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A Quantum Probability Perspective on Borderline Vagueness

Blutner, R., Pothos, E. M. & Bruza, P. (2013). A Quantum Probability Perspective on Borderline Vagueness. Topics in Cognitive Science, 5(4), pp. 711-736. doi: 10.1111/tops.12041


The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon.

Publication Type: Article
Additional Information: This is the accepted version of the following article: Blutner, R., Pothos, E. M. and Bruza, P. (2013), A Quantum Probability Perspective on Borderline Vagueness. Topics in Cognitive Science, 5: 711–736., which has been published in final form at
Publisher Keywords: Borderline contradictions, Contextualism, Fuzzy logic, Neuronal network, Quantum interference, Quantum probability, Vagueness
Subjects: B Philosophy. Psychology. Religion > BF Psychology
Departments: School of Health & Psychological Sciences > Psychology
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