Isaac Newton (1642–1727) lived in a philosophically tumultuoustime. He witnessed the end of the Aristotelian dominance of philosophyin Europe, the rise and fall of Cartesianism, the emergence of“experimental philosophy,” and the development of numerousexperimental and mathematical methods for the study of nature. Indeed,he helped to develop many of those methods. Newton’scontributions to mathematics—including the co-discovery withG.W. Leibniz of what we now call the calculus—and to what is nowcalled physics, including both its experimental and theoreticalaspects, will forever dominate discussions of his lasting influence.His impact on the development of early modern philosophy was alsoprofound; indeed, it is difficult to grasp the history of philosophyin the late seventeenth and early eighteenth centuries withoutconsidering Newton’s role. His engagement with Cartesian ideasand methods early in his life was just as significant to thetransformation of philosophy in the seventeenth century as his debateswith Leibniz were to the setting of the agenda of philosophy in theeighteenth. Obviously, Newton is not part of the traditionalphilosophy canon of the period. That fact reflects an anachronisticapproach to the history of modern philosophy that we have inheritedfrom French and German scholars of the nineteenth century. During theheight of the Enlightenment, Newton was always characterized as acanonical philosopher: for instance, he plays a leading role in thevery first “modern” history of modern philosophy, JohannJacob Brucker’s Historia Critica Philosophiae of 1744.Every major Enlightenment thinker, from Diderot to D’Alembert toKant, was influenced by Brucker’s account of modern philosophy.In tandem, numerous works on “Newton’s philosophy”and his “philosophical discoveries” were publishedthroughout the eighteenth century in every major European language. Bythe early nineteenth century, however, a separation between“science” and “philosophy” had beeneffectuated, which led to Newton’s shunting into the sciencecanon. Recent scholarship has challenged this conception of the canon.Moreover, Newton engaged with, or influenced, many of the standardlycanonical philosophers of the early modern era, including Descartes,Locke, Berkeley, Hume, Leibniz and Kant. His influence on early modernphilosophy is a rich topic.

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1. Placing Newton in the history of natural philosophy

Traditionally, Newton would be characterized as a mathematician forhis work on the calculus and as a scientist for his work in physics.His celebrated talent in mathematics is perhaps equaled not only byhis profound theorizing concerning the physical world, but also hisinfluential experimental methods. Indeed, Newton is remarkable for thefact that his work as a theoretician is matched by his work as anexperimentalist—either aspect of his oeuvre would besufficient to secure his place in the history of modern science. So inthe popular imagination, and in the history books, Newton is seen asone of the greatest scientists of the modern period, on a par with fewothers (perhaps Darwin or Einstein). This view will continue todominate our understanding of Newton in the twenty-first century.

If we attempt to understand Newton’s work from an historicalpoint of view, however, a more complex conception emerges. When Newtonpublished his principal works, he was not contributing to awell-established field, he was helping to create modern mathematicalphysics. This meant that few of his ideas, methods, or approaches,whether in mathematics or in experimental physics, could be taken forgranted. From his first papers in the early 1670s, on optics, untilhis last days working on the third and final edition of his magnumopus the Principia decades later, philosophers,mathematicians and experimenters challenged Newton’s approach.This frequently upset Newton, who had a famous, lifelong aversion tointellectual debate and controversy. But in a sense, it helped toensure the importance of Newton’s ideas for philosophy.Obviously, Newton never wrote a philosophical text on the order ofDescartes’s Meditations, Locke’s Essay,or Spinoza’s Ethics. He never produced what thelumières who studied him would have called a“system” of philosophy. But the intense controversiesproduced by his mathematical, empirical and philosophical methods andideas continually prompted him to broach philosophical topics (Janiak2015). As a result, he was widely considered a leading philosopherthroughout the Enlightenment. In the first modern history ofphilosophy, Brucker’s Historia Critica Philosophiae,Newton plays a central role in discussions of the modern era (Volume4.2: 639-55). He is also a central figure in D’Alembert’sdiscussion of the emergence of modern science and philosophy: Newtonis listed along with Bacon, Descartes, Locke and Leibniz as a keyfigure in the Preliminary Discourse (80-83).

The eighteenth-century tendency to discuss Newton’sphilosophy, rather than his science, may have an oddring to modern ears. In this case, however, the evolution of theEnglish language tracks a substantive intellectual development. As amatter of historical fact, the category of the scientist—alongwith that word in English—is a nineteenth-century invention.Specifically, at a meeting of the British Association for theAdvancement of Science in June of 1833, the Cambridge philosopherWilliam Whewell coined the word “scientist”. Whewell saidthat just as the practitioners of art are called“artists”, the practitioners of science ought to be called“scientists”, indicating that they should no longer becalled philosophers.<1> Indeed, before the early nineteenth century, people like Newton werecalled “philosophers”, or more specifically,“natural philosophers”. During the seventeenth century,and well into the eighteenth (at least until 1750, if not later),figures like Newton worked within the century’s old tradition ofnatural philosophy.<2> The modern disciplines of physics, chemistry, biology and so on, hadnot yet been formed. (The words ‘physics’ inEnglish, ’physique’ in French, and ‘physica’in Latin were often used, but had a very broad meaning, like“natural philosophy.”) Philosophers who studied natureinvestigated such things as planetary motions, the nature of matter,and the possibility of a vacuum, but they also discussed many aspectsof human beings, including the psyche, and how nature reflects itsdivine creator (Hatfield 1996). As the title of Newton’s magnumopus, Philosophiæ Naturalis Principia Mathematica(Mathematical Principles of Natural Philosophy), suggests, heintended his work to be in dialogue with Descartes’sPrincipia Philosophiae (Principles of Philosophy,1644). Descartes’s Principles is a complex text thatincludes discussions of everything from the laws of nature to thenature of God’s causal influence on the world. Descartes hadfamously promised that his physics required nothing more than theprinciples of geometry and pure mathematics (Principles, PartTwo, §64). Although Descartes was a great mathematician, theauthor of a major work in geometry in 1637, Newton thought nonethelessthat he had not lived up to this promise, so he would assuredlyintroduce mathematical principles for natural philosophy.Just as Descartes had sought to replace Aristotelian or“Scholastic” methods and doctrines in natural philosophy,Newton sought to replace Descartes’s. It is therefore morehistorically accurate and more illuminating to interpret Newton withinthe historical stream of natural philosophy.<3>

