Logic from Scratch: A Philosophical Approach to Peirce’s Diagrammatic First-Order Logic (zoom talk)

Rocco Gangle

Center for Diagrammatic and Computational Philosophy, Endicott College.

C.S. Peirce stands alongside  Frege as one of the modern founders of first-order quantificational logic. The standard linear notation used by logicians today in fact derives from Peirce’s original work, not Frege’s. However, Peirce’s later diagrammatic logical notation, which he called Existential Graphs (EG) and which he himself considered his logical “chef-d’oeuvre”, has received scant attention from logicians until recently. This presentation introduces the “alpha” and “beta” levels of EG, corresponding to classical propositional and first-order logic with equality respectively. Peirce’s diagrammatic graphical notation represents logical operators with elementary topological structures in the plane, namely closed curves and continuous lines. Deductive rules are then specified in terms of writing, erasing and copying certain topologically connected components of the logical graphs in determinate ways. Remarkably, the same writing, erasing and copying rules carry over essentially from the “alpha” to the “beta” level, establishing a deeper continuity between propositional and first-order logic than is often considered. In addition to introducing the system of EG and showing how mathematical tools drawn from elementary category theory can aid in formalizing Peirce’s system rigorously, this presentation will emphasize links between Peirce’s diagrammatic logical notation and other aspects of his philosophical thought, particularly his semiotics and his metaphysics of continuity. What is the specifically philosophical importance of Peirce’s diagrammatic logic? It provides insight into the origins of logical thinking by showing how logical form emerges naturally from minimal constructions of continuity and discontinuity. It teaches us how to build up logic from scratch.

The Logic and Reasoning Institute promotes the interdisciplinary study of logic and reasoning at James Madison University. The LRI sponsors and encourages coursework and research, as well as promoting the teaching and application of logic across the university.

Mission:

The mission of the LRI is to develop and maintain an innovative, interdisciplinary undergraduate program in logic and reasoning, and to promote interdisciplinary research in logic, its application, and its pedagogy.

Goals:

The LRI will

• Foster collaboration among faculty and students in the study of logic and reasoning across disciplines
• Emphasize the key role of logic and formal reasoning in the humanities, sciences, and mathematics
• Develop and maintain a logic and reasoning minor
• Develop new and existing courses in logic and reasoning (including interdisciplinary and team-taught courses)
• Emphasize the philosophical foundations of logic and reasoning in and across the disciplines such as mathematics, the sciences, philosophy, and economics.

Dr. Thomas Adajian (Philosophy) is director of the LRI. 

For information on the Logic minor, click here.