None of the captives escaped. Negative.
Some teachers are just. Affirmative.
All trees grow towards heaven. Affirmative.
Some people are not companionable. Negative.
No person is above criticism. Negative.
Dividing both universal and particular propositions as to quality, gives four kinds; namely, universal affirmative, universal negative, particular affirmative and particular negative. No topic in logic demands greater familiarity thanthese four types, as every proposition must be reduced to one of the four before it can be used as a basis of reasoning.
For the sake of brevity the symbols A, E, I and O are used to designate respectively the universal affirmative, the universal negative, the particular affirmative and the particular negative. A and I, symbolizing the affirmative propositions, are the first and second vowels in Affirmo, while E and O, symbolizing the negatives, are the vowels in Nego. The common sign of the universal affirmative, or the A proposition is all; of the universal negative, or E proposition no; of the particular affirmative, or I proposition some; of the particular negative, or O proposition some with not as a part of the copula. The accompanying classification summarizes these facts, S and P being used to symbolize the terms “subject” and “predicate.”
| Illustrations | |||||
| Categorical Propositions |  | Universal | | Affirmative-A | All S is P |
| Negative-E | No S is P | ||||
| Particular | | Affirmative-I | Some S is P | ||
| Negative-O | Some S is not P | ||||
Henceforth the symbols A, E, I, O will be used to designate the four kinds of categorical propositions. The propositions have other quantity signs aside from the ones used above. These may be summarized:
| Quantity signs of | | A—all, every, each, any, whole. |
| E—no, none, all-not. | ||
| I—some, certain, most, a few, many, the greatest part, any number. | ||
| O—some - - not, few. |