SOURCE: "Hegel's Criticism of Newton," in CLIO, Vol. 13, No. 4, Summer 1984, pp. 331-48.

[In the following essay, originally delivered as a lecture in 1981, the critic surveys Georg Wilhelm Friedrich Hegel's criticism of the scientific procedures that formed the basis of Newtonianism. Petry argues that Hegel opposed the conclusions drawn by nineteenth-century Newtonians, including physicists and philosophers, more than he opposed Newton himself]

Introduction

Even now, when we look back upon Newton's Principia and Opticks over a period of nearly three hundred years, it is difficult to imagine what modern physics would have been like had these books never been written. The experimental procedures on which they are based, their manner of exposition, the discoveries they made known, are so indispensable a part of the modern physicist's stock in trade, that he would be at a loss to define his discipline at all clearly were they to be brought into fundamental discredit. Nor is it easy to make out a convincing case for regarding Newton's accomplishment as nothing more than the embodiment of his intellectual presuppositions, his world-view, his conception of scientific method. Although it cannot be denied that his works bear the marks of their time and of the conditions under which they were written, one can hardly help admitting that they also communicate a body of universal scientific knowledge. Is it at all reasonable to assume that if Newton had not announced that "every particle of matter in the universe attracts every other particle with a force that varies inversely as the squares of the distances between them and directly as the products of their masses," no one else would have done so? If he had not demonstrated that "the whiteness of the sun's light is compounded of all the primary colours mixed in due proportion," is it at all likely that we should still be ignorant of the fact?¹ Any modern physicist who takes the trouble to consult Newton's texts soon discovers, moreover, that he was able to make such discoveries because he was informed and clearsighted enough to devise programs of research which would still do credit to the great majority of his modern counterparts. By present-day standards Newton's scientific procedures are limited and cumbersome, but no modern physicist will have any difficulty in realizing that as a fundamental discipline they still constitute the broad tradition within which he lives and moves and has his being.

It is of paramount importance, therefore, that anyone attempting to evaluate the present-day significance of Hegel's manner of philosophizing should take into consideration his attitude to Newtonian physics. If any attempt is to be made to establish the contemporary relevance of Hegelianism, it is essential not to overlook the fact that its originator was highly critical not only of the scientific procedures on which Newtonianism was based, but also of the conclusions being drawn from them by early nineteenth-century physicists and philosophers. What is more, this criticism was by no means a mere sideline, a fortuitous consequence of a broader strategy, something incidental to Hegel's central philosophical convictions, for he made no bones about proclaiming that he was prepared to stake his whole reputation on it. He inaugurated his career as a university teacher with a critical analysis of Newtonian mechanics, and over a period of almost thirty years made a point of publicly announcing the results of experimental work, the main object of which was to demonstrate the superiority of Goethe's theory of colors over its Newtonian counterpart.² To the historian of philosophy, this assessment of Newtonian science is therefore a matter of no little importance. To the contemporary thinker, to anyone aware of the directions given to modern philosophy by dialectical materialism and the Vienna Circle, to anyone attempting to convince anyone worth convincing that Hegelian methodology still warrants serious attention, it should surely be a matter of absolutely central concern.

It is worth noting, therefore, that of the fifteen thousand five hundred main courses in philosophy given in the universities of the German Federal Republic between 1945 and 1970, only two were concerned exclusively with Hegel's treatment of the natural sciences. The neglect of the subject in other countries during this period was even more complete, and one finds no reason to revise one's general assessment of it if one takes the trouble to check on the books and articles that were published. How is one to account for this almost incredible lack of intellectual curiosity? To some extent it was probably due to nothing more than the structure forced upon our university education by the need for specialists, to the widely recognized lack of communication between natural scientists, historians, and philosophers. But it seems also to have been the result of bad history, of inadequate research, of the successful propagation of the simplistic idea that in Newton "the study of nature saw a goal placed before it which, over the following two hundred years, it was to regard as the only thinkable one."³ Such history is never entirely harmless, but in this particular case it has contributed to the establishment of a wholly unacceptable prejudice.

Newton

To say that Newton's scientific accomplishment was more than simply the embodiment of his intellectual presuppositions, is not to say that these presuppositions are irrelevant to the understanding of the intrinsic significance and reception of this accomplishment. The great bulk of his private papers remained unknown to the eighteenth century, but even then it was common knowledge that he was not simply a mathematician and a physicist, that powerful personal convictions had driven him to his scientific work. It was no secret, for example, that he held unorthodox views concerning the nature of the Christian Trinity. The neo-Platonism of his Cambridge colleagues, especially Henry More, had had a great influence upon him, and it was evidently within the framework of this manner of thinking that he conceived of the ontological status of causation. It was William Law who first claimed that Newton had "ploughed with Behmen's heifer when he brought forth the discovery of the three great laws Of matter and motien."⁴ Of recent years, many of his private papers have been examined and published, and modern scholarship has, if anything, tended to overemphasize the importance of his private philosophy. His most recent biographers, for example, have brought out the significance of his psychology and his alchemical interests to such an extent, that there would appear to be the danger of overlooking the fact that his mathematics and physics can also be grasped and appreciated without knowing anything at all about the personal peculiarities of their author.⁵

