A soundness proof of C.S. Peirce's Alpha Existential Graphs using truth trees, with an appendix on the "Alpha" Entitative Graphs

Abstract

This work represents a marriage of Peirce’s syntactic rules for performing inferences in the Alpha Existential Graphs with the recent technique of truth trees. The vitality of this marriage is brought to light by demonstrating the soundness of the Alpha system in a much more diagrammatic way than has ever before been accomplished. While the use of truth trees to work with properties such as soundness and completeness is not new in this work, the employment of a graphical form of the trees is novel, especially in the context of Peirce’s graphical logic. Finally, I suggest how the same method would apply to Peirce’s earlier system, the Entitative Graphs.