Abstract

Counterfactual dependence and probabilistic dependence are two criteria frequently used to analyze causation. ``Mere correlations'' - instances of probabilistic dependence and counterfactual independence - are a well-studied class of cases where these criteria diverge. In this essay, I provide an example of the opposite type of divergence: counterfactual dependence and probabilistic independence. The butterfly effect of chaos theory says that had a butterfly in the distant past not flapped its wings, but everything else was identical, it is possible (and indeed probable) that a present tornado would not have occurred. However, the math of chaos also tells us that whether or not the butterfly flaps its wings, the probability of the tornado is the same. I show how these two claims fit together, highlighting the distinct and unorthodox counterfactual origin of probabilistic independence in chaotic systems. Examining the case under different theories of causation, I find widespread disagreement about whether the butterfly's flap causes the tornado. I argue that this disagreement can be explained by an underlying semantic indeterminacy in our ordinary conception of causation. Rather than being exceptional, we should expect these types of relationships, and thus indeterminacies, to predominate in chaotic systems over long timescales.