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Mathematical Principles of Human Conceptual Behavior

The Structural Nature of Conceptual Representation and Processing

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 new general formulations of seven  fundamental constructs of universal science: invariance, complexity,  information, similarity, dissimilarity, pattern, and representation. These  constructs are unified by a novel mathematical framework that does not  depend on probability theory. The framework also unifies key results from conceptual behavior research with results from other fundamental areas  of cognitive research, such as pattern perception, similarity assessment,  attention, and contextual choice. The result is a unique and systematic  unifying foundation for cognitive science in the tradition of classical  physics.