Philosophiæ Naturalis Principia Mathematica

Summary

The Philosophiæ Naturalis Principia Mathematica, published in London in 1687, set out three laws of motion and a theory of universal gravitation that unified the movement of planets, comets, and falling bodies under a single mathematical account. Written in classical geometric demonstration by Isaac Newton, then Lucasian Professor of Mathematics at Cambridge, the work did not merely solve problems in astronomy: it provided a model of nature as a system governed by quantifiable forces acting according to discoverable laws. European physicians and natural philosophers drew on that model to reconstruct medicine. Within two decades, the Leiden professor Hermann Boerhaave had converted the body into a hydraulic machine whose vessels, fibers, and fluids obeyed Newtonian mechanics. That framework dominated medical education for most of the eighteenth century and generated its own opposition: the vitalist traditions that would eventually feed into the Romantic medicine, the Montpellier school, and — much later — the eclectic and physiomedical traditions of North America.

Background and Composition

Newton began the work that became the Principia in the mid-1660s, prompted in part by Galileo’s question of why objects on a spinning earth do not fly off, which led him to compare the centrifugal force at the earth’s surface with the inward pull required to keep the moon in orbit.(Peter Dear, 2001) At that stage his calculations were not close enough to publish, and he set the problem aside. The decisive moment came in 1684 when Edmund Halley — who would pay for the book’s publication out of his own pocket after the Royal Society exhausted its budget on a natural history of fishes(Peter Dear, 2001) — visited Cambridge and asked Newton what orbit a body would follow if attracted by an inverse-square force. Newton already had the answer. Halley’s visit recalled him to the problem and, within months, the first draft of what would become the Principia was under way.(Peter Dear, 2001)

The intellectual context was a crisis in natural philosophy. After about 1630, Descartes’s writings had persuaded most physical scientists that the universe was composed of microscopic corpuscles and that all natural phenomena could be explained through the shape, size, and motion of those corpuscles.(Kuhn, 1962) This was the mechanical philosophy that had displaced Aristotle’s elements, humors, and final causes in university natural philosophy.(Porter, 2000) Newton had grown up in that tradition but found it inadequate. Matching his mathematical demonstration against Kepler’s empirically established area law, he discovered that a planetary medium dense enough to exert gravitational force would also produce enough resistance to cause measurable deviations from the mathematical prediction. When the calculations showed no such deviations, he concluded that the heavens could not be filled with the aethereal medium the mechanical philosophers had assumed.(Dobbs, Betty Jo Teeter, 1991)

That discovery forced a confrontation with the hardest question in early modern natural philosophy: how could one body act on another across empty space? Newton’s answer, at least in the published text of the Principia, was deliberately non-committal. He described forces — notably gravity — without specifying their mechanical cause, using “attraction” only “in a general sense for any endeavor whatever of bodies to approach one another.”(Dobbs, Betty Jo Teeter, 1991) He declined to give a physical mechanism for how gravity was transmitted. This was not agnosticism born of positivism, as later interpreters often assumed, but a deliberate strategy: by declining to specify the cause of gravity Newton left open whether it operated by attraction, repulsion, or some entirely different mechanism — a studied ambiguity that confused his critics and reflected his genuine uncertainty about gravity’s ultimate source.(Peter Dear, 2001) Continental critics including Leibniz, Huygens, and Régis dismissed the book as mathematical description dressed up as natural philosophy, demanding that Newton supply actual causes.(Peter Dear, 2001) Newton acknowledged privately, in a 1692 letter to Richard Bentley, that “it is inconceivable that inanimate brute matter should, without mediation of something else which is not material, operate upon and affect other matter without mutual contact,” leaving open whether gravity’s agent was “material or immaterial.”(Peter Dear, 2001) Dobbs argues that the positivist reading — which takes Newton’s silence on gravity’s cause as satisfaction with mathematical description alone — cannot survive a close scrutiny of his surviving papers: Newton actively sought a causal explanation and, when his mechanical model failed him, turned to ancient sources in the hope of recovering an explanation once known to wise antiquity.(Dobbs, Betty Jo Teeter, 1991)

Core Arguments

The Principia is organized into three books, presented in the style of Euclidean geometry — deductive, theorem by theorem — rather than in the algebraic calculus Newton had also developed.(Peter Dear, 2001) Book I develops the mathematics of bodies moving under central forces. Book II treats motion in resisting media. Book III, “The System of the World,” applies the mathematical machinery to the solar system, deriving the motions of planets, satellites, comets, and ocean tides from a single inverse-square law of universal gravitation.

