Abstract: The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed. Graphic Abstract: The photo shows a prototype sculpture for the cube. [Figure not available: see fulltext.].
- Aristotelian square of opposition
- Buridan’s octagon
- Klein’s 4-group
- Predicate logic