Categorical Propositions and Immediate Inference
What this domain tests
Immediate inference draws a conclusion from a single premise. The exam tests the square of opposition, conversion, obversion and contraposition, and the exact conditions under which each is valid.
Square of opposition
- Contradictories (A–O, E–I): never both true, never both false.
- Contraries (A–E): never both true, may both be false.
- Subcontraries (I–O): never both false, may both be true.
- Subalterns (A–I, E–O): truth flows down, falsity flows up.
The three operations
- Conversion: swap subject and predicate. E and I convert simply; A converts by limitation ("All S are P" → "Some P are S"); O has no valid conversion.
- Obversion: change the quality and replace the predicate by its complement. Valid for all four forms: "All S are P" → "No S are non-P".
- Contraposition: obvert, convert, obvert again. Valid for A and O; partial and full forms differ in whether the subject is also complemented.
Worked example
Obvert "Some students are not punctual" (O). Change the quality to affirmative and complement the predicate: "Some students are non-punctual" - an I proposition. Obversion is truth-preserving, so the two statements are equivalent and either may replace the other in an argument.
Traps that cost marks
Converting an A proposition simply - "All dogs are animals" does not give "All animals are dogs"; confusing obversion with conversion; applying contraposition to E or I; treating subalternation as reversible.