A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms, sorites, epicheirema, and dilemmas)[1] that strings together any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on.
An example of a categorical polysyllogism is: This argument has the following structure: Note two points: first, the makeup of a polysyllogism need not be limited to two component syllogisms.
In fact, it can have any number of component syllogisms.
[2] An example for a propositional polysyllogism is: Examination of the structure of the argument reveals the following sequence of constituent (pro)syllogisms: A sorites (plural: sorites) is a specific kind of polysyllogism in which the predicate of each proposition is the subject of the next premise.
Lewis Carroll uses sorites in his book Symbolic Logic (1896).