アリストテレスの完全な推論式とは何か

抄録

Aristotle regards four syllogisms of the first-figure as not only valid but also perfect (Prior Analytics. I.4). In order to prove the ten syllogisms of the second-figure and the third-figure, he makes use of the four perfect syllogisms and the rules of conversion (Prior Analytics. I.5-6). He also gives the definition of a perfect syllogism in Prior Analytics I.1 as follows: A syllogism is perfect if it needs nothing beyond the things posited for the necessity to be evident. These facts seem to suggest that he takes the validity of perfect syllogisms to be self-evident and to have no need of proof.

However, what features of perfect syllogisms ensure that they are self-evident? Aristotle uses the dictum de omni et de nullo to explain the validity of perfect syllogisms (I.4). This dictum explains briefly the meaning of universal propositions (the major premises of perfect syllogisms). Modern interpretation of the is divided between orthodox and heterodox versions. The orthodox version views the as saying that the truth of universal propositions is determined by the extensional relations between the argument-terms. The heterodox version views the as saying that the truth of universal propositions is determined by the relations between the argumentterms and their subclasses.

In this paper, I investigate another interpretation of the dictum, which makes the perfect syllogism self-evident. I attempt to give a new view of the perfect syllogism, especially of the major premises. The universal propositions (major premises) should be understood by the accompanying relations between terms.

Through investigation of the perfect syllogism, it may become apparent that there is an affinity with some techniques and methods in Topics. Many concepts which are found in Topics are more developed in Prior Analytics. I argue that the perfect syllogism was established in Prior Analytics against the background of the thinking found in Topics.