Perspective on Turing paradigm An essay

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Kazimierz Trzęsicki


Scientific knowledge is acquired according to some paradigm. Galileo wrote that the “book of nature” was written in mathematical language and could not be understood unless one first understood the language and recognized the characters with which it was written. It is argued that Turing planted the seeds of a new paradigm. According to the Turing Paradigm, the “book of nature” is written in algorithmic language, and science aims to learn how the algorithms change the physical, social, and human universe. Some sources of the Turing Paradigm are pointed out, and a few examples of the application of the Turing Paradigm are discussed.

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Trzęsicki, K. (2022). Perspective on Turing paradigm: An essay. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (73), 281–332. Retrieved from


Alexander de Villa Dei, 1839. Carmen de Algorismo. In: J.O. Halliwell-Phillipps, ed. Rara Mathematica; or, a Collection of Treatises on the Mathematics and Subjects Connected with Them, from Ancient Inedited Manuscripts [Online]. London: J. W. Parker; J.& J.J. Deighton; T. Stevenson, pp.73–83. Available at: <>.

Ares, J., Lara, J., Lizcano, D. and Martínez, M.A., 2018. Who Discovered the Binary System and Arithmetic? Did Leibniz Plagiarize Caramuel? Science and Engineering Ethics [Online], 24(1), pp.173–188.

Aristotle, 1999. Nicomachean Ethics [Online] (W.D. Ross, Trans.). Kitchener, Ontario: Batoche Books. Available at: <> [visited on 13 January 2023].

Babbage, C., 1864. Passages from the Life of a Philosopher [Online]. London: Longman, Green, Longman, Roberts, & Green. Available at: <> [visited on 13 January 2023].

Babbage, C., 2008. Passages from the Life of a Philosopher, Ch. VIII [Online]. Available at: <> [visited on 13 January 2023].

Bachelard, G., 2002. The Formation of the Scientific Mind: A Contribution to a Psychoanalysis of Objective Knowledge (M. McAllester Jones, Trans.), Philosophy of science. Manchester: Clinamen Press.

Bacon, R., 1912. Part of the Opus Tertium of Roger Bacon including a fragment now printed for the first time [Online]. Ed. by A. Little. Vol. 4. Aberdeen: Aberdeen University Press. Available at: <> [visited on 13 January 2023].

Bacon, R., 2010. Mathematical Science. In: J.H. Bridges, ed. The Opus Majus of Roger Bacon [Online]. Cambridge University Press, pp.97–404.

Bocheński, J.M., 1994. Sto zabobonów: krótki filozoficzny słownik zabobonów. Kraków: Philed.

Bostrom, N., 2014. Superintelligence: Paths, Dangers, Strategies. 1st ed. Oxford: Oxford University Press.

Brewster, D., 1855. Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton [Online]. Edinburgh: T. Constable and Co. Available at: <> [visited on 13 January 2023].

Burks, A., Goldstine, H. and von Neumann, J., 1946. Preliminary Discussion of the Logical Design of an Electronic Computing Instrument [Online]. U.S. Army Ordnance Department & Institute for Advanced Study. Available at: <> [visited on 17 January 2023].

Burks, A., Goldstine, H. and von Neumann, J., 1987. Preliminary discussion on the logical design of an electronic computing instrument. In: W. Aspray and A.W. Burks, eds. Papers of John von Neumann on Computing and Computer Theory [Online]. Vol. 12. Cambridge, MA: MIT Press, pp.97–142. Available at: <> [visited on 13 January 2023].

Cantor, M., 1865. Über einen Codex des Klosters Salem. Zeitschrift für Mathematik und Physik [Online], 10, pp.1–16.

Caramuel y Lobkowitz, J., 1670. Ioannis Caramuelis mathesis biceps: vetus et nova. Campaniae: in Officina Episcopali.

Chaitin, G.J., 2004a. Leibniz, Randomness and the Halting Probability [Online]. arXiv.

Chaitin, G.J., 2004b. Meta Math! The Quest for Omega. arXiv:math/0404335 [Online], p.150. Available at: <> [visited on 11 February 2015].

Chaitin, G., 2007. Epistemology as Information Theory: From Leibniz to Ω. In: G. Dodig Crnkovic, ed. Computation, Information, Cognition – The Nexus and The Liminal. Newcastle, UK: Cambridge Scholars Pub., pp.2–17.

Cherry, S., 2017. The Reason of Reason: How Reason, Logic, and Intelligibility Together are Evidence for God. Canterbury: Telos Publishing.

