Duhem, Pierre-Maurice-Marie

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Duhem, Pierre-Maurice-Marie

(b. Paris, France, 10 June 1861; d. Cabrespine, France, 14 September 1916)

physics, rational mechanics, physical chemistry, history of science, philosophy of science.

Duhem was that rare, not to say unique, scientist whose contributions to the philosophy of science, the historiography of science, and science itself (in thermodynamics, hydrodynamics, elasticity, and physical chemistry) were of profound importance on a fully professional level in all three disciplines. Much of the purely scientific work was forgotten until recently. His apparent versatility was animated by a singlemindedness about the nature of scientific theories that was compatible with a rigidly ultra-Catholic point of view, an outlook unusual among historians, philosophers, or practitioners of science—Cauchy is the only other example that comes to mind.

Duhem’s historical work, the major part of which traces the development of cosmology from antiquity to the Renaissance, was meant partly to redeem the centuries of Scholasticism, the great age for his church, from the reputation of scientific nullity, but mainly to exemplify the central epistemological position of his philosophy. This assigned to scientific theories the role of economizers of experimental laws which approach asymptotically some sort of reality, rather than that of models of reality itself or bearers of truth. Thus would the truth be independent of science and reserved for theology. This position coincided in important, although not all, respects with that of contemporary positivists, who came to it from the other extreme ideologically and without concern for defending theology.

Among the areas of agreement between Duhem, Ernst Mach, and Wilhelm Ostwald was a common predilection for the energeticist over the mechanistic position in physics itself, involving skepticism about the reality of known physical entities, although he differed from them in allowing the existence of real entities in principle, however unknowable. A similar skeptical view was held by Henri Poincaré.

Duhem’s father, Pierre-Joseph, was a commercial traveler from Roubaix in the industrialized north of France. His mother, born Alexandrine Fabre, was of a bourgeois family originally from Cabrespine, a town in Languedoc, near Carcassonne. They settled in Paris and sent Duhem, the eldest of their four children, to the Collège Stanislas from his eleventh year. He was a brilliant student and there acquired the firm grasp of Latin and Greek that he would need in his historical scholarship, while being attracted primarily to scientific studies and especially thermodynamics by a gifted teacher, Jules Moutier. His father hoped that for his higher education he would enter the École Polytechnique, where the training and tradition assured most graduates eminent technical careers in the service of the state. His mother, on the other hand, fearful that science or engineering would diminish his religious faith, urged him to study humanities at the École Normale Supérieure. Having placed first in the entrance examinations, he chose the middle ground of science at the École Normale, indicating his desire for an academic career. He published his first paper, on the application of the thermodynamic potential to electrochemical cells, in 1884, while still a student.

He proceeded with distinction through the licence and agrégation, after meeting a setback with a thesis for the doctorate that he presented in 1884 (prior to receiving the licence, an uncommon event). The subject concerned the concept of thermodynamic potential in chemistry and physics, and the argument included an attack on Marcellin Berthelot’s twentyyear-old principle of maximum work, whereby the heat of reaction defines the criterion for the spontaneity of chemical reactions. This principle is false. Duhem, following J. W. Gibbs and Hermann von Helmholtz, properly defined the criterion in terms of free energy. Berthelot was extremely influential, resented the neophyte challenge, and was able to get the thesis refused. At risk to his career, Duhem later published the thesis as a book, Le potentiel thermodynamique (1886). Duhem was placed under the necessity of preparing another subject for the doctorate. He received the degree in 1888 for a thesis on the theory of magnetism, this one falling within the area of mathematics.

Unfortunately the enmity between Berthelot and Duhem was not dissipated until after 1900. Moreover, Duhem was of a contentious and acrimonious disposition, with a talent for making personal enemies over scientific matters. He blamed Berthelot, who was minister of education from 1886 to 1887, together with the circle of liberal and free-thinking scientists who advised successive ministers, for preventing him from ever receiving the expected call to a professorship in Paris. Aside from the hearsay evidence of anecdotes from the personalities involved, it must be admitted that there is no other instance in modern French history of a scientist of equivalent productivity, depth, and originality remaining relegated to the provinces throughout his entire postdoctoral career. Duhem taught at Lille (1887–1893), Rennes (1893–1894), and Bordeaux (1894–1916). He spurned an offer of a professorship in the history of science at the Collège de France shortly before his death, on the grounds that he was a physicist and would not enter Paris by the back door of history. In 1900 he was elected to corresponding membership in the Academy of Sciences. In 1913 he was elected one of the first six nonresident members of the Academy, a recognition that, together with various honorary degrees and foreign academic memberships received earlier, mollified his feelings to some degree.

Duhem had few qualified students, but those he did have considered him an extraordinary teacher. His personal friendships were as warm as his professional enmities were bitter. In October 1890 while at Lille he married Adèle Chayet. She died only two years later while giving birth to their second daughter, who also died. Duhem made his home thereafter with the surviving daughter, Hélène. She saw to the publication of the final five volumes (1954–1959) of his historical masterpiece, Le système du monde, left in manuscript after his death. He died at fifty-five of a heart attack brought on by a walking expedition during vacation days at Cabrespine. His health had never been vigorous.

Duhem’s interests fell roughly into periods. Thermodynamics and electromagnetism predominated between 1884 and 1900, although he returned to them in 1913–1916. He concentrated on hydrodynamics from 1900 to 1906. His interest in the philosophy of science was mostly in the period 1892–1906, and in the history of science from 1904 to 1916, although his earliest historical papers date from 1895. The extraordinary volume of Duhem’s production is impressive—nearly 400 papers and some twenty-two books. Among them, certain wartime writings (La science allemande and La chimie est-elle une science française?) express, as do his philosophical judgments of the style of British science, a certain chauvinism that remains the only unattractive characteristic of his nonscientific writings. It will be best to consider his most important work in the order of philosophy, history, and physics; to do so will reverse its chronology but will respect its intellectual structure.

Philosophy of Science . Duhem published his major philosophical work, La théorie physique, son objet et sa structure, in 1906, after having largely completed his researches in physical science. “A physical theory,” he held there, “... is a system of mathematical propositions, deduced from a small number of principles, which has the object of representing a set of experimental laws as simply, as completely, and as exactly as possible.” In adopting this position, he was explicitly rejecting what he considered to be the two alternatives to which any serious existing or previous account might be reduced.

According to epistemologies of the first sort, proper physical theories have the aim of accounting for observed phenomena by proposing hypotheses about, and preferably by actually revealing, the nature of the ultimate entities underlying the phenomena in question. Duhem rejected this view as illusory because experience showed that acting upon it had had the effect historically of subordinating theoretical physics to metaphysics, thereby encumbering and distracting it with all the difficulties and disputes afflicting that subject. He allowed that physicists may appropriately hope to form theories of which the structure “reflects” reality. It may be thought of such theories that their mode of interrelating empirical laws somehow fits the way in which the real events that give rise to the observations are interrelated. This hope can be based only on faith, however. There is and can be no evidence to support it.

