Terms, Propositions and Categorical Statements
Terms and propositions
A term is a word or phrase that can serve as subject or predicate of a categorical proposition. A proposition is a declarative statement capable of being true or false. Categorical propositions relate two classes, subject (S) and predicate (P), through a copula and a quantifier.
The four categorical forms
- 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.
Quality is affirmative or negative; quantity is universal or particular. Distribution matters: in A, S is distributed; in E, both S and P are distributed; in I, neither is distributed; in O, P is distributed.
Worked example
“No reptiles are warm-blooded animals” is E. Its subject “reptiles” and predicate “warm-blooded animals” are both distributed because the statement excludes every reptile from the entire predicate class. By contrast, “Some reptiles are lizards” is I: neither term is distributed, since it asserts only that at least one reptile is a lizard.
Traps that cost marks
- Mistaking “some” for “some but not all.” In logic, “some” means at least one.
- Treating a singular statement as automatically universal.
- Forgetting that distribution concerns what the proposition says about every member of a class.
- Mixing quantity and quality when naming A, E, I, O.
- Assuming ordinary-language idioms always match standard categorical form.