Branden Fitelson

Let L be a sentential (object) language containing atoms ‘A’, ‘B’, . . . , and two logical connectives ‘&’ and ‘→’. In addition to these two logical connectives, L will also contain another binary connective ‘ ’, which is intended to be interpreted as the English indicative. In the meta-language for L , we will have two meta-linguistic operations: ‘ ’ and ‘ ’. ‘ ’ is a binary relation between individual sentences in L . It will be interpreted as “single premise entailment” (or “single premise deducibility in L ”). ‘ ’ is a monadic predicate on sentences of L . It will be interpreted as “logical truth of the logic of L ” (or “theorem of the logic of L ”). We will not presuppose anything about the relationship between ‘ ’ and ‘ ’. Rather, we will state explicitly all assumptions about these meta-theoretic relations that will be required for Gibbard’s Theorem.

Naive deductivist accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H·X, for any X—even if X is completely irrelevant to E and H. Bayesian accounts of confirmation may appear to have the same problem. In a recent article in this journal Fitelson (2002) argued that existing Bayesian attempts to resolve of this problem are inadequate in several important respects. Fitelson then proposes a new‐and‐improved Bayesian account that overcomes the problem of irrelevant conjunction, and does so in a more general setting than past attempts. We will show how to simplify and improve upon Fitelson's solution.

Corroborating Testimony, Probability and Surprise’, Erik J. Olsson ascribes to L. Jonathan Cohen the claims that if two witnesses provide us with the same information, then the less probable the information is, the more confident we may be that the information is true (C), and the stronger the information is corroborated (C*). We question whether Cohen intends anything like claims (C) and (C*). Furthermore, he discusses the concurrence of witness reports within a context of independent witnesses, whereas the witnesses in Olsson's model are not independent in the standard sense. We argue that there is much more than, in Olsson's words, ‘a grain of truth’ to claim (C), both on his own characterization as well as on Cohen's characterization of the witnesses. We present an analysis for independent witnesses in the contexts of decision-making under risk and decision-making under uncertainty and generalize the model for n witnesses. As to claim (C*), Olsson's argument is contingent on the choice of a particular measure of corroboration and is not robust in the face of alternative measures. Finally, we delimit the set of cases to which Olsson's model is applicable. 1 Claim (C) examined for Olsson's characterization of the relationship between the witnesses 2 Claim (C) examined for two or more independent witnesses 3 Robustness and multiple measures of corroboration 4 Discussion.