Little in Duhem’s philosophical writings clarifies the idea of such a fit, beyond the notion that the evolution of physical theories caused by successive adjustments to conform to experiment should lead asymptotically to a “natural classification” which somehow reflects reality. But his historical writings allude to numerous examples of what he had in mind, and his Notice (1913) indicates that they were in part originally motivated by it. It is no doubt for this reason that, despite his enthusiastic discovery of Scholastic mechanics in the Middle Ages, his favorite philosopher of antiquity was Plato, to whom he attributed the origin of the view (clearly akin to his own) that the healthy role of astronomical or other mathematical theory is to “save the phenomena.” At the same time he had great faith in the syllogism as a logical instrument. He believed that mathematical reasoning could in principle be replaced with syllogistic reasoning, and he went so far as to reject Poincaré’s argument that mathematical induction involves nonsyllogistic elements.1

The second category of philosophies or methodologies of physics that Duhem found unacceptable were those in which theories were expected to provide models in the form of mechanical analogies or constructs that permit visualizing the phenomena and offer handles for thought. He rejected this alternative partly on utilitarian and partly on aesthetic grounds. He felt that physical theories should have practical value, and he preferred the analytic to the geometric mode in mathematical thinking. Theories of the kind he advocated permit deducing many laws from a few principles and thus dispense the physicist from the necessity of trying to remember all the laws. Duhem evidently considered reason a higher faculty than memory. Complex models are distracting to people who can reason but cannot remember a mass of concrete detail. They are not, he believed, likely to lead to discovery of new laws. Merely artificial constructs, they can never attain to the status of natural classifications. Duhem was highly critical of British physics for its reliance upon the use of just such mechanistic models. In his view this national habit resulted from a defect of cultural temperament. He described the British mind in science as wide and shallow, the French as narrow and deep. As will appear in the discussion of his electrodynamics, Maxwell was his bête noire in this respect. It must be acknowledged that a certain rigidity in his opinions accorded ill with the subtle nature of his philosophy.

Duhem’s philosophy was certainly empiricist but never naïvely so. He showed very beautifully that there can be no such thing as simply observing and reporting an experiment. The phenomenon observed must be construed—must be seen—in the light of some theory and must be described in the terms of that theory. Laws arrived at experimentally must be expressed by means of abstract concepts that allow them to be formulated mathematically and incorporated in a theory. At their best they can merely approximate experimental observations. It is quite impossible to test or verify the fundamental hypotheses of a theory one by one. Thus there cannot be a crucial experiment, and induction from laws can never determine a unique set of hypotheses. Thus data and logic leave much to the discretion of the theorist He must supplement their resources with good sense and historical perspective on his problems and his science.

It is an aspect of Duhem’s recognition of the role of taste in scientific research that he never insisted that his philosophy require the adoption of an energeticist, to the exclusion of a mechanistic, point of view. That was an empirical, not a philosophical, issue. What his philosophy purported to establish was that an energeticist approach was no less legitimate than a mechanistic one. The discussion explains how theories are to be judged and looked at merely in point of preference or policy; and in the absence of concrete facts, either type of theory would in principle be acceptable, so long as no metaphysical import be loaded into the choice. The issue was one that Duhem discussed in L’évolution de la mécanique (1902) and also in the essay “Physique de croyant,” included in later editions of La théorie physique.

History of Science. Like Ernst Mach, his contemporary in the positivist school, Duhem relied heavily on historical examples in presenting his philosophy of science. L’évolution de la mécanique may be compared to Mach’s famous Die Mechanik in ihrer Entwicklung, historisch-kritisch dargestellt (1883) as a philosophical critique of a science based upon its history, although Duhem was by far the more faithful to the original texts and the intentions of their authors. A history of the concept of chemical combination appeared in 1902 and a two-volume study of early statics in 1905–1906.

The object of historical examples was to attempt to see the trend toward the “natural classification,” which requires the examination of preceding theories. Duhem was primarily led into his historical studies by following such theories backwards. Thus he always claimed that his conception of physical theory was justified by the history of physics, not because it corresponded to views shared by all, or most, or even (as Mach had tended to imply of his own position) by the best physicists, but because it did yield an analysis of the nature of the evolution of physics and of the dialectic responsible for that process.

The most impressive monument to the scholarly fertility of that claim remains his massive contribution to the knowledge of medieval science in his threevolume Études sur Léonard de Vinci (1906–1913) and the ten-volume Système du monde (1913–1959). These works contain a detailed exposition of two theses: (1) a creative and unbroken tradition of physics, cosmology, and natural philosophy was carried on in the Latin West from about 1200 to the Renaissance, and (2) the results of this medieval activity were known to Leonardo da Vinci and Galileo, and played a seminal role in the latter’s transformation of physics. Duhem was led to his theses, and to the almost single-handed discovery of this medieval activity, by recognizing in Leonardo’s notebooks statements by earlier writers and references to works fortunately available in manuscript in the Bibliothèque Nationale. Pursuing these citations and references still further he found wholly unsuspected “schools of science.” He emphasized the significance of Paris: particularly important was a series of Parisian masters who were relatively unknown before Duhem’s researches—Jordanus de Nemore, Jean Buridan, Francis of Méyronnes, Albert of Saxony, and Nicole Oresme. Duhem also brought out of obscurity the contributions of Mersenne and Malebranche. Expressed in dramatic form and supported by extensive quotation from the original texts (particularly in Le système du monde), Duhem’s discoveries revolutionized, if they did not completely create, the study of medieval physics. While it is true that recent studies have seriously modified and qualified some of his conclusions, Duhem’s studies remain the indisputable starting point for the study of medieval natural philosophy.2

Scientific Thought and Work. It must be recalled that Duhem’s scientific formation took place in the period 1880–1890, well before the discovery of radioactivity and the experiments of Jean Perrin and, later, Henry G. F. Moseley. Discontent with the notion of reducing all physical concepts to classical mechanics or to mechanical models was growing. It was fed by the necessity to modify ad hoc the often contradictory properties of supposedly fundamental atomic or molecular particles in order to maintain the applicability of the model to newly determined phenomena, particularly in chemical dynamics and in the physics of heat and gases. Duhem early became convinced that rather than try to reduce all of physics and chemistry to classical mechanics, the wiser policy would be to see classical mechanics itself as a special case of a more general continuum theory. He believed that such underlying descriptive theory for all of physics and chemistry would emerge from a generalized thermodynamics. The central commitment of his scientific life was the building up of such a science, one that would include electricity and magnetism as well as mechanics. His attempts culminated in the Traité d’énergétique (1911), in which valuable work there is not a single word about atoms or molecules. Duhem always considered that it was his most important—and would prove to be his most lasting—contribution to science. He had not succeeded, however, in his goal of including electricity and magnetism in its purview.

