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He would have encountered such ideas in the curriculum at Trinity College, but there is not much evidence that he took them seriously. There is substantial evidence that Newton took Descartes's ideas very seriously, and expended considerable energy thinking them through and eventually coming to criticize them. Much of that evidence comes from a manuscript that was first transcribed and published in by the great historians of science, Marie Boas Hall and Rupert Hall.

Despite its importance to contemporary understandings of Newton's relation to Cartesianism, and much else besides, De Gravitatione is not without its problems. First and foremost, the manuscript lacks a date, and there is no scholarly consensus regarding that issue. Finally, the manuscript was not published during Newton's lifetime, so there are questions about whether it represents his considered views. Despite these facts, the text contains a treasure trove of argument concerning Cartesian ideas.

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It therefore helps to dispel the easily formed impression that Newton sought, in the Principia , to undermine a Leibnizian conception of space and time, as his defender, Samuel Clarke, would attempt to do years later in the correspondence of —16 discussed below. Newton's extensive attempt in De Gravitatione to refute Descartes's conception of space and time in particular indicates that the Scholium should be read as providing a replacement for the Cartesian conception. Unlike questions about Newton's methods and his apparent deviation from the norms established by mechanist philosophers like Descartes and Boyle, Newton's conception of space and time, along with his view of the divine being, did not immediately engender a philosophical debate.

But Leibniz's philosophical views were relatively unknown when Newton first formed his conception; instead, it was Descartes's view of space, the world, and God, which he pondered in his youth and eventually came to reject. Newton took special interest in the Cartesian view of space, and in related views concerning the causal relations between minds and bodies, and between God and the bodies that constitute the natural world.

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Like many of Newton's contemporaries in Cambridge in those days, he encountered these Cartesian views within the context of Henry More's then famous discussions of Cartesianism a term coined by More himself. Beginning with his correspondence with Descartes in Lewis , and continuing with a series of publications in later years, many of which Newton owned in his personal library Harrison , More argued that Descartes made two fundamental mistakes: first, he wrongly contended that extension and matter are identical and that the world is therefore a plenum ; and second, he mistakenly believed that God and the mind were not extended substances, which made their causal interactions with such substances mysterious.

Just as Princess Elisabeth of Bohemia raised fundamental objections to Cartesian dualism, More raised similar objections against the Cartesian view of the divine see Shapiro Descartes agreed with More's suggestion that God can act anywhere on nature if he so chooses, and came very close to accepting More's contention that such a view entails that God must be present within the world wherever he in fact chooses to act.

Of course, More agreed that God is not made of parts, cannot be imagined, and cannot be affected by the causal activity of material bodies—the causal arrow flows only in one direction. But More concluded that God is extended in his own way. If one fixes Descartes's two basic mistakes, one obtains what More regarded as a proper philosophical view: space is distinct from matter because it is extended but penetrable, whereas matter is extended but impenetrable; and, in tandem, all substances are extended, but whereas some, such as tables and chairs, are impenetrable, others, such as the mind and even God, are penetrable and therefore not material.

Isaac Newton

In a number of texts, including De Gravitatione , the famous discussion of space and time in the Scholium to the Principia , and the discussion of God in the General Scholium, Newton made his generally Morean attitudes perfectly clear. He rejected the Cartesian identification of extension and matter, arguing that space itself exists independently of material objects and their relations , and he contended that all entities, including the human mind and even the divine being, are extended in the sense that they have spatial location, even if they are extended in ways that distinguish them from ordinary material bodies.

As Newton puts it in a famous passage from De Gravitatione :. Space is an affection of a being just as a being. No being exists or can exist which is not related to space in some way. God is every where, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an emanative effect of the first existing being, for if any being whatsoever is posited, space is posited. Newton Space is a fundamental concept in part because Newton not only conceives of it as independent of objects and their relations, but because he argues that every entity must somehow connect with space in some way.

Newton does not shy away from making this conception of the divine explicit in his public writings, despite the fact that it was anathema to his Cartesian and Leibnizian contemporaries. In the General Scholium to the Principia , which was added to the second edition of the text in , for instance, he famously writes of God:. He endures always and is present everywhere, and by existing always and everywhere he constitutes duration and space.

