Predictive processing has recently been advanced as a global cognitive architecture for the brain. I argue that its commitments concerning the nature and format of cognitive representation are inadequate to account for two basic characteristics of conceptual thought: first, its generality—the fact that we can think and flexibly reason about phenomena at any level of spatial and temporal scale and abstraction; second, its rich compositionality—the specific way in which concepts productively combine to yield our thoughts. I consider two strategies for (...) avoiding these objections and I argue that both confront formidable challenges. (shrink)