His conception of the nature of physical theory had in fact influenced both the direction of his work and the form of his writings. His contemporaries (see Secondary Literature) often remarked that many of his papers opened with the barest of assumptions followed by a series of theorems. In his mode of posing “axioms,” he gave little motivation, made hardly any appeal to experiment, and of course made no use whatever of atomic or molecular models. In his concern over extracting the logical consequences of a set of axioms for a portion of physics or chemistry, Duhem was a pioneer. Today a flourishing school of continuum mechanics follows a similar path, with a strong interest in foundations and in finding general theorems about more general fluids or elastic bodies with nonlinear constitutive equations or with fading memory. They often cite Duhem and his more famous predecessors such as Euler and Cauchy. However, because of the special hypotheses and restricted constitutive equations built into Duhem’s thermodynamics from the beginning, modern workers no longer view his generalized thermodynamics as the best way to approach continuum mechanics.3,4.

Duhem began his scientific work with the generalization and application of thermodynamics. While still at the Collège Stanislas and under Moutier’s guidance, he had read G. Lemoine’s description of J. W. Gibbs’s work5 and the first part of Hermann von Helmholtz’ “Die Thermodynamik chemischer Vorgänge.”6 These papers emphasized the characteristic functions, closely related to those invented by F. J. D. Massieu,7 now called the Gibbs and Helmholtz free energies—G and A, respectively. These functions play a role for thermodynamics directly analogous to the one played by the potential of classical mechanics. Duhem was one of the first to see real promise in this, calling Massieu’s functions “thermodynamic potentials.” Using this idea together with the principle of virtual work, he treated a number of topics in physics and chemistry.

Among the subjects treated systematically were thermoelectricity, pyroelectricity, capillarity and surface tension, mixtures of perfect gases, mixtures of liquids, heats of solution and dilution, saturated vapors, solutions in gravitational and magnetic fields, osmotic pressure, freezing points, dissociation, continuity between liquid and gas states, stability of equilibrium, and the generalization of Le Chatelier’s principle. The Duhem-Margules equation was first obtained by Duhem in the course of this work. His success with these problems in the period 1884–1900 rank him with J. H. van’t Hoff, Ostwald, Svante Arrhenius, and Henry Le Chatelier as one of the founders of modern physical chemistry.

Duhem’s results are of course an extension and elaboration of the pioneer work of Gibbs and Helmholtz. But Duhem’s elaboration, explanation, and application of their suggestions in his Traité de mécanique chimique (1897–1899) and Thermodynamique et chimie (1902) provided a whole generation of French physicists and chemists with their knowledge of chemical thermodynamics.

Duhem made a number of other contributions to thermodynamics. In the first part of his rejected thesis, Le potentiel thermodynamique (1886), Duhem presented or rederived by means of the thermodynamic potential a number of known results on vapor pressure of pure liquids and solutions, dissociation of gases and of heterogeneous systems, and the heat effects in voltaic cells. In the second and third parts he obtained new results on solubility and freezing points of complex salt solutions and on electrified systems. There is also the first application of Euler’s homogeneous-function theorem to the extensive properties of solutions. This technique, now common, reduces the derivation of relations among the partial molal properties of a solution to the repeated application of this theorem. One of the equations so derived is the Gibbs-Duhem equation. Also included is a discussion of electrified systems which contains an expression equivalent to the electrochemical potential. This book, popular enough to be reprinted in 1896, is historically important for the systematic use of thermodynamic potentials, when others were still using osmotic pressure as a measure of chemical affinity and using artificial cycles to prove theorems.

Duhem was the first (1887) to publish a critical analysis8 of Gibbs’s “Equilibrium of Heterogeneous Substances.”9 In Duhem’s paper is the first precise definition of a reversible process; earlier versions by others (unfortunately often preserved in today’s textbooks) are too vague. Duhem emphasizes that the reversible process between two thermodynamic states A and B of a system is an unrealizable limiting process. The limit of the set of real processes for getting from A to B is obtained by letting the imbalance of forces between the system and the surroundings at each step tend toward zero. Each member of this set of real processes must pass through nonequilibrium states, or else nothing would happen. However, the limit of this set, where the forces balance at every step, is a set of equilibrium states. Since once the system is in equilibrium nothing can happen, this limit is thus in principle an unrealizable process. This limiting process is now called a “quasi-static” process. If a similar set of realizable processes for getting from B and A has the same (unrealizable) limit, then the common sequence of equilibrium states is defined by Duhem as a reversible process.

Duhem later pointed out in the “Commentaire aux principes de la thermodynamique” (pt. 2, 1893) that there exist situations such as hysteresis where the limiting set of equilibrium states for the direction AB is not the same as that for the direction BA. Therefore, it is possible to go from A to B and back by quasi-static processes, but not reversibly. This distinction was noted fifteen years before the celebrated paper of Carathéodory.10

Duhem believed that the “Commentaire” (1892–1894) was one of his more significant contributions. It contains a very detailed analysis of the steps leading from the statement of the second law of thermodynamics to the definitions of entropy and thermodynamic potential. It also contains an axiomatic treatment of the first law of thermodynamics which is surprisingly good by present-day standards. (A different version is given in the Traité d’énergétique [1911].) The concepts of oeuvre (total energy including kinetic energy) and travail (work) are taken as undefined ideas. Axioms about oeuvre include independence of path, additivity along a path, commutativity, associativity, conservation, plus other matters often left implicit. Important to note is that the concept “quantity of heat” was not assumed but was defined in terms of energy and work. Consequently the definition, although more diffusely stated, was equivalent to and preceded that of C. Carathéodory (1909)10 and Max Born (1921),11 and should be called Duhem’s definition. Duhem’s axiomatic outlook which characterized this discussion of the first law was indeed pioneering for physics and to some extent anticipated the major axiomatic research in mathematics. Thus, although the axiomatization of arithmetic began in the first half of the nineteenth century, the research for axiomatic foundations for other branches of mathematics (Euclidean geometry, fields, groups, Boolean algebra) did not begin in earnest until 1897–1900.

In “Sur les déformations permanentes et I’hystérésis” (1896–1902), Duhem considered in some detail the thermodynamics of nonreversible but quasi-static processes and some irreversible processes, including hysteresis and creep. The results were mostly qualitative, not entirely satisfactory, and of little influence. As of this writing there is no really adequate thermodynamic theory of such systems, although interest in this subject has recently been revived.

Duhem provided the first explicit unrestricted proof of the Gibbs phase rule, based on Gibbs’s suggestions, in “On the General Problem of Chemical Statics” (1898). At the same time he extended it beyond the consideration of just the intensive variables, giving the conditions necessary to specify the masses of the phases as well. The conditions are different for the pairs of variables pressure–temperature and volume–temperature, and their statement is called Duhem’s theorem.12 In addition the properties of “indifferent” systems, of which azeotropes are a simple special case, were discussed in some detail.

