## 1. Life and Works




Pierre Maurice Marie Duhem was born on June 10, 1861, in Paris, in a
modest neighborhood on the Rue des Jeuneurs, near the Grands
Boulevards, just South of Montmartre. His father, Pierre-Joseph Duhem,
was of Flemish origin, the oldest child of a large family who lived in
the French northern industrial city of Roubaix, near the Belgian
border. After the death of his parents, Pierre-Joseph was forced to
discontinue his studies with the Jesuits in order to provide for the
family. He worked in the textile industry as a sales representative,
but never abandoned his love of learning; it is said that, late in
life, he was seen everywhere with the work of a Latin author under his
arm. Pierre Duhem's mother, Marie-Alexandrine Fabre, descended on
her mother's side from the Hubault-Delormes, a bourgeois family
who had settled in Paris during the seventeenth century. Her
father's family had originally come from the southern town of
Cabesprine, near Carcasonne, and it was there, in a house they still
maintained and to which Pierre returned most summers, that he died on
September 14, 1916.




The Duhems made sure that Pierre was well educated. Starting at the
age of seven he was given private lessons with a small group of
students, on grammar, arithmetic, Latin, and catechism. A letter he
wrote about the siege of Chateaudun he experienced in October 1870
attests to his being already a literate writer by the age of nine. The
young Duhem was witness to some troubling times, with the
Franco-Prussian War raging until the armistice in February 1871 and the
Paris Commune in March. The Duhems had avoided the advance of the
Prussians against Paris but were caught up in the siege of Chateaudun;
they barely escaped to Bordeaux, returning to Paris after the armistice
and just before the Paris Commune. That social experiment lasted only
two months, though it set the stage for some wide-ranging
transformations to French culture that were to have great consequences
when they were later established permanently. Among the Commune's
decrees were the separation of church from state, the rendering of all
church property into public property, and the exclusion of religion
from schools. The Duhems did not approve of these measures and were
particularly chagrined by some of the extreme actions taken by the most
radical elements of the Commune, such as the desecration of churches
and graveyards. For the Duhems, the Commune was a paradigm of anarchy
and irreligion.




The Fall of 1872 brought two great tragedies to the Duhem family: a
diphtheria epidemic killed Pierre's younger sister Antoinette and
his recently born brother Jean, leaving only Pierre and
Antoinette's twin sister Marie. Pierre continued his education
(as *demi-pensionnaire*) at a Catholic school, the
College Stanislas in Paris, in 1872 and for the next ten years.
The mature Duhem recalled his college days as most formative. In
particular, he singled out his science teacher as an important
influence:



> 
> 
> Let us return to some twenty-five years back to the time when we
> received our first initiation as a physicist in the mathematics classes
> of the College Stanislas. The person who gave us this
> initiation, Jules Moutier, was an ingenious theorist; his critical
> sense, ever aware and extremely perspicacious, distinguished with sure
> accuracy the weak point of many a system that others accepted without
> dispute; proofs of his inquiring mind are not lacking, and physical
> chemistry owes him one of its most important laws. It was this teacher
> who planted in us our admiration for physical theory and the desire to
> contribute to its progress. ... Being a disciple of Moutier, it
> was as a convinced partisan of mechanism that we approached the courses
> in physics pursued at the Ecole Normale. (1914, 417-18; 1954,
> 275-76.)




Duhem's science teacher Jules Moutier went on to teach at the
Ecole Polytechnique and to publish a number of texts, including *La
thermodynamique et ses principales applications* (Paris:
Gauthier-Villars, 1885). Duhem recognized in his theory of chemical
dissociation and in his thermodynamics generally a first enunciation of
the chemical theories that Josiah Willard Gibbs, an important later
influence on Duhem, was to develop more fully.




In 1882 Duhem enrolled at the prestigious secular institution of higher
education, the Ecole Normale Superieure. When he entered the
Ecole Normale he was first in his class in the Science Section, out of
the approximately 30 students chosen from the best 800 or so graduates
in France that year, and he remained first throughout his years there.
The curriculum at the Ecole Normale usually lasted three years; Duhem
was granted a fourth year and stayed on a fifth year as
*agrege preparateur*. He received a
*license* in mathematics and another in physics at the end of
academic year 1883-84. In his final year, Duhem was offered a position
in Louis Pasteur's laboratory as a chemist-bacteriologist, though
he refused it because of his desire to work in theoretical physics.




One of the turning points in Duhem's career occurred during
academic year 1884-85, while he was only a third-year student. Duhem
presented a thesis in physics for his doctorate. The thesis, on
thermodynamic potential, *Le potentiel thermodynamique et ses
applications a la mecanique chimique et a
l'etude des phenomenes
electriques*, was rejected by a panel composed of three
scholars: the physicist Gabriel Lippmann and the mathematicians Charles
Hermite and Emile Picard. The panel, chaired by Lippmann, seems to have
made a political decision. The prestigious French scientific publisher,
Hermann, published a version of the thesis the following year. Duhem
defended another thesis in applied mathematics, on the theory of
magnetization by induction, *Sur l'aimantation par
influence*, and received his doctorate in October 1888; this time,
the physicist Edmond Bouty, the mathematician Gaston Darboux, and the
mathematician-physicist Henri Poincare constituted the panel
that accepted the dissertation. It would be difficult to understand
fully these events without delving deeply into the social, cultural,
and intellectual context of France at the end of the nineteenth
century. At a time when French scientists were predominantly liberal
and anti-clerical, Duhem was openly conservative and deeply religious;
he was also stubborn and often contentious. The structure of French
academia was surely also a factor in the affair. However, the specific
motives generally cited in the case were Lipmann's
"jealousy" and the fact that Duhem's thesis refuted
the principle of maximum work: that chemical changes tend spontaneously
to produce maximum heat. It was one of the cherished theses of Marcellin
Berthelot, Lippmann's friend and a significant power in the
French scientific establishment. It was reported that Berthelot had
said: "This young man will never teach in Paris."
Berthelot's edict came true. Duhem spent his academic career in
provincial universities far from Paris, the center of academic life in
France. His teaching positions brought him from Lille, then briefly to
Rennes, then to Bordeaux for the remainder of his life, but never to
Paris.




