CBSE Book Class 11 Philosophy Square of Opposition

Square of Opposition

What is opposition of propositions?

Four categorical propositions A, E, I and O are related and at the same time different from each other. The relation among them is explained by a diagram called the "Square of Opposition". A, E, I and O propositions differ from one another to which the traditional logicians have given a name of 'opposition'. The following diagram shows that opposition:

Two categorical propositions are said to be opposite if they differ in:

1. Quantity

2. Quality

3. Both Quantity and Quality

The pair of AI and EO differs in quantity but not in quality. AI has same quality; both are affirmative but A is universal and I is particular. Similarly EO have same quality; both are negative but E is universal and O is particular. AE and IO differ in quality. Both AE are universal in quantity but A is affirmative and E is negative. Similarly both IO are particular; they have same quantity but I is affirmative and O is negative. The pairs AO and EI, however, differ both in quality and quantity.

Contrary propositions :

Universal affirmative A proposition, "All S is P" and universal negative E proposition, "No S is P" are related to each other by the contrary relation. The proposition "All basket ball players are tall" is contrary to "No basket ball players are tall". Similarly, "No lion is black" is contrary to "All lions are black".

Sub-contrary propositions :

Particular affirmative I proposition, "Some politicians are well read scholars" is related to O proposition, "Some politicians are not well read scholars" by sub-contrary relation. Similarly O proposition, "Some animals are not carnivorous" is related to I proposition, "Some animals are carnivorous" by sub-contrary relation.

Subaltern and superaltern propositions :

Universal affirmative A proposition, "All army generals are soldiers" is superaltern to I proposition, "Some army generals are soldiers". Similarly, E proposition, "No fish is mammal" is superaltern to O proposition, "Some fish are not mammals". But I is related to A by subaltern and similarly O is related to E by subaltern. "Some cats are mammals" is subaltern to "All cats are mammals." Similarly, "Some roses are not red things." is subaltern to "No roses are red things."

Contradictory propositions :

The universal affirmative A proposition, "All S is P" is related to particular negative O proposition, "Some S is not P" by contradictory relation. The contradictory of "All men are mortal" is "Some men are not mortal" and vice versa. The contradictory of E proposition, "No egg is red" is I proposition, "Some eggs are red".

1. "All S is P" is contrary to "No S is P" and vice versa.

2. "Some S is P" is sub-contrary to "Some S is not P" and vice versa.

3. (i) "All S is P" is contradictory to "Some S is not P" and vice versa.

(ii) "No S is P" is contradictory to "Some S is P" and vice versa.

4. (i) "Some S is P" is subaltern to "All S is P".

(ii) "Some S is not P" is subaltern to "No S is P".

5. (i) "All S is P" is superaltern to "Some S is P".

(ii) "No S is P" is superaltern to "Some S is not P".

Each opposite relation has certain characteristics

Contrary proposition A and E cannot be both true together though they both can be false at the same time. If one of the contrary propositions is true, then the other contrary proposition is false. But if one of the contrary propositions is false then the other contrary proposition is undetermined

(it can be true or it can be false also). If "All politicians are honest" is false, then "No politician is honest" can be false, or, it can be true also.

Please refer to the link below - CBSE Class 11 Philosophy Square of Opposition