A quantum probability explanation in Fock space for borderline contradictions

• We work out a quantum-theoretic modeling in Fock space for borderline vagueness.
• We analyze the data by Alxatib and Pelletier (2011) on borderline cases.
• We apply the above quantum-theoretic approach to these borderline cases.
• We show that a quantum probability model faithfully describes these data.
• We explain the results above in terms of interference and conceptual emergence.

The construction of a consistent theory for structuring and representing how concepts combine and interact is one of the main challenges for the scholars involved in cognitive studies. All traditional approaches are still facing serious hindrances when dealing with combinations of concepts and concept vagueness. One of the main consequences of these difficulties is the existence of borderline cases which is hardly explainable from the point of view of classical (fuzzy set) logic and probability theory. Resting on a quantum-theoretic approach which successfully models conjunctions and disjuncions of two concepts, we propound a quantum probability model in Fock space which faithfully reproduces the experimental data collected by Alxatib and Pelletier (2011) on borderline contradictions. Our model allows one to explain the occurrence of the latter contradictions in terms of genuine quantum effects, such as contextuality, superposition, interference and emergence. In particular, we claim that it is the specific mechanism of ‘emergence of a new concept’ that is responsible of these deviations from classical logical thinking in the cognitive studies on human thought. This result seems to be compatible with a recent interesting application of quantum probabilistic modeling in the study of borderline vagueness (Blutner, Pothos & Bruza, 2013), and analogies and differences with it are sketched here.