Condorcet, J.-A.-N.d.C., 1785. Essai sur l’application de l’analyse ŕ la probabilité des décisions rendus ŕ la pluralité des voix [Online]. Paris: Imprimerie Royale. Available at: <> [visited on 13 January 2023].

Copeland, J., Shagrir, O. and Sprevak, M., 2016. Is the whole universe a computer? In: J. Copeland, J. Bowen, M. Sprevak and R. Wilson, eds. The Turing Guide [Online]. Oxford; New York: Oxford University Press, pp.445–462.

Couturat, L., 1901. La logique de Leibniz d’aprčs des documents inédits [Online]. Paris: F. Alcan. Available at: <> [visited on 13 January 2023].

Davis, M., 2001. Engines of Logic: Mathematicians and the Origin of the Computer. New York: Norton.

De Morgan, A., 1872. A Budget of Paradoxes [Online]. London: Longmans, Green, and Co. Available at: <> [visited on 13 January 2023].

Dodig-Crnkovic, G., 2013. Alan Turing’s Legacy: Info-computational Philosophy of Nature. In: G. Dodig-Crnkovic and R. Giovagnoli, eds. Computing Nature: Turing Centenary Perspective [Online], Studies in Applied Philosophy, Epistemology and Rational Ethics. Berlin; Heidelberg: Springer, pp.115–123.

Dodig-Crnkovic, G., 2022. In search of a common, information-processing, agency-based framework for anthropogenic, biogenic, and abiotic cognition and intelligence. Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce), (73), pp.7–9.

Donahue, W.H., 1993. Kepler’s First Thoughts on Oval Orbits: Text, Translation, and Commentary. Journal for the History of Astronomy [Online], 24(1-2), pp.71–100.

Du Bois-Reymond, E.H., 1872. Über die Grenzen des Naturerkennens: Ein Vortrag in der zweiten öffentlichen Sitzung der 45. Versammlung deutscher Naturforscher und ärzte zu Leipzig am 14. August 1872. 1st ed. Leipzig: Veit & Co.

Du Bois-Reymond, E.H., 1882. Über die grenzen des Naturerkennens: die sieben Welträthsel zwei Vorträge [Online]. Leipzig: Veit. Available at: <> [visited on 13 January 2023].

Duch, W., 2012. Neuronauki i natura ludzka. In: M. Słomka, ed. Nauki przyrodnicze a nowy ateizm, Filozofia Przyrody i Nauk Przyrodniczych, 8. Lublin: Wydawnictwo KUL, pp.79–122.

Duch, W., 2015. Katolicyzm po kognitywistyce: o nową teologię umysłu. Available at: <> [visited on 17 January 2023].

Duch, W., 2017. Why minds cannot be received, but are created by brains. Scientia et Fides [Online], 5(2), pp.171–198. Available at: <> [visited on 17 January 2023].

Eddington, A.S., 2014. The Nature of the Physical World: Gifford Lectures of 1927: An Annotated Edition. Ed. by H.G. Callaway. Cambridge: Cambridge Scholars Publishing.

Fairweather, E.R., 1956. A scholastic miscellany: Anselm to Ockham. Philadelphia: Westminster Press.

Floridi, L., 2002. What is the Philosophy of Information? Metaphilosophy [Online], 33(1-2), pp.123–145.

Floridi, L., 2008. A defence of informational structural realism. Synthese [Online], 161(2), pp.219–253.

Floridi, L., 2009. The Information Society and Its Philosophy: Introduction to the Special Issue on “The Philosophy of Information, Its Nature, and Future Developments”. The Information Society [Online], 25(3), pp.153–158.

Galileo Galilei, 1615. Letter to Madame Christina of Lorraine, Grand Duchess of Tuscany (S. Drake, Trans.). Available at: <> [visited on 17 January 2023].

Galileo Galilei, 1623. The Assayer (Il Saggiatore) [Online] (S. Drake, Trans.). Available at: <> [visited on 13 January 2023].

Glushkov, V., 2004. Chto skazhet istorija? (in russian). Available at: <> [visited on 17 January 2023].

Guthrie, K.S. and Fideler, D., eds., 1987. The Pythagorean Sourcebook and Library: An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy [Online]. Grand Rapids, MI: Phanes Press. Available at: <> [visited on 13 January 2023].

Hall, A.R., 1956. The Scientific Revolution, 1500-1800: The Formation of the Modern Scientific Attitude [Online]. Boston: Beacon Press. Available at: <> [visited on 13 January 2023].

