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Logical Principles of a Topological Explanation

Peirce’s iconic logic

Ľudmila Lacková and Lukáš Zámečník
From the journal Chinese Semiotic Studies


We aim to demonstrate the applicability of Peirce’s iconic logic in the context of current topological explanations in the philosophy of science. We hold that the logical system of Existential Graphs is similar to contemporary topological approaches, thereby recognizing Peirce’s iconic logic (Beta Graphs) as a valid method of scientific representation. We base our thesis on the nexus between iconic logic and the so-called NonReduction Theorem. We illustrate our assumptions with examples derived from biology (protein folding).

  1. Funding: Lukáš Zámečník was supported in his work on this paper by the Czech Science Foundation (Grant No. 19-04236S “Simplifying Assumptions and Non-causal Explanation”).


We would like to thank Claudio Rodríguez Higuera, Arran Gare, and Colin Garrett for their important comments and help with this paper.


Alberch, Pere. 1991. From genes to phenotype: Dynamical systems and evolvability. Genetica 84. 5– 11. doi:10.1007/BF00123979.10.1007/BF00123979Search in Google Scholar

Ambrosio, Chiara & ChrisCampbell. 2017. The chemistry of relations: Peirce, perspicuous representations, and experiments with diagrams. In Kathleen A. Hull & Richard Kenneth Atkins (eds.), Peirce on perception and Reasoning. From icons to logic, 86–106. New York: Routledge.Search in Google Scholar

Backofen, Rolf. 2001. Bioinformatics and constraints. Constraints 6(2). 141–156. Search in Google Scholar

Beil, Ralph Gregory & Kenneth Ketner. 2006. A triadic theory of elementary particle interactions and quantum computation. Lubbock: Institute for Studies in Pragmaticism.Search in Google Scholar

Brunning, Jacqueline. 1997. Genuine triads and teridentitiy. In Nathan Houser, Don D. Roberts & James van Evra (eds.), Studies in the logic of Charles Sanders Peirce, 252–263. Bloomington, IN: Indiana University Press.Search in Google Scholar

Burch, Robert. 1992. Valental aspects of Peircean algebraic logic. Computers and Mathematics with Applications 23(6–9). 665–677. Search in Google Scholar

Burch, Robert. 1997. Peirce’s reduction thesis. In Nathan Houser, Don D. Roberts & James van Evra (eds.), Studies in the logic of Charles Sanders Peirce, 234–251. Bloomington, IN: Indiana University Press.Search in Google Scholar

Caterina, Gianlucca & Rocco Gangle. 2013. Iconicity and abduction: A categorical approach to creative hypothesis-formation in Peirce’s existential graphs. Logic Journal of the IGPL 21(6). 1028–1043.Search in Google Scholar

Dupré, John. 2010. How to be naturalistic without being simplistic in the study of human nature. In Mario de Caro & David Macarthur (eds.), Naturalism and normativity, 289–303. New York: Columbia University Press.Search in Google Scholar

De Caro, Mario & David Macarthur (eds.). 2010. Naturalism and normativity. New York: Columbia University Press.Search in Google Scholar

Eco, Umberto. 1990. I limiti dell’interpretazione. Milan: Bompiani.Search in Google Scholar

Eco, Umberto. 1997. Kant e l’ornitorinco, Milan: Bompiani.Search in Google Scholar

Eco, Umberto. 2007. Dall’albero al labirinto. Milano: Bombiani.Search in Google Scholar

Fraassen, van Bas. 2002, The empirical stance. New Haven: Yale University Press.Search in Google Scholar

Gross, Jonathan L. & Thomas W. Tucker. 1987. Topological graph theory. New York: Wiley-Interscience.Search in Google Scholar

Havenel, Jérôme. 2010. Peirce’s topological concepts. In Matthew. E. Moore (ed.), New essays on Peirce’s mathematical philosophy. 283–322. Chicago & La Salle: Open Court.Search in Google Scholar

Henderson, Brian & Martin Andrew. 2011. Bacterial virulence in the moonlight: Multitasking bacterial moonlighting proteins are virulence determinants in infectious disease. Infection and Immunity 79(9). 3476–3491. doi:10.1128/IAI.00179-11.10.1128/IAI.00179-11Search in Google Scholar

Huneman, Philippe. 2010. Topological explanations and robustness in biological sciences. Synthese 177(2). 213–245.Search in Google Scholar

Huneman, Philippe. 2015. Diversifying the picture of explanations in biological sciences: Ways of combining topology with mechanisms. Synthese 195(1). 115–146.Search in Google Scholar

Hudry Jean-Louis. 2004. Peirce’s potential continuity and pure geometry. Transactions of the Charles S. Peirce Society 40(2). 229–243.Search in Google Scholar

