We introduce a novel task exploring how people make causal generalizations over the abstract features of the objectsinvolved in a causal interaction. Specifically, we investigate how people generalize from a single observation of two sim-ple objects in which one (the agent, or cause) interacts with another (the recipient, or effect) resulting in some featurechange(s). In line with recent demonstrations of human strength in few-shot concept learning, we find strong and sys-tematic patterns of generalizations that are well explained by a Bayesian inference model favoring simpler causal rules.However, we also identify a clear order effect depending on what order generalizations are made. To capture the observedpatterns, we develop a causal hypothesis generation model that takes peoples natural generalization tendency and the ordereffect into consideration, and outperforms plain Bayesian inference both in computational efficiency and in match to thebehavioral data.