What made the work unlike anything before it was the scope of its unification. A. Rupert Hall would describe the Principia as representing “the climax of the scientific revolution in physical sciences, proving mechanical principles as a universally sufficient basis for explanation and revealing the unity of nature through identical physical laws in heavens and earth.”(Hall, A. Rupert, 1954) Thomas Kuhn, in The Structure of Scientific Revolutions (1962), listed Newton’s Principia alongside Aristotle’s Physica, Ptolemy’s Almagest, and Lavoisier’s Chemistry as works that “served for a time implicitly to define the legitimate problems and methods of a research field for succeeding generations of practitioners.”(Kuhn, 1962) In Kuhn’s account, the Principia did not merely solve outstanding problems; it provided a framework that determined which questions counted as scientific questions — those amenable to mathematical treatment in terms of forces — and which lay outside the boundaries of what normal inquiry could address.(Kuhn, 1962)

The taming of comets was among the Principia’s most striking applications. Comets had traditionally been understood as irregular, even supernatural, intrusions into the orderly heavens. Newton demonstrated that they described conic sections around the sun, subject to the same inverse-square law as the planets, converting them from omens into astronomical objects.(Dobbs, Betty Jo Teeter, 1991) This had a theological as well as scientific significance to Newton himself: restoring comets to their proper place in the celestial order was part of his broader project of restoring true natural philosophy, and through that, true religion.(Dobbs, Betty Jo Teeter, 1991) Newton also assigned comets a restorative function: their tails, he argued, supplied the vegetable spirit and active principles necessary to replenish planetary fluids, providing a cosmic mechanism for the divine activation of micromatter after his earlier model of circulating aethers had been abandoned.(Dobbs, Betty Jo Teeter, 1991)

Newton’s Alchemy and the Janus Face

The image of Newton as the founder of impersonal, mathematical science has never been entirely accurate, and the historian Betty Jo Teeter Dobbs spent two decades documenting the gap. Her 1991 monograph The Janus Faces of Genius argued that Newton’s alchemy — which he practiced from about 1668 until the second or third decade of the eighteenth century, maintaining voluminous notes and manuscripts and running experimental sequences that sometimes lasted months — was not a hobby or a lapse but one of the pillars supporting his mature scientific work.(Dobbs, Betty Jo Teeter, 1991)

Newton drew a sharp distinction between “vegetable” and “mechanical” chemistry as early as the 1660s, identifying alchemy with the former and associating it with a living, animating spirit wholly unlike the inert matter of Cartesian physics.(Dobbs, Betty Jo Teeter, 1991) His fundamental methodological assumption was the unity of Truth, guaranteed by the unity of God: natural philosophy, alchemy, prophecy, and mathematics were complementary paths to the same divine reality, not competing disciplines.(Dobbs, Betty Jo Teeter, 1991) Mathematics was only one avenue to Truth, and Newton’s goals were “incomparably more vast than the discovery of the ‘mathematical principles of natural philosophy.’”(Dobbs, Betty Jo Teeter, 1991) Dobbs observes that this makes the Principia’s apparently austere rationalism misleading: the very work that seemed to many readers “the epitome of austere rationality” was written by a man whose alchemical practice earned him the epithet “philosopher by fire” — titles that contemporaries would have found impossible to reconcile.(Dobbs, Betty Jo Teeter, 1991) The methodological balance Newton struck — allowing senses, reason, and revelation to correct one another — may have reflected the influence of Henry More, who had worked out a comparable balancing procedure in the context of interpreting biblical prophecy.(Dobbs, Betty Jo Teeter, 1991)

At the center of Newton’s alchemical thought was what Dobbs calls “the vegetable spirit” — a universal vital agent that he contrasted with the mechanical aether. In a manuscript from about 1669 (Keynes MS 12A), he described this mercurial spirit as “the vital agent diffused through all things that exist in the world… excited to action by a moderate heat, it is put to flight by a great one, and once an aggregate has been formed, the agent’s first action is to putrefy the aggregate and confound it into chaos. Then it proceeds to generation.”(Dobbs, Betty Jo Teeter, 1991) This vegetative principle eventually became the “force of fermentation” in the published Opticks, providing a direct thread of continuity between his private alchemical manuscripts and his public natural philosophy.(Dobbs, Betty Jo Teeter, 1991) Newton sought this vegetative principle as evidence for the existence of divine activity in the natural world, seeing analogies between the alchemical spirit and light, and between alchemical processes and God’s work at creation — the hidden mechanism by which the universe remained a living providential order rather than the closed mechanical system Descartes had envisioned.(Dobbs, Betty Jo Teeter, 1991)

