“Simpson's paradox,” first described nearly a century ago, is an anomaly that sometimes arises from pooling data. Dramatic instances of the paradox have occurred in real life in the domains of epidemiology and admissions policies. Many writers have recently described hypothetical examples of the paradox arising in other areas of life and it seems possible that the paradox may occur frequently in mundane domains but with less serious implications. Thus, it is not surprising that the paradox should arise in commonsense reasoning, that subarea of artificial intelligence that seeks to axiomatize reasoning in such mundane domains. It arises as the problem “approximate proof by cases” and the question of whether to accept it may well depend on whether we wish to construct performance or competence models of reasoning. This article gives a brief history of the paradox and discusses its occurrence in our own discipline. It argues that if the paradox occurs frequently but undramatically in real life, every uncertain reasoning system will have to deal with the problem in s