The Boutroux Circle and Poincaré's Conventionalism

The Boutroux Circle and Poincaré's ConventionalismAuthor(s): Mary Jo Nye Source: Journal of the History of Ideas, Vol. 40, No. 1 (Jan. - Mar., 1979), pp. 107-120 Published by: University of Pennsylvania Press Stable URL: http://www.jstor.org/stable/2709262 . Accessed: 20/06/2014 22:25 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . University of Pennsylvania Press is collaborating with JSTOR to digitize, preserve and extend access to Journal of the History of Ideas. http://www.jstor.org This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions THE BOUTROUX CIRCLE AND POINCARE'S CONVENTIONALISM BY MARY Jo NYE* In France at the turn of the twentieth century, contemporary observers wrote of a renaissance in French philosophy which by the time of Henri Poincare's death in 1912 was irrevocably linked with his name and the philosophy of conventionalism.1 This conventionalist philosophy asserted that fundamental scientific principles are not reflec- tions of the "real" nature of the universe but are convenient ways of describing the natural world insofar as they are not contradicted by observation or experiment. In addition to developments in philosophy, the 1890s and early 1900s were years of new achievement for French laboratories and science lecture halls, after decades in which the French sciences, like philosophy, had languished in the shadow of German accomplishments. Indeed, at the turn of the century, a renaissance in French philosophy was paralleled by a renaissance in French science associated with the names of Becquerel, the Curies, Perrin, Langevin, and, again, Poincare.2 Inevitably a suspicion comes to mind in studying these two parallel renaissances in French intellectual history that there are links between the two renaissances in this period; one such link surely is in the figure of Henri Poincare (1854-1912), whose reputation as a mathematical physicist at the turn of the century is exceeded perhaps only by that of Einstein. Poincare's conventionalist philosophy has been one of fruitful debate since its inception. Yet, one may ask, how did this con- * I should like to acknowledge with gratitude the financial support of this project by a University of Oklahoma College of Arts and Sciences 1976 Summer Fellowship. 1 See, for example, J. Benrubi, "La Renaissance de la philosophie en France," Revue de metaphysique et de morale, 19 (1911), 499-504. Bergson's philosophy of "intuitionism" was another major component of this renaissance in philosophy, as was the work of Pierre Duhem. For a recent (and unsympathetic) discussion of these developments, see Leszek Kolakowski, The Alienation of Reason. A History of Positivist Thought, trans. Norbert Guterman (Garden City, New York, 1969), 129 ff. 2See Henry Guerlac, "Science and French National Strength," 81-105 in E. M. Earle, ed. Modern France (Princeton, 1951), esp. 88-105; and Harry W. Paul, "The Issue of Decline in Nineteenth-Century French Science," French His- torical Studies, 7 (Spring, 1972), 416-50. 107 This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions 108 MARY JO NYE ventionalist philosophy of science arise from those mid-nineteenth- century years of little distinction in French philosophy and science? In exploring Poincare's intellectual growth and maturation, one dis- covers his position in a group of scientific and educational leaders linked not only by filiation of ideas, but also by ties of family and friendship. At the center of this group was Emile Boutroux (1.845-1921), the Sorbonne philosopher who married Poincare's bright and capable younger sister Aline.3 Boutroux's 1874 doctoral thesis De la Contingence des lois de la nature registered a new analysis in France of the implica- tions of Kant's philosophy for science, and the thesis was hailed in Paris at the time as one of major importance.4 Included also in the group, besides Boutroux and Poincare, were the director of the science curriculum at the Ecole normale superieure, Jules Tannery (1848-1910) and his brother, the engineer and historian of science, Paul Tannery (1843-1904). Although intellectual relations are less clear in his case, another member was Jules Tannery's brother-in-law, the astronomer and director of the Observatoire de Paris, Benjamin Baillaud (1848-1934). These men exerted influences on each other which clearly help explain the appearance at the end of the century of Poincare's conventionalist philosophy. In addition, through their prestigious appointments in the French acadamic establish- ment, their influence on one or two generations of French scientists was profound. The Perrin and Langevin generation, trained directly under Jules Tannery at the Ecole normale superieure in the 1890s, broke with the nineteenth-century phenomenalist and thermodynamic tradition of French physics and chemistry and inaugurated a new period of achieve- ment for French science. Although that generation by no means wholly adopted Poincare's epistemological views, the group did develop its critical skills within the framework of the well-articulated philosophy of conventionalism. Perrin, in particular, offered a critique of both thermodynamics and mechanics which drew attention to their "conven- 3 Aline Boutroux translated several books into French from English, including David J. Hill, La Crise de la democratie aux Etats-Unis (1918) and John H. Finley, Les Frangais au coeur de l'Amerique, preface by Gabriel Hanotaux (1916). 