The Square of Opposition in Aristotle’s Logic and Stoic Logic

Opposition and conflict among united propositions in predicate and subject and the relation between them is one of the judgments of the propositions and investigation of the relations among them (from the viewpoint of concomitance or contradiction), based on which the ‘square of opposition’ is formed. This issue is one of the most important discussions in logic of reasoning and has been the focus of attention from the onset of Aristotlian and stoic logic. Aristotle has limited the opposition of propositions to opposition in veracity, introducing it as the opposition in affirmation and negation. He introduces the opposition of predicates, dividing it into contradiction and contrast. Muslim logicians have regarded the opposition of propositions in contrast to interference of propositions, and those two as types of difference in propositions. They regard opposition as inclusive of opposition in truth and opposition in falsehood. Accordingly, they have added entrance under contrast to instances of opposition if propositions. In addition to affirming the contradiction with its instances as affirmation and negation, stoic philosophers have dealt with opposition between modes of truth such as opposition between necessity and non-necessity and opposition of possibility and refusal. The difference in meaning and instance of opposition in speeches of logicians, which leads to difference in formation of square of opposition, clarifies the necessity to investigate different meanings and instances of opposition and the way the square of opposition is formed for each.