Von Neumann, Turing, and Gödel: On Mind and Machines

Barbora Jurková, Lukáš H. Zámečník

DOI: https://doi.org/10.46938/tv.2022.556

Abstract


The paper discusses some of the poorly explored links between the conceptual systems of logic in Kurt Gödel, the theory of automata in Alan Turing, and the theory of self-reproducing automata in John von Neumann. Traditional controversies are left aside (especially the opposition of Gödel and Turing in the view of mind) and attention is focused on the similarities between all three authors. In individual chapters, the text deals with: the form of differentiation of syntax and semantics in formal system in Gödel, Turing and von Neumann; von Neumann’s variant of Gödel’s theorem and von Neumann’s and Gödel’s conception of Turing machine; and finally the same basis of the view of the relation between mind and automaton in all three authors.

Keywords


syntax and semantics in formal system; Gödel’s theorem; Turing machine; von Neumann’s probe

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References


Allo, Patrick, Donald W. Loveland, Richard E. Hodel, and S. G. Sterrett. Three Views of Logic: Mathematics, Philosophy and Computer Science. Princeton: Princeton University Press, 2005. https://doi.org/10.1007/s11023-015-9375-9.

American Philosophical Society Library, John Von Neumann – Folder 5, https://diglib.amphilsoc.org/islandora/object/john-von-neumann-folder-5#page/1/mode/1up.

Barbieri, Marcello. Code Biology: A New Science of Life. Berlin: Springer, 2015. https://doi.org/10.1007/s12304-012-9147-3.

Barbieri, Marcello. The Semantic Theory of Evolution. London: Harwood Academic Publishers, 1985. https://doi.org/10.1201/9780429290039-10.

Carter, Matt. Minds and Computers: An Introduction to the Philosophy of Artificial Intelligence. Edinburgh: Edinburgh University Press, 2007. https://doi.org/10.1111/j.1468-2265.2009.00484_50.x.

Copeland, Jack B., ed. The Essential Turing. Oxford: Clarendon Press, 2004. https://doi.org/10.1080/01611190508951318.

Davis, Martin. „What Did Gödel Believe and When Did He Believe It?“ Bulletin of Symbolic Logic 11 (2005): 194–206. https://doi.org/10.2178/bsl/1120231630.

Davis, Martin. The Universal Computer. The Road from Leibniz to Turing. New York: W. W. Norton & Company, 2000. https://doi.org/10.2307/2695463.

Dreyfus, Hubert L. Alchemy and Artificial Intelligence. Santa Monica, CA: Rand Corporation, 1965.

Emmmeche, Claus, and Kalevi Kull, eds. Towards a Semiotic Biology: Life is the Action of Signs. London: Imperial College Press, 2011. https://doi.org/10.1142/p771.

Faltýnek, Dan. Sémiotické primitivy v konstrukci gramatik. Olomouc: Univerzita Palackého v Olomouci, 2011.

Feferman, Solomon. „Are There Absolutely Unsolvable Problems? Gödel’s Dichotomy.“ Philosophia Mathematica 14, no. 2 (2006): 134–52. https://doi.org/10.1093/philmat/nkj003.

Franzén, Torkel. Gödel’s Theorem: An Incomplete Guide to its Use and Abuse. Wellesley: A. K. Peters, 2005. https://doi.org/10.1201/b10700.

Gaifman, Haim. „Naming and Diagonalization, from Cantor to Gödel to Kleene.“ Logic Journal of the IGPL 15, no. 5 (2006): 709–28. https://doi.org/10.1093/jigpal/jzl006.

Gödel, Kurt. „Some Basic Theorems on the Foundation of Mathematics and Their Philosophical Implications.“ In Kurt Gödel: unpublished philosophical essays, edited by Francisco A. Rodriguez-Consuegra, 129–70. Basel: Birkhäuser, 1995. https://doi.org/10.1007/978-3-0348-9248-3_6.

Gödel, Kurt. „Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.“ Monatshefte für Mathematik und Physik. Akademische Verlagsgesellschaft, Leipzig 38 (1931): 173–98. https://doi.org/10.1007/BF01700692.

Gödel, Kurt. Collected Works, Volume I (1986, Publications 1929–1936) Volume II (1989, Publications 1938–1974), Volume III (1995, Unpublished Essays and Lectures), Volume IV (2003, Selected Correspondence, AG), Volume V (2003, Selected Correspondence, HZ). Edited by Solomon Feferman, John W. Dawson Jr., Stephen C. Kleene, Gregory H. Moore, Robert M. Solovay, and Jean van Heijenoort. New York: Oxford University Press, 1986–2003.

Gödel, Kurt. „What is Cantor’s Continuum Problem?“ The American Mathematical Monthly 54, no. 9 (1947): 515–25. https://doi.org/10.1080/00029890.1947.11991877.

Haigh, Thomas, and Mark Priestley. „Von Neumann Thought Turing’s Universal Machine Was ,Simple and Neat‘: But That Didn’t Tell Him How to Design a Computer.“ Communications of the ACM 63, no. 1 (2019): 26–32. https://doi.org/10.1145/3372920.

