The Reception of
Newton’s Gravitational
Theory by Huygens,
Varignon, and
Maupertuis:
How Normal Science
may be Revolutionary
Ko ffi Maglo
Massachusetts Institute of Technology
. . . The discrimination of normal from revolutionary episodes demands close historical study, and few parts of history of science have
received it. One must know not simply the name of the change, but
the nature and structure of group commitments before and after it occurred. Often, to determine these, one must also know the manner in
which the change was received when Žrst proposed” Thomas Kuhn
(1970, p. 251).
This paper Žrst discusses the current historical and philosophical framework
forged during the last century to account for both the history and the epistemic
status of Newton’s theory of general gravitation. It then examines the conict
surrounding this theory at the close of the seventeenth century and the Žrst
steps towards the revolutionary shift in rational mechanics in the eighteenth
century. From a historical point of view, it shows the crucial contribution of
the Cartesian mechanistic philosophy and Leibnizian analytic methods to the
emergence of so-called Newtonian mechanics which can also be fairly characterized as a synthetic theory of attraction. From a philosophical standpoint,
the paper suggests that the reworking of Newton’s theory in the 18th century
is better understood in a theoretical framework that reconciles Kuhn’s notion
of “invisible revolution” rather than his notion of “normal science” with
Whewell’s ascription of the completion of dynamical studies to the post
Newtonian period.
Introduction
The question of when the new way of investigating nature, the so-called
ScientiŽc Revolution begun by Copernicus reached its completion is still a
lively debate among historians. Some argue that it culminated with the
publication of Newton’s Principia in 1687 (Westfall 2000).1 Others main1. Richard Westfall (2000, p. 48), for example, wrote: “In any event, with Newton the
Perspectives on Science 2003, vol. 11, no. 2
©2003 by The Massachusetts Institute of Technology
135
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The Reception of Newton’s Gravitational Theory
tain that the narrative itself of the ScientiŽc Revolution emerged only in
Enlightenment texts combined with a partial selection of what came to be
seen as the positive aspect of Newton’s achievement (Dobbs [1994] 2000;
Jacob 2000; Osler 2000).2 This historical issue has a bearing on philosophical appraisal of scientiŽc progress and vice versa. In this paper, I argue
that to solve this problem we need to return to William Whewell’s assessment of the relationship between Newton’s Principia and Laplace’s
Mécanique céleste (Whewell 1823). A suitable philosophical tool to achieve
this is Thomas Kuhn’s notion of invisible revolution (Kuhn 1962). This
however entails the abandonment of Kuhn’s own account of scientiŽc
progress in the eighteenth century in terms of normal science. 3 The background assumption of this reading of Kuhn against Kuhn is that where
Kuhn saw a slow conversion in post revolutionary periods I see a slow revision culminating in substantial changes. It is this notion of gradual but
decisive transformations of scientiŽc theories that Whewell’s assessment,
as we shall see below, implies.
Indeed, before the Principia was accepted in key scientiŽc institutions
on the Continent, it underwent a crisis followed by a deep revolutionary
transformation. Accordingly, it is useful to suggest here a periodization for
new science and the new philosophy of nature found their deŽnitive form in which they
shaped the scientiŽc tradition . . .” Westfall’s paper, published posthumously, is a reaction
to Dobbs’ reassessment of the concept of ScientiŽc Revolution; see below.
2. Casper Hakfoort (1988) also stated the idea of the incompleteness of the ScientiŽc
Revolution. However, Dobbs (2000) took issue with the concept of ScientiŽc Revolution,
usually understood as “a change that is sudden, radical, and complete.” The concept, she
said, is anachronistic and inappropriate as applied to Newton as well as Copernicus. For
her, the patterns of Newton’s thought differ more signiŽcantly from ours than is traditionally believed. She observed that the shaping of Newton’s reputation as the “father of modern science” is due to the decline of alchemy in the eighteenth century. Therefore, the narrative of the ScientiŽc Revolution, except for “its dramatic capitalized title,” she believed,
emerged plainly in d’Alembert’s philosophical writings in the same period. Accordingly,
she considered the problem of delimiting the ScientiŽc Revolution to be a historical one.
Dobbs’ position depends on studies of Newton’s relationship with alchemy and theology
(Dobbs 1975, 1991; Westfall 1980; J. E. McGuire and P. M. Rattansi 1966). Also, Margaret C. Jacob (2000, p. 319) systematically historicized the narrative of Newton’s accomplishments and like Dobbs, directed her criticism against the current understanding of the
ScientiŽc Revolution based on the assumption that “the heroes had to be pure, simply
great ‘scientists,’ and they alone made it happen.” As Margaret J. Osler (2000, p. 5) has
pointed out, the result of Jacob’s “exercise in historicizing the history of science” is to suggest a radical rethinking of the ScientiŽc Revolution. It was constructed in the eighteenth
century when scientists privileged the positive aspect of Newton’s achievement.
3. According to Thomas Kuhn, the making of science has to be divided in two: A revolutionary shift of paradigm and “normal science.” The latter is essentially a period of solving puzzles within the limits of a given paradigmatic framework. A change of paradigm is
the principal element in a scientiŽc revolution.
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the history of so-called Newtonian mechanics. One should distinguish at
least four stages: a period of discovery that ended in 1687; a period of
eclipse 4 during which Huygens, Leibniz, and the Cartesians rejected Newton’s theory of general gravitation, but Varignon strengthened the
Principia as a mathematically based work; a period of revision, from the
1730s to the 1760s, when Maupertuis, Euler, d’Alembert, Clairaut, and to
some extent the Bernoullis, reinterpreted the new physics; and a period of
standardization when Lagrange and Laplace codiŽed “Newtonian” mechanics in its deŽnitive form.
In what follows, I Žrst provide a theoretical framework, let’s call it the
W-K bridge, suitable to account for scientiŽc progress in the eighteenth
century by connecting Whewell’s idea of the completion of the ScientiŽc
Revolution in Laplace’s work with Kuhn’s notion of invisible revolution.
Second, I describe the complex process of theory appraisal that opposed
Newton to his Continental peers at the close of the seventeenth century.
Then I proceed to analyze some of the chief roots of canonical “Newtonianism.”
1. Accountin g for scientifi c growth in the eighte enth centur y
As early as 1823, Whewell wrote: “The student who feels a proper admiration for the system of the Principia, ought to look forward to a complete
development of it in the Mécanique céleste . . .” (Whewell 1923, preface).
According to Whewell, the Mécanique céleste of Laplace rather than Newton’s Principia brought the study of dynamics to its completion. Among
those who cleared the way for such an achievement, he particularly admired Leonhard Euler, a mathematician of the Basel school. This rating of
Laplace’s Mécanique céleste and Newton’s Principia disturbed some scholars
in the twentieth century because it contrasted with the new historical and
philosophical trend. John Herivel (Whewell 1967, p. xv), for one, characterized Whewell’s attitude as temerity and stated his own view as follows:
“With certain notable exceptions, the whole history of dynamics from
Newton to Einstein can be thought of as an exploitation, albeit inŽnitely
4. Julian Huxley ([1942] 1964; Bowler 1983) used the term “eclipse of Darwinism” to
characterize the crisis surrounding Darwin’s theory at the turn of the twentieth century.
During this period, evolution was accepted while natural selection sparked controversial
debate. Similarly, at the turn of the eighteenth century, the fact that Newton had successfully demonstrated the validity of Kepler’s laws by use of the inverse square law was generally acclaimed. But attraction was sharply rejected in key scientiŽc institutions on the
Continent because it was considered an incoherent physical concept, incapable of describing the mechanism of nature. Mendelian discoveries were required to lead the theory of
evolution to a new synthesis. Likewise, Leibnizian discoveries were needed to save the theory of general gravitation from declining and to lead dynamics to completion.
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The Reception of Newton’s Gravitational Theory
ingenious and resourceful, of the deŽnitions, principles and propositions
in the Principia” (Herivel 1965, introduction). Relying on similar assumptions, some scholars in the twentieth century did not seem to Žnd critical
changes between Newton and his immediate followers. 5
The problem with this position is that it is at odds with theoretical
frameworks often applied in the evaluation of scientiŽc achievements such
as Copernicus’ and Newton’s theories. For example, I. Bernard Cohen
(1985) interestingly stressed the fact that the Copernican revolution was
not Copernicus’; as with many other revolutionary ideas, it was only
through the works of such later revolutionaries as Kepler and Galileo that
the Copernican revolution truly occurred. This points to the soundness of
Kuhn’s emphasis on the invisibility of scientiŽc revolutions. Kuhn argued
that a revolution consists of a particular change that is not necessarily a
modiŽcation on a large scale. Thus, small revolutions occur more often
than is usually believed and lie in the reformulation of the tradition of a
given scientiŽc community. Revolutions can even be invisible to their authors. Referring to Newton’s attribution of his own second law of motion
to Galileo, Kuhn (1962, pp. 139…
40) wrote: “. . . Newton’s account hides
the effect of a small but revolutionary reformulation in the questions that
scientists asked about motion as well as in the answers they felt able to
accept . . .” For Kuhn, these kinds of invisible revolutions that alter questions and answers, rather than introduce new empirical evidence, signiŽcantly explain scientiŽc development. They bring about conceptual reconstruction and modiŽcations in a group’s commitments, i.e., symbolic
generalizations, ontological and heuristic models, and exemplars or paradigms (Kuhn 1977, pp. 293…
319).