Heller, M., 2013. Bóg i nauka: moje dwie drogi do jednego celu (E. Nicewicz-Staszowska, Trans.). 1st ed. Kraków: Copernicus Center Press.

Heller, M., 2014. Granice nauki. Kraków: Copernicus Center Press.

Heschmeyer, J., 2012. Two Interesting Arguments for God: Intelligibility & Desire. Available at: <> [visited on 17 January 2023].

Hilbert, D., 1900. Mathematische Probleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse [Online]. Göttingen: Vandenhoeck & Ruprecht, pp.253–297. Available at: <> [visited on 13 January 2023].

Hilbert, D., 1935. Naturerkennen und Logik. Gesammelte Abhandlungen (Dritter Band) [Online]. Berlin: Verlag von Julius Springer, pp.378–087. Available at: <> [visited on 13 January 2023].

Hobbes, T., 1651. Leviathan, Or, The Matter, Form, and Power of a Common-wealth, Ecclesiastical and Civil. London: Andrew Crooke.

Hodges, A., 1997. Turing: A Natural Philosopher. 1st ed., The great philosophers, 3. London: Phoenix.

Ineichen, R., 2008. Leibniz, Caramul, Harriot und das Dualsystem. Mitteilungen der Deutschen Mathematiker-Vereinigung [Online], 16(1), pp.12–15.

Infeld, L., 1980. Quest: An Autobiography. 2d ed. New York, NY; London: Chelsea Pub. Co.

Isidore of Seville, 1911. Etymologiarvm sive Originvm libri XX; [Online]. Ed. by W.M.(.M. Lindsay. Oxonii: e typographeo Clarendoniano. Available at: <> [visited on 13 January 2023].

John of Salisbury, 1159. Metalogicus [Online]. Available at: <> [visited on 14 January 2023].

John of Salisbury, 1955. The Metalogicon of John of Salisbury (D.D. McGarry, Trans.). Berkeley; Los Angeles: University of California Press.

Knuth, D.E., 1997. The Art of Computer Programming: Vol 1. Fundamental Algorithms. 3rd ed. Reading, MA: Addison-Wesley.

Kopania, J., 2018. Leibniz i jego Bóg. Rozważania z Voltaire’em w tle. Studia z Historii Filozofii [Online], 9(3), p.69.

Krajewski, S., 2012. The ultimate strengthening of the Turing Test? Semiotica [Online], 2012(188), pp.203–218.

Krajewski, S., 2020. On the Anti-Mechanist Arguments Based on Gödel’s Theorem. Studia Semiotyczne [Online], 34(1), pp.9–56.

Kuhn, T.S., 1962. The Structure of Scientific Revolutions. Chicago: University of Chicago Press.

Kuhn, T.S., 1974. Second thoughts on paradigms. In: F. Suppe, ed. The Structure of Scientific Theories. Urbana: University of Illinois Press, pp.459–482.

Kurzweil, R., 2005. The Singularity Is Near: When Humans Transcend Biology. New York: Viking.

Leibniz, G.W., 1666. Dissertatio de arte combinatoria, in qua ex arithmeticae fundamentis complicationum ac transpositionum doctrina nouis praeceptis exstruitur ... noua etiam Artis meditandis, seu Logicae inuentionis semina sparguntur. Praefixa est synopsis totius tractatus, & additamenti loco demonstratio existentiae Dei, ad mathematicam certitudinem exacta autore Gottfredo Guilielmo Leibnüzio Lipsensi... [Online]. Lipsiae [Leipzig]: Joh. Simon. Fickium et Joh. Polycarp. Senboldum. Available at: <> [visited on 14 January 2023].

Leibniz, G.W., 1697. Brief an den Herzog von Braunschweig-Wolfenbüttel Rudolph August, 2. Januar 1697 [Online]. Available at: <> [visited on 14 January 2023].

Leibniz, G.W., 1890a. Dialogus. In: C.I. Gerhardt, ed. Die philosophischen Schriften von Gottfried Wilhelm Leibniz, herausg. von C.J. Gerhardt. (Vol. 7) [Online]. Berlin: Weidmann, pp.190–193. Available at: <> [visited on 14 January 2023].

Leibniz, G.W., 1890b. Die philosophischen Schriften von Gottfried Wilhelm Leibniz, herausg. von C.J. Gerhardt. (Vol. 7) [Online]. Ed. by C.I. Gerhardt. Berlin: Weidmann. Available at: <> [visited on 14 January 2023].