4 In general, historians of ideas have assessed that Kant's influence in France was not great in the early nineteenth century, and George Boas argued, too, that Cousin's later interest in Kant was not profound; cf. George Boas, French Philos- ophies of the Romantic Period (Baltimore, 1925), 184. The revival of Kant in France was largely the work of Jules Lachelier and his student Boutroux, who along with Charles Renouvier effected a new analysis and criticism of Kant's philosophy by French intellectuals. See, for example, Lucien Levy-Bruhl, History of Modern Philosophy in France, no translator cited (Chicago, 1899), 444-51; and Dominque Parodi, La Philosphie contemporaine en France, 2nd rev. ed. (Paris, 1920), 164-201. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions POINCARE AND THE BOUTROUX CIRCLE 109 tional" components.5 And as we shall see, many of the conventionalist views on the nature and meaning of scientific change can in fact be traced to Emile Boutroux's philosophy of contingency and creativity, as developed and refined in the bosom of the Boutroux Circle. The Early Years of the Boutroux Circle On the eve of the Franco-Prussian War, young Emile Boutroux was studying at the University of Heidelberg, where his contacts included the historian Heinrich Treitschke (1834-96), the historian of philosophy Eduard Zeller (1814-1908), and the scientist Hermann von Helmholtz (1821-94).6 As a student, Boutroux developed a great admiration for the German ideal of Wissenschaft and for its emphasis on rigorous inter- disciplinary synthesis. To the dismay of the French educational ministry, Boutroux criticized French educational institutions as weak and ineffec- tive in comparison with the German ones; writing from Heidelberg in 1869, he said of the German system: "There are continued relations between professors of different branches, each borrowing from the neighboring sciences." In contrast, "I scarcely see that there has been an exchange of ideas at the Ecole normale between Letters and Sciences, and this separation, which still exists, is becoming deeper."7 "The Ger- mans," he wrote in another letter, "say that the sciences must not exist only alongside one another, but united, working in concert, because truth is one."8 And in keeping with this interdisciplinary ideal for the humanities and the sciences, Boutroux was to be unusual among pro- fessionally trained philosophers in the highly specialized and insulated ambience of French academic life, by maintaining intimate and fruit- ful discussions with colleagues outside the Faculty of Letters. Boutroux left Heidelberg because of the war and became professor of philosophy at the lycee of Caen in 1871.9 There, after teaching his first class, he met his old friend Jules Tannery, newly appointed to teach special mathematics at Caen.'? Boutroux and Louis Liard, both 5For example, see Perrin's discussion, in Traite de chimie physique. Les Principes (Paris, 1903), of the "conventions" adopted in mechanics and thermo- dynamics. On this, see my Molecular Reality. A Perspective on the Scientific Work of Jean Perrin (London and New York, 1972), 69-82. 6 Letters from Emile Boutroux to the Minister of Public Instruction [Victor Duruy], 28 January 1869 at Heidelberg; and 3 March 1869 at Heidelberg. Archives Nationales dossier #F17 22028 (Emile Boutroux). 7Letter from Emile Boutroux to the Minister of Public Instruction, 28 Jan- uary 1869, loc. cit. 8 Letter from Emile Boutroux to the Minister of Public Instruction, 3 March 1869, loc. cit. 9 Archives Nationales dossier #F17 22028 (Emile Boutroux). 10 Emile Boutroux, "Tannery [Jules]," Association amicale de secours des anciens eleves de l'Ecole normale superieure, 8 January 1911, 68-78, on 70. And Archives Nationales dossier #AJ XVI 1524 (Jules Tannery). This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions 110 MARY JO NYE in the philosophical section at the Ecole normale, had been close to Tannery at Paris11; and now at Caen Jules Tannery took Boutroux home to meet his family. Reflecting in later years on his writing of De la Contingence des lois de la nature, Boutroux wrote how "Especially thanks to conversations pursued at Caen with the Tannery brothers, I composed a philosophical thesis where I tried, in a precise way, to see in what measure the world of science coincides with the world of life."12 At this time Jules' older brother Paul Tannery had completed an engineering degree at the Ecole polytechnique and the Ecole d'applica- tion des manufactures de l'Etat where he distracted himself from his scientific studies by taking up Hebrew and studying Comte's Cours de philosophie positive. While beginning a lifelong professional career in the state-controlled Manufacture de Tabac, Paul Tannery continued to read the ancient Greek literature for which he had developed a profound interest in Jules Lachelier's philosophy class at the Caen lycee.'3 By the 1880s Paul Tannery was pursuing two careers, one in engineering and administration, and a second in historical scholarship whereby he gave a cours libre at the Sorbonne in 1884-85 on the history of mathe- matics.'4 In 1887 Paul Tannery published his first book, Pour l'Histoire de la science hellene, which was a self-conscious riposte to the great historicist and Hegelian classic Philosophie der Griechen (1844-52) written by Boutroux's former Heidelberg professor Eduard Zeller.'5 As Emile Boutroux later said of Paul Tannery's work, its aim was to consider the first Greek thinkers as "precursors" of science rather than of philosophy.16 Tannery said of his goal that it was "to show the rational enchainement which has linked the evolution of each of the sciences, with the others, and with that of civilization in general . . to understand the order of ideas, true or erroneous, as well as the characters of transformation in 11 Emile Picard, "La Vie et l'oeuvre de Jules Tannery" [Lecture given at the annual meeting of 14 December 1925 at the Academie des Sciences] (Paris, 1926), 6-7. In Liard's doctoral thesis, Definitions geometriques et definitions empiriques (Paris, 1873), Liard made arguments about the creative role of l'esprit" in fundamental notions of the mathematical sciences. 