From 1835 moreover, a prize of honour for the Sciences was instituted at the Concours Général, for which the supreme glory had been reserved, since 1747, for rhetoric or Latin.

At the level of secondary education in France, the Revolution and Empire therefore sanctioned the emancipation of the scientific disciplines. The organisation of the Imperial University expressed this pedagogical maturity at the level of higher education. The tradition of the medieval University entrusted the complete teaching and learning of the liberal arts, both literary and scientific, to the Faculty of Arts (sometimes later called the Faculty of Philosophy). This Faculty of Arts, described as an “inferior faculty”, corresponded to our secondary education and was a propaedeutic for higher studies at the same time. Napoleonic reform introduced for the first time a very clear distinction between secondary education, confined to the lycées, or high schools, which were modelled after the Jesuit colleges, and higher teaching and learning, which became available after the baccalaureate, and was situated, at least theoretically, in the Faculties. And yet, the Imperial University constituted the Faculty of Arts and the Faculty of Sciences separately, and thus consecrated at highest level the dissociation between vocations that were considered incompatible. In Paris, the Faculty of Sciences, which very quickly received scientists of a high quality, included at its beginning nine chairs for mathematics, physics, chemistry, and the natural sciences. The Faculty of Arts, which formerly had counted sic chairs, now had eight. The equality of rights between the sciences and the arts therefore found itself recognised at the level of the same number of active professors, with a slight advantage to the sciences. These were favoured moreover by the prestige which the great scientific écoles enjoyed, whereas the arts, at the beginning of the nineteenth century, could count no other place a stronghold outside the Faculty of Arts than the École Normale.

The French Faculties of the nineteenth century were dead faculties; it would be necessary to wait until the Third Republic for the constitution of a higher education worthy of the name to be sketched out. But the juridical schema of the Imperial University, sanctioning the acquisitions [33 - 34] of the French Revolution, gave to France a foresight of the future intellectual culture of Western Europe. The same problems would pose themselves everywhere; the same debates followed shortly in England and in Germany,³⁶^36. Cf. for England, S. J. CURTIS, History of Education in Great Britain, London, University Tutorial Press, reedition, 1961; J. W. ADAMSON, A Short History of Education, Cambridge Univesity Press, 1922; for Germany, FR. PAULSEN, Geschichte des gelchrten Unterrichts auf den deutschen Schulen und Universitäten … Leipzig, Veit Verlag, 1896. and their development would unfold in the direction of modern teaching and learning, which turns away from the classical humanities so as to give a greater and greater importance to the technical and scientific disciplines, to the national language and to the modern languages. The incessant conquests of physics, chemistry, and biology, the prodigious expansion of industry and the growing primacy of mass consumption, all exerted a “propaganda of the deed” to the profit of scientific education. Literary individuals, keepers of knowledge without practical utility, made old-fashioned and nostalgic figures, that is, figures seen as reactionary. The pedagogical polemic put in play the same arguments without distinction of its limits; it opposed in reality two types of mind and two systems of values. Henceforth, in the most diverse domains of thought and action, the sciences passed for being liberal and progressive. The scientific man, in the general rule, was a man of the left, whereas the cause of the arts and literature was the cause of conservatives, those who have a heart on the right on the side of the throne and the altar. This misunderstanding, for it is incontestably one, played an immense role in the evolution of ideas in the nineteenth century, with the unanimous approbation of those who feared the progress of the sciences as well as those who celebrated it.

For a very large section of European opinion, Science and Anti-science were matters of faith. Almost everywhere, scientism mobilised contradictory passions. This political and social myth wholly prevented an awareness of the true problems. Throughout all of Europe and America, scientific congresses, parliamentary assemblies, reviews, courses and conferences, all rang out with contradictory professions of faith. Yet the battlelines between the opposite camps coincided with the line of demarcation between the arts and the sciences.

The history of this debate, which is central for the evolution of European thought, still has not seriously been made; it would without doubt illuminate a great number of contemporary arguments. Despite all the vicissitudes of the time, the great mind of Joseph Ernest Renan was both a religious mind, a thinker too, and a great writer, while at the same time being one of the founders in France of Semitic philology and the history of religions. Renan was fascinated by the “chemical glory” of his friend Berthelot, and saw the salvation and progress of humanity only through the ways and means of the experimental sciences.

