Philosophy 22 Lecture Notes

Isaac Newton

Sir Isaac Newton (1642-1727) is without a doubt the best known and most influential of all the philosophers of the seventeenth century. His fame is the result of his scientific investigations, but as we have seen with other seventeenth century philosophers, there was at the time no clear line drawn between scientific and philosophical inquiry. Indeed, the name of his epoch-making book was Mathematical Principles of Natural Philosophy (1687). And as we will see, Newton's scientific views were closely linked with his views of the ultimate nature of reality (metaphysics) and the way in which it is known (epistemology).

The Reception of Newton's Natural Philosophy

It difficult for us now to conceive, given the eventual triumph of Newtonianism, how fierce was the opposition to Newton's doctrines when he first introduced them. The main opposition was centered on the European continent and led by followers of Descartes. Leibniz, who otherwise was a harsh critic of the Cartesians, joined with them in condemning Netwon's views. (A summary of his dispute with Newton is given below.) As a consequence, Newton published a number of philosophical observations on his system to defend it from the barrage of criticism.

It was not until well into the eighteenth century that such noteworthy philosophers as Voltaire (1694-1778) in France and Immanuel Kant (1724-1804) in Prussia were to embrace a Newtonian world-view. At the beginning of the nineteenth century, it was the Frenchman Pierre Laplace (1749-1827), who put the finishing touches on Newton's system of the world. And, of course, at the beginning of the twentieth century, the German-Swiss-American Albert Einstein exposed its inadequacies.

During Newton's lifetime, science was in a very unsettled state. A number of thinkers, including Leibniz, Christian Huygens (1629-1695) and Robert Hooke (1635-1703), were making some progress in mechanics. Robert Boyle (1627-1691) in England, a confidante of Newton's, was forcefully promoting atomism. Newton's work superceded that of all of them, but he acknowledged that he was able to see farther only because he was standing on the shoulders of giants.

The State of Natural Philosophy Before Newton

Let us now review the situation in astronomy as Newton found it. Copernicus had proposed the heliocentric theory of the solar system, and Galileo had provided compelling arguments to accept heliocentrism as a physical reality. Johannes Kepler (1571-1630) at the beginning of the seventeenth century made a crucial contribution to understanding the motions of the planets. He found that their motions conform to an elliptical orbit, with the sun at one focus. Moreover, he established the regularity of planetary motion. Equal areas within the ellipse are swept out by the radius vector in equal times. But Kepler was unable to provide a satisfactory reason for the regularity, nor did he devise a plausible explanation of its cause (he thought it was magnetic).

No improvements on Kepler's results were made before Newton. Some mathematical variations on the ellipse were proposed, and Descartes ventured his hypothesis of the vortices. This would have provided a mechanical account of the motions of the planets, on the analogy with small objects which are whisked around in a whirlpool. But as a twentieth century observer noted, Descartes's hypothesis is "pure speculation unsupported by any facts" (J. L. E. Dryer, A History of Astronomy from Thales to Kepler, p. 422). Newton was to show later that it is utterly impossible. Thus he was left with two tasks: to give a more fundamental explanation of the behavior of the orbits of the planets, and to show by what physical means they are produced.


Newton's solution began with widely-accepted theory then broke with it decisively. Like Galileo and Descartes , Newton attributed to bodies the property of inertia. A body will perserve its state of rest or its state of uniform motion in a straight line unless acted upon by some external force. Since the planets do not move in a straight line on a tangent to their orbit, there is some other force which keeps them on their orbit. If the force is one of attraction, then there can be an equilibrium between the tendency to move tangentially to its orbit and the tendency to move toward the sun. The result is a curved path. A figure taken from Principia Mathematica illustrates the composition of forces.