Duhem assumed the position of Maitre de Conferences at the
Faculte des Sciences at Lille in October 1887. There he met
Adele Chayet, whom he married in October 1890. Their daughter
Helene was born in September 1891. Tragically,
Adele died in childbirth the following summer; the newborn
child also did not survive. Duhem never remarried. He left the
upbringing of Helene to his mother who lived with him
after his father Pierre-Joseph died. The situation in Lille soured for
Duhem. Never one to back off from a dispute, he fought with the Dean
of his faculty over a minor issue: an assistant had failed to unlock
the door of Duhem's laboratory for his students during their
licentiate examinations. The assistant complained about his
mistreatment by Duhem to the Dean, who requested that the assistant
write a letter of apology; Duhem rejected the apology and took issue
with the Dean, who then brought the matter to the Rector, adding
further complaints against Duhem. The minor issue having escalated to
immense proportions, Duhem requested and received a change of
positions at the end of academic year 1893. During these formative
years, Duhem worked very hard on his science. He published six books:
a two-volume work on hydrodynamics, elasticity, and acoustics, his
lectures on electricity and magnetism, in three volumes, and an
introduction to physical chemistry. Duhem was one of the first to
appreciate the work of W. J. Gibbs, writing the earliest critical
examination of Gibbs' "On the Equilibrium of Heterogeneous
Substances" in 1887 and later promoting the French translation
of Gibbs' works (Duhem 1907); for an English translation of
Duhem's 1887 essay on Gibbs and his Commentaries on the
Principles of Thermodynamics, 1892-1894, see Duhem [CPT].



In October 1893, Duhem left Lille for Rennes. He lasted only one year,
leaving for Bordeaux in October 1894. He was hoping for a position in
Paris. The prodigious quantity and quality of his publications in many
fields of science, the philosophy of science, and the history of
science were not able to change his situation. Very late in life, he
was approached about the newly created chair in the History of Science
at the College de France, but he refused to be a candidate for
it. The proud and stubborn Duhem told his daughter: "I am a
theoretical physicist. Either I will teach theoretical physics at Paris
or else I will not go there."




Duhem's curriculum vitae, written in 1913, on the occasion of his
nomination as non-resident member of the Academie des Sciences
(1917, 41-70), lists over 350 items, about 50 of which were books. From
the mid-1880s to 1900, Duhem's primary interests were scientific,
ranging from thermodynamics and physics, but publishing on elasticity
and energetics as late as 1911. In the 1890s, while still at Lille, he
began writing essays on questions of methodology that would lead to the
publication of his most influential books in the philosophy of science,
translated into English as *The Aim and Structure of Physical
Theory* and *To Save the Phenomena*. It was also in the
mid-1890s that Duhem published his first essays in the history of
science, starting on the path that would lead him in 1904 to a new
understanding of the history of science and to his thesis of continuity
between medieval and early modern science. This path would culminate in
such important historical works as *Etudes sur Leonard
de Vinci* and *Le systeme du monde*.




Duhem made a number of enduring contributions to thermodynamics and
physical chemistry. Among these were the Duhem-Margules and
Gibbs-Duhem equations, which deal with reversible processes in
thermodynamics as quasi-static limiting processes and give a general
proof of the Gibbs phase rule. These results were obtained in the
context of a program of generalized thermodynamics called
"energetics." Indeed, Duhem's entire scientific
program was driven by the conviction that a generalized thermodynamics
should be foundational for physical theory, thinking that all of
chemistry and physics, including mechanics, electricity and magnetism,
should be derivable from thermodynamic first principles. Duhem started
from the concept of the thermodynamic potential (the topic of his
failed thesis), deploying it in a manner similar to that of potentials
in mechanics, so as to represent all physical and chemical changes. The
program finds its mature statement in his *Traite
d'energetique* of 1911; it was well received by
late-nineteenth-century energeticists, such as Wilhelm Ostwald and
Georg Helm. So important was energetics for Duhem, that his work in the
history and philosophy of science has been viewed as an attempt to
defend its aims and methods (see Lowinger 1941). More recently, Niall
Martin and others have argued for the importance of religious motives
in Duhem's work (see Martin 1991, Jaki 1991) and it has become
clear in the course of Duhem's writings that he expected the
endpoint of science to harmonize with the teachings of the Catholic
Church.




Whatever was Duhem's initial motivation, his historical and
philosophical work took on a life of its own. One cannot read
Duhem's numerous historical and philosophical tomes and think
that his labor was only in the service of energetics and that the sole
goal of his works was but a defense of its methods and its historical
position. No doubt energetics might be a thread running through
Duhem's various works, and no doubt these works harmonize with
the method of energetics as he conceives it, but energetics cannot be
the whole story.


## 2. Philosophy of Science




Duhem's early methodological views reflected late
nineteenth-century positivism: Physical theory was no more than an aid
to memory, summarizing and classifying facts by providing a symbolic
representation of them; the facts of physical theory are different from
common sense and metaphysics, especially from the mechanical theories
fashionable at the time. Duhem's position was immediately
attacked by a Catholic engineer, Eugene Vicaire, on the grounds
that separating physics from metaphysics implied that physics was the
only real knowledge (another positivistic thesis), and thus conceded
too much to skepticism. Vicaire raised an important point for
turn-of-the-century Catholics because the Church was officially
committed to neo-Thomism, with its generally rationalist apologetics
(see Martin 1991, chap. 2). In his reply Duhem adopted a quasi-Thomist
position: metaphysics is a real form of knowledge, more excellent than
physics, but separated from it in that it has different objects and is
governed by different methods. This immediate response fitted
reasonably well into the framework of neo-Thomism, though it did not go
as far as to reunite the disparate forms of knowledge into a
hierarchical system of sciences including cosmology and metaphysics.
Duhem's mature position was somewhat different, containing three
key ideas elaborated upon on various occasions: (1) the
underdetermination of theory by fact, often referred to as the Duhem
Thesis, (2) the rejection of metaphysics and models in physics, and (3)
natural classification as the endpoint of physical theory.


