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210 KAREL HUBKA 4. Valerianus' theory of syllogism So far our analysis of Valerianus' syllogisms has been based on the actual examples, (11) to (32), which he gives in his seventh tract, « Exercitatio logica ». We shall now briefly discuss the essence of his syllogistic theory as it appears in two following passages, one contained in the chapter 5, the other in chapter 6 of the fourth tract, « Syllogismus formalis ». The rule concerning all three "differentiae ": « •.. sufficit illationi, si minor propositio sit vera; at maior non solum debet esse vera, sed debet esse vera et incommutabilis [scil. neces– saria]: alioquin is qui ratiocinatur non potest inferre necessario et incommutabiliter conclusionem ex praemissis... » 28 • The rule concerning the third "differentia ", in particular: « Id, de quo necessario affirmatur medium negatum, [scil. maior extremitas], necessario negatur de minore extremitate » 29. In both passages there are two occurrences of « necessario ». The function and meaning of the first occurrence was discussed in Section 2.2. Now, there might be doubts, especially with respect to the formulation of the second passage, whether the scope of the second occurrence of « necessario » is limited to the conclusion alone, in which case we would expect also the conclusions of Valerianus' examples, (11) to (32), to be formulated with « necessario/impossi– bile », or whether the second occurrence of « necessario » concerns the « illatio » as a whole, i.e. the relation between premises and conclusion, as the formulation of the first passage would suggest. In the first case we would have to do with Aristotelian modal logic, i.e. with the modes Barbara/Darii - NYN, Celarent/Ferio - NYN, Camestres/Baroco - NYY 30 • However, nothing that would sug– gest such a solution is to be found in Valerianus' tracts. Assuming that Valerianus' Barbara were the same as Aristotle's Barbara - NYN, i.e. cc ei. -.o µe:v A -.cjl B e:~ ocv&yx.'r)~. dt-.'1}1t't"ixt {m&pxov ... , -.o ~e: B -.cjl I' tm&pxov µ6vov, ...e:~jocv&yx.'1}~ -.o A -.cjl r u1t&p~s:t » 31 • Valerianus would have to write « Ergo homo necessario est substan– tia » instead of « Ergo homo est substantia » (11). Under the as- 28 Ibid. 16s. 29 Ibid. 18. 30 Cf. I. M. Bochenski, Ancient Formal Logic, table after p. 62. 31 Aristotelis, Opera, Berolini 1831, 30a17-20.