Quantum Physics and Cognitive Science from a Wittgensteinian Perspective: Bohr’s Classicism, Chomsky’s Universalism, and Bell’s Contextualism

  • Yoshihiro MaruyamaEmail author
Part of the The Frontiers Collection book series (FRONTCOLL)


Although Wittgenstein’s influence on logic and foundations of mathematics is well recognized, nonetheless, his legacy concerning other sciences is much less elucidated, and in this article we aim at shedding new light on physics, artificial intelligence, and cognitive science from a Wittgensteinian perspective. We focus upon three issues amongst other things: the Chosmky versus Norvig debate on the nature of language; a Neo-Kantian parallelism between Bohr’s philosophy of physics and Hilbert’s philosophy of mathematics; the relationships between cognitive contextuality and physical contextuality as shown by recent Bell-type results. The Chosmky versus Norvig debate may be seen as a battle between Wittgenstein’s earlier and later conceptions of meaning, i.e., picture theory and use theory. From a Wittgensteinian point of view, quantum physics may be seen as a physical version of the Linguistic Turn. The parallelism between Bohr’s philosophy of classical concepts and Hilbert’s philosophy of finitism builds upon transcendental philosophy in the Kantian tradition, both Bohr and Hilbert having been influenced by Neo-Kantian thinkers, such as Hertz, whose sign theory is actually a common root of Wittgenstein’s picture theory and Hilbert’s axiomatics. Wittgenstein is considered a root of contextualism in contemporary philosophy. Contextuality has different manifestations in physics and cognitive science, and contextuality studies across the sciences are rapidly developing in cutting-edge research. We elucidate both analogies and disanalogies between contextuality of reality and contextuality of reason in terms of the nature of probabilities involved. In passing, we also give a (less controversial) reformulation of Penrose’s quantum mind thesis.



I am grateful to Samson Abramsky for discussions about contextuality, to Kohei Morita for discussions about Bohr and his philosophy of classical concepts, and to Takeo Uramoto for discussions about quantum physics as well as Wittgenstein’s philosophy of language. I hereby acknowledge financial support from JST (grant number: JPMJPR17G9) and JSPS (grant number: 17K14231).


