 A modern reader will be inclined to see (4–6) as a piece of simple sentence logic: p→q; ¬q; therefore ¬p. Since it was the Stoics who, in antiquity, developed a sentence logic, by contrast with Aristotle’s term logic, it would appear that Boethius’s treatise on hypothetical syllogisms is the tributary of Stoic logic. This conclusion is true to the extent that the tradition Boethius inherited goes back in part to Stoic roots. By the time it had reached Boethius, however, Stoic and Peripatetic elements had become hopelessly confused (cf. Speca 2001). As C.J. Martin (1991) has shown, Boethius himself lacked the conceptual apparatus to think in terms of sentence logic. For him, (4–6) is to be understood as term logic, in which the predicates ‘is light’ and ‘is day’ are attributed to or denied of a vague subject ‘it’. The treatise itself is mainly devoted to a laborious calculation of the various different possible forms of hypothetical syllogism involving two, three (with a first premise such as ‘If it is A, then if it is B, it is C’) and four terms (with a first premise such as ‘If, if it is A then it is B, then, if it is C then it is D’).