Polysyllogism

A polysyllogism (also called multi-premise syllogism, sorites, climax, or gradatio) is a string of 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. Each constituent syllogism is called a prosyllogism except the very last, because the conclusion of the last syllogism is not a premise for another syllogism.

An example for a polysyllogism is:

Examination of the structure of the argument reveals the following sequence of constituent (pro)syllogisms:

A sorites is a specific kind of polysyllogism in which the predicate of each proposition is the subject of the next premise. Example:

The word "sorites" /sɒˈraɪtiːz/ comes from Ancient Greek: σωρίτης, "heaped up", from σωρός "heap" or "pile". In other words, a sorites is a heap of propositions chained together. A sorites polysyllogism should not be confused with the sorites paradox, a.k.a. fallacy of the heap.

Lewis Carroll uses sorites in his book Symbolic Logic (1896). Here is an example:

Carroll's example may be translated thus

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