12 Emile Boutroux, "Tannery [Jules]," 72. 13 "Paul Tannery," Osiris, 4, pt. I (1938), 638-41. 14 Ibid., 651. On Paul Tannery, his wife Marie, their life and accomplishments, see the issue devoted to Paul Tannery, with contributions by Henri Berr, Suzanne Delorme, Rene Taton, Jacques Tannery, et al., in Revue d'histoire des sciences et de leurs applications, 7 (Oct.-Dec. 1954). Also, George Sarton, "Paul, Jules and Marie Tannery," Isis, 38 (1947), 33-51. 15 John Nussbaum, Paul Tannery et I'histoire des physiologues milesiens. Etude critique (Lausanne, 1929), 2-4. 16 Quoted in "Paul Tannery," Osiris, 653. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions POINCARE AND THE BOUTROUX CIRCLE 111 each period.""17 For Boutroux, Paul Tannery was a man "qui savait tout,"8 and it is no wonder that Boutroux in the '70s sketched to Paul Tannery the unfolding plan of his dissertation, questioning his friend on the principles of mechanics and asking him about the works of Comte.19 Jules Tannery was interested in philosophy as well as mathematics, and when his older brother was away, Jules once wrote him his own conclusions about the logical and intuitional bases of mathematics: that mathematical symbols are very useful, but in order not to arrive at absolutely astonishing conclusions, one has to recall from time to time that they are only symbols. Almost in the same breath in this letter, Jules Tannery mentions Boutroux and their friendship.20 One of Jules Tannery's principal concerns was to untangle the ex- periential and intuitional foundations of mathematics from its logical foundations, a problem which deeply preoccupied him while he was writing his doctoral thesis. Entitled "On linear differential equations with variable coefficients," the thesis applied the results and methods of the German Lazarus Fuchs in such a way as to obtain more easily results in geometry already obtained by Bernhard Riemann.21 As with the younger Henri Poincare, it appears that Tannery's epistemological inquiries into the foundations of mathematics and physical sciences are in part bound up with his studies of the structural relations between Euclidean and non-Euclidean geometry.22 Also, both Jules and his brother Paul wrote papers critical of psychophysics during this period, with his own papers, Jules said, causing "some uproar in a small circle for a couple of weeks, probably because they were anonymous and a little impertinent."23 17 Paul Tannery, "Programme d'un cours d'histoire des sciences" [ed. Jules Tannery], Revue du Mois (April 1907), 385-92. In reprint of 7 pp., on p. 2. Among Paul Tannery's important contributions to scholarship in the history of science and philosophy was his edition, with Charles Adam, of the Oeuvres de Descartes, 12 vols. (Paris, 1897-1910). 18 Emile Boutroux, "Tannery [Jules]," 70. 19 Dominique Parodi, "Emile Boutroux" (Issoudun, 1923), 10; also reprinted in Parodi, 121-44 in Du Positivisme a l'idealisme. Etudes critiques. Philosophies d'hier et d'aujourd'hui (Paris, 1930), 133. 20 Letter from Jules Tannery to Paul Tannery, 3 September 1874, in Paul Tannery, Memoires scientifiques, XVI, 430-31. Correspondance, ed. A Dies and Pierre Louis (Toulouse and Paris, 1943). 21 Jules Tannery, Notice sur les travaux scientifiques (Paris, 1901), 16-17. 22 Pierre Boutroux, "L'oeuvre philosophique," 205-61 in Vito Volterra, Jacques Hadamard, Paul Langevin, and Pierre Boutroux, Henri Poincare. L'Oeuvre scien- tifique. L'Oeuvre philosophique (Paris, 1914), 209-13. 23 Jules Tannery, Notice sur les travaux scientifiques, 41-42; and Letter from Jules Tannery to Paul Tannery, undated, in Paul Tannery, Memoires scientifiques, XVI, 432-35. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions 112 MARY JO NYE In his diary-like Pensees, kept during 1870-76, Jules Tannery at- tempted to distinguish precisely science from art, to elucidate the bases of scientific certainty, and to examine the possibility of a science of morals in the face of what he called "The End of Christianity" (a demise which seemed practically possible for French Catholicism after the triumphs of the anti-clerical Republicans in the French elections of the 1870s). In his personal notes of the early 1870s, Jules Tannery reflected on the inability of the sciences to provide absolute or final answers to questions of nature or ethics. That which gives to our sciences this apparent clarity which occasionally dazzles us, this show of rigor, of solidity on which we rest ourselves and of which we are so proud, is that we reason on signs, on symbols, as much as on ideas; we arrange words in an order which pleases us.... If it is thus for the more precise sciences, is it not perhaps necessary to deny the possibility of moral sciences, as obscure, as changeable as are ideas of liberty, good, or justice.. 