As is well known, natural philosophy in the Aristotelian traditions ofthe thirteenth through the sixteenth centuries involved an analysis ofAristotle’s ideas about the natural world, especially within theChristianized context of the medieval period. Philosophers studyingnature were often actually studying texts—such as commentarieson Aristotle—rather than conducting experiments or engaging inobservations, and they often did not employ mathematical techniques.Traditionally, natural philosophy in Aristotelian circles was notconceived of as a mathematical discipline (unlike, say, optics orastronomy); instead, it focused especially on the natures of objectsand on causation. In the seventeenth century, natural philosopherslike Galileo, Boyle, Descartes, and Newton began to reject not onlythe doctrines of the Aristotelians, but their techniques as well,developing a number of new mathematical, conceptual and experimentalmethods. Newton respected Descartes’s rejection of Aristotelianideas, but argued that Cartesians did not employ enough of themathematical techniques of Galileo, or the experimental methods ofBoyle, in trying to understand nature. Of course, these developmentshave often been regarded as central to the Scientific Revolution.Despite the centrality of these changes during the seventeenthcentury, however, the scope of natural philosophy had notdramatically changed. Natural philosophers like Newton expendedconsiderable energy trying to understand, e.g., the nature of space,time and motion, but they regarded that endeavor as a component of anoverarching enterprise that also included an analysis of the divinebeing. Newton was a natural philosopher—unlike Descartes, he wasnot a founder of modern philosophy, for he never wrote a treatise ofthe order of the Meditations. Nonetheless, hisinfluence on philosophy in the eighteenth century wasprofound, extending well beyond the bounds of philosophers studyingnature, encompassing numerous figures and traditions in Britain, onthe Continent, and even in the New World.<4> Newton’s influence has at least two salient aspects.

First, Newton’s achievement in the Opticks and in thePrincipia was understood to be of such philosophical importthat few philosophers in the eighteenth century ignored it. Most ofthe canonical philosophers in this period sought to interpret variousof Newton’s epistemic claims within the terms of their ownsystems, and many saw the coherence of their own views with those ofNewton as a criterion of philosophical excellence. Early in thecentury, Berkeley grappled with Newton’s work on the calculus inThe Analyst (1734) and with his dynamics in De Motu(1721), and he even mentioned gravity, the paradigmatic Newtonianforce, in his popular work Three Dialogues between Hylas andPhilonous (1713). When Berkeley lists what philosophers take tobe the so-called primary qualities of material bodies in theDialogues, he remarkably adds “gravity” to themore familiar list of size, shape, motion, and solidity, therebysuggesting that the received view of material bodies had alreadychanged before the second edition of the Principia hadcirculated widely. Remarkably, in that same year Roger Cotes, theeditor of the second edition of Newton’s Principia, hadargued in his editor’s preface that gravity should indeed beconsidered a primary quality along with the more familiar mechanistproperties that had been the subject of so much discussion in previousyears. (Newton himself approached the topic more cautiously.) For hispart, Hume interpreted Newtonian natural philosophy in an empiricistvein and noted some of its broader implications in his Treatise ofHuman Nature (1739) and Enquiry Concerning HumanUnderstanding (1750). Newton’s work also served as theimpetus for the extremely influential correspondence between Leibnizand the Newtonian Samuel Clarke early in the century, a correspondencethat proved significant even for thinkers writing toward thecentury’s end. Unlike the vis viva controversy andother disputes between the Cartesians and the Leibnizians, which diedout by the middle of the century, the debate between the Leibniziansand the Newtonians remained philosophically salient for decades,serving as an impetus for Émilie Du Châtelet’sinfluential work during the French Enlightenment, Foundations ofPhysics (1740), and also as one of the driving forces behindKant’s development of the “critical” philosophyduring the 1770s, culminating in the Critique of Pure Reasonin 1781. In addition, Newton’s work spawned an immensecommentarial literature in English, French, and Latin, including JohnKeill’s Introduction to Natural Philosophy (1726),Francesco Algarotti’s Newtonianism for the Ladies(1738), Henry Pemberton’s A View of Sir IsaacNewton’s Philosophy (1728), Voltaire’s Elementsof the Philosophy of Newton (1738), Willem Gravesande’sMathematical Elements of Natural Philosophy (1747), ColinMacLaurin’s An Account of Sir Isaac Newton’sPhilosophical Discoveries (1748), and many more besides.Moreover, two subsequent Continental editions of Newton’s textcontained substantial philosophical engagements not only with his ownideas, but with those of his potential rivals like the greatmathematician Johan Bernoulli and also Leibniz. The famous“Jesuit” (or “Geneva”) edition ofPrincipia mathematica published by Fathers Le Seur andJacquier in 1739-1744 in three volumes engaged substantially withLeibnizian ideas (Guicciardini 2015). And Émilie DuChâtelet wrote an extensive “analyticalcommentary” as part of her complete French translation of thePrincipia, published posthumously in 1759. Part of the ideawas to translate Newton’s old “geometric” approachto physics into the new language of analysis, a project that wasintertwined with numerous philosophical issues. Newton’s ideasand methods in mathematics, physics and philosophy therefore continuedto be of substantial importance well into the Enlightenment.

A second aspect of Newton’s influence involves thinkers whoattempted in one way or another to articulate, follow, or extend, theNewtonian “method” in natural philosophy when treatingissues and questions that Newton ignored. Euclidean geometry and itsmethods were seen as a fundamental epistemic model for much ofseventeenth-century philosophy—as is well known,Descartes’ Meditations attempts to achieve a type ofcertainty he likens to that found in geometry, and Spinoza wrote hisEthics according to the “geometrical method”.Propositions deduced from axioms in Euclidean geometry were seen asparadigm cases of knowledge. We might see Newton’s work asproviding eighteenth-century philosophy with one of its primarymodels, and with a series of epistemic exemplars as well. But part ofphilosophy’s task was to articulate precisely what the newNewtonian method involved. David Hume is perhaps clearest about thisaspect of Newton’s influence: his Treatise of 1739 hasthe subtitle, “An Attempt to Introduce the Experimental Methodof Reasoning Into Moral Subjects”, and there can be little doubtthat he meant (at least in part) the method of the Opticksand the Principia (DePierris 2012). Indeed, as Hume’stext makes abundantly clear, various eighteenth-century philosophers,including not only Hume in Scotland but Jean-Jacques Rousseau on theContinent, were taken to be, or attempted to become, “the Newtonof the mind”.<5> For Hume, this meant following what he took to be Newton’sempirical method by providing the proper description of the relevantphenomena and then finding the most general principles that accountfor them. Of course, one aspect of Hume’s work is to provide ananalysis of the concept of causation that is far more extensive thananything found in Newton, which has a substantial impact on whatcounts as an “account” of a phenomenon. This method wouldallow us to achieve the highest level of knowledge attainable in therealm of what Hume calls “matters of fact”.<6>

