Pierre Duhem

Pierre Maurice Marie Duhem (French: [pjɛʁ moʁis maʁi dy.ɛm] (listen); 9 June[3] 1861 – 14 September 1916) was a French theoretical physicist who worked on thermodynamics, hydrodynamics, and the theory of elasticity. Duhem was also a historian of science, noted for his work on the European Middle Ages. As a philosopher of science, he is remembered principally for his views on the indeterminacy of experimental criteria (see Duhem-Quine thesis).

Pierre Duhem
Pierre Duhem
Pierre Maurice Marie Duhem

9 June 1861
Paris, France
Died14 September 1916 (aged 55)
Cabrespine, France
Alma materÉcole Normale Supérieure (diploma, 1882)
Era19th-century philosophy
RegionWestern philosophy
SchoolContinental philosophy
French historical epistemology[1]
Main interests
Thermodynamics, philosophy of science, history of science
Notable ideas
Gibbs–Duhem equation, Duhem–Margules equation, Clausius–Duhem inequality, Duhem–Quine thesis, confirmation holism

Theoretical physics

Among scientists, Duhem is best known today for his work on chemical thermodynamics, and in particular for the Gibbs–Duhem and Duhem–Margules equations. His approach was strongly influenced by the early works of Josiah Willard Gibbs, which Duhem effectively explicated and promoted among French scientists. In continuum mechanics, he is also remembered for his contribution to what is now called the Clausius–Duhem inequality.

Duhem was convinced that all physical phenomena, including mechanics, electromagnetism, and chemistry, could be derived from the principles of thermodynamics.[4] Influenced by Macquorn Rankine's "Outlines of the Science of Energetics",[5] Duhem carried out this intellectual project in his Traité de l'Énergétique (1911), but was ultimately unable to reduce electromagnetic phenomena to thermodynamic first principles.

With Ernst Mach, Duhem shared a skepticism about the reality and usefulness of the concept of atoms.[6] He therefore did not follow the statistical mechanics of Maxwell, Boltzmann, and Gibbs, who explained the laws of thermodynamics in terms of the statistical properties of mechanical systems composed of many atoms.

History of science

Nicole Oresme, a prominent medieval scholar. Duhem came to regard the medieval scholastic tradition as the origin of modern science.

Duhem is well known for his work on the history of science,[7][8][9][10] which resulted in the ten volume Le système du monde: histoire des doctrines cosmologiques de Platon à Copernic (The System of World: A History of Cosmological Doctrines from Plato to Copernicus).[11] Unlike many former historians (e.g. Voltaire and Condorcet), who denigrated the Middle Ages, he endeavored to show that the Roman Catholic Church had helped foster Western science in one of its most fruitful periods. His work in this field was originally prompted by his research into the origins of statics, where he encountered the works of medieval mathematicians and philosophers such as John Buridan, Nicole Oresme and Roger Bacon, whose sophistication surprised him. He consequently came to regard them as the founders of modern science, having in his view anticipated many of the discoveries of Galileo Galilei and later thinkers.[12] Duhem concluded that "the mechanics and physics of which modern times are justifiably proud to proceed, by an uninterrupted series of scarcely perceptible improvements, from doctrines professed in the heart of the medieval schools."[13]

Duhem popularized the concept of "saving the phenomena." In addition to the Copernican Revolution debate of "saving the phenomena" (Greek σῴζειν τὰ φαινόμενα, sozein ta phainomena[14])[15][16] versus offering explanations[17] that inspired Duhem was Thomas Aquinas, who wrote, regarding eccentrics and epicycles, that

Reason may be employed in two ways to establish a point: firstly, for the purpose of furnishing sufficient proof of some principle. [...] Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astronomy the theory of eccentrics and epicycles is considered as established, because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this proof were sufficient, forasmuch as some other theory might explain them. [...][18]

Philosophy of science

Duhem's views on the philosophy of science are explicated in his 1906 work The Aim and Structure of Physical Theory.[21] In this work, he opposed Newton's statement that the Principia's law of universal mutual gravitation was deduced from 'phenomena', including Kepler's second and third laws. Newton's claims in this regard had already been attacked by critical proof-analyses of the German logician Leibniz and then most famously by Immanuel Kant, following Hume's logical critique of induction. But the novelty of Duhem's work was his proposal that Newton's theory of universal mutual gravity flatly contradicted Kepler's Laws of planetary motion because the interplanetary mutual gravitational perturbations caused deviations from Keplerian orbits. Since no proposition can be validly logically deduced from any it contradicts, according to Duhem, Newton must not have logically deduced his law of gravitation directly from Kepler's Laws.[21][22][23][24]

Duhem's name is given to the underdetermination or Duhem–Quine thesis, which holds that for any given set of observations there is an innumerably large number of explanations. It is, in essence, the same as Hume's critique of induction: all three variants point at the fact that empirical evidence cannot force the choice of a theory or its revision. Possible alternatives to induction are Duhem's instrumentalism and Popper's thesis that we learn from falsification.