Duhem attached great importance to his thermodynamics of false equilibrium and friction.13 According to Duhem, false equilibria can be divided into two classes: apparent, as for example a supersaturated solution, which, as a result of a small perturbation, returns instantly to thermodynamic equilibrium; and real, as for example organic compounds, such as diamond or petroleum constituents. Such compounds are unstable thermodynamically with respect to other substances but have remained unchanged for large perturbations throughout geological periods of time. Yet they will transform into the stable products if the perturbations are large enough (diamond to graphite by heating). A similar view was held by Gibbs (his passive resistances). The false equilibrium viewpoint was very useful to E. Jouguet, a major contributor to explosives theory and one of Duhem’s disciples.14 However, real false equilibria can also be considered as instances of extremely slow reaction rates. A violent polemic over this issue took place between 1896 and 1910. Most, but by no means all, of those interested in such questions today prefer the infinitely slow reaction rate view. Since the results are the same from either view, the choice is a personal one.

A major portion of Duhem’s interest was focused on hydrodynamics and elasticity. His second book, Hydrodynamique, élasticité, acoustique (1891), had an important influence on mathematicians and physicists because it called attention to Hugoniot’s work on waves. Jacques Hadamard, a colleague for one year and lifelong friend, remarked that this book and later conversations with Duhem led him into a major portion of his own work in wave propagation, Huygens’ principle, calculus of variations, and hyperbolic differential equations. Duhem was both a pioneer and almost alone for years in trying to prove rigorous general theorems for Navier-Stokes fluids and for finite elasticity in Kelvin-Kirchhoff-Neumann bodies. His results are important and of sufficient interest later that his Recherches sur l’hydrodynamique (1903–1904) was reprinted in 1961.

In hydrodynamics Duhem was the first to study wave propagation in viscous, compressible, heatconducting fluids using stability conditions and the full resources of thermodynamics (Recherches sur l’hydrodynamique). He showed the then startling result that no true shock waves (i.e., discontinuities of density and velocity) or higher order discontinuities can be propagated through a viscous fluid. This is contrary to the result for rigorously nonviscous fluids. The only discontinuities that can persist are transversal, which always separate the same particles; these Duhem identified with the “cells,” observed by Bénard, formed when a liquid is heated from below. Since real fluids are both viscous and heat conducting, how is it possible to have sound waves propagated, as in air? Duhem’s answer was that while true waves are not possible, “quasi waves” are. A quasi wave is a thin layer whose properties, including velocity, change smoothly but rapidly. If we consider a series of similar fluids whose values of the heat conductivity k and viscosity η approach zero, then the thickness of the associated quasi wave also approaches zero and the smooth change of properties approaches a discontinuity. When k and η are small, as in air, such quasi waves behave exactly as a true longitudinal shock wave in a perfect fluid with k = η = 0, i.e, propagating with the Laplace velocity. Duhem’s concept and theory of the quasi wave is more general and more precise than the later ideas of Prandtl (1906) about the “shock layer.” Some of Duhem’s theorems on shock waves have been improved recently. For perspective, it should also be noted that Duhem considered only the then universally accepted Navier-Stokes fluid. There are more general concepts of a fluid with viscosity which do allow wave propagation.4

Duhem generalized and completed earlier results on the stability of floating bodies (including those containing a liquid). He showed that while some earlier methods were incorrect, certain results (in particular the famous rule of metacenters) were still correct. Finally, the article “Potentiel thermodynamique et pression hydrostatique” (1893) contains, but does not develop, the idea of an oriented body that consists not only of points but of directions associated with the points. Such an oriented body can represent liquid crystals or materials whose molecules have internal structure. Eugène and FranÇois Cosserat adapted this idea to represent the twisting of rods and shells in one and two dimensions (1907–1909). This concept has also been useful for some recent theories of bodies with “dislocations.”

In elasticity Duhem was again interested in rigorous general theorems (Recherches sur l’élasticité [1906]). He kept a correct finite elasticity alive and inspired other workers. He was the first to study waves in elastic, heat-conducting, viscous, finitely deformed systems. The results are similar to that for fluids; namely, in any finitely deformed viscous elastic system, whether crystalline or vitreous, no true waves can be propagated and the only possible discontinuities always separate the same particles (as in the Bénard problem). Quasi waves are expected in viscous solids, but Duhem did not carry his analysis that far. Duhem was also the first to study the relationships between waves in isothermal (heatconducting) and adiabatic (nonconducting) finitely deformed systems without viscosity. Duhem was also interested in the general conditions for solids (vitreous or crystalline) to be stable. He had to choose special conditions of stress or strain, but he was able to prove some general theorems. All this was based on the then universally accepted Kelvin-Kirchhoff Neumann elastic body. At the present writing, more general concepts of elastic bodies are being considered.

After Gibbs, Duhem was among the few who were concerned about stability of thermodynamic systems. His techniques were a natural consequence of his interest in thermodynamic potentials. He was the first to consider solutions (“Dissolutions et mélanges” [1893]); and he often returned to stability questions (“Commentaire aux principes de la thermodynamique” [1894]; “On the General Problem of Chemical Statics” [1898]; Recherches sur l’élasticité [1906]; Traité d’énergétique [1911]). Because he tried to be more explicit and more general than Gibbs and because he often took a global point of view, he had to face more difficult problems than did Gibbs. He succeeded fairly well with sufficient conditions but was less successful with necessary ones. In his Énergétique he showed familiarity with Liapounoff’s work, but his own previous results were based on more special hypotheses. As a result, there is some confusion in Duhem’s results over what are the proper necessary and sufficient conditions for thermodynamic stability. Such questions have only recently been rigorously resolved.

Electricity and magnetism and his attempts to bring them into the framework of his Énergétique (which was not the same as the philosophical school of “energetics”) were important to Duhem. If a system’s currents are zero or constant, then its electrodynamic energy is zero or constant. In this case, the total energy divides neatly into internal and kinetic energies, and energetics can be successfully applied. Thus Duhem was able to treat pyroelectricity and piezoelectricity in a general way without needing the special hypotheses of F. Pockels and W. Voigt. However, if currents are not constant, then matters are much more complex, and the electrodynamic energy must be accounted for using some electromagnetic theory.

Although Duhem recognized J. Clerk Maxwell’s ingenuity, he could not appreciate Maxwell’s theory at its real value because of its contradictions and unrigorous development, its mistakes in sign, and its lack of experimental foundation. Duhem preferred an electromagnetic theory due to Helmholtz, since it could be logically derived from the classical experiments. This theory, which Duhem helped to elaborate—and improve—is more general than Maxwell’s because it contains two additional arbitrary parameters. By an appropriate choice of values for these parameters, it can be shown that Maxwell’s equations appear as special cases of Helmholtz’ theory. In particular, if the Faraday-Mossotti hypothesis is adopted (equivalent to one parameter being infinity), then transverse fluxes propagate with the velocity of light. This results in an electromagnetic theory of light and an explanation of Heinrich Hertz’s experiments. If the other parameter (Helmholtz’) is chosen to be zero, then no longitudinal fluxes can be propagated, which circumstance is in agreement with Maxwell’s equations. Duhem, however, believed that there were experiments showing that such longitudinal fluxes exist and are also propagated at the velocity of light. He suggested (1902) that perhaps the recently discovered X rays might be identified with these longitudinal fluxes.

