Google Scholar. German trans. Wolfers ed. Mathematische Grundlagen der Naturphilosophie, Ed Dellian ed. Horsley ed. Breidert ed. Ernst Mach, Die Mechanik in ihrer Entwicklung, repr. Frankfurt a. This is still an open problem in quantum physics; cf. Gino Tarozzi A. Principia, definition 3; cf. Horsley ibid. Also Wolfgang Breidert ed. Windelband, Lehrbuch der Geschichte der Philosophie, H. Heimsoeth ed. Horsley op. III, p. Max Jammer, op. Ideas 23 , p. Richard S. Dijksterhuis, op. Steven Weinberg, Teile des Unteilbaren, Heidelberg , p.
Principia book III, regula philosophandi No. Horsley, op. 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.
Shop Certain Philosophical Questions Newtons Trinity Notebook
Newton was perfectly well aware that the notion of absolute space is not unproblematic. 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. 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. 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.
Catalogue Entry: THEM00092
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!
We have a reasonably good idea of what the tennis ball is, of what the racquet is, and even of what I am, and a Cartesian might wish to stop her analysis there. The ball, 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 likely that a force is itself a physical thing in the sense of being a substance, to use a philosophical notion popular in Newton's day as we saw above in his first optics paper.
So when I hit the tennis ball over the net, the force I impressed on it was the action of hitting the ball, or an action associated with hitting the ball, and not a property of me or of the ball after the action had ceased. This idea confused many of Newton's readers. By the mid-eighteenth century, the time of Hume's analysis of causation in the Treatise and the Enquiry , many philosophers started to think that actions and other kinds of event are important items to have in one's ontology, and they often contended in particular that causal relations hold between events.
But in Newton's day, philosophers typically regarded objects or substances as the causal relata one finds an equivocation between thinking of events and thinking of objects as the relevant causal relata even in Hume. So actions were difficult to analyze or often left out of analyses. As a result, Newton's conception of force proved confusing. Moreover, it was unclear to many of Newton's mechanist readers how his forces fit into their rather austere ontological view that material bodies consist solely of properties such as size, shape, mobility and solidity.
Newton did try to clarify his method of characterizing forces. If one brackets the question of how to understand forces as ephemeral actions that do not persist after causal interactions have ceased, one can make progress by conceiving of forces as quantities. In particular, since Newton's eight definitions and three laws indicate that forces are proportional to mass and to acceleration, and since mass—or the quantity of matter, a concept Newton transformed from its Cartesian origins, where it was understood as a measure of a body's volume—and acceleration are both quantities that can be measured, Newton gives us a means of measuring forces.
This is crucial to his method. If one thinks of forces as measurable quantities, moreover, then one can attempt to identify two seemingly disparate forces as in fact the same force through thinking about measuring them. For instance, in Book III of the Principia , Newton famously argues in proposition five and its scholium that the centripetal force maintaining the planetary orbits is in fact the same as the force of gravity, viz. This was a revolutionary idea at the time, one rendered possible in the first place by Newton's way of thinking about forces as quantities.
This idea then led Newton to the even more revolutionary view in proposition seven of Book III that all bodies gravitate toward one another in proportion to their quantity of matter. That is, it led him to the idea of universal gravity, a view that shocked many of his Continental readers in its boldness. This helped to unify what were once called superlunary and sublunary phenomena, a unification that was obviously crucial for later research in physics. Again, the idea was enabled by Newton's abstract way of understanding forces—without conceiving of a force as involving any specific mechanism or type of physical interaction, Newton thought of forces as quantities that are proportional to other features of nature.
Despite his evident success in obtaining what we now call the law of universal gravitation, Newton admits that he lacks another kind of knowledge about gravity; this lack of knowledge directly reflects an aspect of his abstract characterization of forces. This interpretation is sometimes coupled with the view that some British philosophers in the late seventeenth century regarded Cartesianism as overly reliant on hypotheses in reaching conclusions about phenomena.
But this interpretation may be hard to square with Newton's texts. For instance, in the Scholium to Proposition 96 of Book I of the Principia , Newton discusses hypotheses concerning light rays. Similarly, in query 21 of the Opticks , he proposes that there might be an aether whose differential density accounts for the gravitational force acting between bodies. Hence Newton thinks that he has established the fact that gravity acts on all material bodies in proportion to their quantity of matter, but he has not established the existence of the aether.
