Immediate Inference - Oppositional Inference

A.      Oppositional Inference – it is a type of immediate inference in which we deduce the truth value of another proposition (can be A, E, I, O) from a given truth value of a proposition of the same structure.

Example:

                                “All men are mortals” is true.

                                Therefore, “No men are mortals” is _______.

                                The answer is false.

Types of Oppositional Inference:

1.       Contrary – it is the opposition between A and E propositions.

                        Rule: If one is true, the other is false. If one is false, the other is unknown.

Example:

        If one is true:

                        (A) All men are mortals. – True                  (E) No men are angels. – True

                        (E) No men are mortals. – False                 (A) All men are angels. – False

        If one is false:

                        (A) All men are angels. – False                   (E) No men are mortals. – False

                        (E) No men are angels. – Unknown         (A) All men are angels. – Unknown

Explanation: If one is false, we cannot immediately infer that the other is true because it might be the case that if one is false the other might also be false. Hence, the better answer is unknown.

2.       Sub-contrary – it is the opposition between I and O propositions.

                        Rule: If one is true, the other is Unknown. If one is false, the other is true.

Example:

        If one is true:

                        (I) Some animals are mammals. – True                  

                        (O) Some animals are not mammals. – Unknown

                        (O) Some animals are not mammals. – True

                        (I) Some animals are mammals. – Unknown

Explanation: If one is true, we cannot immediately infer that the other is false since it is possible that the other could also be true; hence, Unknown.

        If one is true:

                        (I) Some animals are flowers. – False                     

                        (O) Some animals are not flowers. – True

                        (O) Some mammals are not animals. – False

                        (I) Some mammals are animals. – True

3.       Sub-altern – it is the opposition between A & I propositions and E & O propositions.

Rule:      If the universal proposition is true, the particular proposition is true. If the universal proposition is false, the particular proposition is Unknown.

                If the particular proposition is false, the universal proposition is false. If the particular proposition is true, the universal proposition is Unknown.

Example:

        If the universal is true:

                        (A) All men are mortals. – True                  (E) No men are angels. – True

                        (I) Some men are mortals. – True             (O) Some men are not angels. – True

If the universal is false:

                (A) All men are angels. – False                   (E) No men are mortals. – False

                (I) Some men are angels – Unknown      (O) Some men are not mortals. Unknown

Explanation: If the universal is false, we cannot immediately infer that the particular is also false since it is possible that the particular can be true.

If the particular is true:

                (I) Some animals are mammals. – True

                (A) All animals are mammals. – Unknown

                (O) Some animals are not mammals. – True

                (E) No animals are not mammals. – Unknown

Explanation: If the particular is false, it is possible that the universal can be true or can be false; hence, Unknown.

If the particular is false:

                (I) Some animals are mammals. – False

                (A) All animals are mammals. – False

                (O) Some animals are not mammals. – False

                (E) No animals are not mammals. – False

4.       Contradictory – the opposition between A & O propositions and E & I propositions.

Rule: If one is true, the other is false. If one is false, the other is true.

Examples:

 (A) All men are mortals. – True | False

(O) Some men are not mortals. – False | True

(O) Some men are not mortals. – False | True

(A) All men are mortals. – True | False

(E) No men are angels. – True | False

(I) Some men are angels. – False | True

(I) Some men are angels. – False | True

(E) No men are angels. – True | False