Causal Models and Counterfactuals

This article compares statistical and set-theoretic approaches to causal analysis. Statistical researchers commonly use additive, linear causal models, whereas set-theoretic researchers typically use logic-based causal models. These models differ in many fundamental ways, including whether they assume symmetric or asymmetrical causal patterns, and whether they call attention to equifinality and combinatorial causation. The two approaches also differ in how they utilize counterfactuals and carry out counterfactual analysis. Statistical researchers use counterfactuals to illustrate their results, but they do not use counterfactual analysis for the goal of causal model estimation. By contrast, set-theoretic researchers use counterfactuals to estimate models by making explicit their assumptions about empty sectors in the vector space defined by the causal variables. The paper concludes by urging greater appreciation of the differences between the statistical and set-theoretic approaches to causal analysis.