_Contradictory_ propositions are those in which one denies _any thing_ that the other affirms; _contrary_ propositions are those in which one denies _every thing_ which the other affirms, or affirms every thing which the other denies. The following pair are contraries. Every A is B and No A is B and the following are contradictories, Every A is B to Some A is not B No A is B to Some A is B A contrary, therefore, is a complete and total contradictory; and a little consideration will make it appear that the decisive distinction between contraries and contradictories lies in this, that contraries may both be false, but of contradictories, one must be true and the other false. We may say, ‘Either P is true, or _something_ in contradiction of it is true;’ but we cannot say, ‘Either P is true, or _every thing_ in contradiction of it is true.’ It is a very common mistake to imagine that the _denial_ of a proposition gives a right to _affirm_ the contrary; whereas it should be, that the _affirmation_ of a proposition gives a right to _deny_ the contrary. Thus, if we deny that Every A is B, we do not affirm that No A is B, but only that Some A is not B; while, if we affirm that Every A is B, we deny No A is B, and also Some A is not B. But, as to contradictories, affirmation of one is a denial of the other, and denial of one is affirmation of the other. Thus, either Every A is B, or Some A is not B: affirmation of either is denial of the other, and _vice versá_. Let the student now endeavour to satisfy himself of the following. Taking the four preceding propositions, A, E, I, O, let the simple letter signify the affirmation, the same letter in parentheses the denial, and the absence of the letter, that there is neither affirmation nor denial. From A follow│(E), I, (O)│From (A) follow O From E │(A), (I), O│From (E) I From I │(E) │From (I) (A), E, O From O │(A) │From (O) A, (E), I These may be thus summed up: The affirmation of a universal proposition, and the denial of a particular one, enable us to affirm or deny all the other three; but the denial of a universal proposition, and the affirmation of a particular one, leave us unable to affirm or deny two of the others.