There are exactly four ways to relate two classes in a categorical proposition. Medieval logicians named them with the vowels of AffIrmo ("I affirm") and nEgO ("I deny").
| Form | Standard form | Quantity | Quality |
|---|---|---|---|
| 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 |
Key idea
Quantity asks "all or some?": A and E are universal, I and O particular. Quality asks "including or excluding?": A and I are affirmative, E and O negative. In logic, some means "at least one".
Why it works
"Some" means at least one because logic only keeps what a statement guarantees. "Some students passed" guarantees that at least one did. It does not guarantee that some failed; the speaker may simply not know. If all of them passed, "Some students passed" is still true, just not the whole story.
Worked example
Worked example: Letter, quantity and quality
Give the form, quantity and quality of "Some campers are not singers."
- Quantifier "some": particular.
- Copula "are not": negative.
- Particular negative is the O form.
Answer: O: particular negative
Worked example: When all of them are
Every student in the class passed the quiz. Is "Some students in the class are students who passed" true?
- In logic, "some" asks only for at least one.
- There is at least one student in the class, and that student passed.
- So the I statement is true, even though the A statement is true as well.
Answer: true
Common mistake
Reading "some" as "some but not all". If every S is P (and there are S), then "Some S are P" is true. Check: ask whether the statement would become false if it turned out that all of them are. For "some", it would not.