Logic from Scratch: A Philosophical Approach to C. S. Peirce’s Diagrammatic First-Order Logic

Rocco Gangle (Endicott College)

Meeting ID 818 4891 1790 Passcode 906010

https://jmu-edu.zoom.us/j/81848911790?pwd=R0xweXRNN201WTJCT3lVNkswdVdtUT09  

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.