From a broader philosophical perspective, Newton was very influential in both metaphysics and scientific methodology. Philosophers such as Locke and Kant attempted to incorporate many of his doctrines into their general accounts of nature. Hume tried to apply the Newtonian method for studying material phenomena to the study of the human mind. Other prominent philosophers, most notably Berkeley and Leibniz, opposed various key Newtonian doctrines. Through his fellow philosopher Samuel Clarke, Newton engaged in an exchange of letters with Leibniz, clashing with him on topics ranging from the nature of space and time to that of miracles.

Newton's crowning achievement was his Mathematical Principles of Natural Philosophy (Latin: Philosophiae Naturalis Principia Mathematica, 1686, second edition, 1713). Using only a few principles, he was the first to give a unified account of many of the motions of bodies, both on earth and in the heavens. His system of the world was the culmination of research begun by Copernicus and carried on by Kepler, Galileo, Descartes, and many others. Newton acknowledged in a letter to Robert Hooke that if his vision surpassed those of others, it was because he was standing on the shoulders of giants.

Our text contains two excerpts from the Principia. The first is the Scholium to a set of definitions laid down at the beginning of the book. The second is a "General Scholium," not tied to any specific section, which appeared in the second edition. Part of Query 31 of the Optics is also reprinted. As these are very small slices of two books, it will be necessary to quote other parts of them at several points.

Method

In the Preface to the first edition of the Principia, Newton described "the whole burden of philosophy" as being: "from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate other phenomena."

Even in this very general statement, the method of Newton can be seen to be quite different from that of Descartes. First, Descartes did not begin with the phenomena of motions, but rather with the nature of God, in formulating laws of motion which would (in Newton's terms) serve to demonstrate other phenomena of motion. Second, as was pointed out by Leibniz, Descartes's laws of motion are not formulated in terms of "forces of nature," but only in terms of the speed and size of bodies.

Leibniz's Discourse on Metaphysics was written in the same year that Newton published the Principia, though it shows no awareness of Newton's doctrines. In it he claims that "all the particular phenomena of nature can be explained mathematically or mechanically by those who understand them" (18). Appeal to forces is central to any such explanation. At times, Leibniz appealed to phenomena of motions to justify claims about forces. For example, in Section 16 of the Discourse, Leibniz notes the behaviour of a pendulum to motivate his claim that "a body falling from a certain height acquires the force to rise up to that height, if its direction carries it that way, at least, if there are no impediments."

On the other hand, Leibniz held that natural philosophy should not confine its investigations to the phenomena. "The general principles of corporeal nature and of mechanics itself are more metaphysical than geometrical, and belong to some indivisible forms or natures as the causes of appearances, rather than to corporeal mass or extension" (18). Newton, at least in the first edition of the Principia, confined himself to forces whose existence can be inferred from the phenomena and rejected any role for metaphysics in natural philosophy. His later writings draw the two closer together.

Leibniz made a further claim that clashes with the procedure of the Principia. Given a belief in God as the author of the universe, "it is unreasonable to introduce a supreme intelligence as orderer of things and then, instead of using his wisdom, use only the properties of matter to explain the phenomena" (Discourse on Metaphysics, 19). Leibniz appeals to an analogy to confirm this point: we should explain a military conquest by appealing to the foresight of the conqueror, rather than merely appealing to the physics of gunfire.

In the 1713 General Scholium, Newton himself gives some teleological explanations of the phenomena of nature, specifically the order and beauty of the Solar System. "This most beautiful system of the sun, planets, and comets could only proceeed from the counsel and dominion of an intelligent and powerful Being." The relation of God to nature was to prove a major point of disagreement between Newton and Leibniz.

Appeals to teleology notwithstanding, Newton tried to be very strict when doing "experimental philosophy." Specifically, he held that "hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy" (General Scholium).