As popular as the Duhem–Quine thesis may be in the philosophy of science, in reality Pierre Duhem and Willard Van Orman Quine stated very different theses. Pierre Duhem believed that experimental theory in physics is fundamentally different from fields like physiology and certain branches of chemistry. Also Duhem's conception of theoretical group has its limits, since not all concepts are connected to each other logically. He did not include at all a priori disciplines such as logic and mathematics within these theoretical groups in physics which can be tested experimentally. Quine, on the other hand, conceived this theoretical group as a unit of a whole human knowledge. To Quine, even mathematics and logic must be revised in light of recalcitrant experience, a thesis that Duhem never held.

Duhem's philosophy of science was criticized by one of his contemporaries, Abel Rey, in part because of what Rey perceived as influence on the part of Duhem's Catholic faith.[25]

Opposition to the English inductivist tradition

Duhem argues that physics is subject to certain methodological limitations that do not affect other sciences. In his The Aim and Structure of Physical Theory[21] (1914), Duhem critiqued the Baconian notion of "crucial experiments". According to this critique, an experiment in physics is not simply an observation, but rather an interpretation of observations by means of a theoretical framework. Furthermore, no matter how well one constructs one's experiment, it is impossible to subject an isolated single hypothesis to an experimental test. Instead, it is a whole interlocking group of hypotheses, background assumptions, and theories that is tested. This thesis has come to be known as confirmation holism. This inevitable holism, according to Duhem, renders crucial experiments impossible. More generally, Duhem was critical of Newton's description of the method of physics as a straightforward "deduction" from facts and observations.

In the appendix to The Aim and Structure, entitled "Physics of a Believer," Duhem draws out the implications that he sees his philosophy of science as having for those who argue that there is a conflict between physics and religion. He writes, "metaphysical and religious doctrines are judgments touching on objective reality, whereas the principles of physical theory are propositions relative to certain mathematical signs stripped of all objective existence. Since they do not have any common term, these two sorts of judgments can neither contradict nor agree with each other" (p. 285). Nonetheless, Duhem argues that it is important for the theologian or metaphysician to have detailed knowledge of physical theory in order not to make illegitimate use of it in speculations.



Duhem's mathematics papers from NUMDAM

Works in English translation

  • Duhem, Pierre (1903). Thermodynamics and Chemistry. A Non-mathematical Treatise for Chemists and Students of Chemistry (1st ed.). New York; London: J. Wiley & Sons; Chapman & Hall. OCLC 3383130. Retrieved 2011-08-31.
  • Duhem, Pierre (1954). The Aim and Structure of Physical Theory. Princeton: Princeton University Press. 2nd. Ed., 1991. (excerpts: excerpt 1, & excerpt 2 "Heavenly bodies: Theory, physics and philosophy")
    • "Physical Theory and Experiment," in Herbert Feigl & May Brodbeck (ed.), Readings in the Philosophy of Science. New York: Appleton-Century-Crofts, Inc., 1953, pp. 235–252.
  • Duhem, Pierre (1969). To Save the Phenomena, an Essay on the Idea of Physical Theory from Plato to Galileo. Chicago: University of Chicago Press. OCLC 681213472. (excerpt)
  • Duhem, Pierre (1985). Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds. Chicago: University of Chicago Press. ISBN 978-0-226-16922-4. OCLC 712044683. (excerpt: "The 12th century birth of the notion of mass which advised modern mechanics ... and void and movement in the void")
  • Duhem, Pierre (1988). The Physicist as Artist: The Landscapes of Pierre Duhem. Edinburgh: Scottish Academic Press. ISBN 0707305349
  • Duhem, Pierre (1990). "Logical Examination of Physical Theory," Synthese, Vol. 83, No. 2, pp. 183–188.
  • Duhem, Pierre (1990). "Research on the History of Physical Theories," Synthese, Vol. 83, No. 2, pp. 189–200.
  • Duhem, Pierre (1991). German Science. La Salle, Ill.: Open Court. ISBN 0812691245
  • Duhem, Pierre (1991). The Origins of Statics The Sources of Physical Theory. Boston Studies in the Philosophy of Science. 123. Dordrecht: Springer Netherlands. doi:10.1007/978-94-011-3730-0. ISBN 9789401137300.
  • Duhem, Pierre (1996). Essays in the History and Philosophy of Science. Indianapolis: Hackett Pub. Co. ISBN 978-0-87220-308-2. OCLC 33968944.
  • Duhem, Pierre (2011). Commentary on the Principles of Thermodynamics by Pierre Duhem. Dordrecht; New York: Springer. ISBN 978-94-007-0311-7. OCLC 733543752.
  • Duhem, Pierre Maurice Marie (2015). The Electric Theories of J. Clerk Maxwell. Boston Studies in the Philosophy and History of Science. 314. Alan Aversa (trans.). Cham: Springer International Publishing. doi:10.1007/978-3-319-18515-6. ISBN 978-3-319-18515-6. Retrieved 2015-07-08.


