All places that are the attic are places where smoke is. Therefore, All places that are the attic are places where fire is. AAA-1 is clearly valid. Enthymemes Another special case occurs when one or more of the propositions in a categorical syllogism is left unstated. In order to show that an enthymeme corresponds to a valid categorical syllogism, we need only supply the missing premise in each case.
Some hawks are sharp-beaked animals.
All hawks are birds. Therefore, Some birds are sharp-beaked animals. Sorites Finally, the pattern of ordinary-language argumentation known as sorites involves several categorical syllogisms linked together. The conclusion of one syllogism serves as one of the premises for another syllogism, whose conclusion may serve as one of the premises for another, and so on. In any such case, of course, the whole procedure will comprise a valid inference so long as each of the connected syllogisms is itself valid.