Advancing the counterfactual analysis of causation

What does it mean to say that one event is a cause of another? The simplest counterfactual analyses identify causation with one of two counterfactual-dependence relations: (1) if event c had not occurred, then (distinct) event e would not have occurred; (2) if c had not occurred, e\u27s probability would have been lower. These analyses enjoy some success. For the first: the dart-throw caused the balloon-pop, because if the throw had not occurred, the pop would not have occurred. For the second: suppose two radioactive samples, A and B, are introduced into a room containing a Geiger counter, and the counter clicks once due to an emission from an A-atom; then the introduction of A is a cause of the click; the click might have occurred without the A-introduction (a B-atom might have emitted), but we can say at least that without the A-introduction, the probability of the click would have been lower. Ultimately, however, these analyses fail, for two clear reasons. Preemption: add to the dart scene that Lucy would have thrown her dart if I had refrained—then although my throw caused the pop, the pop is not dependent on my throw. Failed potential causes: the probability of the click would have been lower without the B-introduction, but the B-introduction did not actually succeed in causing of the click. I defend the two simple analyses against various other objections; I then try to home in on the precise nature of their genuine problems; I examine almost all the attempts to date to improve upon the simple analyses; and finally I propose two new analyses. One of my analyses is deterministic, the other is confined to worlds that are purely indeterministic. Both analyses take causation to be primarily a matter of counterfactual dependence in the circumstances: holding certain features of the world fixed, effects and their probabilities do indeed depend (almost exclusively) on their causes (or their direct causes). My discussion of background issues—counterfactual semantics, objective chance, events—includes arguments for substantial simplifications of David Lewis\u27s theory of events