From Quantum Axiomatics to Quantum Conceptuality

  • Diederik Aerts
  • Massimiliano Sassoli de Bianchi
  • Sandro SozzoEmail author
  • Tomas Veloz


Since its inception, many physicists have seen in quantum mechanics the possibility, if not the necessity, of bringing cognitive aspects into the play, which were instead absent, or unnoticed, in the previous classical theories. In this article, we outline the path that led us to support the hypothesis that our physical reality is fundamentally conceptual-like and cognitivistic-like. However, contrary to the “abstract ego hypothesis” introduced by John von Neumann and further explored, in more recent times, by Henry Stapp, our approach does not rely on the measurement problem as expressing a possible “gap in physical causation,” which would point to a reality lying beyond the mind-matter distinction. On the contrary, in our approach, the measurement problem is considered to be essentially solved, at least for what concerns the origin of quantum probabilities, which we have reasons to believe they would be epistemic. Our conclusion that conceptuality and cognition would be an integral part of all physical processes comes instead from the observation of the striking similarities between the non-spatial behavior of the quantum micro-physical entities and that of the human concepts. This gave birth to a new interpretation of quantum mechanics, called the “conceptuality interpretation,” currently under investigation within our group in Brussels.


Quantum theory Conceptuality interpretation Quantum cognition Extended Bloch representation Quantum structures Quantum probabilities Non-spatiality 



