Mental models and existential graphs: How to define a rule
DOI: 10.23951/2312-7899-2024-2-32-56
The article draws a parallel between Charles Sanders Peirce’s theory of existential graphs and Philip Johnson-Laird’s theory of mental models. The existential graphs (EG) theory is a diagrammatic logical theory. Its deductive capacities are approximately compared with propositional logic, first-order predicate logic, modal logic, and higher-order logics (this section was not completed). In draft notes, Peirce also speculates on the extent to which diagrams can work beyond deduction. The mental models (MM) theory is a psychological theory, which is developed within the framework of the psychology of reasoning. It states that people reason by constructing, combining, revising, and eliminating models that are compatible with given information. In its time, EG theory had a significant impact on the development of MM theory. This article evaluates this influence. In addition, it declares possible ways for their further interaction since modern studies of Peirce’s and MM theories provide new materials. Both theories rely on iconicity and the economy of research; they prefer singular representations to sets and try to model the way in which thoughts are connected. Graphs, like models, can overcome limitations of language linearity. At the same time, they logically represent information processing, i.e. they serve both logical and cognitive purposes. That is why EG theory can specify the process of obtaining conclusions in the theory of MM. I suggest that this can be done by incorporating Peirce’s guiding principle into EG theory and extending this idea to the theory of MM. This principle is a fundamental logical rule, which directs the course of reasoning. It helps to systematise information and draw conclusions, but it cannot be fully represented by signs; therefore, it cannot be reduced to the rules of logical theories. Such rules only describe its steps. I show, how the general logical rule iconically manifests itself within the theory of EG, how specific rules of logical theories reflect its core characteristics and how this rule is integrated into MM theory despite the fact that the latter denies specific rules of logical theories. With such integration, MM theory becomes more dynamic. Finally, the article claims that Peirce’s theory can also contribute to analyses of the dichotomy of embodied or amodal representation. It is useful for clarifying complex aspects of two reasoning systems (system one and system two) collaboration. Both of these aspects are crucial for MM theory. However, they deserve their own attention, since they expect an appeal to both the means of EG theory and diagrammatic elaborations, which Peirce attributed to its pre-theoretical level.
Keywords: existential graphs, mental models, guiding principle, rule of logic, pragmatism, psychology of reasoning
References:
Bar-Hillel, M. (1980). The Base-Rate Fallacy in Probability Judgments. Acta Psychologica, 44(3), 211–233.
Bobrova, A. S. (2017). Logical theory, demonstrated in geometrical order. Logiko-filosofskie shtudii. Ezhegodnik Assotsiatsii logikov Sankt- Peterburga, 15(1), 28–43. (In Russian).
Bobrova, A. S. (2018). What do diagrams teach? Reasoning and perception. Logicheskie issledovaniya, 24(2), 70–76. (In Russian). https://doi.org/10.21146/2074-1472-2018-24-2-70-77
Bobrova, A. S. (2020). “Logic of the Future”, as C.S. Peirce understood it (first volumes of Peirceana). Epistemologiya i filosofiya nauki, 57(3), 176–189. (In Russian). https://doi.org/10.5840/eps202057349
Braine, M. D. S., & O’Brien, D. P. (Eds.). (1998). Mental Logic. Lawrence Erlbaum Associates Publishers.
Craik, K. (1943). The Nature of Explanation. Cambridge University Press.
Hilpinen, R. (1982). On C. S. Peirce’s Theory of the Proposition: Peirce as a Precursor of Game-Theoretical Semantics. The Monist, 65(2), 182–188.
Johnson-Laird, P. N. (1970). The Perception and Memory of Sentences. In J. Lyons (Ed.), New Horizons in Linguistics (pp. 261–270). Penguin Books
Johnson-Laird, P. N. (1983). Mental Models. Towards a Cognitive Science of Language, Inference and Consciousness. Harvard University Press.
Johnson-Laird, P. N. (1994). Mental Models and Probabilistic Thinking, Cognition, 50, 189–209.
Johnson-Laird, P. N. (2002). Peirce, Logic Diagrams, and the Elementary Operations of Reasoning. Thinking and Reasoning, 8(1), 69–95.