Leibniz, G.W., 1929. On calculating machine [Machina arithmetica in qua non additio tantum et subtractio sed et multiplicatio nullo, divisio vero paene nullo animi labore peragantur]. In: D.E. Smith, ed. A Source Book in Mathematics [Online] (M. Kormes, Trans.). New York: McGraw-Hill Book Co., pp.173–181. Available at: <> [visited on 14 January 2023].

Leibniz, G.W., 1979. De progressione dyadica (1679) [with German translation]. Herrn von Leibniz’ Rechnung mit Null und Eins [Online]. Berlin; München: Siemens Aktiengesellshaft, pp.46–47. Available at: <> [visited on 13 January 2023].

Leibniz, G.W., 1990. Leibniz korrespondiert mit China: der Briefwechsel mit den Jesuitenmissionaren (1689-1714). Ed. by R. Widmaier. Frankfurt am Main: V. Klostermann.

Lesne, A., 2007. The discrete versus continuous controversy in physics. Mathematical Structures in Computer Science [Online], 17(2), pp.185–223.

Ligonničre, R., 1992. Prehistoria i historia komputerów: od początków rachowania do pierwszych kalkulatorów elektronicznych (R. Dulinicz, Trans.). Wrocław: Zakład Narodowy im. Ossolińskich.

Marciszewski, W., ed., 1981. Dictionary of Logic as Applied in the Study of Language: Concepts—Methods—Theories, Nijhoff International Philosophy Series, vol. 9. Hague; Boston; London: Martinus Nijhoff.

Marciszewski, W. and Stacewicz, P., 2011. Umysł-komputer-świat. O zagadce umysłu z informatycznego punktu widzenia [Online]. Akademicka Oficyna Wydawnicza EXIT. Available at: <> [visited on 6 March 2014].

Martin, M. and Augustine, K., eds., 2015. The Myth of an Afterlife: The Case Against Life After Death. Lanham, MD: Rowman & Littlefield.

Mazur, J., 2014. Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers. Princeton: Princeton University Press.

Menninger, K., 1958. Zahlwort und Ziffer: eine Kulturgeschichte der Zahl. 2., neubearb. und erw. Aufl. Göttingen: Vandenhoeck & Ruprecht.

Menninger, K., 1969. Number Words and Number Symbols; a Cultural History of Numbers [Online] (P. Broneer, Trans.). Cambridge, MA: MIT Press. Available at: <> [visited on 14 January 2023].

von Neumann, J., 1958. The Computer and the Brain. 1st ed., Mrs. Hepsa Ely Silliman Memorial Lectures. New Haven: Yale University Press.

von Neumann, J., 1963. The general and logical theory of automata. In: A.H. Taub, ed. John Von Neumann Collected Works: Volume V: Design of Computers, Theory of Automata and Numerical Analysis [Online]. Pergamon Press, pp.288–328. [visited on 16 January 2023].

von Neumann, J., 2012. The Computer & the Brain. 3rd ed. New Haven, CT; London: Yale University Press.

von Neumann, J. and Burks, A.W., 1966. Theory of Self-Reproducing Automata. Urbana, IL; London: University of Illinois Press.

Newton, I., 1675. Isaac Newton letter to Robert Hooke [ID 9792]. Available at: <> [visited on 14 January 2023].

Newton, I., 1687. Philosophiae Naturalis Principia Mathematica [Online]. Londini; [London]: J. Societatis Regiae ac Typis J. Streater. Available at: <> [visited on 14 January 2023].

Shannon, C.E., 1958. Von Neumann’s contributions to automata theory. Bulletin of the American Mathematical Society [Online], 64(3), pp.123–129.

Shirley, J.W., 1951. Binary Numeration before Leibniz. American Journal of Physics [Online], 19, pp.452–454.

Sibley, A., 2013. Lessons from Augustine’s De Genesi ad Litteram—Libri Duodecim. Journal of Creation, 27(2), pp.71–77.

Smith, J., 2014. David Hilbert’s Radio Address. Convergence [Online].

Sonar, T., 2018. The History of the Priority Dispute between Newton and Leibniz [Online]. Cham: Springer International Publishing.

Strogatz, S.H., 2019. Infinite Powers: How Calculus Reveals the Secrets of the Universe. Boston: Houghton Mifflin Harcourt.

Swade, D., 2002. The Difference Engine: Charles Babbage and the Quest to Build the First Computer [Online]. New York: Penguin Books. Available at: <> [visited on 14 January 2023].