Curiously, Kuhn (1962, p. 33) did not seem to heed his own creed
about invisible revolutions and, unlike Whewell, he saw the generations
of physicists from Euler and Lagrange to Hamilton, Jacobi, and Herz as
generations of normal scientists whose works produced no revolutionary
changes in the Newtonian paradigm. Though Kuhn’s account of scientiŽc
growth, particularly in the eighteenth century, accords well with that of
many contemporary historians and philosophers, there are good reasons
both historical and philosophical to depart from it. Indeed, mid-eighteenth
century scientists tend to view their own achievements as constituting un5. For example, Alexandre Koyré (1968, pp. 42…
3) emphasized Newton’s responsibility
rather than that of Newton’s followers in the process of achieving a mechanistic worldview.
Newton’s science, he believed, created the enigma of modern man and woman “by substituting for the world of qualities and sensible perceptions—the world in which we live,
love and die—a world of quantities stemming from the deiŽcation of geometry.” See also I.
Bernard Cohen (1980, 1982) about “The Newtonian style,” which scientists would have
followed since the end of the seventeenth century.
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139
precedented progress in the history of science. 6 Moreover, as Niccolò
Guicciardini (1999, p. 6) recently put it rather bluntly, following extensive studies of Newton’s mathematical achievement: “After Euler the
Principia’s mathematical methods belong deŽnitely to what is past and obsolete.” It is rather the “Eulerian mathematical style” or precisely his “calculus and mechanics,” Guicciardini argued, that in the end proved to be
the most progressive way to solve problems in dynamics. This mathematical reworking of mechanics “in its own right,” observed George Smith
(2002b, p. 57), “is no small contribution to the science coming out of the
Principia.”
Earlier, Clifford Truesdell (1970) similarly contested the idea that eighteenth century scientists were merely Newtonians whose work consisted
primarily of simply applying Newton’s laws. He argued that rational mechanics, along with its philosophy of nature, grew as a response to a challenge stemming from Newton’s failures, errors and guesswork in the
Principia. The great architect of the success of rational mechanics, he said,
was Euler. He stressed that what is termed today “Newtonian mechanics”
is rather the result of Euler and Lagrange’s achievement, and that it bears
very little direct relationship to the Principia. He maintained that the
Basel mathematicians, for example, were far from being Newton’s disciples. On the contrary, these savants began “as doubting opponents, who
accepted, grudgingly, only some isolated results. Newton’s achievement,
great though it was, was far from enough to cause the revolution in
scientiŽc thought historians of the last century and ours have been pleased
to imagine” (Truesdell 1970, p. 201).
Not only does this emerging historical trend tend to vindicate
Whewell, but even more important it involves what one may term “the
rediscovery of Euler” or simply, to avoid reductionism, “the rediscovery of
the eighteenth century’s invisible revolution.” This invisible revolution, I
would like to argue, is the result of a triple dissociation from Newton’s
legacy mainly by Continental mathematicians and physicists in the
Leibnizian, Huygenian, and Cartesian circle. These Continental revolutionaries, as I shall call them here, parted company with Newton on the
speciŽc issues of which conceptual frameworks (ontological dissociation),
mathematical techniques (methodological dissociation), and scientiŽc
standards and values (philosophical dissociation) were suitable to put forward in mechanics.
6. D’Alembert, for example, conceived of his Traité de dynamique ([1743] 1758) as a
turning point in history of science while Euler wrote to Clairaut in 1751 praising, certainly with some exaggeration, the resolution of the lunar crisis as a mathematical success
without precedent in history (Birgoudan 1930, pp. 26…
40; Hankins 1970, p. 35).
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The Reception of Newton’s Gravitational Theory
The roots of this triple dissociation, as we shall see below, lie in the
clash of giants prompted by the publication of the Principia at the close of
the seventeenth century. Yet the magnitude of the clash and the Žerce debate it sparked has not been fully appreciated. A closer scrutiny reveals
that what was at stake was not only whether or not attraction is a mechanistic concept (or even intelligible). Rather, the conict went deeper and
apparently concerned even the very standards of scientiŽc rationality. After
a period of eclipse, Newton’s achievement in the Principia, as I will argue
below, underwent a deep revision on the Continent that allowed its subsequent standardization by Lagrange and Laplace. Not all Newtonian roads
led to Laplace.
Take for example Newton’s laws of motion. By the middle of the eighteenth century, Newton’s concept of inertia, understood as vis or the force
inherent to bodies, had become outlandish to the Continental revolutionaries. Jean Le Rond d’Alembert ([1743] 1758) saw Newton’s vocabulary
in the deŽnition of this law, among other things, as very obscure. He set as
a fundamental goal to “expel” force from bodies and to change its status
and conceptual meaning. Accordingly, he formulated his own three laws
of motion “leaving off motive causes in order to focus only on motion as
their effects; thus I completely banished from science the conception of
forces inherent to bodies in motion. These forces are nothing more than
metaphysical and obscure beings that plunge a science which is clear by
itself into darkness” (D’Alembert 1758, p. xvij). Inherent forces and motive causes are key to Newton’s conceptual apparatus. But d’Alembert rejected them as obscure metaphysical entities and, to use Baconian terminology, epistemological impedimenta.
Yet he did not deem it necessary to prohibit the word “force” from science. Then what became of force in his approach? It is shorthand or, as he
stated it, it is an “abbreviated manner of expressing a fact” (D’Alembert
1758, p. xix). Its status and relationship to body are quite similar to those
of velocity: velocity, he asserted, is by no means inherent in body. So, from
a philosophical point of view, when d’Alembert claimed for example to
“follow Newton in using the name ‘force of inertia’ ” to characterize the
properties bodies have to remain in the state they are, he was not at all
standing within the same theoretical framework as Newton. They did not
share the same ontology and scientiŽc values. 7
7. However, Cohen (2002, p. 62) thinks that Newton’s followers did not have any
problem with Newton’s deŽnition of inertia and, as an example of this smooth acceptance,
he refers to d’Alembert. In fact, Cohen (Newton 1999, p. 60) believes that Newton successfully eliminated from the Principia any signiŽcant tracks of the alchemical origins of
his discoveries in such a way that it took three hundred years to get behind the façade of
his book. But Newton’s opponents, particularly Leibniz ([1715] 1973, pp. 37…
40; 1965,
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141
In fact, d’Alembert wanted to axiomatize mechanics (apparently the
mechanics of solid bodies) and his scientiŽc standards and values, heavily
inuenced by Cartesian philosophy (Hankins 1970; De Gandt 2001),
could not tolerate the intrusion of metaphysical entities into this undertaking. His criticism of his predecessors, Newton included, was that they
were primarily concerned with building the “scientiŽc ediŽce” (solving
problems) while neglecting its foundations (the theoretical issues). As a
result of this negligence, thorny problems arose in mechanics, sparking
Žerce and fruitless debate. D’Alembert’s Traité de dynamique indeed aimed
at 1) establishing a new rational basis for mechanics by reducing scientiŽc
principles to just a few and 2) at providing physics with a new method of
solving problems, the so-called d’Alembert’s principle. These two goals
are so closely related, d’Alembert believed, that he proposed to achieve
one by the other. In this setting, Newton’s conceptual tools and scientiŽc
values became irrelevant. Thus d’Alembert’s raising of questions of theoretical foundations is not easy to reconcile with Kuhn’s notion of normal
science.
In the same vein, Euler (1768) expressed frustrations about the theoretical background assumptions of the Principia. He viewed Newton’s language in the deŽnition of inertia, for example, as truly risky. To escape
what he perceived as a naïve theoretical framework, Euler pointed out that
inertia is by no means a force. He parted company with Newton regarding
the class of facts that should be accounted for under the terminology of
force.8 In Kuhnian terminology, Euler and Newton did not perceive the
same thing when talking about rectilinear uniform motion of a body; they
held incommensurable views. In short, Continental revolutionaries were
far from being normal scientists, à la Kuhn. They were making an invisible revolution. John L. Greenberg (1995) also reached the same result recently, and concluded after studying the speciŽc matter of the earth’s
shape that Kuhn’s categories of normal science cannot account for the development of physics from Newton to Alexis Claude Clairaut.
p. 417) already seemed to characterize Newton’s concept of attraction as an obscure entity.
For about a half century, Cartesians fought against the metaphysical assumptions of the
Principia (Brunet 1970; Guerlac 1981).
8. Besides his Letter LXXVI to a princess of Germany, Euler (1750) had indeed pursued Newton’s mathematical work in reformulating Newton’s second law in algebraic
terms, f ma; he published a differential version as df a dm. He distanced himself more
overtly from Newton on several other points. He maintained, for example, that attraction
is a result of the impulse of the subtle uid surrounding all bodies. Just as he followed Cartesian philosophy in the physical description of, let us say, the fall of an apple, he observed
that “force of inertia” is a misnomer, since force is the opposite of the quality of a body remaining in a state of rest or motion. In the new Eulerian framework, force is strictly what
changes the state of bodies.