The force of attraction, Newton continued, is mutual between bodies. It is a function of the masses of the two bodies and the square of the distances between them. From this, Newton was able to derive the elliptical orbits of the planets and Kepler's law of their motion from observations. He generalized his results to the orbit of the earth's moon and those of Jupiter and Saturn. He also applied his results about mutual attraction to explain the tides in terms of the attraction of the sea by the sun and moon. The end product was a comprehensive "system of the world," based on a single explanatory principle—a monumental achievement.

Nonetheless, critics immediately attacked what they saw as the weak point in Newton's theory: gravity, the force of attraction. Newton claimed that it acts at a distance, as between the sun and the earth, or between the moon and the sea. Action at a distance is a direct violation of the mechanical principle that all motion is by contact. Newton's opponents went so far as to call attraction an "occult quality," on the order of a medieval "virtue" which explains nothing.

Newton replied to his critics that he had demonstrated from the phenomena that attraction is a property of some bodies and generalized this claim to include all bodies. In the General Scholium to the Principia, written some twenty-six years after the publication of its first edition, Newton put the matter this way: "To us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and our sea."


Newton recognized that he was not in possession of the cause of gravitation, of whose existence he was convinced. He tried to give a mechanical explanation in terms of an ethereral substance pervading all bodies and filling the space between them. But he was never able to demonstrate its existence in the way he thought he had demonstrated the existence of gravitation itself. In the General Scholium, he asserted that experimental philosophy has no room for such "hypotheses." He would not, like his opponents, invent them merely to fill an explanatory gap.

The statement "hypotheses non fingo" ("I do not frame hypotheses") is one of Newton's most notorious pronouncements. For Newton did operate with hypotheses, even in the Principia, where he gave as "Hypothesis I" that "the center of the system of the world is immovable." In his Optics, Newton formulated a number of "queries," which were hypotheses in all but name. Moreover, he introduced into his natural philosophy absolute space, time, and motion, which he recognized he could not deduce from the phenomena. Finally, Newton in the General Scholium brought God into natural philosophy, as the cause of the order in the world. Thus Newton could not escape the lure of metaphysics, and it was on this ground primarily that he fought his epic battle with Leibniz.

Newton and Leibniz

The "Leibniz-Clarke Correspondence" is a series of letters exchanged through intermediaries between Leibniz and the Newtonian Samuel Clarke (1675-1729). Leibniz had already crossed swords with Newton over accusations of plagiarism in the invention of the calculus. He later criticized the theory of gravitation, which led to a further exchange. His letter to Caroline, Princess of Wales, was passed on to Clarke, thus initiating the exchange. Caroline had hoped, in vain, to reconcile the two philosophical giants of her age. The correspondence ended with the death of Leibniz after Clarke had written a reply to Leibniz's fifth letter. Clarke later translated Leibniz's letters and published the whole exchange. Of the exchange itself, Leibniz wrote, "I am at present engaged in a philosophical quarrel with Newton or, what amounts to the same thing, with his defender Clarke" (Letter to Bernoulli, June 1716).

Space as God's "Sensorium"

In his letter to Caroline, Leibniz expressed concern about the effects of Newton's natural philosophy on religious belief, specifically that it supports materialism. Newton had described space as God's "sensorium," which Leibniz understood to mean "sense organ." This suggests that God's relation to the world is not that of creator but rather of a kind of "world soul" (as Leibniz put it later). We shall follow this thread of the debate first, turning later to the second charge leveled against Newton in the first letter.

As with many of the points discussed, there was disagreement over the meaning of the term involved, 'sensorium.' Clarke immediately denied that it means 'sense organ,' and brushed off Leibniz's citation of a philosophical dictionary which defined it in this way. What Newton meant was that space is God's presence in the world. Leibniz's alternative, Clarke contended, is to banish God from the world as an "supramundane" being. Here Leibniz was forced to clarify his language: "To say that God is above the world is not denying that he is in the world" (Leibniz's Third Paper, Sec. 15).

The real issue, according to Leibniz is whether God is in the world by virtue of space. God is in the world in the sense of sustaining the existence of the world, but "God perceives things in himself. Space is the place of things, and not the place of God's ideas: unless we look upon space as something that makes an union between God and things, in imitation of the imagined union between the soul and the body; which would still make God the soul of the world" (Leibinz's Fourth Paper, Sec. 29).

