Write a note on square of opposition.

The Square of Opposition is a conceptual tool in classical categorical logic that illustrates the relationships between different types of categorical propositions. Developed by medieval logicians such as Aristotle and further refined by later scholars, the square provides a structured framework to understand the logical relationships between universal and particular propositions.

The square consists of four types of categorical propositions:

1. A Propositions (Universal Affirmative): These propositions assert that all members of a class have a certain characteristic. For example, "All humans are mortal."

2. E Propositions (Universal Negative): These propositions deny the presence of a characteristic in the entire class. For example, "No humans are immortal."

3. I Propositions (Particular Affirmative): These propositions affirm the presence of a characteristic in at least some members of the class. For example, "Some humans are wise."

4. O Propositions (Particular Negative): These propositions deny the presence of a characteristic in at least some members of the class. For example, "Some humans are not foolish."

The relationships on the square of opposition can be summarized as follows:

• Contradiction (A vs. O, E vs. I): A and O propositions are contradictories, meaning they cannot both be true and cannot both be false at the same time. Similarly, E and I propositions are contradictories.

• Contrariety (A vs. E): A and E propositions are contraries, meaning they cannot both be true but can both be false. For example, "All humans are mortal" (A) and "No humans are mortal" (E) cannot both be true, but they can both be false.

• Subalternation (A implies I, E implies O): If the universal proposition (A or E) is true, then the corresponding particular proposition (I or O) must also be true. However, the reverse is not necessarily true.

• Subcontrariety (I vs. O): I and O propositions are subcontraries, meaning they can both be true but cannot both be false. For example, "Some humans are wise" (I) and "Some humans are not foolish" (O) can both be true, but they cannot both be false.

The square of opposition provides a concise way to analyze the logical relationships between different types of categorical propositions, offering insights into the interplay of universality, particularity, affirmation, and negation in logical reasoning.