Cooperation plays a central role in theories of development, learning, cultural evolution, and education. We argue that existing models of learning from cooperative informants have fundamental limitations that prevent them from explaining how cooperation benefits learning. First, existing models are shown to be computationally intractable, suggesting that they cannot apply to realistic learning problems. Second, existing models assume a priori agreement about which concepts are favored in learning, which leads to a conundrum: Learning fails without precise agreement on bias yet there is no single rational choice. We introduce cooperative inference, a novel framework for cooperation in concept learning, which resolves these limitations. Cooperative inference generalizes the notion of cooperation used in previous models from omission of labeled objects to the omission values of features, labels for objects, and labels for collections of objects. The result is an approach that is computationally tractable, does not require a priori agreement about biases, applies to both Boolean and first-order concepts, and begins to approximate the richness of real-world concept learning problems. We conclude by discussing relations to and implications for existing theories of cognition, cognitive development, and cultural evolution.