24 Here Tannery demonstrated in the early 1870s his conviction that the theories of science are symbolic creations, a view which led him later to warn students that "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys aways from them in order to oblige them to think." In later years at the Ecole normale, mathematicians like Borel, Painleve, and Picard, and physicists like Perrin and Langevin were to benefit from Jules Tannery's insistence, as professor of mathematics and director of their scientific studies, that students rethink the logical foundations of the sciences they were to teach and practice.25 This stress on logic, defini- tions, and principles was instrumental in the next scientific generation's developing new critiques of both thermodynamics and mechanics which helped lead to a new mechanical theory of the atom in the early 1900s.26 Boutroux's Thesis Considering the closeness of the two men, one is not surprised that Jules Tannery sat in the room as an auditor when Emile Boutroux appeared in Paris to defend his thesis. The anti-positivist novelist Paul Bourget, who sat next to Tannery, later described the occasion: Caro and Janet, trained under Cousin, were disconcerted by the originality of [Boutroux's] philosophy. They had combatted scientism for some years, but it was [Boutroux] who found le defaut de la cuirasse. M. Caro asked [Boutroux] in an almost irritated tone: "But finally, Monsieur, the body 24 Jules Tannery, "Pensees," Revue du Mois, 11 (10 February 1911), 256-78, and (10 April 1911), 407. 25 Quoted in Sarton, "Paul, Jules and Marie Tannery," 43. And Emile Borel, "Jules Tannery," Revue du Mois, 11 (10 January 1911), 5-11. 26 On this point, see my Molecular Reality, 69-82. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions POINCARE AND THE BOUTROUX CIRCLE 113 exists. What do you do with that in your philosophy?" And [Boutroux, who was not a man of robust health] responded, "The body? The body? That is perhaps only an infirmity."27 Boutroux's thesis addressed itself not only to a critique of scientism and the claims of positivist philosophy, but also to recent developments in the sciences, particularly biological evolutionism, the laws of thermo- dynamics, and the extension of mechanical reductionism to psychology. As was the case for Jules and Paul Tannery, Boutroux was particularly concerned with psychophysics and with the materialist psychology of Boutroux's compatriot Hippolyte Taine. What Boutroux attempted in his thesis was an integration of the philosophies of Kant and Comte with mid-nineteenth-century scientific theories; his aim was to steer clear of the post-Kantian romantic idealism in Germany, but also to avoid the excessive claims of scientistic positivism which came with Comte in France. What Boutroux thought wrong-headed in the philosophical movements which had followed upon Kant and Comte was their deter- minism, a determinism which in German philosophy was associated with the historicism of Hegel and in French philosophy with the mechanical determinism of Comte's disciples. Put briefly, Boutroux's analysis emphasized the freedom with which the mind contemplates a natural world characterized by spontaneous movement and life. He demonstrated the extent to which natural laws (including scientific laws and historical laws) are man's freely reasoned creations and not nature's necessity. With Boutroux, scientific knowl- edge partakes of a twofold contingency: the dependence of its laws on man's peculiar and imperfect representations and understanding; and the contingency of its laws due to nature's own spontaneously develop- ing and evolving essence. The idea that nature's laws themselves change in time was a concept which Boutroux based on evolutionary views of nature, which he combined with ideas of spontaneity and finality in nature. "The laws of nature have no absolute existence; they simply express a given phase, a stage .... They are the image, artificially ob- tained and determined, of a model that, in essence, is living and movable (mutable)."28 In his thesis Boutroux distinguished necessity from determinism, arguing that scientific laws do not prescribe with logical necessity that the world cannot be other than it is; rather, scientific laws are deter- ministic only in describing what will occur under certain strictly defined 27 Paul Bourget, 34-67 in Emile Boutroux and Paul Bourget, "Discours prononces dans la seance publique tenue par 1'Academie Frangaise pour la recep- tion de M. Emile Boutroux, le jeudi 22 Janv. 1914," Institut de France. Publica- tions diverses de l'annee 1914, #2 (Paris, 1915), 49. 28 In Emile Boutroux, The Contingency of the Laws of Nature [1874], trans. Fred Rothwell (London and Chicago, 1920), 195. