Abstract
We argue that current discussions of criteria for actual causation are ill-posed in several respects. (1) The methodology of current discussions is by induction from intuitions about an infinitesimal fraction of the possible examples and counterexamples; (2) cases with larger numbers of causes generate novel puzzles; (3) “neuron” and causal Bayes net diagrams are, as deployed in discussions of actual causation, almost always ambiguous; (4) actual causation is (intuitively) relative to an initial system state since state changes are relevant, but most current accounts ignore state changes through time; (5) more generally, there is no reason to think that philosophical judgements about these sorts of cases are normative; but (6) there is a dearth of relevant psychological research that bears on whether various philosophical accounts are descriptive. Our skepticism is not directed towards the possibility of a correct account of actual causation; rather, we argue that standard methods will not lead to such an account. A different approach is required. Once upon a time a hungry wanderer came into a village. He filled an iron cauldron with water, built a fire under it, and dropped a stone into the water. “I do like a tasty stone soup” he announced. Soon a villager added a cabbage to the pot, another added some salt and others added potatoes, onions, carrots, mushrooms, and so on, until there was a meal for all.
Highlights
Once upon a time a wanderer came into a hungry village
Using the counts these representations permit, we argue that (i) the Socratic strategy for finding or testing a characterization of actual causation by intuitions about causal Bayes net cases is futile because the number of cases potentially presenting distinct challenges to theories is unsurveyably large even with small numbers of potential causes
We consider symmetry principles that result in partitions that reduce the number of distinct causal models, but we note (iv) they are insufficient to compensate for the super-exponential growth in cases as the number of potential causes increases
Summary
Many of the deterministic examples in discussions of actual causation implicitly presuppose formal structures of the following kind: 1. Events are represented by variables (usually taking two values but in principle without limit), with one value (e.g., “0”) possibly marked for absences. Since any causal model among the potential causes can be paired with any dependency for the effect, there are 190,517 possible causal models altogether For each of these there are 24 = 16 truth value assignments, so the total number of cases for intuition to survey is 3,048,272, with just three potential causes. Consider the ways that the effect variable can depend on the three potential causal variables: it can be a function of any one of them, on two of them, or on all three of them, and the number of distinct test pair structures depends on the form of the graph, Considering only test pair truth functions we have, per graph among the possible causes. When test pair truth functions for the dependencies are considered, the total number of alternative causal models 9including causal relations among the potential causes) is slightly reduced further. Value negation is obviously a partition of the set of truth functions, for which each class has two members; it preserves the test pair relation, so the number of test pair cases is cut in half: there are 5 cases for 2 arguments, 109 for 3 arguments, but, more than 2 trillion for 5 arguments
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