It is not often realized that although Newton influenced nearly every branch of the physical and human sciences throughout the eighteenth century, the scientific scope of his published work is fairly limited. Although he concerned himself with nearly every branch of pure and applied mathematics, for example, he paid very little attention to the logical foundations of the science, and his contemporaries were not slow in calling attention to this neglect. Nieuwentijt, in Gronden van Zekerheid (1720), showed how essential it is to draw a sharp distinction between the philosophical or logical foundations of pure and of applied mathematics. Berkeley, in The Analyst (1734), while not calling in question the utility of the calculus or the validity of the results obtained by means of it, demonstrated clearly the difficulties implicit in its theoretical foundations. Newton was able to deal successfully with the motion of bodies in the first book of the Principia because he had proved that the force of attraction between two homogeneously layered spheres is directed along the line of their centers and is independent of their diameters. In his study of the miscellaneous problems of fluid mechanics in the second book he was much less successful, however, and it was left to the Bernoullis and Euler to attempt to master the highly complex questions he raised concerning the mechanics of rigid and flexible and fluid and elastic bodies. Since the conclusions he reached concerning the motion of bodies in resisting mediums were so varied and hypothetical, he made no attempt to apply them to the solar system in the third book of the Principia, although it had been his original intention to do SO.⁶ In his Opticks he was highly successful in laying the foundations of the modern physical theory of light and colors, but he barely touched upon the complicated problems of color perception. When Edmund Halley, for example, called his attention to the curious phenomena of colored shadows, he attempted to explain them as a purely objective or physical matter, whereas it was soon to become increasingly apparent, especially to De Godart and Rumford later in the eighteenth century, that a satisfactory explanation of them would also have to involve a consideration of subjective or physiological factors.⁷

If we are to account for Newton's reputation throughout the eighteenth century, it is therefore essential that we should not confine ourselves to a consideration of his personal convictions and the obviously successful aspects of his physics. Some may have been persuaded to put his "philosophy" into practice because they approved of his Unitarianism or Behmenism or because they had grasped the significance of his contributions to mechanics and optics, but the great majority did so because they saw him as the most distinguished exponent of the new Baconian brand of experimentalism, of applied philosophy, of the wholly universal scientific methodology which was in the process of proving the practical effectiveness of philosophy by laying the foundations of modern technology and so improving the material condition of the human lot. As President of the Royal Society of London Newton was the institutionalized head of this movement, the embodiment of the widespread conviction that natural philosophy is not merely an individual preoccupation but essentially an intersubjective or social activity. In the eyes of the general public of Europe, he was the foremost representative of the most progressive and effective intellectual movement of the time, the most distinguished proponent of the idea that nature was to be mastered in the practical interests of man through the application of the Baconian inductive method, through the testing, exchanging, and co-ordinating of information by means of scientific societies and their journals.

It is worth considering rather closely the precise nature of this methodology. As against Cartesianism, it involved the rigorous exclusion of all ideas or hypotheses concerning the natural world which could not be tested against observations and verified by experiment. It shared important ground with Aristotelian physics, with Zabarella, and with the highly successful non-Baconian methods of Galileo and Hobbes in that it took the analytical and synthetic procedures of resolution and composition to be central to all scientific work.

The first task of the scientist was to classify and define his sphere of inquiry. The second was to resolve this sphere, by inductive analysis, into a series of subspheres or subordinate fields of inquiry, into increasingly basic or general causes or presuppositions. The third was to carry out, in the light of this analysis, a systematic reconstruction of the original field of research which would enable it to be seen in the scientific light of the basic analytical work. In Newton's Principia, for example, the solar system was the main sphere of inquiry, the motions of bodies in resisting and nonresisting mediums were the two major subordinate fields, and the layout of the work gave expression to Newton's conception of the interrelationship between the sub-spheres brought to light by his analytical investigations.

