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What is Square of Opposition? 

The square of opposition is a conceptual tool used in categorical logic to visually represent the logical relationships between certain types of propositions based on their form. 
Notes: Square of Opposition | Logical Reasoning for UGC NET

This framework helps in understanding how different propositions relate to each other in terms of truth and falsehood.

Basic Propositions

The square of opposition is built around four basic types of propositions, each occupying a corner of the square:

  1. A Propositions (Universal Affirmatives):

    • Form: All S are P.
    • Example: "All dogs are mammals."
  2. E Propositions (Universal Negatives):

    • Form: No S are P.
    • Example: "No dogs are reptiles."
  3. I Propositions (Particular Affirmatives):

    • Form: Some S are P.
    • Example: "Some dogs are friendly."
  4. O Propositions (Particular Negatives):

    • Form: Some S are not P.
    • Example: "Some dogs are not friendly."

Relationships in the Square of Opposition

  1. Contradictories:

    • Definition: Two propositions are contradictories if they cannot both be true or both be false at the same time. If one is true, the other must be false.
    • Examples:
      • A and O propositions: "All dogs are mammals" (A) and "Some dogs are not mammals" (O).
      • E and I propositions: "No dogs are reptiles" (E) and "Some dogs are reptiles" (I).
  2. Contraries:

    • Definition: Two propositions are contraries if they cannot both be true at the same time, but they can both be false.
    • Examples:
      • A and E propositions: "All dogs are mammals" (A) and "No dogs are mammals" (E). Both cannot be true simultaneously, but both can be false if some dogs are and some dogs are not mammals.
  3. Sub-Contraries:

    • Definition: Two propositions are sub-contraries if they cannot both be false at the same time, but they can both be true.
    • Examples:
      • I and O propositions: "Some dogs are friendly" (I) and "Some dogs are not friendly" (O). Both statements can be true, but they cannot both be false simultaneously.
  4. Sub-Alternation:

    • Definition: This relationship involves a universal proposition (A or E) and its corresponding particular proposition (I or O) with the same subject and predicate. The truth of the universal proposition implies the truth of the particular proposition.
    • Examples:
      • From A to I: If "All dogs are mammals" (A) is true, then "Some dogs are mammals" (I) must also be true.
      • From E to O: If "No dogs are reptiles" (E) is true, then "Some dogs are not reptiles" (O) must also be true.

Notes: Square of Opposition | Logical Reasoning for UGC NET

Immediate Inferences

Immediate inferences can be drawn directly from one proposition to another based on the square of opposition. Here are some examples:

  1. From A Proposition (All S are P):

    • If true:
      • E (No S are P) is false.
      • I (Some S are P) is true.
      • O (Some S are not P) is false.
    • If false:
      • O (Some S are not P) is true.
      • E and I are undetermined.
  2. From E Proposition (No S are P):

    • If true:
      • A (All S are P) is false.
      • I (Some S are P) is false.
      • O (Some S are not P) is true.
    • If false:
      • I (Some S are P) is true.
      • A and O are undetermined.
  3. From I Proposition (Some S are P):

    • If true:
      • E (No S are P) is false.
      • A and O are undetermined.
    • If false:
      • A (All S are P) is false.
      • E (No S are P) is true.
      • O (Some S are not P) is true.
  4. From O Proposition (Some S are not P):

    • If true:
      • A (All S are P) is false.
      • E and I are undetermined.
    • If false:
      • A (All S are P) is true.
      • E (No S are P) is false.
      • I (Some S are P) is true.

The square of opposition is a vital tool in classical logic, allowing for a clear understanding of how different types of categorical propositions relate to one another. By recognizing the relationships of contraries, contradictories, sub-contraries, and sub-alternations, one can determine the truth or falsehood of related propositions, facilitating logical reasoning and argumentation.

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FAQs on Notes: Square of Opposition - Logical Reasoning for UGC NET

1. What is the Square of Opposition in logic?
Ans. The Square of Opposition is a diagram that represents the relationships between the four basic types of categorical propositions in traditional logic: A (universal affirmative), E (universal negative), I (particular affirmative), and O (particular negative).
2. How are the relationships in the Square of Opposition defined?
Ans. The relationships in the Square of Opposition are defined as contradictory, contrary, subcontrary, and subalternation. Contradictory propositions cannot both be true, contrary propositions cannot both be true at the same time, subcontrary propositions cannot both be false at the same time, and subalternation is the relationship between universal and particular propositions.
3. What are immediate inferences in the Square of Opposition?
Ans. Immediate inferences in the Square of Opposition refer to the logical deductions that can be made by looking at the relationships between categorical propositions in the square. These inferences include conversion, obversion, contraposition, and the traditional square of opposition relationships.
4. What are some examples of immediate inferences in the Square of Opposition?
Ans. Examples of immediate inferences in the Square of Opposition include converting an A proposition to an E proposition, obverting an A proposition to an O proposition, contraposing an E proposition to an I proposition, and deriving the truth of a particular proposition based on the truth of its corresponding universal proposition.
5. How can the Square of Opposition be applied in UGC NET exams?
Ans. Understanding the Square of Opposition can help in solving logical reasoning questions in the UGC NET exam. By recognizing the relationships between categorical propositions and applying the rules of immediate inferences, candidates can improve their ability to analyze and deduce conclusions from given statements.
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