Given minimal evidence about novel objects, children might learn only relationships among the specific entities, or they might make a more abstract inference, positing classes of entities and the relations that hold among those classes. Here we show that preschoolers (mean: 57 months) can use sparse data about perceptually unique objects to infer abstract physical causal laws. These newly inferred abstract laws were robust to potentially anomalous evidence; in the face of apparent counter-evidence, children (correctly) posited the existence of an unobserved object rather than revise the abstract laws. This suggests that children's ability to learn robust, abstract principles does not depend on extensive prior experience but can occur rapidly, on-line, and in tandem with inferences about specific relations. (Contains 2 figures and 1 table.)