Abstract
In early modernity, one can find many spatial logic diagrams whose geometric forms share a family resemblance with religious art and symbols. The family resemblance these diagrams bear in form is often based on a vesica piscis or on a cross: Both logic diagrams and spiritual symbols focus on the intersection or conjunction of two or more entities, e.g. subject and predicate, on the one hand, or god and man, on the other. This paper deals with the development and function of logic diagrams, their analogy to religious art and symbols, and their modern application in artificial intelligence.
Similar content being viewed by others
References
Abraham, T.: From theory to data: representing neurons in the 1940s. Biol. Philos. 18, 415–426 (2003)
Alsina, C., Nelsen, R.B.: Venn diagrams. In: Icons of Mathematics: An Exploration of Twenty Key Images, pp. 12–20. Mathematical Association of America, Washington, DC (2011)
Anellis, I.H.: Peirce’s truth-functional analysis and the origin of the truth table. Hist. Philos. Log. 33, 87–97 (2012)
Boole, G.: An Investigation of the Laws of Thought: on Which are Founded the Mathematical Theories of Logic and Probabilities. Walton and Maberly, London (1854)
Calter, P.: Sun disk, moon disk. In: Gorini, C.A. (ed.) Geometry at Work: Papers in Applied Geometry. Mathematical Association of America, Washington, DC (2000)
Clark, G.: New light on Peirce’s iconic notation for the sixteen binary connectives. In: Houser, N., Roberts, D.D., Evra, J.V. (eds.) Studies in the Logic of Charles Sanders Peirce, pp. 304–333. Indiana University Press, Bloomington (1997)
Clarkson, E.: Essay on the symbolic evidences of the temple church. In: Billings, R.W. (ed.) Architectural Illustrations and Account of the Temple Church. Thomas and William Boone, London (1838)
Demey, L., Smessaert, H.: Combinatorial bitstring semantics for arbitrary logical fragments. J. Philos. Log. 47, 325–363 (2018)
Dumit, J.: Plastic diagrams: circuits in the brain and how they got there. In: Bates, D.W., Bassiri, N. (eds.) Plasticity and Pathology: On the Formation of the Neural Subject, pp. 219–268. Fordham University Press, New York (2016)
Edwards, A.W.F.: Cogwheels of the Mind: the Story of Venn Diagrams. John Hopkins University Press, Baltimore, London (2004)
Euler, L.: Letters of Euler on different subjects in physics and philosophy. In: Addressed to a German Princess. Vol. I, transl. and ed. by H. Hunter, 2nd ed. Murray and Highley, London (1802)
Foerster, H.V.: Computation in neuronal nets. In: Understanding Understanding: Essays on Cybernetics and Cognition, pp. 21–100. Springer, New York (2003)
French, K.L.: Gateway to the Heavens: How Geometric Shapes, Patterns and Symbols form our Reality. Watkins, London, New York (2014)
Gardner, M.: Logic Machines and Diagrams, 2nd edn. Harvester, Brighton (1983)
Grattan-Guiness, I.: Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics. Johns Hopkins University Press, Baltimore (2009)
Greaves, M.: The Philosophical Status of Diagrams. CSLI Publications, Stanford (2002)
Großer, S.: Gründliche Anweisung zur Logica. Johann Wilisch, Budißin, Görlitz (1697)
Krause, K.C.F.: Die Lehre vom Erkennen und von der Erkenntniss, als erste Einleitung in die Wissenschaft: Vorlesungen für Gebildete aus allen Ständen, ed by H.K.v. Leonhardi, Dietrich’sche Buchhandlung, Göttingen (1836)
Kreiser, L.: Gottlob Frege: Leben—Werk—, Chap. 3. Meiner, Hamburg (2001)
Lemanski, J.: Periods in the use of Euler-type diagrams. Acta Baltica Historiae et Philosophiae Scientiarum 5, 50–69 (2017)
Lima, M.: The Book of Circles: Visualizing Spheres of Knowledge. Princeton Architectural Press, New York (2017)
Macukow, B.: Neural networks—state of art, brief history, basic models and architecture. In: Saeed, K., Homenda, W. (eds.) Computer Information Systems and Industrial Management. CISIM 2016. Lecture Notes in Computer Science, vol. 9842, pp. 3–14. Springer, S.l. (2016)
Marquand, A.: XXXIII: On logical diagrams for n terms. Lond. Edinb. Dublin Philos. Mag. J. Sci. 12, 266–270 (1881)
McCluskey Jr., E.J.: Minimization of Boolean functions. Bell Syst. Tech. J. 35, 1417–1444 (1956)
McCulloch, W.S.: Machines that Think and Want. In: Halstead, W.C. (ed.) Brain and Behavior: A Symposium, Comparative Psychology Monographs 20:1, pp. 39–50. University of California Press, Berkeley, CA (1950)
