Joseph Halpern and Judea Pearl ([2005]) draw upon structural equation models to develop an attractive analysis of ‘actual cause’. Their analysis is designed for the case of deterministic causation. I show that their account can be naturally extended to provide an elegant treatment of probabilistic causation. IntroductionPreemptionStructural Equation ModelsThe Halpern and Pearl Definition of ‘Actual Cause’Preemption AgainThe Probabilistic CaseProbabilistic Causal ModelsA Proposed Probabilistic Extension of Halpern and Pearl’s DefinitionTwardy and Korb’s AccountProbabilistic FizzlingConclusion

Causal models defined in terms of structural equations have proved to be quite a powerful way of representing knowledge regarding causality. However, a number of authors have given examples that seem to show that the Halpern-Pearl (HP) definition of causality [Halpern and Pearl 2005] gives intuitively unreasonable answers.Here it is shown that, for each of these examples, we can give two stories consistent with the description in the example, such that intuitions regarding causality are quite different for each story. By adding additional variables, we can disambiguate the stories. Moreover, in the resulting causal models, the HP definition of causality gives the intuitively correct answer. It is also shown that, by adding extra variables, a modification to the original HP definition made to deal with an example of Hopkins and Pearl [2003] may not be necessary. Given how much can be done by adding extra variables, there might be a concern that the notion of causality is somewhat unstable. Can adding extra variables in a "conservative" way (i.e., maintaining all the relations between the variables in the original model) cause the answer to the question "Is X = x a cause of Y = y?" to alternate between "yes" and "no"? It is shown that we can have such alternation infinitely often, but if we take normality into consideration, we cannot. Indeed, under appropriate normality assumptions. Adding an extra variable can change the answer from "yes' to "no", but after that, it cannot change back to "yes".

Special science generalizations admit of exceptions. Among the class of non-exceptionless special science generalizations, I distinguish (what I will call) minutis rectis (mr) generalizations from the more familiar category of ceteris paribus (cp) generalizations. I argue that the challenges involved in showing that mr generalizations can play the law role are underappreciated, and quite different from those involved in showing that cp generalizations can do so. I outline a strategy for meeting the challenges posed by mr generalizations.

The discovery of causal relations seems a central activity of the high-level sciences, including the special sciences and certain branches of macrophysics. Those same sciences are less successful in formulating exceptionless laws. if causation must be underwritten by exceptionless laws, we are faced with a puzzle. Attempts have been made to dissolve this puzzle by showing that non-exceptionless generalizations can underwrite causal relations. The trouble is that many of these attempts fail to distinguish between two importantly different types of exception of which highlevel scientific generalizations admit. roughly speaking, one is where the values of high-level variables not represented in the generalization are abnormal: call these 'background factor' (bf) exceptions. For example, the ideal Gas Law (iGL) may be significantly violated by a gas if a strong electric current is passed through it. Another is where the high-level states that are represented by variables in the generalization are realized in certain abnormal ways: call these 'mr exceptions' (exceptions having to do with the multiple realizability of high-level states). For example, the pressure of a gas may not be proportional to its temperature and volume in the way that the iGL describes if the initial macrostate of the gas is realized in a certain unusual microphysical way. While existing attempts to show that non-exceptionless generalizations can underwrite causal relations tend to work well where the generalization admits only of bf exceptions, they work less well when the generalizations in question admit-as most high-level scientific generalizations do-of mr exceptions. i argue that the best prospect for resolving the apparent problem posed by mr exceptions is to regard the generalizations which admit of them as approximations to probabilistic generalizations which don't, and which are themselves able to support relations of probabilistic causation.

We investigate whether standard counterfactual analyses of causation (CACs) imply that the outcomes of space-like separated measurements on entangled particles are causally related.While it has sometimes been claimed that standard CACs imply such a causal relation, we argue that a careful examination of David Lewis's influential counterfactual semantics casts doubt upon this. We discuss ways in which Lewis's semantics and standard CACs might be extended to the case of space-like correlations.