Such was already the opinion in 1849 of the young Renan, just out of the [34 - 35] seminary: “It is not an exaggeration to say that science contains the future of humanity, that only science can give to man a knowledge of his destiny and teach him the manner of attaining his end. Up until now it has not been reason which has lead the world; it has been caprice and the passions. A day will come where the enlightened reason gained through experience will make its empire, the only one which is of divine right, and will drive the world no more by chance, but with the clear view of the goal to be attained.”³⁷^37. RENAN, “Réflexions sur l’état des esprits en 1849”, in Questions contemporaines, (1868), Calmann-Lévy, p. 333. The same essay is reproduced in 1890 in the Avenir de la Science, Calmann-Lévy, p. 36. In the middle of the nineteenth century, it was the affirmation of the Ecycopédistes, taken over by Saint-Simonism, which transformed into an apotheosis of science: “To organise humanity scientifically, such is the final word of modern science; such is its audacious, but legitimate, claim …”³⁸^38. ibid., p. 334. Scientific triumphalism persuaded itself that the humanity of tomorrow would enter into the best of scientific worlds without resistance. “Future democracy,” Renan felt, “will feel before scientists the same sentiment that barbarians had felt in regards to the saints of the Merovingian age (…) . People will understand that the progress of positive research is the clearest of all humanity’s acquisitions, and that this acquisition matters before everything else to those whom it liberates and ennobles. A world without science is slavery (…). The world improved by science will be the kingdom of the mind, the reign of the sons of God.”³⁹^39. RENAN, “L’Instruction supérieure en France”, in Questions contemporaines (1868), Calmann-Lévy, p. 71.

This story of the state of minds in the nineteenth century has dispensed with citing others. Science had raised itself to the hight of an eschatological myth; dialogue was no longer possible with the arts, confined to a base pedagogical drudgery and doomed to disappear with the last poet and the last metaphysician. It is true that the hopes placed in the Bonne Nouvelle of science in the nineteenth century will come to know some disillusionment. The chemists who were successors of Liebig and Berthelot would be the ones preparing the asphyxiation gas of the First World War, and the physicists the ones developing the nuclear apocalypse of 1945 and all the years after. Today we can ask ourselves if scientific reason is not, more than anything else, liable to go mad. One of the scientists portrayed by Dürrenmat in his play Physiciens states melancholically that men of science are today too dangerous to find a place anywhere else than in psychiatric hospitals.

In spite of the darkness which has crept over the picture, the unnuanced opposition between the arts and the sciences remains at the centre of pedagogical debate. In countries which have attained a certain economic and technological level as well as in those which have not reached it, the principal concern of leaders is to provide for the job market in engineers and technicians, and all other kinds capable of contributing to the indefinite development of factories, offices, [35 - 36] design studios, and laboratories. The priority accorded to scientific needs is registered in the five-year plans as well as in the construction programs of schools and universities. Men of science and technology appear today as that new aristocracy the coming of which Saint-Simon—apostle of technocracy—saluted in the early nineteenth century. Science furnishes a content for the replacement for morality and the religion of a new age, just as Renan had well understood it to be. The scientist, poor but honest, obscure, misunderstood, then finally triumphant by force of perseverance, is the saint of former times, whose gospel is read in magazines and sermon is heard on radio and television.

The pious chroniclers of the Middle Age had offered to popular devotion the gilded legend of the men of God as a simple and edifying parable. In the sixteenth century, Vasari, thanks to his Lives of the Most Excellent Painters, Sculptures, and Architects, furnished to the aesthetic sensibility of the renaissance man objects of admiration conforming to his new needs. Thanks to the academies and societies of scientists, modern man would see the appearance of a different sort of Lives of Illustrious Men; the eulogies of departed scientists contributed to creating a gilded legend of science, to which, at the end of the eighteenth century, the prudent intelligence of Fontenelle and his literary talent gave their noble arts. The scientist had become an exemplary man; figures like those of Newton, Darwin, Pasteur, or Fleming were offered for the veneration of the masses; today, the Nobel Prize makes scientific disciplines figures of world celebration.

