UNDERDETERMINIST RESPONSES

explanation” argument in claiming that the nineteenth­century wave theory of light, and particularly the hypothesis that there is a luminiferous ether, should not be regarded as “probably true” on the grounds that it “accounts for all the known phenomena,” including experimental results involving diffraction and interference.

Whether this argument carries any weight depends on what Mill means by speaking of explanations that are “equally possible.” If he means that there are optical theories supported at least as well as the wave theory is by diffraction, interference, and other experimental results (however “sup­port” is to be understood), then the following question needs to be raised:

Q: How does Mill know this? What evidence does he have?

One answer is: he doesn't know this because he has no evi­dence. The only way to know this is to produce such an al­ternative and to show that it is supported as well as the wave theory is by the experiments. One who gives this answer is saying (following Newton): “Put up or shut up!” That is, if you are going to use the “alternative (or competing) explanation” argument, then (a) give me an alternative explanation, and (b) show me how it is supported by the experiments.^[97]

A different answer to (Q) is to say that Mill does have evidence, viz. historical evidence. The history of science (the “pessimistic induction”) shows that in most cases, including that of the wave theory itself, theories that were supported by the evidence available turned out later to be refuted by new data and replaced by conflicting theories, in the light of new data.

Let the hypothesis be:

h: There exists a luminiferous ether.

The “pessimistic induction” does not provide evidence in one of my A-senses (or in the explanatory B-sense) against h. It is not the case that, given the historical fact that most theories have turned out false, there is probably an explanatory con­nection between that fact and the fact that the ether does not exist. If Mill were to claim that he has A- evidence that the ether probably does not exist, then, following Newton, I would say: “Let him produce it; don't cite history” In fact, of course, Mill does not give a historical, or any other, argument that he takes to provide evidence against the existence of the ether. His central claim is that there is no known evidence for its existence.

By saying that there probably are alternative hypotheses that are “equally possible,” I would understand Mill to mean simply that there probably are alternatives that are logically consistent with the experimental data and which, if they were true, would correctly explain those data. But, he is saying, the fact that a hypothesis, if true, would correctly explain some data is no reason whatever to conclude that those data pro­vide evidence for that hypothesis. The Mafia hypothesis in section 1, if true, would correctly explain the results of the coin tossing. But unless there is evidence that the Mafia is in­volved, the experimental results provide no evidence for the Mafia hypothesis. Indeed, this is Mill's own objection against Whewell's version of hypothetico-deductivism. In order to show that observed phenomena provide evidence for a hy­pothesis, you need to show more than that the hypothesis, if true, would explain those phenomena.

Accordingly, Mill's “competing hypothesis” objection might best be put like this: Suppose there is evidence e for a hypothesis h (e.g., causal-inductive evidence that goes be­yond simply e’s being logically consistent with h). Then, if there were some alternative hypothesis h' that, if true, would explain e, that fact would not refute or weaken the claim that e is evidence that h. Put this way, the objection doesn't claim that there are, or probably are, alternative hypotheses that ex­plain e. It is a conditional claim that amounts to what Newton says in his Rule 4: If there are “contrary hypotheses” to h, they do not refute or weaken inductive evidence for h unless they have inductive evidence of their own. So understood, the “competing hypothesis” objection does not establish un­derdetermination. The only time invoking a competing hy­pothesis h' will serve to show that the original hypothesis h is not supported by e is when the “support” for h simply amounts to its explaining e.

It might be suggested that the way to generate underde­termination is to combine three ideas, each of which may be lurking in the minds of those who preach the doctrine: (a) a hypothetico-deductive view of evidence (the thesis that a set of observed phenomena constitutes evidence for a system of hypotheses if and only if this system deduc­tively explains those phenomena); (b) an existence claim about competing hypotheses (the thesis that for any system of hypotheses that deductively explains the observed phe­nomena, there exists a competing system of hypotheses that does, too); and (c) a claim about evidence (if e is evidence for some system of hypotheses H, then e cannot be evidence for H', where H' is incompatible with H). Suppose, then, that H represents some system of hypotheses, and that H deductively explains a set O of observed phenomena, so that, in accordance with (a), set O constitutes evidence for H.

This doesn't yield underdetermination, only a contradic­tion. The three ideas together are inconsistent. Suppose that H deductively explains O. Then, by (a), O is evidence that H. But if, in addition, (b) and (c) hold, then O cannot be evi­dence that H.

Of these three ideas, I can accept only (c). Indeed, (c) is entailed by my concepts of potential, veridical, and ES-evi- dence (as well as by the upgraded and explanatory Bayesian concepts in chapter 1), since all these require probabilities greater than % for e to be evidence that h. Claim (a) I reject because, in accordance with my A-concepts of evidence (as well as all the Bayesian ones I have noted), e can be evidence that h even if h does not deductively explain e. Indeed, entail­ment of e by h, whether or not this is explanatory, is neither a necessary nor a sufficient condition for e to be evidence that h. Claim (b), the existence claim about competitors, I find dubious for the same reason Newton does: Don't give me possibilities; give me reasons to think that for every system of hypotheses that deductively explains the observed phe­nomena there exists a competitor that does, too. (This is par­ticularly important if, like Whewell, you demand that the competing system, as well as the original one, deductively explain phenomena of different kinds (“consilience”) and that the assumptions of the explanation satisfy “coherence”^[99]). But even if you can give reasons to think that for any system of hypotheses there are competitors of these sorts, your argument won't work unless you accept (a), a hypothetico- deductive view of evidence, which I, and Bayesians, do not.

Finally, then, if you are an underdeterminist, there are two positions you could take with regard to simplicity. On both positions, you could say that theories are underdetermined by evidence, in the sense that no matter what the evidence, it does not give a sufficient reason to believe the theory. According to the first position, simplicity is an epistemic virtue, so that if a theory is simple (or the simplest of the competitors), then the evidence plus simplicity give a good reason to believe the theory. According to the second posi­tion, simplicity is not an epistemic virtue. Since theories are underdetermined by the evidence, and since simplicity is not an epistemic virtue (nor are any other criteria such as explanatory power, unification, and so forth), you are never epistemically justified in believing a theory. (At best you are only pragmatically justified in using it for certain purposes.) The former position requires accepting a claim I rejected in chapter 2, viz. that simplicity is an epistemic virtue. 'lhe latter lands you in the position of epistemic skepticism. Both consequences are avoided by utilizing an A- or B-explanatory concept of evidence and rejecting underdetermination of the sort I have been considering.

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