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The Reception of Newton’s Gravitational Theory
Now, if a scholar favors other philosophical terminology he or she can
rightly reply that in spite of the philosophical and ontological dissociations with the Principia, Continental revolutionaries were still working
within Newton’s program of research. That might mean, in Imre Lakatos’
terms (1970), for example, that Newton’s theory contained an irrefutable
“hard core” deŽned by the three laws of motion and the law of general
gravitation. For any Newtonian, dealing with any kind of problem, these
laws could not be altered. 9
This however does not seem to be in agreement with the facts.
D’Alembert changed some of Newton’s laws of motion as suggested
above. Through systematic revision, reformulation and substitution, he
proposed as his own three laws the law of inertia, the law of composition
of motion, and the law of equilibrium. But in the end all these laws seem
to be reduced to a single fundamental law of equilibrium (D’Alembert
1758). Moreover, during the lunar apogee crisis, Alexis Claude Clairaut
(1749, pp. 334…
7) declared himself very dissatisŽed with Newton’s theory
and resolved to accept nothing from Newton henceforth. He cast doubt
upon the universal validity of the inverse square law, preferring “to investigate directly the determination of the celestial movements on the sole
supposition of their mutual attraction.” He bypassed Newton’s law.
Actually, Clairaut still admitted attraction as a working hypothesis. But,
during the crisis years, he abandoned his previous enthusiastic and holistic
defense of Newton’s laws. From a philosophical point of view, what does
Clairaut’s boldness demonstrate? It shows 1) that there was no methodological decision on the part of Newton’s followers to keep Newton’s laws
unchanged when anomalies occurred, and 2) that scientists could question
even the inner core of their Želd or research program.10 From an historical
9. Lakatos (1970, p. 133) wrote: “In Newton’s programme the negative heuristic bids
us to divert the modus tollens from Newton’s three laws of dynamics and his law of gravitation. This ‘core’ is ‘irrefutable’ by the methodological decision of its protagonists: anomalies must lead to changes only in the ‘protective’ belt of auxiliary, ‘observational’ hypothesis and initial conditions.”
10. Kuhn (1962, p. 81) underrated the importance of attempts to change Newton’s
gravitational law during this crisis. He contended that these claims were not of great importance. Yet Clairaut, who demonstrated in the 1750s that the crisis arose from a mathematical error, appealed for a radical modiŽcation of Newton’s gravitational law in the
1740s. Clairaut’s proposal fostered sharp debate in the French Academy. In the late 1740s,
Euler also became skeptical about the universal validity of Newton’s law. When Lakatos
(1978, pp. 193…
222) became aware of these refutations of his philosophy in a paper (published posthumously), he seemed disarmed and simply contended that Newton’s methodology supplies no answers for the philosophical questions raised by the behavior of such
scientists as Clairaut, Euler, and Poincaré.
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143
point of view, it shows how Newton’s immediate followers on the Continent were rather skeptical “disciples” keen to innovate.
Euler’s Mechanica (1736) clearly indicates the demand for innovation
felt by the Continental revolutionaries. Euler was not only frustrated by
the theoretical assumptions of the Principia but also by the mathematical
methods used by Newton. According to him, though the reader of Newton’s book may be convinced about the accuracy of Newton’s Žndings, he
or she “cannot understand them clearly and distinctly” and, moreover,
cannot Žnd in the synthetic method of uxions used by Newton tools to
solve problems just slightly different from those resolved in the Principia.
Euler (1736) wrote in his preface: “. . . This was in fact my own experience
when I undertook a detailed study of Newton’s Principia . . . Although I
somewhat understand the resolution of several problems, I was unable to
solve problems just a bit different . . .” There is no more elegant way to say
that Newton’s Magnus Opus, undoubtedly a marvelous achievement, did
not however supply appropriate heuristic methods and exemplars or paradigms for solving problems acceptable to the Continental revolutionaries.
Thus, what I call a W-K bridge is a conceptual framework that allows
us to acknowledge that many scientiŽc theories, e.g., general gravitation
and evolution, are born incomplete but grow by revolutionary transformations. It provides not only a historical description of the process of transformation but also a philosophical assessment of the change. In this
instance, it makes perceptible and intelligible the Continental revolutionaries’ ontological, methodological, and philosophical dissociation from
Newton. To further illustrate this triple dissociation, I have chosen to
focus here on Varignon and Maupertuis. I postpone the cases of Euler,
Clairaut, and d’Alembert to another occasion.11 However, to strengthen
the idea of a period of eclipse that I have introduced here apropos the appraisal of the history of the Principia, I shall show how some noteworthy
Continental mathematicians perceived this book from the very beginning.
According to Kuhn, to discriminate a normal from a revolutionary
change, it is important to know how the revolutionary change was perceived when it Žrst occurred and what became group commitments, if any,
among the proponents of the change.
2. Another “sup reme mathema tician” reacting to the Principia
Derek T. Whiteside (1970, p. 6) once remarked that in Newton’s lifetime
only Christiaan Huygens, Gottfried Wilhelm Leibniz, Pierre Varignon,
11. For more details, see my article “The Rise of Newtonian Mechanics, or the Hidden
Revolution of Euler, d’Alembert, and Clairaut,” in progress.
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The Reception of Newton’s Gravitational Theory
Abraham De Moivre and Roger Cotes were able to penetrate the technical
content of the Principia. But what is striking is that the only physicists
who were unquestionably Newton’s peers on that list were to Newton
what Albert Einstein, Louis De Broglie and Erwin Schrödinger, among
others, would later be to the school of Copenhagen-Göttingen. Leibniz
and Huygens were never able to accept the theoretical framework of Newton’s oeuvre.
The case of Huygens is particularly interesting for at least three reasons. First, unlike Leibniz, he did not seem to be involved in personal
quarrels with Newton. Second, from 1666 on, the young French Academy
depended on his intellectual assistance. There can be no doubt that he
contributed greatly to its ourishing. This scientiŽc institution, along
with the Basel mathematical school, was an active agent in revising Newton’s science. Third, Leibniz referred to Huygens when he wrote to
Newton about the Principia. He called Newton’s attention to the work of
“Christiaan Huygens, that other supreme mathematician,” as a possible way
of completing the Principia. 12 But there is more. Newton himself recommended Huygens’ Horologium oscillatorium to Richard Bentley as a work
“that will make you much more ready” to understand the Principia (Newton 1961 vol. 3, pp. 155…
6). Likewise, Huygens greatly hoped to see a revised version of the Principa (OCCH vol. 10, p. 209)13 and even acknowledged for example that Newton’s treatment of motion in resisting media
was superior to Leibniz’ and his own work on the subject (OCCH vol. 9,
p. 367). Both men indeed showed great interest in the work of the other,
and some scholars have even suggested that the Horologium oscillatorium
might have served “as a model” for the Principia despite the innovative
style of the latter (Guicciardini 1999, pp. 30, 128). All in all, Huygens’
attitude towards the Principia provides reliable clues for assessing the reception of Newton’s achievement on the Continent at the close of the seventeenth century. This attitude can be described in a sequential form as
follows.
Act one: skepticism and caution. Before he received a copy of the
Principia, Nicolas Fatio de Duillier (OCCH vol. 9, p. 167), in a letter of
June 24, 1687, provided Huygens with a brief account of the philosophy
of nature encompassed by the book. Fatio reported that Newton’s work
bypassed Cartesian philosophy. In his response to Fatio on July 11 of the
same year, Huygens adopted an attitude of prudence. He wrote simply,
12. “. . . I do not doubt,” Leibniz wrote to Newton, “that you have weighed what
Christiaan Huygens, that other supreme mathematician, has remarked, in the appendix to his
book, about the cause of light and gravity . . .” (Newton 1961 vol. 3258, my emphasis).
13. OCCH Oeuvres complètes de Christiaan Huygens.
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145
but interestingly: “I want to see Newton’s book. I am willing to admit he
is not Cartesian so long as he does not make suppositions like that of attraction” (OCCH vol. 9, p. 190). Huygens sharply drew the limits of
scientiŽc acceptability: one can be anti-Cartesian; however, scientiŽc
achievement has some requirements that one cannot get around.
Act two: astonishment and admiration. When he read the Principia in
1688 Huygens exclaimed: “See all the difŽculties that the celebrated Mr.
Newton has made to disappear along with the Cartesian vortices; and he
has taught us that the planets are kept in their orbits by gravity. And that
the eccentrics must necessarily become elliptic Žgures” (OCCH vol. 21,
p. 143). Huygens was astonished to see that Newton had solved all the
problems relative to Kepler’s laws. He was so impressed that towards the
close of the same year he asked his brother Constantine, who had just arrived in England, to assist him in meeting the “celebrities” of the Royal
Society once again. Huygens particularly desired to meet Newton. He
stated: “I admire greatly the beautiful discoveries that I Žnd in the work
he has sent me” (OCCH vol. 9, p. 305). The beautiful discoveries concerned mathematics. 14
Act three: regret and confession. Huygens then declared that he had
long had the intuition that the spherical Žgure of the sun and of the earth
could be produced by the same cause. But still having the Cartesian vortices in mind, he could not generalize the action of gravity. Huygens then
stated that he had nothing against attraction as long as Newton did not
afŽrm that it acts from an inherent quality of matter (OCCH vol. 21,
pp. 472…
4).
