Opposition exists between propositions having the same subject and predicate, but differing in quality or quantity, or both. The Laws of Opposition are as follows:
I. (1) If the universal is true, the particular is true. (2) If the particular is false, the universal is false. (3) If the universal is false, nothing follows. (4) If the particular is true, nothing follows.
II. (1) If one of two contraries is true, the other is false. (2) If one of two contraries is false, nothing can be inferred. (3) Contraries are never both true, but both may be false.
III. (1) If one of two sub-contraries is false, the other is true. (2) If one of two sub-contraries is true, nothing can be inferred concerning the other. (3) Sub-contraries can never be both false, but both may be true.
IV. (1) If one of two contradictories is true, the other is false. (2) If one of two contradictories is false, the other is true. (3) Contradictories can never be both true or both false, but always one is true and the other is false.
In order to comprehend the above laws, the student should familiarize himself with the following arrangement, adopted by logicians as a convenience:
| Universal | Affirmative Negative | (A) (E) | |||
| Propositions | |||||
| Particular | Affirmative Negative | (I) (O) |
Examples of the above: Universal Affirmative (A): "All men are mortal;" Universal Negative (E): "No man is mortal;" Particular Affirmative (I): "Some men are mortal;" Particular Negative (O): "Some men are not mortal."
The following examples of abstract propositions are often used by logicians as tending toward a clearer conception than examples such as given above:
(A) "All A is B."