Swetz, F.J., 2003. Leibniz, the Yijing, and the Religious Conversion of the Chinese. Mathematics Magazine [Online], 76(4), pp.276–291.

Swift, J., 1892. Gulliver’s Travels into Several Remote Nations of the World [Online]. Ed. by D. Price. London: George Bell amd Sons. Available at: [visited on 14 January 2023].

Tegmark, M., 2008. The Mathematical Universe. Foundations of Physics [Online], 38(2), pp.101–150.

Tegmark, M., 2014. Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. 1st ed. New York: Alfred A. Knopf.

Trzęsicki, K., 2006a. From the Idea of Decidability to the Number ’Omega’. Studies in Logic, Grammar and Rhetoric [Online], 9(22), pp.73–142. Available at: <> [visited on 14 January 2023].

Trzęsicki, K., 2006b. Leibniza idea systemu binarnego. In: J. Kopania and H. Święczkowska, eds. Filozofia i myśl społeczna XVII wieku. Białystok: Wydawnictwo Uniwersytetu, pp.183–203.

Trzęsicki, K., 2006c. Leibnizjańskie inspiracje informatyki. Filozofia Nauki [Online], 14(3 (55)), pp.21–48. Available at: <> [visited on 14 January 2023].

Trzęsicki, K., 2016. Can AI Be Intelligent? Studies in Logic, Grammar and Rhetoric [Online], 48(1), pp.103–131.

Trzęsicki, K., 2020a. Idea of Artificial Intelligence. Studia Humana [Online], 9(3/4), pp.37–65.

Trzęsicki, K., 2020b. Idea sztucznej inteligencji. Filozofia i Nauka. Studia Filozoficzne i Interdyscyplinarne [Online], 8(1), pp.69–96.

Turing, A.M., 1937. On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society [Online], 42 (series 2)(1), pp.230–265.

Turing, A.M., 1950. Computing Machinery and Intelligence. Mind [Online], 59(236), pp.433–460.

Turing, A.M., 1952. The Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences [Online], 237(641), pp.37–72. Available at: <> [visited on 4 November 2015].

Westfall, R.S., 1983. Never at Rest: A Biography of Isaac Newton. Cambridge: Cambridge University Press.

Wheeler, J.A., 1989. Information, Physics, Quantum: The Search for Links. Proceedings of the 3rd International Symposium Foundations of Quantum Mechanics in the Light of New Technology: Central Research Laboratory, Hitachi, Ltd., Kokubunji, Tokyo, Japan, August 28-31, 1989. Tokyo: Physical Society of Japan, pp.354–368.

Whitehead, A.N., 1911. An Introduction to Mathematics [Online]. London; New York: Williams & Northgate; H. Holt. Available at: <> [visited on 16 January 2023].

Wolfram, S., 2002. A New Kind of Science [Online]. Champaign, IL: Wolfram Media. Available at: <> [visited on 16 January 2023].

Wolfson, H.A., 1962. The Problem of the Souls of the Spheres from the Byzantine Commentaries on Aristotle Through the Arabs and St. Thomas to Kepler. Dumbarton Oaks Papers [Online], 16, pp.65–93.

Wouk, H., 2010. The Language God Talks: On Science and Religion. 1st ed. New York, NY: Little, Brown and Co.

Zenil, H., 2012. Afterword to Konrad Zuse’s Calculating Space. In: A. German and H. Zenil, eds. A Computable Universe: Understanding Computation & Exploring Nature As Computation (with a Foreword by Sir Roger Penrose) [Online]. Singapore; Hackensack, NJ: World Scientific, pp.787–794. Available at: <> [visited on 13 January 2023].

Zuse, K., 1967. Rechnender Raum. Elektronische Datenverarbeitung [Online], 8, pp.336–344. Available at: <> [visited on 16 January 2023].

Zuse, K., 1969. Rechnender Raum. Vol. 1, Schriften zur Datenverarbeitung. Braunschweig: Vieweg.

Zuse, K., 2010. Der Computer – Mein Lebenswerk [Online]. 5., unveränd. Aufl. Berlin; Heidelberg: Springer.

Zuse, K., 2012a. Calculating Space (Rechnender Raum). A Computable Universe [Online]. WORLD SCIENTIFIC, pp.729–786.

Zuse, K., 2012b. Calculating space (Rechnender Raum) [Online]. Ed. by A. German and H. Zenil. Available at: <> [visited on 16 January 2023].