Despite the influence of Newton’s “method” oneighteenth-century philosophy, it is obvious that thePrincipia’s greater impact on the eighteenth century isto have effected a branching within natural philosophy that led to thedevelopment of mathematical physics on the one hand, and philosophy onthe other (Cohen and Smith, 2002, 1-4). And yet to achieve anunderstanding of how Newton himself approached natural philosophy, wemust carefully bracket such historical developments—they did notsolidify until sometime after 1750, a generation after Newton’sdeath. Indeed, if we resist the temptation to understand Newton asworking within a well established discipline called mathematicalphysics, if we see him instead as a philosopher studying nature, hisachievement is far more impressive, for instead of contributing to awell-founded field of physics, he had to begin a process that wouldeventually lead aspects of natural philosophy to be transformed into anew field of study. This transformation took many decades, involving aseries of methodological and foundational debates about the propermeans for obtaining knowledge about nature and its processes. Newtonhimself not only engaged in these debates from his very firstpublication in optics in 1672, but his work in both optics and in thePrincipia generated some of the most significantmethodological discussions and controversies in the late seventeenthand early eighteenth centuries. These debates concerned such topics asthe proper use of hypotheses, the nature of space and time, the bestunderstanding of the forces of nature, and the appropriate rules forconducting research in natural philosophy. Newton’s achievementwas in part to have vanquished both Cartesian and Leibnizianapproaches to natural philosophy; in the later eighteenth century, andindeed much of the nineteenth, physics was a Newtonian enterprise morethan anything. But this achievement, from Newton’s ownperspective, involved an extensive, life-long series of philosophicaldebates. Those debates focused on numerous substantive issues, butalso included extensive discussions of the proper methodology innatural philosophy.

2. Methodology I: the optics debates of the 1670s

Philosophers have long known about the aspects of Newton’s workthat are salient for understanding debates in the early modern period.For instance, no history of debates about the ontology of space andtime would exclude a discussion of Newton’s famous conception of“absolute” space (see below). Similarly, any discussion ofthe role of hypotheses in philosophical reasoning would mention Newtonprominently. These aspects of Newton’s work continue to besignificant in contemporary scholarship, but the scope of discussionsof Newton has greatly expanded, encompassing the whole of hisintellectual life. This is especially evident in discussions ofNewton’s earliest published work, which was in the field ofoptics. In at least three relevant respects, Newton’s early workin optics, which was published in the PhilosophicalTransactions of the Royal Society beginning in 1672, set thestage for the principal themes of his long career in naturalphilosophy (he remained active well into his seventies). Firstly,Newton’s letter to the Society’s secretary, HenryOldenburg, often called the “New theory about light andcolors”, generated an immediate, extensive, and protracteddebate that eventually involved important philosophers such as RobertHooke in Britain and Christiaan Huygens, G.W. Leibniz and IgnatiusPardies on the Continent (the beginning of the very long title of thepaper is: “A letter of Mr. Isaac Newton, Mathematick Professorin the University of Cambridge, containing his New Theory about Lightand Colors”). Newton consistently regarded these figures notmerely as disagreeing with his views, but as misinterpreting them.This experience helped to shape Newton’s famous and lifelongaversion to intellectual controversy, a feature of his personalitythat he often mentioned in letters, and one that he would neveroutgrow. Secondly, because Newton regarded himself as having beendeeply misinterpreted by his critics, he had recourse to meta-level ormethodological discussions of the practice of optics and of the kindsof knowledge that philosophers can obtain when engaging in experimentswith light. The novelty and power of Newton’s work in thePrincipia years later would eventually generate similarcontroversies that led him to analogous kinds of methodologicaldiscussions of his experimental practice within natural philosophy andof the kinds of knowledge that one can obtain in that field usingeither experimental or mathematical techniques. From ourpoint of view, Newton’s science was unusually philosophical forthese reasons. Thirdly and finally, in his earliest optical workNewton began to formulate a distinction that would remain salientthroughout his long intellectual career, contending that a philosophermust distinguish between a conclusion or claim about some feature ofnature that is derived from experimental or observational evidence,and a conclusion or claim that is a mere “hypothesis”, akind of speculation about nature that is not, or not yet anyway, soderived. Newton’s much later proclamation in the second editionof the Principia (1713), “Hypotheses nonfingo”, or “I feign no hypotheses”, wouldinfuriate his critics just as much as it would prod his followers intomaking the pronouncement a central component of a newly emergingNewtonian method (see below for details).

The field of optics has its origins in the Ancient Greek period, whenfigures like Euclid and Ptolemy wrote works on the subject, but theyoften focused primarily on the science of vision, analyzing (e.g.) thevisual rays that were sometimes thought to extrude from the eye,enabling it to perceive distant physical objects. In the early modernperiod, Kepler and Descartes each made fundamental contributions tothe field, including the discovery of the inversion of the retinalimage (in the former case) and an explanation of refraction (in thelatter case). Newton’s work helped to shift the focus of opticsfrom an analysis of vision to an investigation of light. In “Newtheory about light and colors”, published in thePhilosophical Transactions in 1672, Newton presented a numberof experiments in which sunlight was allowed to pass through one ortwo prisms in order to probe some of its basic features. The paperrecounts a number of experiments that Newton says he had conductedseveral years earlier. But what precisely counts as a featureof light? Numerous philosophers during the seventeenth century,including Hooke and Huygens, developed doctrines concerning thefundamental physical nature of light in answer to the question: islight a stream of particles (or “corpuscles”), or a wave?Both Hooke and Huygens were wave theorists. This question obviouslycontinued to have relevance into the twentieth century, whenwave-particle duality was discovered. In his experiments with theprism, however, Newton apparently sought to investigate somethingelse, viz. what he calls “the celebrated Phenomena ofColours”. Newton’s various prism experiments, whichhe describes in considerable depth, suggested what he called a“Doctrine” that he expresses in thirteen consecutivenumbered propositions. Included in these propositions are thefollowing claims about features of rays of light: first, the rays oflight that emerge when sunlight passes through a prism exhibit variouscolors; second, these colors differ in their “degrees ofRefrangibility”, which means that they exhibit and retain anindex of refraction, even when they are passed through a second prism;third, these colors—or colorful rays—are not modificationsof sunlight itself, but are “Original and connateproperties” of it; and, fourth, these facts mean thatalthough ordinary sunlight appears white, or perhaps colorless, to ourperception, it actually contains numerous colors within it, which canbe experimentally revealed. This final point suggests, in turn, thatfrom Newton’s point of view, colors are not solely perceived, oreven perceptible, aspects of physical objects; they can also beconceived of as hidden features of light which cannot be perceiveddirectly under any ordinary circumstance (the physical influence ofthe prism is required for them to become perceptible).

