In his very interesting paper at the Rutgers Epistemology Conference, Higher-Order Evidence (PDF), David Christensen discusses a lot of cases where, in the process of investigating whether p, we learn something about our ability to detect whether p. In the primary cases Christensen discusses, we first come to believe p, then come to believe that our capacities are impaired in some way. And one of the epistemologically interesting questions is what we should do at this stage. I wanted to consider a slightly different question.
S is investigating a murder. She gets evidence E, and on the basis of that quite reasonably concludes that it is quite likely the butler did it (her credence in that is 2/3), a serious possibility that the gardener did it (her credence in that is 1/4), and very little chance that neither did it (her credence in that is 1/12).
S then is told, by a usually reliable source, that she has taken some drug that leads to people systematically underestimating how strongly their evidence supports various propositions. So if someone’s taken this drug, and believes p to degree 2/3, then p is usually something that’s more or less guaranteed to be true by their evidence.
What should S do?
I think that if there is an answer, it is nothing, and that’s true of any such case where S comes to a rational conclusion, then gets evidence that she has been irrational. She can’t coherently raise her credences in all of these propositions, after all. And if anything was justified in response to learning about the drug, it would be raising her credence in all the propositions. So no reaction to learning about the drug is justified.
My impression is that my reaction to these cases is not the most popular one, to say the least. But I wondered what everyone else thought about the case.