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The (virtual) conceptual necessity of quantum probabilities in cognitive psychology

Published online by Cambridge University Press:  14 May 2013

Reinhard Blutner  and
Peter beim Graben
Reinhard Blutner
Affiliation:
ILLC, Universiteit van Amsterdam, Amsterdam, 1090 GE, The Netherlands. [email protected]://www.blutner.de/
Peter beim Graben
Affiliation:
Department German Language and Linguistics, Humboldt Universität zu Berlin, 10099 Berlin, Germany. [email protected]://www.beimgraben.info/
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Abstract

We propose a way in which Pothos & Busemeyer (P&B) could strengthen their position. Taking a dynamic stance, we consider cognitive tests as functions that transfer a given input state into the state after testing. Under very general conditions, it can be shown that testable properties in cognition form an orthomodular lattice. Gleason's theorem then yields the conceptual necessity of quantum probabilities (QP).

Type
Open Peer Commentary
Information
Behavioral and Brain Sciences , Volume 36 , Issue 3 , June 2013 , pp. 280 - 281
Copyright
Copyright © Cambridge University Press 2013 

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References

Atmanspacher, H., Römer, H. & Walach, H. (2002) Weak quantum theory: Complementarity and entanglement in physics and beyond. Foundations of Physics 32:379–406.Google Scholar
Baltag, A. & Smets, S. (2005) Complete axiomatization for quantum action. International Journal of Theoretical Physics 44(12):2267–81.Google Scholar
Barsalou, L. W. (2008) Grounded cognition. Annual Review of Psychology 59:617–645.Google Scholar
beim Graben, P. & Atmanspacher, H. (2009) Extending the philosophical significance of the idea of complementarity. In: Recasting reality. Wolfgang Pauli's philosophical ideas and contemporary science, ed. Atmanspacher, H. & Primas, H., pp. 99–113. Springer.Google Scholar
Blutner, R. (2012) Questions and answers in an orthoalgebraic approach. Journal of Logic, Language and Information 21(3):237–77.Google Scholar
Busemeyer, J. R. & Bruza, P. D. (2012) Quantum models of cognition and decision. Cambridge University Press.Google Scholar
Chomsky, N. (1995) The minimalist program. MIT Press.Google Scholar
Chomsky, N. (2005) Three factors in language design. Linguistic Inquiry 36(1):1–22.Google Scholar
Gigerenzer, G. (1997) Bounded rationality models of fast and frugal inference. Swiss Journal of Economics and Statistics 133:201–18.Google Scholar
Gleason, A. M. (1957) Measures on the closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics 6:885–94.Google Scholar
Johnson, E. J., Haubl, G. & Keinan, A. (2007) Aspects of endowment: A query theory of value construction. Journal of Experimental Psychology: Learning, Memory and Cognition 33(3):461–73.Google Scholar
Kuhn, T. S. (1996) The structure of scientific revolutions. University of Chicago Press.Google Scholar
Piron, C. (1976) Foundations of quantum physics. WA Benjamin, Inc.Google Scholar
Richman, F. & Bridges, D. S. (1999) A constructive proof of Gleason's theorem. Journal of Functional Analysis 162(2):287–312 CrossRefGoogle Scholar
Trueblood, J. S. & Busemeyer, J. R. (2011) A comparison of the belief-adjustment model and the quantum inference model as explanations of order effects in human inference. Cognitive Science 35(8):1518–52.CrossRefGoogle Scholar
van Benthem, J. (2011) Logical dynamics of information and interaction. Cambridge University Press.CrossRefGoogle Scholar