THE WEAKNESS ASSUMPTION

I will illustrate this assumption by reference to three standard theories of evidence. The first theory is a Bayesian one: for a fact e to be evidence that a hypothesis h is true it is both necessary and sufficient that e increase h's probability over its prior probability.

A second standard theory of objective evidence is hypothetico-deductive. For e to be evidence that h it suffices that e be derivable deductively from h. So, for example, since the rectilinear propagation of light is derivable from the classical wave theory of light it is evidence for that theory. This is a very weak notion of evidence, because it allows the same fact to be evidence for a range of conflicting theories. (The same is true of the previous Bayesian account.) For example, since the rectilinear propagation of light is also deriv­able from the classical particle theory, it is evidence for that theory as well.

A third approach to objective evidence is a “satisfaction” theory of the sort proposed by Hempel (1965).

Let me say why I believe such notions of evidence are too weak for scientists to take an interest in. Why do scientists and others want evi­dence for their theories? What does evidence that h give you? My answer is that it gives you a good reason to believe h. Not necessarily a conclusive one, or the best possible one, but a good one nonetheless. If the results of the biopsy constitute evidence that the patient's tumor is malignant then there is a good reason to believe the patient has cancer. By contrast, if you visit your doctor complaining of a stomach ache persisting for the last few days I don't believe the doctor would or should count this fact by itself as evidence that you have cancer, even if the probability that you do is raised slightly by this symptom. By itself it is not a good reason to believe this hypothesis. Similarly, although the fact that I am entering an elevator increases my chances of being in an elevator accident, it is not evidence that this will be so, even a little bit of evidence, since by itself it fails to provide any reason to believe this hypothesis.

Now I do think that evidence is related to probability but that it is a “threshold” concept with respect to probability. In order for e to be evidence that h there must be a certain threshold of probability that e gives to h, not just any amount greater than zero. What is the threshold? Returning to the idea that evidence provides a good reason to believe, let me state a principle that I find quite intuitive, namely, that if e is a good reason to believe h, then it cannot also be a good reason to believe not-h or some proposition incompatible with h.

Indeed, if I am right, and what scientists seek when they seek evidence is a good reason to believe h, then e can be evidence that h even if e lowers h's probability from what it was before. Suppose that the initial informa­tion is that Peter is taking medicine M to relieve symptoms S, where M is 95% effective. Suppose there is new information that Peter has just taken another medicine M' to relieve symptoms S, where M' is 90% effective in relieving S and where M' completely cancels M. (Peter decides to take M', let us say, because he has just been told that it has fewer side effects.) Now, I would say that the fact that Peter has taken M' is a good reason to believe, is evidence that, his symptoms S will be relieved, despite the fact that the probability of this hypothesis on this information is less than it was before. So evidence need not raise the probability of a hypothesis and can even lower it.

Does this mean that it is impossible to have evidence for conflicting theories? Yes and no. Yes, it is impossible for the same fact to be evidence for conflicting theories. The fact that I am about to toss this fair coin is not evidence that it will land heads and evidence that it will land tails. It is not evidence—not even a little bit of evidence—that either “theory” is true.

Suppose, however, that we consider a different coin, whose fairness we don't yet know.

What happens when the two bodies of evidence are combined? Will the combination be evidence for both theories? Not necessarily. It may be evidence for neither. In our coin-tossing example, if we consider the two experiments to have equal probative value and we combine their outcomes in the simplest manner, the result would be 200 tosses with this coin, yielding a total of 100 heads and 100 tails. This combined infor­mation by itself would not be evidence that the coin is heads-biased and evidence that it is tails-biased. The combined results in this case do not provide a good reason for believing either or both of the bias theories.

Do the combined results provide evidence, and hence a good reason to believe, that the coin is fair (since there were 100 heads out of the 200 total)? In this case, where similarly conducted experiments yield re­markably different outcomes, a reasonable conclusion might be to express puzzlement and say that the combined information by itself does not give us a reason to believe the coin is fair either, or indeed to believe anything about the fairness or bias of the coin.

In brief it is possible to have evidence, i.e., different bodies of evidence, for conflicting theories, provided that each body is considered in the absence of the other. My claim is only that a single body of information is not evidence for conflicting theories. When it seems otherwise, I suggest, we are considering and isolating parts of that information in such a way that one part in the absence of others would be evidence. The combined results of the two coin-tossing experiments constitute evidence for heads­bias and for tails-bias only in this restricted sense.

Now some philosophers who are objective Bayesians about evidence suggest that there is a concept of evidence according to which e is evi­dence that h if and only if h's probability on e is sufficiently high, say greater than 1/2. This notion is much stronger than the weak increase­in-probability account. And it has the advantage of ruling out the unwanted lottery, elevator, and stomachache cases. However, even if probability greater than 1/2 is a necessary condition, it is not sufficient. High proba­bility by itself is too weak for evidence, since h's probability may be high with or without e. It may have nothing to do with e. Let e be the fact that Michael Jordan eats Wheaties. (He used to promote Wheaties on TV.) Let h be the hypothesis that Michael Jordan will not become pregnant. Now h's probability with or without e is close to 1. Yet surely the fact that Michael Jordan eats Wheaties is not evidence, or a good reason to believe, that he will avoid pregnancy. For e to be evidence that h, for e to be a good reason to believe h, not only must h's probability on e be sufficiently high, but there must be some other connection between e and h, or the probability of such a connection: e must have “something to do” with h. What that amounts to is a question I discuss elsewhere (see chapter 1), and I will not try to deal with here.

Very briefly, the h-d and “satisfaction” views of evidence are much too weak because, like the two probability views just mentioned, they fail to provide a good reason to believe.

On all of the views of evidence I have cited—the two Bayesian views, hypothetico-deductivism, Hempel's satisfaction theory, and Glymour's bootstrapping conception—it is too easy to get evidence. More important, what you get does not necessarily give you a good reason, or indeed, any reason, to believe a hypothesis. This, then, is the first reason scientists don't and shouldn't take such philosophical accounts of evidence seriously: they are too weak to be taken seriously. They don't give scientists what they want, or enough of what they want, when they want evidence.

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