By 1675, with his “Hypothesis explaining the Properties of Light” sent to the Royal Society, three notable shifts had occurred from his earlier private “Vegetation” manuscript: gravity had become more active (spiritualized), more universal (extended beyond the earth to the solar system), and theologically reconfigured by his Arian conversion of the early 1670s.(Dobbs, Betty Jo Teeter, 1991) In consequence, the gravitational and vegetative functions of the aether were by that date fused so closely that gravity itself bore the life-giving properties of the vegetable spirit.(Dobbs, Betty Jo Teeter, 1991) Newton even extended this animistic earth-aether system to the sun and other planets, suggesting that the sun imbibed this Spirit copiously to conserve its shining and keep the planets from receding — an extension he later claimed as evidence that he had possessed the concept of universal gravity as early as 1675.(Dobbs, Betty Jo Teeter, 1991)

The crisis that produced the Principia also deepened this tension. In 1684, Newton discovered mathematically that no material aether could account for gravity without producing detectable retardation — the mechanical philosophy failed on its own terms. For Newton, this meant that gravity must have a non-mechanical cause, analogous to the way fermentation had a non-mechanical cause in the vegetable spirit.(Dobbs, Betty Jo Teeter, 1991) He began revising his commentary on the Emerald Tablet at roughly this time, canceling a phrase about subtlety (appropriate to a subtle corporeal fluid) and substituting vim penetrantem spiritus — “the penetrating force of spirit.”(Dobbs, Betty Jo Teeter, 1991) Only spirit, in Newton’s emerging view, could both account for gravity and avoid the retardation problem.

In the Principia’s General Scholium (added to the second edition of 1713), Newton allowed that the evidence pointed toward “an incorporeal medium” or “spirits emitted” — quasi-material inhabitants of the gray area between complete incorporeality and full bodily solidity — as gravity’s intermediary.(Dobbs, Betty Jo Teeter, 1991) He left the question formally open. But privately he had come to two tentative solutions: that God himself, omnipresent in the literal sense of being “intimately present with every thing,” directly subsumed gravity; or that an intermediate non-material agent served as its vehicle.(Dobbs, Betty Jo Teeter, 1991) The General Scholium’s invocation of Hebrew and Old Testament sources (Kings, Psalms, Job, Jeremiah, Deuteronomy) alongside ancient Greek authorities was not decorative but integral to Newton’s argument.(Dobbs, Betty Jo Teeter, 1991) Newton had also privately worked out that the Pythagoreans and the Stoics had recognized gravitational force and encoded this knowledge in mythological forms; the unpublished Classical Scholia, composed as additions to Propositions IV through IX of Book III of the Principia, developed that argument in detail, though Newton never released them for publication.(Dobbs, Betty Jo Teeter, 1991)

By the end of the eighteenth century, this whole dimension of Newton’s thought had been systematically erased. The theology and the alchemy were purged from Newtonianism as it consolidated into a rational-empiricist ideology aligned with Lockean epistemology and Latitudinarian Anglicanism.(Peter Dear, 2001) The movement that came to bear Newton’s name took on its characteristic shape only after he became President of the Royal Society in 1703, consolidated through institutional patronage and through the theological packaging of his ideas by Boyle lecturers such as Bentley and Clarke — a process of selective inheritance through which the mathematical-deductive core of the Principia was preserved while its alchemical and prophetical dimensions were quietly discarded.(Peter Dear, 2001) William Blake’s famous portrait of Newton as “Urizen” — the embodiment of cold, restrictive reason — was a profound misreading, but it captured with precision how thoroughly the Principia had been reinterpreted. Newton himself had written that “when I wrote my treatise about our Systeme I had an eye upon such Principles as might work with considering men for the beleife of a Deity,” and “the almost total misperception of Newton’s system in the eighteenth century is surely one of history’s greater ironies.”(Dobbs, Betty Jo Teeter, 1991)

