Causes must occur before effects. So causal relations are irreflexive and asymmetric. Causes are also transitive-along-causal-pathways in that along a given causal pathway, to causally contribute to something that causally contributes to an effect is to causally contribute to that effect. This may generate counterintuitive judgement where a feature causally contributes both to an effect occurring and to it not occurring along different pathways. But these results should be accepted, we argue, because it is often important to know both are occurring (even though at the cost of complicating relations between causal contributions and legal or moral responsibility). Notational conventions are outlined.

Causes are INUS conditions: Insufficient but Necessary parts of Unnecessary but Sufficient conditions for a contribution to the effect. (This does not imply that INUS conditions are causes: the correlation may be spurious.) ‘Contribution to’ because the effect may have a different overall magnitude because other sets of factors contribute as well. INUS conditions are graphed in epidemiology as sets of ’causal pie’. The other members of such a set are labelled ‘support factors’ (or ‘moderators’) for the cause of focus and include the absence of features that can derail the process. Sometimes, particularly in qualitative comparative analysis, factors are represented as yes–no variables. Other studies allow features to vary in magnitude. A support factor of a given magnitude is represented as part of a set contributing a given magnitude to the effect. For a causal process to occur, a full causal pie must exist at each step.

Causal equation models are sets of equations showing the functional dependence of effect variables upon cause variables – it is supposed that all individuals in a given population satisfy these equations. We describe ‘situation-specific’ causal equation models (SCEMs) which apply this modelling method (common in social science) to the particular circumstances associated with singular causation. These are taken to represent the range of causal possibilities that occur in these particular circumstances. To construct a SCEM, work backwards step by step from the final outcome, constructing a potential outcomes equation for each stage until the initial cause. The resulting set of equations is the core of the SCEM for this case. We illustrate how such a model may be generated using our example of sugar-sweetened beverage taxation in Barbados. We admit the causal equation models thus generated are complex, but contend this only represents complexity in nature.

This book shows how to warrant claims about causation in a particular place at a particular time, ‘here and now’, ‘there and then’ – ‘singular’ causation. Good warrant matters if your efforts to affect change are to work. But you cannot properly warrant that a relation obtains without understanding what that relation is. To this end, Part 1 offers a set of features that characterise singular causal relations. These make up a ‘thick’ theory of singular causation, offering far more information than the usual ‘thin’ definitions, like those based on counterfactual or probabilistic dependence, difference-making or production. Details about how causal processes work play a central role here. This theory then provides the grounds for, in Part 2, identifying and systemising what kinds of evidence can warrant singular causal claims. Part 3 shows how this account may be used in practice, using examples from child protection.