We propose a conceptually new approach to unify symbolic reasoning and probabilistic reasoning, both core aspects of human higher-order cognitive function. The key underlying idea is inference of abstraction, or selective ignorance, in which abstract symbolic knowledge is derived directly from concrete data via models in formal logic. We compare this simple idea with the semantics of Bayesian networks and show that our idea does not need the assumption of independence or conditional independence of symbolic knowledge, an unrealistic but necessary assumption of Bayesian networks and their variants. We also show that, in the machine learning context, the idea can be seen as an all-neighbour method, which is a further generalisation of an all-nearest neighbour method, itself a generalisation of the k-nearest neighbour method. We use the MNIST dataset to empirically justify the theoretical advantage of the idea.