Abstract not found

We extend a quantum model in Hilbert space developed in Aerts (2007a) into a quantum field theoric model in Fock space for the modeling of the combination of concepts. Items and concepts are represented by vectors in Fock space and membership weights of items are modeled by quantum probabilities. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items regarding the disjunction of concepts match with great accuracy the complete set of results of an experiment conducted by Hampton (1988b). It are the quantum effects of interference and superposition of that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. It is essential for the perfect matches we obtain between the predictions of the quantum field model and Hampton’s experimental data that items can be in superpositions of ‘different numbers states ’ which proves that the genuine structure of quantum field theory is needed to match predictions with experimental data.

The broader scope of our investigations is the search for the way in which concepts and their combinations carry and influence meaning and what this implies for human thought. More specifically, we examine the use of the mathematical formalism of quantum mechanics as a modeling instrument and propose a general mathematical modeling scheme for the combinations of concepts. We point out that quantum mechanical principles, such as superposition and interference, are at the origin of specific effects in cognition related to concept combinations, such as the guppy effect and the overextension and underextension of membership weights of items. We work out a concrete quantum mechanical model for a large set of experimental data of membership weights with overextension and underextension of items with respect to the conjunction and disjunction of pairs of concepts, and show that no classical model is possible for these data. We put forward an explanation by linking the presence of quantum aspects that model concept combinations to the basic process of concept formation. We investigate the implications of our quantum modeling scheme for the structure of human thought, and show the presence of a two-layer structure consisting of a classical logical layer and a quantum conceptual layer. We consider connections between our findings and phenomena such as the disjunction effect and the conjunction fallacy in decision theory, violations of the sure thing principle, and the Allais and Elsberg paradoxes in economics.

It is proposed that the ability of humans to flourish in diverse environments and evolve complex cultures reflects the following two underlying cognitive transitions. The transition from the coarse-grained associative memory of Homo habilis to the fine-grained memory of Homo erectus enabled limited representational redescription of perceptually similar episodes, abstraction, and analytic thought, the last of which is modeled as the formation of states and of lattices of properties and contexts for concepts. The transition to the modern mind of Homo sapiens is proposed to have resulted from onset of the capacity to spontaneously and temporarily shift to an associative mode of thought conducive to interaction amongst seemingly disparate concepts, modeled as the forging of conjunctions resulting in states of entanglement. The fruits of associative thought became ingredients for analytic thought, and vice versa. The ratio of associative pathways to concepts surpassed a percolation threshold resulting in the emergence of a self-modifying, integrated internal model of the world, or worldview.

We prove a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments from [26] to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights, as for example in [17], can accomplish what classical membership weights cannot do. 1

We elaborate a theory for the modeling of concepts using the mathematical structure of quantum mechanics. Items and concepts are represented by vectors in the complex Hilbert space of quantum mechanics and membership weights of items are modeled by quantum weights calculated following the quantum rules. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items with respect to the disjunction of concepts match with great accuracy the results of an experiment conducted by Hampton (1988b). It is the quantum effects of interference and superposition that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. We show that the complex numbers of the Hilbert space are essential to obtaining the experimental predictions, i.e. vector space models over real numbers do not provide predictions matching the experimental data. We put forward an explanation of the effects of overextension and underextension by interpreting the quantum model applied to the modeling of the disjunction of concepts.

We elaborate a theory for the modeling of concepts using the mathematical structure of quantum mechanics. Items and concepts are represented by vectors in the complex Hilbert space of quantum mechanics and membership weights of items are modeled by quantum weights calculated following the quantum rules. We apply this theory to model the disjunction of concepts and show that the predictions of our theory for the membership weights of items with respect to the disjunction of concepts match with great accuracy the results of an experiment conducted by Hampton (1988b). It is the quantum effects of interference and superposition that are at the origin of the effects of overextension and underextension observed by Hampton as deviations from a classical use of the disjunction. We show that the complex numbers of the Hilbert space are essential to obtaining the experimental predictions, i.e. vector space models over real numbers do not provide predictions matching the experimental data. We put forward an explanation of the effects of overextension and underextension by interpreting the quantum model applied to the modeling of the disjunction of concepts.