Duhem was a pitiless critic of Maxwell’s theory, claiming that it not only lacked rigorous foundation but was not sufficiently general to explain the existence of permanent magnets (Les théories électriques de J. Clerk Maxwell [1902]). Similar reservations about lack of rigor were expressed by many Continental physicists (e.g., Poincaré), and Helmholtz worked out his own electromagnetic theory because of his dissatisfaction with Maxwell’s approach. Duhem later admitted that not only had his criticisms not been accepted, they had not even been read or discussed; and of course Maxwell’s theory has triumphed. However, both L. Roy15 and A. O’Rahilly16 have contended that the logical derivation of Maxwell’s equations from a continuum viewpoint comes best through the Helmholtz-Duhem theory with the proper choice of constants.

The foregoing discussion covers an extraordinary output of purely scientific work. It is curious that until recently working scientists were almost completely unaware of these contributions, with the exception of the Gibbs-Duhem and Duhem-Margules equations, which have been well known to physical chemists. The reason for the neglect of Duhem’s scientific work, the failure to call him to Paris, and the long delay in his election to the Academy— despite the high quality of his work and the foreign honors accorded him—are interesting and are summarized below. They involve aspects of Duhem’s personality as well as differences between competing scientific schools of the period. (A more complete account of the antagonisms and suppression, interwoven with a biography, may be found in Miller, Physics Today, 19 , no. 12 [1966], 47–53.)

Duhem’s contentious characteristics have already been noted. On the one hand, his extremely conservative religious and political views conflicted sharply with those of the freethinkers and liberals who then dominated French science. On the other hand, the polemical nature of his writings on such controversies as energetics vs. atomism, Maxwell’s theory vs. Helmholtz’, relativity, false equilibrium, and the maximum work principle made personal enemies of many of his scientific contemporaries. Their combined opposition blocked his career and resulted in partial suppression of his work or in its being taken over without citation.

In part, however, the neglect of his work is to be explained by the triumph of views that he bitterly opposed, such as atomic theories and Maxwell’s theory. His objection to relativity derived from its “mutilation” of classical mechanics in order to leave unaltered Maxwell’s theory and atomic theories of electrons.

With the crystal clarity of a half century of hindsight, it would seem that Duhem should not have opposed corpuscular models so strongly. Since he had based his whole philosophy on the deliberate avoidance of such aids and given the rigid nature of his personality, he could not change his views as the evidence mounted and the use of such models became more plausible. It is essential to recall, however, that Duhem was not alone in his objection to corpuscular models, Maxwell, and relativity. At the time he was in the company of many eminent scientists.

Pierre Duhem is a fascinating example of a brilliant scientist caught up in historical and personal circumstances that blocked his career and partially suppressed his scientific work. Right-wing, royalist, anti-Semitic, anti-Dreyfus, anti-Republican, and a religious extremist, he was exiled to the provinces and his scientific work was almost systematically ignored in France.

Nevertheless, Duhem’s scientific ideas and outlook had a major influence on French physical chemistry and particularly on Hadamard, Jouguet, and the Cosserats. He was a pioneer in attempting to prove rigorous general theorems about thermodynamics, physical chemistry, Navier-Stokes fluids, finite elasticity, and wave propagation. His purely scientific investigations and results in these fields are important, useful, and significant today, although the ascendancy of atomic theories has diminished the relative importance of his contributions to science as a whole.

By midcentury Duhem’s scientific work had been almost completely forgotten. Since then, his contributions have been rediscovered, and are being increasingly cited and given the recognition they deserve.3,4,12 There has never been, of course, any question about the importance of his work in the philosophy and history of science. Since his contributions to any one of the fields of pure science, philosophy, or history would have done credit to one person, the ensemble from the pen of a single man marks Duhem as one of the most powerful intellects of his period.


1. “La nature du raisonnement mathématique.” in Revue de philosophie, 21 (1912). 531–543.

2. M. Clagett, Science of Mechanics in the Middle Ages (Madison, Wis., 1959).

3. C. Truesdell and R. Toupin, “The Classical Field Theories,” in S. Flügge, ed., Encyclopedia of Physics, III, pt. l (Berlin, 1960); C. Truesdell and W. Noll, “The Non-Linear Field Theories of Mechanics,” ibid., III. pt. 3 (Berlin, 1965).

4. B. D. Coleman, M. E. Gurtin, I. Herrara, and C. Truesdell, Wave Propagation in Dissipative Materials (New York, 1965).

5. G. Lemoine, Études sur les équilibres chimiques (Paris, 1882).

6. H. von Helmholtz, “Die Thermodynamik chemischer Vorgängc,” in Sitzungsberichte der Deutschen Akademie der Wissenschaften zu Berlin, 1 (1882), 22–39.

7. F. J. D. Massieu, “Sur les fonctions caractéristiques des divers fluides.” in Comptes rendus hebdomadaires des séances de l’Académie des sciences, 69 (1869), 858–864. 1057–1061.

8. P. Duhem, “Étude sur les travaux thermodynamiques de J. Willard Gibbs,” in Bulletin des sciences mathématiques, 2nd ser. 11 (1887), 122–148, 159–176.

9. J. W. Gibbs, “On the Equilibrium of Heterogeneous Substances,” in Transactions of the Connecticut Academy of Arts and Sciences. 3 , pt. 1 (1876), 108–248: 3 , pt. 2 (1878).343–520.

10. C. Carathéodory, “Untersuchungen über die Grundlagen der Thermodynamik,” in Mathematische Annalen, 67 (1909), 355– 386.

11. M. Bom, “Kritische Betrachtungen zur traditionellen Darstellung der Thermodynamik,” in Physikalische Zeitschrift, 22 (1921), 218–224, 249–254, 282–286.

12. I. Prigogine and R. Defay, Chemical Thermodynamics (New York, 1954), ch. 13.

13. P. Duhem, “Théorie thermodynamique de la viscosité du frottement, et des faux équilibres chimiques.” in Mémoires de la Société des sciences physiques et naturelles de Bordeaux, 5th sen, 2 (1896). 1–208; Thermodynamique et chimie (Paris, 1902; 2nd ed., 1910).

14. E. Jouguet, Mécanique des explosifs, étude de dynamique chimique (Paris, 1917).

15. L. Roy, L’électrodynamique des milieux isotropes en repos d’aprés Helmholtz et Duhem (Paris, 1923).

16. A. O’Rahilly, Electromagnetics (London, 1938), ch. 5; repr. as Electromagnetic Theory, 2 vols. (New York, 1965).


I Original Works. Duhem published twenty-two books in forty-five volumes, as well as nearly 400 articles and book reviews in scientific and philosophical journals. An extensive bibliography (although lacking some twentyfive articles and more than fifty book reviews) is given by O. Manville, in Mémoires de la Société des sciences physiques et naturelles de Bordeaux, 7th ser., 1 , pt. 2 (1927), 437–464.

