Mayo vs. Earman on Severity
Mayo vs. Earman
On page 187, Mayo tries to argue against Earman's criticism of error-severity. But first let us see what Earman said:
Deborah Mayo (1991) has argued that the concern with novelty is misplaced. What is really at issue, she maintains, is the severity of a test of a hypothesis, and the resort to novelty is but a ham-handed way of trying to guarantee severity. While I tend to agrtee with her diagnosis, I am concerned that her own criterion of severity is too demanding. According to her account, passing a test with outcome E counts as support for hypothesis H only if the test is severe in that the probability is high that such a passing result would not have occurred were E false. I take this subjunctive clause to imply that Pr(E | ªæH&K) is low (where K is the background knwledge). If this consequence obtained, it would be a beautiful result, since if H and ªæH have comparable priors, it follows that outcome E gives H a high posterior probability ... . The difficulty is that when high-level theoretical hypotheses are at issue, we are rarely in a position to justify a judgment to the effect that Pr(E | ªæH&K) ª‡.5. If we take H to be Einstein's general theory of relativity and E to be the outcome of the eclipse test, then in 1918 and 1919 physicists were in no position to be confident that the vast and then unexplored space of possible gravitational theoried denoted by ªæGTR does not contain alternatives to GTR that yield the same prediction for the bending of light as GTR. Today we know that ªæGTR contains an endless string of such theories. (Earman 1992, 117)
First of all, we have to correct a typographical error: in the phrase "the probability is high that such a passing result would not have occurred were E false", "E" should be replaced by "H" (see the formula). Then, we have got to notice three factors in this argument of Earman's. (1) First, Earman understands Mayo's phrase "the probability is high that such a passing result would not have occurred were H false" as Pr(E |ªæH&K), which looks reasonable, given Mayo's original phrase. (2) Second, Earman's worry is that this probability may often be not as low as Mayo supposes in her definition of severity. And finally, (3) the example of GTR (or ªæGTR) comes as an illustration for the second point (2), in terms of higher-level alternatives (that is, higher-level with respect to the observation of bending of light).
Now let us examine each point quickly. As for (1), Earman's rendering has no problem, and Mayo has no objection; but notice that ªæH may welll introduce what Mayo called the "catchall factor". And as for (3), I have already admitted that Mayo is right, and the Bayesian can learn from Mayo's view, in that higher-level alternatives are not at issue when we are testing how much the light may deflect around the sun. However, as for (2), which is crucial in Earman's worry, I suspect Earman may be right, since, as I have shown in "Why this definition of severity", a far stronger worry than Earman's can be reconstructed in terms of alternative hypotheses at the same low-level. From this, I think the problem of "catchall" factor appears in the error statistics as well as in the Bayesian statistics, and the former is in no better position than the latter.
Earman, John (1992) Bayes or Bust? MIT Press
Mayo, Deborah (1991) "Novel Evidence and Severe Tests" Philosophy of Science 58, 1991.
INDEX- CV- PUBLS.- PICT.ESSAYS- ABSTRACTS- INDEXªELAPLACE- OL.ESSAYS-CRS.MATERIALS
Last modified Jan. 26, 2003. (c) Soshichi Uchii