Begin with global counterexamples. Let us say that determinism is true at our world. Familiar arguments purport to show that, if this is the case, then no one has the ability to do anything, except perhaps for what she actually does (for several developments of such an argument, see van Inwagen 1983, 55–105). But if (CA) is true, then agents would have the ability to perform various actions that they do not actually perform. For it is plausible that the conditionals in terms of which (CA) analyz