Chapter 17

The objection that ‘this is not the reason why the result is false’, which we frequently make in argument, is made primarily in the case of a reductio ad impossibile, to rebut¹ the proposition which was being proved by the reduction. For unless a man has contradicted this proposition he will not say, ‘False cause’, but urge that something false has been assumed in the earlier parts of the argument; nor will he use the formula in the case of an ostensive proof; for here what one denies is not assumed as a premiss. Further when anything is refuted ostensively by the terms ABC, it cannot be objected that the syllogism² does not depend on the assumption laid down. For we use the expression ‘false cause’, when the syllogism is concluded in spite of the refutation of this position; but that is not possible in ostensive proofs: since if an assumption is refuted, a syllogism can no longer be drawn³ in reference to it. It is clear then that the expression ‘false cause’ can only be used in the case of a reductio ad impossibile, and when the original hypothesis is so related to the impossible conclusion, that the conclusion results indifferently whether the hypothesis is made or not. The most obvious case of the irrelevance⁴ of an assumption to a conclusion which is false is when a syllogism drawn from middle terms to an impossible conclusion is independent of the hypothesis, as we have explained in the Topics. For to put that which is not the cause as the cause, is just this: e.g. if a man, wishing to prove that the diagonal of the square is incommensurate with the side, should try to prove Zeno’s theorem that motion is impossible, and so establish a reductio ad impossibile: for Zeno’s false theorem has no connexion at all with the original assumption. Another case is where the impossible conclusion is connected with the hypothesis, but does not result from it. This may happen whether one traces the connexion upwards⁵ or downwards⁶, e.g. if it is laid down that A belongs to B, B to C, and C to D, and it should be false that B belongs to D: for if we eliminated A and assumed all the same that B belongs to C and C to D, the false conclusion would not depend on the original hypothesis. Or again trace the connexion upwards; e.g. suppose that A belongs to B, E to A and F to E, it being false that F belongs to A. In this way too the impossible conclusion would result, though the original hypothesis were eliminated. But the impossible conclusion ought to be connected with the original terms: in this way it will depend on the hypothesis, e.g. when one traces the connexion downwards, the impossible conclusion must be connected with that term which is predicate in the hypothesis: for if it is impossible that A should belong to D, the false conclusion will no longer result after A has been eliminated. If one traces the connexion upwards, the impossible conclusion must be connected with that term which is subject in the hypothesis: for if it is impossible that F should belong to B, the impossible conclusion will disappear if B is eliminated. Similarly when the syllogisms are negative.

It is clear then that when the impossibility is not related to the original terms, the false conclusion does not result on account of the assumption. Or perhaps even so it may sometimes be independent. For if it were laid down that A belongs not to B but to K, and that K belongs to C and C to D, the impossible conclusion would still stand. Similarly if one takes the terms in an ascending⁷ series. Consequently since the impossibility results whether the first assumption is suppressed or not, it would appear to be independent of that assumption. Or perhaps we ought not to understand the statement that the false conclusion results independently of the assumption, in the sense that if something else were supposed the impossibility would result; but rather we mean that when the first assumption is eliminated, the same impossibility results through the remaining premisses; since it is not perhaps absurd that the same false result should follow from several hypotheses, e.g. that parallels meet, both on the assumption that the interior angle is greater than the exterior⁸ and on the assumption that a triangle contains more than two right angles.

1 rebut   

v.辩驳，驳回

参考例句：

• He attempted to rebut the assertions made by the prosecution witness.他试图反驳控方证人所作的断言。
• This open letter is to rebut the argument of abstractionism.这封公开信是反驳抽象派论点的。

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 drawn   

v.拖，拉，拔出；adj.憔悴的，紧张的

参考例句：

• All the characters in the story are drawn from life.故事中的所有人物都取材于生活。
• Her gaze was drawn irresistibly to the scene outside.她的目光禁不住被外面的风景所吸引。

4 irrelevance   

n.无关紧要；不相关；不相关的事物

参考例句：

• the irrelevance of the curriculum to children's daily life 课程与孩子们日常生活的脱节
• A President who identifies leadership with public opinion polls dooms himself to irrelevance. 一位总统如果把他的领导和民意测验投票结果等同起来，那么他注定将成为一个可有可无的人物。 来自辞典例句

5 upwards   

adv.向上，在更高处...以上

参考例句：

• The trend of prices is still upwards.物价的趋向是仍在上涨。
• The smoke rose straight upwards.烟一直向上升。

6 downwards   

adj./adv.向下的（地），下行的（地）

参考例句：

• He lay face downwards on his bed.他脸向下伏在床上。
• As the river flows downwards,it widens.这条河愈到下游愈宽。

7 ascending   

adj.上升的，向上的

参考例句：

• Now draw or trace ten dinosaurs in ascending order of size.现在按照体型由小到大的顺序画出或是临摹出10只恐龙。

8 exterior   

adj.外部的，外在的；表面的

参考例句：

• The seed has a hard exterior covering.这种子外壳很硬。
• We are painting the exterior wall of the house.我们正在给房子的外墙涂漆。