Johnson-Laird, P. N. (2004). The History of Mental Models. In K. Manktelow, & M. C. Chung (Eds.), Psychology of Reasoning: Theoretical and Historical Perspectives (pp. 179–212). Psychology Press.
Johnson-Laird, P. N. (2006). How We Reason. Oxford University Press.
Johnson-Laird, P. N. (2010). Against Logical Form. Psychologica Belgica, 50, 193–221.
Johnson-Laird, P. N. (2013a). Inference with Mental Models. IN K. Holyoak, & R. Morrison (Eds.), The Oxford Handbook of Thinking and Reasoning (pp. 134–154). Oxford University Press.
Johnson-Laird, P. N. (2013b). Mental Models and Cognitive Change. Journal of Cognitive Psychology, 25(2), 131–138.
Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: A theory of meaning, pragmatics, and inference. Psychological Review, 109, 646–678.
Ma, M., & Pietarinen, A.-V. (2022). Peirce’s Dragon-Head Logic (R 501, 1901). Arch. Hist. Exact Sci., 76, 261–317.
Markman, A. B., & Dietrich, E. (2000). Extending the Classical View of Representation. Trends in Cognitive Science, 4, 470–475.
Peirce, C. S. (1931–1958). Collected Papers. Vols. 1–8. Cambridge University Press.
Peirce, C. S. (1967, 1971). Manuscripts in the Houghton Library of Harvard University. Identified by Richard Robin, Annotated Catalogue of the Papers of Charles S. Peirce, Amherst: University of Massachusetts Press, 1967, and The Peirce Papers: A supplementary catalogue. Transactions of the C. S. Peirce Society, 7, 37–57.
Peirce, C. S. (2000). Selected works. Logos. (In Russian).
Peirce, C. S. (2019– 2021). Logic of the Future. Peirce’s Writings on Existential Graphs. In 3 vols. Edited by A.-V. Pietarinen. Mouton De Gruyter.
Pietarinen, A.-V. (2006). Signs of Logic. Peircean Themes on the Philosophy of Language, Games, and Communication. Springer.
Pietarinen, A.-V. (2008). The Proof of Pragmatism: Comments on Christopher Hookway. Cognitio, 9(1), 85–92.
Pietarinen, A.-V. (2015). Two Papers on Existential Graphs by Charles Peirce. Synthese, 192, 881–922.
Pietarinen, A.-V. (2021). Pragmaticism as a Logical Study of Consciousness. Cognitive Semiotics, 14(1), 29–46.
Pietarinen, A.-V. (2023). Peirce’s Diagrammatic Reasoning and Abduction. In L. Magnani (Ed.), Handbook of Abductive Cognition (pp. 741–759). Springer.
Pietarinen, A.-V., & Bellucci, F. (2017). Two Dogmas of Diagrammatic Reasoning. A View from Existential Graphs. In K. A. Hull, & R. K. Atkins (Eds.). Peirce on Perception and Reasoning. From Icons to Logic (Routledge Studies in American Philosophy. Vol. 10) (pp. 174–196). Routledge.
Stenning, K., & Yule, P. (1997). Image and Language in Human Reasoning: a Syllogistic Illustration. Cognitive Psychology, 34, 109–159.
Stjernfelt, F. (2015). Iconicity of Logic – and the Roots of the “Iconicity” Concept. In M. K. Hiraga, W. J. Herlofsky, K. Shinohara, & K. Akita (Eds.), Iconicity of Language and Logic: East Meets West (pp. 35–56). Benjamins.
Van Heuveln, B. (2006). Using Existential Graphs to Integrate Mental Logic Theory and Mental Model Theory. Journal of Experimental and Theoretical Artificial Intelligence, 18(2), 149–155.
Wason, P. C. (1968). Reasoning about a Rule. Quarterly Journal of Experimental Psychology, 20, 273–281.
Zeman, J. (1964 ). The Graphical Logic of C. S. Peirce. Diss. University of Chicago.
( 723.51 kB ) 
( 684.09 kB )
Issue: 2, 2024
Series of issue: Issue 2
Rubric: ARTICLES
Pages: 32 — 56
Downloads: 262