The Aim and Structure of Physical Theory

366 Pages·1954·7.513 MB·English

by  Pierre Maurice Marie Duhem

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1954
The Aim and Structure
of Physical Theory

Copyright, 1954, by Princeton University Press
London: Geoffrey Cumberlege, Oxford University Press
l. c. card 55-6383
❖
Translated from the second edition,
published in 1914 by Marcel Rivière & Cie., Paris,
under the title
La Théorie Physique; Son Objet, Sa Structure
Printed in the United States of America
by Princeton University Press at Princeton, New Jersey
FOREWORD
Pierre Duhem’s Life and Work
Born in Paris on June 10, 1861 and passing away in his country
home at Cabrespine (Aude) on September 14, 1916 at the age of
fifty-five, Pierre Duhem was one of the most original figures of
French theoretic physics a half-century ago. Apart from his strictly
scientific works which were brilliant indeed, notably in the domain
of thermodynamics, he acquired an extremely extensive knowledge
of the history of the physico-mathematical sciences and, after having
given much thought to the meaning and scope of physical theories,
he shaped a very arresting opinion concerning them, expounding
it in various forms in numerous writings. Thus, an excellent theo­
retician of physics and historian of the sciences, possessing enormous
erudition, he also made for himself a great name in scientific
philosophy.
Very gifted in mathematics and physics, Pierre Duhem at the age
of twenty entered the École Normale Supérieure on the Rue d’Ulm
in Paris; in this outstanding institution of higher education which
has given France so many great teachers of literature and science,
he was a brilliant student, and his attention was turned very quickly
toward the study of thermodynamics and its applications, a domain,
furthermore, which he was never to cease cultivating.
Reflecting on the works of Thomson (Lord Kelvin), Clausius,
Massieu, Gibbs and the other great originators of thermodynamic
conceptions, he was especially struck by the analogy between the
methods of Lagrange’s analytical mechanics and those of thermody­
namics. These reflections led him at the age of twenty-three to in­
troduce in a quite general way the notion of thermodynamic
potential and to publish soon afterward a book, Le Potentiel
thermodynamique et ses applications à la mécanique chimique et
à la théorie des phénomènes électriques [Paris, 1886—Translator].
Having received first place in 1885 in the competitive examina­
tions for teaching physics, Duhem, already known in scientific cir­
cles, became two years later lecturer in the Faculty of Sciences of
Lille University, where he taught with brilliance hydrodynamics,
elasticity, and acoustics. Very soon after his marriage in Lille his
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LOUIS DE BROGLIE
wife died, leaving him an only daughter with whom he was to spend
the rest of his life. At thirty-two he became full professor in the
Faculty of Sciences of Bordeaux University, and kept this post until
his death.
All his life Pierre Duhem retained in his scientific works his
initial orientation. His preoccupation with regard to theory was the
construction of a kind of general energetics (including classical
analytical mechanics as a special case) and abstract thermo­
dynamics. Essentially a systematic mind, he was attracted by axio­
matic methods which lay down exact postulates in order to derive
by rigorous reasoning unassailable conclusions; he prized their
solidity and rigor, and was far from repulsed by their dryness and
abstractness. He rejected, it might be said, with horror, the idea of
substituting for the formal arguments of energetics the uncertain
images or models furnished by atomic theories; he had no inclina­
tion to follow Maxwell, Clausius, and Boltzmann in the construc­
tion of a kinetic theory of matter permitting a concrete interpretation
of the abstract conceptions of thermodynamics. If he admired Wil­
lard Gibbs for the rigor of his purely thermodynamic arguments
and for the algebraic elegance of his demonstration of the phase
rule, he certainly did not follow the great American thinker when
the latter tried to base the atomic interpretation of thermodynamics
on general statistical mechanics. From his Commentaires sur la
Thermodynamique, his youthful work, to his great Traité dÉner-
gétique générale, which in his maturity crowned his works on matter,
Duhem pursued his efforts at axiomatization and rigorous deduc­
tion. He sifted out all the fundamental notions admitted by thermo­
dynamics; for example, he gave a purely mathematical definition
of the quantity of heat and thus deprived it of any physical intuitive
meaning in order to avoid any begging of the question. This con­
stant effort at abstraction gives the theoretical work of Duhem
a rather austere appearance which, despite the very remarkable
results it has brought, may not please all minds.