By the time of the General Scholium, Newton was increasingly embroiled in philosophical disputes with Leibniz. In order to account for the motions of the planetary bodies in his Tentamen of , Leibniz introduces ex hypothesi the premise that some kind of fluid surrounds, and is contiguous to, the various planetary bodies, and then argues that this fluid must be in motion to account for their orbits. A debate between the two philosophers on this score would bring them to the question of the mechanical philosophy: whereas Newton would object to Leibniz's reasoning on methodological grounds, Leibniz would reply that Newton's theory of gravity involves action at a distance, which his vortex hypothesis avoids see below for more details.
Once the Principia was published, Newton had a vexed relationship with the mechanical philosophy, an orientation within natural philosophy that is associated strongly with nearly every significant early modern philosopher, including Descartes, Boyle, Huygens, Leibniz, and Locke. His second law indicates that a body moving rectilinearly will continue to do so unless a force is impressed on it. This is not equivalent to claiming that a body moving rectilinearly will continue to do so unless another body impacts upon it. A vis impressa —an impressed force—in Newton's system is not the same as a body, nor even a quality of a body, as we have seen; but what is more, some impressed forces need not involve contact between bodies at all.
For instance, gravity is a kind of centripetal force, and the latter, in turn, is a species of impressed force. Hence a body moving in a straight line will continue to do so until it experiences a gravitational pull, in which case it will deviate from a straight line motion, even if no body impacts upon it. Indeed, the gravitational pull might originate with a mass that is millions of miles away. As we have seen, an impressed force is an action exerted on a body. Hence the gravity exerted on a moving body is an action the Latin term is actio , which is obviously a causal notion.
This is not an empirical claim per se ; it is merely a reflection of Newton's laws, together with his notion of an impressed force, and his further idea that gravity is one kind of impressed force. These elements of the Principia make conceptual room for a causal interaction between two bodies separated by a vast distance, one enabled by Newton's concept of an impressed force.
Aspects of this idea became known in philosophical circles as the problem of action at a distance Hesse Many of Newton's most influential contemporaries objected vigorously to the fact that his philosophy had made room for—if not explicitly defended—the possibility of distant action between material bodies. Leibniz and Huygens in particular rejected this aspect of Newton's work in the strongest terms, and it remained a point of contention between Newton and Leibniz for the rest of their lives.
Both Leibniz and Huygens were convinced that all natural change occurs through contact action, and that any deviation from this basic mechanist principle within natural philosophy would lead to serious difficulties, including the revival of outmoded Aristotelian ideas. Newton's gloss on Rule 3 in the Principia , discussed below, only made matters worse from Leibniz's point of view, since it tacitly or functionally treats gravity as a kind of universal quality akin to extension or impenetrability. But unlike them, it was occult, imperceptible and unintelligible.
Newton was well aware that the Principia's methodology of discovering the forces present in nature was controversial, and not merely because of questions about action at a distance. So when he revised the text, under the editorship of Roger Cotes, for publication in a second edition in , he added other methodological remarks. The third rule concerns an induction problem: we have perceptions and experiments that provide us with knowledge of the objects and natural phenomena in our neck of the universe, but on what basis can we reach a conclusion concerning objects and phenomena throughout the rest of the universe?
Newton himself reached such a conclusion about gravity in proposition seven of Book III of the Principia. Part of Newton's answer is presented in rule Those qualities of bodies that cannot be intended and remitted [i. We know, say, that a clump of dirt has certain qualities such as extension and mobility, but how do we know that the entire earth has such qualities? It surely lies beyond the reach of our experiments, or at any rate, it did in Newton's day. Newton says that the sun and the earth interact according to his law of gravity, but how do we know that the sun contains a quantity of matter, that it is a material body with the same basic qualities that characterize the earth or the moon?
It wasn't at all obvious at the time that the sun is a material body at all. Newton thinks that gravity reaches into the very center of the sun, but what did anyone in know about such things? Newton glosses his third rule in part as follows, connecting it with his laws of motion:. That all bodies are movable and persevere in motion or in rest by means of certain forces which we call forces of inertia we infer from finding these properties in the bodies that we have seen.
The extension, hardness, impenetrability, mobility, and force of inertia [ 23 ] of the whole arise from the extension, hardness, impenetrability, mobility and force of inertia of each of the parts; and thus we conclude that every one of the least parts of all bodies is extended, hard, impenetrable, movable, and endowed with a force of inertia. And this is the foundation of all natural philosophy. Newton — But at the end of his gloss of Rule 3, Newton applies this same or analogous reasoning to the force of gravity, arguing as follows: since we experience the fact that all bodies on or near the earth gravitate toward the earth—in cases such as free fall—and that the moon gravitates toward the earth, etc.