The ideal in Cartesian physics had been the resolution of physical investigations into mathematics, or, more precisely, into algebraic formulae. The physicist carried out his empirical investigations with the ultimate objective of discovering clear and distinct conceptions which could be expressed in mathematical terms. The purpose of Spinoza's Algebraic Calculation of the Rainbow, for example, was to translate the physical complexity of the phenomenon itself into a series of algebraic equations.⁸ In Cartesianism, therefore, mathematics was the ultimate standard by which the success or final validity of empirical inquiry was to be judged. In Newtonianism it was not a standard but a tool which was to be used for calculating on the basis of data. Newton knew, for example, that he could make no progress with his mathematical theory concerning the motions of the Moon without the observations of the astronomer Flamsteed.⁹ He was fully aware that as an intersubjective discipline mathematics was no more than the language which enables us to communicate the nature of the regularities we have discovered in nature. Although he was not always as consistent on the point as he should have been, he therefore insisted on drawing a clear distinction between the material realities being investigated and the mathematical formulation of the results of the research. In his famous letters to Richard Bentley on the religious implications of Newtonianism, for example, he censures him for losing sight of this distinction: "You some times speak of gravity as essential and inherent to matter. Pray, do not ascribe that notion to me; for the cause of gravity is what I do not pretend to know, and therefore would take more time to consider of it."¹⁰

Newtonianism

Since Hegel concerned himself not only with Newton's own writings but also with those of his followers, it is essential, when dealing with the significance of his criticism of eighteenth-century physics and metaphysics, that one should distinguish between the expert Newtonianism of the mathematicians and physicists who were aware of both the importance and the limitations of Newton's accomplishment, and the uncritical popularization of his ideas. We have already noticed that although no one who knew anything at all about mathematics and physics could possibly have doubted the usefulness of the calculus, many of the experts were puzzled and perplexed concering its logical foundations and the ontological status of the computations that could be made by means of it. The prevailing conception of physical reality was that it was basically atomistic. In thinking about the occurrence of motion within this reality, eighteenth-century mathematicians and physicists were therefore obliged to wrestle with the ancient paradoxes of space, time, and motion put forward by Zeno, which had been restated with admirable clarity and sharpness and brought to the attention of the general public by means of Bayle's Dictionary. Since it was not yet general practice to distinguish between the purely formal or mathematical aspect of the calculus and its ontological significance, Zeno's paradoxes concerning physical reality gave rise to mathematical perplexities. Berkeley criticized Newton's fluxions as being "the ghosts of departed quantities," and argued that the idea of supposing a finite ratio to exist between two absolutely evanescent terms was absurd and unintelligible. Newton's views on the existence of variables which reach their limits were therefore brought into general discussion, and his followers were obliged to reject the idea of the existence of infinitely small quantities. One of the best modern histories of the development of the calculus therefore characterizes the eighteenth century as "the period of indecision.¹¹ It was only toward the end of it, and during the early decades of the nineteenth century, that such mathematicians as Lagrange, Lacroix, and Cauchy began to lay the foundations of a rigorous formulation of the calculus by distinguishing with increasing sharpness between its formal and its applied aspects.

Newton's cosmology was also the subject of constant questioning and revision among the experts during the eighteenth century. Buffon attempted to explain the origin of the centrifugal force within the solar system by postulating a collision between the Sun and a comet as a result of which a jet of matter had been torn away from the Sun's surface and had condensed into the planets at various distances from the central body. Laplace suggested that the solar system had originated from an immense incandescent nebula, rotating from west to east, which had eventually broken up into the rotating masses of the solar bodies. The observation of irregularities in the movements of Mercury and of the new planet Uranus discovered in 1781, made it a matter of general knowledge that Newton's law of gravitation could not easily account for all planetary motions.¹²

Apart from the discovery of the importance of physiological factors in the perception of color, the scientists of the eighteenth century also found it necessary to supplement and revise Newton's ideas on the physics of light. Newton had argued, for example, that since all refracting substances disperse the prismatic colors in a constant proportion to their mean refraction, refraction could not be produced without color, and no improvement could therefore be expected from the refracting telescope. As early as 1733, however, a telescope exhibiting objects free from color had been constructed, and by 1758 John Dollond had made the invention public. In 1800 Thomas Young published a paper in which he criticized Newton's rejection of Huyghens's undulatory theory of light, and after calling attention to similarities between the phenomena of sound and light, suggested that a wave theory of light would be an improvement upon Newton's corpuscular theory in providing the basis for progressive research in the field.¹³

While the experts were engaged in developing and revising Newton's contributions to the three main fields in which he had published, and while the technologists were reaping the benefits of a well-founded experimentalism, various popular philosophers were engaged in puffing Newtonianism up into a dogma, a worldview. These popularizers had little interest in Newton's private philosophy, his Unitarianism, neo-Platonism or Behmenism, and the last thing they were capable of doing was to appreciate the significance of his methodology, an attempt to exclude hypothetical theorizing by means of rigorous experimentalism, the practical and theoretical implications of the methods of resolution and composition, the conception of mathematics as a tool and not as a standard, the distinction between material reality and the mathematical formulation of the results of research. Their object was to enlist their interpretation of the scientific advances being made in the service of their conception of enlightenment, and they were not prepared to confine enlightenment to the sober and carefully formulated objectives of Baconianism. The social ideal put forward in Bacon's New Atlantis is a Christian monarchy in which institutions cultivating the natural sciences are encouraged by the government as part of a broad policy of furthering social harmony and welfare. Voltaire's book on Newton was part of his general program of opposition to the church and monarchical absolutism. Enlightenment was to be exhibited as incompatible with clericalism and monarchism, and as involving the application of an attitude of mind which had proved its effectiveness in revolutionizing man's conception of the natural world, to the solution of social and cultural problems.¹⁴