Havlík, Vladimír. „Kurt Gödel a AI.“ In Meze formalizace, analytičnosti a prostoročasu, editovali Tomáš Čana a Vladimír Havlík, 161–77. Praha: Filosofia, 2007.

Hofstadter, Douglas R. Gödel, Escher, Bach: Existenciální gordická balada: metaforická fuga o mysli a strojích v duchu Lewise Carrolla. Praha: Argo/Dokořán: 2012.

Igamberdiev, Abrir U., and Joseph E. Brenner. „Mathematics in Biological Reality: The Emergence of Natural Computation in Living Systems.“ BioSystems 204 (2021): 104395. https://doi.org/10.1016/j.biosystems.2021.104395.

Lucas, John R. „Minds, Machines and Gödel.“ Philosophy 36, no. 137 (1961): 112–27. https://doi.org/10.1017/S0031819100057983.

Macrae, Norman, John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More. Lexington, MA: Plunkett Lake Press, 2019.

Nagel, Ernest, and Newman, James Roy. Gödel’s Proof. Edited by Douglas R. Hofstadter. New York: New York University Press, 2002.

Papineau, David. Philosophical Devices. Oxford: Oxford University Press, 2012.

Partee, Barbara Hall, Alice ter Meulen, and Robert E. Wall. Mathematical Methods in Linguistics. Dordrecht: Kluwer Academic Publishers, 1990.

Pattee, Howard. „The Physics and Metaphysics of Biosemiotics.“ Journal of Biosemiotics 1 (2005): 281–301.

Pattee, Howard, and Kalevi Kull. „A Biosemiotics Conversation: Between Physics and Semiotics.“ Sign System Studies 37, no. 1/2 (2009): 331–21. https://doi.org/10.12697/SSS.2009.37.1-2.12.

Penrose, Roger. Shadows of the Mind. Oxford: Oxford University Press, 1994.

Penrose, Roger. The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics. Oxford: Oxford University Press, 1990. https://doi.org/10.1093/oso/9780198519737.001.0001.

Peregrin, Jaroslav. Kapitoly z analytické filosofie. Praha: Filosofia, 2014.

Rédei, Miklós. John von Neumann: Selected Letters. Providence, RI: American Mathematical Society, 2005. https://doi.org/10.1090/hmath/027.

Russell, Stuart, and Peter Norvig. Artificial Intelligence: A Modern Approach. Hoboken: Pearson, 2021.

Ryle, Gilbert. The Concept of Mind. London: Routledge, 2009. https://doi.org/10.4324/9780203875858.

Smullyan, Raymond. Gödel’s Incompleteness Theorems. Oxford: Oxford University Press, 1992. https://doi.org/10.1093/oso/9780195046724.001.0001.

Tarski, Alfred. „The Semantic Conception of Truth: And the Foundations of Semantics.“ Philosophy and Phenomenological Research 4, no. 3 (1944): 341–76. https://doi.org/10.2307/2102968.

Turing, Alan. „Computing Machinery and Intelligence.“ Mind 59 (1950): 444–45.

Turing, Alan. „On Computable Numbers, with an Application to the Entscheidungsproblem.“ Proceedings of the London Mathematical Society s2-42, no. 1 (1937): 230–65. https://doi.org/10.1112/plms/s2-42.1.230.

Turing, Alan. „Systems of Logic Based on Ordinals.“ Proceedings of the London Mathematical Society s2-45, no. 1 (1939): 161–228. https://doi.org/10.1112/plms/s2-45.1.161.

Tvrdý, Filip. Turingův test: Filozofické aspekty umělé inteligence. Praha: Togga, 2014.

von Neumann, John. Collected Works: Volume 5: Design of Computers, Theory of Automata and Numerical Analysis. Edited by Abraham H. Taub. Oxford: Pergamon Press, 1963.

von Neumann, John. The Computer and the Brain. New Haven: Yale University Press, 2012.

von Neumann, John. The Theory of Self-Reproducing Automata. Urbana: University of Illinois Press, 1966.

Wang, Hao. A Logical Journey: From Gödel to Philosophy. Cambridge, MA: MIT Press, 1996. https://doi.org/10.7551/mitpress/4321.001.0001.

Whitehead, Alfred North, and Bertrand Russell. Principia Mathematica. Volume I. Cambridge: Cambridge University Press, 1963.

Zach, Richard, “Hilbert’s Program.” In Stanford Encyclopedia of Philosophy. Stanford University, 1997–. Article revised May 24, 2019. https://plato.stanford.edu/archives/fall2019/entries/hilbert-program.

Zámečník, Lukáš H., and Jaroslav Krbec. „Describing Life: Towards the Conception of Howard Pattee.“ Linguistic Frontiers 2, no. 1 (2019): 1–9. https://doi.org/10.2478/lf-2018-0012.

Zlatoš, Pavol, Ani matematika si nemôže byt’ istá sama sebou: Úvahy o množinách, nekonečne, paradoxoch a Gödelových vetách. Bratislava: IRIS, 1995.




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