  1. Aerts, D. (1982). Description of many physical entities without the paradoxes encountered in quantum mechanics. Foundations of Physics, 12, 1131–1170.CrossRefGoogle Scholar
  2. Aerts, D. (1984). The missing elements of reality in the description of quantum mechanics of the EPR paradox situation. Helvetica Physica Acta, 57, 421–428.Google Scholar
  3. Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics. Journal of Mathematical Physics, 27, 202–210.CrossRefGoogle Scholar
  4. Aerts, D. (1998). The entity and modern physics: the creation discovery view of reality. In E. Castellani (Ed.) , Interpreting bodies: classical and quantum objects in modern physics (pp. 223–257). Princeton: Princeton Unversity Press.Google Scholar
  5. Aerts, D. (1999a). Foundations of quantum physics: a general realistic and operational approach. International Journal of Theoretical Physics, 38, 289–358.CrossRefGoogle Scholar
  6. Aerts, D. (1999b). The stuff the world is made of: physics and reality. In D. Aerts, J. Broekaert, E. Mathijs (Eds.) , Einstein meets Magritte: an interdisciplinary reflection (pp. 129–183). Dordrecht: Springer.Google Scholar
  7. Aerts, D. (2009). Quantum particles as conceptual entities: a possible explanatory framework for quantum theory. Foundations of Science, 14, 361–411.CrossRefGoogle Scholar
  8. Aerts, D. (2010a). Interpreting quantum particles as conceptual entities. International Journal of Theoretical Physics, 49, 2950–2970.CrossRefGoogle Scholar
  9. Aerts, D. (2010b). A potentiality and conceptuality interpretation of quantum physics. Philosophica, 83, 15–52.Google Scholar
  10. Aerts, D. (2013). La mecánica cuántica y la conceptualidad: Sobre materia, historias, semántica y espacio-tiempo. Scientiae Studia, 11, 75–100. Translated from: Aerts, D. (2011). Quantum theory and conceptuality: matter, stories, semantics and space-time. arXiv:1110.4766 [quant-ph].CrossRefGoogle Scholar
  11. Aerts, D. (2014). Quantum theory and human perception of the macro-world. Frontiers in Psychology, 5, Article 554.CrossRefGoogle Scholar
  12. Aerts, D., & Aerts, S. (1995). Applications of quantum statistics in psychological studies of decision processes. Foundations of Science, 1, 85–97.CrossRefGoogle Scholar
  13. Aerts, D., & Czachor, M. (2004). Quantum aspects of semantic analysis and symbolic artificial intelligence. Journal of Physics A: Mathematical and Theoretical, 37, L123–L132.CrossRefGoogle Scholar
  14. Aerts, D., & Durt, T. (1994). Quantum, classical and intermediate, an illustrative example. Foundations of Physics, 24, 1353–1369.CrossRefGoogle Scholar
  15. Aerts, D., & Gabora, L. (2005a). A theory of concepts and their combinations I: the structure of the sets of contexts and properties. Kybernetes, 34, 167–191.CrossRefGoogle Scholar
  16. Aerts, D., & Gabora, L. (2005b). A theory of concepts and their combinations II: a Hilbert space representation. Kybernetes, 34, 192–221.CrossRefGoogle Scholar
  17. Aerts, D., & Sassoli de Bianchi, M. (2014). The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem. Annals of Physics, 351, 975–1025.CrossRefGoogle Scholar
  18. Aerts, D., & Sassoli de Bianchi, M. (2016). The extended Bloch representation of quantum mechanics. Explaining superposition, interference and entanglement. Journal of Mathematical Physics, 57, 122110.CrossRefGoogle Scholar
  19. Aerts, D., & Sassoli de Bianchi, M. (2017a). Quantum measurements as weighted symmetry breaking processes: the hidden measurement perspective. International Journal of Quantum Foundations, 3, 1–16.Google Scholar
  20. Aerts, D., & Sassoli de Bianchi, M. (2017b). Beyond-quantum modeling of question order effects and response replicability in psychological measurements. Journal Mathematical Psychology, 79, 104–120.CrossRefGoogle Scholar
  21. Aerts, D., & Sassoli de Bianchi, M. (2017c). Do spins have directions? Soft Computing, 21, 1483–1504.CrossRefGoogle Scholar
  22. Aerts, D., & Sassoli de Bianchi, M. (2018a). The extended Bloch representation of quantum mechanics for infinite-dimensional entities. arXiv:1704.06249 [quant-ph].
  23. Aerts, D., & Sassoli de Bianchi, M. (2018b). Quantum perspectives on evolution. In S. Wuppuluri, & F.A. Doria (Eds.) , The map and the territory: exploring the foundations of science, thought and reality (pp. 571–595): Springer: The Frontiers collection.Google Scholar
  24. Aerts, D., & Sozzo, S. (2011). Quantum structure in cognition: why and how concepts are entangled? Quantum Interaction. Lecture Notes in Computer Science, 7052, 116–127.CrossRefGoogle Scholar
  25. Aerts, D., & Sozzo, S. (2014). Quantum entanglement in concept combinations. International Journal of Theoretical Physics, 53, 3587–3603.CrossRefGoogle Scholar
  26. Aerts, D., & Sozzo, S. (2015). What is quantum? Unifying its micro-physical and structural appearance. In H. Atmanspacher, et al. (Ed.) , Quantum interaction. QI 2014, Lecture notes in computer science (Vol. 8951 pp. 12–23). Cham: Springer.Google Scholar
  27. Aerts, D., Aerts, S., Coecke, B., D’Hooghe, B., Durt, T., Valckenborgh, F. (1997a). A model with varying fluctuations in the measurement context. In M. Ferrero, & A. van der Merwe (Eds.) , New developments on fundamental problems in quantum physics (pp. 7–9). Dordrecht: Springer Netherlands.Google Scholar
  28. Aerts, D., Coecke, B., Durt, T., Valckenborgh, F. (1997b). Quantum, classical and intermediate I: a model on the Poincaré sphere. Tatra Mountains Mathematical Publications, 10, 225.Google Scholar
  29. Aerts, D., Broekaert, J., Smets, S. (1999a). A quantum structure description of the liar paradox. International Journal of Theoretical Physics, 38, 3231–3239.CrossRefGoogle Scholar