From a contemporary point of view, Newton’s 1672 paper exhibitsan intriguing blend of experimental evidence and philosophicalargumentation. The latter hinges on Newton’s interpretation ofthe concept of a property or a quality, as the following passage,which follows the “Doctrine” expressed in thirteenpropositions, tellingly reveals:

These things being so, it can be no longer disputed, whether there becolours in the dark, nor whether they be the qualities of the objectswe see, no nor perhaps, whether Light be a Body. For, since Coloursare the qualities of Light, having its Rays for their entireand immediate subject, how can we think those Rays qualitiesalso, unless one quality may be the subject of and sustain another;which in effect is to call it substance. We should not knowBodies for substances, were it not for their sensible qualities, andthe Principal of those being now found due to something else, we haveas good reason to believe that to be a substance also. (Newton1959–, vol. 1: 100)

Newton seems here to be arguing as follows: since rays of light havecolors as basic features, we should regard these colors as qualitiesor properties of the rays (despite the fact that these properties areimperceptible under any ordinary circumstance); but doing so requiresus to think of the rays as bearers of qualities, which is to say, assubstances in their own right. And if rays of light are substances,this means that we cannot also think of them as qualities orproperties of anything else. This last point follows from a widelyaccepted notion of a substance at the time, one easily found in Descartes<7>, viz., that substances are those items that can exist independently ofother items (whether they can exist independently even of God is afurther question that we can ignore here). And if we cannot think ofrays of light as properties or qualities, then they are not waves, forwaves are features of some medium—think of waves on the surfaceof a lake. Newton concludes: light is a stream of particles (he doesuse the word ‘perhaps’ to hedge a bit here). Clearly,philosophical argumentation is a significant aspect of Newton’sreasoning in this paper, as are various philosophical concepts. It isintriguing to ponder the question, what overall conception of“sensible qualities” does Newton presuppose in this piece?If a ray of sunlight passes through my window, the fact that itappears white to me does not undermine Newton’s view (or so hethinks) that the ray actually contains a series of colors as its“qualities”. Are these qualities “sensible” iftheir presence can be detected only through the use of one or moreprisms but never through the inspection of the sunlight throughordinary means (unaided perception, glasses, a magnifying glass,etc.)? These are apt to strike us as canonical philosophicalproblems.

Newton’s line of argument quoted above became one of thecenterpieces of the debate that his paper generated. In some parts ofhis paper, when Newton wrote of the “rays” of light, hehad evidently intended to remain neutral on the question of whetherthe rays are particles or waves (this is reminiscent of the ancientGreek practice of avoiding physical discussions of visual rays). Butthen towards the paper’s end, Newton added his new line ofargument, which employed some philosophical analysis together withsome experimental evidence to support the conclusion that rays oflight cannot be waves after all. Newton’s critics pounced. Thisled to the first problem he encountered in response to his paper: whathe calls his “theory” of light and colors was not merelyrejected, but rather immediately misunderstood, at least from his ownperspective. Just days after Newton’s paper was read at theRoyal Society, Robert Hooke responded with a detailed letter toOldenburg. In the first few sentences, Hooke indicates that from hispoint of view, Newton’s “Hypothesis of saving thephenomena of colours” essentially involves the contention thatrays of light are particulate, rather than wavelike.<8> Hooke argues, in contrast, that light “is nothing but a pulseor motion propagated through an homogeneous, uniform and transparentmedium;” that is, he argues that light is indeed wavelike. Hemakes it perfectly clear, moreover, that his hypothesis—the namedid not carry a negative connotation in his work—can save thephenomena of colors just as well as Newton’s, which is to say,his hypothesis is compatible with the experimental evidence Newton hadgathered. Evidently, the line of argument in the passage quoted abovecaught Hooke’s eye. Among philosophers, he was not alone. In aletter to Huygens explaining Newton’s theory of light, Leibnizwrites that Newton takes light to be a “body” propelledfrom the sun to the earth which, according to Leibniz, Newton takes toexplain both the differential refrangibility of rays of light and thephenomena of colors.<9> Since Newton had employed the concepts of substance, quality andsensible quality when concluding in his paper that light is(presumably) particulate, we are apt to regard the paper ascontributing to important discussions within philosophy. After theextensive correspondence, and controversy, generated in response toNewton’s early optical views and experiments, he oftenthreatened to avoid engaging in mathematical and philosophicaldisputes altogether. He insisted to friends and colleagues that hefound intellectual controversy unbearable. But he never followedthrough with his threat to disengage from discussions in naturalphilosophy, sending many important letters throughout his longintellectual career.