Act four: incomprehension and rejection. A year later, on November
18, 1690, Huygens asserted in a letter addressed to Leibniz that attraction
is an absurd principle and that he did not admit the theories Newton built
on it. Attraction is unacceptable since it is, in all its forms, inexplicable by
the principles of mechanics and the laws of motion. Consequently,
Huygens confessed that he was deeply perplexed that Newton was able to
build so much research and such difŽcult calculations on such a weak theoretical foundation (OCCH vol. 9, p. 538).15
14. According to Marie Boas Hall (1980, p. 78), direct contact with Newton in 1689
and the study of the Principia may have furnished Huygens with the necessary stimulation
to complete the Traité de la lumière. They may also have reinforced the conviction he expressed a year before about the validity of the elliptic orbit of the planets deŽned by Kepler’s Žrst law. Whiteside (1964) stressed the fact that Newton himself at Žrst accepted only
with hesitation Kepler’s Žrst two laws.
15. However, Huygens, at several occasions, stated his strong opposition to the use of
the concept of attraction in science. See for example his letter to Hudde (OCCH vol. 9,
p. 267) or to Guillaume de l’Hospital (OCCH vol. 10, p. 354). Thus the chronology of the
correspondence as a whole is not crucial to my story.
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The Reception of Newton’s Gravitational Theory
The case of Huygens demonstrates that Newton’s Principia, though
clearly a mathematical work of genius, was not compelling for Continental mathematicians and physicists because, compared against Cartesian
scientiŽc standards and values, it depended on incoherent physical concepts. In contrast to the general acceptance of Newton’s theory in England, Continental mathematicians, physicists and philosophers were in the
end reluctant to endorse it as a whole. This allows us to distinguish among
several kinds of interpretations and among the different degrees and kinds
of support accorded to Newton’s theory in different countries, scientiŽc
institutions, disciplines, and time periods. Huygens’ deŽnitive position is
only favorable to Newton’s mathematical ability. But when it came to the
progress of physical science as a whole, the appraisal of Newton’s theory in
signiŽcant part stumbled against the theoretical bases of the Principia.
How to understand Huygens’ problem? Cohen put forward an interesting idea that might explain it. According to him, Huygens’ problem
stemmed from failing to understand Newton’s scientiŽc style. This style
allowed Newton to employ a purely mathematical treatment of nature,
yielding an idealized result that could then be subjected to the verdict of
experiment. Cohen (1980, p. 81) wrote: ‘‘Hugyens, disturbed by the intrusion of the concept of attraction, failed to discern that this term appears
primarily towards the end of bk. one of the Principia, where Newton is
still concerned with mathematics rather than with physics, with what I
have chosen to call here a mathematical construct, and not with physical
reality. This was a distinction that Huygens himself was not able to make,
or was not willing to make . . .’’
We shall return to the interest of Cohen’s description of Newton’s
methodology later. But Huygens’ problem appears to be a complex one involving both theoretical and empirical considerations.16 In the Discours de
la cause de la pesanteur (OCCH vol. 21), for example, Huygens seems to indicate that his reasons for pursuing the discussion about the shape of the
earth is that empirical data lend support to his theoretical anticipations. If
so, I would like to try to articulate an alternative explanation to Huygens’
problem. It is possible that Huygens would still have opposed Newton
even if he had made a distinction between mathematical construction and
physical reality in the Principia. Moreover, Newton himself has been unable to provide a “positivistic” defense of his masterpiece. For example, in
the general Scholium of the 1713 edition of the Principia, Newton stated
that he had not yet assigned a cause to gravity (“sed causam gravitatis
nondum assignavi”). This indicates that the adjustment of the theoretical
framework of his theory was still a relevant task for him. The fact is that at
16. See for example Huygens’ letter to Hudde in (OCCH vol. 9).
Perspectives on Science
147
the end of the seventeenth century the aim of physicists, Newton included, was not mathematical calculation and experimental proof only, as
it would be the case in the post Comtian positivistic era. Their aim seems
to be that of judging whether the descriptive terms and the basic concepts
used in a physical explanation adequately represent the phenomena to
which they refer, and whether the calculations attached to them give an
exact account of the phenomena as shown by experiment. It is in this connection that Huygens, Leibniz and the Cartesians thought that Newton
had failed and that therefore physical explanation, and consequently mechanics as such, remained a task still open before them.
Huygens’ problem seems to arise from a radical opposition between
two different perceptions of scientiŽc practice though, as mentioned earlier, empirical considerations might also have played a role.17 For him, the
scientiŽc explanation of the “secret mechanisms” of nature must utilize
only “mechanical arguments,” that is to say, considerations of shape and
motion in the Cartesian style. To do otherwise would be to abandon all
hope of understanding anything at all in physics (OCCH vol. 21, p. 446).
For Cartesians, the framework of science is delimited by the use of concepts with mechanical meanings. All natural phenomena must be explained in terms of impact or contact between bodies: the shock of their
contact generates motion. The dynamical properties result only from the
impenetrability of matter. On the Continent, the perception of scientiŽc
practice rested on a kind of aprioristic rationalism.
By contrast, for Newton (1687), who intended to develop mathematics
in relation to natural philosophy,18 rational mechanics consists Žrst of all
in starting from experiment or observational propositions of general import based on the nature of things.19 Then it consists in submitting the results to mathematical treatment, and, Žnally, in relating the mathematical
results to natural phenomena.20 Query 31 of the Opticks also deŽned this
procedure with the qualiŽcation that it consists in starting from experiment, or from other certain Truths.21 From the beginning of the Principia,
17. See E. Schlisser and G. Smith, “Huygens’s 1688 Report to the Directors of the
Dutch East India Company on the Measurement of Longitude at Sea and the Evidence it
Offered Against Universal Gravity” (to be published). According to Schlisser and Smith’s
reconstruction, “Huygens had cogent empirical reasons to reject Isaac Newton’s theory of
universal gravity . . .” I thank the authors for generously sending me their manuscript.
18. See the preface.
19. See particularly Book 3, Rule IV.
20. See Book 1, Proposition 69.
21. But which ones? It is not certain that it is here a case of modern scientiŽc laws, but
rather of truths of the prisca sapientia. Newton in his De systemate mundi for example believed that heliocentrism and his own inverse square law belong to this tradition (See also
Newton 1961 vol. 3, p. 193).
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The Reception of Newton’s Gravitational Theory
Newton afŽrmed that geometry is a branch of mechanics, on which the
description of mathematical Žgures depends. In one of his letters to
Oldenburg, he stressed that the mathematical sciences depend just as
much on physical principles as on mathematical demonstrations (Newton
1959 vol. 1, p. 187).
It is thus quite likely that “force” is a physico-mathematical construct
in the Principia and Newton’s interlocutors on the Continent seemed
to perceive it this way. Far more disconcerting, the concept of attraction, wherever it Žrst occurred in the Principia, did not Žt Huygens’ “neoCartesian” rationalism. In addition, the Dutch scientist perceived the
inuence of this non-rationalistic conception of attraction on Newton’s
mathematics. He wrote: “I am not in agreement with a principle that he
assumes in this calculation and elsewhere, which is that all the parts one
could imagine in two or more different bodies mutually attract and tend
to approach one another” (OCCH vol. 21, p. 471). The derivation of the
shape of the earth, Huygens’ subject here, and the inverse square law, were
connected to the underlying concept of attraction. Notice that Huygens
was not the only one to perceive the close connection between the
signiŽcance of attraction and Newton’s mathematics. Bernard le Bovier de
Fontenelle (1734, p. 217) also pointed out that the proportionality of
weight to mass and the reciprocity of action indicate that attraction is obscurely inherent in bodies.
Attraction was not a neutral concept vis-à-vis Newton’s calculations.
As a central concept that he required in constructing physical theory, it
placed the Principia beyond the bounds of acceptable science according to
Cartesian standards and values. Huygens consequently disapproved of
Newton’s theory while recognizing that he himself had to pay a price for
what Koyré (1968, pp. 158…
9) has called “his loyalty to extreme Cartesian
rationalism.” As Koyré reminds us, having dismissed attraction to the
outer boundaries of science, Huygens lacked a concept that allowed him
1) to convert centrifugal force to centripetal force, 2) to demonstrate the
elliptical form of the planetary orbits, and 3) to generalize the effect of
weight.
Despite this wonderful explanatory power, Huygens denied that the
concept was fruitful for physics because it violated his criteria of sound
achievement in mechanics. He maintained that attraction, clinamen, and
levitas all reected the same kind of error from which Descartes had wisely
saved physics. The rise of modern science was due to a break with these
conceptual traditions. In this way, Newton’s philosophy of science contrasts sharply with Huygens’: for example, prior to attributing his law of
inertia to Galileo in the Principia, in a fragmentary draft connected to his
book, Newton had already attributed it to Ancients such as Lucretius,
Perspectives on Science
149
Aristotle, and Anaxagoras.22 In brief, while tradition might be for Newton a good criterion for theory appraisal, for Huygens it was an obstacle to
the development of science. I will tentatively call these two philosophical
attitudes respectively “backward looking” epistemology and “forward
looking” epistemology.23
Thus making a distinction between mathematical demonstration and
physical account in the Principia would not necessarily have had an impact
on the debate. In point of fact, Huygens may have had empirical and theoretical reasons to reject Newton’s theory. In addition, he simply did not
seem to believe that mathematical description could exhaust physical science. For Huygens, Newton made beautiful mathematical discoveries but
failed to complete the scientiŽc revolution begun by people like Descartes.
