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. 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.

BIBLIOGRAPHY

WORKS BY DUHEM

“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.

??ZEIN TA ?AINOMENA: 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.

OTHER SOURCES

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