THE METHOD OF HYPOTHESIS AND INDUCTIVISM

According to a simple version of the method of hypothesis, if the observed phenomena are explained by, or derived from, an hypothesis, then one may infer the truth or probability of that hypothesis.

Whewell (1967, pp. 60—74) offered four conditions which, if satisfied, will make an hypothesis inferable with virtual certainty. First, it should explain all the phenomena which initially prompted it. Second, it should predict new phenomena. Third, it should explain and/or predict phe­nomena of a “kind different from those which were contemplated in the formation of... [the] hypothesis” (p. 65). If this third condition is sat­isfied Whewell says that there is a “consilience of inductions.” Whewell's fourth condition derives from the idea that hypotheses are part of a the­oretical system the components of which are not framed all at once, but are developed over time. The condition is that as the theoretical system evolves it becomes simpler and more coherent.

Since both Laudan and Cantor claim that the wave theorists followed the method of hypothesis while the particle theorists rejected this method in favor of inductivism, it will be useful to contrast Whewell's version of the former with Mill's account of the latter. This contrast should be of special interest for two reasons.

One of the best places to note the contrast in Mill is in his discussion of the “deductive method” (which he distinguishes from the “hypothetical method” or method of hypothesis) (Mill 1959, pp. 299-305). Mill asserts that the deductive method is to be used in situations where causes sub­ject to various laws operate, in other words, in solving typical problems in physics as well as other sciences. It consists of three steps. First, there is a direct induction from observed phenomena to the various causes and laws governing them. Mill defines induction as “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” (p. 188). This concept of inductive generalization is used together with his four famous canons of causal inquiry to infer the causes operating and the laws that govern them. The second part of the deductive method Mill calls “ratiocination.” It is a process of calculation, deduction, or explanation: from the causes and laws we calculate what ef­fects will follow. Third, and finally, there is “verification”: “the conclusions [derived by ratiocination] must be found, on careful comparison, to accord with the result of direct observation wherever it can be had” (p. 303).

Now, in rejecting the method of hypothesis, Mill writes:

The Hypothetical Method suppresses the first of the three steps, the in­duction to ascertain the law, and contents itself with the other two opera­tions, ratiocination and verification, the law which is reasoned from being assumed instead of proved. (p. 323)

Mill's major objection to the method of hypothesis is that various con­flicting hypotheses are possible from which the phenomena can be de­rived and verified. In his discussion of the wave theory of light, Mill rejects the hypothesis of the luminiferous ether on these grounds.

This supposition cannot be looked upon as more than a conjecture; the exis­tence of the ether still rests on the possibility of deducing from its assumed laws a considerable number of actual phenomena.... most thinkers of any degree of sobriety allow, that 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, for want of any­thing analogous in our experience, our minds are unfitted to conceive. (p. 328)

With Whewell's ideas about prediction and consilience in mind, Mill con­tinues:

But it seems to be thought that an hypothesis of the sort in question is en­titled to a more favourable reception if, besides accounting for all the facts previously known it has led to the anticipation and prediction of others which experience afterwards verified.... Such predictions and their fulfill­ment are, indeed, well calculated to impress the uninformed, whose faith in science rests solely on similar coincidences between its prophecies and what comes to pass.... Though twenty such coincidences should occur they would not prove the reality of the undulatory ether.... (pp. 328-329)

Although in these passages Mill does not discuss Whewell's ideas about coherence and the evolution of theories, it is clear that Mill would not regard Whewell's four conditions as sufficient to infer an hypothesis with virtual certainty or even high probability. The reason is that Whewell's conditions omit the first crucial step of the deductive method, the induc­tion to the causes and laws.

If Laudan and Cantor are correct in saying that nineteenth-century wave theorists followed the method of hypothesis and rejected inductiv- ism, then, as these opposing methodologies are formulated by Whewell and Mill, this would mean the following: Nineteenth-century wave theo­rists argued for the virtual certainty or high probability of their theory by first assuming, without argument, various hypotheses of the wave theory; then showing how these will not only explain the known optical phe­nomena but will explain and/or predict ones of a kind different from those prompting the wave hypotheses in the first place; and finally arguing that as the theory has evolved it has become simpler and more coherent. Is this an adequate picture? Or, in addition, did wave theorists employ a crucial inductive step to their hypotheses at the outset? Or do neither of these methodologies adequately reflect the wave theorists' argument?

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