In recent years, scientists have increasingly taken to investigate the predictive nature of cognition. We argue that prediction relies on abstraction, and thus theories of predictive cognition need an explicit theory of abstract representation. We propose such a theory of the abstract representational capacities that allow humans to transcend the "here-and-now". Consistent with the predictive cognition literature, we suggest that the representational substrates of the mind are built as a hierarchy, ranging from the concrete to the abstract; however, we argue that there are qualitative differences between elements along this hierarchy, generating meaningful, often unacknowledged, diversity. Echoing views from philosophy, we suggest that the representational hierarchy can be parsed into: modality-specific representations, instantiated on perceptual similarity; multimodal representations, primarily instantiated on the discovery of spatiotemporal contiguity; and categorical representations, primarily instantiated on social interaction. These elements serve as the building blocks of complex structures discussed in cognitive psychology (e.g., episodes, scripts) and are the inputs for mental representations that behave like functions, typically discussed in linguistics (i.e., predicators). We support our argument for representational diversity by explaining how the elements in our ontology are all required in order to account for humans' predictive cognition (e.g., in subserving logic-based prediction; in optimizing the trade-off between accurate and detailed predictions) and by examining how the neuroscientific evidence coheres with our account. In doing so, we provide a testable model of the neural bases of conceptual cognition, and highlight several important implications to research on self-projection, reinforcement learning, and predictive-processing models of psychopathology.