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THE SYLLOGISTIC OF VALERIANUS MAGNI 213 6. Conclusions The purpose of this article has been to clarify the structure of Valerianus' syllogistic and to examine the way he uses the particle « necessario/impossibile » (Section 2). His examples of the six « modi perfectissimi » as well as the lack, in his tracts, of the theory of supposition indicate that he ranks with those logicians who con– sidered the propositions with singular terms as being equivalent to particular propositions (Section 2.1). Thus his three « differentiae » appear to be based on the following couples of Aristotelian assertoric modes: (1) Barbara/Darii, (2) Celarent/Ferio, (3) Camest::-es/Baroco. It has been shown that, with the exception of Cesare/Festino that can easily be reformulated as Celarent/Ferio, the above three couples are the only in which the major premise remains the same, while the universality/particularity of the conclusion is determined by the universality/particularity of the minor premise. The key role of the major premise seems to have drawn Valerianus' attention and he expressed its universality by means of adding « necessario/impos– sibile » to its verbal expression (Section 2.2). The order of premises (minor- major) in which Valerianus' syl– logisms are stated is determined, first, by different epistemologic status ascribed to each of them by Valerianus, namely the minor registering an empirical fact, the major declaring some sort of neces– sary truth, and, second, by certain practical reason, i.e. the achie– vement of the so-called « illatio conexa » without superfluous rewrit– ing of premises (Section 3). The discussion of two occurrences of « necessario » in Valeria– nus' rules has made it clear that the scope of its second occurrence cannot be taken as limited to the conclusion alone, in which case we would have to do with a certain kind of modal sy]ogistic. It must be understood as referring to the « illatio » as a whole and as meaning « follows logically from the premises » ( Section 4). Valerianus' reformulation of the Aristotelian Bocardo contains the major premise, « (B - C) e C », wich can be readily compared with his example of the necessary proposition par excellence, i.e. « 2 + 3 = 5 ». Since the necessary proposition of the type represented by examples: « 2 + 3 = 5 », « (B - C) e C » as well as the one of the type exemplified by « Animal est substantia » are both considered by Valerianus to be « aeternae veritates », it appears that he treated the two types of necessary propositions as belonging tc the same category (Section 5). Against the background of five centuries of an almost unchanged syllogistic tradition Valerianus' innovations meant more than one