Impact on Medicine: Iatromechanism

The Principia did not produce iatromechanism directly or immediately. But it provided the model and the authority. The mechanical philosophy had already entered medicine through Descartes’s Traité de l’homme and the Paduan tradition of mechanical anatomy; Newton’s synthesis intensified and legitimated the project of explaining living bodies as machines governed by mathematical laws. Porter’s account in The Enlightenment (2000) describes how after 1660 the Aristotelian metaphysics of elements, humors, substances, qualities and final causes were “superseded by models of Nature viewed as matter in motion, governed by laws capable of mathematical expression,” and how “clockwork thinking invaded physiology and medicine.”(Porter, 2000)

The central figure in this transmission was Hermann Boerhaave (1668–1738), professor of medicine, botany, and chemistry at Leiden, probably the most influential physician of the entire eighteenth century.(King, 1958) Boerhaave fused ancient Greek medical tradition with Harvey’s circulation, microscopic anatomy, and Newtonian mechanics into what Lester King called “a polished doctrinal edifice, almost monolithic, that captured men’s attention, satisfied their curiosity — and restricted their imagination.”(King, 1958) His Institutiones medicae (1708) and Aphorismi de cognoscendis et curandis morbis (1709) were the primary textbooks at Leiden, Edinburgh, Vienna, and most European medical schools for half a century; William Cullen recalled that in his student days “I learned the system of Boerhaave; and except it may be the names of some ancient writers… I heard of no other names or writers on physic.”(King, 1958)

Boerhaave’s physiology rested on two structural components: fluids (humors of many types) and solids (ultimately composed of fibers). Disease emerged from disordered interactions between them. The hydraulic architecture was explicitly Newtonian: “the body exemplified Newtonian mechanics: particles of differing mass obeyed the laws of motion while flowing through tubes or vessels of various diameters.”(King, 1958) Boerhaave postulated a hierarchy of vessel orders of decreasing diameter — sanguiferous, serous, and lymphatic — each carrying progressively smaller humoral particles. The arteries, veins, nerves, and lymphatics formed a system of pipes and conduits whose pressures, velocities, and viscosities could, in principle, be calculated.

Porter identifies Archibald Pitcairne and George Cheyne as among the most explicit iatromechanists: they “cast the human body as a system of pulleys, springs and levers, pipes and vessels, its fluids being governed by the laws of hydraulics. Life itself was potentially explicable within the new mechanical framework.”(Porter, 2000) George Cheyne’s The English Malady (1733) blended Newtonian mechanics with a teleological natural theology that understood the body’s mechanisms as “infinitely wise contrivances” designed by God — warning systems against intemperance, built into the human frame to prevent self-destruction.(Garson, 2022) Cheyne is thus a figure who both inhabited and strained the mechanical model: his mechanisms were teleological through and through, each designed for a providential end, making him “one of the last theorists to openly and unabashedly endorse” a dual teleological conception of illness as both punishment and gift.(Garson, 2022)

The Principia was also politically useful. Its publication in 1687, on the eve of the Glorious Revolution, enabled Newton’s supporters to align his science with the new political and religious order. His protégé Richard Bentley used the Principia in the first Boyle Lectures (1692) to demonstrate God’s providential design. Samuel Clarke and other lecturers followed in subsequent years, “bolstering Latitudinarian Anglicanism, and hammering home the value of empirical inquiry, intellectual freedom and rational religion.”(Porter, 2000)

The Vitalist Reaction

The mechanical model was never without critics, and the medical tradition it generated provoked systematic opposition within a generation of Boerhaave’s death. The central challenge was simple: no mechanical account could explain why organized matter was alive rather than inert, or why it healed, reproduced, or responded to its environment in ways that clockwork mechanisms did not.

Porter describes how by the middle of the eighteenth century “strict mechanism was being judged incapable of accounting for the full complexities of living phenomena, especially properties like growth and reproduction.” The Scottish surgeon John Hunter “substituted a vitalism, which held that organized matter had an inherent vital force which distinguished it from the inorganic,” and Erasmus Darwin drew analogous conclusions.(Porter, 2000) This was not a return to Galenism or to the Renaissance Neoplatonism that mechanism had displaced; it was a new vitalism that accepted the experimental and anatomical gains of the preceding century while insisting that life required something beyond matter in motion.

Canguilhem, in Ideology and Rationality in the History of the Life Sciences (1988), traced a related irony at the cosmological level: Newtonian natural theology, by framing the fitness of organisms and their environments as evidence of divine design, actually made the Darwinian hypothesis conceptually impossible for over a century. The idea of species transformation by random variation and selection “was inconceivable until a previous idea, that of a preordained adaptation of each species to its way of life, had been destroyed.”[cang-ir88-ch05-001] Newtonianism delayed its own supersession by providing too attractive a framework for understanding why organisms were the way they were.

