Quantum mechanics meets cognitive science: explanatory vs descriptive approaches

We reflect on several aspects of the general claim that a quantum-like approach to Cognitive Science is advantageous over classical approaches. The classical approaches refer to the symbolic approaches including models using a classical (Kolmogorov) probability calculus. The general claim seems to be right from a descriptive viewpoint but not necessarily from an explanatory viewpoint. The explanatory perspective needs a more careful analysis since adding some additional arbitrary parameters (such as phase shift parameters in quantum probabilities) does not automatically increase the explanatory value of the approach; rather, it seems to decrease it. We argue further that there is another class of traditional models - the class of geometric models of cognition. These models have a much longer tradition than the symbolic models. Interestingly, quantum mechanics does not contradict the geometric models. Hence, real progress at the meeting between quantum mechanics and cognitive science could be made by unifying these geometric models with ideas from quantum theory.