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202 KAREL HUBKA to 5, where Valerianus' modes are being compared to the so-called Aristotelian ones (54-65) 2 • 2. « Necessario/impossibile » used as a sign for the universality of the major premise 2.1. Syllogismus with singular terms Let us pursue Valerianus' own account of how he came to exactly six modes arranged by couples into three « differentiae ». He gives their patterns as follows: (1) « A est B. (minor) B est C. (major) Ergo A est C. (2) A est B. (minor) B non est C. (major) Ergo A non est C. (3) A non est B. (minor) C est B. (major) Ergo A non est C ». The way how he develops his three « differentiae » 3 is abbreviated in the following diagram: conclusio - diff. (1), (2) A minor extremitas _____...,A~-----.. '\ praemissa -~- mmor ma10r B medium C maior extremitas r---L--, ~c < +B< A -C -B diff. (1) + affirmat-a/-um negat-a/-um diff. (2) C c"-- L--y---1 ~+ B diff. (3) conclusio - diff. (3) 2 Of the remaining tracts the fifth, « Materia syllogismi », deals with the traditional terminology of the Scholastic logic as far as « terminus » is concerned. The six tract, « Syllogismus demonstrativus », specifies the functioning of his syllogistic with respect to his concept of « praedicamenta », as outlined in chapter 6 of the preceding tract. Both tracts are important as a link between Valerianus' formal syllogistic and his metaphysics. 3 « Syllogismorum autem perfectorum non sunt nisi tres differentiae, quas sic expono. Posita minore extremitate, medium vel affirmatur vel negatur de ilia. Si medium affirmatur de minore extremitate, necessario maior extremitas vel affirmatur vel negatur de medio. Hine vero resultant duae differentiae syllogismorum perfectorum: 1) una est de maiore extremitate affirmata de medio affirmato, 2) altera differentia est de maiore extremitate