Jeffery, Constance J. 2014. An introduction to protein moonlighting. Biochemical Society Transactions 42. 1679–1683. doi:10.1042/BST20140226.10.1042/BST20140226Search in Google Scholar

Legg, Catherine. 2012. The hardness of the iconic must: Can Peirce’s existential graphs assist modal epistemology? Philosophia Mathematica 20(1). 1–24.Search in Google Scholar

Kauffman, Louis H. 2001. The mathematics of Charles Sanders Peirce. Cybernetics and Human Knowing 8(1–2). 79–110.Search in Google Scholar

Ketner, Kenneth, Elize Bisanz, Scott R Cunningham, Clyde Hendrick, Levi Johnson, Thomas McLaughlin & Michael O’Boyle. 2011. Peirce’s NonReduction and Relational Completeness claims in the context of first-order predicate logic. Interdisciplinary Seminar on Peirce. KODIKAS/CODE: Ars Semeiotica 34(1–2). 3–14.Search in Google Scholar

Kostić, Daniel. 2018. Mechanistic and topological explanations: An introduction. Synthese 195(1). 1–10. doi: 10.1007/s11229-016-1257-z.10.1007/s11229-016-1257-zSearch in Google Scholar

Lindsley, Janet. 2005. DNA Topology: Supercoiling and Linking. In: Encyclopedia of Life Sciences. John Wiley and Sons: Hoboken, NJ, pp. 1–7. doi:10.1038/npg.els.0003904.10.1038/npg.els.0003904Search in Google Scholar

Peirce, Charles Sanders. 1987. The logic of relatives. The Monist 7(2). 161–217.Search in Google Scholar

Peirce, Charles Sanders. [CP]. 1960. Collected papers of Charles Sanders Peirce. Edited by Charles Hartshorne & Paul Weiss. Volumes 3–5. Cambridge, MA: Harvard University Press.Search in Google Scholar

Pietarinen, Ahti-Veikko. 2006. Signs of logic: Peircean themes on the philosophy of language, games, and communication. Dordrecht: Springer.Search in Google Scholar

Pietarinen, Ahti-Veikko. 2008. Iconic logic of existential graphs: A case study of commands. In Gem Stapleton, John Howse & John Lee (eds), Diagrammatic representation and inference. Diagrams. Proceedings of the 5th International Conference, Diagrams 2008, Herrsching, Germany, September (Lecture notes in computer science 5223). Berlin & Heidelberg: Springer.Search in Google Scholar

Pietarinen, Ahti-Veikko & Frederik Stjernfelt. 2015. Peirce and diagrams: Two contributors to an actual discussion review each other. Synthese 190(4). 1073–1088. Search in Google Scholar

Pigliucci, Massimo. 2010. Genotype–phenotype mapping and the end of the “Genes as Blueprint” metaphor. Philosophical Transactions of the Royal Society B 365. 557–566. doi:10.1098/rstb.2009.0241.10.1098/rstb.2009.0241Search in Google Scholar

Quine, Willard van Orman. 1954. Reduction to a dyadic predicate. The Journal of Symbolic Logic 19(3). 180–182.Search in Google Scholar

Reutlinger, Alexander. 2016. Is there a monist theory of causal and noncausal explanations? The counterfactual theory of scientific explanation. Philosophy of Science 83(5). 733–745.Search in Google Scholar

Shin, Sun-Joo. 2002. The iconic logic of Peirce’s graphs. Massachusetts: MIT Press.Search in Google Scholar

Stjernfelt, Frederik. 2007. Diagrammatology. An investigation on the borderlines of phenomenology, Ontology, and Semiotics. Dordrecht: Springer.Search in Google Scholar

Whitehead, Alfred North. 1929. Process and reality: An essay in cosmology. New York: Macmillan.Search in Google Scholar

Williamson, Timothy. 2014. What is naturalism? In Matthew C. Haug (ed.), Philosophical methodology. The armchair or the laboratory? 29–32. New York & London: Routledge.Search in Google Scholar

Zalamea, Fernando. 2017. Peirce’s inversions of the topological and the logical. Forgotten roads for our contemporary world. RIivista di storia della filosofia 2017(3). 415–434.Search in Google Scholar

Zeman, Joseph Jay. 1964. The graphical logic of C. S. Peirce. Ph.D. Dissertation, Department of Philosophy, Chicago: University of Chicago.Search in Google Scholar

Zeman, Joseph Jay. 1986. Peirce’s philosophy of logic. Transactions of the Charles S. Peirce Society 22(1): 1–22.Search in Google Scholar

Published Online: 2020-08-19
Published in Print: 2020-08-26

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