### 2.1 Against "Newtonian Method": The Duhem Thesis




Duhem's work was important for members of the Vienna Circle,
including Otto Neurath and Philipp Frank, as it had been for Ernst
Mach (for a comparison between Duhem and Mach on thought experiments
and conventionalism, see Buzzoni 2015). Despite Duhem's
conservative beliefs, his work was also taken up by participants in
the Viennese political scene, such as Friedrich Adler, who had
translated *La theorie physique* into German in
1908. The Duhem thesis surfaced fully in Anglo-American philosophy in
the 1950s through the work of W. V. O. Quine. In Quine's
"Two Dogmas of Empiricism," the second dogma is
reductionism, the belief that "each meaningful statement is
equivalent to some construct upon terms which refer to immediate
experience" (1953, 20). Quine argues that reductionism is an
ill-founded dogma. He asserts that although reductionism has ceased to
figure in some empiricists' thoughts, there remains a more
subtle form of reductionism that each statement taken in isolation can
admit confirmation or disconfirmation. Against this dogma Quine
suggests that "our statements about the external world face the
tribunal of sense experience not individually, but only as a corporate
body" (1953, 41), and, in a footnote of the reprinted article in
his collected essays, *From a Logical Point of View*, says that
the doctrine was well argued by Pierre Duhem. Quine proceeds to detail
an "empiricism without the dogmas" in which knowledge is
to be likened to a field of force where "a conflict with
experience at the periphery occasions readjustments in the interior of
the field" (1953, 42), and "any statement can be held true
come what may, if we make drastic enough adjustments elsewhere in the
system" (1953, 43). Because of Quine's reference to Duhem,
the thesis formed from the two sub-theses, that (i) since empirical
statements are interconnected, they cannot be singly disconfirmed, and
(ii), if we wish to hold a particular statement true we can always
adjust another statement, has become known as the Duhem-Quine
thesis.The antecedent of sub-thesis (i) is often referred to as
"holism." Quine attributes only sub-thesis (i) to Duhem;
Duhem would have recognized sub-thesis (i) as an offspring of his, but
would not have fully agreed with it as formulated by Quine.




Duhem does not claim that when there is some conflict with
experience, we can always make enough adjustments elsewhere in the
system. He makes a weaker claim, also limited in other ways, but which
would be equivalent to: when there is some conflict with experience
what is disconfirmed is necessarily ambiguous. Duhem's
formulation of his non-falsifiability thesis is that "if the
predicted phenomenon is not produced, not only is the questioned
proposition put into doubt, but also the whole theoretical scaffolding
used by the physicist" (1914, 281; 1954, 185). He does not take
the second Quinean step of holding any statement true come what may,
but says "the only thing the experiment teaches us is that, among
all the propositions used to predict the phenomenon and to verify that
it has not been produced, there is at least one error; but where the
error lies is just what the experiment does not tell us" (1914,
281; 1954, 185). He refers to two possible ways of proceeding when an
experiment contradicts the consequences of a theory: a timid scientist
might wish to safeguard certain fundamental hypotheses and attempt to
complicate matters by invoking various cases of error and multiplying
the corrections, while a bolder scientist can resolve to change some of
the essential suppositions supporting the entire system (1914, 329;
1954, 216-17). The scientist has no guarantee of success: "If
they both succeed in satisfying the requirements of the experiment,
each is *logically* permitted to declare himself content with
the work he has accomplished" (1914, 330; 1954, 217).




Moreover, Duhem does not argue directly for the non-falsifiability
thesis. He seems to regard it as an obvious corollary of another
thesis, which could be called the non-separability thesis, that the
physicist can never submit an isolated hypothesis to experimental test:
"To seek to separate each of the hypotheses of theoretical
physics from the other assumptions upon which this science rests, in
order to subject it in isolation to the control of observation, is to
pursue a chimera" (1914, 303; 1954, 199-200).




The Duhemian thesis usually makes its appearance in the context of
Duhem's critique of the inductive method (or what he calls the
Newtonian method), which rejects any hypothesis about imperceptible
bodies and hidden movements and admits only general laws known by
induction from observation. Duhem accuses this method of being
unmanageable; he asserts that a science can only follow the Newtonian
method when its means of knowing are those of common sense: "When
science no longer observes facts directly but substitutes for them
measurements, given by instruments, of magnitudes that mathematical
theory alone defines, induction can no longer be practiced in the
manner that the Newtonian method requires," (1917, 153; [EHPS,
234]). He clearly indicates that some sciences can use the Newtonian
method, derive their principles by induction from observation and
disconfirm them as tests warrant. What Duhem thinks is wrong with
inductivism is that it cannot be used by all sciences. For Duhem the
non-falsifiability thesis is a consequence of the non-separability thesis, and
the non-separability thesis is an empirical thesis depending upon factors
that do not govern all sciences. This is supported as well by
Duhem's assertions, in *La theorie physique*, that
he is imposing narrow limits on his inquiry, and is restricting his
generalizations to physics; when he first announces the non-separability
thesis, he announces it as a principle about what physicists do, whose
consequences will be developed in the remainder of the
book.




