In medicine and the social sciences, researchers must frequently integrate the findings of many observational studies, which measure overlapping collections of variables. For instance, learning how to prevent obesity requires combining studies that investigate obesity and diet with others that investigate obesity and exercise. Recently developed causal discovery algorithms provide techniques for integrating many studies, but little is known about what can be learned from such algorithms. This article argues that there are causal facts that one could learn by conducting (...) a large study but which could not be learned by combining many smaller studies. Moreover, I characterize the frequency with which combining many studies increases underdetermination and exactly how much information is lost. 1 Introduction2 Causal Inference from Observational Data3 Piecemeal Causal Inference4 The Extent and Frequency of the Problem of Piecemeal Induction5 Conclusion. (shrink)