This argument would appear to suggest that gravity—which, as we have seen, is a kind of impressed force, an action—is somehow akin to qualities like extension and impenetrability. So is Newton suggesting that gravity is actually a quality of all bodies? Leibniz and his followers pounced: if Newton is, at least tacitly, regarding gravity as a quality, then he had indeed revived the occult qualities of the Scholastics, for here we have a quality that is not explicable in mechanical terms, and what is worse, one that is not intelligible to philosophers.
This question became the subject of intense debate throughout the first half of the eighteenth century see the last section below. Although the first editions of Newton's Principia and of Locke's Essay were published a mere three years apart in and , respectively their authors worked independently and did not influence the first editions of one another's principal texts.
But right around the time of the publication of the first edition of the Essay , Newton and Locke became close friends and apparently influenced each other's thinking about philosophy, religion, and theology in various ways they first met in London in Most historians think that each questioned the standard Anglican interpretation of the Trinity, contending that Jesus of Nazareth was not a divine figure on the same level as God the creator.
Interpreting the Bible through historical and philosophical analysis in a fashion that was not constrained by standard Anglican doctrine in the late seventeenth century was fantastically important to Newton, occupying his attention for many years. Given their controversial and politically sensitive nature, his so-called anti-Trinitarian views were largely kept secret among a small circle of friends. Locke was apparently sympathetic with Newton's approach. With respect to their public views, Newton and Locke were often taken to represent two aspects of the same experimental-philosophical approach toward the close of the seventeenth century Stein ; Wilson —; and Domski forthcoming.
It is perhaps not difficult to understand why, for Newton was mentioned in one of the most famous passages in all of Locke's writings. The Commonwealth of Learning, is not at this time without Master-Builders, whose mighty designs, in advancing the sciences, will leave lasting monuments to the admiration of posterity; but every one must not hope to be a Boyle, or a Sydenham; and in an age that produces such masters, as the great—Huygenius, and the incomparable Mr. Newton, with some other of that strain; 'tis ambition enough to be employed as an under-labourer in clearing ground a little, and removing some of the rubbish, that lies in the way to knowledge; which certainly had been very much more advanced in the world, if the endeavors of ingenious and industrious men had not been much cumbred with the learned but frivolous use of uncouth, affected, or unintelligible terms, introduced into the sciences, and there made an art of, to that degree, that philosophy, which is nothing but the true knowledge of things, was thought unfit, or uncapable to be brought into well-bred company, and polite conversation.
Locke Clearly, Locke seeks in this passage, among other things, to align his work in the Essay with the work of figures such as Newton. This would become a popular conception of Newton's philosophical approach. Locke may have regarded Newton as a fellow enthusiast for the experimental philosophy, but there are reasons to think that his embrace of the mechanical philosophy presented him with a difficulty in interpreting the consequences of Newton's theory of universal gravity in the Principia.
For Newton's theory seemed to be in tension with a mechanist constraint on views of causation, at least from Locke's own point of view. Impulse refers here to contact action. In correspondence with Locke that would prove to be influential, Bishop Edward Stillingfleet questioned this view from the Essay , contending that Locke must jettison the idea of human liberty if he insists that bodies can operate solely by impulse, presumably on the grounds that the human will cannot be understood to cause bodily action in that manner. In a famous exchange, Locke responded in part by reformulating his commitment to the mechanist view that all causation involving material bodies must be by contact impulse alone:.
And so I thought when I writ it, and can yet conceive no other way of their operation. But I am since convinced by the judicious Mr. Newton's incomparable book, that it is too bold a presumption to limit God's power, in this point, by my narrow conceptions. The gravitation of matter toward matter by ways inconceivable to me, is not only a demonstration that God can, if he pleases, put into bodies, powers and ways of operations, above what can be derived from our idea of body, or can be explained by what we know of matter, but also an unquestionable and every where visible instance, that he has done so.
And therefore in the next edition of my book, I shall take care to have that passage rectified. Locke vol. This was not merely his privately held view. For instance, near the beginning of his Elements of Natural Philosophy , Locke writes:. Two bodies at a distance will put one another into motion by the force of attraction; which is inexplicable by us, though made evident to us by experience, and so to be taken as a principle in natural philosophy.