These kinds of criticisms, which were fairly common on the Continent,
prompted what I called the eclipse of Newton’s theory of general gravitation in key Continental scientiŽc institutions. But they also showed Continental revolutionaries how the Principia needed to be redirected. In particular, the conceptual mismatch between the theory of attraction and the
new philosophy of nature, deeply entrenched on the Continent, seems to
have engendered in “Newtonians” of the Paris and Basel mathematical
schools a kind of cognitive dissonance. A slow process of revision began,
resulting in the triple dissociation mentioned earlier.
3. Th e analytic redirection of the Principia
In the seventeenth century, as A. Rupert Hall (1975 vol. 13, pp. 233…
4)
reminds us, the French and the English were rivals. They alone had well
organized and well Žnanced scientiŽc institutions. French and English
journals were current sources for other editors. When Newton’s Principia
appeared at the close of the century, Cartesian physics had already shaped
science in France. For example, Rohault’s Traité de physique, published in
1671 was in its fourth edition in 1682 and in its twelfth in 1708. Also,
Fontenelle’s Entretiens sur la pluralité des mondes in 1686 and Regis’ Système
de philosophie in 1690 aimed at beeŽng up the Cartesian system. Thus, the
two Royal Academies differed greatly in their way of perceiving and describing physical objects. This difference seems to have determined the
scientiŽc style of the Žrst great French mathematical proponent of Newton’s theory, Pierre Varignon.
As Voltaire (1988, pp. 70…
1) wrote, things changed so critically between the English and the French after the publication of the Principia
that there was no way to come to an agreement even on the deŽnition of
22. See I. Newton, MS. Add. 3970, fol.652a.
23. See below for more details.
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The Reception of Newton’s Gravitational Theory
mind or matter. 24 However, the mathematical accomplishment of the
Principia was attractive even to such great opponents of Newton’s as
Leibniz, an inuential and respected authority in France. Even though
Leibniz opposed the physical account of the world in Newton’s book, he
praised Newton for having made an “astonishing discovery” about Kepler’s laws and encouraged him to persevere in handling nature mathematically.25 In the same vein, he encouraged the young French mathematician
Varignon to pursue the process of mathematizing nature.26 Varignon was
also cognizant of the genius of the Principia, and his writings already referred to it in the 1690’s. By then, French scholars vehemently rejected
Newton’s theory of attraction, much as did Huygens and Leibniz.
Varignon, however, was aware of the conservative motivations involved in
such a scientiŽc debate, as he had himself to Žght against those whom he
called the old style mathematicians in order to save the new Leibnizian
methods.27 In this atmosphere of vigorous controversy, Varignon successfully paved a new way for Newton’s theory without making any outstanding discovery: that was the path of mathematical analysis. He seemed to
turn the Leibnizian project of connecting mechanics and the differential
calculus 28 into a new program of research, that of applying the new analytic methods to Newton’s Principia. Varignon’s achievement was the Žrst
signiŽcant step in the methodological redirection of the Principia.
24. Voltaire’s eloquent description seems to have anticipated the idea of incommensurability between two theories.
25. In his letter to Newton, already partially quoted, Leibniz encouraged Newton to
“continue to handle nature in mathematical terms . . .” He then added: “You have made
the astonishing discovery that Kepler’s Ellipses result simply from the conception of attraction or gravitation and passage in a planet. And yet I would incline to believe that all
these are caused or regulated by the motion of a uid medium, on the analogy of gravity
and magnetism as we know it here. Yet this solution would not at all detract from the
value and truth of your discovery . . .” (Newton 1961 vol. 3, p. 258).
26. Notice that Varignon’s Projet d’une nouvelle méchanique, appeared in the same year as
the Principia. By means of the parallelogram of forces, Varignon also dealt with some problems that the Principia ignored. Similarly, his Nouvelles conjectures sur la pesanteur appeared in
the same year as Huygens’ Discours sur la cause de la pesanteur.
27. See Varignon’s letter to Johann Bernoulli on August 6, 1697 (Bernoulli 1955…
92
vol. 2, p. 124). In 1700…
1701, Varignon refuted Michel Rolle’s contention that the new
calculus was not coherent and that it was misleading.
28. For example, Leibniz published two papers in 1689 in the Acta eruditorium
(Schediasma de resistentia medii & motu projectorum gravium in medio resistente and then his
Tentamen de motuum coelestium causis), where he systematically attempted to solve mechanical
problems with his new methods. Leibniz claimed that he wrote the Tentamen before reading
the Principia. But recent studies seem to indicate that this may not be the case (Bertoloni
Meli 1988, 1991, 1993).
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151
It must be noticed above all that it was not only the adversaries of the
Principia who tried to select out its mathematical aspects. In England,
Newton’s followers such as John Keill and Richard Bentley, to name but
few, saw a weapon against atheism in the theory of gravitation. Nevertheless, Keill (1698) argued that one should exploit the mathematical aspect
of Newton’s work rather than its cosmological dimension.29 But the crucial fact was that the English mathematical movement remained in conformity with Newtonian symbolism and methods (Guicciardini 1989).30
It is only during the second half of the eighteenth century, as Guicciardini
(1999, p. 193) reminds us, that “British authors” became “convinced that
slavish adherence to the Principia’s geometrical methods would ultimately
lead to total sterility.”31 In striking contrast to the English intellectual
universe, Varignon initiated an entirely new path about a half century earlier. It consisted in transposing the most important propositions of the
Principia into Leibnizian symbolism. Indeed, at the turn of the eighteenth
century, Varignon (1700a, b, c, 1710, 1725; Peiffer 1990) began to use
the differential calculus to treat certain problems of the Principia in the
context of developing the general theory of central forces. This kind of
connection between Newton’s mechanics and Leibniz’ methods, that is to
say, between the geometrico-inŽnitesimal and the differential approach,
was an important step towards analytic mechanics.
It is now generally accepted that Newton and Leibniz independently
discovered analytic methods.32 However, for Leibniz, who searched for a
characteristica universalis, the differential calculus is superior to previous
mathematical methods and is nothing less than an ars inveniendi, an art of
invention or a method of discovery that can operate by cogitatio caeca or
blind reasoning. For Newton, who hoped to retrieve a prisca sapientia and
geometria, analysis may help discover scientiŽc truths but the synthetic
method of uxions presents the advantage of allowing a visualization of
such truths. He accordingly chose a geometrical representation of force in
the Principia. Historical records and recent studies indicate that Newton
29. But Keill (1758) himself tried, with some inŽdelity to Newton, to derive Newton’s
laws of motion from experiment. He presented inŽnite divisibility purely and simply as an
indemonstrable postulate. Further, for some scholars, the Principia offered a model of
scientiŽc approach to be transferred to almost all the domains of knowledge (see for example the Principia medicinae theoreticae mathematica of Cheyne, the Mathematical Elements of
Natural Philosophy conŽrmed by Experiments . . . of ‘sGravesande).
30. On British natural philosophy versus mathematics see SchoŽeld (1970).
31. Indeed, the attempts to connect the Principia and the analytic methods by people
like Cotes, Gregory, and Keill were limited.
32. For more details on the subject of this paragraph see Guicciardini (1999) and
De Gandt (1995).
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The Reception of Newton’s Gravitational Theory
was perfectly able to provide an extensive analytic account of force in his
masterpiece but at least partly because of the particular philosophy of science he adhered to, i.e., the backward looking epistemology, he increasingly became convinced of the superiority of geometrical approaches over
analytical ones (Guicciardini 1999, pp. 17…
38, 99…
117). Indeed, the
backward looking epistemology posits that the intellectual achievements
of the Ancients (such as the Egyptians, Phoenicians, Chaldeans, and the
Greeks) hide scientiŽc methods and truths about nature that are if not
superior at least equivalent to those of the Moderns (Casini 1984).33 From
a methodological point of view, Newton sought to align himself with the
Ancients who, he claimed, discovered their theories analytically but presented them geometrically (Newton 1967…
81 vol. 8, pp. 453…
5). It is interesting that d’Alembert ([1805] 1965 vol. 2, p. 320; 1770 vol. 4,
p. 176) and Laplace ([1884] 1878…
1912 vol. 6, p. 464), just as Euler
(1736), were already cognizant of this methodological difference when
they pointed out the importance of the geometry of the Ancients in
Newton’s public work. In brief, where Leibniz wanted to promote blind
mathematical reasoning, Newton praised intuition and visualization
(Guicciardini 1999, pp. 136…
68; De Gandt 1995). Thus not only is a distinctive ontology imbedded in Newton’s theory but also a speciŽc methodology driven by a particular philosophy of science.