3. Newton’s relation to Cartesianism

Like many philosophers who worked in the wake of Galileo and ofDescartes, it seems that Newton never extensively analyzedAristotelian ideas about nature. He would have encountered such ideasin the curriculum at Trinity College, but there is not much evidencethat he took them seriously. Instead, he focused on the“modern” thinkers that enterprising young students weretold to read outside of the standard curriculum.<10> And in England in Newton’s day, the greatest modern philosopherof nature was thought to be Descartes (Heilbron 1982: 30). There issubstantial evidence that Newton took Descartes’s ideas veryseriously, and expended considerable energy thinking them through andeventually coming to criticize them. Some of that evidence comes froma manuscript that was first transcribed and published in 1962 by thegreat historians of science, Marie Boas Hall and A. Rupert Hall. Theuntitled manuscript, now known as “DeGravitatione” after its first line, has been the subject ofextensive discussions over the past fifty years because it indicatesthe depth of Newton’s interest in Cartesian ideas in metaphysicsand natural philosophy. Despite its importance to contemporaryunderstandings of Newton’s relation to Cartesianism, and muchelse besides, De Gravitatione is not without its problems.First and foremost, the manuscript lacks a date, and there is noscholarly consensus regarding its precise provenance.<11> Second, the manuscript was never finished, so it is difficult toassess its relationship with Newton’s mature thinking inphilosophy. Finally, the manuscript was not published duringNewton’s lifetime, so there are questions about whether itrepresents his considered views. Despite these facts, the textcontains a treasure trove of arguments concerning Cartesian ideas. Forinstance, it dispels the easily formed impression that Newton sought,in the Principia, to undermine a Leibnizian conception ofspace and time, as his defender, Samuel Clarke, would attempt to doyears later in the correspondence of 1715–16 (discussed below).Although Leibniz did eventually express what became the canonicalearly modern formulation of “relationalism” concerningspace and time—the view, roughly, that space is nothing but theorder of relations among physical objects, and time nothing over andabove the succession of events involving those objects—andalthough Newton and Clarke were highly skeptical of such a view, it ismisleading to read the Principia through the lens provided bythe later controversy with the Leibnizians. Newton’s extensiveattempt in De Gravitatione to refute Descartes’sconception of space and time in particular indicates that the Scholiumshould be read as providing a replacement for the Cartesian conception.<12> That is, Newton had a Cartesian, and not a Leibnizian, opponentprimarily in mind when he wrote his famous articulation of“absolutism” concerning space and time. Unlike questionsabout Newton’s methods and his apparent deviation from the normsestablished by mechanist philosophers like Descartes and Boyle,Newton’s conception of space and time, along with his view ofthe divine being, did not immediately engender a philosophical debate.It was Leibniz more than any other philosopher who eventuallysucceeded in fomenting a philosophical debate in which the“Newtonian” conception of space, time and the divine wouldplay a central role (see below). But Leibniz’s philosophicalviews were relatively unknown when Newton first formed hisconception--to the young Newton writing the Principia,Leibniz was another mathematician and not yet a contributor to naturalphilosophy. Instead, it was Descartes’s view of space, theworld, and God, which he pondered in his youth and eventually came toreject.

Newton took special interest in the Cartesian view of space and body,and in related views concerning the causal relations between minds andbodies and between God and the bodies that constitute the naturalworld. Like many of Newton’s contemporaries in Cambridge inthose days, he encountered these Cartesian views within the context ofHenry More’s then famous discussions of Cartesianism (a termcoined by More himself). Beginning with his correspondence withDescartes in 1648 (Lewis 1953), and continuing with a series ofpublications in later years, many of which Newton owned in hispersonal library (Harrison 1978), More argued that Descartes made twofundamental mistakes: first, he wrongly contended that extension andmatter are identical (and that the world is therefore a plenum); andsecond, he mistakenly believed that God and the mind were not extendedsubstances, which made their causal interactions with such substancesmysterious. Just as Princess Elisabeth of Bohemia had raisedfundamental objections to Cartesian dualism (see Shapiro 2007) in theearly 1640s, More raised similar objections against the Cartesian viewof the divine a few years later (Lewis 1953). Descartes agreed withMore’s suggestion that God can act anywhere on nature if he sochooses, and came very close to accepting More’s contention thatsuch a view entails that God must be present within the world whereverhe in fact chooses to act. For how could God part the Red Sea,suggested More, unless God were present precisely where the Red Sea islocated? Of course, More agreed that God is not made of parts, cannotbe imagined, and cannot be affected by the causal activity of materialbodies—the causal arrow flows only in one direction. But Moreconcluded that God is extended in his own way. If one fixesDescartes’s two basic mistakes, one obtains what More regardedas a proper philosophical view: space is distinct from matter becauseit is extended but penetrable, whereas matter is extended butimpenetrable; and, in tandem, all substances are extended, but whereassome, such as tables and chairs, are impenetrable, others, such as themind and God, are penetrable and therefore not material.<13> Newton was deeply influenced both by More’s criticisms ofDescartes and by his positive philosophical conception of space andthe divine.

In a number of texts, including De Gravitatione, the famousdiscussion of space and time in the Scholium to thePrincipia, and the discussion of God in the General Scholium,Newton made his generally Morean attitudes perfectly clear. Herejected the Cartesian identification of extension and matter, arguingthat space itself exists independently of material objects (and theirrelations), and he contended that all entities, including the humanmind and even the divine being, are extended in the sense that theyhave spatial location, even if they are extended in ways thatdistinguish them from ordinary material bodies.<14> In Newton’s hands, space becomes a fundamental concept ofnatural philosophy, an attitude that is foreign to Cartesians. AsNewton puts it in a famous passage from De Gravitatione:

Space is an affection of a being just as a being. No being exists orcan exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that itoccupies; and whatever is neither everywhere nor anywhere does notexist. And hence it follows that space is an emanative effect of thefirst existing being, for if any being whatsoever is posited, space isposited. (Newton 2004: 25)

Space is a fundamental concept in part because Newton not onlyconceives of it as independent of objects and their relations, butbecause he argues that every entity must somehow connect with space insome way. For Newton, then, if one follows the Cartesians and thinksof the mind, or of God, as existing without any spatiallocation—as existing either “beyond” the naturalworld or somehow outside of it—then that is equivalent toconceiving of them as non-existent. Newton does not shy away frommaking this conception of the divine explicit in his public writings,despite the fact that it was anathema to his Cartesian and Leibniziancontemporaries. In the General Scholium to the Principia,which was added to the second edition of the text in 1713, forinstance, he famously writes of God:

He endures always and is present everywhere, and by existing alwaysand everywhere he constitutes duration and space. Since each and everyparticle of space is always, and each and every indivisiblemoment of duration is everywhere, certainly the maker andlord of all things will not be never or nowhere… God is one and the same God always and everywhere. He isomnipresent not only virtually but alsosubstantially; for active power cannot subsist withoutsubstance. (Newton 1999: 941)

For Newton, just as bodies are present in some spatial location, God,an infinite being, is present throughout all of space throughout allof time. There could not be a clearer expression of agreement withMore in his debate with the Cartesians concerning the substantialpresence of the divine within space.

