El octágono medieval de Oposición para oraciones con predicados cuantificados

Abstract

The traditional Square of Opposition consists of four sentence types. Two are universal and two particular; two are affirmative and two negative. Examples, where “S” and “P” designate the subject and the predicate, are: “every S is P”, “no S is P”, “some S is P” and “some S is not P”. Taking the usual sentences of the square of opposition, quantifying over their predicates exhibits non-standard sentence forms. These sentences may be combined into non-standard Squares of Opposition (an Octagon in this case), and they reveal a new relationship not found in the usual Square. Medieval logicians termed “disparatae” sentences like “every S is some P” and “some S is every P”, which are neither subaltern nor contrary, neither contradictory nor subcontrary. Walter Redmond has designed a special language L to express the logical form of these sentences in a precise way. I will use this language to show how Squares of Opposition, standard and non-standard, form a complex network of relations which bring to light the subtleties contained in this traditional doctrine.