It is a question here of a phenomenon linked to the very structure of contemporary culture, a question on which we must take a stance. As an English historian has written: “The development of the science of nature is the dominant character of Western Society (…). Compared to modern science, capitalism, the nation state, art and literature, Christianity, and democracy, all appear to be regional idiosyncrasies, for which the past is full of vicissitudes, and the future full of a dark uncertainty. Each of these aspects of Western civilisation has carried a contribution towards the development of science, for which their combination was perhaps essential. But one can imagine that science continues to prosper after the disappearance of any one of these elements, or all of them together. In fact, it is this which is happening now. Modern science was the fruit of a form of society which lasted for around four hundred years, and which played a dominant role in universal history. Presently, this form of society finds itself in the process of dissolution; but it seems improbable that science will necessarily disappear with it …”⁴⁰^40. A. RUPERT HALL, The Scientific Revolution, London Longmans Green, 2nd edition, p. 367.

1.3 Science and Scientism.

Science appears therefore to represent a most modern form of hopefulness. And so, one must deplore the fact that the very concept of science remains so imprecise; this word corresponds to a knot of unelucidated values, which one must search for in the origin of the mental attitudes that have been adopted since the mechanist revolution by those who concerned themselves with placing in order knowledge of the material world. “Experimental philosophy” expressed the success of mathematical physics. Observation and calculation, which lend themselves to a mutual application, brought out the reality of a new, intelligible world that made sense of appearances and continued to grow in rigour and scope from Kepler and Galilee up to Newton, Lavoisier, and Laplace. Without a doubt, this prodigious conquest of the universe, reduced to rigorous norms of thought, still forms the principal kernel of signification of the idea of science today. Other disciplines can lay claim to scientific dignity, in the full sense of the term, only insofar as they vouch for their capacity to assume the form of mathematical physics. Only yesterday, logical positivism intended to reduce all human truth, no matter what order it may have been, to the test of experimental verification according to the norms which are imposed in laboratories. Art and religion, affective and everyday life, all of which could not allow themselves be reduced to the obedience of physico-mathematical norms, thus found themselves discredited and in turmoil.

Logical positivism is well within the logic of positivism in general, because positivism represents the philosophical countereffect of the triumphal emergence of experimental knowledge. Fascinated by the extent of its success, human thought devotes itself to a sort of relentless headlong rush. Human experience in general is left to be confused with scientific experience in particular. Its criteria, which have a meaning in certain situations and in view of certain ends, are supposed to be universally valuable. The preponderance of scientific and technological concerns, phenomena of the times, are considered as an eternal truth. Such an attitude, which claims to submit the totality of values to the jurisdiction of scientific Truth, rests on a prior judgement of value, impossible to justify in reason.

The growing preponderance of sciences corresponds to a global modification in the equilibrium of knowledge. Hellenic culture was organised according to the harmony of the cosmos; medieval culture was founded on an affinity with God. Humanist culture of the Renaissance endeavoured to define a regulating idea of the accomplished personality. After the mechanist revolution, however, it was an affinity with the world that would come to overstep the affinity with God and the self. Hence, there is a sort of extraversion characteristic of modern man, in which the major concern [37 - 38] is no longer that of edifying himself in obedience to God or in exulting in such-and-such a value, but that of knowing the reality of the world so as to take possession of it for the profit of human society.

The traditional debate between the sciences and the arts presupposes, therefore, the option of a metaphysical order. The opposition is defined clearly by a quotation of the philosopher Lachelier in the article on Science in Lalande’s Vocabulaire de la Philosophie. “The opposition of the arts and the sciences is fundamentally that of the opposition between human subjectivity and the objectivity of nature. Study given exclusively or even predominantly to the sciences of nature, and to mathematics in particular, could lead one to see in everything only spatiality, reciprocal exteriority, and mechanism; the spirit of these sciences is empiricist and materialist. However, if we want the philosopher to understand what the true foundation of things might be, for example spirit and liberty, it is the moral and interior man which it is necessary to develop. Philosophy is essentially the science of the subject, and is interested—as its object—only in what it can find there in the subject. And so the education of the philosopher is therefore the study of the arts, a study which must be continued for the longest time, a study to which the mind must take and be held firmly in place.”

