Modernizing Peirce’s Existential Graphs

Abstract: Peirce’s Existential Graphs have found a new home in contemporary categorical logic. Recent work has provided a categorical foundation for Peirce’s graphical syntax and inference rules and at the same time affirms a number of Peirce’s insights and claims about the graphs. These insights include the important role teridentity plays in generalizing from binary relations to n-ary relations, as well as Peirce’s intuitions about ‘lines of identity.’ This essay describes these recent developments and begins to situate them with respect to Peirce’s philosophical writings on the graphs. Key contributions include a renewed emphasis on the scroll or ‘double-cut’ and a return to Peirce’s early algebraic work in ‘Note B.’ The result is a dramatic new perspective on the graphs.