Articles contributed to the 1912 Catholic Encyclopedia

The above bibliography is not exhaustive. See his complete primary sources and secondary sources at the Duhem entry of the Stanford Encyclopedia of Philosophy.


  1. ^ Donald Broady, "The epistemological tradition in French sociology", 1996.
  2. ^ John T. Blackmore, Ernst Mach: His Work, Life, and Influence, 1972, p. 196.
  3. ^ Jaki, Stanley L. (1987). Uneasy Genius: The Life and Work of Pierre Duhem. Dordrecht: Martinus Nijhoff, p. 3.
  4. ^ Roger Ariew (2007). "Pierre Duhem". Stanford Encyclopedia of Philosophy. Retrieved 2009-11-07.
  5. ^ Macquorn Rankine (1855). "Outlines of the Science of Energetics," The Edinburgh New Philosophical Journal, Vol. II, pp. 120–140.
  6. ^ See Hentschel (1988) on these and other parallels between Duhem and Mach, and on their correspondence.
  7. ^ "Pierre Duhem, himself a distinguished physicist, initiated in heroic fashion, almost singlehandedly, the modern study of the history of medieval science by the simple but effective expedient of reading and analyzing as many medieval scientific manuscripts as possible." — Palter, Robert M. (1961). Preface to Toward Modern Science, Vol. I. New York: The Noonday Press, p. ix.
  8. ^ Paul, Harry W. (1972). "Pierre Duhem: Science and the Historian's Craft," Journal of the History of Ideas, 33, pp. 497–512.
  9. ^ Murdoch, John E. (1991). "Pierre Duhem and the History of Late Medieval Science and Philosophy in the Latin West," in R. Imbach & A. Maierù, eds., Gli Studi di Filosofia Medievale fra Otto e Novecento. Rome: Edizioni di Estoria e Letteratura, pp. 253–302.
  10. ^ "By his numerous publications, Duhem made medieval science a respectable research field and placed the late Middle Ages in the mainstream of scientific development. He thus filled the hiatus that had existed between Greek and Arabic science, on the one extreme, and early modern science in the seventeenth-century Europe, on the other. For the first time, the history of science was provided with a genuine sense of continuity." — Grant, Edward (1996). The Foundations of Modern Science in the Middle Ages. Cambridge University Press, p. xi.
  11. ^ Duhem, Pierre (1914). Le système du monde: histoire des doctrines cosmologiques de Platon à Copernic (The System of World: A History Cosmological Doctrines from Plato to Copernicus).
  12. ^ Wallace, William A. (1984). Prelude, Galileo and his Sources. The Heritage of the Collegio Romano in Galileo's Science. N.J.: Princeton University Press.
  13. ^ Lindberg, David C.; Westman, Robert S., eds. (27 Jul 1990) [Duhem, Pierre (1905). "Preface". Les Origines de la statique 1. Paris: A. Hermman. p. iv.]. "Conceptions of the Scientific Revolution from Bacon to Butterfield". Reappraisals of the Scientific Revolution (1st ed.). Cambridge: Cambridge University Press. p. 14. ISBN 978-0-521-34804-1.
  14. ^ An ancient view (attributed to Plato by Simplicius of Cilicia) on hypotheses, theories and phaenomena, on what scientists, or more historically accurately (ancient) astronomers, are for, are supposed to do; see Geminus of Rhodes; James Evans; J.L. Berggren (2006). "10. Reality and Representations in Greek Astronomy: Hypotheses and Phenomena". Geminos's Introduction to the Phenomena: A Translation and Study of a Hellenistic Survey of Astronomy. Princeton University Press. pp. 49–51. Wherein "The oldest extant text in which the expression "save the phenomena" is only of the first century A.D. namely Plutarch's On the Face in the Orb of the Moon", hence see also (in Greek) Plutarch, De faciae quae in orbe lunae apparet, 923a (or in English) at the Perseus Project
  15. ^ Cf. Duhem, Pierre (1969). To save the phenomena, an essay on the idea of physical theory from Plato to Galileo. Chicago: University of Chicago Press. OCLC 681213472. (excerpt on pg. 132).
  16. ^ Cf. Andreas Osiander's Ad lectorem introduction to Copernicus's De revolutionibus orbium coelestium.
  17. ^ Pierre Duhem thinks "Kepler is, unquestionably, the strongest and most illustrious representative of that tradition," i.e., the tradition of realism, that physical theories offer explanations in addition to just "saving the phenomena."
  18. ^ Summa Theologica, I q. 32 a. 1 ad 2
  19. ^ Duhem, Pierre Maurice Marie (1991). The Aim and Structure of Physical Theory (9932 ed.). Princeton: Princeton University Press. ISBN 978-0691025247.
  20. ^ Cady, Walter G. (1946). Piezoelectricity. New York, NY, USA: McGraw-Hill. p. 245.
  21. ^ a b c Duhem, Pierre; Philip P. Wiener (1954). La Théorie Physique: son Objet et sa Structure [The Aim and Structure of Physical Theory]. Jules Vuillemin. Princeton University Press. ISBN 978-0-691-02524-7.
  22. ^ Lakatos, Imre; Paul Feyerabend; Matteo Motterlini (1999). For and Against Method: Including Lakatos's Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence. University of Chicago Press. pp. 45–49. ISBN 978-0-226-46774-0.
  23. ^ Lakatos, Imre; John Worrall; Gregory Currie (1980). "5: Newton's Effect on Scientific Standards". The Methodology of Scientific Research Programmes. Cambridge University Press. ISBN 978-0-521-28031-0.
  24. ^ Lakatos, Imre; John Worrall; Gregory Currie (1978). "5: The Method of Analysis-Synthesis". Mathematics, Science, and Epistemology. Cambridge University Press. ISBN 978-0-521-21769-9.
  25. ^ Page 2018, p. 5


