We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion article. Essentially, an explanation is a fact that is not known for certain but, if found to be true, would constitute an actual cause of the fact to be explained, regardless of the agent's initial uncertainty. We show that the definition handles well a number of problematic examples from the literature.

It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account only for one step (...) of revision. The paper discusses and rejects two solutions within the confines of AGM theory. It then introduces ranking functions (as I prefer to call them now; in the paper they are still called ordinal conditional functions) as the proper (and, I find, still the best) solution of the problem, proves that conditional independence w.r.t. ranking functions satisfies the so-called graphoid axioms, and proposes general rules of belief change (in close analogy to Jeffrey's generalized probabilistic conditionalization) that encompass revision and contraction as conceived in AGM theory. Indeed, the parallel to probability theory is amazing. Probability theory can profit from ranking theory as well since it is also plagued by the problem of iterated belief revision even if probability measures are conceived as Popper measures (see No. 11). Finally, the theory is compared with predecessors which are numerous and impressive, but somehow failed to explain the all-important conditional ranks in the appropriate way. (shrink)

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

David and Mary Norton present the definitive scholarly edition of Hume's Treatise, one of the greatest philosophical works ever written. This set comprises the two volumes of texts and editorial material, which are also available for purchase separately. David Hume is one of the greatest of philosophers. Today he probably ranks highest of all British philosophers in terms of influence and philosophical standing. His philosophical work ranges across morals, the mind, metaphysics, epistemology, religion, and aesthetics; he had broad interests not (...) only in philosophy as it is now conceived but in history, politics, economics, religion, and the arts. He was a master of English prose. The Clarendon Hume Edition will include all of his works except his History of England and minor historical writings. It is the only thorough critical edition, and will provide a far more extensive scholarly treatment than any previous editions. This edition offers authoritative annotation, bibliographical information, and indexes, and draws upon the major advances in textual scholarship that have been made since the publication of earlier editions - advances both in the understanding of editorial principle and practice and in knowledge of the history of Hume's own texts. (shrink)

We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion article. Essentially, an explanation is a fact that is not known for certain but, if found to be true, would constitute an actual cause of the fact to be explained, regardless of the agent's initial uncertainty. We show that the definition handles well a number of problematic examples from the literature. (...) 1. Introduction2. Causal models and the definition of actual causality: a review2.1Causal models2.2Syntax and semantics2.3The definition of cause3. Explanation: the basic definition4. Partial explanations and explanatory power5. The general definition6. DiscussionAppendix: the formal definition of causality. (shrink)