Categorical Propositions and Immediate Inference
What the exam tests
Categorical propositions relate two classes. The exam tests the A-E-I-O forms, quantity and quality, distribution, the traditional square of opposition, and immediate inferences such as conversion, obversion, and contraposition.
Core rules
- A: All S are P (universal affirmative). E: No S are P (universal negative). I: Some S are P (particular affirmative). O: Some S are not P (particular negative).
- Distribution: A distributes S only; E distributes both S and P; I distributes neither; O distributes P only.
- Square: A and O are contradictories; E and I contradictories; A and E contraries (not both true); I and O subcontraries (not both false); A→I and E→O by subalternation under existential import.
- Conversion: E and I convert simply; A converts per accidens only if S exists; O cannot convert.
- Obversion: change quality, replace predicate by its complement, keep quantity. Valid for all four forms.
- Contraposition: valid for A and O; not valid for E and I without further assumptions.
Worked example
Take “All poets are dreamers” (A). Obverse: “No poets are non-dreamers” (E). This is equivalent: changing quality and complementing the predicate preserves truth. Conversion per accidens: “Some dreamers are poets,” valid only if poets exist. Contraposition: “All non-dreamers are non-poets,” obtained by obverting to E, converting, and obverting again. By contrast, “All poets are dreamers” does not convert simply to “All dreamers are poets.”
Traps
The commonest error is simple conversion of an A proposition. Do not change quantity during obversion-only quality and predicate complement. Do not apply subalternation or per accidens conversion when the subject class may be empty. In the square, contraries can both be false, and subcontraries can both be true.