  30. Aerts, D., Coecke, B., Smets, S. (1999b). On the origin of probabilities in quantum mechanics: creative and contextual aspects. In G. Cornelis, S. Smets, J.P. Van Bendegem (Eds.) , Metadebates on science (pp. 291–302). Dordrecht: Springer.Google Scholar
  31. Aerts, D., Sozzo, S., Veloz, T. (2015). Quantum structure of negation and conjunction in human thought. Frontiers in Psychology, 6, 1447.CrossRefGoogle Scholar
  32. Aerts, D., Sassoli de Bianchi, M., Sozzo, S. (2016). On the foundations of the brussels operational-realistic approach to cognition. Frontiers of Physics, 4, 17. Scholar
  33. Aerts, D., Sassoli de Bianchi, M., Sozzo, S., Veloz, M. (2018a). On the conceptuality interpretation of quantum and relativity theories. Foundations of Science,
  34. Aerts, D., Sassoli de Bianchi, M., Sozzo, S, Veloz, T. (2018). Quantum cognition goes beyond-quantum: modeling the collective participant in psychological measurements. arXiv:1802.10448 [q-bio.NC].
  35. Atmanspacher, H., Römer, H., Walach, H. (2002). Weak quantum theory: complementarity and entanglement in physics and beyond. Foundations of Physics, 32, 379–406.CrossRefGoogle Scholar
  36. Bell, J. S. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38, 447–452.CrossRefGoogle Scholar
  37. Busemeyer, J. R., & Bruza, P. D. (2012). Quantum models of cognition and decision. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  38. Birkhoff, G, & von Neumann, J. (1936). The logic of quantum mechanics. The Annals of Mathematics, 37, 823–843.CrossRefGoogle Scholar
  39. Foulis, D. J., & Randall, C. H. (1978). Manuals, morphisms and quantum mechanics. In A.R. Marlow (Ed.) , Mathematical foundations of quantum theory (pp. 105–126). New York: Academic Press.Google Scholar
  40. Gabora, L., & Aerts, D. (2002). Contextualizing concepts using a mathematical generalization of the quantum formalism. Journal of Experimental & Theoretical Artificial Intelligence, 14, 327–358.CrossRefGoogle Scholar
  41. Gleason, A. M. (1957). Measures on the closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics, 6, 885–893.Google Scholar
  42. Gudder, S. P. (1970). On hidden-variable theories. Journal of Mathematical Physics, 11, 431–436.CrossRefGoogle Scholar
  43. Haven, E., & Khrennikov, A.Y. (2013). Quantum social science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  44. Jauch, J. M. (1968). Foundations of quantum mechanics. Reading: Addison-Wesley Publishing Company.Google Scholar
  45. Jauch, J. M., & Piron, C. (1963). Can hidden variables be excluded in quantum mechanics? Helvetica Physica Acta, 36, 827–837.Google Scholar
  46. Khrennikov, A. (1999). Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social and anomalous phenomena. Foundations of Physics, 29, 1065–1098.CrossRefGoogle Scholar
  47. Khrennikov, A. Y. (2010). Ubiquitous quantum structure. Berlin: Springer.CrossRefGoogle Scholar
  48. Kochen, S., & Specker, E. P. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 17, 59–87.Google Scholar
  49. Ludwig, G. (1983). Foundations of quantum mechanics I, texts & monographs in physics. New York: Springer.Google Scholar
  50. Mackey, G. (1963). Mathematical foundations of quantum mechanics. W. A. Benjamin: Reading.Google Scholar
  51. Piron, C. (1976). Foundations of quantum physics. W. A. Benjamin: Reading.Google Scholar
  52. Rauch, H., Zeilinger, A., Badurek, G., Wilfing, A., Bauspiess, W., Bonse, U. (1975). Verification of coherent spinor rotation of fermions. Physics Letters, 54A, 425–427.CrossRefGoogle Scholar
  53. Sassoli de Bianchi, M. (2013a). The delta-quantum machine, the k-model, and the non-ordinary spatiality of quantum entities. Foundations of Science, 18, 11–41.CrossRefGoogle Scholar
  54. Sassoli de Bianchi, M. (2013b). Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aerts’ machine-models. Central European Journal of Physics, 11, 147–161.Google Scholar
  55. Sassoli de Bianchi, M. (2015). God may not play dice, but human observers surely do. Foundations of Science, 1, 77–105.CrossRefGoogle Scholar
  56. Sassoli de Bianchi, M. (2017). Theoretical and conceptual analysis of the celebrated 4π-symmetry neutron interferometry experiments. Foundations of Science, 22, 627–653.CrossRefGoogle Scholar
  57. Sassoli de Bianchi, M. (2018). On Aerts’ overlooked solution to the EPR paradox. arXiv:1805.02869 [quant-ph].
  58. Stapp, H. P. (2009). Mind, matter and quantum mechanics, QThe Frontiers Collection. Berlin: Springer.CrossRefGoogle Scholar
  59. Stapp, H. P. (2011). Mindful universe, the frontiers collection. Berlin: Springer.CrossRefGoogle Scholar
  60. Von Neumann, J. (1932). Grundlehren, Math. Wiss. XXXVIII.Google Scholar
  61. Wendt, A. (2015). Quantum mind and social science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  62. Werner, S. A., Colella, R., Overhauser, A. W., Eagen, C. F. (1975). Observation of the phase shift of a neutron due to precession in a magnetic field. Review Letters, 35, 1053.CrossRefGoogle Scholar

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© Neuroscientia 2019

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Massimiliano Sassoli de Bianchi
    • 1
    • 2
  • Sandro Sozzo
    • 3
    Email author
  • Tomas Veloz
    • 1
    • 4
    • 5
  1. 1.Center Leo Apostel for Interdisciplinary StudiesBrussels Free UniversityBrusselsBelgium
  2. 2.Laboratorio di Autoricerca di BaseLuganoSwitzerland
  3. 3.School of Business and IQSCSUniversity of LeicesterLeicesterUK
  4. 4.Instituto de Filosofía y Ciencias de la Complejidad IFICCSantiagoChile
  5. 5.Departamento Ciencias Biológicas, Facultad Ciencias de la vidaSantiagoChile

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