Solving the tacking problem with contrast classes

Abstract
The traditional Bayesian qualitative account of evidential support (TB) takes assertions of the form 'E evidentially supports H' to affirm the existence of a two-place relation of evidential support between E and H. The analysans given for this relation is $C(H,E) =_{def} Pr(H\arrowvertE) \models Pr(H)$ . Now it is well known that when a hypothesis H entails evidence E, not only is it the case that C(H,E), but it is also the case that C(H&X,E) for any arbitrary X. There is a widespread feeling that this is a problematic result for TB. Indeed, there are a number of cases in which many feel it is false to assert 'E evidentially supports H&X', despite H entailing E. This is known, by those who share that feeling, as the 'tacking problem' for Bayesian confirmation theory. After outlining a generalization of the problem, I argue that the Bayesian response has so far been unsatisfactory. I then argue the following: (i) There exists, either instead of, or in addition to, a two-place relation of confirmation, a three-place, 'contrastive' relation of confirmation, holding between an item of evidence E and two competing hypotheses H₁ and H₂. (ii) The correct analysans of the relation is a particular probabilistic inequality, abbreviated C(H₁, H₂, E). (iii) Those who take the putative counterexamples to TB discussed to indeed be counterexamples are interpreting the relevant utterances as implicitly contrastive, contrasting the relevant hypothesis H₁ with a particular competitor H₂. (iv) The probabilistic structure of these cases is such that ∼C(H₁, H₂, E). This solves my generalization of the tacking problem. I then conclude with some thoughts about the relationship between the traditional Bayesian account of evidential support and my proposed account of the three-place relation of confirmation
Keywords confirmation theory  tacking problem  contrastive Bayesianism  Law of Likelihood
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