  • Dijksterhuis, E.J. (1959). "The Origins of Classical Mechanics from Aristotle to Newton", in M. Clagett (ed). Critical Problems in the History of Science, pp. 163–184. University of Wisconsin Press.
  • Hentschel, Klaus (1988). "Die Korrespondenz Duhem-Mach: Zur 'Modellbeladenheit' von Wissenschaftsgeschichte", Annals of Science, 73–91.
  • Lowinger, Armand (1941). The Methodology of Pierre Duhem. Columbia University Press.
  • Martin, R. N. D. (1991). Pierre Duhem: Philosophy and History in the Work of a Believing Physicist. ISBN 978-0-8126-9160-3.
  • Miller, Donald G. (1970). "Pierre Duhem". In Gillispie, Charles (ed.). Dictionary of Scientific Biography. 3. New York: Scribner & American Council of Learned Societies. pp. 225–233. ISBN 978-0-684-10114-9.
  • Moody, Ernest A. (1951). "Galileo and Avempace: The Dynamics of the Leaning Tower Experiment". Journal of the History of Ideas. 12 (3): 375–422. doi:10.2307/2707752. JSTOR 2707752.
  • Moody, Ernest A. (1966). "Galileo and his Precursors", in C.L. Gollino, ed., Galileo Reappraised. Berkeley: University of California Press, 23–43.
  • Martin, R. N. D. (1991). Pierre Duhem: Philosophy and History in the Work of a Believing Physicist. ISBN 978-0-8126-9160-3.
  • Needham, Paul (2008). "Pierre Duhem". Dictionary of Scientific Biography.
  • Page, Meghan D. (17 January 2018). "Sense and Reference of a Believer". American Catholic Philosophical Quarterly. 92: 145–157. doi:10.5840/acpq2018116143. Retrieved 21 January 2018.
  • Picard, Émile (1922). "La Vie et l'Oeuvre de Pierre Duhem," in Discours et Mélanges. Paris: Gauthier-Villars.
  • Stoffel, Jean-François; Stanley L. Jaki (1996). Pierre Duhem et ses Doctorands: Bibliographie de la Littérature Primaire et Secondaire. Centre Interfacultaire d'Étude en Histoire des Sciences. p. 325. ISBN 978-2-930175-00-3.
  • Stoffel, Jean-François; Jean Ladrière (2002). Le Phénoménalisme Problématique de Pierre Duhem. Brussels: Classe des Lettres, Académie Royale de Belgique. p. 391. ISBN 978-2-8031-0190-0.