This Newtonian world-view tended to draw its inspiration not from Newton himself, or from the experts who were engaged in the apparently dry and shortsighted business of developing the rather specialized fields of scientific research he had opened up, but from those engaged in popularizing natural science—the schoolteachers, the itinerant lecturers, the ordinary run of university professors, the writers of textbooks and encyclopedias. It is important to remember that the eighteenth century, no less than the nineteenth, was the great age of popularized and potted natural science. It was still possible for the layman to get a fairly good grasp of fairly comprehensive fields of inquiry by applying himself to a textbook or attending a series of lectures. As we have seen from the extract from his letter to Bentley, Newton was well aware that when he used the concept of force in order to bring various qualitatively distinct fields of research in relation to the law of gravitation and hence within the scope of quantitative computation, a distinction had to be drawn between the mathematical and physical significance of his expositions. Those who popularized his work were often entirely unaware of the necessity of this distinction, and proceeded without inhibition to treat all branches of natural science as nothing more than quantitative procedures, exploration of the whole extent of which was simply a matter of computation. As Koyré has pointed out, one of the most pernicious results of this methodological confusion was that "the eighteenth century, with very few exceptions, became reconciled to the ununderstandable."¹⁵ When considering the intrinsic significance of Hegel's criticism of Newton it is certainly worth noting, therefore, that he had in his private library not only Newton's own works, but also several of the most popular and influential expositions of them.¹⁶

What seems to have fascinated the popular scientists of the eighteenth century more than anything else was Newton's postulation of the two mutually opposed forces inherent within planetary motion. Just as the opposition between the centripetal and the centrifugal forces was used to enlighten the interested layman as to the true nature of elliptical orbits, of a planet's radius vector always describing equal areas in equal times, of the cubes of the mean distances of the planets from the Sun being proportional to the squares of their times of revolution, so similarly opposed forces were postulated in order to account for the most diverse phenomena. Everything was to be made philosophical by being exhibited as arising out of the interaction of opposites, and hence as an illustration and confirmation of the central Newtonian insight. It seems unlikely that the universality with which the idea was accepted was entirely unrelated to the ease with which it may be comprehended. What is more, the grasping of this simple triadicity had the inestimable advantage of opening up the most diverse fields of inquiry to philosophical interpretation without requiring that the philosopher should be too deeply acquainted with the perplexing intricacies of empirical research. The Yugoslavian Jesuit Roger Boscovich extended the theory of gravitation to the nature of the atom, which he took to be the non-spatial point-center of the opposed forces of attraction and repulsion. The Scottish chemist Joseph Black, though by no means averse to exact empirical research, attempted to base the whole of physics and chemistry upon the Newtonian conception of opposing forces. The English Roman Catholic John Needham, as the result of his use of the microscope in examining organisms, attempted to prove that animals are brought to life from putridity, that they are formed by an expansive and a resistant force, and that they degenerate into vegetables. The Dutch civil servant Frans Hemsterhuis imported the Newtonian forces into psychology, and made use of mathematical analogies in explicating the nature of human desires and abnegations. The Irish statesman Edmund Burke, in a work on aesthetics which anticipates romanticism, related the twin emotions toward the sublime and the beautiful to the expansion and contraction of the nerves. The German polymath Johann von Herder even attempted to define God as the supreme unification of opposed forces.¹⁷

This eighteenth-century obsession with the uncritical postulation of opposed forces in the most diverse and heterogeneous contexts could be dismissed as nothing more than a harmless academic eccentricity were it not for the catastrophic effect it had upon peoples' lives through the way in which it influenced medical practice. During the seventeenth century Lorenzo Bellini had put forward the not entirely improbable idea that virtually all pathological states were the result of aberrations in the circulation of the blood. Taking this interesting suggestion to be a verified truth, Archibald Pitcaime set about transforming the medical sciences into a branch of Newtonian mathematics. What Pitcaime lacked in common sense he made up for in self-assurance. In his inaugural oration at the University of Leiden (1691) he maintained that empirical investigation, the search for physical causes, was "entirely useless and unnecessary to physicians," and that it was "not allowable to advance anything into a principle either in the theory or practice of medicine, which is called in question by the mathematicians." This general approach was inflated into a comprehensive Newtonian "philosophy" of the medical sciences by Richard Mead, who displayed a certain genius for dressing up even the most fantastic hypotheses in the form of mathematical truths. The movement reached its climax in the continental influence exercised by the medical writings of the Scotsman John Brown. According to Brown, the health of an organism depends upon its maintaining a due equilibrium between its inherent "excitability" and various stimuli. Consequently, disease is the result of either over- or under-stimulation. All the doctor has to do, therefore, is to prescribe the right means for correcting the equilibrium. Although the beautiful simplicity of this totally quantified and mathematicizable medicine failed to impress Brown's countrymen, it was taken up with great enthusiasm all over the continent. It stimulated academic passions to such an extent that in Gottingen in 1802, for example, a troop of Hanoverian cavalry had to be used to put down the rioting which broke out between Brown's disciples and their opponents. It is interesting to note, moreover, that Brown managed to kill more people by means of his medicine than Napoleon did by means of his wars.¹⁸