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions 114 MARY JO NYE conditions.29 Like the romantics, especially Goethe whom he greatly admired, Boutroux emphasized the complexity of the natural world and the incompleteness, indeed the falsity, with which mathematical and other quantitative procedures attempt to capture its essence.30 But con- trary to Goethe, Boutroux argued that mathematical symbols as well as mechanical analogies are entirely valid as schemata for aiding the mind's understanding in its attempt to know nature objectively through clear and distinct ideas.31 Unlike Kant, Boutroux did not believe that the categories of under- standing are the eternal apparatus of the human mind for acting on the natural world.32 Influenced by Spencerian evolutionary arguments and by contemporary historical and anthropological studies, Boutroux found implausible Kant's static view of the mind's structure. How- ever, with Boutroux, the mind's capacity for change does not obviate the objectivity of knowledge. The symbols might change, but as Comte had said and as Poincare would say, certain relations in nature persist, or at least subsist for a long time. Since the scientist relies closely on observation and experimentation, his understanding is linked intimately to the phenomenal world via his intuition, and his understanding is that of the real phenomenal world.33 This is not to say that Boutroux accepted Kant's distinction between the phenomenal and noumenal worlds, for here lies perhaps his major difference with the Kantian philosophy. Boutroux would not accept Kant's distinction between a phenomenal world as the abode of absolute determinism and a noumenal world as that of liberty. For Boutroux, all that exists is an integrated whole; man is not a Frankenstein "monster" 29 Emile Boutroux, Natural Law in Science and Philosophy [1895], trans. Fred Rothwell (New York, 1914), 90-93, 126, 157. 30 Boutroux's intense admiration for Goethe is remarked in Emile Boutroux, Pages Choisies (Paris, 1915), 21. For one such discussion of the insufficiencies of mathematical representations, see Emile Boutroux, Contingency, 50-56. 31 Invoking the tradition of Descartes, Boutroux argued that the intelligent person's belief in universal mechanism is due to one's confidence in the truth of clear ideas (cf. Natural Law, 123). In using the idea of "schemata," Boutroux employed Kantian arguments. See, for example, his chapter on Kant (255-330) in Historical Studies in Philosophy [1897], trans. Fred Rothwell (London, 1912), 284-86. 32 See, for example, Emile Boutroux, "Science et religion," Bulletin de la Societe' francaise de philosophie, 8 (Feb. 1908), 31-32. 33 See Boutroux, Natural Law, 5-6. In arguing that reason cannot be inde- pendent from intuition, Boutroux employed Kant's dictum that "Intuitions with- out concepts are blind; concepts without intuitions are empty." In Rene Berthelot, Emile Boutroux, et al., "Sur la Necessite, la finalite, et la liberte chez Hegel," Bulletin de la Societe francaise de philosophie, 7 (April, 1907), 154. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions POINCARE AND THE BOUTROUX CIRCLE 115 in nature; he is either free in the phenomenal world or he is not free at all.34 Drawing upon the detailed studies of Greek philosophy which he had made under Eduard Zeller at Heidelberg, Boutroux argued, much as Aristotle had done, that nature, which includes man, is like an organism, its parts organized hierarchically and also holistically. The whole of the structure of nature is more than the sum of its parts, for, made up of worlds which share a common matter, nature finds its essence in the synthetic linkages between matter and form. The organismic metaphor was almost as Comtian as it was Aristotelian. Comte, too, had dis- tinguished the sciences from one another, on the basis that each has its proper method and subject, with the more complex containing an element qualitatively different from the less complex and irreducible to any combination of elements from the less complex.35 But whereas Comte argued in favor of a synthesis of the sciences which would eliminate metaphysics as a separate study, Boutroux sided once again with Aristotle and the Greeks in envisioning philosophy as the highest vocation of man and one which transcends, rather than merely synthesizes, the methods of the sciences. Like Aristotle, Boutroux dis- tinguished a lower form of reason, whose object is an understanding of what we call the brute mechanisms of nature, from the higher reason of the nous whose object is an understanding of purpose, good, and finality in the universe.36 Or, as Boutroux put it by quoting Pascal and returning to Aristotle's concept of the heart as the center of man's esprit, "The heart has its reasons which Reason ["geometrical reason"] does not know."37 Boutroux argued that in this higher reason, the rational under- standing of the natural world is united with rational moral liberty of action. Philosophy is the achievement of this higher reason, the nous. Philosophy is ever dependent on the sciences for sustenance and substance, but it is not merely their synthesis, as had been argued by positivists since the time of Auguste Comte.38 In making his formulation, 34 See Emile Boutroux, "The Relation between Thought and Action from the German and from the Classical Point of View," The Herbert Spencer Lecture Delivered at Oxford, Oct. 20, 1917 (Oxford, 1918), esp. 8-10, 20. 35 For his anti-reductionism, see, for example, Boutroux, Contingency, 152 and 158-63. Also, Natural Law, 31-32. Boutroux said of Comte that it was Comte's singular merit to have seen that if the general idea of science is one, "il n'y en a pas moins autant de methodes scientifiques distinctes que de classes d'etres pour nous irreductibles." In Boutroux, "Morale et religion," 1-47 in Emile Boutroux, Henri Poincare, G. Richard, et al., Questions du temps present (Paris, 1910), on 16-17. 36 Boutroux, "The Relation between Thought and Action," 21. 37 Quoted by Boutroux, ibid., 22. 