Further reading

  • Alexander, Peter (1964). "The Philosophy of Science, 1850–1910," in D.J. O'Connor, ed., A Critical History of Western Philosophy. New York: The Free Press, pp. 402–425.
  • Ariew, Roger (2011) Pierre Duhem, Stanford Encyclopedia of Philosophy, January 20, 2011.
  • Dawson, Christopher (1959). "The Scientific Development of Medieval Culture," in Medieval Essays. New York: Image Books, pp. 122–147.
  • Deltete, Robert J. (2008). "Man of Science, Man of Faith: Pierre Duhem's 'Physique de Croyant'," Zygon 43 (3), pp. 627–637.
  • Jaki, Stanley L. (1985–86). "Science and Censorship: Hélène Duhem and the Publication of the 'Système du Monde'," The Intercollegiate Review 21 (2), pp. 41–49 [Rep., in The Absolute Beneath the Relative and Other Essays. University Press of America, 1988].
  • Jaki, Stanley L. (1992). Reluctant Heroine, The Life and Work of Helene Duhem. Scottish Academic Press.
  • Jaki, Stanley L. (1993). "Medieval Christianity: Its Inventiveness in Technology and Science," in Technology in the Western Political Tradition. Ed. M.R. Zinman. Cornell University Press, pp. 46–68.
  • Kahler, Erich (1943). "Reason and Science," in Man: The Measure. New York: Pantheon Books, Inc.
  • Quinn, Philip L. (1974). "What Duhem Really Meant," in Robert S. Cohen & Marx W. Wartofsky, eds., Methodological and Historical Essays in the Natural and Social Sciences. Dordrecht: Reidel Publishing Company.
  • Schaffers, V. (1922). "Pierre Duhem et la Théorie Physique," Revue des Questions Scientifiques, pp. 42–73.
  • Bordoni, Stefano (2012). Taming complexity: Duhem's third pathway to thermodynamics. Urbino: Montefeltro. ISBN 9788885363588.

External links

1916 in philosophy

1916 in philosophy

A. I. Sabra

Abdelhamid I. Sabra (1924-2013) was a professor of the history of science specializing in the history of optics and science in medieval Islam. He died December 18, 2013. Sabra provided English translation and commentary for Books I-III of Ibn al-Haytham's seven book Kitab al-Manazir (Book of Optics), written in Arabic in the 11th century.

Sabra received his undergraduate degree at the University of Alexandria. He then studied philosophy of science with Karl Popper at the University of London, where he received a PhD in 1955 for a thesis on optics in the 17th century. He taught at the University of Alexandria 1955-62, at the Warburg Institute 1962-72, and at Harvard University from 1972 until he retired in 1996.

In his article on "The Appropriation and Subsequent Naturalization of Greek Science in Medieval Islam", he argued, against the theories of Pierre Duhem, that Islamic cultures did not passively receive and preserve ancient Greek science, but actively "appropriated" and modified it.In 2005 he was awarded the Sarton Medal for lifetime achievement in the history of science by the History of Science Society.

Clausius–Duhem inequality

The Clausius–Duhem inequality is a way of expressing the second law of thermodynamics that is used in continuum mechanics. This inequality is particularly useful in determining whether the constitutive relation of a material is thermodynamically allowable.This inequality is a statement concerning the irreversibility of natural processes, especially when energy dissipation is involved. It was named after the German physicist Rudolf Clausius and French physicist Pierre Duhem.


Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality. Although this attitude is commonly held with respect to the rules of grammar, its application to the propositions of ethics, law, science, mathematics, and logic is more controversial.

Duhem–Margules equation

The Duhem–Margules equation, named for Pierre Duhem and Max Margules, is a thermodynamic statement of the relationship between the two components of a single liquid where the vapour mixture is regarded as an ideal gas:

where PA and PB are the partial vapour pressures of the two constituents and xA and xB are the mole fractions of the liquid.