It is not generally known that Duhem in his lifetime confronted an
extension of his thesis in the fashion of Quine and had previously
rejected it. In the 1913 essay entitled "Examen logique de la
theorie physique," republished as part II of the overview
of all his work, Duhem sketched the set of theses constituting the
Duhem thesis and stated:



> 
> 
> Separated from the various schools of Pragmatists on the subject of
> the value of physical theory, we do not take our stand, in any
> circumstance, among the number of their followers. The analysis we have
> given of experiments in physics shows fact to be completely
> interpenetrated by theoretical interpretation, to the point where it
> becomes impossible to express fact in isolation from theory, in such
> experiments. This analysis has found great favor on the side of many
> Pragmatists. They have extended it to the most diverse fields: to
> history, to exegesis, to theology. (1917, 156 [EHPS, 237])




Thus, already by 1913, the scope of Duhem's thesis had been
stretched beyond Duhem's intentions. "The several authors
we have just cited often draw from this analysis of the experimental
method used in physics conclusions which go beyond the boundaries of
physics; we shall not follow them that far, but shall stay always
within the limits of physical science" (1914, 218n; 1954, 144n).
While Duhem did not identify these authors, these
"pragmatists," as early as 1905, in a footnote of *La
theorie physique*, he asserts that some of his friends and
acquaintances and, in particular, Gaston Milhaud, Edouard Le Roy, and
Joseph Wilbois had adopted his analysis of experimental method, as
discussed in his earlier articles (1914, 217-218n; 1954, 144n). And
these same thinkers, together with Duhem's very good friend,
Maurice Blondel, were referred to favorably as "French
pragmatists" by William James in 1907 in his *Lectures on
Pragmatism*: "If my lectures interest any reader in the
general subject, he will doubtless wish to read farther. I therefore
give him a few references. ... Furthermore, see J. Milhaud, *Le
Rationnel*, 1898, and the fine articles by Le Roy in the *Revue
de Metaphysique*, vols. 7, 8, and 9. Also articles by Blondel and
de Sailly in the *Annales de Philosophie Chretienne*,
4eme Serie, vols. 2 and 3. Papini announces a book on
Pragmatism, in the French language, to be published very soon"
(James, 1981, 3; a quick glance at Milhaud's *Le
Rationnel* reveals numerous references to Duhem). Thus the Duhem
thesis in its extended form was favorably received in the Anglophone
world during the first few decades of the twentieth century, well
before Quine's reference to it. Duhem's reaction to the
extension of his thesis was as follows:



> 
> 
> We do not deny that this extension is legitimate to some extent.
> However different the problems may be, it is always the same human
> intellect that exerts itself to resolve them. In the same way, there is
> always something common in the several procedures reason employs. But
> if it is good to notice the analogies between our diverse scientific
> methods, it is on condition that we do not forget the differences
> separating them. And, when we compare the method of physics, so
> strangely specialized in the application of mathematical theory and by
> the use of measuring instruments, to other methods, there are surely
> more differences to describe than analogies to discover. (1917, 156
> [EHPS, 237])


### 2.2 Against "Cartesian Method": Metaphysics and Models




In the overview of all his scholarly works in the document
supporting his candidacy for membership to the Academie des
Sciences Duhem contrasted the methodology of energetics with the two
leading methodologies at the time, what he called the method of the
Cartesians and that of the Newtonians. We have discussed his critique
of the Newtonians; we now turn to that of the Cartesians. The salient
feature of energetics was that "the principles it embodies and
from which it derives conclusions do not at all aspire to resolve the
bodies we perceive or the motions we report into imperceptible bodies
or hidden motions" (1917, 151 [EHPS, 232]). What energetics
offered was a formal theory, with the character of logical system,
which instead of reducing physical qualities in the manner of
mechanistic theories, limited itself to marking by means of a numerical
scale the various intensities of such qualities. Duhem's critique
of mechanistic theories (or the method of Cartesians and atomists) was
that they are not autonomous:



> 
> 
> The physicist who wishes to follow them can no longer use the
> methods proper to physics exclusively. ... Here he enters the
> domain of cosmology. He no longer has the right to shut his ears to
> what metaphysics wishes to tell him about the real nature of matter;
> hence, as a consequence, through dependence on metaphysical cosmology,
> his physics suffers from all the uncertainties and vicissitudes of that
> doctrine. Theories constructed by the method of the Cartesians and
> atomists are also condemned to infinite multiplication and to perpetual
> reformulation. They do not appear to be in any state to assure
> consensus and continual progress to science. (1917, 152 [EHPS,
> 233-34])




For Duhem, the contemporary scientist who exemplified the method of
the "Cartesians" was James Clerk Maxwell. Duhem issued
three interconnected complaints against Maxwell's work: (i)
Maxwell's theory is overly bold or not systematic enough; (ii) it
is too dependent on models; and (iii) its concepts are not continuous
with those of the past.




The justification Duhem gives for the accusation of extreme boldness is
that:



> 
> 
> When a physicist discovers facts unknown until then, when his
> experiments have allowed him to formulate new laws that the theory had
> not foreseen, he must first try with the greatest care to represent
> these laws, to the required degree of approximation, as consequences
> of admitted hypotheses. Only after having acquired the certainty that
> the magnitudes treated until now by the theory cannot serve as symbols
> for the observed quantities, that received hypotheses cannot flow from
> the established laws, is he authorized to enrich physics with a new
> magnitude, to complicate it with a new hypothesis (1902,
> 7).




According to Duhem, the founders of electrodynamics--Coulomb,
Poisson, and Ampere--followed these principles, but Maxwell did
not. Duhem cites with approbation Ampere's attempt to represent
the attraction or repulsion of currents in wires using Coulomb's
formula. He also praises the fact that Ampere abandoned the attempt
only after experimental facts about the magneto-optical rotation,
discovered by Faraday, showed clearly that Ampere could not succeed in
the attempt. But, again, according to Duhem, Maxwell does not follow
these principles. In fact, he goes so far as to accuse Maxwell of
following the "inverse path":



> 
> 
> At the moment when Maxwell introduced a new magnitude in
> electrodynamics, the displacement currents, at the moment when he
> marked, as essential hypotheses, the mathematical form of the laws to
> which this magnitude should be submitted, no properly observed
> phenomenon required this extension of the theory of currents; that
> theory was sufficient for representing, if not all phenomena known
> until then, at least all those whose experimental study had achieved a
> sufficient degree of clearness. No logical necessity pressed Maxwell to
> imagine a new electrodynamics. (1902, 8.)




