WHEWELL VERSUS NEWTON (MOSTLY)

With respect to Newton's first rule, Whewell's complaint is that it is ei­ther trivial and uninteresting, or interesting but stifling to science, or else it is quite simply Whewell's own rule of “consilience,” i.e., a rule requiring us to find a cause that explains various classes of phenomena, not just the ones we started with.

I think Newton would and should have a fit with this. His first rule does not say simply “look for true causes,” although I suppose it is com­mitted to at least that much. It is clear from Newton's formulation, from his brief discussion following that formulation, and from his actual use of that rule in deriving the law of gravity that Newton has something more in mind, namely, a principle of simplicity: don't infer as true more causes than are needed. Indeed, immediately after formulating the rule, Newton writes: “Nature does nothing in vain, and more causes are in vain when fewer suffice. For nature is simple and does not indulge in the luxury of superfluous causes.” Nor, contrary to Whewell, does Newton restrict in­ferred causes to ones of a type already known to operate—he simply says that if one suffices, don't postulate two, and that effects of the same kind should be assigned to the same cause, not that these causes must be ones already known.

Whewell has the following objection to Newton's rule 2: it doesn't tell us much, since it doesn't tell us how to determine whether effects are “of the same kind.” For example, Whewell asks, why take planetary motions to be motions of the same kind as that of

1.

2. bodies “swept round by a whirling current,” as Descartes did?

Newton has, I would think, two replies. One is a tu quoque. Whewell himself when he characterizes what he calls the “consilience of induc­tions,” writes that

But the evidence in favor of our induction is of a much higher and more forcible character when it enables us to explain and determine cases of a kind different from those which were contemplated in the formation of our hypothesis. (his emphasis, not mine)

Whewell, like Newton, does not tell us how to determine whether cases are of the same kind or a different one. But this is because the question is an empirical one, not one to be settled a priori in advance for all cases. This reply is one with which Whewell should agree. Newton's second re­sponse would be to reject Whewell's loaded descriptions of the observed effects such as (1) and (2)—“loaded” in that they presuppose something important about the cause being inferred. In the astronomical case, Newton's same “effects,” from which he infers a common cause, concern observed Keplerian facts about the orbits of the planets and their satellites and (contra Whewell) not claims such as (1) and (2) about what is, or is not, producing those orbits (whether the cause is a whirling current, or is not a contact force). The effects, as described by Newton, are logically compatible with Newton's central force cause, as well as with Cartesian vortices. Which of these causes to infer is an empirical issue. All Newton is claiming, using his rules 1 and 2, is that the orbital Keplerian “effects” being the same all have the same cause, whatever that is.

Finally, let me mention what Whewell mainly objects to about Newton's rules 3 and 4. According to Whewell, Newton makes it seem that, indepen­dently of any other considerations, anytime we find a common property of bodies in the ones examined, we can generalize to all bodies. But, Whewell insists, “the assertion of the universality of any property of bodies must be grounded upon the reason of the case, and not upon any arbitrary maxim” (such as Whewell takes Newton's rule 3 to be).

Let me discuss this objection by turning to Mill, whom Whewell re­gards as an even more unenlightened opponent than Newton, at least about scientific methodology. Mill is more explicit about how to respond to Whewell's claim than is Newton, but I think both would respond in the same way.

Recall Mill's definition of induction as “the process by which we con­clude that what is true of certain individuals of a class is true of the whole class.” Mill does not say, and indeed he explicitly denies, that any induction so defined is justified. Whether it is, he says, depends on “the number and nature of the instances.” For Mill, and I think Newton as well, whether a particular inductive inference from “all observed As are Bs” to “all As are Bs” is justified is an empirical issue, not an a priori one. Mill writes that we may need only one observed instance of a chemical fact about a substance to validly generalize to all instances of that substance, whereas many observed instances of black crows are required to generalize about all crows (Mill 1872, pp. 205-206). This is due to the empirical fact that instances of chemical properties of substances tend to be completely uni­form, whereas bird coloration, even in the same species, tends not to be.

In making an inductive generalization to a law of nature, Mill requires that we vary the instances and circumstances in which they are obtained in a manner described by his “four methods of experimental inquiry.” Whether the instances and circumstances have been varied, and to what extent, is an empirical question, not determined a priori by the fact that all the observed members of the class have some property.

I think it is reasonable to say that Newton, like Mill, is not claiming that any induction from “all observed As are Bs” to “all As are Bs” is valid.

We [should not] depart from the analogy of nature, since nature is always simple and ever consonant with itself.

Newton does not say how he knows nature is “ever consonant with itself,” or indeed what this entails. Mill is more explicit, though not completely so. Perhaps a little bit charitably, given his discussion on pages 200-206 of A System of Logic, I would take him to be saying at least, and perhaps not more than, this: there are uniformities in nature, i.e., general laws govern­ing various types of phenomena—laws that are inductively and validly in­ferred, perhaps using Mill's “four methods of experimental inquiry.” That such laws exist is for Mill an empirical claim. Suppose that phenomena governed by such laws bear a similarity to others which by induction we infer are governed by some similar set of laws. Then we can use the fact that one set of phenomena is so governed to strengthen the inference to laws regarding the second set. Whether this is Newton's idea as well, indeed whether it is even all of what Mill has in mind, I can't say. But I be­lieve at least that neither Newton nor Mill regarded inductive inferences as subject to a purely formal rule allowing one to validly infer that for any sample and population the former matches the latter.

3.