Toward an Ecological Theory of Concepts

Abstract

Psychology has had difficulty accounting for the creative, context-sensitive manner in which concepts are used. We believe this stems from the view of concepts as identifiers rather than bridges between mind and world that participate in the generation of meaning. This article summarizes the history and current status of concepts research and provides a nontechnical summary of work toward an ecological approach to concepts. We outline the rationale for applying generalizations of formalisms originally developed for use in quantum mechanics to the modeling of concepts, showing how it is because of the role of context that deep structural similarities exist between the two. A concept is defined not just in terms of exemplary states and their features or properties but also by the relational structures of these properties and their susceptibility to change under different contexts. The approach implies a view of mind in which the union of perception and environment drives conceptualization, forging a web of conceptual relations or “ecology of mind.”

Notes

¹In the theory theory in developmental psychology, theory is defined as scientific theory and examples such as the child's development of biological knowledge are provided (Carey, 1985; Gopnik & Meltzoff, 1997; Keil, 1979). However, the aims of the developmental use of theory are somewhat different from those of the categorization theorists relevant to our present topic.

²It was proven that any process that involves interaction with an incompletely specified context (and thus nondeterminism) entails a non-Kolmogorovian probability model (Aerts, 1993, 1999, 2002; Pitowsky, 1989).(A classical probability model is saidtobe Kolmogorovian because it satisfies the axiomatic system for classical probability theory developed by Andrei Nikolaevich Kolmogorov. In a classical [Kolmogorian] probability model, the fact that we are dealing with probabilities reflects a lack of knowledge about the precise state of the system. If, however, these inequalities are violated, no such classical [Kolmogorian] probability model exists. The probability model is said to be nonclassical or non-Kolmogorovian.) Pitowsky's proof makes usa of Bell inequalities, which are mathematical equations that constitute the definitive test for the presence of quantum structure. Pitowsky proved that if Bell inequalities are satisfied for a set of probabilities concerning the outcomes of the considered experiments, there exists a classical probability model that describes these probabilities. Hence, the violation of Bell inequalities shows that the probabilities involved are nonclassical (non-Kolmogorovian).

³SCOP is a general mathematical structure that grew out of (but differs from) the quantum formalism, where the context (in this case measurement context) is explicitly incorporated in the theory. We emphasize that this kind of generalization and reapplication of a mathematical structure has nothing to do with the notion that phenomena at the quantum level affect cognitive processes.

⁴This is the same methodology as that used to describe the (usually infinite) number of different states for a physical system in physics. The paradox, namely, that it is impossible to incorporate all potential contexts into the description, is resolved in a similar way as it is resolved in physics. For concrete mathematical models, one limits the description to a well-defined set of the most relevant contexts, hence a corresponding well-defined set of states for the entity. But in principle it is possible to refine the model indefinitely and hence incorporate ever more contexts and states.

⁵The complex numbers are the numbers x + iy, where x and y are real numbers and i is the square root of −1, and appropriate rules for adding and multiplying complex numbers are defined, such that the set of complex numbers is a number field.