A sorites is a chain of three or more premises leading to one conclusion. It packs several enthymemes together: each step produces an unstated intermediate conclusion that becomes a premise of the next step.
Key idea
A sorites is valid when every link in the chain is a valid syllogism. To test it, put the premises in chain order, draw each intermediate conclusion, and test each link.
Why it works
Each link takes the conclusion so far and one new premise, and produces a new conclusion. If every link is valid, the truth of the premises passes along the chain like a relay, all the way to the end. One bad link breaks the relay: what comes after it is no longer guaranteed, even if every later link is fine.
Worked examples
Worked example: Ordering the chain
What follows? "All anglers are bakers. All actors are climbers. All climbers are anglers."
- Find the term that is never a predicate: actors. Start there: All actors are climbers.
- Next, the premise about climbers: All climbers are anglers. Link 1 (Barbara): All actors are anglers.
- Then the premise about anglers: All anglers are bakers. Link 2 (Barbara): All actors are bakers.
Answer: All actors are bakers.
Worked example: A negative last link
What follows? "All poets are hikers. No singers are runners. All hikers are singers."
- Chain: poets → hikers → singers, then "no singers are runners".
- Link 1: All poets are hikers, all hikers are singers, so all poets are singers (Barbara).
- Link 2: No singers are runners, all poets are singers, so no poets are runners (Celarent).
Answer: No poets are runners.
Lewis Carroll, the author of Alice in Wonderland, wrote famous sorites puzzles with silly premises, such as chains about babies, crocodiles and logic. Silly premises are a good reminder that validity is about form, not about whether the premises are true.
Common mistake
Checking only the first and last premises. Each step in the chain must be a valid syllogism on its own; one undistributed middle in the middle of the chain breaks the whole sorites. Check: write out every intermediate conclusion and test each link.