It could be argued with some justification that by resolving such concepts as atoms, chemical compounds, organisms, etc., into two components, and then reconstructing the original unity from out of these "opposites," the eighteenth-century popularizers of Newtonianism were doing something not so very different from Newton himself when he applied the method of resolution and composition. It should be noted, however, that Newton and those who made genuine advances upon his work would never have dreamed of deciding beforehand that the analysis of a complex field of inquiry can only bring to light two significant sub-fields and that these have always to be regarded as "opposites." The truth of the matter is that those who dealt in these triads were nearly always guilty of not having considered the significance of Newton's distinction between pure and applied mathematics. They were in fact foisting an entirely arbitrary formalistic interpretation upon fields of research in which genuine experimental work, a valid inductive search for causes or presuppositions, would have yielded not tidy triads but a whole multitude of distinctly untidy and certainly perplexing sub-disciplines. It was, of course, easier to accept Pitcairne's advice and plump for the facility of a mathematical solution, disregarding the distinction between its pure and applied aspects. In doing so, however, they were rendering themselves incapable of making any authentic contribution to scientific knowledge, and therefore disqualifying themselves as genuine natural philosophers.

Although the methodological confusions out of which this manner of thinking arose were essentially those of the natural sciences, toward the end of the eighteenth century they began to be used in the development of a new brand of historicism. A monstrous misrepresentation of physical reality began to give birth to an even more monstrous philosophy of history. Kant, in his review of Herder's main work on the subject, gave forthright expression to the apprehension with which he regarded this new development: "What is one to think of the hypothesis of invisible forces producing organization, and the device of attempting to explain what one does not understand by means of what one understands even less? To assume an affinity among them, whereby either one genus would have arisen from the other and all from one original genus, or possibly from one generative mother womb, would give rise to ideas so monstrous that reason recoils from them."¹⁹

In one instance, and in one instance only, did this naive faith in the relevance of purely a priori mathematical or triadic reasoning to the organization of empirical research give rise to a significant scientific discovery. As early as 1724 Christian Wolff observed that "If one divides the distance of the Earth from the Sun into 10 parts, the distance of Mercury consists of 4 of them, that of Venus 7, that of Mars 15, that of Jupiter 52, and that of Saturn 95." Even before the discovery of Uranus in 1781, the distance of which was found to consist of 196 parts, Heinrich Lambert put forward the idea that it might be worthwhile to look for a planet moving in the gap between Mars and Jupiter. Johann Titius opined that the "Lord Architect" of the universe would never have violated the regularity of the arithmetical series by leaving the gap empty. The Berlin astronomer Johann Bode suggested that it was unlikely that the "Founder of the Universe" would have tolerated such untidiness. Piety and a faith in the a priori validity of mathematics, in a tidy universe, motivated the search for a planetary body to complete the series, and on January 1, 1801, they were rewarded when an Italian astronomer discovered the largest asteroid.²⁰

Hegel

In a few lines at the end of his inaugural dissertation on the planetary orbits, which he defended at the University of Jena at the end of August 1801, Hegel criticizes Bode's uncritical projection of an a priori mathematical pattern onto the empirical facts provided by observation, and suggests, evidently not without some irony, that the sequence attributed to the demiurge by Plato might provide a better guide to research, since it not only accounts for the known planetary sequence, but also simplifies consideration of the satellites of Jupiter and Saturn. Hegel should have known that the empirical facts had been altered by the observation of January 1, 1801, but it is, perhaps, worth remembering that no theoretical justification for Bode's Law has yet been found, and that the discovery of Neptune in 1846 disproved it to some extent.²¹

Just prior to Hegel's arrival at Jena, his friend Schelling had developed a new form of natural philosophy which drew its inspiration from the popular triadic Newtonianism of Herder and the teleological thinking analyzed and advocated by Kant in his Critique of Judgement. According to Schelling, the analytical work carried out by the various branches of the natural sciences is to be used as the basis for viewing the whole of nature from the telos of consciousness. Consciousness is to comprehend nature as a hierarchy or sequence of levels approximating with increasing degrees of adequacy to that which is comprehending them. Hegel accepted the broad outlines of Schelling's conception, but criticized him severely for relying too heavily upon Herder and the popularizers, for not paying enough attention to the empiricists and the scientific professionals, and for failing to apply the methods of resolution and composition to their findings with the requisite rigor.²²

It would be no exaggeration to say that until very recently the only outcome of research into Hegel's philosophy of the natural sciences has been an almost universal miscomprehension of is criticism of Bode's Law and a totally undifferentiated assessment of his indebtedness to Schelling.