Newton also took issue with Cartesian ideas about motion. Hisrejection of Cartesian views of space, and his embrace of space as afundamental concept in philosophy following More’s influence,aligns with his famous discussion of space and time in the Scholiumthat follows the opening definitions in the Principia. Thistext influenced nearly every subsequent philosophical discussion ofspace and time for the next three centuries, so its contours are wellknown (see DiSalle 2006: ch. 2). In his Principles ofPhilosophy of 1644, Descartes had distinguished between the“ordinary” and the “proper” view of motion:whereas the ordinary view presents motion as a body’s change ofplace, the philosopher knows that properly speaking, motion is abody’s change of relations to the bodies that surround it(recall Descartes’s plenum). Newton contends in DeGravitatione that this idea of proper motion, according to whichthe motion of a body is at least partially a function of its relationsto other bodies, is in tension with Descartes’s own laws ofnature, also presented in the Principles. For according tothe conception of (what we now call) inertia that Descartes presentsas his first two laws, a body moving rectilinearly will continue to doso unless caused to deviate from its path—hence a body’smotion is not a function of its spatial relations to other bodies, butrather of its causal relations. That is, according to thefirst two laws, changing a body’s spatial relations to othersbodies will not alter its rectilinear motion unless a causalinteraction occurs. This tension runs deep in the Cartesian system.Newton’s Scholium reflects his idea that the concept of motionin the Principia ought to cohere with the laws of motion heendorses. He distinguishes between absolute and relative motion, trueand apparent motion, and mathematical and common motion (the samedistinctions hold for time, space and place). The former item in eachof these three pairings is a concept that coheres with the laws ofmotion. Newton’s first law reflects Descartes’s laws: itis a new version of the principle of inertia, one incorporating theconcept of an impressed force. Since this law indicates that abody’s motion is not a function of its spatial relations toother bodies, but rather of whether forces are impressed onit—which replaces the Cartesian concept of causal interactionsthat involve only impact (see below)—Newton cannot rely on abody’s motion relative to other bodies if he is to avoid thekind of tension he found in the Cartesian view. Hence he indicatesthat a body’s true motion—rather than its apparent motion,which depends on our perceptions, or its relative motion, whichdepends on its spatial relations—is a body’s change ofposition within space itself. That is, true motion should beunderstood as absolute motion. This means, in turn, that we mustdistinguish between the common idea of space, according to which spaceis conceived of as involving relations among various objects (like thespace of our air), and the mathematical idea, one presumably obtainedfrom geometrical reasoning, that space is independent of any objectsor their relations. In order to account for the idea that true motionis absolute motion, then, the famous “absolute space” ispostulated.

Newton was perfectly well aware that the notion of absolute space isnot unproblematic.<15> For instance, if a body’s true motion just is itsabsolute motion, its motion with respect to space itself, then theimperceptibility of space would appear to render any detection of truemotion difficult, if not hopeless. Indeed, how would we detect anybody’s true motion on this view? We might be able to detect abody’s changing spatial relations with its neighbors, but notits changing relationship with space itself! Newton’s solutionto this problem is ingenious. Under certain circumstances, we candetect a body’s true motion by detecting its acceleration. Wecan do so when the body is rotating or has a circular motion, for suchmotions often have detectable effects. This is one way ofunderstanding what has become one of the most famous, if not infamous,experiments of the early modern period, Newton’s bucket.(He grew up in part on a farm in the English countryside, and oftenused deceptively simple examples.) If one takes an ordinary bucket andfills it with water, and then attaches a rope to the top of thebucket, one can then twist the rope and let it go in order to make thebucket spin. When the bucket full of water spins around, we can detectthe water’s acceleration by its changing surface. As Newton putsit, using his laws of motion, the water endeavors to recede from theaxis of its motion (hence its changing surface). But even an observeruntutored in physics would grasp the importance of the water’schanging surface--that is, perceiving the effect does not depend onunderstanding the laws. In this way, despite the fact that Newtonwishes to conceive of the water’s true motion as its absolutemotion within space itself, which cannot be perceived, he shows hisreaders how they might detect the water’s true motion throughits effects. Newton provides another simple experiment to illustrate asimilar point. If two balls are joined together by a rope and thenspun around, say over one’s head, then the changing tension inthe rope will indicate that the balls are accelerated. Since anyacceleration is a true motion—although not all true motions areaccelerations, since a so-called inertial motion is not—thiscase indicates that we can detect a body’s true motion eventhough space itself is imperceptible. In this way, Newton did notmerely develop an alternative to the Cartesian view of motion, alongwith its allied conception of space; he presented a view that could beemployed to pick out some of the true motions of objects withinnature. Once one has found a true motion, one can then ask whatcaused that motion (for Newton, as we will see, it is forcesthat are understood to cause motions). As the last line of theScholium in the Principia indicates, that is one reason thatNewton wrote his magnum opus in the first place.

Newton’s idea of space, then, fulfilled at least two roles.First, it enabled him to avoid the tension between the concept of truemotion and the laws of motion of the kind found in Descartes. Second,it also enabled him to articulate what he took to be God’srelation to the natural world. Many regarded his achievements as animportant advance over the Cartesian system. However, it would be amistake to think that Newton vanquished Cartesian ideas within hislifetime: even in England, and certainly on the Continent,Cartesianism remained a powerful philosophical force for severaldecades after Newton published his primary works.<16> Typically, however, Descartes’s followers emphasized theimportance of his ideas about the mechanisms that pervade naturerather than his views of space and time. In that arena, Newton’sviews were especially prominent, and came in for significant criticismfrom Leibniz.

4. Methodology II: the Principia

Many legends concerning momentous events in history are apocryphal,but the legend of Halley’s visit to Newton in 1684 is not: itexplains what prompted Newton to write his magnum opus. InAugust of 1684, Edmond Halley—for whom the comet isnamed—came to visit Newton in Cambridge in order to discover hisopinion about a subject of much dispute in celestial mechanics. Atthis time, many in the Royal Society and elsewhere were at work on acluster of problems that might be described as follows: how can onetake Kepler’s Laws, which were then considered among the verybest descriptions of the planetary orbits, and understand them in thecontext of dynamical or causal principles? What kind of cause wouldlead to planetary orbits of the kind described by Kepler? Inparticular, Halley asked Newton the following question: what kind ofcurve would a planet describe in its orbit around the Sun if it wereacted upon by an attractive force that was inversely proportional tothe square of its distance from the Sun? Newton immediately repliedthat the curve would be an ellipse (rather than, say, a circle).<17> Halley was amazed that Newton had the answer at the ready. But Newtonalso said that he had mislaid the paper on which the relevantcalculations had been made, so Halley left empty handed (whether therewas any such paper is a subject of dispute). But he would not bedisappointed for long. In November of that year, Newton sent Halley anine-page paper, entitled De Motu (on motion), that presentedthe sought-after demonstration, along with several other advances incelestial mechanics. Halley was delighted, and immediately returned toCambridge for further discussion. It was these events thatprecipitated the many drafts of De Motu that eventuallybecame Principia mathematica by 1686. Several aspects of thePrincipia have been central to philosophical discussionssince its first publication, including Newton’s novelmethodology in the book, his conception of space and time, and hisattitude toward the dominant orientation within natural philosophy inhis day, the so-called mechanical philosophy, which had importantmethodological consequences.