The correct method of experimental philosophy is to begin with the phenomena, "deduce" particular propositions from the phenomena, and finally to use induction to render the propositons universal. Newton gives several examples of what he discovered in this way, that of gravity being the most important.

The phenomena of the motions of the sun, the earth, the oceans, etc. are explained by their "gravitating" toward each other. More specifically, there is a centripetal force (a force toward the center) which varies with the mass of the bodies and the square of their distance from each other. Such a force is, by induction, said to hold of all bodies.

Newton held that "it is certain that [the force of gravity] must proceed from a cause" that has various specific characteristics. But he was never able to discover from the phenomena a cause of this force which would explain why gravity has the properties that it does. Newton famously proclaimed that what is not deduced from the phenomena is a hypothesis, and "I frame no hypotheses" ("hypotheses non fingo"). In the very next paragraph, he announces the existence of an "electric and elastic spirit" which causes a number of phenomena, both physical and biological. He does not seem to treat this spirit as a hypothesis, though he does acknowledge that we do not "have at hand sufficient experiements by which the laws of action of this electric and elastic spirit can accurately be determined and demonstrated."

True Motion

So what are the phenomena to be explained through the mathematical principles of natural philosophy? Certainly Newton's force of gravitation explains very well the apparent motions of the sun (circling around the sky), of the ocean (rising and falling in relation to the land), and of many other bodies. But the more fundamental goal is to explain the "true motions" in the visible universe:

But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it. (Scholium)

The true motions of bodies are contrasted with their merely apparent motions. The senses present us with a vast number of what appear to be motions, but appearance of motion is not sufficient to establish that there really is motion. Galileo, Descartes, and Leibniz admitted that a body may be described as being in motion or being at rest depending on the position of the observer. Here is Leibniz's statement of the matter:

For if we consider only what motion contains precisely and formally, that is, change of place, motion is not something entirely real, and when several bodies change position among themselves, it is not possible to determine, merely from a consideration of these changes, to which body we should attribute motion or rest, as I could show geometrically, if I wished to stop and do this now. (Discourse on Metaphysics, 18).

For Newton, to understand what true motion is, we must begin with an understanding of what motion is. The definition he gives at least superficially resembles the "precise and formal" notion of motion Leibniz stated by Leibniz: motion is the "translation" of a body from one place to another. Newton did not understand place purely relatively to bodies, as did Descartes and Leibniz. Rather, place is defined as the part of space which is occupied by a body.

So now we are left to ask what space is. The reply is that we all know the answer to that question. The string of definitions ends with an undefined conception of space. Putting together the definition of motion and of place, we have it that motion is the translation of a body from one part of space to another. Newton claimed that there are two kinds of space, and it was this that allowed him to distinguish (but not define) two kinds of motion.

Absolute Space

One way to think of space is as a relation between bodies. Leibniz had held that space is a way in which different bodies can exist together at the same time. "As for my own opinion, I have said more than once that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistence, as time is an order of successions" (Leibniz's third letter, section 4). Thus for Leibniz, real motion cannot be understood through space any more than it could be understood through place. Both Leibnizian place and Leibnizian space are relative only.

Newton allowed that there is relative space, but he claimed in addition that there is an absolute space which is not relative to bodies. Absolute space serves as a place for bodies. "All things are placed in time as to order of succession, and in space as to order of situation" (Scholium).

We might then ask how absolute and relative space are related to each other. The chief difference between them is that absolute space, and all the places within it, are immovable. Relative space, on the other hand, can move from one part of absolute space to another. But the two are the same in an important way: in "form and magnitude."

Consider the space defined by the boundaries of the interior of a modular classroom. If the classroom were to be relocated carefully to another part of campus, there might be no change at all in the boundaries of its interior. In that case, the space of its interior would have moved to another part of absolute space. Since the size and shape of the relative space remain the same, it is the same size and shape as the part of absolute space it first occupied and the part it occupied later.

