The ability to learn concepts lies at the very core of human cognition, enabling us to efficiently classify, organize, identify, and store complex information. In view of the basic role that concepts play in our everyday physical and mental lives, the fields of cognitive science and psychology face three long standing challenges: discovering the laws that govern concept learning and categorization behavior in organisms, showing how they inform other areas of cognitive research, and describing them with the mathematical systematicity and precision found in the physical sciences. In light of these theoretical and methodological shortcomings, this volume will introduce a set of general mathematical principles for predicting and explaining conceptual behavior.
The author’s theory is based on seven fundamental constructs of universal science: invariance, complexity, information, similarity, dissimilarity, pattern, and representation. These constructs are joined by a novel mathematical framework that does not depend on probability theory, and derives key results from conceptual behavior research with other key areas of cognitive research such as pattern perception, similarity assessment, and contextual choice. The result is a unique and systematic unifying foundation for cognitive science in the tradition of classical physics.
1. Introduction 2. Concepts and Cognition 3. Process and Structure 4. Categorical Invariance and Logical Manifolds 5. A Cognitive Mechanism for Invariance Detection 6. Principles of Invariance Detection 7. A Law of Invariance in Human Conceptual Behavior 8. On Modal Concepts and Goodness of Pattern 9. Information as a Change in Conceptual Complexity 10. A Path toward Probabilistic Processes and Functional Descriptions 11. Contextual Choice and Structure 12. Concluding Remarks and Open Problems