44. Rules on the Truth or Falsity of Opposed Propositions. -- (1) Contradictories are never either both true or both false, seeing that one is the negation pure and simple of the other. The truth of the one, then, carries with it the falsity of the other; and vice versa, the falsity of the one implies the truth of the other: If it is true that every man is just, it cannot be true that one man is not just.

(2) Contrarics cannot both be true, but they can both be false.

Contraries cannot both be true; otherwise contradictories would be true at the same time. Suppose the proposition, "Every man is just," to be true; the contradictory, "One man is not just," is false. If it is false to say that one man -- even a single individual -- is not just, much more is it false to say that every man is not just, or -- which comes to the same thing -- that no man is just. The proposition, "No man is just," is the contrary of the proposition, "Every man is just."

But the falsity of a proposition does not imply the truth of the contrary. It may be false that all men are just without its being true that no man is just; there may be some just men, even though not all are just.

(3) By a rule opposed to that of contraries, sub-contraries may both be true. E. g.: Some man is just; some man is not just. Justice may be an attribute of one portion of mankind and not of the other.

But sub-contradictories cannot both be false, or both of two contradictories would be false. Let the proposition, "Some man is just," be false; the contradictory, "No man is just," is therefore true. Much more, then, is it true that some man is not just, which is the sub-contrary.