 Like most things in the history of logic, hypothetical syllogistic also begins with Aristotle. In the Prior Analytics, he says that every syllogism is either direct or from a hypothesis. Traditional syllogistic is direct and hence all syllogisms that do not fall into the patterns of inference defined by the three Aristotelian figures, but which are nevertheless valid syllogisms, must be hypothetical. Aristotle’s principal example is a syllogism through impossibility. If we reason from a hypothesis P via a syllogism to a conclusion Q that is impossible, then we can conclude that not-P is true and P false (An. Pr. 41a23–30).