Conjunction Conditionalization and Irrelevant Semifactuals

Are counterfactuals with true antecedents and consequents trivially true? The principle of Conjunction Conditionalization ((A∧C)→(A>C)) is highly controversial. Many philosophers view it as an attractive feature of Lewis's semantics for counterfactuals that it can easily be modified to avoid this principle. However, Walters and Williams (2013) beg to differ. They argue that Conjunction Conditionalization is an indispensable ingredient of any Lewisian semantics, since CC is entailed by standard Lewisian theorems and a plausible semantic claim about irrelevant semifactuals. If this is true, the entire tradition of revisionist counterfactual semantics is misguided, and so are many philosophical theories in which counterfactuals play a role. We argue, in defence of the revisionist tradition, that Walters and Williams' ‘plausible semantic claim’ is in fact anything but plausible. It turns out to entail semantic principles far more controversial than Conjunction Conditionalization.