Duhem’s correspondence consists of letters to him from some 500 correspondents and is being copied with the permission of Duhem’s daughter, Mlle. Hélène PierreDuhem. Copies will ultimately be deposited in the University of California, Berkeley, and University of California, San Diego, libraries. Few letters by Duhem survive. Little of the correspondence seems to have major scientific value, although there are a few interesting historical items.

Duhem’s major scientific books are Le potentiel thermodynamique et ses applications à la mécanique chimique et á la théorie des phénoménes électriques (Paris, 1886); Hydrodynamique, élasticité, acoustique, 2 vols. (Paris, 1891); Leçons sur l’électricité et le magnétisme, 3 vols. (Paris, 1891–1892); Traité élémentaire de la mécanique chimique, 4 vols. (Paris, 1897–1899); Les théories électriques de J. Clerk Maxwell: Étude historique et critique (Paris, 1902); Thermodynamique et chimie (Paris, 1902; 2nd ed., 1910), English trans, by G. Burgess (New York, 1903); Recherches sur l’hydrodynamique, 2 vols. (Paris, 1903–1904; repr., 1961); Recherches sur l’élasticité (Paris, 1906); and Traité d’énergétique, 2 vols. (Paris, 1911).

His major historical books are Le mixte et la combinaison chimique. Essai sur l’évolution d’une idée (Paris, 1902); L’évolution de la mécanique (Paris. 1902); Les origines de la statique, 2 vols. (Paris, 1905–1906); Études sur Léonard de Vinci, ceux qu’il a lus et ceux qui l’ont lu, 3 vols. (Paris, 1906–1913); and Le système du monde. Histoire des doctrines cosmologiques de Platon à Copernic, 10 vols. (Paris, 1913-1959>).

His philosophy of science is stated in La théorie physique, son objet et sa structure (Paris, 1906; 2nd ed., 1914; 3rd ed., 1933), German trans, by F. Adler, with foreword by E. Mach (Leipzig, 1908); English trans, by Philip P. Wiener as The Aim and Structure of Physical Theory (Princeton, 1954; repr. New York, 1963). See also “Notation atomique et hypothèse atomistique,” in Revue des questions scientifiques, 2nd ser., 31 (1892), 391; Les théories électriques de J. Clerk Maxwell (Paris, 1902); “Analyse de l’ouvrage de Ernst Mach,” in Bulletin des sciences mathématiques, 2nd ser, 27 (1903), 261; and ΣωΞειν τα ϕαινoμενα (Paris, 1908).

Duhem’s most Important scientific papers include “Étude sur les travaux thermodynamiques de J. Willard Gibbs,” in Bulletin des sciences mathématiques, 2nd ser, 11 (1887), 122, 159; “Commentaire aux principes de la thermodynamique,” in Journal de mathématiques pures et appliquées, 8 (1892), 269; 9 (1893), 293: and 10 (1894), 207; “Le potentiel thermodynamique et la pression hydrostatique,” in Annales scientifiques de l’École normale supérieure, 10 (1893), 183; “Dissolutions et mélanges,” in Travaux et mémoires des Facultés de Lille, 3 . no. 11 (1893), no. 12 (1893), and no. 13 (1894); “Sur les déformations permanentes et 1’hystérésis,” in Mémoires de l’Académie royale de Belgique. Classe des sciences, 54 , nos. 4 , 5, and 6 (1896); 56 , no. 6 (1898); and 62 , no. 1 (1902); “Théorie thermodynamique de la viscosité, du frottement, et des faux équilibres chimiques,” in Mémoires de la Société des sciences physiques et naturelles de Bordeaux, 5th ser., 2 (1896), 1; and “On the General Problem of Chemical Statics,” in Journal of Physical Chemistry, 2 (1898). 91.

Some of Duhem’s papers on electrodynamics may be found in Annales de la Faculté des sciences de l’Université de Toulouse, 7 , B, G (1893); 10 , B (1896); 3rd ser., 6 (1914). 177; American Journal of Mathematics, 17 (1895), 117; L’éclairage électrique, 4 (1895), 494; and Archives néerlandaises des sciences exactes et naturelles, 2nd ser., 5 (1901). 227. His principal papers on floating bodies are found in Journal de mathématiques pures et appliquées, 5th ser., 1 (1895), 91; 2 (1896). 23; 3 (1897), 389; 6th ser., 7 (1911), 1

His major historical papers are “Les théories de la chaleur,” in Revue des deux-mondes, 129 (1895), 869; and 130 (1895), 380, 851.

For Duhem’s own assessment of his work to 1913, see Notice sur les titres et travaux scientifiques de Pierre Duhem (Bordeaux, 1913), prepared by him for his candidacy at the Académie des Sciences. There remains an unpublished work on capillarity written several years before his death

II. Secondary Literature. Mémoires de la Société des sciences physiques et naturelles de Bordeaux, 7th ser., 1 , pt 2 (1927) is a special issue entitled “L’oeuvre scientifique de Pierre Duhem”; in addition to the bibliography by O. Manville, cited above, it contains Manville’s detailed discussion of Duhem’s physics, pp. 1–435, and shorter discussions of his mathematical work by J. Hadamard, pp. 465–495, and of his historical work by A. Darbon, pp. 497–548.

See also E. le Roy, “Science et philosophie,” in Revue de métaphysique et de morale, 7 (1899), 503; and “Un positivisme nouveau,” ibid., 9 (1901), 143–144; A. Rey, “La philosophie scientifique de M. Duhem,” ibid., 12 (1904), 699–744; a short review of Duhem’s scientific work by his best-known disciple, E. Jouguet, in Revue générale des sciences, 28 (1917), 40; L. Roy, L’électrodynamique des milieux isotropes en repos d’après Helmholtz et Duhem (Paris, 1923); and A. Lowinger, The Methodology of Pierre Duhem (New York, 1941).

Biographical sources include P. Humbert, Pierre Duhem (Paris, 1932); E. Jordan, in Annuaire de l’Association des anciens élèves de l’École normale supérieure (1917), pp. 158–173, and Mémoires de la Société des sciences physiques et naturelles de Bordeaux, 7th ser., 1 , pt. 1 (1917); D. Miller, in Physics Today, 19 , no. 12 (1966), 47–53, based in part on several interviews with Hélène Pierre-Duhem; E. Picard, La vie et l’oeuvre de Pierre Duhem (Paris, 1921), which also includes a summary review of all his work; and Hélène Pierre-Duhem, Un savant français: Pierre Duhem (Paris, 1936).

Donald G. Miller

Duhem, Pierre-Maurice-Marie

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(b. Paris, France, 10 June 1861;

d. Cabrespine, France, 14 September 1916), physics, rational mechanics, physical chemistry, history of science, philosophy of science. For the original article on Duhem see DSB, vol. 4.