Now we can distinguish between absolute and relative place. The former is a part of absolute space and the latter a part of relative space. As an example of relative place, we might consider the part of the interior of the classroom occupied by the instructor's table. So one might answer the question, "Where are the instructor's glasses?" by saying, "His glasses are on the table in the classroom." Sensory appearances are perfectly adequate by themselves for determining the relative place of a thing. One cannot determine through sensory appearances which part of absolute space an object is in, but one can perhaps determine whether it has changed its absolute place.

Absolute Motion

We finally return to the conception with which we began, true motion. This Newton identified with absolute motion. That is, true, or absolute, motion is the translation of a body from one absolute place to another, or, equivalently, from one part of absolute space to another. Apparent motion would then be the translation of a body from one part of relative space to another. If the relative space is itself not moving, relative motion is the same as absolute motion. If the relative space is moving, the body may not be truly moving at all.

For example, suppose that the earth is absolutely at rest, and you are on a boat that is moving at a rate of one mile per hour to the west. Since the earth is at rest, the motion of the boat is both absolute and relative to the place of the earth. Now suppose you are walking on the boat to the east, also at one mile per hour. You start at the stern of the boat and end up at the bow, and you have moved relative to a moving body. But absolutely you would be at rest, since you have not changed your position relative to absolute space. However, unless you could determine that the earth is absolutely at rest, you could not tell that you had not moved absolutely.

So is there any way to determine whether absolute motion has occurred, even though absolute space cannot be perceived? Newton thought there is. Like Leibniz, he regarded absolute, true, motion, as a real change in a body. And a real change in a body occurs when there is a force involved. So if there is a force which can be detected, it might be used to determine change of absolute place.

Newton gave two examples of such a test. We will consider the second one. Suppose two balls are attached to each other by a string. Now suppose the balls are suspended in a vacuum and appear to be revolving around a point at their common center of gravity. Are the balls moving absolutely, or is the observer moving relative to them? If the string is taut, this is an indication that the balls are really revolving. Revolving bodies "endeavor" to move away from the axis of revolution, and the tautness of the string indicates that the bodies are in this case endeavoring to move away from the axis of revolution.

If we establish that the bodies are actually moving, we could then establish that other bodies are not moving, just because the former have a motion relative to the latter. Newton proposed that we might be able to establish the absolute rest of the fixed stars, which could then be used as a reference-point for other absolute motions. The most obvious application of such a determination would be that the earth rotates absolutely on its axis.

Leibniz Against Absolute Space

Newton's account of the determination of absolute motion came under sharp criticism first by Berkeley (Principles of Human Knowledge, Sections 109-117) in the eighteenth century, then in the late nineteenth century by Ernst Mach, and were dealt a death-blow in the twentieth century by Albert Einstein. All these criticisms were epistemological or based on considerations of physics. We are here concened with the criticism of Leibniz, which were primarily metaphysical or theological.

At the level of physics, Newton and Leibniz were in agreement to some extent. Both held that there is true motion of bodies, and moreover that there is true motion just in case there is a force of a certain kind being exerted by the body. But there was a metaphysical disagreement. Newton believed that the very definition of motion must make a reference to a space which is real and independent of motion. Leibniz thought that no such appeal is necessary, and moreover that the postulation of absolute space leads to serious difficulties.

The first problem Leibniz found was that absolute space would be infinite and eternal. These two attributes belong only to God, so absolute space would have to be God. But absolute space has parts, while God does not, so it could not be God. (Here Leibniz agrees with Spinoza that God can have no parts.)

One response to this would be to claim that absolute space not an attribute of God, but rather a way in which God is related to the world. Newton, in Query 31 of the Optics (1704), had used the word "sensorium" to describe the relation of space to God: Space is God's sensorium. Leibniz interpreted "sensorium" as "sense organ," and noted that God has no need to resort to sense-organs to perceive the material world. Clarke tried to rebut this criticism by interpreting "sensorium" to mean nothing more than God's presence in the world. But if God is present in the world, then it would seem, according to Leibniz, that God would have to be the soul of the world, a charge Newton himself denied in the General Scholium. Moreover, mere presence is not sufficient for perception (Leibniz's fourth letter, section 11).