Such powers or ways of operations would in this case result in gravitational interactions, presumably amongst bodies that are spatially separated from one another by great distances. So Locke has concluded that bodies can operate on one another through some means other than impulse, but he retains his firmly held belief that any such operation is not intelligible to us. Locke did apparently accept the conclusion that spatially separated bodies causally interact with one another in accordance with the law of universal gravitation, but concluded that the law itself did not render that causal interaction intelligible.
This is precisely the kind of reaction to Newton's theory of universal gravity bemoaned by Leibniz, who would argue that any operations or powers attributed to material bodies must meet the basic criterion of intelligibility established by the mechanist approach; he might also be inclined to argue that any laws regarded as governing the interactions of bodies must also meet that criterion by being derivable in some way from our basic concept of matter see below. Regardless, this is an excellent example of a case in which Newton's theory in the Principia had a direct impact on the development of philosophical views of causation in the late seventeenth century.
When the great English natural philosopher Robert Boyle died at the end of , he endowed a lecture series designed to promote Christianity against what Boyle took to be the atheism that had infected English culture after the revolutionary period of the mid-century. When preparing his lectures for publication—they had been presented to a public audience in London in —Bentley conferred with Newton, hoping to solicit his help in deciphering enough of the Principia to use its results as a bulwark against atheism Bentley Newton obliged, and a famous correspondence between the two began eventually published as Bentley The exchange is of great philosophical interest, for Bentley elicited a number of important clarifications that have no peer within Newton's published oeuvre.
Bentley sought Newton's assistance in particular because he wanted guidance in divining how the theory of the Principia indicates that the solar system must have been designed by an intelligent agent and could not have arisen through the physical interactions of material bodies. In the first edition of the Principia in , Newton had made such a claim in a very brief statement Newton vol. Through their correspondence, Bentley learned that from Newton's point of view, the positions of the planets relative to one another—and especially to the sun—indicate that mere chance, or the ordinary physical interactions of the planetary bodies, could not have placed each planet in precisely the right orbit to maintain a solar system like ours for an extended period of time.
With this argument, Newton seems to be indicating that mere chance would have produced an unstable planetary system, one in which the planets would eventually either be too strongly attracted to the sun, falling into it, or be too weakly attracted, flying off into space. In this episode, a theologian appeals to the new authority of Newtonian natural philosophy when attempting to undermine atheism. And that was apparently the very kind of interchange that Boyle had envisioned when endowing the lecture series. Newton's correspondence with Bentley is justly famous for another reason.
The criticisms of Newton's theory of gravity by Leibniz and Huygens, outlined briefly above, would prove essential to the Continental reception of Newtonian natural philosophy more generally in the late seventeenth and early eighteenth centuries. Newton presented no such defense; moreover, there is actually evidence that Newton himself rejected the possibility of action at a distance, despite the fact that the Principia allows it as a conceptual possibility, if not an empirical reality.
The evidence lies in Newton's correspondence with Bentley. In February of , after receiving three letters from Newton, Bentley wrote an extensive reply that attempted to characterize Newton's theory of gravity, and his understanding of the nature of matter, in a way that could be used to undermine various kinds of atheism. With the three earlier letters as his guide, Bentley makes the following estimation of Newton's understanding of the possibility that gravity could somehow be an essential feature of material bodies:.
For let them assign any given time, that Matter convened from a Chaos into our System, they must affirm that before the given time matter gravitated eternally without convening, which is absurd. Newton —vol. In reply to this letter, Newton refers back to this second proposition, making one of the most famous of all his pronouncements concerning the possibility of action at a distance:. The last clause of the second position I like very well.
It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.
Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers. Newton —3 [ 24 ]. It certainly seems that Newton was uncomfortable with the very idea of action at a distance.
Certain Philosophical Questions: Newton's Trinity Notebook
But of course, things are not always as they seem in interpretations of difficult philosophical texts: some historians and philosophers have argued strongly that there are other readings of the letter. The idea might be roughly as follows: Newton wanted to leave open the possibility that God had endowed bodies with a power to act at a distance on one another, a position that is at least reminiscent of Locke's view in his correspondence with Stillingfleet see above.
The reason is that Newton held the standard view at the time that matter itself is passive, requiring some kind of divine intervention in order to interact causally with other matter. If the world consisted solely of a bunch of material objects, say rocks floating in interstellar space, then they would not experience any changes in their states of motion unless some external force acted upon them—if left to its own devices, matter is passive and does not move.
