Violation of Leggett–Garg Inequality in Perceiving Cup-like Objects and Cognitive Contextuality

This paper is devoted to an experimental investigation of cognitive contextuality inspired by quantum contextuality research. This contextuality is related to, but not identical to context-sensitivity which is well-studied in cognitive psychology and decision making. This paper is a part of quantum-like modeling, i.e., exploring the methodology of quantum theory outside of physics. We examined the bistable perception of cup-like objects, which strongly depends on experimental contexts. Our experimental data confirmed the existence of cognitive hysteresis, the important role of memory, and the non-commutative structure of cognitive observables. In physics, quantum contextuality is assessed using Bell-CHSH inequalities, and their violation is incorrectly believed to imply the nonlocality of Nature. The violation of Bell-type inequalities in cognitive and social science strongly indicates that the metaphysical implications of these inequalities are quite limited. In our experiments, modified Leggett-Garg inequalities were also significantly violated, but this only means that experimental data from experiments performed in different contexts cannot be modeled by a unique set of noncontextual, jointly distributed random variables. In our experiments, we know the empirical probability distributions measured in different contexts; thus, we can obtain much more detailed and reliable information about contextuality in human cognition by performing nonparametric compatibility tests.