Abstract

The first part of the paper aims at showing that the notion of an Aristotelian square may be seen as a special case of a variety of different more general notions: the one of a subAristotelian square, the one of a semiAristotelian square, the one of an Aristotelian cube, which is a construction made up of six semiAristotelian squares, two of which are Aristotelian. Furthermore, if the standard Aristotelian square is seen as a special ordered 4-tuple of formulas, there are 4-tuples describing rotations of the original square which are non-standard Aristotelian squares. The second part of the paper focuses on the notion of a composition of squares. After a discussion of possible alternative definitions, a privileged notion of composition of squares is identified, thus opening the road to introducing and discussing the wider notion of composition of cubes.