Topology of Modal Propositions Depicted by Peirce’s Gamma Graphs: Line, Square, Cube, and Four-Dimensional Polyhedron

Abstract

This paper presents the topological arrangements in four geometrical figures of modal propositions and their derivative relations by means of Peirce's gamma graphs and their rules of transformation. The idea of arraying the gamma graphs in a geometric and symmetrical order comes from Peirce himself who in a manuscript drew two cubes in which he presented the derivative relations of some (but no all) gamma graphs. Therefore, Peirce's insights of a topological order of gamma graphs are extended here backwards from the cube to the line and the square; and then forwards from the cube to the four-dimensional polyhedron.