Background

Pierre Maurice Marie Duhem was born on June 9, 1861, in Paris, France, the eldest of the four children. His 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.

Education

Duhem went 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 twenty years 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.

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.

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 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. 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.

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 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 three-volume 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: 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 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.

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 work and the first part of Hermann von Helmholtz’ “Die Thermodynamik chemischer Vorgänge.” These papers emphasized the characteristic functions, closely related to those invented by F. J. D. Massieu, 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 analysis of Gibbs’s “Equilibrium of Heterogeneous Substances.” In Duhem’s paper is the first precise definition of a reversible process; earlier versions by others 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” 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.

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. In addition the properties of “indifferent” systems, of which azeotropes are a simple special case, were discussed in some detail.

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 or higher order discontinuities can be propagated through a viscous fluid. This is contrary to the result for rigorously nonviscous fluids.

Duhem generalized and completed earlier results on the stability of floating bodies. He showed that while some earlier methods were incorrect, certain results 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.”

After Gibbs, Duhem was among the few who were concerned about the stability of thermodynamic systems. His techniques were a natural consequence of his interest in thermodynamic potentials. He was the first to consider solutions; and he often returned to stability questions. 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 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.

Achievements

• Pierre 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. His 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. 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.

Works

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  • The Aim and Structure of Physical Theory 1908
  • Commentary on the Principles of Thermodynamics by Pierre Duhem 2011
  • To Save the Phenomena: An Essay on the Idea of Physical Theory from Plato to Galileo 1969
  • Medieval cosmology: Theories of infinity, place, time, void, and the plurality of worlds 1985
  • The Evolution of Mechanics 1903
  • German Science 1915
  • Essays in History and Philosophy of Science 1996
  • The physicist as artist 1988
  • Thermodynamics and Chemistry 1903
  • The Origins of Statics 1906
  • Lettres de Pierre Duhem a sa fille Helene 1994

Religion

Duhem grew up in a very religious family, and remained a devout Catholic for the rest of his life.

Politics

Duhem was a right-wing, royalist, anti-Semitic, anti-Dreyfus, and anti-Republican.

Views

For Duhem "a physical theory" 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.

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 model 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 the 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.

Duhem attached great importance to his thermodynamics of false equilibrium and friction. 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. A similar view was held by Gibbs.

Duhem was a pitiless critic of Maxwell’s theory, claiming that it not only lacked a rigorous foundation but was not sufficiently general to explain the existence of permanent magnets.

Membership

In 1900 Duhem 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.

Personality

Duhem was of a contentious and acrimonious disposition, with a talent for making personal enemies over scientific matters. He blamed Berthelot, who was a 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 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.

Interests

• Philosophers & Thinkers

  Plato

Connections

In October 1890 while at Lille Duhem 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.

Father:

Pierre-Joseph Duhem

Mother:

Alexandrine Fabre

Spouse:

Adèle Chayet

Daughter:

Hélène Duhem

teacher:

Jules Moutier

References

• Critical Problems in the History of Science
  1959
• Revue De Métaphysique Et De Morale, Volume 7
  1899
• L'électrodynamique des milieux isotropes en repos d'après Helmholtz et Duhem
  1923
• The Methodology of Pierre Duhem
  1941