It is fair to insist on the fact that Duhem, though he was constantly
preoccupied with the establishment of an impeccable axiomatic
system in the theories he developed, never lost sight of the problems
of application. Notably in the domain of physical chemistry, familiar
to him from his youth, he came to grips with the applications of
theory to experiment by examining in detail all the consequences
of the often difficult ideas of Willard Gibbs, whose presentation he
knew how to make precise, and he was one of the first to spread
them in France.
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FOREWORD
Duhem also occupied himself a great deal with hydrodynamics
and with the theory of elasticity, branches of science which his
conceptions led him to consider, besides, as particular chapters of
general energetics. His works on the propagation of waves in fluids,
notably on waves of impact, have retained all their validity. It
seems his researches on electromagnetism were less happy, for he
always had a great hostility toward Maxwell’s theory and preferred
Helmholtz’ ideas, which are quite forgotten today. His deep an­
tipathy with regard to all pictorial models prevented him, more­
over, from understanding the importance of the Lorentz theory of
electrons, then in full development, and rendered him as unjust as
he was shortsighted about the rise of atomic physics, then in its
beginnings.
Pierre Duhem was also a great historian of the sciences belong­
ing to the domains, familiar to him, of mechanics, astronomy, and
physics. Very conscious of the continuous evolution which manifests
itself in the development of science, justly persuaded that all the
great innovators have had forerunners, he demonstrated strongly
that the great revival of mechanics, astronomy, and physics at the
time of the Renaissance and in modern times has its roots deep in
the intellectual work of the Middle Ages, a work whose importance
from the scientific point of view had been too often unrecognized
prior to Duhem’s researches. In several of his writings, and par­
ticularly in his important three-volume work, Léonard de Vinci,
ceux qu’il a lus et ceux qui Vont lu, he insisted on the part played by
the scholars of the medieval universities, and particularly by those
of the University of Paris, from the thirteenth to the sixteenth cen­
tury. He showed that a reaction took place after the death of Saint
Thomas Aquinas against the ideas of Aristotle and the Aristotelians,
and that this was at the origin of the movement of ideas which,
rejecting the Greek philosopher’s conceptions of motion, was going
to end with the principle of inertia, with the work of Galileo, and
with modem mechanics. He established that John Buridan, Rector
of the Sorbonne about 1327, had the first idea of the principle
of inertia and introduced under the Latin name of impetus a magni­
tude which, though not too well defined, is closely related to what
we today call kinetic energy and quantity of motion. He analyzed
the important progress due, a little later, to the works of Albert
of Saxony and Nicholas Oresme. The latter especially accomplished
considerable work, for with his ideas on the solar system he was
the precursor of Copernicus, and with his first attempts at analytical
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LOUIS DE BROGLIE
geometry he was the forerunner of Descartes. He was even ac­
quainted with the form of the laws of uniformly accelerated mo­
tion, so important in the study of weight. Then Duhem shows us
Leonardo da Vinci, that admirable and many-sided man of genius,
assimilating and pursuing the work of his predecessors and pre­
paring the road on which, after various scientific scholars of the six­
teenth century, Galileo and his continuators were definitively to
begin modem mechanics.
Through writings of this sort and notably through a valuable
sketch of the history of mechanics, Pierre Duhem, who had also
studied closely the science of the seventeenth century and brought
to light the often unrecognized contributions of Father Mersenne
and Malebranche, was classed in the first rank of contemporary
historians of the sciences. In his maturity he undertook, it is said
with numerous anonymous collaborators, a colossal work: the his­
tory of cosmogonic doctrines, i.e. of conceptions about the system
of the world from antiquity to the modern period. At his death
he had already written eight volumes of this work, but only five
have been published: the publication of the last three, whose manu­
scripts had been entrusted to the Academy of Sciences of Paris,
having been postponed as a consequence of the financial difficulties
of publication. It is a work of profound erudition, a mine of precious
documents concerning the history of ideas and of philosophy in
ancient times and in the Middle Ages at least as much as what is
properly called the history of science. It would be immensely de­
sirable for subscriptions abroad to help complete the publication
of this vast synthesis which the author nearly had time, despite his
premature death, to bring to its completion.
A theoretic physicist of indisputable value, possessing an enor­
mous erudition in the history of the sciences, accustomed through
this twofold intellectual formation to reflect on the growth, develop­
ment, and scope of physical theories, Pierre Duhem naturally turned
toward the philosophy of science. An essentially systematic mind,
he worked out for the meaning of the theories of physics a very
precise opinion which he expounded in numerous publications. The
most important of these is his book entitled La Théorie Physique:
Son Objet, Sa Structure, which enjoyed a great success in France and
which the present volume offers in an English translation for Ameri­
can (and other English-speaking) readers. It is a capital work
whose clarity and often impassioned tone are an exact reflection
of the mind that created it. Without wishing to analyze completely
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FOREWORD
a work so rich in substance, we should like to underscore rapidly
a few essential points.