Lachelier, keeper of French university spiritualism, was the teacher of Bergson, in the works of whom can be found arguments against extroverted intelligence and who situates mind in the captivity of material forms. The opposite of this is Karl Marx, who, when he attempted to perfect a “scientific” socialism, proclaimed the primacy of objective reality and the concerns of technical efficacy. In the perspective of this kind of positivism, subjective preoccupations and values—which are linked together—are only secondary formations, designed to conceal the mechanisms of the order of things.

The question is of knowing whether this opposition is inevitable, and whether this manner of posing the question does not include, in its very origin, a distortion and a falsification of reality. Husserl, at the end of his life, insisted on the aberrant character of the replacement of the real world in the West since the advent of Galilean experimental science. “It is extremely important,” he said, “to observe this replacement, already accomplished in the works of Galileo, of a world of intelligible essences articulated mathematically in the place of single real world, the world given reality in perception, the only one capable of experience and experienced in fact—the world of our everyday life.”⁴¹^41. E. HURSSEL “Die Krisis der europäischen Wissenschaft und die transzendentale Phänomenologie” (Prague 1935), in Gesammelte Werke, Band VI, Haag, Nijhoff, 1962, p. 49. And yet, it is this life-world (Lebenswelt) which constitutes “the forgotten foundation of the meaning of the science of nature.”⁴² Both mathematician and logician, [38 - 39] Husserl underlines the arbitrary and fallacious character of the disjunction decisively brought about between scientific truth, given as unconditionally valid,^42. ibid., p. 48. and the concrete reality of human experience, considered as approximate and incapable of generating knowledge. The disjunction in question constituted the initial innovation of the mechanist revolution, the French version of which we can find in the Cartesian parable of the morceau de cire or “piece of wax.”

The perception of the scientist is an appirition of truth, but it is still an apparition. It is an absurd claim to make the type of truth which constitutive of the order of things, reign in the human domain. Already, in the eighteenth century, dazzled by the triumph of Newton, a certain number of great minds tried hard and in vain to discover a rigorous law which would reduce the totality of biological, psychological, political, and economic phenomena in their generality to a common regularity. The attempt was in vain, because each epistemological sector has its own intelligibility proper to it; and the mode of knowledge which gives authority in one of them cannot be indistinctly equal in all of them.

When they claimed to be searching for the truth of the world exclusively in the order of mathematical essences, scientists were setting off on a path without solution. Moreover, the foundations and principles of rigorous sciences have been criticised, revised, and renewed on multiple occasions, and their validity is self-evident only subjected to further examination. The extraordinary progress of the sciences in recent times has thus lead to a relaxation of certain, too rigid, schemas. The exact sciences are no longer considered as dogmatic systems, cloaked in a sacrosanct dignity, but rather as technical languages designed to illuminate such-or-such an aspect of a reality which is extremely vague in itself.

Under these conditions, the epistemological discourses of diverse disciplines are called on to become aware of their insufficiency and ability to be made better. None of these discourses by themselves can claim to recover the totality of that which is; rather, that which is refers to a total discourse, or at least to a complete discourse, a common horizon of partial discourses, which would be the discourse of the ensemble of human reality as a function of our situation in world, such that we can discover it.

There exists here a reversal of the values of knowledge, which one finds evidence of, among others, in the works of one of the great contemporary physicists. “One of the most important characteristics of the evolution of modern physical analysis,” Werner Heisenberg feels, “is the fact that the concepts of normal language, with their vague definitions, seem more stable in the course of the expansion of knowledge than the precise terms of scientific language, which are an idealisation applicable only under a limited group of phenomena. This is not surprising, since the concepts [39 - 40] of normal language are furnished by direct contact with the real: they represent reality. It is true that they are not well defined and that they are therefore subject to change over the course of centuries—exactly as reality is itself—but they never loose contact with the real.”⁴³^43. WERNER HEISENBERG, Physique et Philosophie, trans. J. Hadamard, Albin Michel, 1961, pp. 235-236.

