The Cube of Opposition: the Interrelations of Infinites



Some contemporary logicians have introduced a new simple method of logical consequences and reduced all immediate arguments to Conversion and Obversion. By dint of positive and infinite terms, one of the logicians, Reza Akbari, increased the four traditional quantified propositions to 32 ones: the 4 well-known positives, 4 subject-infinites, 4 predicate-infinites, 4 two-sided-infinites, and the same 16 with ‘A’ and ‘B’ in which converted. Akbari, also, stated among some of the 32 propositions the interrelations: the opposition square, conversion, conversion by contradiction, obversion, inversion, and two new relations: “contraposition of the subject” and the “unknown”. This theory extending the classical 4-quntified-theory can be named “32-quntified-theory”. In this paper, I show that the 32 propositions are equivalent four-by-four, hence, we can reduce the 32 propositions to 8 ones and their relations to the six: equivalence, implication, inconsistency, inclusive ‘or’, exclusive ‘or’ and none (which is the same as Akbari’s “unknown”. By this, I decrease the perplexities of the theory and express so easily and elegantly the relations between the eight in a cube similar to the “Square of Opposition,” which I call the “Cube of Opposition.”