Pierre Duhem held firmly to separating physics from metaphysics:
he saw in the history of physical theories, whether they were based
on continuous or discontinuous images, or whether they were of
the field or atomic type of physics, a proof of our radical inability
to reach the depths of reality. It was not that Pierre Duhem, a con­
vinced Catholic, rejected the value of metaphysics; he wished to
separate it completely from physics and to give it a very different
basis, the religious basis of revelation. This preoccupation with a
complete separation of physics from metaphysics led him, as a
logical but curious consequence, to be ranked, at least with respect
to the interpretation of physical theories, among positivists with
an energetistic or phenomenological tendency. In fact, he sum­
marized his opinion concerning physical theories in the following
conclusion: “A physical theory is not an explanation; it is a system
of mathematical propositions whose aim is to represent as simply,
as completely, and as exactly as possible a whole group of experi­
mental laws.”
Physical theory would then be merely a method of classification of
physical phenomena which keeps us from drowning in the extreme
complexity of these phenomena. And Duhem, arrived at this posi­
tivist and pragmatist conception of nature bordering closely on the
conventionalism (commodisme) of Henri Poincare, was in com­
plete agreement with the positivist Mach in proclaiming that physi­
cal theory is above all an “economy of thought.” For him all hy­
potheses based on images are transitory and infirm; only relations
of an algebraic nature which sound theories have established among
phenomena can stand imperturbably. Such, in the main, is the es­
sential idea which Duhem produced about physical theory. It cer­
tainly pleased the physicists of the school of energetics, his con­
temporaries; it certainly is also favored by a great number of
quantist physicists of the present day. Others were already finding
it or will still find it a little narrow, and will reproach it for diminish­
ing too much the knowledge of the depth of reality which the
progress of physics can procure for us.
We must be fair and emphasize the fact that Duhem did not
fall into the extremes to which his views might perhaps have led
him. He believed instinctively, as all physicists do, in the existence
of a reality external to man, and did not wish to allow himself to
be dragged into the difficulties raised by a thoroughgoing “ideal­
ism.” Hence, taking a position which is a very personal one at that,
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LOUIS DE BROGLIE
and separating himself on this point from pure phenomenalism,
he declared that the mathematical laws of theoretical physics, with­
out informing us what the deep reality of things is, reveal to us
nonetheless certain appearances of a harmony which can only be
of an ontological order. In perfecting itself physical theory pro­
gressively takes on the character of a “natural classification” of
phenomena, and he made precise the meaning of the adjective
“natural” by saying: “The more theory is perfected, the more we
apprehend that the logical order in which it arranges experimental
laws is the reflection of an ontological order.” In this manner, it
seems, he had been led to mitigate the rigor of his scientific posi­
tivism because he felt, and we think justifiably so, the force of the
following objection: “If physical theories are only a convenient
and logical classification of observable phenomena, how does it
come about that they can anticipate experiment and foresee the
existence of phenomena as yet unknown?” In order to answer this
objection he really felt that we must attribute to physical theories
a deeper bearing than that of a mere methodical classification of
facts already known. In particular, he was clearly aware, and some
passages of his book show this to be so, that the analogy of the
formulas employed by physical theories bearing on different phe­
nomena most often do not reduce to a mere formal analogy but may
correspond to deep connections among diverse appearances of
reality.
Such in the main is the conception which Duhem propounded con­
cerning the scope of physical theories—an idea more subtly nuanced
in the end than one might first believe. It is possible, however, to
think that despite the subtlety of his doctrine brought about by the
idea of a natural classification, Duhem, led on by the uncompro­
mising tendency of his mind, often maintained judgments that were
too absolute. Thus, inspired by a genuine horror of all mechanical
or pictorial models, he kept on combatting atomism and, faithful
to the school of energetics, he never became interested in the inter­
pretation of the abstract concepts of classical thermodynamics,
though it was so instructive and fruitful, which statistical mechanics
furnished in his own lifetime. Thus preparing himself for perhaps
too easy a success, he attacked the simplistic representation of atoms
by small, hard, and elastic corpuscles; he attacked the ideas, at
times somewhat naive, of Lord Kelvin on the representation of
natural phenomena by gears or vortices. He does not seem to have
been aware of the tremendous revival which the atomic theory in
x