Proceedings of the Annual Meeting of the Cognitive Science Society

The classical (symbol system) theory of cognition is supposed to explain systematicity---the coexistence of cognitive abilities. However, the classical theory does not explain why cognitive systems should be symbolic, nor why cognition sometimes fails to be systematic, so the symbol system assumption is seen by some as ad hoc: motivated only to fit the data. A mathematical theory is presented as a framework towards addressing these questions in terms of the available cognitive resources and the intended goals. A cognitive system is supposed to be resource-dependent and goal-driven. Accordingly, systematicity, or lack thereof follows from a universal construction principle (in a category theory sense) in this context---systems of symbols arise (or, fail to arise) as the "best" possible mapping given the available resources and the intended goal.