In Unstated Premises you saw that people leave obvious premises unsaid. A syllogism with a premise or the conclusion left out is called an enthymeme. To evaluate it, you first supply the missing part, and test it like any syllogism.
Key idea
Supply the missing statement that makes the syllogism valid and is as plausible as possible. Then judge the whole argument: valid, and are the premises (including the one you supplied) true?
Why it works
A fair reader fills the gap the way the speaker most likely meant it: with a premise that makes the reasoning work. Supplying a premise that makes the argument invalid would attack a position nobody held. But the supplied premise must also be believable; choosing a claim that is stronger than needed and plainly false would be unfair in the other direction.
Worked examples
Worked example: A missing premise
Supply the missing premise: "Some swimmers are cyclists, so some swimmers are not knitters."
- The conclusion's terms are swimmers (S) and knitters (P). The stated premise uses swimmers and cyclists, so cyclists is the middle term.
- The missing premise must link cyclists and knitters, and since the conclusion is negative, it must be negative.
- "No knitters are cyclists" gives EIO-2 (Festino), which is valid. ("No cyclists are knitters" says the same.)
Answer: No knitters are cyclists
Worked example: Weak or strong?
Supply a premise: "Leo is invited on the hike, because all the campers are invited."
- In standard form: All campers are invited people / ∴ All people identical to Leo are invited people. The missing premise links Leo and campers.
- "All people identical to Leo are campers" (Leo is a camper) makes it Barbara, valid.
- A stronger premise such as "Everyone in town is a camper" would also work, but it is plainly false. The fair choice is the weaker, plausible one.
Answer: Leo is a camper.
Common mistake
Supplying a premise that makes the syllogism invalid (such as "All cyclists are knitters" in the first example, which leaves two affirmative premises with a negative conclusion), or one so strong that it is plainly false when a weaker true one would work. Check: test the completed syllogism, then ask if the premise you added is believable.