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THE LOGIC AND POSSIBILITIES OF AN ICONIC ANALYSIS OF REASONING // ΠΡΑΞΗMΑ. Journal of Visual Semiotics. 2021. Issue 1 (27). P. 7-24

The article contributes to the debates on logical diagrams and reasoning studies. Diagrams in logic are multidimensional, multimodal, and language free (reasoning does not need a certain language to be introduced). They emphasize structural peculiarities and, consequently, tell us about reasoning in a way that causes difficulties for the algebraic approach. The article lists historical landmarks in developing such schemes (from Juan Luis Vives to Charles S. Peirce, and other contemporary investigations) and pays attention to the essential aspect of diagrammatic constructions, namely, their iconic nature. For a long time, diagrams had a supportive function; they were used as a tool for “dull-witted students”, but later they became an object of research. Today both diagrammatic approaches are developed and the essence of diagrams is studied. From a semiotic point of view, diagrams are icons. It means they are signs that resemble their objects. In contrast to symbols, icons represent information; they make it observable. Briefly, if symbols connote, icons denote. However, this detailed definition has to be substantially clarified. That is why issues of the second and third sections introduce the variety of iconic signs and characteristics of an iconic analysis, respectively. Different diagrams have different specific iconic features: Leonhard Euler’s schemes possess meaning-carrying relationships, John Venn’s circles (or cells) demonstrate the elimination of “unnecessary information”, while Peirce’s approach introduces the procedure of transforming premises into conclusions. Strictly speaking, if the conclusion is observational in Euler’s diagrams, Peirce’s constructions shift this observational advantage to the process (transformation with the line of identity is observational). First of all, these differences can be explained with various types of icons (image, diagram, and metaphor), but also, which is even more important, with levels of iconicity (optimal and operational). In addition, contemporary scholars propose to distinguish two types of logical languages (“type-referential” and “occurrence-referential”). If we admit that different diagrams belong to different kinds of languages, we get another clarification of diagrammatic variety. The icon and iconicity specification provides possibilities for applying diagrams in investigations on the nature of reasoning in the near future. Indeed, these logical schemes can study reasoning from various perspectives and answer such questions as “How does reasoning flow?”, “What is the logical essence of reasoning validity?”, “How does reasoning provide new knowledge?”, etc.

Keywords: diagrams in logic, Euler, Venn, Peirce, icon, iconic analysis, reasoning

Mental models and existential graphs: How to define a rule // ΠΡΑΞΗMΑ. Journal of Visual Semiotics. 2024. Issue 2 (40). P. 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