The second problem has to do with the uniformity of space (as well as time). If all the parts of space are qualitatively identical (though numerically distinct), then it makes no difference where the universe is located in space (or time). That being so, God would have no reason to place the universe in one part of space rather than another. But this violates the principle of sufficient reason, according to which God does not act unless there is a reason why acting that way is better than acting any other way or not acting at all. "When two incompatible things are equally good, and neither in themselves nor by their combination with other things, has the one any advantage over the other, God will produce neither of them" (Leibniz's fourth letter, section 18).

The Newtonian response to this charge was to hold that God's very willing the creation of the universe in one part of space is in itself a reason for this action. (Here Newton would agree with Descartes that God's will is indifferent and God's decrees determine what is best.) Leibniz's rebuttal is that "A will without reason would be the chance of the Epicureans. A God who should act by such a will would be a God only in name" (Leibniz's fourth letter, section 18).

Leibniz against Divine Intervention

Another item of dispute between Leibniz and Newton concerned the how well-made the universe is. Newton had argued that natural philosophy is a great support of moral philosophy. As we have seen from the General Scholium, the mathematical study of nature presents us with astonishing regularities that could only be explained by there being an intelligent creator. For example, the elliptical orbits of planets could not have come about by chance, in Newton's opinion. Thus, he must have been stung by Leibniz's charge that his mathematical philosophy of nature had contributed to the decline of religion in England (Leibniz's first letter, section 1).

Newton did not limit God's role to designing and creating (or preserving) the universe. He held instead that God actively intervenes in its workings. One reason has to do with explaining the motion in the universe. As noted above, Newton believed that absolute motion exists only when there is force applied to bodies. But he recognized that the fundamental force of his physics, the force of attraction, was too little to account for all the motions of the universe.

To make up for part of the deficit, Newton postulated "certain active principles" whose cause has not been discovered (Query 31 of the Opticks). These would be causes of gravity, fermentation, and the cohesion of bodies. (Compare these "principles" with the "electric and elastic spirit" described in the General Scholium.) Then Newton added a third kind of force, "the dictates of a will." Leibniz and Clarke may have interpreted this as meaning that God's will supplies what natural forces cannot. (In the 1717 edition of the Opticks, the year the Leibniz-Clarke correspondence was published, Newton dropped reference to dictates of a will.)

Two reasons Newton may have thought this third kind of force is needed are given in Query 31. One was that the solar system would become disorderly over time, and intervention would be needed to restore order.

A second reason is that that motion is lost when bodies interact. When two bodies moving toward each other in a straight line collide, one of two things will happen. If they are elastic, they will rebound off each other, but the motion will be less than the original. If they are inelastic, say by being perfectly hard or perfectly soft (like two lumps of clay), then all motion will be lost. It might seem, then, that supernatural intervention is sometimes needed to keep the quantity of force at a level sufficient to sustain the system of the universe.

Leibniz criticized the apparent invocation of divine intervention in the universe, on the grounds that it implies a defect in God's workmanship. God could not be so inept as to create a system which was not capable of running on its own. To this, Clarke replied that it is actually a good thing for God to be involved in the world rather than making it and walking away from it, so to speak. At this point, the dispute becomes purely theological.

Conclusion

We have only touched on some points of philosophical interest in the work of Newton. One of the most controversial points in his system of nature was his postulation of the force of attraction, which acts at a distance. He took it to be established by observation and induction that bodies attract one another as a function of their mass and the square of their distance. But he was unable to discover the cause of gravitational attraction, so he had to leave it unexplained. For this, he was accused of having postulated an "occult quality." Other points of interest are Newton's embrace of atomism and the void, and his devastating refutation of Descartes's theory of the motions of the planets.

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