Newton’s backward looking epistemology contrasts with Varignon’s
forward looking epistemology. Starting from Žgures like Descartes,
Huygens, and Leibniz, the forward looking epistemology posits that the
intellectual achievements of the Moderns surpass the accomplishments of
the past and hence provide universal standpoints. For example, though
Leibiniz claimed that the Moderns do not give enough credit to the
Ancients on speciŽc matters such as mechanistic philosophy,34 he never
33. See my article “Newton Science and Alchemy: Half a Century of Controversy,” in
progress.
34. Notice for example that Leibniz wrote his Discourse on Metaphysics in 1686, the same
year Newton wrote De mundi systemate. In the Discourse, Leibniz made a move back to the
scholastics to reintroduce substantial forms into modern philosophy. He even went so far as
to contend that if their achievements were examined and clariŽed by an open-minded person according to the methods of analytic geometry they might yield a great treasure of
demonstrative truths. Newton all along has been convinced of something similar and in
the De mundi systemate, as in other several writings, argued that scientiŽc theories such as
the heliocentric one were already known by the Ancients and are hidden in their works. It’s
as if Newton were the open-minded analytic geometer Leibniz hoped for. What Leibniz
could not, however, accept was attraction. We can say, based for example on the Tentamen,
the Monadology, and the letters to Clarke, that, according to Leibniz, Newton went to the
other extreme in the rehabilitation of the Ancients: bodies, though not reducible to pure
extension, act on each other only through actual contact.
Perspectives on Science
153
doubted, unlike Newton, the superiority of the differential calculus over
previous mathematical methods. Likewise, Varignon, as we have seen,
sharply drew the line between the mathematicians of the “old” school who
deprecate the new analytic methods and those of the Leibnizian school
who promote it. The whole controversy, he suggested, is due to the fact
that Leibnizian methods allow young mathematicians to surpass mathematicians of the old style. He complained about the behavior of “mathematicians of the old style worried to see young mathematicians become
their equals and even surpass them thanks to the calculus” (Bernoulli
1955…
92 vol. 2, p. 124). Thus, as early as 1697, Varignon already realized
that the differential calculus opens progressive scientiŽc avenues, and a
few years later he undertook extensive translation of the Principia from its
original geometrical style into the more progressive analytic methods.
Varignon’s achievement inuenced not only the second edition of the
Principia by Cotes in 1713, but equally the Phoronomia of Jakob Hermann,
which constituted the “mathematical mother’s milk” of Euler until 1727
(Fellmann 1988). Moreover, thanks to their use of analytical and differential instruments, the annotated edition of the Principia by Thomas LeSeur
and François Jacquier, from 1739 to 1742, inuenced d’Alembert decisively.
How original was Varignon’s achievement? Later writers such as
Charles Bossut, Jean Etienne Montucla, and Pierre Duhem were skeptical
on the subject. They perceived Varignon as simply developing methods
discovered by others (Duhem 1991 vol. 1, pp. 420…
1). For example,
Varignon’s work on the inverse problem was just a bit more than a synthesis of Johann Bernoulli’s and Herman’s Žndings. However, Lagrange
(1788), for one, had already pointed out that Varignon had a share in the
development of both the principle of the composition of forces and the basic axiom of statics, the principle of virtual work. D’Alembert extended
the latter to dynamics. This enabled Lagrange to specify the class of problems which can be solved by the more systematic method of identifying a
so-called Action integral which, when minimized, leads to Lagrange’s
equations of motion.
Recently, scholars have tended to emphasize Varignon’s contribution to
the rise of analytic mechanics. His originality, as Michel Blay (1992,
pp. 153…
221) noted, consisted in this: by formalizing the problems of
geometry systematically by means of Leibnizian methods, he traced a new
trajectory for the science of motion. In Comtian terms, he reduced mechanical problems to simple analytical procedures, that is to say, to simple
calculations by differentiation or by integration. In contrast to Leibniz and
Newton, Blay observed, Varignon achieved this result by the construction
of a notion of velocity and of accelerating force at each instant.
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The Reception of Newton’s Gravitational Theory
Varignon was not the only one to connect Newton to Leibniz. Johann
Bernoulli and Guillaume de l’Hospital did much the same (Aiton 1986,
1989). Varignon was one of the very Žrst Frenchmen to begin using the
new Leibnizian methods, thanks to Johann Bernoulli (Fleckenstein 1945;
Robinet 1960; Costabel 1976). Moreover, works of such distinguished
“Newtonians” as Euler, though following Varignon’s path, clearly show a
strong inuence of Johann Bernoulli. However, Bernoulli and de
l’Hospital did not seem to have perceived, as Varignon did, that there was
a great deal at stake in systematically basing Newton’s physics on this new
instrument. Varignon had transformed the casual connection of Newton’s
theory to Leibnizian methods into a systematic enterprise that seemed to
orient physics in a more self-sufŽcient or “agnostic” way.
Varignon contributed to the rise of a new conception of mechanics as
simply a domain of analysis. A new scientiŽc style began to emerge. Later,
physics was conceived as a purely logical deduction starting from a general
algorithmic expression, which liberated mathematics from the realistic intuition that was crucial for Newton. The formalization of the central aspects of the Principia by means of the differential calculus constituted a
Žrst reworking of Newton’s achievement and the starting point of the
methodological dissociation from Newton by the Continental revolutionaries. Initially, mechanics implied a theoretical description of physical objects. The successes of this reworking and methodological dissociation
produced a new perspective on the interpretation of Newton’s theory. The
analytic redirection began somehow to mask the ontology of force, the target of Huygens and Leibniz. Varignon’s version of “Newtonianism,”
which found its most complete fulŽllment some decades later, systematically reduced the questions of physics to the art of solving equations. It is
this appropriation of Newton to a Leibnizian mode of thought that
brought about what Francois De Gandt (1995, pp. 271…
2) called a “neutralization of the study of force.”
The methodology of the Principia can be described from different perspectives yet not necessarily mutually exclusive thanks to the extreme
rigor and extraordinary creativity displayed by Newton in the course of
the geometrical translation of force. For example, Cohen (1980), as we
have seen, described it as a “mathematical construct.” George Smith
(2002a, pp. 142…
3) characterized it from logical point of view as an
“if-then” logical approach contrasting it with Galileo’s and Huygens’ approaches that he identiŽed as a “when-then” form of reasoning. In fact,
Newton’s mathematical and logical ability allowed him to subject force to
a quantitative treatment. The backbone of this treatment is the “Žrst and
ultimate ratios” for which he actually provided a geometric as well as analytic version. Cohen’s and Smith’s descriptions provide useful explanations
Perspectives on Science
155
of how Newton became methodologically capable of postponing a physical account of force. However, being able methodologically to postpone
this task is different from masking the problematic ontology of force or
stripping the geometrical “translate” of force from any ontology. Apparently, Newton’s theory conjoined geometry and ontological assumptions
in such a way that it took the analytic move of Varignon to help progressively “desensitize” its reception on the Continent.
Otherwise put, the fact that Newton didn’t Žll the Principia with descriptions of alchemical processes and theological designs to account for
gravity but successfully subjected force to a geometrical treatment was a
great revolutionary step. But to analytically map motion in a way that
progressively “neutralizes” the ontological underpinnings of the notion of
force is another step towards a revolution. I maintain that this analytic
mapping of motion that began with Varignon created a methodological
distance between Newton and the Continental revolutionaries. It led to
the emergence in the mid-eighteenth century of new exemplars of solving
problems that Curtis Wilson called “a newer new analysis” (Wilson 1995,
2002).
Varignon’s great discretion in the controversy between Newtonians and
Cartesians, while matched by a resolute exploitation of the mathematical
aspects of Newton’s work, appear to inaugurate a new attitude in the reception of Newton’s theory and consequently in the practice of physics as
such.35 This attitude encouraged exibility with respect to theoretical
problems. And for good reason: As d’Alembert (1967 vol. 1, p. 74) wrote,
young mathematicians from all over Europe solved the conict between
Cartesianism and Newtonianism. It was in mathematics that a new relation to the Principia began to take shape. As a result, a new image and a
new style of scientiŽc practice emerged. Varignon thus seemed to initiate
not only a new style, but also new ideals and standards different from
Newton’s. Though he did not convince the French Academicians to accept
Newton’s theory, he helped resuscitate the Principia from its eclipse as a
valuable achievement in physics. However, to save the theory of general
gravitation on the Continent deŽnitively, a kind of holistic defense of the
Principia was needed.
35. Similarly, Varignon avoided taking sides in the conict between Leibniz and Newton over the calculus. Varignon became close to Newton from 1713 on and, in 1714, he
was elected to the Royal Society. Newton had already been elected Foreign Member of
the French Academy in 1699. Varignon played an important role in the reception of
Newton’s Opticks in France. This reception was easier than the reception of the Principia
thanks to Malebranche and his followers. Guerlac (1981) argued that the attitude of the
so-called Malebranchist group weakened the Cartesians’ position in the debate over the
Principia.
