A statement is true or false. A categorical proposition is a statement of one special shape: it relates two classes, named by terms, by saying that one is included in the other or shut out of it, in whole or in part.
Every categorical proposition in standard form has four parts, in this order:
- the quantifier: All, No or Some;
- the subject term: the class the statement is about;
- the copula: are or are not;
- the predicate term: the class the subject is related to.
Key idea
Standard form is Quantifier – subject term – copula – predicate term, with both terms naming classes: "All whales are mammals that breathe air."
Why it works
Fixing one shape lets us compare statements part by part. Once every claim reads "All/No/Some ___ are (not) ___", we can see at a glance which two classes it relates and how, and the rest of this course (the square, conversion, syllogisms) works on those parts. The terms must name classes ("mammals that breathe air", not "breathe air") so that both sides of the copula are the same kind of thing.
Worked example
Worked example: Finding the terms
Name the four parts of "Some books on the top shelf are not novels by Jane Austen."
- Quantifier: the first word, Some.
- Subject term: everything between the quantifier and the copula: books on the top shelf.
- Copula: are not.
- Predicate term: everything after the copula: novels by Jane Austen.
Answer: Some / books on the top shelf / are not / novels by Jane Austen
Common mistake
Taking the grammatical subject or the verb for the logical terms. In "All whales are mammals that breathe air", the predicate term is the whole phrase mammals that breathe air, not "mammals" and not "breathe". Check: the predicate term is everything after "are" or "are not".
In an E proposition ("No dogs are cats") the word "no" belongs to the quantifier, so the copula is plain are. Only the O form ("Some dogs are not puppies") has are not.