Chapter 16

To beg and assume the original question is a species of failure to demonstrate the problem proposed; but this happens in many ways. A man may not reason syllogistically¹ at all, or he may argue from premisses which are less known or equally unknown, or he may establish the antecedent by means of its consequents; for demonstration² proceeds from what is more certain and is prior. Now begging the question is none of these: but since we get to know some things naturally through themselves, and other things by means of something else (the first principles through themselves, what is subordinate to them through something else), whenever a man tries to prove what is not self-evident by means of itself, then he begs the original question. This may be done by assuming what is in question at once; it is also possible to make a transition to other things which would naturally be proved through the thesis proposed, and demonstrate it through them, e.g. if A should be proved through B, and B through C, though it was natural that C should be proved through A: for it turns out that those who reason thus are proving A by means of itself. This is what those persons do who suppose that they are constructing parallel straight lines: for they fail to see that they are assuming facts which it is impossible to demonstrate unless the parallels exist. So it turns out that those who reason thus merely say a particular thing is, if it is: in this way everything will be self-evident. But that is impossible.

If then it is uncertain whether A belongs to C, and also whether A belongs to B, and if one should assume that A does belong to B, it is not yet clear whether he begs the original question, but it is evident that he is not demonstrating: for what is as uncertain as the question to be answered cannot be a principle of a demonstration. If however B is so related to C that they are identical, or if they are plainly convertible³, or the one belongs to the other, the original question is begged. For one might equally well prove that A belongs to B through those terms if they are convertible. But if they are not convertible, it is the fact that they are not that prevents such a demonstration, not the method of demonstrating. But if one were to make the conversion⁴, then he would be doing what we have described and effecting a reciprocal proof with three propositions.

Similarly if he should assume that B belongs to C, this being as uncertain as the question whether A belongs to C, the question is not yet begged, but no demonstration is made. If however A and B are identical either because they are convertible or because A follows B, then the question is begged for the same reason as before. For we have explained the meaning of begging the question, viz. proving that which is not self-evident by means of itself.

If then begging the question is proving what is not self-evident by means of itself, in other words failing to prove when the failure is due to the thesis to be proved and the premiss through which it is proved being equally uncertain, either because predicates which are identical belong to the same subject, or because the same predicate belongs to subjects which are identical, the question may be begged in the middle and third figures in both ways, though, if the syllogism⁵ is affirmative, only in the third and first figures. If the syllogism is negative, the question is begged when identical predicates are denied of the same subject; and both premisses do not beg the question indifferently (in a similar way the question may be begged in the middle figure), because the terms in negative syllogisms are not convertible. In scientific demonstrations⁶ the question is begged when the terms are really related in the manner described, in dialectical arguments when they are according to common opinion so related.

1 syllogistically   

adv.三段论法式地，演绎式地

参考例句：

2 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。

3 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。

4 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。

5 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。

6 demonstrations   

证明( demonstration的名词复数 )； 表明； 表达； 游行示威

参考例句：

• Lectures will be interspersed with practical demonstrations. 讲课中将不时插入实际示范。
• The new military government has banned strikes and demonstrations. 新的军人政府禁止罢工和示威活动。