McCulloch, W.S.: Three of Von Neumann’s biological questions. In: RLE Quarterly Progress Report, pp. 129–138. Massachusetts Institute of Technology, Cambridge (1957)
McCulloch, W.S.: Stable, reliable, and flexible nets of unreliable formal neurons. In: RLE Quarterly Progress Report, pp. 118–129. Massachusetts Institute of Technology, Cambridge (1958)
McCulloch, W.S.: Agathe tyche of nervous nets—the lucky reckoners. Natl. Phys. Lab. Symp. 10, 613–625 (1959)
McCulloch, W.S.: The reliability of biological systems. In: Yovits, M.C., Cameron, S. (eds.) Self-Organizing Systems: Proceedings of an Interdisciplinary Conference 5 and 6 May, 1959, pp. 264–281. Pergamon Press, Oxford (1960)
McCulloch, W.S.: What is a number, that a man may know it, and a man, that he may know a number? What is a number. Gen. Semant. Bull. 26(27), 7–18 (1960)
McCulloch, W.S., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133 (1943)
Meegan, W.J.: God’s Ambiance: is Revealed in the Matrix of Wisdom. Outskirts Press, Denver (2016)
Mira, J.M.: Symbols versus connections: 50 years of artificial intelligence. Neurocomputing 71, 671–680 (2008)
Moktefi, A.: Schopenhauer’s Eulerian diagrams. In: Lemanski, J. (ed.) Language. Logic and Mathematics in Schopenhauer. Birkhäuser, Basel (2019)
Moktefi, A., Shin, S.-J.: A history of logic diagrams. In: Gabbay, D.M., Woods, J. (eds.) Logic. A History of its Central Concepts, pp. 611–682. North Holland, Oxford (2012)
More, T.: On the construction of Venn diagrams. J. Symb. Log. 24, 303–304 (1959)
Nakatsu, R.T.: Using Venn diagrams to perform logic reasoning: an algorithm for automating the syllogistic reasoning of categorical statements. Int. J. Intell. Syst. 29, 84–103 (2014)
Oldford, R.W., Cherry, W.H.: Picturing probability: the poverty of Venn diagrams, the richness of eikosograms. Retrieved from University of Waterloo, http://www.math.uwaterloo.ca/~rwoldfor/ (July 2017)
Peirce, C.S.: A proposed logical notation (MS 530). In: Pietarinen, A.-V.J. (eds) Charles S. Peirce: Logic of the Future Peirce’s Writings on Existential Graphs. De Gruyter (forthcoming)
Peirce, C.S.: Collected Papers of Charles Sanders Peirce, vols. 1–6, ed. by C. Hartshorne, P. Weiss, vols. 7–8, ed. by A.W. Burks. Harvard University Press, Cambridge, MA (1931–1935, 1958)
Perkel, D.H.: Logical neurons: the enigmatic legacy of Warren McCulloch. Trends Neurosci. 11, 9–12 (1988)
Quine, W.V.O.: A way to simplify truth functions. Am. Math. Mon. 62, 627–631 (1955)
Randolph, J.F.: Cross-examining propositional calculus and set operations. Am. Math. Mon. 72, 117–127 (1965)
Roes, A.: An Iranian standard used as a christian symbol. J. Hell. Stud. 57, 248–251 (1937)
Schang, F.: Abstract logic of oppositions. Log. Log. Philos. 21, 415–438 (2012)
Siegel, C.C.F.: Kreuz im Cultus der Christen. In: Handbuch der christlich-kirchlichen Alterthümer in alphabetischer Ordnung, vol. 3, pp. 113–143. Schumann, Leipzig (1837)
Schopenhauer, A.: Philosophische Vorlesungen. In: Deussen, P., Mockrauer, F. (eds.) Sämmtliche Werke, vol. IX. Piper, München (1913)
Swanson, R.: Information Sciences 1965 (AFOSR 66-0130), p. 92 (no. 6–9). Air Force Office of Scientific Research, Washington, DC (1966)
Venn, J.: Symbolic Logic, 2nd edn. Macmillan, London (1881)
Wittgenstein, L.: Tractatus Logico-Philosophicus: With an Introduction by Bertrand Russell. Harcourt, Brace and Company, New York (1922)
Zellweger, S.: Sign-creation and man-sign engineering. Semiotica 38, 17–54 (1982)
Zellweger, S.: Untapped potential in Peirce’s iconic notation for the sixteen binary connectives. In: Houser, N., Roberts, D.D., Van Evra, J. (eds.) Studies in the Logic of Charles Sanders Peirce, pp. 334–386. Indiana University Press, Bloomington (1997)
Acknowledgements
I would like to express my gratitude to the audience of the 2nd World Congress on Logic and Religion in Warsaw 2017, to the journal’s anonymous reviewers for comments that contributed to the improvement of this paper. I would also like to thank Ahti-Veikko Pietarinen, Marcin Trepczynski, Stanislaw Krajewski and Theodor Berwe, who supported me in writing this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Lemanski, J. Logic Diagrams, Sacred Geometry and Neural Networks. Log. Univers. 13, 495–513 (2019). https://doi.org/10.1007/s11787-019-00239-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11787-019-00239-9