Existential Graphs as a Basis for Structural Reasoning

摘要

On the verge of the 20th century, Charles S. Peirce was convinced that his Existential Graphs were the best form of presenting every deductive argument. Between 1900 and 1909, Peirce chose the scroll as a basic sign in his Alpha system for Existential Graphs. According to a recent paper by Francesco Bellucci and Ahti-Veikko Pietarinen, the reason for this choice lies mainly in the non-ana-lyzable nature of the scroll: Only one sign expresses the basic notion of illation. In this paper, some analogies between this early version of the Alpha system and Structural Reasoning (in the sense of Kosta Dosen and Peter Schroder-Heister) are explored. From these analogies, it will be claimed that the system Alpha based on the scroll can be used as an accurate framework for (i) constructing basic structural deductions and (ii) accomplishing a diagrammatic interpretation of logical constants of First-Order Language. Moreover, EGs show cognitive advantages with respect to sequent systems. In this paper, the basic conception is outlined in an informal way, without making an exposition of the technical details.