HOLISM

This leads to the most important difference between Mill and Whewell regarding induction. Whewell seems committed to some fairly strong form of holism regarding inductive reasoning; Mill is not.

Now there are two holistic positions Whewell might be taking re­garding the role of consilience with respect to inductive reasoning:

1. The premises of an inductive argument provide a strong reason to believe the conclusion of the argument if and only if there is a system containing the premises and conclusion that is consilient, that is, that can explain and predict a range of phenomena of different types.

2. (“Duhem-Quine holism”) That which is justified is not an individual hypothesis but an entire system of hypotheses. And that which justifies is not an individual phenomenon (or its description) but an entire system of phenomena. If and only if consilience is satisfied with respect to this set of phenomena, then it is the system that is justified. The inductive inference is from the set of phenomena to the system of hypotheses, not from an individual phenomenon to a single hypothesis.

Both of these positions have consequences that an inductivist such as Mill will reject.

The second position results in entirely rejecting inductive arguments of the sort Mill and Newton have in mind. On this position one cannot make a valid inductive inference from any (“isolated”) phenomenon or set to some (“isolated”) hypothesis. Consider a passage from book 3 of Newton's Principia in which he explicitly endorses an inductive inference from the fact (“phenomenon”) that bodies on or near the earth gravitate toward the earth, that the moon gravitates toward the earth, that our sea gravitates toward the moon, and that the planets gravitate toward one another, to the proposition that all bodies gravitate toward one another. On position (2) such an inference cannot be made, since it is not holistic. This position amounts to a rejection of Newton's inductive rule 3, and indeed of any inductive generalization that is not a generalization to an entire system of hypotheses (in Newton's case, e.g., a generalization to a set of hypotheses including, in addition to the universal law of gravity, his three laws of motion and perhaps his claims regarding space and time in book 1). Position (2) amounts to a rejection of inductive generalization as customarily understood.

Inductivists such as Mill and Newton can accept a much weaker but I think more plausible position which might be called “modest (or very modest) holism”:

3. (Modest holism): Whether and how much an induction involving the claim that all observed As are Bs supports the inductive conclusion that all As are Bs usually depends on empirical facts not reported in the inductive premise—facts that may be assumed within some system that can be appealed to in defending the inductive generalization.

Is this altogether too modest? Who would deny it? Well, Carnap (1962) would, for example.

Finally, given Whewell's holism, construed in either of the stronger senses, and given Mill's rejection of it, I think we can better understand one of the most interesting but intractable elements in the debate be­tween the two. Earlier I mentioned that Mill declared inductive general­ization to be a necessary first stage in a process he called the “deductive method.” The second stage of the process he calls “ratiocination,” which involves combining the laws inductively inferred and producing deduc­tive explanations and predictions. The third stage, verification, involves empirical testing of the predictions generated.

Now Mill claims that Whewell omits the first stage in the process, the induction to the laws in the system. He simply has the scientist making a conjecture by imposing some conception on nature. As far as reasoning is concerned, Mill claims, Whewell simply has the second and third stages, the ratiocination and the verification, and even if we impose the Whewel- lian idea of consilience on the resulting scientific theory, an argument to its truth or probability will be unjustified. Mill claims that without the in­ductive step (in his sense) there may be an incompatible set of hypotheses which also explain and predict the phenomena and are equally consilient. This is Mill's famous “competing hypothesis” objection, and it is one that Newton also urged against hypothetico-deductivists. Their claim is that with the first inductive step (which for both Mill and Newton could in­clude reasoning generalizing from effects to causes) we eliminate, or at least render improbable, alternative explanations; without it we don't. Whewell's claim is that consilience suffices for this purpose.

I won't try to resolve this “competing hypothesis” debate here. But I will mention one of Whewell's favorite examples, the classical wave theory of light, which he claimed must be true because it completely satisfies his criterion. Mill refused to accept this theory at a time when it was almost universally accepted by physicists. He did so because there was no causal- inductive argument to the existence of the luminiferous ether needed to support the waves. And he remarked (1872, p. 328):

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.

Nor, Mill believes, will this problem be solved by adding the further Whewellian condition of consilience. Historically, of course, Mill turned out to be right: the quantum theory of light was just such a theory that mid-nineteenth-century minds were “unfitted to conceive.” Whether Mill was logically or methodologically right here, I'll leave for another occasion.