Abstract
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.
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References
Abramsky, Samson, and Brandenburger, Adam, 2011, The Sheaf-Theoretic Structure Of Non-Locality and Contextuality, New Journal of Physics, vol. 13, 113036.
Baird, David, et al. (eds.), 1998, Heinrich Hertz: Classical Physicist, Modern Philosopher, Netherlands: Springer.
Bays, Timothy, 2008, Two arguments against realism, Philosophical Quarterly, vol. 58, pp. 193–213.
Bella, Mara, 2001, Quantum Dialogue: The Making of a Revolution, Chicago: University of Chicago Press.
Berman, Morris, 1981, The Reenchantment of The World, Ithaca: Cornell University Press.
Bohr, Niels, 1934, The quantum of action and the description of nature, in: Atomic theory and the description of nature, Cambridge: Cambridge University Press.
Bohr, Niels, 1949, Discussions with Einstein on Epistemological Problems in Atomic Physics, in: Philosopher Scientist, pp. 199–241.
Bourguignat, Christophe, 2014, Interpretable VS Powerful Predictive Models : Why We Need Them Both, Medium, 17 September 2014, retrieved on 23 June 2019.
Busemeyer, Jerome, and Bruza, Peter, 2014, Quantum Models of Cognition and Decision, Cambridge: Cambridge University Press.
Cass, Stephen, 2011, Unthinking Machines, MIT Technology Review, 4 May 2011, retrieved on 23 June 2019.
Cassirer, Ernst, 1923, Substance and Function, and Einstein’s Theory of Relativity, Chicago: Open Court.
Cassirer, Ernst, 1945, Structuralism in Modern Linguistics, Word, vol. 1, pp. 99–120.
Cassirer, Ernst, 1955, The Philosophy of Symbolic Forms, New Haven: Yale University Press.
Chalmers, David, 1995, Minds, Machines, and Mathematics, Psyche, vol. 2, pp. 11–20.
Chalmers, David, 1996, The Conscious Mind: In Search of a Fundamental Theory, Oxford: Oxford University Press.
Cervantes, Victor, and Dzhafarov, Ethibar, Snow Queen is Evil and Beautiful: Experimental Evidence for Probabilistic Contextuality in Human Choices, Decision, vol. 5, 193–204.
Chomsky, Noam, 1957, Syntactic Structures, Berlin: Mouton & Co.
Chomsky, Noam, 1975, Recent contributions to the theory of innate ideas, in: S. Stitch (ed.), Innate Ideas, Berlin: California University Press.
Chomsky, Noam, and Ronat, Mitsou, 1979, Language and Responsibility: Based on Conversations with Mitsou Ronat, Paris: Pantheon Books.
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: https://mit150.mit.edu/symposia/brains-minds-machines.html, retrieved on 23 June 2019.
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.
Corry, Leo, 2004, David Hilbert and the Axiomatization of Physics (1898–1918), Netherlands: Springer.
Dreyfus, Hubert, 2007, Why Heideggerian AI failed and how fixing it would require making it more Heideggerian, Philosophical Psychology, vol. 20, 247–268.
Dzhafarov, Ethibar, et al., 2016, On contextuality in behavioural data, Philos. Trans. A Math. Phys. Eng. Sci., vol. 374, 20150234.
Faye, Jan, 1991, Niels Bohr His Heritage and Legacy: An Anti-Realist View of Quantum Mechanics,
Faye, Jan, 2002, Copenhagen Interpretation of Quantum Mechanics, Stanford Encyclopaedia of Philosophy.
Frege, Gottlob, 1884, Grundlagen der Arithmetik.
Friedman, Michael, 2000, A Parting of the Ways: Carnap, Cassirer, and Heidegger, Chicago: Open Court Press.
Gold, Kevin, 2011, Norvig vs. Chomsky and the Fight for the Future of AI, TOR.COM, 21 June 2011, retrieved on 26 June 2019.
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.
Gödel, Kurt, 1995, Collected Works, vol. III, New York: Oxford University Press.
Gray, Jeremy, 2008, Plato’s Ghost: The Modernist Transformation of Mathematics, Princeton: Princeton University Press.
Griffin, David, et al., 1992, Founders of Constructive Postmodern Philosophy: Peirce, James, Bergson, Whitehead, and Hartshorne, New York: SUNY Press.