As a result, Maxwell reversed "with an incredible
rashness" the natural order according to which physical theory
evolves--he broke with the past before he needed to.




Duhem is well known for his attack on the use of models in physical
science. At first, it seems that Duhem tries to link his attack on
model building with his espousal of instrumentalism for the physical
sciences. He accuses the English scientists of believing that "to
understand physical phenomena is to compose a model" (1914, 103;
1954, 71-72) and of "confusing model with theory" (1913,
102; 1954, 71). He specifically blames Maxwell of these
misunderstandings, indicating that in his 1855-56 essay Maxwell
proposed only "to illustrate" the theory of dielectrics,
whereas in his 1861-62 essay he proposed "to represent or to
explain" the electrical and magnetic actions by a mechanical
model. Duhem even seems scornful of Maxwell's interchangeable use
of the verbs "to represent" and "to explain."
He states, "for an English physicist, the two words have the same
meaning" (1902, 9).




For Duhem there is a crucial difference between representing and
explaining. He divides theories into two large categories, explanatory
and purely representative theories, and argues that physical theories
should not be considered as explanatory, but as purely representative
or classificatory. The argument, as we have seen, is that, in order for
physical theory to be explanatory, it would have to be subordinate to
metaphysics and not autonomous. The reference to the two words having
the same meaning for Maxwell and English scientists is thus a reference
to what Duhem would consider a confusion about the aim of physical
theory, one that arises in the identification of the model with the
theory, in thinking that what is represented by the theory and/or model
is real.




But Duhem broadens the critique of model building to include
mathematical models along with mechanical models. He decides that, for
an English scientist, theory is "for him neither an explanation
nor a rational classification of physical laws, but a model of these
laws, a model not built for the satisfying of reason but for the
pleasure of the imagination" (1914, 117; 1954, 81). The complaint
is clear: model building has no real place in physical theory (beyond a
minor heuristic role); it can neither be grounded in realism, in the
thought that physical theories are explanatory structures, nor in
instrumentalism, in the thought that physical theories are
classificatory or representative structures. In fact, model building is
not even connected to the higher intellectual faculty of reason but to
the lower faculty of imagination. So, ultimately, Duhem's attack
on model building is rooted in something more fundamental than his
instrumentalist methodology for the physical sciences.




Duhem banishes model building from physical theory (as he previously
banished Maxwell's rashness) because model building breaks with
historical continuity; in fact, model building is not only historically
non-continuous, but present models are even often
"non-continuous" among themselves. Some model builders even
find pleasure in building two or more models of the same law. The fact
that the English physicist can accept disparate models, breaking up the
historical continuity of science and even its present unification, is
what shocks Duhem; it is what reconfirms for him that English physics
is not the work of reason, but the work of imagination.




A principle of historical continuity is invoked in the conclusion of
Duhem's primary work on Maxwell. Duhem evaluates there an
interpretation of Maxwell's work he attributes to Heaviside,
Hertz, and Cohn, among others. He quotes Hertz as stating that:
"what is essential in Maxwell's theories is Maxwell's
equations." He takes this to be Hertz's way of salvaging
what is valuable in Maxwell from the midst of logical errors and
incoherence, which are not only difficult to correct, but which have
frustrated many illustrious mathematicians. But Duhem cannot accept
Hertz's implied criterion of identity for physical theories. He
asserts that he might accept such a criterion for algebra but "a
physicist is not an algebraist":



> 
> 
> An equation does not simply bear on letters; such letters symbolize
> physical magnitudes which must be either measurable experimentally or
> formed from other measurable magnitudes. Therefore, if a physicist is
> given only an equation, he is not taught anything. To this equation
> must be joined rules by which the letters that the equation bears upon
> are made to correspond to the physical magnitudes they represent. And
> that which allows us to know these rules is the set of hypotheses and
> arguments by which one has arrived at the equations in question. [The
> set of rules] is the theory that the equations summarize in a symbolic
> form: *in physics, an equation, detached from the theory that leads
> to it, has no meaning*. (1902, 223.)




Duhem proceeds to detail two complete theories that can recover
Maxwell's equations within a logical and coherent structure, the
theories of Boltzmann and Helmholtz. The only criterion he gives for
choosing between these two theories, though without elaborating upon it
or justifying it, is that Helmholtz's theory is to be preferred
over Boltzmann's theory because it is a natural "extension
of the doctrines of Poisson, Ampere, Weber, and Newmann; it leads
logically from the principles posited at the start of the nineteenth
century to the most seductive consequences of Maxwell's theories,
from the laws of Coulomb to the electromagnetic theory of light; [it
does so] without losing any of the recent victories of electrical
science; it reestablishes the continuity of tradition" (1902,
225).




