We now reach the third act of the mind, reasoning. In Premises and Conclusions you found premises and conclusions. A categorical syllogism is an argument with exactly two premises and a conclusion, all three of them categorical propositions, using exactly three terms, each used twice.
Key idea
The conclusion decides the names. Its predicate is the major term (P); its subject is the minor term (S). The term in both premises but not in the conclusion is the middle term (M).
Why it works
The middle term is the go-between. The conclusion claims some relation between S and P, and the premises can only support it by relating each of them to a third class. If S is tied to M and M is tied to P in the right way, the tie carries over to S and P, and then M disappears from the conclusion. That is why each term appears exactly twice: S and P once in a premise and once in the conclusion, M once in each premise.
Worked example
Worked example: Naming the terms
Name the major, minor and middle terms: "Some readers are runners. All runners are early risers. So some readers are early risers."
- Start with the conclusion: "Some readers are early risers".
- Its predicate, early risers, is the major term (P). Its subject, readers, is the minor term (S).
- Runners appears in both premises and not in the conclusion: the middle term (M).
Answer: major: early risers; minor: readers; middle: runners
Common mistake
Naming the major term by size ("animals" sounds bigger) or by which premise comes first. Only the conclusion decides: its predicate is the major term, its subject the minor term, whatever order the premises were spoken in.
The names come from Aristotle: in his first figure the major term is usually the widest class and the minor term the narrowest. The rule we use (look at the conclusion) works for every syllogism.