When Newton wrote the Principia between 1684 and 1686, he wasnot contributing to a preexisting field of study called mathematicalphysics; he was attempting to show how philosophers could employvarious mathematical and experimental methods in order to reachconclusions about nature, especially about the motions of materialbodies (Janiak 2015, Chapter One). In his lectures presented as theLucasian Professor at Cambridge, Newton had been arguing since atleast 1670 that natural philosophers ought to employ geometricalmethods in order to understand various phenomena in nature.<18> The Principia represented his attempt to reorient naturalphilosophy, taking it in a direction that neither his Aristotelianpredecessors, nor his Cartesian contemporaries, had envisioned. He didnot immediately convince many of them of the benefits of his approach.Just as his first publication in optics in 1672 sparked an intensedebate about the proper methods for investigating the nature oflight—and much else besides—his Principia sparkedan even longer lasting discussion about the methodology thatphilosophers should adopt when studying the natural world. Thisdiscussion began immediately with the publication of thePrincipia, despite the fact that its first edition containedfew explicit methodological remarks (Smith 2002: 138–39). Itintensified considerably with the publication of its second edition in1713, which contained many more remarks about methodology, includingmany attempts at defending the Newtonian method. Indeed, many ofNewton’s alterations in that edition changed the presentation ofhis methods. Discussions of methodology would eventually involvenearly all of the leading philosophers in England and on the Continentduring Newton’s lifetime.

In Cartesian natural philosophy, all natural change is due to theimpacts that material bodies make upon one another’s surfaces(this is reflected in Descartes’s first two laws of nature). Theconcept of a force plays little if any role. Unlike Descartes, Newtonplaced the concept of a force at the very center of his thinking aboutmotion and its causes within nature. In that regard, his reactions tothe shortcomings of Cartesian natural philosophy parallelLeibniz’s, who coined the term “dynamics”, and whoobviously regarded force as a fundamental concept in metaphysics aswell (Westfall 1971). But Newton’s attitude toward understandingthe forces of nature involved an especially intricate method thatgenerated intense scrutiny and debate amongst many philosophers andmathematicians, including Leibniz (Garber 2012). Newton’scanonical notion of a force, which he calls a vis impressa or“impressed force”, is the notion of an “actionexerted on a body” that changes its state of motion. This was aconfusing notion at the time. Perhaps it is not difficult to see whythat should be so. To take one of Newton’s own examples: supposeI hit a tennis ball with my racquet—according to Newton, I haveimpressed a force on the tennis ball, for I have changed its state ofmotion (hopefully!). We have a reasonably good idea of what the tennisball is, of what the racquet is, and even of what I am, and aCartesian might wish to stop her analysis there. But what exactly isthis “force” that I impressed on the tennis ball? Theball, the racquet and I are physical things of one sort or another,but is the force physical? Is it not physical? It does not seem likelythat a force is itself a physical thing in the sense of being asubstance, to use a philosophical notion popular in Newton’s day(as we saw above in his first optics paper). The reason is that inDefinition Four in the Principia, which defines an impressedforce for the first time, Newton remarks: “This force consistssolely in the action and does not remain in a body after the actionhas ceased”. So when I hit the tennis ball over the net, theforce I impressed on it was the action of hitting the ball, or anaction associated with hitting the ball, and not a property of me orof the ball after the action had ceased. This idea confused many ofNewton’s readers. By the mid-eighteenth century, the time ofHume’s analysis of causation in the Treatise and theEnquiry, many philosophers started to think that actions andother kinds of event are important items to have in one’sontology, and they often contended in particular that causal relationshold between events. But in Newton’s day, philosopherstypically regarded objects or substances as the causal relata. Indeed,one actually finds an equivocation between thinking of events andthinking of objects as the relevant causal relata even in Hume: in hisEnquiry, he first defines a “cause” so that“objects” are the causal relata, but then gives an examplein which one of the relata is the vibration of a string(Enquiry, §VII, 51). So actions were difficult toanalyze, left out of analyses, or conflated with objects. As a result,Newton’s conception of force proved confusing, even to his mostsympathetic interpreters. Moreover, it was unclear to many ofNewton’s mechanist readers how his forces fit into their ratheraustere ontological view that material bodies consist solely ofproperties such as size, shape, mobility and solidity.

Newton did try to clarify his method of characterizing forces. If onebrackets the question of how to understand forces as ephemeral actionsthat do not persist after causal interactions have ceased, one canmake progress by conceiving of forces as quantities. Inparticular, since Newton’s eight definitions and three lawsindicate that forces are proportional to mass and to acceleration, andsince mass—or the quantity of matter, a concept Newtontransformed from its Cartesian origins, where it was understood as ameasure of a body’s volume—and acceleration are bothquantities that can be measured, Newton gives us a means of measuringforces. This is crucial to his method. If one thinks of forces asmeasurable quantities, moreover, then one can attempt to identify twoseemingly disparate forces as in fact the same force through thinkingabout measuring them. For instance, in Book III of thePrincipia, Newton famously argues in proposition five and itsscholium that the centripetal force maintaining the planetary orbitsis in fact the same as the force of gravity, viz., the force thatcauses the free fall of objects on earth. This was a revolutionaryidea at the time, one rendered possible in the first place byNewton’s way of thinking about forces as quantities. This ideathen led Newton to the even more revolutionary view in propositionseven of Book III that all bodies gravitate toward one another inproportion to their quantity of matter. That is, it led him to theidea of universal gravity, a view that shocked many of his Continentalreaders in its boldness. This helped to unify what were once calledsuperlunary and sublunary phenomena, a unification that was obviouslycrucial for later research in physics. The idea was enabled byNewton’s abstract way of understanding forces—withoutconceiving of a force as involving any specific mechanism or type ofphysical interaction, Newton thought of forces as quantities that areproportional to other features of nature.