The eclectic and physiomedical traditions of nineteenth-century North America inherited the vitalist reaction at several removes. Joseph R. Buchanan, dean of the Eclectic Medical Institute in Cincinnati, “lamented the materialism of the reigning medical philosophies of his day, particularly the theories of Descartes and… Huxley,” allying himself explicitly with the vitalistic doctrines of Van Helmont, Georg Ernst Stahl, John Hunter, Harvey, and Bichat.(Haller, 1994) The eclectic motto vires vitales sustinete (sustain the vital forces) was a direct declaration against the depletion therapies that the mechanistic model had licensed — heroic doses, bleeding, purging — and against the assumption that disease management meant overriding the body’s own processes rather than supporting them.(Haller, 1994) The vitalist critique of mechanism thus passed, through the eclectic tradition, into the herbal medicine practice that Thomas Easley inherits.

Arthur Ladbroke Wigan observed in 1844 that Newton’s achievement in physics lay in his reframing of the fundamental question: “the question was no longer, why do things move? The basic question was: why do they ever change the way they move?” Wigan drew an explicit parallel between that reframing and what he was attempting in psychiatry.(Garson, 2022) The observation captures something essential about what the Principia did for natural philosophy more broadly: it shifted the entire field’s default question away from causes-in-substances toward causes-in-forces, a move whose medical consequences took more than a century to fully work through.

Wider Significance

Thomas Kuhn named Newton alongside Copernicus, Lavoisier, and Einstein as one of the “famous episodes in scientific development that have often been labeled revolutions” — each of which “necessitated the community’s rejection of one time-honored scientific theory in favor of another incompatible with it.”(Kuhn, 1962) Kuhn’s analysis of how the Principia functioned in the subsequent history of physics applies in modified form to medicine. The Boerhaavian synthesis it made possible functioned as what Kuhn called an exemplary achievement: “sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity… sufficiently open-ended to leave all sorts of problems for the redefined group of practitioners to resolve.”(Kuhn, 1962) For half a century, normal medical inquiry consisted largely in articulating that model, refining it, applying it to new phenomena, and extending it to new clinical problems.

The Principia’s influence on the broader intellectual culture of the Enlightenment was shaped partly by the theological use to which it was put. Newton’s supporters presented his natural philosophy as the empirical vindication of rational religion, and science was popularized through public lectures offering demonstrations “with globes, orreries and other instruments displaying the marvels of the clockwork universe.”(Porter, 2000) This popularization carried the mechanical model into general educated culture in ways that pure academic natural philosophy would not have done.

Eighteenth-century “Newtonianism” was, as Dear has argued, itself a hybrid. By the later decades of the century, “what counted as ‘Newtonianism’ was in many ways quite different from what Newton himself had believed and argued. The ‘Newtonianism’ of the later eighteenth century was itself a hybrid of Newton’s, Descartes’s, Leibniz’s, and many other people’s work and ideas.”(Peter Dear, 2001) The Principia as a text remained fixed; what changed was the use to which it was put, and what aspects of it were treated as constitutive versus incidental. The alchemy and the theology were incidental to Newton’s successors. The mathematical-deductive method and the law of universal gravitation were constitutive. That selective inheritance shaped a century of medicine.

Scholarly Assessment

Betty Jo Teeter Dobbs’s The Janus Faces of Genius (1991) remains the most thorough treatment of Newton’s alchemy and its relationship to the Principia. Dobbs argues against both positivist readings (Newton as proto-modern empiricist who happened to dabble in alchemy) and the view that the alchemy was marginal to his science. Her conclusion — that Newton’s natural philosophy, alchemy, and theology formed an integrated system aimed at understanding God’s providential activity in nature — has not been seriously contested, though the question of exactly how the alchemical and the mathematical strands interacted continues to be debated.

Peter Dear’s Revolutionizing the Sciences (2001) provides the clearest account of how Newton’s break with Cartesian mechanism appeared to contemporaries, and why Continental philosophers initially dismissed the Principia as mere mathematical description rather than natural philosophy. Roy Porter’s The Enlightenment (2000) traces the medical appropriation of Newton’s work through iatromechanism and natural theology. Lester King’s The Medical World of the Eighteenth Century (1958) provides the most detailed account of how Boerhaave converted Newton’s framework into clinical medicine.