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The Reception of Newton’s Gravitational Theory
4. Maupertuis’ mechan istic reinterp retation of the Principia
Two strategies characterized the controversy about Newton’s theory in
the French Academy. One can be called the Žlter solution, the other intratheoretic perseverance. The Žlter solution consisted in interpreting the
spirit and the fundamental concepts of a theory by use of an alien ontology. As a result, the signiŽcance of both Newton’s and Descartes’ concepts
was radically modiŽed. Intra-theoretic perseverance was the attitude that
consisted in claiming that one still supports the same theory one is radically reinterpreting 36. By using these strategies in the context of the debates over Newton’s Principia, Maupertuis seemed to suggest that the theory of attraction was a perfect completion of the mechanistic science that
Descartes sought, but failed to achieve. Thus, according to Maupertuis,
Newton’s science displays the true structure of mechanism. I will call this
paradoxical union between two rival theories a theoretical two-in-one.
During the eclipse and under the direct inuence of Huygens and
Leibniz, Cartesians perceived attraction as “absurd” or “occult” or as a “return of chimeras.” They blamed Newton vehemently for violating the
mechanistic framework and scientiŽc standards of the new philosophy of
nature. Varignon limited his defense of Newton’s theory to an analytical
strengthening of the Principia. For Maupertuis, however, things had
changed and the time had come to furnish another reading of the
Principia. He was quite aware that he was distancing himself from Newton. He presented his main thesis in 1732 as a simple hypothesis. After
the success of his Discours sur les différentes Žgures des astres, he wrote modestly that he was himself very cautious about his own conjectures about attraction, and, that if he “decided to go some steps further than Newton, it
was not without awe and hesitation” (Maupertuis [1756] 1974 vol. 2,
p. 287).
How did he differ from Newton? In 1732, Maupertuis proclaimed that
Newton believed that attraction could be a result of some subtle matter
produced by material bodies, and that it could really be an effect of impulse (Maupertuis [1732] 1974 vol. 1, p. 92). Clearly, this would allow attraction to be understood almost in the same manner as Cartesian vortices.
Maupertuis, however, inquired in his Discours whether a reasonable understanding of the Principia (Maupertuis 1974 vol. 1, p. 94) could be
achieved by linking attraction directly to material bodies. He declared
that attraction is not a mysterious reality but just an empirical principle,
36. Notice that such Cartesians as Malebranche, Louville, Dortous de Mairan, and
Johann Bernoulli also used the same strategies. For example, Bernoulli’s reinterpretation of
Descartes’ vortices borrowed from Newton’s theory.
Perspectives on Science
157
or, more exactly, “a Žrst fact” that must be validated in nature (Maupertuis
1974 vol. 1, p. 92). How to justify this natural character of attraction?
Maupertuis adopted a triple strategy. After offering an account of the
physical data involved in the debate, he combined 1) a metaphysical discussion and a philosophical evaluation with 2) the principle of the black
box in view of 3) redeŽning the objective and the goal of science.
If attraction is a simple, natural, empirical principle, it must necessarily be linked to matter. But then it must not be metaphysically impossible. Maupertuis stressed that attraction did not imply any metaphysical
impossibility or even a logical contradiction. For Cartesians, attraction
was, metaphysically speaking, a monster. It implied action at a distance
and could not be explained by the received mechanistic philosophy. To refute this view, Maupertuis’ Žrst step was to reply that there is no relevant
conceptual barrier for conceiving attraction as a material property. In fact,
if attraction cannot be linked to matter as Newton maintained, then it
must be hidden somewhere in an unknowable space as an unknowable entity. As such, it would be a real metaphysical monster at least viewed from
the Cartesian perspective.
Once Maupertuis brought attraction entirely back into the material
universe, the only question that remained to be solved was how, as a material property, it was related to material things. Maupertuis’ second step
was to enlarge Locke’s agnostic perspective. He argued that we are not
only ignorant of the essence of things, as Locke taught, but also that we do
not have exhaustive knowledge of their material properties or of the way
in which properties reside in bodies. Our knowledge of bodies in general
is strongly limited (Maupertuis 1974 vol. 1, pp. 94…
8).
Here in fact Maupertuis was breaking through the barriers set by
Huygens; he sharply undermined Cartesian philosophy on two points.
First he contended that, in addition to its geometrical properties, matter
may have many other properties, however unknown to us. To reinforce
this argument he elaborated on both Locke and Malebranche (Hankins
1967)37 in establishing a philosophical equivalence between attraction and
impulse. Neither the one nor the other is directly intelligible to us
(Maupertuis 1974 vol. 1, pp. 98…
103). Second, in consequence, he argued
37. Newton himself seemed already to have created a climate of ambiguity around the
notion of impulse, by using it now and then strategically, as if it had the same status as attraction. And Locke had clearly called its intelligibility in doubt in his Essay. Similarly, for
Malebranche in his Search after Truth, impact was only an occasion for the expression of the
real cause of impulse, which is the will of God. Consequently, Maupertuis concluded, impulse is not intelligible to us unless we lose the habit of asking ourselves about it because
of its familiarity.
158
The Reception of Newton’s Gravitational Theory
that the appraisal of scientiŽc theory could no longer be a theoretical affair
but must be an empirical enterprise. His point seems to be that if attraction is neither metaphysically impossible nor logically self-contradictory
and if, further, our knowledge of physical properties is limited, we must
inquire by experimental means only whether attraction has an effective
place in Nature: “Attraction is nothing else, so to speak, but a question of
fact; it is in the system of the Universe that we must inquire whether it
is a principle that, effectively, has a place in Nature, up to what point it is
necessary in order to explain the phenomena, or, Žnally, if it is introduced
uselessly to explain facts that can be explained without it” (Maupertuis
1974 vol. 1, pp. 103…
4).
Maupertuis’ results are threefold: he lifted the metaphysical interdiction of the Cartesians; he easily burst through the Cartesian-Huygenian
impasse by his enlargement of the agnostic perspective; and he showed
that settling the question about attraction required empirical testing but
not a theoretical dispute. This means that scientists can reject attraction
only if they have proved by experiment that it doesn’t occur. In terms of
consequences, if attraction is only a question of fact, we can apparently
tuck away in a black box the question of the cause of which it is the effect,
leaving it, Maupertuis asserted, to more “sublime Philosophers” who are
capable of lifting themselves towards “the wisdom of the Sovereign Intelligence” (Maupertuis 1974 vol. 1, p. 93). On this reading then, the sole
task we should reserve for science is to deduce the explanation of natural
phenomena from a Žrst empirical principle. What Maupertuis seemed to
argue here was that the debate over attraction no longer had a place within
science. The dispute was philosophical and should be cut off from
scientiŽc practice. Empirical testing should be the unique criterion of
scientiŽc undertaking.
Actually, Maupertuis’ strategies led him to a very special shift in the
theoretical framework. He reinterpreted the concept of attraction so that
it became congruent with mechanistic semantics. It signiŽed henceforth a
physical effect resulting from the mechanistic nature of bodies, having the
same ontological status as impulse, compared to which it nevertheless had
superior explanatory power. Here lies Maupertuis’ originality: in Žltering
the concept of attraction to Žt into mechanistic contexts, he elaborated a
kind of two-in-one that could bring mechanical philosophers and
Newtonians into the same camp. This quasi-mechanistic status that
Maupertuis (1974 vol. 1:pp. 132…
3, 136, 138, 140…
1) elaborated for attraction produced an empiricist philosophy of science according to which
scientiŽc practice would consist in verifying whether a proposed theory is
empirically valid or whether it is excess baggage. This means that science
Perspectives on Science
159
could then dispense with a clear philosophical description of its fundamental concepts as long as experiment validated them.38
Maupertuis was not alone: Newton himself had already claimed that
his theory of attraction was experimentally based. However, he did not
convince his peers on the Continent because of the ambiguous status of attraction in his theory. ‘sGravesande, who inuenced French “Newtonians,”
also found in Newton’s work a framework for the development of experimental physics and a defense of empiricism. But Maupertuis differed from
them in building a systematic mechanistic revision of Newton’s framework. This very mechanistic and empirical reduction explicitly allowed
modiŽcation not only of the goals of science, but also of the relations between philosophy and science. Like the other Continental revolutionaries,
Maupertuis undertook here an ontological and philosophical dissociation
from Newton.
Maupertuis’ mechanistic and empiricist framework might have inuenced Clairaut in 1747 during the lunar apogee crisis. Referring to
Buffon’s metaphysical argument, Clairaut declared that nonmathematical
argument had no weight in the debate over Newton’s theory (Euler,
1911…
86 vol. 4, p. 186).39 At the same time, Maupertuis’ conceptual inversion of the meaning of attraction seems to have profoundly changed the
reading of the Principia. His pupil, Voltaire ([1734] 1988, p. 86), attributed to Newton the idea that “there is a central force in all bodies” which
acts from one end of the universe to the other, on the nearest and the farthest bodies, according to the immutable laws of mechanics. Following
Maupertuis, he added that we should keep in mind that we could not
know the cause either of impulse or of attraction, which is also a “property
of matter” (Voltaire [1738] 1992, p. 344).