Donald Miller’s article gives an excellent overview of Duhem’s scientific work and describes the main lines of Duhem’s historical work. A manuscript in which Duhem summarizes the main lines of argument in his 10-volume Le Système du Monde was subsequently published as L’aube du savoir: épitomé du système du monde, with a comprehensive critical introduction by the editor. Extensive discussions of biographical material have been given in Jaki’s Uneasy Genius, which also relates Duhem’s work in philosophy to Thomist philosophy as well as discussing his work in history and physics, and Brouzeng’s Duhem: Science et Providence, which also traces the first developments in irreversible thermodynamics to Duhem’s Traité d’énergétique. Miller presents what was the standard interpretation of Duhem’s philosophical position as aligned in important respects with contemporary positivism and as reserving truth for theology. This article will be mainly concerned with the interpretation of Duhem’s philosophical position and its relation to his historical and scientific interests in chemistry.

Natural Classification . The classic source of the antirealist interpretation of Duhem is his discussion of Plato’s dictum “to save the phenomena” in his book of the same name. As Duhem described there, ancient and medieval astronomers concluded that where one mathematical construction reproducing the observable features of planetary motions could be produced, others were possible. Yet there were also attempts to describe the real motions of the planets. The debate continued in the early twenty-first century.

Tycho Brahe devised a model of the Solar System that was observationally equivalent to Copernicus’s system in the sense that the motions of the planets did not distinguish between these models. Antirealists argue that in the absence of crucial observation tests supporting the one and contradicting the other, there is no reason to believe the underlying explanation of the one rather than the other. But such cases hold only for a limited domain, and it is open for an advocate of one system to point to further observations that would justify preferring it. In fact, Tycho thought the way heavy bodies fall in a straight line and the absence of centrifugal forces counted against Copernicus’s system, and Galileo tried to argue that observation of the tides favored Copernicus’s system. The anti-realist who wishes to make a general argument for not accepting the truth of theories must be assured that the observations supporting them are not limited to some restricted class, but cover all possible observations. Even with respect to some restricted class of observations, it is usually difficult enough to produce one adequate theory, and it is unusual to find alternative, equally well-developed mathematical theories of phenomena in the history of science.

Duhem, whose philosophical position was intimately connected with his reading of the history of science, would have been well aware of such historical facts, and he certainly made no attempt to develop the antirealist argument by arguing for the existence in principle of observational equivalents of theories with respect to all possible observations, as, for example, Quine has tried to do in “On Empirically Equivalent Systems.” Further, his holistic view of theory, which shows, as Miller puts it, “that there can be no such thing as simply observing and reporting an experiment” (p. 227), throws into grave doubt the assumption that he would have allowed the notion of observation presupposed by the antirealist argument under consideration. Again, Quine’s efforts in Word and Object and later writings well illustrate the need for a specific account of observation sentences within a general holistic framework. Nothing of the sort is to be found in Duhem’s writings. None of this detracts from the good sense of refraining from taking a stand on what the evidence and theoretical discussion leaves indeterminate. But that is not antirealism.

On the contrary, Duhem thought the aim of physical theory was to develop into a natural classification. This is the limiting form of physical theory that finally becomes a “reflection of the true order according to which the realities escaping us are organized” (La théorie physique, p. 41), to which Duhem thought the history of science points by showing that those aspects which have proved their worth by “anticipating observation” (p. 39) and facilitating correct predications are retained and integrated into an ever more coherent and unified body of theory more adequately mirroring a coherent world.

Energetics . Miller discusses Duhem’s conception of energetics as a unifying theory incorporating the well-established results of science under a range of conditions, which he developed in the 1911 book Traité d’énergétique, although he failed to cover electromagnetic radiation. The term energetics came to prominence as a term for theories developed by Georg Helm and by Wilhelm Ostwald. These were so heavily criticized by Ludwig Boltzmann and Max Planck after a famous meeting in Lübeck in 1895 that it may seem surprising that Duhem continued to use the term. Duhem made no allusion to these authors’ understanding of energetics in his own developments of the subject, however, and was undaunted by the criticisms. The charges of making technical errors, such as confounding exact and inexact differentials, and of failing to understand and incorporate the notion of entropy into the theory of energy certainly could not be directed against him. And their philosophical motivations of energetics—the explicitly positivist eschewing of theoretical in favor of observational terms in the case of Helm, and the reification of energy to which matter and all other physical concepts were to be reduced in the case of Ostwald— were not his. Although, like them, he was critical of the nineteenth-century project of attempting to reduce all science to mechanics, he entertained no vision of replacing it with an alternative reductive project of reducing theoretical terms to observational terms or treating energy as the only ultimate physical reality. As he put it in an early study, having “constituted, under the name Thermodynamics, a science which covers in shared principles all the changes of state of bodies, including both changes of position and changes in physical qualities,” he hoped it would be “easier to get away from what has hitherto been the most dangerous stumbling block of theoretical Physics, the search for a mechanical explanation of the Universe” (“Commentaire aux principes de la Thermodynamique. Troisième Partie,” p. 285).

All energeticists, Duhem included, opposed atomism. Although such opposition is often construed as a form of antirealism, this can hardly be said of Duhem’s antireductive stance, which has it that science should incorporate systematically whatever principles are needed to cover new discoveries rather than dogmatically adhere to previously conceived reductionist theses which cannot be shown to save the phenomena. There is nothing in his texts to suggest that he sought anything but a literal interpretation of such principles.

Anti-atomism . The antirealist interpretation of Duhem is naturally associated with his critical view of atomic theories. There is, however, certainly no suggestion of observationally equivalent theories in his arguments against the atomic view, which he is better understood as taking not to be a theory at all. As Miller emphasizes, Duhem regarded scientific theories as logically organized structures with a clear axiomatic base from which their import can be properly developed in terms of its logical consequences. Of course, first formulations may not achieve this ideal. But they are to be clearly distinguished from pictures and models, which have no comparably clear import. They were regarded by Duhem as a haven for ad hoc and conflicting speculations, and, the contrary claims of their proponents notwithstanding, as providing no real explanation of phenomena. Although he accepted that “as Dalton showed, it is easy to deduce the fundamental laws of chemistry” (“Notation atomique,” p. 441), by which he meant the laws of constant and multiple proportions, this was only because they were directly read into the nature of the atoms. Later in the century, Adolf Wurtz described the role of atoms in chemistry in terms of their “atomicities.” But once more, Duhem discounted this as simply reading the notion of valency as codified in the macroscopic behavior of the elements into the atoms, rather than as actually providing an explanation of valency in terms of characteristics of atoms ascribed to them by some systematic theory. This stood in sharp contrast to the genuine theory of chemical combination that Duhem was helping to develop in the last two decades of the nineteenth century on the basis of thermodynamic potentials.