God's Workmanship

Leibniz's second accusation against Newton is that God is diminished because God is required periodically to make adjustments to the course of the universe. (Newton had held that the interactions between the planets and the comets would lead gradually to a breakdown of the order of the solar system.) God's need to intervene indicates a defect in God's production, which would have to be accounted for by an imperfection in God's craftsmanship. Clarke responded by claiming that this involvement in the world is most appropriate for its ruler. Leibniz's God, by contrast, is comparable to a monarch who is entirely uninvolved with the governance of his kingdom. To this Leibniz responded that his conception of God is like that of a monarch so wise to have set up the kingdom so that it would take care of itself.


If God were to intervene in the course of the world, it would be a miracle, and Leibniz maintained that miracles should not be used to explain natural events. (On the other hand, if it is not a miracle, then God would be part of nature, as "world-soul.") Clarke replied that there is no real distinction between a miraculous act of God and a non-miraculous act, other than from the human perspective. We call those acts miraculous which occur infrequently. Leibniz responded that a miraculous act is one which is beyond the capacity of created things. This characterization of the miraculous allowed Leibniz to make another charge against Newton: that action at a distance would be miraculous. Even if this action occurs at all times, its frequency would not obviate its miraculousness. Here the argument degenerates again into a debate over the use of words. Leibniz claimed the authority of theologians and Clarke called Leibniz's definition "vulgar."


A serious counter-charge leveled against Leibniz by Clarke was that of fatalism. Since God always does things for the best, God is constrained to create the world as it is. "Whatever God can do, he cannot but do; and consequently . . . he cannot but make every thing infnite and every thing eternal. Which is making him no governor at all, but a mere necessary agent, that is, indeed, no agent at all, but mere fate and nature and necessity" (Clarke's Fourth Reply to Leibniz's Third Paper, 22 and 23). Leibniz's stock response here is his distinction between absolute and hypothetical necessity. God's essence inclines but does not necessitate God to create the world God does create.

Besides, Leibniz counters, what is the alternative? If God does not act by virtue of possession of a sufficient reason, if God acts purely from will, then God acts from blind chance. Clarke replied that God's action is not mere chance, but an act of will in circumstances of indifference between two results. Leibniz's rebuttal was that "'Tis true, chance is blind; but a will without motive would be no less blind, no less owing to mere chance" (Leibniz's Fifth Paper, Sec. 71). So we have arrived at the classic impasse: strict application of the principle of sufficient reason threatens fatalism. Exceptions to the principle seem to make the nature of the universe virtually equivalent to the outcome of a toss of a coin.


The debates over the presence of God in the universe, the governance of the universe, miracles, and so forth are metaphysical rather than scientific. Leibniz initiated the correspondence by questioning the effect of Newtonianism on religion, but he was also concerned about matters which have no little or no religious content. For example, he rejected the existence of atoms on the grounds that all would be indiscernible from one another and hence identical. But the most important debate was over the nature of space and time.

Space and Time

We have seen that Newtonian space and time are related to the divine presence in the universe. But this is not the reason they were originally introduced in the Principia. They are, Newton believed, necessary for the existence of absolute motion and rest in the physical universe. Copernicus and Galileo had exploited the fact that the appearance of motion or rest are relative to the point of view of the observer. Thus the earth appears at rest from the standpoint of people moving along with it, but it can equally well be regarded as in motion from another vantage point, say, the sun.

Newton recognized that relativity poses no difficulties in common usage, "but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them" (Scholium on Absolute Space and Time). Here Newton echoes the demand of philosophers from the time of the Greeks to distinguish reality from mere appearance. True motion is motion relative to absolute space, but absolute space is not itself an object of perception, so it cannot be a standard of comparison. Nor can the position of the "fixed" stars, which may be absolutely in motion although at rest relative to us.