Duhem - Margulus equation give the relation between change of mole fraction with partial pressure of a component in a liquid mixture.

Let consider a binary liquid mixture of two component in equilibrium with their vapour at constant temperature and pressure. Then from Gibbs - Duhem equation is

nAA + nBB = 0 ...(I)

Where nA and nB are number of moles of the component A and B while μA and μB is their chemical potential.

Dividing equ. (i) by nA + nB , ththen

(nA / nA + nB ) dμA + (nB / nA + nB) dμB= 0


xAA + xBB = 0. ...(ii)

Now the chemical potential of any componentv in mixture is depend upon temperature, pressure and composition of mixture. Hence if temperature and pressure taking constant then chemical potential

A = (dμA / dxA )T, P dxA ...(iii)

B = (dμB / dxB )T, P dxB. ...(iv)

Putting these values in equ. (ii), then

xA(dμΑ / dxA)T, P dxA + xB(dμB / dxB)T, P dxB = 0 ...(v)

Because the sum of mole fraction of all component in the mixture is unity i.e.,

x1 + x2 = 1


dx1 + dx2 = 0 or dx1 = -dx2

puting these value in equ. (v), then

xA(dμΑ / dxA)T, P = xB(dμB / dxB)T, P …(vi)

Now the chemical potential of any component in mixture is such that

μ = μo + RT In P , where P is partial pressure of component. Now differentiating this equ.

dμ / dx = RT (d In P / dx)

Above equ.can be written for component A and B is

A / dxA = RT (d In PA / dxA) …(vii)

B / dxB = RT (d In PB / dxB) …(viii)

Substituting these value in equ.(vi), then

xA (d In PA / dxA) = xB (d In PB / dxB)


(d In PA / d lnxA) = (d In PB / d lnxB)

this is the final equation of Duhem- Margules equation.

Duhem–Quine thesis

The Duhem–Quine thesis, also called the Duhem–Quine problem, after Pierre Duhem and Willard Van Orman Quine, is that it is impossible to test a scientific hypothesis in isolation, because an empirical test of the hypothesis requires one or more background assumptions (also called auxiliary assumptions or auxiliary hypotheses). In recent decades the set of associated assumptions supporting a thesis sometimes is called a bundle of hypotheses.

European science in the Middle Ages

European science in the Middle Ages comprised the study of nature, mathematics and natural philosophy in medieval Europe. Following the fall of the Western Roman Empire and the decline in knowledge of Greek, Christian Western Europe was cut off from an important source of ancient learning. Although a range of Christian clerics and scholars from Isidore and Bede to Buridan and Oresme maintained the spirit of rational inquiry, Western Europe would see a period of scientific decline during the Early Middle Ages. However, by the time of the High Middle Ages, the region had rallied and was on its way to once more taking the lead in scientific discovery. Scholarship and scientific discoveries of the Late Middle Ages laid the groundwork for the Scientific Revolution of the Early Modern Period.

According to Pierre Duhem, who founded the academic study of medieval science as a critique of the Enlightenment-positivist theory of a 17th-century anti-Aristotelian and anticlerical scientific revolution, the various conceptual origins of that alleged revolution lay in the 12th to 14th centuries, in the works of churchmen such as Aquinas and Buridan.In the context of this article, "Western Europe" refers to the European cultures bound together by the Roman Catholic Church and the Latin language.

Experimentum crucis

In the sciences, an experimentum crucis (English: crucial experiment or critical experiment) is an experiment capable of decisively determining whether or not a particular hypothesis or theory is superior to all other hypotheses or theories whose acceptance is currently widespread in the scientific community. In particular, such an experiment must typically be able to produce a result that rules out all other hypotheses or theories if true, thereby demonstrating that under the conditions of the experiment (i.e., under the same external circumstances and for the same "input variables" within the experiment), those hypotheses and theories are proven false but the experimenter's hypothesis is not ruled out.

For an opposite view putting into question the decisive value of the experimentum crucis in choosing one hypothesis or theory over its rival see Pierre Duhem.

Gibbs–Duhem equation

In thermodynamics, the Gibbs–Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamic system:

where is the number of moles of component the infinitesimal increase in chemical potential for this component, the entropy, the absolute temperature, volume and the pressure. is the number of different components in the system. This equation shows that in thermodynamics intensive properties are not independent but related, making it a mathematical statement of the state postulate. When pressure and temperature are variable, only of components have independent values for chemical potential and Gibbs' phase rule follows. The Gibbs−Duhem equation cannot be used for small thermodynamic systems due to the influence of surface effects and other microscopic phenomena.

