INTRODUCTION
For some time now induction, particularly inductive generalization, has been under siege. A frontal attack, based on the sort of skepticism attributed to Hume, is made by Popper (1959), according to which no inductive generalization can be rationally justified.
But other nonskeptical attacks are meant to be just as devastating. For example, it is claimed that good scientists do not use inductive generalization, and that if and when they appear to be using such reasoning they are really employing something else, such as “deductive reasoning” (again, Popper), or “inference- to-the-best-explanation” (Harman 1965, Lipton 1991), or statistical reasoning invoking “severe testing” (Mayo 1996). It is also claimed that inductive generalization, as typically characterized, is too incomplete, too vague, or too puerile to adequately express complex and sophisticated scientific reasoning (Whewell 1967). At best it occurs only when one can directly observe instances of a low-level empirical generalization, and it is not applicable to more theoretical science. Finally, some have claimed that although there is such a thing as inductive generalization, contrary to what inductivists believe, it is not subject to formal and universal rules of the sort usually proposed (Norton 2005).I want to argue that induction, as traditionally formulated by inductiv- ists such as John Stuart Mill and Isaac Newton, can withstand these attacks. Or at least these inductivists can put up a better fight than their opponents might imagine. I will look at a historically important controversy between William Whewell, on the one hand, and Newton and Mill, on the other. Admittedly, all three claim to be endorsing inductive generalization. But Whewell claims that Newton and Mill really got it wrong. The latter are usually thought of as the more typical inductivists, deserving of philosophical scorn, while Whewell is currently more popular with a disparate group who classify him as one of their own, either as a hypothetico-deductivist, or a defender of inference to the best explanation, or a Quinean holist, or even a Kantian a priorist.
I propose to defend Mill and Newton against this formidable opponent. I will also defend Mill and Newton against a more recent formidable opponent, John Norton, who goes even further than Whewell in his rejection of inductivists such Mill and Newton.Mill (1872, p. 188) offers a classic definition of induction:
Induction, then, is that operation of the mind by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.[33]
Isaac Newton never explicitly defines “induction” in his works but, like Mill, considers it to be a necessary component of scientific reasoning to general propositions:
In... experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. (Newton, 1999)
The closest Newton comes to a definition of induction is in rules 3 and 4 in the opening section of book 3 of the Principia:
Rule 3: The 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.
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 exception.
Newton treats rule 3 as an inductive rule applicable to “qualities of bodies that cannot be intended and remitted.”[34]
These two inductive rules are to be used in conjunction with two causal rules:
Rule 1: No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena.
Rule 2: Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same.
Newton explicitly invokes all four of these rules in deriving the law of universal gravitation in book 3 of the Principia. Very briefly, his derivation starts with six phenomena pertaining to the Keplerian motions of the planets and their satellites that he claims have been astronomically established. Arguing from propositions established in book 1 showing that such motions are produced by an inverse square attractive force, and then using his causal rules of reasoning 1 and 2, he concludes that this force is the same force in each case that causes the Keplerian motions of all the planets and their moons. In accordance with his rule 3 of inductive generalization, he infers that all bodies in the universe are subject to this force. Finally, by rule 4, since the law is derived from phenomena by induction, it should be considered true, or at least approximately true, until new phenomena are discovered that show that the law needs modification.
Whewell takes on both Newton and Mill in his works. Chapter 13 of his The Philosophy of the Inductive Sciences is devoted to showing what is wrong with each of Newton's four rules and how to substantially reformulate them in Whewellian terms. However, a far greater criticism is reserved for his contemporary Mill in sections of the book that develop his own doctrines of “colligation” and “consilience.” I will discuss Whewell's arguments against Newton and Mill, as well as Norton's arguments against all three.
2.