Absolute motion can be detected, Newton maintained, through its causes and effects. "The causes by which true and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion" (Scholium on Absolute Space and Time). But then the question becomes how to detect when a force is impressed on one body (that absolutely moving) rather than another (which is absolutely at rest but moving relative to the absolutely moving body).

To overcome this problem, Newton devised some thought-experiments involving circular motion. One of these involves a bucket which begins to rotate when a twisted cord holding it up uncoils itself. At the beginning, the water in the bucket has the greatest motion relative to the bucket itself. It appears to be standing still relative to the bucket, while from the standpoint of the water, the bucket is moving around it. As the cord unwinds, the water begins to creep up the side of the bucket, until it reaches a point where it appears to rotate at the same rate as the bucket. Thus it is at rest relative to the bucket. Newton contended that at this point of relative rest, the water has a "real circular motion," which is manifest by its rising in the bucket. This indicates its endeavor to move away from the axis of its motion, which in turn indicates that a force is acting upon it: the circular motion of the water is real.

Interestingly, Leibniz did not dispute the existence of absolute motion and rest, only the definition of it as motion or rest relative to absolute space. "I grant there is a difference between an absolute true motion of a body and a mere relative change of its situation with respect to another body. For when the the immediate cause of the change is in the body, that body is truly in motion, and then the situation of other bodies with respect to it will be changed consequently, though the cause of that change is not in them" (Leibniz's Fifth Letter to Clarke, Section 53). We can say that Leibniz accepted Newton's criterion for absolute motion as being what constitutes absolute motion. Absolute space and time then become superfluous.

Leibniz believed that he had proved the non-existence of absolute space and time by invoking the principle of sufficient reason. The argument is that if absolute space and time exist, then the actual position of the universe with respect to them could differ from other possible positions of the universe. Space and time themselves are independent of anything existing in them and so are indifferent with respect to the location of the universe. Furthermore, the parts of space and time are indistinguishable from one another. So there is nothing in the nature of space and time which would make one location of the universe preferable to any other, and as a result, there is no sufficient reason for the universe's actual location. But every existing thing has a reason for its existing in the manner it does, so the universe does not exist in absolute space and time, which was to be shown.

A variant on the argument is that there would be no possibly observable difference between any two placements of the universe. The situations would be indiscernible and consequently identical. For example, if God were to transpose East and West, the relations between all things would be preserved. On Leibniz's view, space is nothing more than an ideal order of the co-existence of substances. (One analogy that might be useful is that space is like the idealized lines drawn on a genealogical table.) We can describe things as standing at a certain distance from one another, as being adjacent to or between one another, and so forth. But there is nothing fixed against which the position of things can be determined in an absolute way.

Clarke proposed an ingenious thought-experiment in an attempt to reduce Leibniz's view to absurdity. According to the relative notion of space, the motion of the entire universe would be undetectable, since position in one part of space is no different from position in any other part of space. But if the universe were moving at a high speed relative to absolute space, and then were suddenly stopped, there would be a great shock, and hence there would be an observable difference between the universe's being in different parts of space. To this Leibniz replied that such motion presupposes the existence of absolute space, which he had already shown not to exist.

The Void

A consequence of Leibniz's notion of relative space is that a vacuum, void or space not filled with objects is impossible. Leibniz regarded belief in a void as based on confusing what is merely idea with what is real. As for those contemporary experiments in which a vacuum apparently was created in a chamber from which the air has been pumped out, our inability to detect the presence of matter does not prove that it does not exist in the vacuum-chamber. There may remain all sorts of more subtle, even invisible, matter, such as that constituting light or magnetic force, permeating the chamber.

Other Issues

We shall end the discussion of the debate at this point, though it contains a number of other arguments on the issues touched on here, and many other interesting issues. Do atoms exist? Would the pre-established harmony be miraculous if true? What is the basis for the identity of indiscernibles? All these questions make the whole work a fascinating study.

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