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206 KAREL HUBKA (3) Camestres/Baroco 14 • We must, however, account for two more facts. 1) Why was his choice exactly the six modes in question and not some other? 2) Why did he express the universality of the major premise by means of « necessario/impossibile », leaving the univer– sality of the affirmative as well as of negative minor premise (and of conclusion) without any sign whatsoever? We shall see that the answer to the second question follows from the answer to the first. In the traditional aeio-notation Valerianus modes (11) to (32) admit of being abbreviated as follows (the letters A, B, C are used in conformity with Valerianus, the major premise always preceding the minor): ( 11/12) B a C A a/i B A a/i C ( 21/22) B e C A a/i B A e/o C ( 31/32) C a B Ae/oB A e/o C Now, if all 19 Aristotelian modes were given the above notation, then it is immediately apparent, apart from Cesare/Festino which by the simple conversion of their major premise yield the differ– ence (2), that there do not exist any other couples of modes except the above three stated by Valerianus in which the major premise would remain the same, while the universality/particularity of the conclusion were determined by the universality/particularity of the minor premise respectively 15 • The key function of the major universal premise in his three « differentiae » 16 may now seem to have been sufficient motive for Valerianus to express it· by means of adding « necessario/impossi– bile » in its formulation. But, what really does count is that Valerianus himself identifies universality with necessity in the following passage: Ego vero non distinguo modos syllogismorum penes differentem materiam, circa quarn sunt, sed penes id quod influit in ipsarn illatio– nem. Quod enirn minor extrernitas sit universalis vel particularis, id 14 Speaking about Aristotle's reduction of Camestres and Baroco to Celarent and Barbara he maintains: « iis enim reductionibus tollit et damnat [scil. Aristotle] omnem illationem de medio negato, cum tamen homini sit naturale et necessarium argumentari seu syllogizare ex medio negato de praesupposita minori extremitate scibili, quapropter hi duo modi sunt naturales, sunt necessarii, nullo modo reducendi ad meliores » (Opus philo– sophicum, pars secunda, 61). 1s More on the Aristotelian assertoric modes as compared with those of Valerianus see Section S. 16 Cf. the corresponding rule in the medieval Aristotelian tradition: « opportet alteram premissam esse universalem » (P. Hispanus, op. cit. 45).