Book I chapter 5

Whenever the same thing belongs to all of one subject, and to none of another, or to all of each subject or to none of either, I call such a figure the second; by middle term in it I mean that which is predicated of both subjects, by extremes the terms of which this is said, by major extreme that which lies near the middle, by minor¹ that which is further away from the middle. The middle term stands outside the extremes, and is first in position. A syllogism² cannot be perfect anyhow in this figure, but it may be valid³ whether the terms are related universally or not.

If then the terms are related universally a syllogism will be possible, whenever the middle belongs to all of one subject and to none of another (it does not matter which has the negative relation), but in no other way. Let M be predicated of no N, but of all O. Since, then, the negative relation is convertible⁴, N will belong to no M: but M was assumed to belong to all O: consequently N will belong to no O. This has already been proved. Again if M belongs to all N, but to no O, then N will belong to no O. For if M belongs to no O, O belongs to no M: but M (as was said) belongs to all N: O then will belong to no N: for the first figure has again been formed. But since the negative relation is convertible, N will belong to no O. Thus it will be the same syllogism that proves both conclusions.

It is possible to prove these results also by reductio ad impossibile.

It is clear then that a syllogism is formed when the terms are so related, but not a perfect syllogism; for necessity is not perfectly⁵ established merely from the original premisses; others also are needed.

But if M is predicated of every N and O, there cannot be a syllogism. Terms to illustrate⁶ a positive relation between the extremes are substance, animal, man; a negative relation, substance, animal, number-substance being the middle term.

Nor is a syllogism possible when M is predicated neither of any N nor of any O. Terms to illustrate a positive relation are line, animal, man: a negative relation, line, animal, stone.

It is clear then that if a syllogism is formed when the terms are universally related, the terms must be related as we stated at the outset: for if they are otherwise related no necessary consequence follows.

If the middle term is related universally to one of the extremes, a particular negative syllogism must result whenever the middle term is related universally to the major whether positively⁷ or negatively, and particularly to the minor and in a manner opposite to that of the universal statement: by ‘an opposite manner’ I mean, if the universal statement is negative, the particular is affirmative: if the universal is affirmative, the particular is negative. For if M belongs to no N, but to some O, it is necessary that N does not belong to some O. For since the negative statement is convertible, N will belong to no M: but M was admitted to belong to some O: therefore N will not belong to some O: for the result is reached by means of the first figure. Again if M belongs to all N, but not to some O, it is necessary that N does not belong to some O: for if N belongs to all O, and M is predicated also of all N, M must belong to all O: but we assumed that M does not belong to some O. And if M belongs to all N but not to all O, we shall conclude that N does not belong to all O: the proof is the same as the above. But if M is predicated of all O, but not of all N, there will be no syllogism. Take the terms animal, substance, raven⁸; animal, white, raven. Nor will there be a conclusion when M is predicated of no O, but of some N. Terms to illustrate a positive relation between the extremes are animal, substance, unit: a negative relation, animal, substance, science.

If then the universal statement is opposed to the particular, we have stated when a syllogism will be possible and when not: but if the premisses are similar in form, I mean both negative or both affirmative, a syllogism will not be possible anyhow. First let them be negative, and let the major premiss be universal, e.g. let M belong to no N, and not to some O. It is possible then for N to belong either to all O or to no O. Terms to illustrate the negative relation are black, snow, animal. But it is not possible to find terms of which the extremes are related positively and universally, if M belongs to some O, and does not belong to some O. For if N belonged to all O, but M to no N, then M would belong to no O: but we assumed that it belongs to some O. In this way then it is not admissible to take terms: our point must be proved from the indefinite nature of the particular statement. For since it is true that M does not belong to some O, even if it belongs to no O, and since if it belongs to no O a syllogism is (as we have seen) not possible, clearly it will not be possible now either.

Again let the premisses be affirmative, and let the major premiss as before be universal, e.g. let M belong to all N and to some O. It is possible then for N to belong to all O or to no O. Terms to illustrate the negative relation are white, swan, stone. But it is not possible to take terms to illustrate the universal affirmative relation, for the reason already stated: the point must be proved from the indefinite nature of the particular statement. But if the minor premiss is universal, and M belongs to no O, and not to some N, it is possible for N to belong either to all O or to no O. Terms for the positive relation are white, animal, raven: for the negative relation, white, stone, raven. If the premisses are affirmative, terms for the negative relation are white, animal, snow; for the positive relation, white, animal, swan. Evidently then, whenever the premisses are similar in form, and one is universal, the other particular, a syllogism can, not be formed anyhow. Nor is one possible if the middle term belongs to some of each of the extremes, or does not belong to some of either, or belongs to some of the one, not to some of the other, or belongs to neither universally, or is related to them indefinitely. Common terms for all the above are white, animal, man: white, animal, inanimate. It is clear then from what has been said that if the terms are related to one another in the way stated, a syllogism results of necessity; and if there is a syllogism, the terms must be so related. But it is evident also that all the syllogisms in this figure are imperfect: for all are made perfect by certain supplementary⁹ statements, which either are contained in the terms of necessity or are assumed as hypotheses, i.e. when we prove per impossibile. And it is evident that an affirmative conclusion is not attained¹⁰ by means of this figure, but all are negative, whether universal or particular.

1 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。

2 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。

3 valid   

adj.有确实根据的；有效的；正当的，合法的

参考例句：

• His claim to own the house is valid.他主张对此屋的所有权有效。
• Do you have valid reasons for your absence?你的缺席有正当理由吗？

4 convertible   

adj.可改变的，可交换，同意义的；n.有活动摺篷的汽车

参考例句：

• The convertible sofa means that the apartment can sleep four.有了这张折叠沙发，公寓里可以睡下4个人。
• That new white convertible is totally awesome.那辆新的白色折篷汽车简直棒极了。

5 perfectly   

adv.完美地，无可非议地，彻底地

参考例句：

• The witnesses were each perfectly certain of what they said.证人们个个对自己所说的话十分肯定。
• Everything that we're doing is all perfectly above board.我们做的每件事情都是光明正大的。

6 illustrate   

v.举例说明，阐明；图解，加插图

参考例句：

• The company's bank statements illustrate its success.这家公司的银行报表说明了它的成功。
• This diagram will illustrate what I mean.这个图表可说明我的意思。

7 positively   

adv.明确地，断然，坚决地；实在，确实

参考例句：

• She was positively glowing with happiness.她满脸幸福。
• The weather was positively poisonous.这天气着实讨厌。

8 raven   

n.渡鸟，乌鸦；adj.乌亮的

参考例句：

• We know the raven will never leave the man's room.我们知道了乌鸦再也不会离开那个男人的房间。
• Her charming face was framed with raven hair.她迷人的脸上垂落着乌亮的黑发。

9 supplementary   

adj.补充的，附加的

参考例句：

• There is a supplementary water supply in case the rain supply fails.万一主水源断了，我们另外有供水的地方。
• A supplementary volume has been published containing the index.附有索引的增补卷已经出版。

10 attained   

（通常经过努力）实现( attain的过去式和过去分词 )； 达到； 获得； 达到（某年龄、水平、状况）

参考例句：

• She has attained the degree of Master of Arts. 她已获得文学硕士学位。
• Lu Hsun attained a high position in the republic of letters. 鲁迅在文坛上获得崇高的地位。