 There are other differences as well, a number of which are explored in an important paper by Briggs (2012). We have already noted that strong centering holds in Lewis’ semantics but not for counterfactuals with an interventionist interpretation. In addition, the inference from (i) “if \(p\) or \(q\) were the case, \(r\) would be the case” to (ii) “if \(p\) were the case, \(r\) would be the case” is invalid within Lewis’ semantics but valid if these counterfactuals are given an interventionist interpretation (Briggs 2012; Fine 2012). It is arguable that in each of these cases, the assessments provided by the interventionist interpretation are correct, assuming that what we want to capture are those counterfactuals that behave in a way that is appropriate for causal interpretation. In addition, Woodward 2003 describes several specific examples in which the two approaches diverge in their judgments about which causal relations are present and in which the interventionist approach seems more  satisfactory.[3]