SIMPLICITY AND NEWTON’S PROPOSITIONS 5 AND 6

the centers of Jupiter, Saturn, and the sun and decrease ac­cording to the same ratio and law (in receding from Jupiter, Saturn, and the sun) as the force of gravity (in receding from the earth).^[109]

And in a Scholium at the end of his discussion of proposition 5, he writes:

Hitherto we have called “centripetal” that force by which ce­lestial bodies are kept in their orbits.

In these two passages from the discussion of proposi­tion 5, Newton appeals to the simplicity-based Rule 2 (in the first and second passage) and to the simplicity-based Rule 1 and to Rule 4 (in the second passage), which is indirectly simplicity based. So, is simplicity driving these inferences? This is a tougher question. In both passages he refers to his previous discussion in the moon argument, in which he concluded that the force keeping the moon in its orbit is the very same force as that producing accelerations of bodies near the earth. Now, in defense of the claim that there is a single force keeping the planets in their orbits around the sun and the moons of Jupiter and Saturn in their orbits around these planets—viz. (universal) gravity—he appeals to the fact that certain observed effects of this putative force are the same (Keplerian motions), and to the fact that the observed rate of accelerations of bodies falling toward the earth is the same as that of the moon falling toward the earth. It looks like there is a very big leap here from what is observed to the claim that there is one force of gravity operating. After all, although he has calculations of accelerations in the moon ar­gument, he has no such calculations in the case of the moons of Jupiter and Saturn toward these planets, and of the planets with respect to the sun.

So, you might say, Newton needs help here from his simplicity-based Rules 1 and 2. Given that he does infer a cause in each case (an inverse-square force of attraction), from the fact that the effects observed in all these cases are “of the same kind,” in virtue of his claim (in the discussion of Rule 1) that “nature is simple and does not indulge in the luxury of superfluous causes,” and in virtue of Rule 2, he must infer that the cause is the same. He needs to invoke Rules 1 and 2 because the observed effects by themselves aren't suf­ficient to justify such an inference. They may be sufficient to justify an inference to an inverse-square force in each case, but not to the claim that there is one force operating, rather than many. For that you need simplicity, or so it might be thought.

But if this is what is really going on, then, as I asked be­fore, why not invoke Rules 1 and 2 before he embarks on the moon argument? Why not say that since “nature is simple and does not indulge in the luxury of superfluous causes,” and since the observed Keplerian motions of the planets and their moons are “of the same kind,” and since I have assigned a cause in each case (viz. an inverse-square central force), in accordance with Rule 2, I must conclude that there is one force here, not many? '1 his, of course, he does not do. He invokes Rules 1 and 2 only when he has what he takes to be enough of the right kind of effects to do so.

So, we have a dilemma. Either Newton, at some point, has effects of the right kind to make the inference (ones that show empirically that there are not different forces acting, as in the moon argument) or he doesn't. If he does, then sim­plicity becomes irrelevant. If he doesn't, then why does he wait to appeal to simplicity? Just invoke simplicity as soon as you get some common effects and make your inference to one cause. Newton doesn't do that, either, presumably be­cause he doesn't yet have enough of the right kind of effects. In either case, it is the presence or absence of the right kind of observed effects that is driving or preventing the infer­ence.

The same applies to his simplicity-based Rule 3, which he invokes in corollary 2 of proposition 6. Proposition 6 asserts: “All bodies gravitate toward each of the planets, and at any given distance from the center of any one planet the weight of any body whatever is proportional to the quan­tity of matter [mass] which the body contains.” Corollary 6 states: “All bodies universally that are on or near the earth are heavy [or gravitate] toward the earth, and the weights of all bodies that are equally distant from the center of the earth are as the quantities of matter [mass] in them. This is a quality of all bodies on which experiments can be performed and therefore by Rule 3 is to be affirmed of all bodies univer­sally.” (This is the first time Newton actually invokes Rule 3.)

One of the most important parts of proposition 6 and of corollary 3 is the claim that the weight of any body is pro­portional to its mass. This Newton defends by experiments he performed on pendulums made of different materials but with bobs of the same weight. There is no mention of any of the rules here, but these experiments presumably allow Newton to infer at least the second clause in corollary 6, viz. that the weights of all bodies equally distant from the center of the earth are proportional to the masses of the bodies.

Similarly, in extending this result to the planets and their moons, Newton proceeds by giving empirical reasons for this conclusion, not appeals to simplicity. For example,

Further, that the weights of Jupiter and its satellites toward the sun are proportional to the quantities of their matter is evident from the extremely regular motion of the satellites, according to Book I, Prop. 65, Cor. 3. For if some of these were more strongly attracted toward the sun in proportion to the quantity of the matter than the rest, the motions of the satellites (ac­cording to Book I, Prop.

Newton repeats the same argument for the satellites of Saturn. It is only in corollary 2 of proposition 6 that Newton appeals explicitly to his simplicity-based inductive Rule 3, when he generalizes this idea to all bodies. But why does he wait so long to do so? If Rule 3 is capable of doing any work, then why not invoke it right after his experimental results with pendulums on the earth? Presumably, the reason is that he needs more experimental or observational results, par­ticularly pertaining to the motions of the planets and their moons, to make the inference justified. But then it is those results that are really driving the inference, not simplicity. If

154 | SPECULATION: WITHIN AND ABOUT SCIENCE it were simplicity, then he could have stopped after the pen­dulum experiments and made the bold inference about all bodies.

Newton reaches proposition 7, which asserts that “gravity exists in all bodies universally and is proportional to the quantity of matter [mass] in each.” '1 his, together with pre­viously proved propositions about the inverse-square nature of the force required to keep the planets and their satellites in their orbits, where the latter is generalized to all bodies, yields Newton's law of gravity. '1 he forces involved all obey the same law, which relates the magnitude of the force to the masses of the bodies and to the inverse-square distance between them. He argues, in effect, that since all the bodies in question are subject to the same force law, there is one force operating, not many. The latter is true, not because one force is simpler than many but because he has shown, or claims that he has, that the law holds universally. In his argument for proposition 7, there is no mention of the simplicity-based rules at all.

I conclude that even though Newton on several occasions invokes simplicity or, rather, simplicity-based rules, in his com­plex argument for the law of gravity, this is doing no real epi- stemic work. What is doing the epistemic work are his appeals to results of experiments and observations—what Newton calls the “Phenomena”—and his calculations from these, to­gether with theorems that follow from his laws of motion.

7.