§ 472. To be suddenly thrown back upon the strictly particular view of I and O in the special case of opposition, after having been accustomed to regard them as indefinite propositions, is a manifest inconvenience. But the received doctrine of opposition does not even adhere consistently to this view. For if I and O be taken as strictly particular propositions, which exclude the possibility of the universal of the same quality being true along with them, we ought not merely to say that I and O may both be true, but that if one be true the other must also be true. For I being true, A is false, and therefore O is true; and we may argue similarly from the truth of O to the truth of I, through the falsity of E. Or--to put the Same thing in a less abstract form--since the strictly particular proposition means 'some, but not all,' it follows that the truth of one sub-contrary necessarily carries with it the truth of the other, If we lay down that some islands only are inhabited, it evidently follows, or rather is stated simultaneously, that there are some islands also which are not inhabited. For the strictly particular form of proposition 'Some A only is B' is of the nature of an exclusive proposition, and is really equivalent to two propositions, one affirmative and one negative.
§ 473. It is evident from the above considerations that the doctrine of opposition requires to be amended in one or other of two ways. Either we must face the consequences which follow from regarding I and O as indefinite, and lay down that sub-contraries may both be false, accepting the awkward corollary of the collapse of the doctrine of contradiction; or we must be consistent with ourselves in regarding I and O, for the particular purposes of opposition, as being strictly particular, and lay down that it is always possible to argue from the truth of one sub-contrary to the truth of the other. The latter is undoubtedly the better course, as the admission of I and O as indefinite in this connection confuses the theory of opposition altogether.
§ 474. Of the several forms of opposition contradictory opposition is logically the strongest. For this three reasons may be given--
(1) Contradictory opposites differ both in quantity and in quality, whereas others differ only in one or the other.