A Category Theory Explanation for Systematicity

Abstract

A theory of cognitive architecture should explain why systematicity is a necessary, not just possible consequence of the theory's core principles and base assumptions, without relying on arbitrary (ad hoc) modifications to close explanatory gaps. Cognitive capacities are systematically distributed around common structures. Category theory, a mathematical theory of structure, provides a framework for a theory of systematicity that explains the nature of these structures. Underlying each collection of systematically related capacities is a categorical universal construction: each capacity is uniquely composed of a common (universal) component and capacity-specific component; constructions not admitting this form of compositionality are not categorical universal constructions. Hence, our category theoretical explanation transcends problems with other (classical/symbolic, connectionist) approaches, which admit both systematic and non-systematic architectures.