Mill, John Stuart (1806–73)

5. Inductive science

Mill does not raise purely sceptical questions about simple generalization from experience; he none the less thinks it a highly fallible method. His aim is to show how reasoning methods can evolve from it which greatly reduce the fallibility of induction, even though they can never wholly eliminate it.

Humankind begins with ‘spontaneous’ and ‘unscientific’ inductions about particular unconnected natural phenomena or aspects of experience. As these generalizations accumulate and interweave, they justify the second-order inductive conclusion that allphenomena are subject to uniformity, and more specifically, that all have discoverable sufficient conditions. In this less vague form, the principle of general uniformity becomes, given Mill’s analysis of causation, the Law of Universal Causation. It in turn provides (Mill believes) the grounding assumption for a new style of reasoning about nature – eliminative induction.

In this type of reasoning, the assumption that a type of phenomenon has uniform causes, together with a (revisable) assumption about what its possible causes are, initiates a comparative inquiry in which the actual cause is identified by elimination. Mill formulates the logic of this eliminative reasoning in his well-known ‘Methods of Experimental Inquiry’ (Chapter 7, Book 2 of System of Logic). (A full account is given in Mackie (1974).) His picture of the interplay between enumerative and eliminative reasoning, and of the way it entrenches, from within, our rational confidence in the inductive process, is elegant and penetrating.

The improved scientific induction which results from this new style of reasoning spills back onto the principle of Universal Causation on which it rests, and raises its certainty to a new level. That in turn raises our confidence in the totality of particular enumerative inductions from which the principle is derived. So the amount of confidence with which one can rely on the ‘inductive process’ as a whole depends on the point which has been reached in its history – though the confidence to be attached to particular inductions always remains variable.

Mill’s inductivism – his view that enumerative induction is the only ultimately authoritative method of inference to new truths – was rejected by William Whewell (see Whewell, W. §2), who argued that the really fundamental method in scientific inquiry was the Hypothetical Method, in which one argues to the truth of a hypothesis from the fact that it would explain observed phenomena (see Inference to the best explanation). Mill had read Whewell’s History of the Inductive Sciences (1837), and could hardly fail to be aware of the pervasiveness of hypotheses in the actual process of inquiry, or of their indispensability in supplying working assumptions – their ‘heuristic’ value, as Whewell called it. But what Mill could not accept was that the mere fact that a hypothesis accounted for the data in itself provided a reason for thinking it true.

Yet Whewell’s appeal was to the actual practice of scientific reasoning, as observed in the history of science. An appeal of that kind was precisely what Mill, on his own principles, could not ignore. If the disposition to hypothesize is spontaneous, why should it not be recognized as a fundamental method of reasoning to truth, as enumerative induction is?

Mill’s refusal to recognize it is not arbitrary. The essential point underlying it is a powerful one: it is the possibility that a body of data may be explained equally well by more than one hypothesis. Mill does not deny the increasingly deductive and mathematical organization of science – he emphasizes it. That is quite compatible with his inductivism, and indeed central to his account of the increasing reliability of the inductive process. He further agrees that a hypothesis can sometimes be shown, by eliminative methods of inductive reasoning which he accepts, to be the only one consistent with the facts. And he allows various other cases of apparently purely hypothetical reasoning which are, in his view, genuinely inductive.

When all such cases have been taken into account, we are left with pure cases of the Hypothetical Method, in which the causes postulated are not directly observable, and not simply because they are assumed to operate – in accordance with known laws, inductively established – in regions of time or space too distant to observe. What are we to say of such hypotheses? For example of the ‘undulatory’ theory of light? They cannot, Mill says, be accepted as inductively established truths, not even as probable ones.

An hypothesis of this kind is not to be received as probably true because it accounts for all the known phenomena; since this is a condition sometimes fulfilled tolerably well by two conflicting hypotheses; while there are probably many others which are equally possible, but which from want of anything analogous in our experience, our minds are unfitted to conceive.

(1843: 500)

Such a hypothesis can suggest fruitful analogies, Mill thinks, but cannot be regarded as yielding a new truth itself. The data do not determine a unique hypothesis: it is this possibility of underdetermination which stops him from accepting hypothetical reasoning as an independent method of achieving truth.

In seeing the difficulty Mill is certainly on solid ground. What he does not see, however, is how much must be torn from the fabric of our belief if inductivism is applied strictly. So it is an important question whether the difficulty can be resolved – and whether it can be resolved within a naturalistic framework which does not appeal to an underlying idealism, as Whewell did. If naturalism can endorse the hypothetical method, then among other things it can develop a more plausible empiricism about logic and mathematics than Mill’s. But the ramifications of his inductivism are even wider, as becomes apparent from an examination of his general metaphysics.