 Probably his main difference from Aristotle in categorical syllogisms is his treatment of the pairs of formal premises (i.e., with letters for terms) where Aristotle says “no syllogism occurs” in the sense that no syllogistic conclusion follows validly. Al-Fārābī calls these premise-pairs “nonproductive” (ghayr muntij). Aristotle had used the fact that valid inference rules preserve truth as a means to proving nonproductivity of a formal premise-pair; for any proposed conclusion, he found nouns that could be put for the letters, in such a way that the premises came out true and the conclusion false. During the Roman Empire period a tendency developed for logicians to skip these proofs and fall back instead on “laws of syllogism” that were supposed to give necessary and sufficient conditions for a premise-pair to be productive (cf. Lee 1984: 119f). This was generally a lapse from the rigor of Aristotle’s work, because the arguments given to justify the laws of syllogism were of a poor standard. Though al-Fārābī does once briefly mention Aristotle’s counterexample method ([Syllogism] 20.2–5), in practice he relies entirely on the laws of syllogism. By contrast the earlier logic texts of Paul the Persian and Ibn al-Muqaffa‘, both heirs of the Alexandrian view, copied Aristotle’s nonproductivity proofs in categorical logic with total formal rigor. 