In his inaugural dissertation, as in all the systematic works he published after 1801, Hegel's methodology involves a radical and comprehensive application of the methods of resolution and composition to the general state of knowledge and research in the empirical sciences. With regard to the problem of motion, for example, he accepts Kant's conclusion that space and time, without which there could be no motion, are the a priori elements, the presuppositions of our knowledge of the natural world. He also points out, however, that not only our knowledge, but also the natural world itself, presupposes space, time, and motion. What is more, space, time, and simple mechanical motions can be systematically considered without also considering their specific involvement in planetary, plant, or animal movements, whereas these movements cannot be considered without presupposing the more universal factors of space, time, and mechanics. It is therefore essential to a clear and consistent natural philosophy, and indeed to any other branch of philosophy, that such asymmetrical relationships should be borne in mind when dealing with the multifarious details and the metaphysical pretensions of the empirical sciences.²³

Kant had shown that not only space and time, but also certain universal logical categories have to be regarded as the systematic presuppositions of human knowledge. In this respect also, Hegel extends the presuppositional structure of Kant's conception to include the natural world, and treats the working out of the systematic interrelationships between logical categories by means, of the methods of resolution and composition as a philosophical science antecedent to natural philosophy. It is within this fundamental or purely abstract science that he works out the asymmetrical relationships subsisting between the logical categories employed in mathematics. Taking the unit to be the most basic category of pure mathematics, he develops a survey of the logical structure of the various branches of the science by indicating the way in which measure, ratio, infinity, intensive and extensive magnitude, number, quantity, etc., are systematically interrelated. He is, therefore, in full agreement with the mathematicians of his time—Lagrange, Lacroix, Cauchy, etc.—who were attempting to establish a logical foundation for the calculus by drawing a sharp distinction between its formal and its applied aspects. Although the methodological basis of his distinction between pure and applied mathematics is not identical with theirs, it certainly justifies his joining them in their criticism of the uncritical Newtonianism of those who were unaware of the necessity of distinguishing between mathematics and physics. He first published his critical analysis of the logical and categorial structure of mathematics in 1812, and he revised it with detailed reference to current developments at the end of his life. It is, therefore, high time that someone attempted to place it in the general context of ideas on the logical foundations of mathematics.²⁴

Since Hegel pays so much attention to the categorial structure of pure mathematics, it cannot be said that he regards the science simply as a tool in the hands of the physicist. He is ready to admit, however, that the physicist can make valid use of it in communicating the formal structure of the regularities he has discovered in nature. He himself makes good use of mathematics in his expositions of celestial mechanics and musical sounds, for example, and he praises J. B. Richter for having followed up Kant's suggestion and developed stoichiometry, the calculation of the ratios in which chemical substances have an effect upon one another, as a branch of applied mathematics.²⁵ What he never fails to object to is the failure to realize that such calculations are quite distinct from empirical research, and the metaphysical theorizing that can arise out of this confusion: "The import of this reflection is simply this, that the distinctions and determinations employed by mathematical analysis, and the course to which its methods commit it, should be sharply distinguished from whatever is supposed to have a physical reality. It is not the assumptions, procedures, and results which analysis requires and affords which are questioned here, but the physical worth and the physical significance of its determinations and procedure. It is here that attention should be concentrated, in order to explain why physical mechanics has been flooded by a monstrous metaphysic, which, contrary to both experience and the Notion, has its sole source in these mathematical determinations.²⁶

What Hegel proposes as the alternative to the confusions of popular Newtonianism is a systematic treatment of the mechanical sciences very similar to that of the Principia. Just as Newton's use of the analytical and synthetic procedures of resolution and composition had led him to break down the solar system, his major sphere of inquiry, into the two subordinate fields of the motions of bodies in resisting and non-resisting mediums, so Hegel's use of these procedures led him to break down the same major sphere into the subordinate fields of Kepler's laws, universal gravitation, fall, impact, inertia, matter, motion, etc. He works out the subordinate asymmetrical relationships between these fields with greater precision than Newton, and the details of his exposition reflect the empirical advances made during the intervening period. Evidently building upon the work of the Bemoullis and Euler, for example, he treats the subject-matter of Newton's second book, the mechanics of rigid and flexible and fluid and elastic bodies, as having its systematic context in physics rather than mechanics, that is to say, as presupposing the simpler motions of classical mechanics.²⁷ In thus revising the general complexity relationships of eighteenth-century mechanics and physics, he evidently relied fairly heavily upon the work of the French mathematician and physicist L. B. Francoeur. Once again, one can only hope that the precise nature of his assessment of this basic work will eventually be submitted to a thorough investigation.²⁸

