CONTRASTING METHODS OF DEFENSE

The Newton-Mill-Whewell Tradition of Proof

Within the empiricist tradition of the sort with which Maxwell was familiar, especially in the works of Newton, Mill, and Whewell, is the view that one defends a scientific theory by attempting to prove that it is true.

For Mill, using his “Four Methods of Experimental Inquiry,” we vary circumstances under which phenomena of one type follow those of an­other, and by doing so we can determine whether causation exists and how general it is.^[200] As in the case of Newton, such causal-inductive argu­ments should establish these laws with as much certainty as is possible in empirical science. Mill speaks of arguments of these sorts as providing “proof” of the propositions. Indeed, in his initial definition of “induction” he defines it as “the operation of discovering and proving general propo­sitions.” In cases typical in the theoretical sciences where effects are ex­plained by reference to multiple causes, Mill introduces his “deductive method,” which requires three steps in order to infer the truth of a the­oretical system: causal-inductive generalizations from observations to a set of causal laws comprising the system; “ratiocination,” which involves inferences showing how this set, if true, can explain and predict various observable effects; and verification of new effects predicted.

By contrast, Whewell, who rejects the inductive methodology of Newton and Mill, advocates a robust form of IBE. If the universal causal laws in question not only explain the phenomena used to generate them, but explain and predict phenomena of types different from those that generated the laws to begin with, then Whewell says there is a “consil­ience of inductions,” and we have no basis for any reasonable doubt.^[201] If this continues over time as new phenomena are discovered, and does so in such a way that the theory is simple and coherent, then one can infer with the highest possible certainty that the theory is true.

Newton, Mill, and Whewell do recognize that propositions are intro­duced into science without proof. Newton calls them “hypotheses,” and although in the Principia he claims that they “have no place in experi­mental philosophy,” he does in fact employ them, clearly labeling them as such. Overall his view seems to be that you can introduce them and consider their implications, but you are not justified in inferring that they are true, even if the implications are experimentally verified, since con­flicting hypotheses may be equally successful. Mill has a very similar view. According to Whewell, if the theory explains known phenomena and pre­dicts new ones only of the same type, you can conclude that the theory is “valuable,” or even (so far at least) “verified” by positive instances. But this is not sufficient for proof, which is what Whewell seeks in “testing,” since such theories often turn out to be false.

For purposes of contrast with Maxwell, then, I shall understand these “proof-demanding” writers to be claiming (a) that it is one of the principal aims of scientists to provide empirical proof of a theory; (b) that scien­tists are justified in believing a theory only if they have such proof; and (c) that merely showing that observations constitute positive instances of the theory, or are entailed or explained by it, or even (following contem­porary Bayesians) that the probability of the theory is increased by these observations, is not sufficient for proof.

The Method of Hypothesis

What can you do to defend a theory in the absence of experimental proof? One standard approach is to employ some version of the “method of hypothesis.”

Maxwell writes:

The method which has been for the most part employed in conducting such inquiries is that of forming an hypothesis, and calculating what would happen if the hypothesis were true. If these results agree with the actual phenomena, the hypothesis is said to be verified, so long, at least, as some­one else does not invent another hypothesis which agrees still better with the phenomena.^[202]

Maxwell rejects this “method of hypothesis” on grounds that apply to even more sophisticated versions, namely, that its users have no empirical basis from which to generate their hypotheses. Because of this, either they leave “their ideas vague and therefore useless” or else they engage in an “illegitimate use of the imagination.” By the former Maxwell means that one thing users of the method of hypothesis sometimes do is invent very general hypotheses that are not sufficiently precise or developed to be tested. By the latter he means that the fact that hypotheses accommodate the phenomena by itself constitutes insufficient empirical warrant for those hypotheses, since there may be other conflicting hypotheses that accom­modate the phenomena at least as well, if not better.^[203] Even if Maxwell were to agree (which he does not) that the type of “verification” claimed by the method of hypothesis provided some support for a hypothesis, it cannot provide enough to justify a belief in the hypothesis. Maxwell wants a method that can do the latter when proof by “methodized experiment and strict demonstration” is not available. He also seeks a method that will enable one to provide a set of hypotheses that are not “vague and therefore useless.” This is the entering point for the “method of physical speculation.”

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