38 Emile Boutroux, "Du Rapport de la philosophie aux sciences," Revue de metaphysique et de morale, 19 (1911), 424-25, 429-31, 434. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions 116 MARY JO NYE Boutroux reasserted the place of traditional philosophy in an intellectual milieu which had been dominated for several decades by positivists like Georges Wyrouboff, Emile Littre, Hippolyte Taine, and the young Ernest Renan, all of whom had taught that science would eliminate so- ciety's need for metaphysics and any philosophy that was not scientific. For Boutroux, in contrast, philosophy offers an understanding of a uni- verse characterized by life and movement, where there is a levelling up rather than the levelling down by the reduction of vital phenomena to physical causes. In the universe there subsists a purposiveness which is perfection and which, for Boutroux, is God.39 The Secularization of Boutroux's Thesis in Conventionalism Boutroux was a profoundly religious man, although his philosophy is by no means inseparable from his Christianity. The philosophy of contingency and creativity was the response of a believer to what he deemed the excesses of an often avowedly atheistic, materialist reduc- tionism. The old static Newtonian mechanism had been reconcilable with religious tradition, and Boutroux accepted the idea that mechanism could still be harmonized with Christian belief, and especially with the traditional creed of moral freedom and responsibility.40 Like Boutroux, Paul Tannery was a religious man, as was another member of the Boutroux Circle, Benjamin Baillaud. A comrade of Boutroux and Jules Tannery at the Ecole normale, Baillaud taught mathematics in Paris lycees for several years before turning exclusively to astronomy. Jules Tannery married Baillaud's sister Esther, forging into brotherly ties the earlier ones of friendship and intellect.41 Like Paul 39 Boutroux, Contingency, 172-83. As one analyst put it, Boutroux posits a moral necessity, la finalite, while denying mechanical necessity. Pure reason is not the only spiritual activity of man; for the sense of duty compels man to action through his practical reason. Pure Reason and Practical Reason are not separate, but rather different manifestations of the same active reason. Cf. Lucy Shepard Crawford, The Philosophy of Emile Boutroux. As Representative of French Idealism in the Nineteenth Century (Ithaca, N. Y., 1924), 120 and 120 n. 2. 40 On this point, see my discussion in "The Moral Freedom of Man and the Determinism of Nature: The Catholic Synthesis of Science and History in the Revue des Questions Scientifiques," British Journal for the History of Science, 9, #3 (1976), 274-92. According to his grandson, M. Villey, Emile Boutroux was "croyant et fervent de Pascal," although not a practicing Catholic. In letter to the author, 18 November 1977. 41 Emile Borel, Robert Deltheil, Ernest Eslangon, et al., Benjamin Baillaud, 1848-1934 (Toulouse, 1937), esp. 7-9; and Archives Nationales dossier #F17 23735 (Benjamin Baillaud). From 1878 to 1908 Baillaud taught at Toulouse, directed its Observatory, and founded the Observatoire du Pic du Midi; he then returned to Paris. See my "The Scientific Periphery in France: The Faculty of Sciences at Toulouse (1880-1930)," Minerva, 13 (Autumn, 1975), 380-387. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions POINCARE AND THE BOUTROUX CIRCLE 117 Tannery, Baillaud was a practicing Catholic at a time when this affilia- tion hindered academic advancement in France, particularly in the sciences. As with Pierre Duhem and Paul Tannery,42 Baillaud's suit- ability for a chair in Paris was questioned not on the basis of his abilities, but because of his religious affiliations. As his rector at Toulouse wrote in his defense, "Everyone knows that he is a Catholic and a practicing Catholic. But from there to 'militant clerical' is a long way!"43 Boutroux's philosophy had explicit links to religious belief, then. It solved for some Catholics the problem of free will which the Catholic scientist Joseph Boussinesq had attempted unsuccessfully to resolve by invoking indeterminism in mathematical physics itself.44 Yet Boutroux's approach need not be bound up with Christianity,45 as is demonstrated by the independent contributions of Jules Tannery, who lost his belief in the 1870s. Henri Poincare, while sympathetic to some aspects of Christianity and Catholicism, was likewise not a religious man, although as Boutroux characterized Poincare, he "felt the effects of ... that which one could call the metaphysical and religious emotion."46 Poincare met Boutroux after Boutroux had completed his thesis in 1874 and went on to teach from 1876-79 at the Faculty of Letters at Nancy. There Emile Boutroux began what became a lifelong intimacy 42 See Harry W. Paul, "The Crucifix and the Crucible: Catholic Scientists in the Third Republic," Catholic Historical Review, 58 (1972), 195-219; and his "Scholarship vs. Ideology: The Chair of the General History of Science at the College de France (1892-1913)," Isis, 67 (Sept. 1976), 376-97. 43 Letter from [Rector] Claude-Marie Perroud to "M. le Directeur" [perhaps of the Observatoire de Paris], dated 15 October 1907. Archives Nationales dossier #F17 23735 (Benjamin Baillaud). 