The equation is named after Josiah Willard Gibbs and Pierre Duhem.

Historiography of science

The historiography of science is the study of the history and methodology of the sub-discipline of history, known as the history of science, including its disciplinary aspects and practices (methods, theories, schools) and to the study of its own historical development ("History of History of Science", i.e., the history of the discipline called History of Science).

Since historiographical debates regarding the proper method for the study of the history of science are sometimes difficult to demarcate from historical controversies regarding the very course of science, it is often (and rightly) the case that the early controversies of the latter kind are considered the inception of the sub-discipline. For example, such discussions permeate the historical writings of the great historian and philosopher of science William Whewell. He is thus often (and rightly) viewed as the grandfather of this discipline; other such distinguished grandfathers are Pierre Duhem and Alexandre Koyré.

As to the explicit presentation of the Historiography of Science it is usually dated in the early Sixties of the 20th century. Thus, for example, in 1965, we find Gerd Buchdahl reporting "A Revolution in Historiography of Science" referring to the innovative studies of Thomas Kuhn and Joseph Agassi. He suggested that these two writers had inaugurated the sub discipline by distinguishing clearly between the history and the historiography of science, as they argued that historiographical views greatly influence the writing of the history of science.


In philosophy of science and in epistemology, Instrumentalism is a methodological view that ideas are useful instruments, and that the worth of an idea is based on how effective it is in explaining and predicting phenomena. Instrumentalism is a pragmatic philosophy of John Dewey that thought is an instrument for solving practical problems, and that truth is not fixed but changes as problems change. Instrumentalism is the view that scientific theories are useful tools for predicting phenomena instead of true or approximately true descriptions.The truth of an idea is determined by its success in the active solution of a problem. A successful scientific theory reveals nothing known either true or false about nature's unobservable objects, properties or processes. Scientific theories are assessed on their usefulness in generating predictions and in confirming those predictions in data and observations, and not on their ability to explain the truth value of some unobservable phenomenon. The question of "truth" is not taken into account one way or the other. According to instrumentalists, scientific theory is merely a tool whereby humans predict observations in a particular domain of nature by formulating laws, which state or summarize regularities, while theories themselves do not reveal supposedly hidden aspects of nature that somehow explain these laws. Initially a novel perspective introduced by Pierre Duhem in 1906, instrumentalism is largely the prevailing theory that underpins the practice of physicists today.Rejecting scientific realism's ambitions to uncover metaphysical truth about nature, instrumentalism is usually categorized as an antirealism, although its mere lack of commitment to scientific theory's realism can be termed nonrealism. Instrumentalism merely bypasses debate concerning whether, for example, a particle spoken about in particle physics is a discrete entity enjoying individual existence, or is an excitation mode of a region of a field, or is something else altogether. Instrumentalism holds that theoretical terms need only be useful to predict the phenomena, the observed outcomes.There are multiple versions of instrumentalism. Instrumentalism is a variety of scientific anti-realism.

John Hennon

John (Johannes) Hennon (died after 1484) was a Dutch medieval philosopher in the late Scholastic tradition. He was from Nijmegen, and studied at the University of Paris, where he received his magister artium and baccalaureus formatus in sacra pagina (1463).

As a student of Paris, Hennon was heavily influenced by William of Ockham and Roger Bacon. He wrote a Latin commentary on the Physics of Aristotle, the Commentarii in Aristotelis libros Physicorum, which was completed on 1 October 1473 if a seventeenth-century source is to be believed. Examining the state of science in the late Middle Ages, physicist, historian, and philosopher Pierre Duhem, in Le système du monde, isolates Hennon's account of the vacuum and a plurality of worlds.

Hennon believed that nature abhors a vacuum and therefore no natural void was possible, though God could create one. A void, however, is not defined by a positive distance between surfaces in which there is nothing, but rather as the capacity (potentialitas) for a body to be interposed between the two surfaces equal to that which is there when it is full. Hennon affirms that ice is denser than liquid water, and that a sealed vase of water will break upon freezing because nature abhors a vacuum. He believes further that two smooth plates could not be separated (again, because nature abhors a vacuum) unless there were some air still between them, which with enough force may become rarefied, allowing the plates to be separated.