Duhem does not attempt to justify his criterion of historical
continuity in his study of Maxwell, perhaps because he previously
broached the question. In an early methodological article, he asserts:



> 
> IF WE RESTRICT OURSELVES TO INVOKING CONSIDERATIONS OF PURE
> LOGIC, *we cannot prevent a physicist from representing different
> sets of laws, or even a single group of laws, by several irreconcilable
> theories. We cannot condemn incoherence in the development of physical
> theory*. (1893, 366 and elsewhere; [EHPS, 66])


Thus historical continuity as a consideration falls outside of pure
logic and outside reasons of physics proper, but deals with the
relation between physics and metaphysics, what Duhem calls
"metaphysical cosmology." Surprisingly, if one considers
him as an instrumentalist, for Duhem, we must judge a physical theory
in comparison to an ideal and perfect theory that provides the total
and adequate metaphysical explanation of the nature of material
things, that is, the natural classification of laws. (For more on Duhem on natural classification and conventionalism, see Dion 2013, Dion 2017, and Ivanova 2015.) For that reason, a coherent physical theory is more perfect than an incoherent set of
incompatible theories. Elaborating upon this point and commenting upon
the connection between cosmology--that is, metaphysics, natural
classification, or the ideal form of physical theory--and
physical theory itself, Duhem asserts:



> 
> 
> It is not enough for cosmologists to know very accurately the doctrines
> of contemporary theoretical physics; they must also know past
> doctrines. In fact, current theory need not be analogous with
> cosmology, but with the ideal theory toward which current theory tends
> by a continual progress. Therefore, it is not up to philosophers to
> compare physics as it is now with their cosmology, by congealing
> science in some manner at a precise moment of its evolution, but rather
> to appreciate the development of theory and to surmise the goal toward
> which it is directed. Now, nothing can guide them safely in
> conjecturing the path that physics will follow if not the knowledge of
> the road it has already covered. (1914, 460; 1954, 303.)




Duhem supports this statement using an analogy with the trajectory
of a ball. We cannot guess its end point with an instant glance at the
ball, but we can prolong its trajectory if we followed the ball from
the moment it was struck. So we cannot guess the end point of physical
theory, the natural classification, by looking at any particular
theory. We must appeal to the trajectory of physical theory, to its
history, to enable us to tell whether any particular theory is likely
to contribute toward the ultimate natural classification. Duhem's
doctrine of natural classification provides the grounds for various
commentators to argue that Duhem is not an instrumentalist, that his
philosophy of science considered as a whole looks more like convergent
or motivational realism (see Maiocchi in Ariew and Barker 1990 and
others).


### 2.3 Later Developments




As presented so far, Duhem is a philosopher who weaves together two
large patchworks of theses: (i) instrumentalism or fictionalism,
anti-atomism or anti-Cartesianism, anti-modelism, and autonomy of
physics from metaphysics and (ii) anti-inductivism or critique of
Newtonian method, the Duhem thesis, that is, non-falsifiability and
non-separability. Both sets of theses are intended as empirical theses
about the workings of science and both are important to understanding
Duhem's thought. The first set of theses effectively demarcates
physical theory as an autonomous domain apart from other domains, that
is, rejects any external method, and the second set then operates on
the internal workings of physical theory. Having set apart physical
theory, Duhem asserts that no internal method leads inexorably to the
truth.




For Duhem, there are always at least two basic ways of proceeding in
science. Some scientists prefer the clutter of concrete details and
thus do not mind ad hoc explanations, complications, and corrected
theories; others prefer abstract, simple, and uncomplicated theories,
even if they are gotten at the price of conceptual novelty. As we have
seen, Duhem discusses this dichotomy under the rubric of the English
mind and the French mind--what he also calls "esprit de
finesse" and "esprit de geometrie,"
following Blaise Pascal. Despite the labels "English" and
"French," Duhem's categories are analytic ones, not
mere epithets to be used rhetorically against his adversaries. In fact,
from the start, when he described the broad-shallow English mind, his
archetype was Napoleon Bonaparte, a great genius of military
details--not an Englishman. Duhem's ideal of the narrow-deep
French mind was Newton, the geometer of physics--not a Frenchman.
Thus, when Duhem accused Faraday and Maxwell of having English minds,
he did so by trying to establish something about how they conducted
their science, not by referring to their ancestry.




In his last work, *La science allemande*, mostly a work of
wartime propaganda, Duhem added a third kind of mind to his original
two, namely, the German mind. If there are two basic types, the French
mind and the English mind, then what could the German mind possibly be?
Citing Pascal, Duhem tells us that truth requires both reason and
argument--*raison* and *raisonnement*. Logic, or our
ability to link propositions with one another, allows us to deduce one
truth from another; but that ability, by itself, merely gets us back to
first principles or axioms. We also need a faculty that allows us to
intuit the truth of the first principles or axioms, that is, *bon
sens* (good sense). *Bon sens* is to "esprit de
finesse" what "pure logic" is to "esprit de
geometrie." Moreover, *bon sens*, our
faculty of recognizing fundamental truth gets perfected by the practice
of history, by our becoming more aware of the failures and successes of
previous theories, by thinking about the trajectory of scientific
theories, rather than by considering a single theory frozen in time.
The dual scheme can now be expanded. We need logic, the ability to
systematize, but we also need intuition, the recognition of truth. When
one of these is allowed to dominate, we get a science which is all
intuition, all "esprit de finesse," but no logical
coherence, namely, English science; or we get a science which is all
logic, lacking bon sens, namely, German science. German science then is
a degenerate kind of French science, the latter being predominantly
"esprit de geometrie," corrected by *bon
sens*.




As a result, we can talk about a continuum of sciences; at one extreme
on the theoretical side is German science, or logicism, and at the
other extreme on the experimental side is English science, or crude
modelism. In the middle is French science, which allegedly tempers the
logical bent with historicism.




In a well-known chapter of *Social Theory and Social Structure*,
the sociologist of science Robert Merton refers to Duhem's
critique of German science as one of the many polemics against national
kinds affirming a universalistic standard: "Dispassionate
scientists impugned 'enemy' contributions, charging
nationalistic bias, log-rolling, intellectual dishonesty, incompetence,
and lack of creative capacity. Yet this very deviation from the norm of
universalism actually presupposed the legitimacy of the norm. For
nationalistic bias is opprobrious only if judged in terms of the
standard of universalism... Thus by the very process of condemning
their violation, the mores are reaffirmed" (1968, 8).




