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THE SYLLOGISTIC OF VALERIANUS MAGNI 211 sumption, however, that the scope of the second « necessario » is limited to the conclusion alone, he would have to write also « Ergo lapidem impossibile est esse hominem » instead of « Ergo lapis non est homo» (31), whereas Aristotle's Camestres - NYY admits only the assertoric conclusion. Therefore the only plausible solution is to consider the second occurrence of « necessario » as referring to the inference as a whole. To put it more exactly, the second « necessario » means the same as « follows logically from the premises ». Thus only as far as « fol– lows logically» is an intended interpretation of the strict implication, which in its turn is definable in modal terms 32 , the second « neces– sario » can be conceived of as a modal particle expressing logical necessity: (p.q) i-3 r df N ([p.q] ::J r) p, q ... ' conclusion r ... conclusion 5. Valerianus' reformulation of the Aristotelian Bocardo and his concept of necessity Assuming that Valerianus' syllogistic is an adaptation of certain Aristotelian assertoric modes, let us examine the way Valerianus re– formulates each Aristotelian « modus imperfectus » as some of his « six modi perfectissimi ». Thereby we shall be able to clarify still further his concept of necessity 33 • Valerianus' reformulation of any Aristotelian « modus imper– fectus » which is directly reducible to Barbara, Darii, Cela:-ent, Ferio, i.e. to Valerianus' « differentia » (11), (12), (21), (22) respectively is easy to follow 34 • Camestres, though admitting of being reformulated as Celarent, i.e. Valerianus' « differentia » (21), remains :mchanged, 32 Cf. G. E. Hughes - M. J. Cresswell, An Introduction to Modal Logic. London 1968, 6, 26s, 335. Valerianus' use of the second « necessario » appears to be the same as Aristotle's use of &;vcl:yx"f/ in the contexts where it describes the validity of an assertoric syllogism. For Aristotle's &;vci:yx"f/ used in this manner see I. M. Bochenski, A History of Formal Logic, 69, 81. J. Lukasiewicz (op. cit. 45-47, 138) has tried to interpret it as an universal quantifier over the term-variables, which just as Aristotle's avci:yX"f/ « may be omitted when it stands at the head of a true formula ». Cf. also the discussion of the definition of valid consequence (ea. 1550-1650) surveyed by E. J. Ashworth, ap. cit. 122 ss. 33 A part of the exercise Valerianus has prepared for Theophilus, the fi~tious disciple– character of his cursus, is to be spent by « revocare ad nostras [scil. Valeriani] tres differentias syllogismorum novemdecim modos syllogizandi traditos ab Aristotele ac distri– butos in tres figuras » (Opus philosophicum, 53s). 34 Reformulation of Aristotelian Disamis (P. Hispanus, op. cit. 50) as Valerianus' « differentia » (12), i.e. Darii (Opus philosophicum, 63), may serve as a representative example.