Denial, Disjunction and Other Signs of Logic: A Contribution to the Philosophy of Notation

The paper examines and critically discusses the transition fromPeirce’s earlier Entitative Graphs (EntGs) to the later ExistentialGraphs (EGs). We explore the dual notions of denial and disjunctionand examine their implications for the philosophy of logical nota-tion. We investigate the sheet of assertion’s role in both systems, theduality between conjunction and disjunction, and the implicationsof assertion’s distribution over conjunction versus disjunction. Ourstudy reveals Peirce’s preference for EGs due to their naturalness andiconicity, despite the expressive equivalence of both systems. Thepaper concludes with philosophical reflections on the normativity oflogic as illuminated by Peirce’s early yet impactful contribution to thetheory of graphical methods of logic and analysis.