What do diagrams teach? Reasoning and perception

Abstract

My paper concerns Peirce’s Existential Graph Theory (Graph theory) and its basic units that are diagrams or graphs. Graph theory is a valued logical system. It is algebra demonstrated in geometrical order. The theory is divided into several parts. They approximately correspond to propositional logic, first order logic, and modal logic. I will discuss the philosophical peculiarities of the theory rather than the technical ones. Philosophical ideas of this diagrammatic approach and its graphical syntax open new prospects for looking at the objective of logic. Graph philosophy will be scrutinized through the lens of information exchange and the growth of new knowledge. Special attention will be paid to the conceptual grounds to apply graph theory in practice. I will argue that diagram construction and perception can develop students’ logical skills. The existential graph theory realizes Peirce’s claim that logic is another name for semiotic. It deals with signs. Diagrams are signs (icons). These syntactical structures can be supplemented with interpretation (the theory accepts Tarski style semantics, game-theory semantics, etc.). A work with graphs is a graphical equivalent to scientific experiments. In the course of such experiments, we are not only able to discover necessary conclusions, which are implicitly or explicitly given in graphs, but also discover new knowledge and to observe the processes of information exchange. In short, graph theory allows us to perceive the nature of propositions, concepts and reasoning. The latter is treated as graph transformations (modifications regulated with the rules). DOI: 10.21146/2074-1472-2018-24-2-70-77