Counterlegal dependence and causation’s arrows: causal models for backtrackers and counterlegals

A counterlegal is a counterfactual conditional containing an antecedent that is inconsistent with some set of laws. A backtracker is a counterfactual that tells us how things would be at a time earlier than that of its antecedent, were the antecedent to obtain. Typically, theories that evaluate counterlegals appropriately don’t evaluate backtrackers properly, and vice versa. Two cases in point: Lewis’ (Noûs 13:455–476, 1979a) ordering semantics handles counterlegals well but not backtrackers. Hiddleston’s (Noûs 39(4):632–657, 2005) causal-model semantics nicely handles backtrackers but not counterlegals. Taking Hiddleston’s account as a starting point, I offer steps toward a theory capable of handling both counterlegals and backtrackers. The core contribution of this paper is a means for evaluating counterlegals relative to minimally-illegal models.