44 Boussinesq argued that certain kinds of differential equations admit more than one solution and that, for these equations, there is no way to denote one solution as superior to another. Where such equations are descriptive of the physical world, and especially where they apply to mechanical processes within living bodies, Boussinesq suggested that there might be an immeasurable force which determines in an unpredictable fashion the solution to the equation. In Joseph Boussinesq, "Conciliation du veritable determinisme mecanique avec l'existence de la vie et de la verite morale, precede d'un rapport a l'Academie des Sciences morales et politiques par Paul Janet," ed. Paul Janet (Paris, 1878). 45 Caution must be employed in labelling any Catholic's philosophical views as "Catholic" since there was a great deal of disagreement among Catholics them- selves over certain philosophical issues. In addition, a Catholic intellectual can arrive at conclusions which coincidentally serve Catholicism without necessarily intending these results. For example, see R. N. D. Martin, "The Genesis of a Medieval Historian: Pierre Duhem and the Origins of Statics," Annals of Science, 33 (1976), 119-29. 46 Emile Boutroux, "Henri Poincare," La Revue de Paris, 20 (15 Feb. 1913), 673-702 and (1 March 1913), 90. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions 118 MARY JO NYE with the Poincare family.47 By the mid-1880s Poincare had achieved international recognition for translating non-Euclidean geometrical sys- tems into properties of Euclidean figures through the Fuchsian functions. This translation allowed him also to resolve a problem involving a sys- tem of curvilinear triangles which he had not solved through traditional Euclidean geometry.48 Here there are clear parallels with the interests of Jules Tannery, as there are parallels and indeed direct influences on Poincare's conventionalist philosophy from the epistemology of Boutroux and Jules Tannery, along with the historical studies of Paul Tannery. Some of the essays which were eventually collected in Poincare's La Science et l'Hypothese (1902) first appeared in philosophical journals such as the Revue de metaphysique et de morale. In the Revue de l'Universite de Bruxelles, Poincare warned against the dogmatism of both "the positivist schools" and Catholicism which alike "deprive us of impartiality of judgment."49 "The scientist's love of truth is not the love of certitude. . . . The faith of the scientist would rather resemble the faith of the heretic ... it makes us catch a glimpse of [entrevoir] an ideal of which we can have only a vague notion, and it gives us the confidence that, without ever permitting us to attain it, our efforts for approaching it will not be without fruit."50 Even if unmoored from God, science is not simply pragmatism, or at least not a pragmatism which subordinates knowledge to action as in the philosophy of Poincare's contemporary and Bergson's protege Edouard Le Roy. Rather, for Poincare: "In my eyes, on the contrary, it is knowledge which is the goal, and action which is the means."51 The equations of science express relations which are real: "they teach us now, as they did then, that there is such and such a relation between this thing and that; only the something which we then called motion, we now call electric current."52 In the tradition of Jules Tannery, Poincare criticized classical mechanical treatises for their failure to distinguish clearly between what 47 Dominique Parodi, "Emile Boutroux," 11. See also Andre Bellivier, Henri Poincaire ou la vocation souveraine, 2nd ed. (Paris, 1956), including the genealog- ical chart on 22-23. 48 As described by Pierre Boutroux, Poincare used non-Euclidean geometry in order to study a system of curvilinear triangles formed of arcs of circles which cut orthogonally a given fundamental circle. He found that the properties of the arcs thus defined are exactly those that Nicholas Lobatchevsky's geometry attrib- utes to straight lines. Pierre Boutroux, "L'oeuvre philosophique," 211. 49 Poincare, "Le libre examen en matiere scientifique," Revue de l'Universite de Bruxelles, 15 (1909-10), 289. 50 Poincare, Savants et ecrivains (Paris, 1910), vii. 51 Poincare, "Sur la Valeur objective de la science," Revue de metaphysique et de morale, 10 (1902), 266. In this article, Poincare takes to task the "nominalist" views of Le Roy"s "Science et philosophie," Revue de metaphysique et de morale, 7 (1899), 375-425, 503-62, 706-31; and 8 (1900), 37-72. 52 Poincare, Science and Hypothesis, trans. W. J. Greenstreet from original 1902 ed. (New York, 1952), 161. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions POINCARE AND THE BOUTROUX CIRCLE 119 is experiment, what is mathematical reasoning, what is convention, and what is hypothesis.53 Like Paul Tannery he marked ". . the ephemeral nature of scientific theories . . . abandoned one after another . . . ruins piled upon ruins . . . ," but recognized a rational enchainement in their history.54 Like Boutroux, Poincare argued that experimental laws are only approximate, and if some appear exact to us, it is because we have transformed them artificially into principles. "We have made this transformation freely and as the caprice which has determined us to do this is something eminently contingent, we have communicated this contingency to the law itself. It is in this sense that we have the right to say that determinism presupposes liberty, since it is our free choice that we have become deterministic."55 Poincare parted company with Boutroux on the issue of the con- tingency of nature's laws arising from nature's own