We see that with A and I, only part of P is in some of the cases shaded; whereas with E and O, the whole of P is in every case shaded; and it is thus made clear that negative propositions distribute, while affirmative propositions do not distribute, their predicates.
(2) To illustrate the opposition of propositions. Comparing two contradictory propositions, e.g., A and O, we see that they have no case in common, but that between them they exhaust all possible cases. Hence the truth, that two contradictory propositions cannot be true together but that one of them must be true, is brought home to us under a new aspect. Again, comparing two subaltern propositions, e.g., A and I, we notice that the former gives us all the information given by the latter and something more, since it still further limits the possibilities. The other relations involved in the doctrine of opposition may be illustrated similarly.
(3) To illustrate the conversion of propositions. Thus it is made clear by the diagrams how it is that A admits only of conversion per accidens. All S is P limits us to one or other of the following,—
What then do we know of P? In the first case we have All P is S, in the second Some P is S ; and since we are ignorant as to which of the two cases holds good, we can only state what is common to them both, namely, Some P is S.
Again, it is made clear how it is that O is inconvertible. Some S is not P limits us to one or other of the following,—