These intentions expressed by a scientist consecrate the demise of the naïve scientism which, in a manner more or less admitted to, has dominated the course of Western thought for a century. It appears, henceforth, that in the place of searching exclusively for the truth of the world in mathematical essences, it is now necessary to establish mathematical truths in relation to the human reality of the human world. “All comprehension,” continues Heisenberg, “must be based on normal language, because it is only there that we can be sure of touching reality, and we must therefore show ourselves to be sceptical in the face of all scepticism towards this normal language and its essential concepts; we can consequently use these concepts as they always have been use. It is in this manner that modern physics has perhaps opened the door to a larger point of view on the affinity between the human spirit and reality.”⁴⁴^44. ibid., p. 238

The idea of unified science, which the tenants of positivism had hoped to realise under the form of a universal mathematics, has changed its meaning. Rigorous sciences, which were threatening the alienation of human reality, have returned to human consciousness. They must take their place in a new theory of human ensembles, the difficult and exultant task of which will be to bring together all the information concerning the situation of man in the universe. This task represents today the major imperative called for in all people of culture.

The unnuanced opposition between the sciences and the arts today finds itself obsolete; it no longer represents more than an outdated obstacle to the progress of consciousness and knowledge. There exists no choice between two contradictory vocations, as if the mind of finesse were incompatible with the mind of geometry, or the order of truth with the order of values. The two intellectual and spiritual attitudes are complementary, and those who would adopt one to the exclusion of the other will be menaced by a sort of alienation, as incapable of assuming human existence in its fulness.

We will remark moreover that the debate between the tenants of science education and arts education do not take account of the human sciences. Nevertheless, the human sciences furnish a third term which allows us to resolve the impasse. They first came to awareness in the course of the eighteenth century, in a second phase of the mechanist revolution, where the new ideal of [41] knowledge, after having supported the conquest of the world, returned to man and attempted to discover his nature according to the ways and means which had been successful in the exploration of the order of things. In a manner almost imperceptible, the age of Aufklärung furnished a program of replacement, substituting the traditional ideal of classical humanities with a science of man. The nineteenth century would see the triumph of the historical, philological, and anthropological disciplines in most of the domains of human thought.

However, the epistemological status of the sciences of man was ambiguous. It appeared incompatible with the thesis of an impenetrable opposition between the sciences and the arts, since the disciplines in question were situated precisely in between the two of them. In the beginning, everything happened as though the science of things, by turning themselves towards man, had attempted to envelope him in determinism. But the very progress of knowledge gave rise to the appearance of specific methodologies, in which the rigour of explanation had been composed with a comprehensive grace [souplesse], the only type capable of receiving the intrinsic richness of the human phenomenon. No one would consider contesting the scientific character of the human sciences, confirmed by the objectivity of its procedures and the precision of its reasoning. And yet, these sciences are for the most part at home in the Faculty of Arts, which, moreover, sanctioned this fact when, in France, it changed its name and became the “Faculté des Lettres et des Sciences humaines” (Faculty of Arts and Human Sciences).

Such a formula which makes the “Arts” and the “Science” cohabit demonstrates that the claimed disjunction between the two orders is today obsolete. The scientific mind impregnates literary culture, without distorting it in any way; the sciences of culture have enlarged our mental space; they have multiplied our sensibility and confer to man today a marvellous faculty of presence beyond the limited horizons of local geography and contemporary history. Through a reversal of perspective, the sciences of nature now appear as an constituent element of culture, unique to each period of civilisation. Mathematics, physics, and biology return to the humans who created them; they are moments and aspects of that plenary consciousness of the human condition which takes form in the best minds in each epoch of the human journey.

The unity of a knowledge which is never given suggests itself as task to undertake. As an impossible task, perhaps, and discouraging in any case. But this task defines the highest necessity of culture. Therefore, whether it be the mathematician or botanist, philologist or historian, the attitude of the specialist who withdraws jealously to the narrow confines of their own competencies must be considered as a failure of responsibility. All dissociation of knowledge is a negation of knowledge. The present duty is to work towards reunification, to the reconstitution of that which a century of analysis has dismembered. The presupposition of specialisation must make room for the presupposition of [41 - 42] convergence. The sciences and the arts, the sciences of nature and the sciences of man, each seemed doomed to a slow yet independent growth. But they must be aware that they are each in their own way like parallel lines, which, without deviating from their own separate directions, will come together again at infinity.