Griffin, David, 2001, Reenchantment without Supernaturalism, Ithaca: Cornell University Press.
Hilbert, David, 1983, “On the Infinite", in: Philosophy of Mathematics: Selected Readings, Cambridge: Cambridge University Press.
Katz, Yarden, 2012, Noam Chomsky on Where Artificial Intelligence Went Wrong, The Atlantic, 1 November 2012, retrieved on 23 June 2019.
Kamp, Hans, and Partee, B., 1995, Compositionality and Prototypes, Cognition, vol. 57, pp. 129–191.
Kuhn and Johnson, 2013, Applied Predictive Modeling, New York: Springer.
Kripke, Saul, 1982, Wittgenstein on Rules and Private Language, Massachusetts: Harvard University Press.
Lofts, Steve, 2000, Cassirer: A “Repetition" of Modernity, Albany: SUNY Press.
Markie, Peter, 2017, Rationalism vs. Empiricism, Stanford Encyclopedia of Philosophy
Maxwell, James Clerk, 1990, The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862, Cambridge: Cambridge University Press.
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)
Parsons, Charles, 2014, Philosophy of Mathematics in the Twentieth Century: Selected Essays, Massachusetts: Harvard University Press.
Patton, Lydia, 2014, Hilbert’s Objectivity, Historia Mathematica, vol. 41, pp. 188–203.
Penrose, Roger, 1989, The Emperor’s New Mind, Oxford: Oxford University Press.
Penrose, Roger, 1994, Shadows of the Mind, Oxford: Oxford University Press.
Peter C. Kjaergaard, 2002, Hertz and Wittgenstein’s Philosophy of Science, Journal for General Philosophy of Science, vol. 33, pp 121–149.
Pothos, Emmanuel, and Busemeyer, Jerome, 2009, A quantum probability explanation for violations of ‘rational’ decision theory, vol. 276, 1665.
Putnam, Hilary, 1983, Realism and Reason, Philosophical Papers vol. 3, Cambridge: Cambridge University Press.
Quine, Willard Van Oman, 1969, Ontological Relativity and Other Essays, New York: Columbia University Press.
Rorty, Richard, 1962, Realism, Categories, and the “Linguistic Turn”, International Philosophical Quarterly, vol. 2, pp. 307–322.
Rorty, Richard, ed., 1967, The Linguistic Turn: Recent Essays in Philosophical Method, Chicago, The University of Chicago Press.
Rorty, Richard, 1970, Philosophy and the Mirror of Nature, Princeton: Princeton University Press.
Rysiew, Patrick, 2016, Epistemic Contextualism, Stanford Encyclopedia of Philosophy, Stanford: Stanford University.
Sen, Amartya, 1977, Rational fools: A critique of the behavioral foundations of economic theory, Philosophy and Public Affairs, vol. 6, pp. 317–344.
Tegmark, Max, 2000, Importance of quantum decoherence in brain processes, Phys. Rev. E, vol. 61, 4194.
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.
Tversky, A., and Kahneman, D., 1982, Judgments of and by representativeness, in: Judgment under uncertainty: heuristics and biases, Cambridge: Cambridge University Press.
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.
Weir, Kristen, 2016, A reproducibility crisis?, American Psychological Association, retrieved 23 June 2019.
Wittgenstein, Ludwig, 1961, Tractatus Logico-Philosophicus, New York: Humanities Press.
Wittgenstein, Ludwig, 1969, On Certainty, Oxford: Basil Blackwell.
Wittgenstein, Ludwig, 1970, Zettel, California: University of California Press.
Wittgenstein, Ludwig, 1986, Philosophical Investigations, Oxford: Basil Blackwell.
Zach, Richard, 2003, Hilbert’s program, Stanford Encyclopedia of Philosophy.
Zach, Richard, 2007, Hilbert’s program then and now, in: Philosophy of Logic, Amsterdam: North Holland. pp. 411–447.
Acknowledgements
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).
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Maruyama, Y. (2020). Quantum Physics and Cognitive Science from a Wittgensteinian Perspective: Bohr’s Classicism, Chomsky’s Universalism, and Bell’s Contextualism. In: Wuppuluri, S., da Costa, N. (eds) WITTGENSTEINIAN (adj.). The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-27569-3_20
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