And this, in turn, might lead us on a slippery slope to atheism, for on this view, matter would act on its own, without any divine intervention. Or so Bentley and Newton might be interpreted. Clearly, one reasonable motive for uncovering a nuanced interpretation of Newton's letter to Bentley is the obvious fact that Newton apparently regarded action at a distance as perfectly possible when writing the Principia. Indeed, it is difficult to reconcile the Principia with the Bentley correspondence. One can argue that although he left open the possibility of action at a distance in his main work, Newton himself did not accept that possibility because of his more general commitments Janiak and forthcoming.
The debate on such matters continues unabated.
However, regardless of Newton's personal attitude toward distant action among material bodies, his mechanist interlocutors and readers continued to object to the physical theory outlined in Book III of the Principia on the grounds that, at the very least, it left open the conceptual possibility of a kind of action that cannot in fact exist anywhere in nature. That remained one of Leibniz's principal objections against Newtonian natural philosophy throughout the last twenty years of his life, animating his correspondence with numerous figures, including most prominently the Newtonian theologian and philosopher Samuel Clarke.
In many ways, Leibniz and Newton grew up in the same philosophical environment: each came of age during the heyday of Cartesianism, and each argued in particular that Cartesian views in natural philosophy failed to include a sufficiently robust conception of the forces of bodies in nature. Force would lie at the center of Newton's mature physics Westfall , and would become even more central to Leibniz's thinking, playing an essential role in his metaphysics as well Garber The two knew one another as mathematicians already in the s, and as we have seen, Leibniz discussed Newton's first optical work with Huygens; but after the publication of the Principia in , their philosophical relationship, which was marked originally by respectful disagreement, began to develop in earnest.
Just two years after the Principia appeared, Leibniz published his Essay on the Causes of Celestial Motions or Tentamen , and then in , the two corresponded with one another on both mathematical and philosophical issues Newton —9. He had described such a fluid medium, or vortex, in detail in his own Essay. The background to Leibniz's comment is his unwavering commitment—one shared by Huygens, whose theory of gravity's cause Leibniz mentions in the same letter—to the mechanical philosophy's requirement that all changes in motion must be the result of bits of matter impacting on one another.
Thus for Leibniz, one can e. For since celestial motions are more regular than if they arose from vortices and observe other laws, so much so that vortices contribute not to the regulation but the disturbance of the motions of planets and comets; and since all phenomena of the heavens and of the sea follow precisely, so far as I am aware, from nothing but gravity acting in accordance with the laws described by me; and since nature is very simple, I have myself concluded that all other causes are to be rejected and that the heavens are to be stripped as far as may be of all matter, lest the motions of planets and comets be hindered or rendered irregular.
But if, meanwhile, someone explains gravity along with all its laws by the action of some subtle matter, and shows that the motion of planets and comets will not be disturbed by this matter, I shall be far from objecting. Newton —9. This is obviously a passage rich with significant meaning. Leibniz clearly insisted that vortices, or some physical object or fluid, must be in contact with the planetary orbits if we are to explain why they deviate from the tangents along the orbital paths when circling the sun.
Newton's reply is that giant swirling fluids in the heavens would actually disturb the regular orbital paths, and the paths of comets through the solar system. That reply might be thought of as empirical in character, for it depends on observational data regarding the actual paths of the heavenly bodies. But Leibinz's perspective is obviously not merely empirical in character: he does not postulate vortices or anything akin to them on observational grounds; he infers their existence because he thinks we know perhaps we can add, we know a priori that physical bodies such as comets or planets can deviate from a rectilinear path—they can accelerate—only if some other physical item impacts upon them.
Since gravity is an action—clearly, a causal notion—it seems clear that Newton's answer to Leibniz's idea that vortices cause the planetary orbits is that gravity itself causes them, and nothing else. And it is not much of a leap to conclude, in turn, that this reply commits Newton to the idea that bodies involved in gravitational interactions, such as the sun and the earth, act at a distance on one another through the force of gravity. It is not hard to divine why Leibniz and Huygens would have concluded that Newton had relinquished any commitment to the norms of the mechanical philosophy.