Since each and every particle of space is always , and each and every indivisible moment of duration is everywhere , certainly the maker and lord of all things will not be never or nowhere … God is one and the same God always and everywhere. He is omnipresent not only virtually but also substantially ; for active power cannot subsist without substance. For Newton, just as bodies are present in some spatial location, God, an infinite being, is present throughout all of space throughout all of time. There could not be a clearer expression of agreement with More in his debate with the Cartesians concerning the substantial presence of the divine within space.

Newton also took issue with Cartesian ideas about motion. His rejection of Cartesian views of space, and his embrace of space as a fundamental concept in philosophy following More's influence, aligns with his famous discussion of space and time in the Scholium that follows the opening definitions in the Principia. This text influenced nearly every subsequent philosophical discussion of space and time for the next three centuries, so its contours are well known see DiSalle ch. Newton contends in De Gravitatione that this idea of proper motion, according to which the motion of a body is at least partially a function of its relations to other bodies, is in tension with Descartes's own laws of nature, also presented in the Principles.

For according to the conception of what we now call inertia that Descartes presents as his first two laws, a body moving rectilinearly will continue to do so unless caused to deviate from its path—hence a body's motion is not a function of its spatial relations to other bodies, but rather of its causal relations. That is, according to the first two laws, changing a body's spatial relations to others bodies will not alter its rectilinear motion unless a causal interaction occurs. This tension runs deep in the Cartesian system.

Newton's Scholium reflects his idea that the concept of motion in the Principia ought to cohere with the laws of motion he endorses. He distinguishes between absolute and relative motion, true and apparent motion, and mathematical and common motion the same distinctions hold for time, space and place , and the former item in each of these three pairings is a concept that coheres with the laws of motion. Newton's first law reflects Descartes's laws: it is a new version of the principle of inertia, one incorporating the concept of an impressed force.

Since this law indicates that a body's motion is not a function of its spatial relations to other bodies, but rather of whether forces are impressed on it—which replaces the Cartesian concept of causal interactions that involve only impact see below —Newton cannot rely on a body's motion relative to other bodies if he is to avoid the kind of tension he found in the Cartesian view.

Hence he indicates that a body's true motion—rather than its apparent motion, which depends on our perceptions, or its relative motion, which depends on its spatial relations—is a body's change of position within space itself. That is, true motion should be understood as absolute motion. This means, in turn, that we must distinguish between the common idea of space, according to which space is conceived of as involving relations among various objects like the space of our air , and the mathematical idea, one presumably obtained from geometry or geometrical reasoning, that space is independent of any objects or their relations.

Newton was perfectly well aware that the notion of absolute space is not unproblematic.

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Indeed, how would we detect any body's true motion on this view? We might be able to detect a body's changing spatial relations with its neighbors, but not its changing relationship with space itself! Newton's solution to this problem is ingenious. Under certain circumstances, we can detect a body's true motion by detecting its acceleration.

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We can do so when the body is rotating or has a circular motion, for such motions often have detectable effects. This is one way of understanding what has become one of the most famous, if not infamous, gedankenexperimenten of the early modern period, Newton's bucket. If one takes an ordinary bucket and fills it with water, and then attaches a rope to the top of the bucket, one can then twist the rope and let it go in order to make the bucket spin.

When the bucket full of water spins around, we can detect the water's acceleration by its changing surface. As Newton puts it, using some concepts from his laws of motion, the water endeavors to recede from the axis of its motion hence its changing surface. In this way, despite the fact that Newton wishes to conceive of the water's true motion as its absolute motion within space itself, which cannot be perceived, he shows his readers how they might detect the water's true motion through its effects.

Newton provides another gedankenexperiment to illustrate a similar point. If two balls are joined together by a rope and then spun around, say over one's head, then the changing tension in the rope will indicate that the balls are accelerated. Since any acceleration is a true motion—although not all true motions are accelerations, since a so-called inertial motion is not—this case indicates that we can detect a body's true motion even though space itself is imperceptible.