To a great extent, Hegel's criticism of Newton's Opticks was determined by his acceptance of the general validity of the theory put forward in Goethe's Theory of Colours. Both Hegel and Goethe performed a large number of experiments involving the passage of light through various mediums—gases, liquids, crystals, etc. From them they drew the conclusion that colored light is not, as Newton had maintained, the result of the resolution of the composite nature of white light into its constituents, but that it arises from the homogeneous nature of white light being dimmed or darkened by a medium. The colors which appear when white light is passed through a prism, for example, are not the result of its being resolved into its constituents, but of its being dimmed in a series of gradations resulting from the various degrees of refraction brought about by the physical structure of the prism.

Although a modern scientist has to regard Goethe's theory of the physics of light and colors as essentially erroneous, it was a plausible hypothesis at the time, and it was backed up with some first-rate experimental work and a critical analysis of Newton's experiments and the conclusions he drew from them which is still worth taking seriously and examining in detail. The most valuable part of Goethe's Theory of Colours is not its physics, however, but the contribution it makes to our understanding of the perception of color. Goethe explored the implications of the discoveries made by Halley, De Godart, and Rumford, and showed conclusively that the explanation of phenomena such as colored shadows involved consideration of physiological as well as physical factors. Heisenberg has therefore pointed out that Newton's and Goethe's contributions to our understanding of color are in fact complementary.²⁹

Hegel's handling of the Newton-Goethe controversy is by no means as satisfactory as it would have been had he made proper use of his own philosophical principles. He could easily have provided a systematic assessment of Newton's Opticks in his Physics and a corresponding assessment of Goethe's theory in his Physiology and Psychology, and so brought out the complementary nature of the two apparently rival approaches. He decided instead to treat the physiological and psychological aspects of color perception in an extremely cursory manner, and to concentrate upon defending Goethe and refuting Newton in respect of the physics of light. Although he accepted Goethe's postulate of the essential homogeneity of white light, he also regarded it as involving a complexity of motions which required that it should be classified as a physical rather than a merely mechanical phenomenon. As a field of inquiry, he therefore took white light to be the initiation of the sphere of physics, in the sense that its motions constitute the absolute presupposition of physical phenomena. He also regarded color as an essentially physical phenomenon, but since he took it to involve not only white light but also the darkening of white light, he could only deal with it within a rational or systematic physics once the factors in this darkening had also been given their systematic exposition. In his Physics, therefore, the treatment of light is followed by the treatment of specific gravity, cohesion, shape, magnetism, crystallography, transparency, refraction, etc. Only once refraction has been given its systematic exposition, does he present his theory of colors, his criticism of Newton, and his defense of Goethe. The implication of this procedure is not, of course, that white light and colors do not occur together in the physical world, but simply that a systematic or philosophical exposition of color involves such an analytical and synthetic survey of its presuppositions, of the factors in its occurrence which have been brought to light by empirical physics.³⁰

Conclusion

Despite the limitedness of the fields in which he published, Newton's contribution to natural science is still an integral part of modern physics, largely on account of the excellence of his experimental work and his realistic assessment of the significance of mathematics. When attempting to gauge the significance of Hegel's criticism of this contribution, it is therefore essential that a distinction should be drawn between Newton's own work and the way in which it was interpreted and exploited throughout the eighteenth century. As we have shown, the main thrust of Hegel's arguments is directed against the Newtonians of his own time rather than Newton himself. Even the very limited research carried out so far has made it clear that in such fields as the logical foundations of mathematics, the basic methodology of the science of mechanics, even the perception of color, Hegel's work has to be regarded as complementing rather than refuting Newton's. What is more, both Newton and Hegel insisted that all valid knowledge concerning the natural world must be based upon observation and experiment, both made good use of the methods of resolution and composition, and both objected forthrightly to the metaphysics of those intent upon popularizing empirical knowledge for non-scientific purposes.

If there is a fundamental difference between them, it is that between the natural scientist, wholly preoccupied with the empirical precision and the pragmatic significance of his discoveries, and the philosopher, primarily concerned with the wider implications of the methodology of the sciences. These are, however, not mutually exclusive but complementary interests, and even a cursory reading of Hegel's writings on the natural sciences will soon show that he was well aware of the fact.

Notes

¹ Newton, Mathematical Principles, ed. F. Cajori and tr. A. Motte (1687; Berkeley, 1934), bk. I, prop. 76, cor. 3 and 4; Opticks, ed. I. B. Cohen (1704; New York, 1952), bk. I. pt. 2 (prop. 5, theorem 4).

² Hegel, De orbitis planetarum, ed. and tr. F. De Gandt (1801; Paris, 1979); Philosophy of Nature, ed. and tr. M. J. Petry, 3 vols. (1842; London, 1970), 11:135-60 (320).

