Opposition, obversion, and duality
pp. 107-124
in: Roberto Poli (ed), Consciousness, knowledge, and truth, Berlin, Springer, 1993Abstract
Squares of opposition have a long history: they were employed from the early middle ages onwards as a simple diagrammatic codification of the logical relationships among the four kinds of categorical propositions, but they apply to modal logics, deontic logics and many others. The purpose of this short paper is to demonstrate that squares of opposition are in fact a very general phenomenon, arising whenever we have a ternary division, that is, a division of some domain into three mutually exclusive and jointly exhaustive possibilities, instead of the two of a simple binary division. The logic of such opposition is however not confined to the relationships exhibited by squares of opposition, which in fact leave quite a few things in the dark. It transpires that a square in only a square of opposition if a further condition is fulfilled apart from codifying a ternary division, and we shall look into what this is.