Book I chapter 7

It is evident also that in all the figures, whenever a proper syllogism¹ does not result, if both the terms are affirmative or negative nothing necessary follows at all, but if one is affirmative, the other negative, and if the negative is stated universally, a syllogism always results relating the minor² to the major term, e.g. if A belongs to all or some B, and B belongs to no C: for if the premisses are converted it is necessary that C does not belong to some A. Similarly also in the other figures: a syllogism always results by means of conversion³. It is evident also that the substitution of an indefinite for a particular affirmative will effect the same syllogism in all the figures.

It is clear too that all the imperfect syllogisms are made perfect by means of the first figure. For all are brought to a conclusion either ostensively or per impossibile. In both ways the first figure is formed: if they are made perfect ostensively, because (as we saw) all are brought to a conclusion by means of conversion, and conversion produces the first figure: if they are proved per impossibile, because on the assumption of the false statement the syllogism comes about by means of the first figure, e.g. in the last figure, if A and B belong to all C, it follows that A belongs to some B: for if A belonged to no B, and B belongs to all C, A would belong to no C: but (as we stated) it belongs to all C. Similarly also with the rest.

It is possible also to reduce all syllogisms to the universal syllogisms in the first figure. Those in the second figure are clearly made perfect by these, though not all in the same way; the universal syllogisms are made perfect by converting the negative premiss, each of the particular syllogisms by reductio ad impossibile. In the first figure particular syllogisms are indeed made perfect by themselves, but it is possible also to prove them by means of the second figure, reducing them ad impossibile, e.g. if A belongs to all B, and B to some C, it follows that A belongs to some C. For if it belonged to no C, and belongs to all B, then B will belong to no C: this we know by means of the second figure. Similarly also demonstration⁴ will be possible in the case of the negative. For if A belongs to no B, and B belongs to some C, A will not belong to some C: for if it belonged to all C, and belongs to no B, then B will belong to no C: and this (as we saw) is the middle figure. Consequently, since all syllogisms in the middle figure can be reduced to universal syllogisms in the first figure, and since particular syllogisms in the first figure can be reduced to syllogisms in the middle figure, it is clear that particular syllogisms can be reduced to universal syllogisms in the first figure. Syllogisms in the third figure, if the terms are universal, are directly made perfect by means of those syllogisms; but, when one of the premisses is particular, by means of the particular syllogisms in the first figure: and these (we have seen) may be reduced to the universal syllogisms in the first figure: consequently also the particular syllogisms in the third figure may be so reduced. It is clear then that all syllogisms may be reduced to the universal syllogisms in the first figure.

We have stated then how syllogisms which prove that something belongs or does not belong to something else are constituted, both how syllogisms of the same figure are constituted in themselves, and how syllogisms of different figures are related to one another.

1 syllogism   

n.演绎法，三段论法

参考例句：

• The ramifications or the mystery of a syllogism can become a weariness and a bore.三段论证法的分歧或者神秘会变成一种无聊、一种麻烦。
• The unexpected bursts forth from the syllogism.三段论里常出岔子。

2 minor   

adj.较小(少)的，较次要的；n.辅修学科；vi.辅修

参考例句：

• The young actor was given a minor part in the new play.年轻的男演员在这出新戏里被分派担任一个小角色。
• I gave him a minor share of my wealth.我把小部分财产给了他。

3 conversion   

n.转化，转换，转变

参考例句：

• He underwent quite a conversion.他彻底变了。
• Waste conversion is a part of the production process.废物处理是生产过程的一个组成部分。

4 demonstration   

n.表明，示范，论证，示威

参考例句：

• His new book is a demonstration of his patriotism.他写的新书是他的爱国精神的证明。
• He gave a demonstration of the new technique then and there.他当场表演了这种新的操作方法。