At first glance Duhem's polemics against German science might
seem to arise from a universalistic standard. Duhem does talk at times
of a perfect form of science, one without personal or national
character: "Quite often the great masters possess a reason in
which all the faculties are so harmoniously proportioned that their
very perfect doctrines are exempt from all individual character, as
from all national character. ... In such works one no longer sees
the genius of this or that people, but only the genius of
Humanity" (1915, 105 [EHPS, 253]). Such perfection for Duhem is an
equilibrium of disparate elements, not itself a single ideal type.
Duhem might regret what he sees as an overabundance of esprit de
geometrie in German science, and might wish that it be
tempered by a bit more finesse, but there is no suggestion in Duhem
that there is only one way to proceed in science.




Duhem specifically states that the



> 
> 
> perfect form of science could not be obtained except by a very precise
> separation of the various methods concurring in the discovery of truth.
> Each of the many faculties that human reason puts into play when it
> wishes to know more and better would have to play its role, without
> anything being omitted, without any faculty being overlooked. This
> perfect equilibrium between the many organs of reason does not occur in
> any one man. In each of us one faculty is stronger and another weaker.
> In the conquest of truth the weaker will not contribute as much as it
> should and the stronger will take on more than its share. (1915, 104
> [EHPS, 252]).




At bottom, despite his talk of ideal type and equilibrium,
Duhem's science is not universalistic. The strength of his
analysis is that there is no single direction within science that each
individual must follow. For that, one would need to ground physics in a
particular metaphysics--which Duhem explicitly rejects with his
instrumentalism--or rather, to be guided by what one projects
metaphysics will look like over the long run. Unfortunately, Duhem took
this last thought too rigidly and ultimately condemned all innovations
as breaking with the past, either due to an excess of *esprit de
geometrie*, as with non-Euclidean geometry and
relativity, or an excess of *esprit de finesse*, as with
electron theory. But his philosophy of science itself contained the
seeds of scientific pluralism, which are the foundations of the Duhem
thesis, that is, the thought that there are many legitimate and
disparate ways of proceeding in science.




Duhem's famous critique of crucial experiments follows a similar
pattern. Duhem argues that crucial experiments resemble false dilemmas:
hypotheses in physics do not come in pairs, so that crucial experiments
cannot transform one of the two into a demonstrated truth. For example,
the Newtonian emission theory predicts that light travels faster in
water than in air; according to the wave theory, light travels slower
in water than in air. Dominique Francois Arago proposed a
crucial experiment comparing the respective velocities. Leon
Foucault then devised an apparatus to measure the speed of light in
various media and found a lower velocity in water than in air. Arago
and Foucault concluded for the wave theory, thinking that the
experiment refuted the emission theory. Discussing Foucault's
experiment, Duhem asks whether we dare assert that no other hypothesis
is imaginable and suggests that instead of light being either a simple
particle or wave, it might be something else, perhaps a disturbance
propagated within a dielectric medium, as theorized by Maxwell (1914,
285-89; 1954, 188-90).



More than a century after Duhem argued for his non-falsifiability
thesis, the set of issues connected with it are still elaborated upon,
criticized, and defended in the large literature on the philosophy of
science. Given holism, non-falsifiability follows logically and thus,
when an experiment goes wrong, there is no set way to determine which
hypothesis among many hypotheses is defective. Duhem proposed *bon
sens* as a resolution to the problem, but that solution seemed
unsatisfactory to many: it looked more psychological than
epistemological and it sounded too vague. Thus scholars attempted to
articulate further what Duhem might have meant as *bon sens*
(see Ivanova 2010, Kidd 2011, Ivanova 2011, and Ivanova and Pasternote
2013). Others proposed their own resolutions to the problem,
attempting to isolate defective hypotheses by extra-logical means,
whether by inference to the best explanation, Bayesian devices,
error-statistical methods, or though elaborate experimental practices;
for an analysis of such solutions, see Dietrich and Honenberger 2020
or Ivanova 2021).


## 3. History of Science




For most of the nineteenth century, scholars treated "medieval
science" as an oxymoron. Since nothing from the Middle Ages was
worthy of the name "science," no history of medieval
science could be written. For example, William Whewell referred to
Greek philosophy as "the period of the first waking of
science" and to the medieval era as "that of its mid-day
slumber" (1857, I, Introduction). As a result, Whewell's
chapter on medieval science from the *History of the Inductive
Sciences*, entitled "Of the Mysticism of the Middle
Ages," was just two-pages long.




With work such as Whewell's being typical of Duhem's
intellectual context, when Duhem wrote *L'evolution de
la mecanique*, in 1903, he dismissed the Middle Ages as
scientifically sterile. Similarly, Duhem's history of chemical
combination, *Le mixte et la combinaison chimique*, published in
book-form in 1902, had jumped from Aristotle's concept of
*mixtio* to modern concepts. It was only in 1904, while writing
*Les origines de la statique* that Duhem came across an unusual
reference to a then-unknown medieval thinker, Jordanus de Nemore. His
pursuit of this reference, and the research to which it led, is widely
acknowledged to have created the field of the history of medieval
science. Where Duhem's previous histories had been silent,
*Les origines de la statique* contained a number of chapters on
medieval science: one treated Jordanus de Nemore; another treated his
followers; a third argued their influence on Leonardo de Vinci. In the
second volume, Duhem greatly extended his historical scope. As
expected, he covered seventeenth-century statics, but he also returned
to the middle ages, spending four chapters on geostatics, including the
work of Albert of Saxony in the fourteenth century. *Les origines de
la statique* is thus a transition from Duhem's early
conventional histories to the later work for which he is best known,
*Etudes sur Leonard de Vinci*, and *Le Systeme
du monde*, in which his thesis of the continuity of late medieval
and early modern science is fully displayed.




