BCCCAP00000000000000000000668

204 KAREL HUBKA Two things are apparent from the comparison of the two columns: 1) Among the so-called Aristotelian syllogisms (12') and (22') are not, in the strict sense of the word, Aristotelian, since they contain the singular term, « Petrus». 2) As far as Valerianus' syllogisms are concerned, there is no sign for the quantity of both the minor premise and the conclusion in the inodes with the universal minor premise, i.e: in (11), (21) and (31), while « necessario/impossibile » stands for « omnis/nullus » in the major premise of all of his exam– ples, i.e. (11) to (32). We shall first briefly discuss 1) and then come back to 2), which is the main topic of this article. Throughout the history of. logic the syllogisms with singular terms stand in close relation to the expository syllogism ( « syllo– gismus expositorius »). The Latin « expositorius » and « per exposi– tionem » are translations of the Greek « -.Ip h&foltou », or rather « -.Ip ix.&fo&ocL 1t0Le°i:v -.~v (ht6~eL~Lv» 5, which was one way of Aristotle's « perfectioning » an « he"A~c; » syllogism. A most explicit form of the proof by « ex.&ecnc; » is to be found in chapter 4 of Analytica Priora I, where it is used for the proof of Darapti 6 • Different interpretations of the verb « ix.&fo&ocL » can be ventured. It depends, principally, on the status and function of this kind of proof required for the validity test of a syllogism. The Latin « per expositionem » seems to suggest that « ex.&ecrLc; » means « some kind of explanation » of the syllogism in question by means of an auxiliary syllogism with singular terms, whereas Bochenski 7 seems to accentuate the « taking out » of some part from the extension of the middle term, thus understanding the Greek « ix.&fo&ocL » in its original meaning (ex.--.tS'Y)µL ). There has always been some uncertainty as to whether the part taken out from the middle term should be considered « a singular term given by perception (-.L -.wv {m' (l(.tcr&'Y)crLv 1tm-.6v't(J)V) », which was the stand– point of e.g. Alexander Afrodisiensis, or whether it should be con– sidered a universal term of the same order as the remaining terms of Darapti, this being maintained by Lukasiewicz 8 • For our purpose it is not necessary to give a detailed survey of the whole development of expository syllogisms and syllogisms with 5 Aristotelis, Opera, ex rec. I. Bekkeri, Berolini 1931, 28a23. ' Ibid. 28a24-28. 7 I. M. Bochenski, Ancient Formal Logic, Amsterdam 1951, 47. 8 J. Lukasiewicz, Aristotelevskaja sillogistika· s tocki zrenija sovremennoj formal'noj logiki, transl. N. I. Stjazkin - A. L. Subbotin, Moskva 1959, 109-111 [English: Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, Oxford 2 1957]. He opposes the view of Alexander and gives a neat formal proof of Darapti with the universal exposed term.