  1. Abramsky, Samson, and Brandenburger, Adam, 2011, The Sheaf-Theoretic Structure Of Non-Locality and Contextuality, New Journal of Physics, vol. 13, 113036.CrossRefGoogle Scholar
  2. Baird, David, et al. (eds.), 1998, Heinrich Hertz: Classical Physicist, Modern Philosopher, Netherlands: Springer.Google Scholar
  3. Bays, Timothy, 2008, Two arguments against realism, Philosophical Quarterly, vol. 58, pp. 193–213.CrossRefGoogle Scholar
  4. Bella, Mara, 2001, Quantum Dialogue: The Making of a Revolution, Chicago: University of Chicago Press.Google Scholar
  5. Berman, Morris, 1981, The Reenchantment of The World, Ithaca: Cornell University Press.Google Scholar
  6. Bohr, Niels, 1934, The quantum of action and the description of nature, in: Atomic theory and the description of nature, Cambridge: Cambridge University Press.Google Scholar
  7. Bohr, Niels, 1949, Discussions with Einstein on Epistemological Problems in Atomic Physics, in: Philosopher Scientist, pp. 199–241.Google Scholar
  8. Bourguignat, Christophe, 2014, Interpretable VS Powerful Predictive Models : Why We Need Them Both, Medium, 17 September 2014, retrieved on 23 June 2019.Google Scholar
  9. Busemeyer, Jerome, and Bruza, Peter, 2014, Quantum Models of Cognition and Decision, Cambridge: Cambridge University Press.Google Scholar
  10. Cass, Stephen, 2011, Unthinking Machines, MIT Technology Review, 4 May 2011, retrieved on 23 June 2019.Google Scholar
  11. Cassirer, Ernst, 1923, Substance and Function, and Einstein’s Theory of Relativity, Chicago: Open Court.Google Scholar
  12. Cassirer, Ernst, 1945, Structuralism in Modern Linguistics, Word, vol. 1, pp. 99–120.CrossRefGoogle Scholar
  13. Cassirer, Ernst, 1955, The Philosophy of Symbolic Forms, New Haven: Yale University Press.Google Scholar
  14. Chalmers, David, 1995, Minds, Machines, and Mathematics, Psyche, vol. 2, pp. 11–20.Google Scholar
  15. Chalmers, David, 1996, The Conscious Mind: In Search of a Fundamental Theory, Oxford: Oxford University Press.Google Scholar
  16. Cervantes, Victor, and Dzhafarov, Ethibar, Snow Queen is Evil and Beautiful: Experimental Evidence for Probabilistic Contextuality in Human Choices, Decision, vol. 5, 193–204.CrossRefGoogle Scholar
  17. Chomsky, Noam, 1957, Syntactic Structures, Berlin: Mouton & Co.Google Scholar
  18. Chomsky, Noam, 1975, Recent contributions to the theory of innate ideas, in: S. Stitch (ed.), Innate Ideas, Berlin: California University Press.Google Scholar
  19. Chomsky, Noam, and Ronat, Mitsou, 1979, Language and Responsibility: Based on Conversations with Mitsou Ronat, Paris: Pantheon Books.Google Scholar
  20. Chomsky, Noam, 2011, Keynote Panel: The Golden Age — A Look at the Original Roots of Artificial Intelligence, Cognitive Science, and Neuroscience, MIT Symposium on Brains, Minds, and Machines, held in 2011, recording available at:, retrieved on 23 June 2019.
  21. Christiansen, Frederik Voetmann, 2006, Heinrich Hertz’s Neo-Kantian Philosophy of Science, and its Development by Harald Hoffding, Journal for General Philosophy of Science, vol. 37, pp. 1–20.CrossRefGoogle Scholar
  22. Corry, Leo, 2004, David Hilbert and the Axiomatization of Physics (1898–1918), Netherlands: Springer.CrossRefGoogle Scholar
  23. Dreyfus, Hubert, 2007, Why Heideggerian AI failed and how fixing it would require making it more Heideggerian, Philosophical Psychology, vol. 20, 247–268.CrossRefGoogle Scholar
  24. Dzhafarov, Ethibar, et al., 2016, On contextuality in behavioural data, Philos. Trans. A Math. Phys. Eng. Sci., vol. 374, 20150234.CrossRefGoogle Scholar
  25. Faye, Jan, 1991, Niels Bohr His Heritage and Legacy: An Anti-Realist View of Quantum Mechanics,Google Scholar
  26. Faye, Jan, 2002, Copenhagen Interpretation of Quantum Mechanics, Stanford Encyclopaedia of Philosophy.Google Scholar
  27. Frege, Gottlob, 1884, Grundlagen der Arithmetik.Google Scholar
  28. Friedman, Michael, 2000, A Parting of the Ways: Carnap, Cassirer, and Heidegger, Chicago: Open Court Press.Google Scholar
  29. Gold, Kevin, 2011, Norvig vs. Chomsky and the Fight for the Future of AI, TOR.COM, 21 June 2011, retrieved on 26 June 2019.Google Scholar
  30. Gödel, Kurt, 1961, The modern development of the foundations of mathematics in the light of philosophy, in: Collected Works, vol. III, 1981, Oxford: Oxford University Press.Google Scholar
  31. Gödel, Kurt, 1995, Collected Works, vol. III, New York: Oxford University Press.Google Scholar
  32. Gray, Jeremy, 2008, Plato’s Ghost: The Modernist Transformation of Mathematics, Princeton: Princeton University Press.CrossRefGoogle Scholar
  33. Griffin, David, et al., 1992, Founders of Constructive Postmodern Philosophy: Peirce, James, Bergson, Whitehead, and Hartshorne, New York: SUNY Press.Google Scholar
