There Is No Cube of Opposition

Abstract

The theory of opposition has been famously crystallized in a square. One of the most common generalizations of the square is a cube of opposition. We show here that there is no cube such that each of its faces is a square of opposition. We discuss the question of generalization and present two other generalizations of the theory of opposition to the third dimension: one based on Blanché’s hexagon of opposition, the other on the square of contrariety.