Woodward has useful comments about Nancy Cartwright's intriguing skeptical attitude toward causal explanations. See, e.g., Nancy Cartwright, The Dappled World: A Study of the Boundaries of Science (Cambridge University Press 1999) and her more recent book (which I have not yet read) Hunting Causes and Using Them: Approaches in Philosophy and Economics (Cambridge University Press 2007).
Woodward professes to be an admirer of Judea Pearl -- and Woodward's approach in some particulars does follow Pearl's. But Woodward (I am pleased to say) emphasizes more than Pearl has (I think) that rational relevance judgments are possible (and common) even in the absence of anything that might resemble a full-blown theory (or even a half-baked theory) of causal connections in a particular situation.
James Woodward uses nice examples (mostly from the sciences) to illustrate his points.
Amazon.com's "book description" of Cartwright's 2007 collection of papers (see citation above) suggests that Cartwright uses her latest book to make a counterattack against critics such as Woodward:Hunting Causes and Using Them argues that causation is not one thing, as commonly assumed, but many. There is a huge variety of causal relations, each with different characterizing features, different methods for discovery and different uses to which it can be put. In this collection of new and previously published essays, Nancy Cartwright provides a critical survey of philosophical and economic literature on causality, with a special focus on the currently fashionable Bayes-nets and invariance methods – and it exposes a huge gap in that literature. Almost every account treats either exclusively how to hunt causes or how to use them. But where is the bridge between? It’s no good knowing how to warrant a causal claim if we don’t know what we can do with that claim once we have it. This book will interest philosophers, economists and social scientists.