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212 KAREL HUBKA since it represents his « differentia » (31) itself. Now, it is well-known that inside the Aristotelian system neither Baroco nor Bocardo are susceptible of the direct reduction and for that matter of the refor– mulation in the shape of any mode belonging to the first Aristotelian figure, i.e. Valerianus' modes (11), (12), (21), (22). Their validity can only be proved indirectly, by means of « reductio ad absurdum » 35 . Valerianus' choice of Baroco, i.e. « differentia » (32), as a kind of an « undemonstrable » of his system 36 spares him the trouble of such a reformulation in this case only. But how does he treat Bo– cardo? It is being reformulated as « differentia » (22) in the following manner: « Id, quod est animal, de quo negatur rationale, impossibile est, sit rationale. (major) Quoddam corpus est animal, de quo negatur rationale. (minor) Ergo quoddam corpus non est rationale» 37 • For the sake of brevity let us write the extension of the expression «animal (B), de quo negatur (-) rationale (C)», as «B-C». Thus using the traditional notation we obtain: (B-C) e C Ai (B-C) AoC (major) (minor) « differentia » (22) Focusing the attention on the major premise it is to be seen that the proposition « (B - C) e C » is a necessary proposition of the same order as Valerianus' example « 2 + 3 = 5 ». We leave the ques– tion open, whether this kind of necessary propositions is to be described as the Kantian « synthetisches Urteil a priori» or as an analytical proposition in the sense of the logical positivism. From the historical point of view it is important that according to Vale– rianus' doctrine of « aeternae veritates » the propositions: « (B - C) e C », « 2 + 3 = 5 » appear to have the same status as the propo– sition « Animal est substantia » 38 • 35 Cf. Petrus Hispanus, op. cit. 49-51. 36 Cf. note 14. 37 Opus philosophicum, 64. Cf. Valerianus' example of the Aristotelian Bocardo, « Quoddam animal non est rationale (major). Omne animal est corpus (minor). Ergo quad– dam corpus non est rationale » (ibid. 64). 38 Cf. Section 2.2. The first and second example suggest the interpretation of the third example as « Animal ex definitione est substantia ». If this were so, Valerianus' syllogistic would be related with Theophrastus' concept of the Aristotelian modal syllogisms. Cf. I. M. Bochenski, A history of Formal Logic, 102s, and S. McCall, Aristotle's Modal Syllogisms, Amsterdam 1963, 15-18.