chapter 13

Logical sequences follow in due course when we have arranged the propositions thus. From the proposition ‘it may be’ it follows that it is contingent¹, and the relation is reciprocal. It follows also that it is not impossible and not necessary.

From the proposition ‘it may not be’ or ‘it is contingent that it should not be’ it follows that it is not necessary that it should not be and that it is not impossible that it should not be. From the proposition ‘it cannot be’ or ‘it is not contingent’ it follows that it is necessary that it should not be and that it is impossible that it should be. From the proposition ‘it cannot not be’ or ‘it is not contingent that it should not be’ it follows that it is necessary that it should be and that it is impossible that it should not be.

Let us consider these statements by the help of a table:
A.     B.
It may be.     It cannot be.
It is contingent.     It is not contingent.
It is not impossible that it should be.     It is impossible that it should be.
It is not necessary that it should be.     It is necessary that it should not be.
C.     D.
It may not be.     It cannot not be.
It is contingent that it should not be.     It is not contingent that it should not be.
It is not impossible that it should not be.     It is impossible that it should not be.
It is not necessary that it should not be.     It is necessary that it should be.

Now the propositions ‘it is impossible that it should be’ and ‘it is not impossible that it should be’ are consequent upon the propositions ‘it may be’, ‘it is contingent’, and ‘it cannot be’, ‘it is not contingent’, the contradictories² upon the contradictories. But there is inversion³. The negative of the proposition ‘it is impossible’ is consequent upon the proposition ‘it may be’ and the corresponding positive in the first case upon the negative in the second. For ‘it is impossible’ is a positive proposition and ‘it is not impossible’ is negative.

We must investigate the relation subsisting⁴ between these propositions and those which predicate necessity. That there is a distinction is clear. In this case, contrary propositions follow respectively from contradictory⁵ propositions, and the contradictory propositions belong to separate sequences. For the proposition ‘it is not necessary that it should be’ is not the negative of ‘it is necessary that it should not be’, for both these propositions may be true of the same subject; for when it is necessary that a thing should not be, it is not necessary that it should be. The reason why the propositions predicating necessity do not follow in the same kind of sequence as the rest, lies in the fact that the proposition ‘it is impossible’ is equivalent, when used with a contrary subject, to the proposition ‘it is necessary’. For when it is impossible that a thing should be, it is necessary, not that it should be, but that it should not be, and when it is impossible that a thing should not be, it is necessary that it should be. Thus, if the propositions predicating impossibility or non-impossibility follow without change of subject from those predicating possibility or non-possibility, those predicating necessity must follow with the contrary subject; for the propositions ‘it is impossible’ and ‘it is necessary’ are not equivalent, but, as has been said, inversely⁶ connected.

Yet perhaps it is impossible that the contradictory propositions predicating necessity should be thus arranged. For when it is necessary that a thing should be, it is possible that it should be. (For if not, the opposite follows, since one or the other must follow; so, if it is not possible, it is impossible, and it is thus impossible that a thing should be, which must necessarily be; which is absurd.)

Yet from the proposition ‘it may be’ it follows that it is not impossible, and from that it follows that it is not necessary; it comes about therefore that the thing which must necessarily be need not be; which is absurd. But again, the proposition ‘it is necessary that it should be’ does not follow from the proposition ‘it may be’, nor does the proposition ‘it is necessary that it should not be’. For the proposition ‘it may be’ implies a twofold possibility, while, if either of the two former propositions is true, the twofold possibility vanishes. For if a thing may be, it may also not be, but if it is necessary that it should be or that it should not be, one of the two alternatives will be excluded. It remains⁷, therefore, that the proposition ‘it is not necessary that it should not be’ follows from the proposition ‘it may be’. For this is true also of that which must necessarily be.

Moreover the proposition ‘it is not necessary that it should not be’ is the contradictory of that which follows from the proposition ‘it cannot be’; for ‘it cannot be’ is followed by ‘it is impossible that it should be’ and by ‘it is necessary that it should not be’, and the contradictory of this is the proposition ‘it is not necessary that it should not be’. Thus in this case also contradictory propositions follow contradictory in the way indicated, and no logical impossibilities occur when they are thus arranged.

It may be questioned whether the proposition ‘it may be’ follows from the proposition ‘it is necessary that it should be’. If not, the contradictory must follow, namely that it cannot be, or, if a man should maintain that this is not the contradictory, then the proposition ‘it may not be’.