evolution and devel- opment. In contrast, for Poincare, "In treating the problem of con- tingency and determinism in science, we say that every law is only an imperfect and provisional statement which should be replaced some day by another superior law, of which it is only a gross image." "One does not say, however, that it is the laws which have evolved, but circum- stances which have been modified."56 Boutroux recognized that Poincare did not share his view of the evolution of the "intrinsic laws of nature," a view which according to Boutroux, ... does not make sense to the scientist. The work of the scientist is precisely to transform change into fixity, fact into law, evolution into an equation. Science is an interpretation of nature ruled by the hypothesis that all is similar, all is only addition or subtraction of similarities. It would be paradoxical to ask of science if it can see things from a point of view opposite to the scien- tific view.57 Poincare, then, hardly rose like a lone phoenix from the ashes of decay in French philosophy and science at the turn of the century. Rather, he and the conventionalist philosophy with which his name is identified are to an important degree part of an integrated and inter- disciplinary philosophical movement which began to flourish in the 1870s with the return of Emile Boutroux from Germany and the philo- sophical inquiries shared by members of the Boutroux Circle. Boutroux's philosophy itself does not seem to have achieved explicit recognition and admiration in most scientific circles, perhaps in part because of its links with the Catholicism to which the French administra- tion of the Third Republic was intractably opposed. Boutroux's philos- ophy of contingency and creativity may sometimes have been misunder- stood as an apologia for Catholicism, particularly by intellectuals who 53Ibid., 104-06. 54Ibid., 160. 55 Poincare, "Sur la valeur objective de la science," 285-86. 56 Ibid., 283, 285. 57 Emile Boutroux, "Henri Poincare," 690. Their differences are also discussed in Mathieu Schyns, La Philosophie d'Emile Boutroux (Brussels, 1923), 223-26. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions 120 MARY JO NYE were not in his intimate circle and especially by those of a radically positivist or anticlerical bias. Paradoxically for his conservative aims, Boutroux's philosophy pro- vided an opportunity for the budding of philosophical and scientific relativism, and Poincare was to spend long hours defending convention- alism against this skeptical variant. The relativistic offshoot took root at Paris in Bergson's intuitionism, and, in reaction, the French scientific community, including Poincare himself, may well have sought defen- sively to emphasize more than ever experimentalism and the dependence of science on observed data, rather than to take risks in speculative metaphysical approaches. If so, the influence of the Boutroux Circle in the long run may have increased the already experimental character of French science at the turn of the century, a character which still could be seen after the First World War in French skepticism about quantum mechanics and general relativity theory, including misgivings about the work of their own Louis de Broglie.58 However, the experimentalism of the Langevin and Perrin genera- tion, associated with the renaissance of French science in the early 1900s, was by no means the professed phenomenalism of the earlier generation of French scientists, a phenomenalism expressed in Henry LeChatelier's remark that the method of science is "limiting its investigations to real facts and to the laws which group them."59 Such radically positivist claims had been affected decisively by the criticism of the Boutroux Circle. And, indeed, in looking at the science of the decades after the First World War, the conclusion seems inescapable that Boutroux's principle of the scientist's creative role in the natural laws of science was to be vindicated in physics by the 1930s. Perhaps in the end, the dem- onstration proved its debts to German idealism, for it came in the imag- inative approaches of general relativity theory and quantum mechanics, with German-educated scientists rather than the French leading the way. University of Oklahoma. 58 In taped interviews for the collection Sources for the History of Quantum Physics, Edmond Bauer, Leon Brillouin, and Francis Perrin all comment on the experimental character of French physics at the turn of the twentieth century and the lack of enthusiasm for both relativity theory and quantum mechanics. Bauer, for example, specifically mentions Langevin's resistance to quantum theory and Paul Painleve's objections to Einstein's theory of general relativity. Interview of Edmond H. Bauer with T. S. Kuhn and T. Kahan, #1 of 2 sessions, 8 Jan. 1963, 13-14; and #2 of 2 sessions, 14 Jan. 1963, 1-2. Interview of Leon Brillouin with P. P. Ewald, G. Uhlenbeck, T. S. Kuhn, and Mrs. Ewald, #2 of 2 sessions, 3 April 1962, 8. And, interview of Francis Perrin with T. S. Kuhn and T. Kahan, 12 Jan. 1963, 4. Sources for the History of Quantum Physics (depository at the University of California at Berkeley). 59 Henry Le Chatelier, "Les phenomenes de combustion et la production de la puissance mecanique, de la chaleur et de l'electricite," Revue scientifique, [41, 9 (1898), 226. This content downloaded from 62.122.76.48 on Fri, 20 Jun 2014 22:25:20 PM All use subject to JSTOR Terms and Conditions