In this way, Newton did not merely develop an alternative to the Cartesian view of motion, along with its allied conception of space; he presented a view that could be employed to pick out some of the true motions of objects within nature. Once one has found a true motion, one can then ask what caused that motion for Newton, as we will see, it is forces that are understood to cause motions.

As the last line of the Scholium in the Principia indicates, that is one reason that Newton 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 true motion and the laws of motion of the kind found in Descartes. Second, it also enabled him to articulate what he took to be God's relation to the natural world. Many regarded his achievements as an important advance over the Cartesian system.

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However, it would be a mistake to think that Newton vanquished Cartesian ideas within his lifetime: even in England, and certainly on the Continent, Cartesianism remained a powerful philosophical force for several decades after Newton published his primary works. In that arena, Newton's views were especially prominent, and came in for significant criticism from Leibniz. Many legends concerning momentous events in history are apocryphal, but the legend of Halley's visit to Newton in is true, and explains what prompted Newton to write his magnum opus.

In August of , Edmond Halley—for whom the comet is named—came to visit Newton in Cambridge in order to discover his opinion about a subject of much dispute in celestial mechanics. At this time, many in the Royal Society and elsewhere were at work on a cluster of problems that might be described as follows: how can one take Kepler's Laws, which were then considered among the very best descriptions of the planetary orbits, and understand them in the context of dynamical or causal principles?

What kind of cause would lead to planetary orbits of the kind described by Kepler? In particular, Halley asked Newton the following question: what kind of curve would a planet describe in its orbit around the Sun if it were acted upon by an attractive force that was inversely proportional to the square of its distance from the Sun? Newton immediately replied that the curve would be an ellipse rather than, say, a circle. But Newton also said that he had mislaid the paper on which the relevant calculations had been made, so Halley left empty handed whether there was any such paper is a subject of dispute.

But he would not be disappointed for long. In November of that year, Newton sent Halley a nine-page paper, entitled De Motu on motion , that presented the sought-after demonstration, along with several other advances in celestial mechanics. Halley was delighted, and immediately returned to Cambridge for further discussion. It was these events that precipitated the many drafts of De Motu that eventually became Principia mathematica by Several aspects of the Principia have been central to philosophical discussions since its first publication, including Newton's novel methodology in the book, his conception of space and time, and his attitude toward the dominant orientation within natural philosophy in his day, the so-called mechanical philosophy, which had important methodological consequences.

When Newton wrote the Principia between and , he was not contributing to a preexisting field of study called mathematical physics; he was attempting to show how philosophers could employ various mathematical and experimental methods in order to reach conclusions about nature, especially about the motions of material bodies. In his lectures presented as the Lucasian Professor at Cambridge, Newton had been arguing since at least that natural philosophers had to employ geometrical methods in order to understand various phenomena in nature. He did not immediately convince many of them of the benefits of his approach.

Just as his first publication in optics in sparked an intense debate about the proper methods for investigating the nature of light—and much else besides—his Principia sparked an even longer lasting discussion about the methodology that philosophers should adopt when studying the natural world. This discussion began immediately with the publication of the Principia , despite the fact that its first edition contained few explicit methodological remarks Smith —39 and it intensified considerably with the publication of its second edition in , which contained many more remarks about methodology, including many attempts at defending the Newtonian method.

Indeed, many of Newton's alterations in that edition changed the presentation of his methods.

Discussions of methodology would eventually involve nearly all of the leading philosophers in England and on the Continent during Newton's lifetime. In Cartesian natural philosophy, all natural change is due to the impacts that material bodies make upon one another's surfaces this is reflected in Descartes's first two laws of nature. The concept of a force plays little if any role. Unlike Descartes, Newton placed the concept of a force at the very center of his thinking about motion and its causes within nature. But Newton's attitude toward understanding the forces of nature involved an especially intricate method that generated intense scrutiny and debate amongst many philosophers and mathematicians, including Leibniz Garber This was a confusing notion at the time.

Perhaps it is not difficult to see why that should be so. To take one of Newton's own examples: suppose I hit a tennis ball with my racquet—according to Newton, I have impressed a force on the tennis ball, for I have changed its state of motion hopefully!