  to the conclusions of the relevant syllogisms. Boethus suggested substantial modifications to Aristotle’s theories: he claimed that all categorical syllogisms are complete, and that hypothetical syllogistic is prior to categorical (Galen Inst. Log. 7.2), although we are not told what this priority was thought to consist in.  The Stoic Posidonius (c. 135–c. 51 BCE) defended the possibility of logical or mathematical deduction against the Epicureans and discussed some syllogisms he called ‘conclusive by the force of an axiom’, which apparently included arguments of the type ‘As the 1st is to the 2nd, so the 3rd is to the 4th; the ratio of the 1st to the 2nd is double; therefore the ratio of the 3rd to the 4th is double’, which was considered conclusive by the force of the axiom ‘things which are in general of the same ratio, are also of the same particular ratio’ (Galen Inst. Log. 18.8). At least two Stoics in this period wrote a work on Aristotle’s Categories. From his writings we know that Cicero (1st c. BCE) was knowledgeable about both Peripatetic and Stoic logic; and Epictetus’ discourses (late 1st–early 2nd c. CE) prove that he was acquainted with some of the more taxing parts of Chrysippus’ logic. In all likelihood, there existed at least a few creative logicians in this period, but we do not know who they were or what they created.