The term ‘poetic syllogism’ appears in the late antique Greek commentary and scholia literature. Arabic philosophers, however, are the first to explain how this kind of syllogism is constructed; al-Fārābī introduces one type and Avicenna adds two more. Each syllogism that follows one of these three types includes among its premises or its conclusion at least one figurative statement. The poetic syllogism plays a key role in Arabic ‘philosophical’ poetics, which contains an important theory of figurative language.—A treatise on Poetics by Ibn Ṭumlūs discusses the relationship between the three types. The present study closely analyses Ibn Ṭumlūs’s reasoning. Furthermore, it clarifies previously unexplained or misunderstood terms such as ‘poetic statement’, ‘poetic premise’ and ‘poetic definition’. It finally points to an example for a specific type of sophistical inference Aristotle introduces in his Sophistical Refutations which Avicenna and other Arabic philosophers cite as a poetic syllogism. Commentators, perhaps as early as late antiquity, could have taken this type of inference to be the poetic syllogism they failed to find in Aristotle’s Poetics.