³ E. J. Dijksterhuis, De Mechanisering van het Wereldbeeld (Amsterdam, 1977), 543.

⁴Notes and Records of the Royal Society of London (1966), XXI: 124-25; Stephen Hobhouse, Isaac Newton and Jacob Boehme (Belgrade, 1937).

⁵ F. E. Manuel, A Portrait of Isaac Newton (London, 1980); R. S. Westfall, Never at Rest. A Biography of Isaac Newton (Cambridge, 1980), emphasizes the importance of Newton's unpublished alchemical notes.

⁶ C. Truesdell, "Reactions of Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton's Principia," in R. Palter, The Annus Mirabilis of Sir Isaac Newton (Cambridge, Mass., 1967), 192-234.

⁷Opticks, bk. I, prop. X, Prob. V, p. 183; Journal de Physique de Rozier (1776), VIII: 270; Philosophical Transactions of the Royal Society (1794), pt. 1, p. 107.

⁸Spinoza. Kernmomenten in zijn denken (Baarn, 1977), 31-43.

⁹The Correspondence of Isaac Newton 1694-1709, ed. J. F. Scott (Cambridge, 1967), IV:87-303.

¹⁰Correspondence, 111:233-43

¹¹ C. B. Boyer, The History of the Calculus and its Conceptual Development (Dover Books, 1959), ch. vi.

¹² G. L. L. Buffon, Histoire Naturelle (Paris, 1749-1804), supplement vol. V; P. S. Laplace, Exposition du Systeme du Monde (Paris, 1796); N. R. Hanson, Leverrier: The Zenith and Nadir of Newtonian Mechanics, Isis 53 (1962): 359-78.

¹³Opticks, bk. I, pt. i, prop. 7, theor. 6; Philosophical Transactions of the Royal Society (1758), 733-43; vol. 90 (1800), 106; H. J. Steffens, The Development of Newtonian Optics in England (New York, 1977); K. F. Weinmann, Die Natur des Lichts (Darmstadt, 1980), 83-135.

¹⁴Elemens de la Philosophie de Neuton, mis a la portee de tout le monde (Amsterdam, 1738).

¹⁵ Alexandre Koyré, Newtonian Studies (London, 1965), 163.

¹⁶Verzeichniss der von dem Professor … Hegel… hinterlassenen Bücher-Sammlung (Berlin, 1832), nos. 1277-1515; Colin Maclaurin, An Account of Sir Isaac Newton's Philosophical Discoveries, 1748; French tr. 1749; Latin tr. from French, Vienna, 1761); Benjamin Martin, A Plain and Familiar Introduction to the Newtonian Philosophy, tr. German Berlin (1778).

¹⁷ L. L. Whyte, Roger Joseph Boscovich (New York, 1964); A. L. Donovan, Philosophical Chemistry in the Scottish Enlightenment (Edinburgh, 1975); J. T. Needham, Nouvelles Observations Microsopiques (Paris, 1750); F. Hemsterhuis, Lettre sur les Desirs in Oeuvres philosophiques (Paris, 1809), 1:61-90; E. Burke, On the Sublime and the Beautiful, ed. I. T. Bulton (1757; London, 1958); J. G. Herder, Gott, einige Gespräche, ed. F. H. Burkhardt (1787; New York, 1940).

¹⁸The Works of Dr. Archibald Pitcairne (London, 1704), 10; Authentic Memoirs of the Life of Richard Mead (London, 1755); W. Coleman, "Mechanical Philosophy and Hypothetical Physiology" in R. Palter, pp. 322-32; Hegel, Philosophy of Nature, III:378-80.

¹⁹ Kant, Werke (Akademie Ausgabe, 1784/5), VIII:43-58.

²⁰ H. A. M. Snelders, "Numerology in German Romanticism," Janus 60 (1973): 25-40.

²¹ B. Beaumont, Hegel and the Seven Planets, Mind 63 (1954): 246-48; Hegel, Les Orbites des Planetes (note 2).

²²Philosophy of Nature, 1:46-48, 179-93.

²³Philosophy of Nature, 1:223-44, 260-83; III:49, 102-107.

²⁴Wissenschaft der Logik, ed. G. Lasson, 2 pts. (Hamburg, 1975), 154-387; Philosophy of Nature, 1:336-38.

²⁵Philosophy of Nature, 1:263-81; II:73-81, 210-13.

²⁶Philosophy of Nature, 1:265.

²⁷Philosophy of Nature, II:42-69.

²⁸Philosophy of Nature, 1:264, 332; L. B. Francoeur, Traité elementaire de Mécanique (Paris, 1801).

²⁹Die Goethesche und die Newtonsche Farbenlehre im Lichte der modernen Physik in Wandlungen in den Grundlagen der Naturwissenschaft (1941; Hamburg, 1967).

³⁰Philosophy of Nature, II:9-160.