I’ll present an approach from mathematical logic which shows how sub-symbolic dynamics may give rise to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This approach posits that learners posses a system for expressing isomorphisms with which they create mental models with arbitrary dynamics. The theory formalizes one account of how novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. Moreover, the account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in an existing connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories cognition and computation can be translated into simple and neurally plausible underlying dynamics.