 We noted above that interventionist versions of manipulability theories are counterfactual theories. What is the relationship between such theories and more familiar versions of counterfactual theories such as the theory of David Lewis? Lewis’ theory is an account of what it is for one individual token event to cause another while, as explained above, versions of interventionist treatments are available for different sorts of type causal claims as well as token causal claims. But if we abstract away from this, there are both important similarities and important differences between the two approaches. As readers of Lewis will be aware, any counterfactual theory must explain what we should envision as changed and what should be held fixed when we evaluate a counterfactual the antecedent of which is not true of the actual world—within Lewis’ framework, this is the issue of which worlds in which the antecedent of the counterfactual holds are “closest” or “most similar” to the actual world. Lewis’ answer to this question invokes a “similarity” ordering that ranks the importance of various respects of resemblance between worlds in assessing overall similarity. (Lewis 1979). For example, avoiding diverse, widespread violations of law is said to be the most important consideration, preserving perfect match of particular fact over the largest possible spatio-temporal region is next in importance and more important than avoiding small localized violations of law, and so on. As is well-known the effect of this similarity ordering is, at least in most situations, to rule out so-called “back-tracking” counterfactuals (e.g., the sort of counterfactual that is involved in reasoning that if the effect of some cause had not occurred, then the cause would not have occurred). When the antecedent of a counterfactual is not true of the actual world, Lewis’ similarity metric commonly leads us (at least in deterministic contexts) to think of that antecedent as made true by a “small” miracle.