 In Aristotle’s syllogistic, a syllogism relates two or more premises and a single conclusion. In fact, Aristotle focuses on arguments with exactly two premises (the major premise and the minor premise), but nothing in his definition forbids arguments with three or more premises. Surely, such arguments should be permitted: if, for example, we have one syllogism from two premises \(A\) and \(B\) to a conclusion \(C\), and we have another from the premises \(C\) and \(D\) to the conclusion \(E\), then in some sense, the longer argument from premises \(A, B\) and \(D\) to conclusion \(E\) is a good one. It is found by chaining together the two smaller arguments. If the two original arguments are formally valid, then so too is the longer argument from three premises. On the other hand, on a common reading of Aristotle’s definition of syllogism, one-premise arguments are ruled out—but this seems arbitrary, as even Aristotle’s own “conversion” inferences are thus excluded. 