LOGIC AND LANGUAGE Boethius, however, is more interested in syllogisms where all the premisses and the conclusion too are hypothetical, such as If it’s A, it’s B; if it’s B it’s C; so if it’s A it’s C He elaborates schemata including negative premisses as well as aYrmative ones and premisses involving conjunctions other than ‘if ’, e.g ‘Either it is day or it is night’ Hypothetical syllogisms, he maintains, are parasitic on categorical syllogisms, because hypothetical premisses have categorical premisses as their constituents, and they depend on categorical syllogisms to establish the truth of their premisses Once again, Boethius is siding with Aristotle against the Stoics, this time about the relationship between predicate and propositional logic In discussing hypothetical syllogisms Boethius makes an important distinction between two diVerent sorts of hypothetical statement He uses ‘consequentia’ (‘consequence’) as a term for a true hypothetical; perhaps the nearest equivalent in modern English is ‘implication’ In some consequences, he says, there is no necessary connection between the antecedent and the consequence: his example is ‘Since Wre is hot, the heavens are spherical’ This appears to be an example of what modern logicians have called ‘material implication’; Boethius’ expression is ‘consequentia secundum accidens’ On the other hand, there are consequences where the consequent follows necessarily from the antecedent This class includes not only the logical truths that modern logicians would call ‘formal implications’ but also hypothetical statements whose truth is discovered by scientiWc inquiry, such as ‘If the earth gets in the way, there is an eclipse of the moon’ (PL 64 835b) True consequences can be derived, Boethius believes, from a set of supreme universal propositions which he calls ‘loci’, following Cicero’s rendering of the Aristotelian Greek ‘topos’ The kind of proposition he has in mind is illustrated by one of his examples: ‘Things whose deWnitions are diVerent are themselves diVerent’ He wrote a treatise, De Topicis DiVerentiis, in which he oVered a set of principles for classifying the supreme propositions into groups The work, though it appears arid to a modern reader, was inXuential in the early Middle Ages.6 De Topicis DiVerentiis, trans Eleonore Stump (Ithaca, NY: Cornell University Press, 1978) 122