Arguments from mathematical system theory are used to show that the behaviorist-cognitivist debate in psychology is actually a non-issue: abstractly, the two are equivalent; but from the standpoint of a predictive, scientific theory of brains and behavior only the cognitivist program holds any promise. 

After a brief summary of the algebraic theory of systems, the paper employs these algebraic tools to propose a functional means by which a brain (human or artificial) may compactly store and retrieve information. This scheme is then extended to provide a means for the generation of thoughts and emotions, as well. 

Finally, the paper concludes with a discussion of the interconnections between the brain model suggested here and a number of other models proposed in the literature.