Peirce's Triadic Logic: Modality and Continuity

Abstract:In early 1909, Charles S. Peirce conducted a series of experiments with three-valued logic, anticipating the pioneering work of Jan Łukasiewicz and Emil Post by ten years. These experiments are entirely contained within six or seven pages of Peirce's Logic Notebook. Due to the work of Atwell Turquette, the formalisms contained in those pages are relatively well understood. What is less understood are Peirce's philosophical reasons for conducting those experiments. His explanation of the need for his "triadic" logic is very brief, taking up little more than a single short page in the Notebook. Here he gives us two clues about his motivations, one connected to modal notions and one to his views on continuity. There are two previous accounts of the philosophical motivations behind triadic logic, due to Max Fisch and Turquette, and to Robert Lane. In this paper, I re-evaluate those views and connect the two clues to Peirce's hypothetical cosmology. I argue that in conducting his three-valued experiments, Peirce was trying to create a logic to capture his notion of the evolving universe.