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130 study. Though this opinion is a hasty one, it is quite natural, and logicians have only themselves to blame, if they do not provide for contingencies that are certain to bring their general rules into disrepute.

The chief difficulty to which I allude is found in the theory of Opposition. There are other instances of similar importance, but they cannot receive any attention in the present article. I can only consider those which concern a very large portion of existing discussions and controversy, and which at the same time show such discrepancies between formal principles and material practice as to very seriously impugn the practical value of logic, unless we are at the same time informed of principles operating independently of the formal law.

The theory of Opposition has a certain speculative value, and is also assumed to have an equally practical value. Throwing aside the former characteristic for a moment, the second feature is supposed to describe the law of consistency and inconsistency between propositions, in order that we have a practical criterion for deciding the truth or falsity of certain statements in a controversy. Thus, if a man asserts proposition A (universal affirmative) we may test its validity, in a measure, by comparing it with E and O (respectively the universal and the particular negatives). The controversialist is said to refute A easiest by the proof of O, and that he exposes himself to a like refutation by I (particular affirmative) if he attempts to base his refutation upon the assertion or proof of E. But now it is to be shown that, while this may be true for the formal laws of Opposition, practice is so different from this that we must either set up a new law, or modify the assumptions made about the nature and signs of particular propositions as well as universals.

The Square of Opposition is based upon certain assumed peculiarities of the quality and quantity of propositions. Thus, A and O, and E and I, are said to be contradictories, which is to say that they are mutually inconsistent, while A and E are only contraries, which is to say that though both cannot be true, they may both be false at the same time. But in actual