None of this led Duhem to approve of the policy enforced by Marcelin Bertholet of banishing any mention of atoms from the science curriculum in France. But he thought that it was important to properly understand the import which science could justifiably ascribe to the chemical formulas usually described as based on the notion of an atom. His 1892 article “Notation atomique et hypothèses atomistiques” and much of Le mixte et la combinaison chimique are devoted to spelling this out. Building on a detailed statement of the doctrine of chemical proportions that is neutral with respect to the atomic or continuous view of matter, he established the notion of a compositional formula (formule chimique brute). Defining a notion of chemical type in the manner of Dumas on the basis of chemical substitution, elaborated to incorporate distinctions of valency, he then established the notion of a structural formula (formule développée), which can

distinguish isomers sharing the same compositional formula. These essentially topological (not two-dimensional) structures are finally elaborated with “a new element taken from geometry” (Le mixte et la combinaison chimique, p. 128) allowing the three-dimensional representation of optical isomers. Even here he would not allow that the van't Hoff structure should be viewed as literally picturing the spatial arrangement of atoms in a molecule because there was still no account of what the atoms were, and certainly no explanation of the rotation of plane polarized light in terms of atomic features.

Conception of Mixture . Duhem thought the foundation underlying chemical formulas had “yet to be discovered” (Le mixte et la combinaison chimique, p. 147), and clearly understood his account as abstracting from the concrete interpretation imposed by any specific theory of the nature of matter, whether atomic or continuous, so as to provide a statement of what could justifiably be held as true. He was interested in this foundational question, however, and clearly favored a view of compounds inspired by Aristotle’s theory of mixing, according to which the original ingredients are no longer actually present in the resulting homogeneous mixture. This is usually understood to be a continuous theory of matter because Aristotle developed it in opposition to Democratian atomism. But the dichotomy in terms of which Duhem describes the historical development of the concept of a mixt in Le mixte et la combinaison chimique is based on the issue of whether the original ingredients are present in the mixt or not. He interprets ancient atomism to take the negative line. However, Descartes’s theory, which is continuous and not atomic, is also classified as non-Aristotelian because, according to Duhem, it treats the original ingredients as present in a mixt. Perhaps, although he gives no example of this, an atomic theory might conceivably be Aristotelian in this sense. The Aristotelian view needs to be complemented, Duhem says, to accommodate later discoveries such as the law of constant proportions on which the distinction, not recognized by Aristotle and many after him, between compounds and solutions is based. (This is one reason why Duhem uses the term “mixt.”) But nothing, he maintained, had been discovered which directly contradicted the Aristotelian notion. How, exactly, it is to be considered compatible with the general analysis of mixtures in Gibbs’s phase rule raises some questions, but beyond the brief discussion of some simple, single-phase examples, Duhem does not really say.

An idiosyncrasy in Duhem’s view of mixture is the principle of co-occupancy—according to which different bodies or quantities of matter can occupy the same place at the same time—which he very clearly states in some of his thermodynamics texts, such as the 1892 paper “Commentaire aux principes de la thermodynamique. Première partie” and the 1911 book Traité d’énergétique. This principle was emphatically denied by Aristotle, raising a question about Duhem’s claim that nothing new in science contradicts the original Aristotelian conception of a mixt. The principle was adopted by the Stoics after Aristotle as a way of allowing that the original ingredients are actually present in a mixt without adopting the atomic view of matter, as Duhem discusses in a section of Le Système du Monde entitled “La physique Stoïcienne et la compénétration des corps” (Vol. I, Ch. V, §IX). The Stoic view of mixture is normally thought of as opposed to Aristotle's, and is anti-Aristotelian according to the dichotomy in Le mixte et la combinaison chimique, although nothing is said of it there. Nevertheless, Duhem seems not to have thought there was any tension.



“Commentaire aux principes de la thermodynamique” Journal de mathématiques pures et appliquées 8: (1892): 269; 9: (1893):293; 10 (1893): 207.

“Notation atomique et hypothèses atomistiques.” Revue des questions scientifiques, 31 (1892): 391–457. Translated by Paul Needham as “Atomic Notation and Atomistic Hypotheses.” Foundations of Chemistry 2 (2000): 127–180.

Le mixte et la combinaison chimique: Essai sur l’évolution d’une idée. Paris: C. Naud, 1902; reprinted Paris: Fayard, 1985. Translated in Mixture and Chemical Combination, and Related Essays, translated and edited by Paul Needham. Dordrecht, Holland and Boston: Kluwer, 2002.

ΣΩZEIN TA ΦAINOMENA: Essai sur la notion de théorie physique de Platon à Galilée. Paris: A. Hermann et Fils, 1908. Translated by Edmund Doland and Chaninah Maschler as To Save the Phenomena: An Essay on the Idea of Physical Theory from Plato to Galileo. Chicago: University of Chicago Press, 1969.

Traité d’énergétique ou de thermodynamique générale. Paris: Gauthier-Villars, 1911.

La théorie physique: Son objet – sa structure, 2nd ed. Paris: Marcel Rivière & Cie, 1914; reprinted Paris: Vrin, 1981.

The Evolution of Mechanics. Translated by Michael Cole. Alphen aan den Rijn, The Netherlands: Sijthoff & Noordhoff, 1980.

Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds. Edited and translated by Roger Ariew. Chicago: University of Chicago Press, 1985. Abridged English translation of parts of Le Système du Monde.

Pinkava, Jindrich, ed. The Correspondence of the Czech Chemist Frantisek Wald with W. Ostwald, E. Mach, P. Duhem, J. W. Gibbs and other Scientists of That Time. Praha: Academia, 1987.

German Science. Translated by John Lyon. La Salle, IL: Open Court, 1991.

The Origins of Statics. Translated by Grant F. Leneaux, Victor N. Vagliente and Guy H. Wagener. Dordrecht, Netherlands, and Boston: Kluwer, 1991.

Essays in the History and Philosophy of Science. Translated and edited by Roger Ariew and Peter Barker. Indianapolis, IN: Hackett, 1996.

L’aube du savoir: épitomé du système du monde. Textes établis et présentés par Anastasios Brenner. (Collection histoire de la pensée.) Paris: Hermann, 1997.


Brenner, Anastasios. Duhem: Science, Réalité et Apparence. Paris: Vrin, 1990.

Brouzeng, Paul. Duhem: Science et Providence. Paris: Belin, 1987.

Jaki, Stanley L. Uneasy Genius: The Life and Work of Pierre Duhem. The Hague and Boston: Nijhoff, 1984. Includes a complete biography of Duhem’s works.

Martin, Russell N. D. Pierre Duhem: Philosophy and History in the Work of a Believing Physicist. La Salle, IL: Open Court, 1991.

Needham, Paul. “Duhem’s Theory of Mixture in the Light of the Stoic Challenge to the Aristotelian Conception.” Studies in History and Philosophy of Science 33 (2002): 685–708.

Quine, Willard V. O. Word and Object. Cambridge, MA: MIT Press, 1960.

———. “On Empirically Equivalent Systems of the World.” Erkenntnis 9 (1975): 313–328.

Paul Needham

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