Humans learn to represent complex structures (e.g. natural language, music, mathematics) from experience with their environments. Often such structures are latent, hidden, or not encoded in statistics about sensory representations alone. Accounts of human cognition have long emphasized the importance of structured representations, yet the majority of contemporary neural networks do not learn structure from experience. Here, we describe one way that structured, functionally symbolic representations can be instantiated in an artificial neural network. Then, we describe how such latent structures (viz. predicates) can be learned from experience with unstructured data. Our approach exploits two principles from psychology and neuroscience: comparison of representations, and the naturally occurring dynamic properties of distributed computing across neuronal assemblies (viz. neural oscillations). We discuss how the ability to learn predicates from experience, to represent information compositionally, and to extrapolate knowledge to unseen data is core to understanding and modeling the most complex human behaviors (e.g. relational reasoning, analogy, language processing, game play).