  34. Griffin, David, 2001, Reenchantment without Supernaturalism, Ithaca: Cornell University Press.Google Scholar
  35. Hilbert, David, 1983, “On the Infinite", in: Philosophy of Mathematics: Selected Readings, Cambridge: Cambridge University Press.Google Scholar
  36. Katz, Yarden, 2012, Noam Chomsky on Where Artificial Intelligence Went Wrong, The Atlantic, 1 November 2012, retrieved on 23 June 2019.Google Scholar
  37. Kamp, Hans, and Partee, B., 1995, Compositionality and Prototypes, Cognition, vol. 57, pp. 129–191.CrossRefGoogle Scholar
  38. Kuhn and Johnson, 2013, Applied Predictive Modeling, New York: Springer.CrossRefGoogle Scholar
  39. Kripke, Saul, 1982, Wittgenstein on Rules and Private Language, Massachusetts: Harvard University Press.Google Scholar
  40. Lofts, Steve, 2000, Cassirer: A “Repetition" of Modernity, Albany: SUNY Press.Google Scholar
  41. Markie, Peter, 2017, Rationalism vs. Empiricism, Stanford Encyclopedia of PhilosophyGoogle Scholar
  42. Maxwell, James Clerk, 1990, The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862, Cambridge: Cambridge University Press.Google Scholar
  43. Norvig, Peter, 2011, On Chomsky and the Two Cultures of Statistical Learning, in: W. Pietsch, J. Wernecke, M. Ott (eds.), Berechenbarkeit der Welt? (pp. 61–83), Wiesbaden: Springer. (made available online in 2011; published in 2017)CrossRefGoogle Scholar
  44. Parsons, Charles, 2014, Philosophy of Mathematics in the Twentieth Century: Selected Essays, Massachusetts: Harvard University Press.Google Scholar
  45. Patton, Lydia, 2014, Hilbert’s Objectivity, Historia Mathematica, vol. 41, pp. 188–203.CrossRefGoogle Scholar
  46. Penrose, Roger, 1989, The Emperor’s New Mind, Oxford: Oxford University Press.Google Scholar
  47. Penrose, Roger, 1994, Shadows of the Mind, Oxford: Oxford University Press.Google Scholar
  48. Peter C. Kjaergaard, 2002, Hertz and Wittgenstein’s Philosophy of Science, Journal for General Philosophy of Science, vol. 33, pp 121–149.CrossRefGoogle Scholar
  49. Pothos, Emmanuel, and Busemeyer, Jerome, 2009, A quantum probability explanation for violations of ‘rational’ decision theory, vol. 276, 1665.CrossRefGoogle Scholar
  50. Putnam, Hilary, 1983, Realism and Reason, Philosophical Papers vol. 3, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  51. Quine, Willard Van Oman, 1969, Ontological Relativity and Other Essays, New York: Columbia University Press.Google Scholar
  52. Rorty, Richard, 1962, Realism, Categories, and the “Linguistic Turn”, International Philosophical Quarterly, vol. 2, pp. 307–322.CrossRefGoogle Scholar
  53. Rorty, Richard, ed., 1967, The Linguistic Turn: Recent Essays in Philosophical Method, Chicago, The University of Chicago Press.Google Scholar
  54. Rorty, Richard, 1970, Philosophy and the Mirror of Nature, Princeton: Princeton University Press.Google Scholar
  55. Rysiew, Patrick, 2016, Epistemic Contextualism, Stanford Encyclopedia of Philosophy, Stanford: Stanford University.Google Scholar
  56. Sen, Amartya, 1977, Rational fools: A critique of the behavioral foundations of economic theory, Philosophy and Public Affairs, vol. 6, pp. 317–344.Google Scholar
  57. Tegmark, Max, 2000, Importance of quantum decoherence in brain processes, Phys. Rev. E, vol. 61, 4194.CrossRefGoogle Scholar
  58. Turney, Peter, and Pantel, Patrick, 2010, From Frequency to Meaning: Vector Space Models of Semantics, Journal of Artificial Intelligence Research, vol., 37, pp. 141-188.CrossRefGoogle Scholar
  59. Tversky, A., and Kahneman, D., 1982, Judgments of and by representativeness, in: Judgment under uncertainty: heuristics and biases, Cambridge: Cambridge University Press.Google Scholar
  60. Wang, Zheng, Solloway, Tyler, Shiffrin, Richard, and Busemeyer, Jerome, 2014, Context effects produced by question orders reveal quantum nature of human judgments, Proc. Nac. Aca. Sci., vol. 111, 9431–9436.CrossRefGoogle Scholar
  61. Weir, Kristen, 2016, A reproducibility crisis?, American Psychological Association, retrieved 23 June 2019.Google Scholar
  62. Wittgenstein, Ludwig, 1961, Tractatus Logico-Philosophicus, New York: Humanities Press.Google Scholar
  63. Wittgenstein, Ludwig, 1969, On Certainty, Oxford: Basil Blackwell.Google Scholar
  64. Wittgenstein, Ludwig, 1970, Zettel, California: University of California Press.Google Scholar
  65. Wittgenstein, Ludwig, 1986, Philosophical Investigations, Oxford: Basil Blackwell.Google Scholar
  66. Zach, Richard, 2003, Hilbert’s program, Stanford Encyclopedia of Philosophy.Google Scholar
  67. Zach, Richard, 2007, Hilbert’s program then and now, in: Philosophy of Logic, Amsterdam: North Holland. pp. 411–447.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.The Hakubi Centre for Advanced ResearchKyoto UniversityKyotoJapan

Personalised recommendations