Game of Logic

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes are sweet," and is an instructive introduction to the concepts of logic.

The game takes place in a world divided into four quadrants. In the northwest quadrant, the cakes are fresh and sweet, in the northeast, they are fresh and not-sweet, in the southwest, they are not-fresh and sweet, and in the southeast, they are not-fresh and not-sweet. The game is played with four red coins and five gray coins. A red coin is used to indicate the presence of some (one or more) cakes in a sector, while a gray coin indicates that the sector is empty.

A red coin in the northwest sector is a representation of the proposition "Some fresh cakes are sweet." By using more coins it is possible to represent more complex propositions. For example, one red coin in the northwest sector together with one in the northeast is a representation of the double proposition "Some fresh cakes are sweet and some not-sweet."

The world of cakes is then divided in the two subclasses of the eatable and not-eatable cakes, allowing the representation of even more complex propositions. It is also possible to represent syllogisms, in which two propositions (the premises) are used to deduce a third (the conclusion).

In the second half Carroll's book, an 8-cell diagram is introduced (a flattened  cube) for problems involving three propositions at once.

REFERENCES

Carroll, L. Symbolic Logic/Game of Logic: Mathematical Recreations of Lewis Carroll, 2 Books Bound As 1. New York: Dover, 1972.

Harry Ransom Center. http://www.hrc.utexas.edu/exhibitions/online/carroll/images/gameoflogicbig.html.