The human ability to learn quickly about causal relationships requires abstract knowledge that provides constraints and biases regarding what relationships are possible and likely. There has been a long and vigorous debate about the extent to which these biases are learned. Psychologists and philosophers since Plato's time have tried to answer this question with a wide range of techniques, including arguments from intuition, proofs giving bounds on what is learnable, and experimentation.
Hierarchical Bayesian models are a relatively new tool that allows us to address the question of causal induction with a directness that was impossible in the past. Bayesian models solve problems by combining a priori expectations with evidence to learn about unobservable variables like category membership or status as a cause. Using a hierarchical organization allows those expectations to be learned, shaped by yet more abstract inductive biases. Using these models, we can develop hypotheses about the origins of abstract knowledge and make precise predictions which can then be tested experimentally. In some cases, these models reveal new ways to learn abstract properties of the world, and more specifically, causal relationships.
Here I will discuss two kinds of abstract knowledge: knowledge about the forms of causal relationships, and knowledge about the nature of the preferences that cause people to make the choices they do. First, I will show that people can learn that a causal relationship takes a particular form and use that knowledge in their later inferences, consistent with the predictions of a hierarchical Bayesian model. In addition, I will describe experiments with adults and children that indicate that adults' strong inductive biases about the forms of causal relationships may be the result of long experience, rather than innate constraints. Second, I will use a model from economics to explain a range of developmental findings in preference learning, including a shift in which children come to treat other people as having distinct preferences. In both cases, the hierarchical Bayesian models explain developmental differences, offer new predictions about causal learning, and offer a broader view of causal induction.