Categorical Propositions and Immediate Inference
The four forms
Categorical propositions relate two classes. Standard forms: A (All S are P), E (No S are P), I (Some S are P), O (Some S are not P). Quantity is universal (A, E) or particular (I, O); quality is affirmative (A, I) or negative (E, O).
Distribution
A term is distributed when the proposition says something about every member of the class it names.
- A: subject distributed, predicate undistributed.
- E: both distributed.
- I: neither distributed.
- O: predicate distributed, subject undistributed.
Square of opposition
A–E are contraries (not both true); I–O subcontraries (not both false); A–O and E–I contradictories (opposite truth values); A–I and E–O subalterns (truth flows down, falsity flows up).
Immediate inference
Conversion swaps subject and predicate: valid for E and I; A converts only per accidens (to “Some P are S”); O does not convert. Obversion changes quality and complements the predicate - valid for all four forms. Contraposition replaces subject and predicate by their complements - valid for A and O.
Worked example
“All poets are imaginative” (A). Obverse: “No poets are non-imaginative.” Contrapositive: “All non-imaginative beings are non-poets.” Both preserve truth. Its converse, “All imaginative beings are poets,” is invalid because the predicate was undistributed in the original.
Traps that cost marks
Do not distribute the predicate of an A proposition; do not convert an O; remember that per accidens conversion depends on the subject class existing.