From 1906 to 1913, Duhem delved deeply into his favorite guide for the
recovery of the past, the scientific notebooks of Leonardo de Vinci. He
published a series of essays uncovering de Vinci's medieval
sources and their influences on the moderns. The third volume of
Duhem's *Etudes sur Leonard de Vinci* gained a new
subtitle, Les precurseurs parisiens de Galilee,
announcing Duhem's bold new thesis that even the works of Galileo
had a medieval heritage; reviewing his historical accomplishments,
Duhem summarized them as follows:



> 
> 
> When we see the science of Galileo triumph over the stubborn
> Peripatetic philosophy of somebody like Cremonini, we believe, since we
> are ill-informed about the history of human thought, that we are
> witness to the victory of modern, young science over medieval
> philosophy, so obstinate in its mechanical repetition. In truth, we are
> contemplating the well-paved triumph of the science born at Paris
> during the fourteenth century over the doctrines of Aristotle and
> Averroes, restored into repute by the Italian Renaissance. (1917, 162
> [EHPS, 193])




Duhem presented Galilean dynamics as a continuous development out of
medieval dynamics. He recovered the late medieval theory of impetus,
tracing it from John Philoponus' criticism of Aristotle to its
mature statements in the fourteenth century works of John Buridan and
Nicole Oresme: "The role that impetus played in Buridan's
dynamics is exactly the one that Galileo attributed to *impeto*
or *momento*, Descartes to 'quantity of motion,' and
Leibniz finally to *vis viva*. So exact is this
correspondence that, in order to exhibit Galileo's dynamics,
Torricelli, in his *Lezioni accademiche*, often took up
Buridan's reasons and almost his exact words" (1917, 163-62
[EHPS, 194]). Duhem then sketched the extension of impetus theory from
terrestrial dynamics to the motions of the heavens and earth:



> 
> 
> Nicole Oresme attributed to the earth a natural impetus similar to
> the one Buridan attributed to the celestial orbs. In order to account
> for the vertical fall of weights, he allowed that one must compose this
> impetus by which the mobile rotates around the earth with the impetus
> engendered by weight. The principle he distinctly formulated was only
> obscurely indicated by Copernicus and merely repeated by Giordano
> Bruno. Galileo used geometry to derive the consequences of that
> principle, but without correcting the incorrect form of the law of
> inertia implied in it. (1917, 166 [EHPS, 196])




Duhem's essays on Leonardo de Vinci concluded with a
speculation about the means for the transmission of medieval ideas to
modern science. Since the studies of Buridan and Oresme had remained in
large part in manuscript, Duhem suggested that Albert of Saxony, whose
works were printed and reprinted during the sixteenth century, was the
likely link to Galileo. Duhem's key to understanding the
transmission of medieval science was Galileo's use of the phrase
*Doctores Parisienses*, a conventional label denoting Buridan
and Oresme, among others. Based on evidence including references to
certain unusual doctrines and the particular order in which the
questions were arranged, Duhem conjectured that Galileo had consulted
George Lokert's compilation of Albert of Saxony, Themo Judaeus,
and others, and the works of the Dominican Domingo de Soto (1906-13,
III.582-83). Duhem's conjecture has been revised and expanded
upon: The means of transmission has been made clearer because of the
labor of A. C. Crombie, Adriano Carugo, and William Wallace.




In the three years before his death in 1916, Duhem wrote *Le
Systeme du monde*, but did not succeed in finishing it. He
intended it as a twelve-volume work on the history of cosmological
doctrines, ending with Copernicus. He completed nine volumes, the
first five being published from 1914 to 1919, and the next four having
to wait until the 1950s; a tenth, incomplete volume was also published
then. These tomes impart an enormous amount of information about
medieval astronomy, astrology, tidal theory, and geostatics, again
presenting many sources for the first time in the modern era. They
also trace developments in doctrines associated with such concepts as
infinity, place, time, void, and the plurality or unity of the world.
Duhem intended to write a 300-page summary of his results after he was
done with the *Le Systeme du monde*; he did not have the
time to accomplish what would have surely been an amazing
volume. (Duhem [LAS] is an attempt to construct such a single volume
from the ten volumes of the *Le Systeme du monde*.)




Unlike his philosophical work, Duhem's influential contemporaries
did not receive his historical work with sympathy. As early as 1916,
Antonio Favaro, the editor of *Le Opere di Galileo Galilei*,
rejected the continuity of medieval and early modern science. The next
generation of historians of science, Alexandre Koyre for
example, acknowledged Duhem's studies as the foundation for
modern studies of medieval science, but subjected them to harsh
criticism. Two themes divide Koyre's historical work from
that of Duhem. It presents histories of science in which metaphysics
plays a primary role in explaining scientific change and it espouses a
historiography that gives a central place to the concept of revolution.
Medieval thought and early modern science are judged to be different in
kind as well as in content.




At the beginning of an essay on void and infinite space, Koyre
quotes a passage from Duhem that has become infamous: "If we were
obliged to assign a date to the birth of modern science, we would
undoubtedly choose 1277, when the Bishop of Paris solemnly proclaimed
that a multiplicity of worlds could exist, and that the system of
celestial spheres could, without contradiction, be endowed with
straight line motion" (1906-13, II.411; see also 1913-59, VII.
4). Koyre calls the two theses from the condemnations of 1277
"absurdities," noting that they arise in a theological
context, and rejects Duhem's date for the birth of modern
science; he remarks that Duhem gives another date elsewhere,
corresponding to Buridan's impetus theory being extended to the
heavens, but dismisses it also, saying that "it is as false as
the first date" (1961, 37n). For Koyre, the introduction
of Platonic metaphysics, the mathematization of nature, marks a break
with the Aristotelian Middle Ages.




Koyre's work influenced Thomas Kuhn and others who made
"scientific revolutions" a central feature of their
historical accounts. Still, the work of Kuhn and later historically
oriented philosophers and sociologists of science did attempt to
reintegrate the philosophical and historical studies that Duhem pursued
together but that were separated for a good part of the twentieth
century.