Nancy Cartwright begins her recent book, Hunting Causes and Using Them, by noting that while a few years ago real causal claims were in dispute, nowadays "causality is back, and with a vengeance." In the case of the social sciences, Keith Morrison writes that "Social science asks 'why?'. Detecting causality or its corollary-prediction-is the jewel in the crown of social science research." With respect to the health sciences, Judea Pearl writes that the "research questions that motivate most studies in the health sciences are causal in nature." However, not all data used by people interested in making causal claims come from experiments that use random assignment to control and treatment groups. Indeed, much research in the social and health science depends on non-experimental, observational data. Thus, one of the most important problems in the social and health sciences concerns making warranted causal claims using non-experimental, observational data; viz., "Can observational data be used to make etiological inferences leading to warranted causal claims?" This paper examines one method of warranting causal claims that is especially widespread in epidemiology and the health sciences generally-the use of causal criteria. It is argued that cases of complex causation generally, and redundant causation-both causal overdetermination and causal preemption-specifically, undermine the use of such criteria to warrant causal claims.