In this monograph, Professor Joseph Y. Halpern develops an account of actual causality – causality in specific instances outside the quantum world – based on directed acyclic graphs (DAGs) and probabilities. The DAGs are used to represent causal structure while probabilities are used to represent uncertainties. The aim is to capture many of our causal intuitions.
After a short introduction (Chapter 1), the author introduces his causal models for investigating causality (Chapter 2.1) and gives a definition of \(\vec X=\vec x\) being an actual cause of \(\varphi\) in the causal setting \((M,u)\) (Chapter 2.2). \(\vec X=\vec x\) denotes a conjunction of primitive events and \(\varphi\) denotes a Boolean combination of primitive events. The author gives three different (yet closely related) versions of actual causality which all harken back to Pearl’s notion of a causal beam. The first two versions are due to Pearl and the author, the third version is due to the author only. Next, relations between these definitions are investigated (Theorem 2.2.3) and demonstrated on examples (Sections 2.3 and 2.8). Further examples show how application of the definitions deals with overdetermination and causation by omission (Section 2.3), transitivity (Section 2.4) and sufficient causation (Section 2.6). Uncertainty is incorporated by means of a probability assignment to the deterministic causal models; “pulling out the probability” via attaching probabilities to the exogenous variables (Section 2.5). In Section 2.7, the author extends the framework to non-recursive models, i.e., the causal graphs models may be cyclic.
Chapter 3 introduces graded causality which enables one to model that some events are judged to be stronger causes than other. This is achieved by introducing a partial pre-order on worlds which ranks worlds according to their normality. This pre-order needs to be specified by the modeller. The relativity of causality to a causal model is discussed in Chapter 4. In particular, introduction of new variables and changing the range of variables and the modification of the causal structure and the normality pre-order are discussed. For conservative extensions, a particular way of modifying the causal model, relations of judgements of causality are investigated (Theorems 4.4.2, 4.4.4–4.4.6).
Chapter 5 investigates computational complexity of causal reasoning and offers a sound and complete axiomatisation for Halpern’s language of causality. The author goes on to formalise intuitions of responsibility and blame which matter much in legal contexts (Chapter 6). In Chapter 7, the author offers a definition of what it means for \(\vec X=\vec x\) to be an explanation of \(\varphi\) within a set of contexts. The next and final chapter discusses three real-world applications of the author’s approach. At the end of every chapter, notes provide further background, proofs and references.
Throughout, the author emphasises that the three proposed definitions of causality strike him as reasonable and the that there is no “correct” model/definition of causality. Since sensible people may rationally disagree about the choice of the most appropriate model, they may make different causal judgements.