Granting the truth of the propositions in the first column, it follows that those in the second column differ in quantity. That is, in “Some men are mortal” a _smaller_ number of men is referred to than in “All men are mortal.” A similar variation in quantity obtains with the other propositions in the second column. Moreover, the propositions in the third column are the negative of the corresponding ones in the first; while the fourth column propositions differ from the first in _both_ quantity and quality. Thus opposition exists to a greater or less degree between all. We may now ask ourselves the question, “When the propositions are related to each other in opposition which ones are true and which ones are false?” Giving attention to the propositions in row “I,” we note that if the universal affirmative, “All men are mortal,” is true, then the particular affirmative, “Some men are mortal,” is likewise true; because of the principle, “What is true of the whole of the class is true of a part of that class.” But the universal negative, “No men are mortal,” and the particular negative, “Some men are not mortal,” are both false. Briefly stated: If A is true, then I is true, but, both E and O are false. Regarding row “II” we may conclude that if E is true, then O is likewise true, but both A and I are false. As to rows “III” and “IV,” granting the truth of the I propositions, “Some men are wise” and “Some men are mortal,” we are able to assert that of the two A propositions, “All men are wise,” and “All men are mortal,” the first is false while the second is true. A is, therefore, indeterminate, or doubtful. Of the O propositions, “Some men are not wise,” is true while, “Some men are not mortal,” is false. Therefore, O is doubtful. Both of the E propositions are false. Hence, the conclusion relative to rows “III” and “IV” is: If I is true, A and O are doubtful, while E is false. Concerning rows “V” and “VI” it will be seen without further explanation that if O is true, then E and I are doubtful and A is false. THE SCHEME OF OPPOSITION. The conditions of opposition are easily comprehended and remembered when recourse is made to the following scheme: A E I O If A be true true false true false If E be true false true false true If I be true doubt false true doubt If O be true false doubt doubt true To use the above scheme, read horizontally from left to right. For example: If A be true, then all in the row opposite obtains; that is, A is true, E is false, I is true, and O is false. (We take it for granted that the student will see that the first column belongs to A, the second to E, the third to I, and the fourth to O.) If E be true, then A is false, E is true, I is false, O is true, etc.