Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “counter­support” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H.

Hempel’s Converse Consequence Condition (CCC), Entailment Condition (EC), and Special Consequence Condition (SCC) have some prima facie plausibility when taken individually. Hempel, though, shows that they have no plausibility when taken together, for together they entail that E confirms H for any propositions E and H. This is “Hempel’s paradox”. It turns out that Hempel’s argument would fail if one or more of CCC, EC, and SCC were modified in terms of explanation. This opens up the possibility that Hempel’s paradox (...) can be solved by modifying one or more of CCC, EC, and SCC in terms of explanation. I explore this possibility by modifying CCC and SCC in terms of explanation and considering whether CCC and SCC so modified are correct. I also relate that possibility to Inference to the Best Explanation. (shrink)

Proposals for rigorously explicating the concept of confirmation in probabilistic terms abound. To foster discussions on the formal properties of the proposed measures, recent years have seen the upshot of a number of representation theorems that uniquely determine a confirmation measure based on a number of desiderata. However, the results that have been presented so far focus exclusively on the concept of incremental confirmation. This leaves open the question whether similar results can be obtained for the concept of absolute confirmation. (...) This article closes the gap by providing a representation theorem for absolute confirmation measures. (shrink)