Despite his evident success in obtaining what we now call the law ofuniversal gravitation, Newton admits that he lacks another kind ofknowledge about gravity; this lack of knowledge directly reflects anaspect of his abstract characterization of forces. In the GeneralScholium, he reminds his readers that gravity is proportional to abody’s quantity of matter (its mass) and reaches across vastdistances within our solar system, adding: “I have not as yetbeen able to deduce from phenomena the reason for these properties ofgravity, and I do not feign hypotheses”.<19> With this phrase, one of the most famous in all of Newton’swritings, he returned to a key theme of his very first optical paperfrom forty years earlier, viz. the proper role of hypotheses and ofhypothetical reasoning within natural philosophy.<20> Some of Newton’s interpreters have regarded this phrase assignaling a strong commitment to the broad doctrine that allhypotheses concerning natural phenomena ought to be avoided inprinciple. This interpretation is sometimes coupled with the view thatsome British philosophers in the late seventeenth century regardedCartesianism as overly reliant on hypotheses in reaching conclusionsabout phenomena. But this interpretation may be hard to square withNewton’s texts. For instance, in the Scholium to Proposition 96of Book I of the Principia, Newton discusses hypothesesconcerning light rays. Similarly, in query 21 of the Opticks,he proposes that there might be an aether whose differential densityaccounts for the gravitational force acting between bodies. In lightof such examples, one can read the General Scholium’spronouncement in this way: a philosopher concerned with explainingsome feature of nature—such as the fact that gravity isinversely proportional to the square of spatial separation,rather than, say, the cube—may legitimately entertainand propose hypotheses for consideration, but she may not“feign” the hypothesis in the sense of taking it as havingbeen established either through experiment, observation, or some formof reasoning (including mathematical reasoning). Hence Newton thinksthat he has established the fact that gravity acts on all materialbodies in proportion to their quantity of matter, but he hasnot established the existence of the aether. What, then, doesNewton’s slogan hypotheses non fingo actually rule out?By the time of the General Scholium, Newton was increasingly embroiledin philosophical disputes with Leibniz. After reading the copy of thePrincipia that Newton had sent him, Leibniz wrote an essay(“Tentamen”) on the causes of planetary motion for thefamous journal Acta Eruditorum. In order to account for themotions of the planetary bodies in his Tentamen, published in1689, Leibniz introduces ex hypothesi the premise that somekind of fluid surrounds, and is contiguous to, the various planetarybodies, and then argues that this fluid must be in motion to accountfor their orbits.<21> Newton may have argued that Leibniz had “feigned” thehypothesis of the vortices. That is, he would have objected toLeibniz’s conclusion that there must be vortices in the solarsystem (as opposed to the suggestion, for instance, that we try todetect their presence through observations of things like comets). Adebate between the two philosophers on this score would bring them tothe question of the mechanical philosophy: whereas Newton would objectto Leibniz’s reasoning on methodological grounds, Leibniz wouldreply that Newton’s theory of gravity involves action at adistance, which his vortex hypothesis avoids (see below for moredetails).

Once the Principia was published, Newton had a vexedrelationship with the mechanical philosophy, an orientation withinnatural philosophy that is associated with nearly every significantearly modern philosopher, including Descartes, Boyle, Huygens,Leibniz, and Locke.

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<22> One of the reasons for this complex relationship can be understood ifwe consider Newton’s attitude toward forces in an abstract way.His second law indicates that a body moving rectilinearly willcontinue to do so unless a force is impressed on it. This is notequivalent to claiming that a body moving rectilinearly will continueto do so unless another body impacts upon it. A visimpressa—an impressed force—in Newton’s systemis not the same as a body, nor even a quality of a body, as we haveseen; but what is more, some impressed forces need not involve contactbetween bodies at all. For instance, gravity is a kind of centripetalforce, and the latter, in turn, is a species of impressed force. Hencea body moving in a straight line will continue to do so until itexperiences a gravitational pull, in which case it will deviate from astraight line motion, even if no body impacts upon it. Indeed, thegravitational pull might originate with a mass that is millions ofmiles away. As we have seen, an impressed force is an action exertedon a body. Hence the gravity exerted on a moving body is an action(the Latin term is actio), which is obviously a causalnotion. This is not an empirical claim per se; it is merely areflection of Newton’s laws, together with his notion of animpressed force, and his further idea that gravity is one kind ofimpressed force. These elements of the Principia makeconceptual room for a causal interaction between two bodies separatedby a vast distance, one enabled by Newton’s concept of animpressed force. Aspects of this idea became known in philosophicalcircles as the problem of action at a distance (Hesse 1961). Many ofNewton’s most influential contemporaries objected vigorously tothe fact that his philosophy had made room for—if not explicitlydefended—the possibility of distant action between materialbodies. Leibniz and Huygens in particular rejected this aspect ofNewton’s work in the strongest terms, and it remained a point ofcontention between Newton and Leibniz for the rest of their lives.Both Leibniz and Huygens were convinced that all natural change occursthrough contact action, and that any deviation from this basicmechanist principle within natural philosophy would lead to seriousdifficulties, including the revival of outmoded Aristotelian ideas. Bythe seventh proposition of Book III of the Principia, as wehave seen, Newton reached the following conclusion (1999: 810):“Gravity acts on all bodies universally and is proportional tothe quantity of matter in each”. Leibniz eventually accusedNewton of regarding gravity as a kind of “occult quality”,that is, as a quality of bodies that is somehow hidden within them andbeyond the philosopher’s understanding. They understood Newtonto be saying that gravity is a kind of hidden power to attractembedded in material bodies.

Newton was well aware that the Principia’s methodologyof discovering the forces present in nature was controversial, and notmerely because of questions about action at a distance. So when herevised the text, under the editorship of Roger Cotes, for publicationin a second edition in 1713, he added other methodological remarks.These remarks included what Newton called “regulaephilosophandi”, or rules of philosophy, which became thefocal point of vigorous discussion and debate well into the eighteenthcentury. The first two rules concern causal reasoning, but it is thethird rule that generated the most debate, for it involved both anaspect of Newton’s controversial argument for universal gravityand also a rare public statement by Newton of wh