Hennon is less original on a plurality of worlds, where he borrows text verbatim from Albert of Saxony's Quaestiones in libros de Caelo et Mundo. He follows Albert and John Buridan in asserting that a multiplicity of worlds is not contradictory and therefore possible through divien omnipotence. In fact, God could create an infinite multitude of beings, since Hennon finds no contradiction between infinity and magnitude. Duhem in his analysis of Hennon's chapter De Caelo et Mundo, argues that Hennon relied on the Condemnations of 1277 by Stephen Tempier to attack Aristotelian physics, and thus the position that the earth cannot move.

Jules Tannery

Jules Tannery (24 March 1848 – 11 December 1910) was a French mathematician, brother of the mathematician and historian of science Paul Tannery, who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard. Tannery's theorem on interchange of limits and series is named after him.Under Hermite, he received is doctorate in 1874 for his thesis Propriétés des Intégrales des Équations Différentielle Linéaires à Coefficients Variables.

Tannery discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think."

He notably influenced Pierre Duhem, Paul Painlevé, Jules Drach, and Émile Borel to take up science.

His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking.

Tannery was "an original thinker, a successful teacher, and a writer endowed with an unusually clear, brilliant and attractive style."

List of lay Catholic scientists

Many Catholics have made significant contributions to the development of science and mathematics from the Middle Ages to today. These scientists include Galileo Galilei, René Descartes, Louis Pasteur, Blaise Pascal, André-Marie Ampère, Charles-Augustin de Coulomb, Pierre de Fermat, Antoine Laurent Lavoisier, Alessandro Volta, Augustin-Louis Cauchy, Pierre Duhem, Jean-Baptiste Dumas, Alois Alzheimer, Georgius Agricola, and Christian Doppler.

For additional Catholic scientists, see the List of Catholic churchmen-scientists.

List of philosophers of science

This is a chronological list of philosophers of science. For an alphabetical name-list, see Category:Philosophers of science.


Precursorism, called in its more extreme forms precursoritis or precursitis, is a characteristic of that kind of historical writing in which the author seeks antecedents of present-day institutions or ideas in earlier historical periods. This kind of anachronism is considered to be a form of Whig history and is a special problem among historians of science. The French historian of medieval science, Pierre Duhem, exemplifies several of the characteristics of the quest for precursors of modern scientific ideas. Duhem was trained as a physicist, rather than as a historian; he was French and many of the precursors he identified were French or studied at the University of Paris; he was a devout Catholic and many of the precursors of the theologically troubling Italian, Galileo, were members of religious orders. Most striking among them was the French bishop and scholastic philosopher, Nicole Oresme.The concept has been applied to those who would find precursors of Darwin in the early nineteenth century, and to those who would find anticipations of modern science in ancient cultures from the Near East to Mesoamerica. Precursorism has recently been identified as a significant factor in some studies of the work of Islamic scientists.It is now commonly assumed that historians of science should study past scientific "ideas in their own right, avoiding anachronism and precursoritis."

Scientific formalism

Scientific formalism is a family of approaches to the presentation of science. It is viewed as an important part of the scientific method, especially in the physical sciences.


In the philosophy of science, observations are said to be "theory‐laden" when they are affected by the

theoretical presuppositions held by the investigator. The thesis of theory‐ladenness is most strongly

associated with the late 1950s and early 1960s work of Norwood Russell Hanson, Thomas Kuhn, and Paul Feyerabend, and was probably first put forth (at least implicitly) by Pierre Duhem about 50 years earlier.

Thermodynamic potential

A thermodynamic potential (in fact, rather energy than potential) is a scalar quantity used to represent the thermodynamic state of a system. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. One main thermodynamic potential that has a physical interpretation is the internal energy U. It is the energy of configuration of a given system of conservative forces (that is why it is called potential) and only has meaning with respect to a defined set of references (or data). Expressions for all other thermodynamic energy potentials are derivable via Legendre transforms from an expression for U. In thermodynamics, external forces, such as gravity, are typically disregarded when formulating expressions for potentials. For example, while all the working fluid in a steam engine may have higher energy due to gravity while sitting on top of Mount Everest than it would at the bottom of the Mariana Trench, the gravitational potential energy term in the formula for the internal energy would usually be ignored because changes in gravitational potential within the engine during operation would be negligible. In a large system under even homogeneous external force, like the earth atmosphere under gravity, the intensive parameters () should be studied locally having even in equilibrium different values in different places far from each other (see thermodynamic models of troposphere].

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