Despite Leibniz's and Huygens's criticisms of his theory of gravity in particular, and his methods in natural philosophy in general, Newton stuck to his guns. Nearly twenty years after their illuminating exchange in , Leibniz and Newton narrowly missed a second opportunity to discuss their philosophical differences directly. In May of , Leibniz published a letter to Nicholas Hartsoeker that was highly critical of the Newtonians; it was published in English translation in the Memoirs of Literature , a journal to which Roger Cotes, the editor of the Principia's second edition, held a subscription Newton Here is part of Newton's paraphrase of Leibniz's original letter:.
But he [i. For a miracle at least must keep the planet in. But certainly God could create planets that should move round of themselves without any other cause than gravity that should prevent their removing through the tangent. For gravity without a miracle may keep the planets in.
Thus Newton repeats the view he mentions to Leibniz in , viz. But in this posthumously published letter, Newton did not merely repeat his basic understanding of gravity from his exchange with Leibniz; he also included a wider discussion of mechanist norms within philosophy more generally. Again, Newton begins by quoting Leibniz:.
But Mr. Leibniz goes on. Indeed, Leibniz raises the stakes by contending that God himself could not explicate how such interactions are possible based on the idea of matter. Leibniz would argue, perhaps on metaphysical grounds, that any laws said to govern the interaction of bodies, and any qualities attributed to bodies, must be intelligible in the terms available to philosophers through the mechanist orientation.
In particular, laws and qualities must be intelligible in terms of the shape, size, motion and impenetrability or solidity of bodies. Newton's reply to Leibniz's argument is illuminating. Instead of presenting a narrow defense of his view, perhaps by denying that he has postulated any non-mechanical causation with his theory of gravity, he challenges the mechanical philosophy itself by contending that it should not be understood as holding for all natural phenomena:.
The same ought to be said of hardness. So then gravity and hardness must go for unreasonable occult qualities unless they can be explained mechanically. And why may not the same be said of the vis inertiae [force of inertia] and the extension, the duration and mobility of bodies, and yet no man ever attempted to explain these qualities mechanically, or took them for miracles or supernatural things or fictions or occult qualities.
They are the natural, real, reasonable, manifest qualities of all bodies seated in them by the will of God from the beginning of the creation and perfectly incapable of being explained mechanically, and so may be the hardness of primitive particles of bodies. And therefore if any man should say that bodies attract one another by a power whose cause is unknown to us, or by a power seated in the frame of nature by the will of God, or by a power seated in a substance in which bodies move and float without resistance and which has therefore no vis inertiae but acts by other laws than those that are mechanical: I know not why he should be said to introduce miracles and occult qualities and fictions into the world.
For Mr. Leibniz himself will scarce say that thinking is mechanical as it must be if to explain it otherwise be to make a miracle, an occult quality, and a fiction. The first aspect of Newton's argument, it seems, is to indicate that mechanical explanations are predicated on referencing certain kinds of qualities when investigating natural phenomena, and that these qualities themselves are therefore not subject to mechanical explanation. For instance, since mechanist explanations—say, of the way in which magnets attract iron filings across a table—must refer to qualities such as the extension of the bodies subject to the explanations, then we cannot give a mechanist explanation of extension itself.
The second aspect of Newton's argument is more intriguing—it also harks back to Locke's discussion with Stillingfleet, for Locke had contended that God may have superadded not only gravity to material bodies, but also the power of thought, linking them because he believed that neither could be rendered intelligible using any philosophical means at his disposal. That is, from Locke's point of view, we know that human beings—which are, or at least contain, material bodies with size, shape, motion and solidity, along with parts characterized by those qualities—are capable of thought, but since we cannot discern how any material thing could possibly have that capacity, we conclude that God may have superadded that feature to us, or to our bodies.
Thought and gravity are dis-analogous in the sense that we did not require anything like Newton's theory to convince us that human beings can think, but they are otherwise analogous. Newton then attempts to make the following argument: since Leibniz would have to agree that thinking is not a mechanical process, and not mechanically explicable, he must agree that there is at least one aspect of the world that has the following two features, 1 it is not mechanical; and, 2 it is clearly not to be rejected on that ground alone. He attempts to liken gravity as he understands it to thinking as he believes Leibniz is required to understand it , arguing that despite the fact that it is not mechanical—it cannot be explained mechanically—it should not be rejected on that ground.
This argument may be predicated on the view that human beings, material things, or at least partially material things, do the thinking, rather than immaterial things, such as minds or souls, for if one attributes all thought to an immaterial mind or soul, then there is no pressure to say that anything in nature, or perhaps even any aspect of anything in nature, has a feature that cannot be mechanically explicated.
