The category theory concept of a commutative diagram is used to construct a model of the way in which symbolic processes are applied to problem solving. The model provides for a relationship between symbolic processes and the problem which depends on structural isomorphism and consistency, but is independent of similarity between symbol elements and problem elements. It is then shown that several different levels of thought can be distinguished within the basic model. More information is needed to assign symbolic processes to a problem in a consistent way with higher-level thought processes than with lower-level processes. These information-processing requirements permit the approximate age of mastery of each level to be predicted, thereby offering an alternate theory of cognitive developmental stages. Two experiments designed to test the theory are reported.