  But the rest is there by implication. For example, there is enough to show that I and O are subcontraries: they cannot both be false. For suppose that I is false. Then its contradictory, E, is true. So E’s contrary, A, is false. So A’s contradictory, O, is true. This refutes the possibility that I and O are both false, and thus fills in the bottom relation of subcontraries. Subalternation also follows. Suppose that the A form is true. Then its contrary E form must be false. But then the E form’s contradictory, I, must be true. Thus if the A form is true, so must be the I form. A parallel argument establishes subalternation from E to O as well. The result is SQUARE.