If one accepts Locke's view apparently also endorsed by Newton that we should attribute thinking to material things, or to aspects of material things, then perhaps Newton has successfully followed Locke in likening gravity to thought, thereby making room for aspects of nature that are not mechanical after all.
This vexing issue would continue to generate debates amongst Newton's and Leibniz's various followers in England, and on the Continent, respectively. Leibniz's most extensive debate with the Newtonians would not occur until the very end of his life. His celebrated correspondence with Samuel Clarke, Newton's friend and supporter in London in the early part of the eighteenth century, is his most famous interaction with the Newtonians, occurring right before his death in Clarke and Leibniz Leibniz fomented the correspondence in November of by sending a short, provocative letter to Princess Caroline of Wales, one designed to provoke a response from Newton's circle in London.
Leibniz knew well that Princess Caroline was a leading intellectual and political figure in England at the time, one who would surely wish to see the views of her countrymen defended against Leibniz's rather shocking claims about the religious consequences of Newtonian thinking. He opens his initial letter by mentioning both Locke and Newton, along with the issues about materiality and thinking that arose in his near exchange with Newton in Natural religion itself seems to decay [in England] very much.
Many will have human souls to be material; others make God himself a corporeal being. Locke and his followers are uncertain at least whether the soul is not material and naturally perishable. Sir Isaac Newton says that space is an organ which God makes use of to perceive things by. But if God stands in need of any organ to perceive things by, it will follow that they do not depend altogether on him, nor were produced by him. Clarke and Leibniz L 1: 1—3. Thus Leibniz charges both Lockeans and Newtonians with presenting philosophical views of the human and of the divine that lead to theologically unsavory consequences, such as the idea that the human soul might be material, and the view that God must employ something akin to an organ in order to perceive happenings in the world.
These were fighting words. Moreover, Samuel Clarke had given the Boyle lectures in and again in , so he was a public figure associated with the state of Christianity in England. Once Clarke took the bait, replying that same month to Leibniz's charges, Locke's views quickly dropped from view and the two focused specifically on Leibniz's numerous objections to Newtonian ideas and methods.
But why did Clarke respond on Newton's behalf, and what was Newton's actual role in the correspondence? There is no documentary evidence, such as letters, between Clarke and Newton indicating the contours of his role; then again, at this time, both men lived in London and Clarke was Newton's parish priest, so the lack of letters or other papers is perhaps unsurprising.
In any event, there is no doubt that Clarke was taken by Leibniz and his followers to be speaking for Newton and his circle. Nonetheless, there are certainly aspects of Clarke's views that may deviate from Newton's own opinions, so it would be unwise to as it were remove Clarke from our conception of the correspondence by regarding it as effectively Newton's work.
Leibniz's correspondence with Clarke is methodologically characteristic: he leaves much of his own systematic and complex metaphysical theorizing—including the monadology—in the background, bringing to the fore only those elements that are both necessary for his criticisms of the Newtonians and also likely to garner support from Clarke. Thus the key to many of Leibniz's criticisms is the principle of sufficient reason PSR , which he knows Clarke will endorse although with a distinct conception of its scope: Leibniz asserts, while Clarke denies, that the principle demands that each act of divine willing requires a reason; for Clarke, divine willing itself is reason enough for some physical state of affairs to obtain, or event to occur.
Leibniz argues in particular that several key aspects of the Newtonian worldview are simply incompatible with the PSR, including the idea of absolute space. If space were in fact completely independent of all physical objects and all relations among them, as the Newtonians seem to assert, then a problem arises:. I have many demonstrations to confute the fancy of those who take space to be a substance or at least an absolute being. But I shall only use, at present, one demonstration, which the author here gives me occasion to insist upon.
I say, then, that if space were an absolute being, something would happen for which it would be impossible that there should be a sufficient reason—which is against my axiom. And I prove it thus: space is something absolutely uniform, and without the things placed in it, one point of space absolutely does not differ in any respect whatsoever from another point of space.
Now from this it follows supposing space to be something in itself, besides the order of bodies among themselves that it is impossible there should be a reason why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner and not otherwise—why everything was not placed the quite contrary way, for instance, by changing east into west.
But if space is nothing else but this order or relation, and is nothing at all without bodies but the possibility of placing them, then those two states, the one such as it is now, the other supposed to be the quite contrary way, would not at all differ from one another.