Now both of these are false of that which necessarily is. At the same time, it is thought that if a thing may be cut it may also not be cut, if a thing may be it may also not be, and thus it would follow that a thing which must necessarily be may possibly not be; which is false. It is evident, then, that it is not always the case that that which may be or may walk possesses also a potentiality in the other direction. There are exceptions. In the first place we must except those things which possess a potentiality not in accordance with a rational principle, as fire possesses the potentiality of giving out heat, that is, an irrational⁸ capacity. Those potentialities which involve a rational principle are potentialities of more than one result, that is, of contrary results; those that are irrational are not always thus constituted. As I have said, fire cannot both heat and not heat, neither has anything that is always actual any twofold potentiality. Yet some even of those potentialities which are irrational admit of opposite results. However, thus much has been said to emphasize the truth that it is not every potentiality which admits of opposite results, even where the word is used always in the same sense.

But in some cases the word is used equivocally. For the term ‘possible’ is ambiguous, being used in the one case with reference to facts, to that which is actualized, as when a man is said to find walking possible because he is actually walking, and generally when a capacity is predicated because it is actually realized; in the other case, with reference to a state in which realization⁹ is conditionally¹⁰ practicable, as when a man is said to find walking possible because under certain conditions he would walk. This last sort of potentiality belongs only to that which can be in motion, the former can exist also in the case of that which has not this power. Both of that which is walking and is actual, and of that which has the capacity though not necessarily realized, it is true to say that it is not impossible that it should walk (or, in the other case, that it should be), but while we cannot predicate this latter kind of potentiality of that which is necessary in the unqualified sense of the word, we can predicate the former.

Our conclusion, then, is this: that since the universal is consequent upon the particular, that which is necessary is also possible, though not in every sense in which the word may be used.

We may perhaps state that necessity and its absence are the initial principles of existence and non-existence, and that all else must be regarded as posterior to these.

It is plain from what has been said that that which is of necessity is actual. Thus, if that which is eternal is prior, actuality also is prior to potentiality. Some things are actualities without potentiality, namely, the primary substances; a second class consists of those things which are actual but also potential, whose actuality is in nature prior to their potentiality, though posterior in time; a third class comprises those things which are never actualized, but are pure potentialities.

1 contingent   

adj.视条件而定的；n.一组，代表团，分遣队

参考例句：

• The contingent marched in the direction of the Western Hills.队伍朝西山的方向前进。
• Whether or not we arrive on time is contingent on the weather.我们是否按时到达要视天气情况而定。

2 contradictories   

n.矛盾的，抵触的( contradictory的名词复数 )

参考例句：

3 inversion   

n.反向，倒转，倒置

参考例句：

• But sometimes there is an unusual weather condition called a temperature inversion.但有时会有一种被称作“温度逆增”的不平常的天气状态。
• And finally,we made a discussion on the problems in the cooperative inversion.最后，对联合反演中存在的问题进行了讨论。

4 subsisting   

v.（靠很少的钱或食物）维持生活，生存下去( subsist的现在分词 )

参考例句：

• Perfect God and perfect man, of a reasonable soul and human subsisting. 衪是完全的神又是完全的人，且有理性的灵魂和人类血肉之躯。 来自互联网
• The benevolence subsisting in her character draws her friends closer to her. 存在于她性格中的仁慈吸引她的朋友们接近她。 来自互联网

5 contradictory   

adj.反驳的，反对的，抗辩的；n.正反对，矛盾对立

参考例句：

• The argument is internally contradictory.论据本身自相矛盾。
• What he said was self-contradictory.他讲话前后不符。

6 inversely   

adj.相反的

参考例句：

• Pressure varies directly with temperature and inversely with volume. 压力随温度成正比例变化，与容积成反比例变化。 来自《简明英汉词典》
• The amount of force needed is inversely proportional to the rigidity of the material. 需要的力度与材料的硬度成反比。 来自《简明英汉词典》

7 remains   

n.剩余物，残留物；遗体，遗迹

参考例句：

• He ate the remains of food hungrily.他狼吞虎咽地吃剩余的食物。
• The remains of the meal were fed to the dog.残羹剩饭喂狗了。

8 irrational   

adj.无理性的，失去理性的

参考例句：

• After taking the drug she became completely irrational.她在吸毒后变得完全失去了理性。
• There are also signs of irrational exuberance among some investors.在某些投资者中是存在非理性繁荣的征象的。

9 realization   

n.实现；认识到，深刻了解

参考例句：

• We shall gladly lend every effort in our power toward its realization.我们将乐意为它的实现而竭尽全力。
• He came to the realization that he would never make a good teacher.他逐渐认识到自己永远不会成为好老师。

10 conditionally   

adv. 有条件地

参考例句：

• We will provide necessary English training to the new employees conditionally. 公司将为员工提供必要的英语培训。
• China should conditionally support and participate in the coordination. 我国对此宜持有条件支持并参与的立场。