Polysyllogism
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A polysyllogism, sometimes called multi-premise syllogism, is a string of any number of syllogisms such that the conclusion of one is a premise for the next, and so on.
A sorites argument is a specific kind of polysyllogism. Sorites comes from the Greek word for "heap" or "pile." In other words, a sorites is a heap of propositions chained together. Example:
All A are B
All B are C
All C are D
All D are E
Therefore all A are E