WHEWELL VERSUS MILL: ARE INDUCTIVE PREMISES RESTRICTED TO SIMPLE OBSERVATIONS?
I will return now to Whewell and deal with several important charges leveled by him against Mill (and implicitly against Newton as well) that were not discussed earlier. I will also examine Mill's actual and possible replies.
Understanding this debate between Whewell and Mill goes a long way toward understanding later skepticism about the role or importance of inductive generalization.[39]Whewell writes:
Induction is familiarly spoken of as the process by which we collect a general proposition from a number of particular cases; and it appears to be frequently imagined that the general proposition results from a mere juxtaposition of the cases, or at most, from merely conjoining and extending them. But if we consider the process more closely... we shall perceive that this is an inadequate account of the matter. The particular facts are not merely brought together, but there is a new element added to the combination by the very act of thought by which they are combined. There is a conception of the mind introduced in the general proposition, which did not exist in any of the observed facts.[40]
Whewell claims that to think of inductive generalization as something that merely goes from particular cases to a general proposition, or from the composition of a sample to that of a population, is to omit an extremely important aspect of such reasoning, that is, “the act of invention which is requisite in every inductive inference.”
For example, when in book 3 of the Principia Newton makes an inductive generalization to his universal law of gravity from the six phenomena he cites plus his theorems proved in book 1, one of the most important parts, the part that represents the heart of the discovery, is the attribution of a central inverse-square force continually drawing the planets and their satellites away from rectilinear motion.
The existence of such a force for each planet and satellite was not a simple observation, but itself a conclusion that required the mind to impose the conception of a central inverse-square force on observed planets and satellites. This process, in which “we bind together facts by superinducing upon them a new conception,” Whewell calls “colligation.” It is, he thinks, required in a scientific induction; it is crucial for understanding what goes on when an induction is made; it is something omitted in standard accounts of inductive reasoning, such as those given by Newton and Mill; and without it inductions are restricted to simple observational generalization of the “all crows are black” variety.I take Whewell to be saying, then, that it is only by recognizing that the mind imposes a conception on what is observed that we can understand how inferences can be made to unobservables. Mill's inductions, which do not introduce such an idea, are confined to generalizations about observables.
I will examine two related claims Whewell makes and Mill's responses to them. The first, discussed in the remainder of this section, involves Whewell's charge against Mill that inductive premises of the sort invoked by Newton (in which it is claimed that an inverse-square force acts on each of the planets) cannot be established by simple observation. The second, to be treated in the following section, involves Whewell's claim, contra Mill, that inductive premises are not mere descriptions of the data.
There is no incompatibility between Whewell's ideas about colligation and Mill's definition of induction, nor between Whewellian colligation and Newton's inductive rule 3. One can accept Mill's definition and Newton's rule 3 (given in section 1), while subscribing to Whewell's view that in determining what is true of certain individuals or at certain times, or what qualities observable bodies have, the mind introduces a conception (e.g., inverse-square force) not in the facts.
One could even claim, with Whewell, that when an inductive generalization is made in science this step is often the most original and important. Perhaps recognizing that each of the known planets and satellites is drawn away from rectilinear motion by an inverse-square force was the most original and difficult part for Newton; perhaps generalizing to all bodies was simple. Admitting this, however, does nothing to weaken Mill's definition of induction or Newton's rule 3. Nor does it mean that the general proposition inductively inferred is unimportant. Newton's claim that all bodies in the universe are subject to the same inverse-square attractive force— induced from the claim that all the planets and their satellites are subject to such a force—is one of the boldest and most original scientific claims ever made. Nor does saying that Mill's definition of induction and Newton's rule 3 are compatible with Whewell's ideas about colligation mean that either Mill or Newton would have to accept those ideas. (In the next section I will return to this.)When Whewell claims that Newton imposed a conception of an inversesquare force acting on bodies in the solar system, and that Kepler imposed a conception of an ellipse on the observed positions of Mars (a claim Mill focuses on in his discussion), one of the things Whewell may be saying is this: Newton could not observe this force in the way that one can feel an impact on one's own body, and Kepler could not observe the elliptical path of Mars in the way that one can observe the elliptical path of a model train around the track. Newton's force and Kepler's elliptical path had to be inferred from other observations, together with various empirical assumptions, using a good deal of mathematics. This can be granted without in any way denying that Newton made an inductive generalization from an inverse-square force operating on known planets and satellites to its operating on all bodies, or that Kepler made an inductive generalization from a fact about the orbit of Mars to a claim about the orbits of all the planets.
Inductive generalization, as defined by Mill and as employed by Newton, does not require that the facts from which such a generalization is inferred be “directly observable” without inference.Nevertheless, Whewell has a legitimate complaint against Mill. Although Mill's definitions of induction do not require inferences only from what is “directly observable,” some of Mill's discussions of the definitions, for example his discussion of Kepler, suggest otherwise.[41] In the latter case Mill makes it sound as if he is saying that the fact that the successive positions of Mars lie on an ellipse can be determined by “direct observation” without inference. This is certainly not true in the case of Kepler (as Whewell himself emphasizes). Since the Martian orbit with respect to the sun had to be determined from observations made not on the sun but on the moving earth, Kepler in fact attempted to calculate directions of sides in an earth-sun- Mars triangle on the basis of observations of the earth-Mars line. Establishing an elliptical orbit for Mars was an intricate task, involving among other things inferences from the positions of Mars observed from the earth. If, despite his definition of induction, Mill believed that induction can be made only from facts themselves ascertained solely by observation without inference, then Whewell's complaint in this regard would be legitimate.
Despite passages from Mill that seem to suggest such a simple view of induction, Mill does not in fact believe this is so. He writes that
in many branches of science single facts have to be proved, as well as [general] principles; facts as completely individual as any that are debated in a court of justice.... A remarkable example of this is afforded by astronomy.[42]
Mill's examples are the magnitudes of particular bodies in the solar system, their mutual distances, the shape of the earth, and its rotation. He writes:
scarcely any of them [is] accessible to our means of direct observation: they are proved directly by the aid of inductions founded on other facts which we can more easily reach.
He cites the determination of the distance of the moon from the earth— summarizing the “circuitous process” by which this was determined. Mill's point here is that these “particular facts” are themselves inferred from others using inductions.11 Once established, however, they can then form the basis for inductive generalizations.
On Newton's view many of the “phenomena” which form the basis for an inductive generalization are not directly observed but are themselves inferred from other phenomena. For example, Newton's phenomenon 3 states that
The orbits of the five primary planets—Mercury, Venus, Mars, Jupiter, and Saturn—encircle the sun.
Newton infers this proposition from the observed phases of these planets.
6.