In logic the square of opposition and the hexagon of opposition allow to visualise the relations among logical statements, but they present some debated issues. Lewis Carroll’s Game of Logic is a little book where he presented a visual method to solve syllogisms. Inspired by this book, and by his triadic approach (void, nonvoid, undefined), I present here a proposal to solve these issues through an extension of the above mentioned figures of opposition: the 3x3square of opposition, that unifies the ancient and modern squares of opposition, as well as the hexagon of opposition. This new triadic square (represented also as cuboctahedron) is closer to the use of quantifiers in everyday language, is more consistent and is a useful didactic tool to explain both ancient and modern logic quantifiers in an easier way.
Moreover, Carroll’s Game of Logic is not a real game, but it is a method. I succeeded to transform it into a real game for 2 players, where creating and solving syllogisms allows you to create constraints of movements for your opponent. I merged Carroll’s Game of Logic with the famous game Quarto! If you want to know more, contact me via email or social media.