A scholar today can legitimately wonder to what extent these reinterpretations of the Principia were mechanistic. However, it must be remembered that the “Newtonians” were themselves aware of their mechanistic
outlook. In addition, such “Cartesians” as Johann Bernoulli and
Fontenelle clearly recognized the mechanizing process to which the
Principia had been subjected by the “Newtonians”. Bernoulli strongly disapproved of the change in meaning that the “Newtonians” tried to effect
in the conceptual framework of the Principia. He urged the partisans of
Newton to follow the example of their master instead of claiming that the
38. However, Maupertuis did not forbid himself to meddle with metaphysics and although his principle of least action seemed to rest on the foundation of an empiricist philosophy, Maupertuis read in it a proof of the existence of God (De Gandt 1999).
39. About the conict over the role of mathematics in physics see Gingras (2001).
160
The Reception of Newton’s Gravitational Theory
void and attraction were realities in the nature of things and that they
were principles of existence (Bernoulli 1735 1:265). In a word, Bernoulli
was chastising his fellow Continental revolutionaries for their ontological
dissociation with Newton.
Indeed, as Fontenelle noticed, the semantic changes undertaken by the
“Newtonian” Continental revolutionaries led them towards a change in
the theoretical framework of the Principia. He seems to have been particularly shocked by the process of redirecting Newton’s theory. He exclaimed:
“Behold attraction, which shows itself here unveiled; for all the tendencies
of bodies towards central points can always be reduced to mechanical
ideas, or at least it would not seem to be impossible that they should be;
but as soon as a body acts by its mass on another distant body, we cannot
conceal the fact that this is attraction in the strict sense of the term”
(Fontenelle 1732, pp. 132…
3).
That is precisely what the “Newtonian” Continental revolutionaries
aimed at through their mechanizing Žlter, changing the descriptive and
ontological perspective of the gravitational theory. Unlike Bentley and
Cotes, for example, Maupertuis made attraction undergo a real slippage in
meaning by a systematic ontological and philosophical revision of Newton’s Principia. He created a conceptual gap between his theory and
Newton’s. Maupertuis seemed to have realized that the only way to save
the Principia on the Continent was to reorient the understanding of its
central concepts in mechanistic style. For Maupertuis, curiously, the reading of the Principia that Newton had sharply disapproved of was the only
one that Žt this purpose. Maupertuis linked attraction directly to material
bodies though Newton had written: “That Gravity should be innate, inherent and essential to Matter, so that one Body may act upon another at a
distance thro’ a Vacuum, without the Mediation of any thing else, by and
through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity, that I believe no Man who has in
philosophical Matters a competent Faculty of thinking, can ever fall into
it.”40
Maupertuis might not be a talented philosopher in Newton’s sense, but
he did demonstrate outstanding philosophical ability. In fact, if attraction
could be conceived as a property of matter, if the agnostic perspective
about our knowledge of material body could be enlarged, and if a theory of
attraction could be supported by strong experimental proofs, then there
would be sound reasons to interpret the Principia as exemplifying an em40. Newton was writing to Bentley on February 25, 1693. However, the fact that
Maupertuis may not be aware of this particular claim from Newton is irrelevant to the discussion.
Perspectives on Science
161
pirically based mechanistic philosophy. In an extraordinary tour de force,
Maupertuis praised Newton’s theory as the true mechanism, in contrast to
Cartesian mechanism, which would henceforth exhibit only an appearance
of mechanism. He wrote: “[The Cartesians] were so delighted to have introduced an appearance of mechanism in their explanation of Nature that
they rejected the true mechanism without any analysis” (Maupertuis
[1756] 1974 vol. 2, p. 284).
For Maupertuis, the mere use of the concept of attraction did not separate mechanistic from non-mechanistic achievements. The demarcation
between mechanism and non-mechanism was provided by the empirical
reasons used to advance a theory. Accordingly, he dismissed the use of the
concept by some French savants, particularly Fermat, as non-mechanistic,
because those people, he said, had no critical distance vis-à-vis the concept. Moreover, unlike Newton, they did not have any good evidence in
support of their theories (Maupertuis [1732] 1974 vol. 1, pp. 138…
40). As
far as gravitational theory is empirically proven, we may admit that Newton conceived attraction mechanistically.
To appreciate the subtlety of Maupertuis’ argument it will help to contrast it with that of Cartesians such as Fontenelle. Fontenelle (1968 vol. 1,
p. 611) argued that Newton’s theory, though remarkably supported by experiment, was nonetheless false as a physical theory. Newton’s theory was
false because it did not rest on coherent mechanistic bases. Accordingly,
Newton’s contribution to science lay solely in geometry, while Descartes
was the real instigator of a sound physical achievement even though the
Cartesian theory was not supported by experiment. It was this logic of
theory appraisal that Maupertuis changed. For him, a truly mechanistic
theory ought to be experimentally based; if Newton’s and Descartes’ theories were truly mechanistic theories, they both had to be proved by experiment. Only Newton’s theory was proved by experiment, therefore, only
Newton’s was a truly mechanistic theory. Otherwise put, since a theory of
attraction is supported by experiment, the theory of attraction that is
proven by experiment is a truly mechanistic theory. Logically, the relevant
scientiŽc issue about attraction is then experimental. Armed with this
theoretical revision, Maupertuis launched into a vigorous onslaught
against the French Academy while using derision to humiliate his opponents.41
41. To be sure, reason is a motif with limited force, and, as La Baumelle emphasizes,
“attraction no longer pleases young academicians who did not have their own prejudices to
combat,” but was detested by all those who “renounced only with pain the opinions
of their youth.” On the non-scientiŽc methods used by Maupertuis, see La Baumelle
(1856, pp. 31…
4). Maupertuis, who, according to d’Alembert, was the Žrst to believe “that
one could be a good citizen without blindly adopting the physics of one’s country,”
162
The Reception of Newton’s Gravitational Theory
Clearly, on current understanding, Maupertuis’ theoretical two-in-one,
through which Newton and Descartes were ultimately embedded in the
same theory, is incommensurable vis-à-vis Newton’s views in the Principia.
However, at the same time it undermines the concept of incommensurability on one point: scientiŽc theories are ontologically permeable and
inter-penetrable. Indeed, Continental revolutionaries were so successful in
changing Newton’s ontological and philosophical framework in the light
of the competing mechanistic theory that the habit arose of reading the
Principia as a purely mechanistic accomplishment comparable to that of
Descartes or Boyle. In the last two centuries, historians have maintained
that Newton had puriŽed the concept of attraction as far as possible of its
occult signiŽcation and that he had always followed Boyle’s mechanistic
style (Hall 1958, pp. 243…
4). During the period of eclipse, it is clear that
Newton was not understood in this way. For Leibniz (1965, p. 417), the
Principia constituted the breaking point with the key tenets of such mechanical philosophers as Boyle.
The possibility of interpreting Newton in a mechanistic way was a major accomplishment, forged by Continental revolutionaries, and this interpretation was not possible until after the transformation wrought by
Maupertuis and, later, by d’Alembert and Euler. Maupertuis’ point was
that, though the concept of attraction could rightly be described as
non-mechanistic in certain cases, Newton had constructed it in a highly
mechanistic way in the Principia. Thus, far from being an opponent of
mechanism as it was constructed on the Continent, Newton brought
mechanistic science to completion. In this way, Maupertuis seems to have
established the basis for a modern reading of the Principia. Later on Voltaire and Madame du Châtelet joined him in the Žght against what more
and more appeared to be French ideological resistance to Newton.
The eclipse was over and Newton’s theory could be developed with
great exibility in a kind of mechanistic framework. An intensive period
of technical revision started on the Continent, mainly with Euler,
d’Alembert and Clairaut. Maupertuis (1974 vol. 2, p. 286), later, referred
to the works of these three people as showing how Newton’s theory was
Žnally successful on the Continent.
Conc lusion
I have been arguing that when the Principia was published in 1687
Newton’s theory of general gravitation underwent an eclipse in key Conti(D’Alembert 1967, p. 73) was fully aware of the ideological motivations of the debate. At
about the time of publication of Maupertuis’ Discours, the writings of such Cartesians as
Dortous de Mairan (1733) and Joseph Privat de Molières (1734…
9) became more favorable
to Newton.
Perspectives on Science
163
nental scientiŽc institutions. It took Varignon’s analytic redirection and
Maupertuis’ mechanistic reinterpretation of the theory to help resuscitate
it. Through various strategies, Continental scientists reformulated the
theory, dissociating themselves ontologically, methodologically, and
philosophically from Newton. I maintain that the result of this revisionary
enterprise is better understood in a theoretical framework that reconciles
Kuhn’s notion of invisible revolution and Whewell’s ascription of the
completion of dynamical studies to the post Newtonian period. At the institutional level, despite the undeniable contribution of the British school,
the major agents in this reworking of Newton’s theory towards what can
be characterized as a synthetic theory of attraction were the Basel and
Paris’ mathematical schools. These two institutions were shaped in the
main by a combination of German (Leibiniz), Dutch (Huygens), French
(Descartes), and, of course, English (Newton) inuences. The double connection of the gravitational theory to the Leibnizian calculus and Cartesian mechanistic outlook created in the mid-eighteenth century a new
scientiŽc agenda particularly for Euler, d’Alembert, and Clairaut.
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