Opposition, in the ordinary sense, is the opposition of incompatible propositions, and it was with this only that Aristotle concerned himself. But from an early period in the history of Logic, the word was extended to cover mere differences in Quantity and Quality among the four forms A E I O, which differences have been named and exhibited symmetrically in a diagram known as: The Square of Opposition. A______Contraries______E |\ /| | \ s | | C e | | o i | | n r | | t o | S r t S u a c u b \ i b a \ d a l \/ l t /\ t e / d e r / i r n a c n s r t s | t o | | n r | | o i | | C e | | / s | |/ \| I____Sub-contraries____O The four forms being placed at the four corners of the Square, and the sides and diagonals representing relations between them thus separated, a very pretty and symmetrical doctrine is the result. _Contradictories_, A and O, E and I, differ both in Quantity and in Quality. _Contraries_, A and E, differ in Quality but not in Quantity, and are both Universal. _Sub-contraries_, I and O, differ in Quality but not in Quantity, and are both Particular. _Subalterns_, A and I, E and O, differ in Quantity but not in Quality. Again, in respect of concurrent truth and falsehood there is a certain symmetry. Contradictories cannot both be true, nor can they both be false. Contraries may both be false, but cannot both be true. Sub-contraries may both be true, but cannot both be false. Subalterns may both be false and both true. If the Universal is true, its subalternate Particular is true: but the truth of the Particular does not similarly imply the truth of its Subalternating Universal. This last is another way of saying that the truth of the Contrary involves the truth of the Contradictory, but the truth of the Contradictory does not imply the truth of the Contrary. There, however, the symmetry ends. The sides and the diagonals of the Square do not symmetrically represent degrees of incompatibility, or opposition in the ordinary sense.