NEWTON’S SIMPLICITY-BASED ARGUMENT FOR GRAVITY

In the final part of this chapter I return to Newton, who had strong views about simplicity and put them to use in his ar­gument for universal gravity. His argument is based on the assumption that nature is simple, and that simplicity is an epistemic guide to truth.

Newton invokes simplicity in his argument for the law of gravity when he employs his first, second, and third “Rules for the study of natural philosophy” in the proof of gravity. The first rule (“No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena”), Newton defends by saying that “nature is simple and does not indulge in the luxury of superfluous causes.” 'lhe second rule (“'lherelore, the causes assigned to natural effects of the same kind must be, so far as possible, the same”), Newton regards as following from his simplicity­based Rule 1. 'lhe third rule (“'Ihose qualities of bodies that cannot be intended and remitted and that belong to all bodies on which experiments can be made should be taken as qual­ities of all bodies universally”), Newton defends by saying “nature is always simple and ever consonant with itself.”

There is a fourth rule that Newton invokes in his argu­ment for gravity that is not defended by appeal to simplicity, or in any way, for that matter. (Rule 4: “In experimental phi­losophy propositions gathered from phenomena by induc­tion should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.”) However, in effect, what Newton is saying in Rule 4 is that if you have followed the simplicity­based inductive Rule 3 (and I would add, the simplicity­based causal Rules 1 and 2), then the satisfaction of these rules justifies your claiming the truth or approximate truth of the causal law you have inferred, until new phenomena are discovered that can change the picture.

My question is this: When Newton uses these simplicity­based rules in arguing for his law of gravity, do they in fact carry much, if any, weight? At the beginning of Book 3 of the Principia, after stating these rules, Newton introduces a set of six “Phenomena.” These are facts pertaining to the motions of the known planets and their moons that Newton takes to have been established by astronomical observations. They claim, in effect, that all the known planets and their moons obey Kepler's second and third laws of motion: in their orbits a line drawn to them from the orbited body sweeps out equal areas in equal times, and the square of their periods of rev­olution is proportional to the cube of their distances from the orbited body. Newton follows the six “Phenomena” with a set of what he calls “propositions” (or “theorems”) that he derives from the “Phenomena,” his three laws of motion in Book 1, and theorems that follow from the latter. The first, second, and third of the propositions in Book 3 pertain to the forces operating on the moons of Jupiter and Saturn, on the known planets, and on our moon: they are all cen­tral forces (produced by a central body about which they rotate), and they are all inverse-square forces. Proposition 4 says: “the moon gravitates toward the earth and by the force of gravity is always drawn back from rectilinear motion and kept in its orbit.” Proposition 5 makes a corresponding claim for the satellites of Jupiter and Saturn (with respect to Jupiter and Saturn) and for the planets (with respect to the sun). Proposition 6 asserts that all bodies gravitate toward each of the planets and that at any distance that a body is from a planet, the weight (or “heaviness”) of that body toward the planet is proportional to the mass of the body. Proposition 7 says: “Gravity exists in all bodies universally and is propor­tional to the quantity of matter [mass] in each.” Proposition 7, together with the earlier derived idea that the force is an inverse-square one, gives us Newton's law of gravity.

Where does Newton invoke the simplicity-based rules in his argument for universal gravity? Not at all in his argu­ment for the first three propositions, which claim that the forces acting to keep the moons of Saturn and Jupiter and the planets in their orbits are central inverse-square forces. This proposition he derives, without appeal to his simplicity rules, from the “Phenomena” he cites at the beginning of Book 3 and from theorems he has proved in Book 1, using his three laws of motion. The simplicity-based rules (at least the first and second) are invoked for the first time in his argument in the discussion of proposition 4. Let's look at this.

Here, Newton wants to show not simply that the force keeping our moon in its orbit about the earth and the force causing unsupported bodies near the earth to fall toward the earth are both central inverse-square forces but that they are the same force. There is one force here, not two—i.e., the force in both cases is governed by the same law. This he argues for by introducing empirically determined measurements of the mean distance of our moon from the earth, the circumfer­ence of the earth, and the mean time the moon takes to make one revolution. From these he calculates the acceleration the moon would have near the earth if it were deprived of its inertial motion and fell toward the earth. (Newton calculates this to be 15 1/2 Paris feet; one Paris foot is 0.9383 feet.) The magnitude of this acceleration is exactly the same as that of bodies near the earth falling toward the earth. From the fact that the magnitudes of the accelerations produced by these two forces are the same, and since he has already shown that the forces are both central, inverse-square, and directed to­ward the center of the earth, he concludes that “the force by which the moon is kept in its orbit... is that very force which we generally call gravity.” '1 his is, or should be, enough to convince us empirically that the forces are identical.

To be sure, in reaching the “one force, not two” conclu­sion, Newton explicitly cites the simplicity-based Rules 1 and 2. But if simplicity were providing any real basis for the in­ference to the same force, why doesn't he invoke it earlier, be­fore he gets to the moon argument? Using Rule 2 (“the causes assigned to natural effects of the same kind must be, so far as possible, the same”), why, in propositions 1, 2, and 3, doesn't he argue from the fact that the forces operating on the known planets and their satellites keeping them in their orbits are central inverse-square forces to the (simple) conclusion that the same force (“the same cause”) is operating in all these cases? After all, the effects of these forces that he notes in the “Phenomena” are the same (effects satisfying Kepler's second and third laws). If simplicity is capable of doing genuine epi- stemic work, why wait until the moon argument, in proposi­tion 4, to invoke it? Using his Rule 2, wouldn't it be sufficient to argue from the fact that the observed Keplerian motions of the planets and their satellites are the same to the conclusion that there is one force producing these effects, not many?

In fact, Rule 2 mandates that he should do so. It does not say that (in accordance with simplicity) from effects of the same kind, you may infer the same cause. It tells you some­thing you must do, “so far as possible.” Newton appears to violate this rule, or at least to ignore it, in his discussions of propositions 1, 2, and 3, since here he assigns causes (viz. central inverse-square forces) to effects of the same kind (effects described in his “Phenomena”) without assigning the same cause (universal gravity). Perhaps he thought that the observed effects in question described in propositions 1, 2, and 3 were not yet sufficient to invoke Rule 2 (to use Newton's expression in Rule 2, it was not yet “possible” to make the inference). He needed more effects, and ones that are even more convincing, particularly the effects involving the moon's acceleration toward the earth and the acceleration of falling bodies near the earth.

The answer has to do with empirically determining a critically important new effect: the magnitude of the accel­eration produced by the force exerted on the moon by the earth. Newton writes:

For if gravity [on the earth] were different from this force [on the moon] then bodies making for the earth by both forces acting together would descend twice as fast and in the space of one second would by falling describe 30 1/6 Paris feet, entirely contrary to experience.^[108]

The latter empirical defense is important to Newton because it shows that if the forces acting on such bodies were different

forces, then bodies falling toward the earth would fall with a different acceleration than observed bodies do. More gener­ally, if there are, among the observed common effects, some that would be otherwise if the causes were different ones, then at least some of the observed effects would be “con­trary to experience.” But then what is driving the inference to one cause rather than several different ones is not the sim­plicity of one cause rather than many but the set of observed common effects, particularly those of the kind just noted. It is not that Newton is arguing for one force here because one force is simpler than two. In this passage, he is arguing for the existence of one force rather than two on the grounds that if there were two, then the combined accelerative effects of these forces would be incompatible with what is observed.

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