Book I chapter 3

Again, privative terms inevitably¹ form one branch of dichotomous division, as we see in the proposed dichotomies. But privative terms in their character of privatives admit of no subdivision. For there can be no specific forms of a negation², of Featherless for instance or of Footless, as there are of Feathered and of Footed. Yet a generic³ differentia must be subdivisible; for otherwise what is there that makes it generic rather than specific? There are to be found generic, that is specifically subdivisible, differentiae; Feathered for instance and Footed. For feathers are divisible into Barbed and Unbarbed, and feet into Manycleft, and Twocleft, like those of animals with bifid hoofs⁴, and Uncleft or Undivided, like those of animals with solid hoofs. Now even with differentiae capable of this specific subdivision it is difficult enough so to make the classification, as that each animal shall be comprehended in some one subdivision and in not more than one; but far more difficult, nay⁵ impossible, is it to do this, if we start with a dichotomy into two contradictories⁶. (Suppose for instance we start with the two contradictories, Feathered and Unfeathered; we shall find that the ant, the glow-worm, and some other animals fall under both divisions.) For each differentia must be presented by some species. There must be some species, therefore, under the privative heading. Now specifically distinct animals cannot present in their essence a common undifferentiated element, but any apparently⁸ common element must really be differentiated⁷. (Bird and Man for instance are both Two-footed, but their two-footedness is diverse and differentiated. So any two sanguineous groups must have some difference in their blood, if their blood is part of their essence.) From this it follows that a privative term, being insusceptible of differentiation⁹, cannot be a generic differentia; for, if it were, there would be a common undifferentiated element in two different groups.

Again, if the species are ultimate indivisible groups, that is, are groups with indivisible differentiae, and if no differentia be common to several groups, the number of differentiae must be equal to the number of species. If a differentia though not divisible could yet be common to several groups, then it is plain that in virtue¹⁰ of that common differentia specifically distinct animals would fall into the same division. It is necessary then, if the differentiae, under which are ranged all the ultimate and indivisible groups, are specific characters, that none of them shall be common; for otherwise, as already said, specifically distinct animals will come into one and the same division. But this would violate one of the requisite¹¹ conditions, which are as follows. No ultimate group must be included in more than a single division; different groups must not be included in the same division; and every group must be found in some division. It is plain then that we cannot get at the ultimate specific forms of the animal, or any other, kingdom by bifurcate¹² division. If we could, the number of ultimate differentiae would equal the number of ultimate animal forms. For assume an order of beings whose prime differentiae are White and Black. Each of these branches will bifurcate, and their branches again, and so on till we reach the ultimate differentiae, whose number will be four or some other power of two, and will also be the number of the ultimate species comprehended in the order.

(A species is constituted by the combination differentia and matter. For no part of an animal is purely¹³ material or purely immaterial; nor can a body, independently of its condition, constitute an animal or any of its parts, as has repeatedly been observed.)

Further, the differentiae must be elements of the essence, and not merely essential attributes. Thus if Figure is the term to be divided, it must not be divided into figures whose angles are equal to two right angles, and figures whose angles are together greater than two right angles. For it is only an attribute of a triangle and not part of its essence that its angles are equal to two right angles.

Again, the bifurcations must be opposites, like White and Black, Straight and Bent¹⁴; and if we characterize one branch by either term, we must characterize the other by its opposite, and not, for example, characterize one branch by a colour, the other by a mode of progression, swimming for instance.

Furthermore, living beings cannot be divided by the functions common to body and soul, by Flying, for instance, and Walking, as we see them divided in the dichotomies already referred to. For some groups, Ants for instance, fall under both divisions, some ants flying while others do not. Similarly as regards the division into Wild and Tame; for it also would involve the disruption of a species into different groups. For in almost all species in which some members are tame, there are other members that are wild. Such, for example, is the case with Men, Horses, Oxen, Dogs in India, Pigs, Goats, Sheep; groups which, if double, ought to have what they have not, namely, different appellations¹⁵; and which, if single, prove that Wildness and Tameness do not amount to specific differences. And whatever single element we take as a basis of division the same difficulty will occur.

The method then that we must adopt is to attempt to recognize the natural groups, following the indications afforded by the instincts of mankind, which led them for instance to form the class of Birds and the class of Fishes, each of which groups combines a multitude of differentiae, and is not defined by a single one as in dichotomy. The method of dichotomy is either impossible (for it would put a single group under different divisions or contrary groups under the same division), or it only furnishes a single ultimate differentia for each species, which either alone or with its series of antecedents has to constitute the ultimate species.

If, again, a new differential character be introduced at any stage into the division, the necessary result is that the continuity of the division becomes merely a unity¹⁶ and continuity of agglomeration¹⁷, like the unity and continuity of a series of sentences coupled together by conjunctive particles. For instance, suppose we have the bifurcation Feathered and Featherless, and then divide Feathered into Wild and Tame, or into White and Black. Tame and White are not a differentiation of Feathered, but are the commencement of an independent bifurcation, and are foreign to the series at the end of which they are introduced.

As we said then, we must define at the outset by multiplicity of differentiae. If we do so, privative terms will be available, which are unavailable to the dichotomist.

The impossibility of reaching the definition of any of the ultimate forms by dichotomy of the larger group, as some propose, is manifest also from the following considerations. It is impossible that a single differentia, either by itself or with its antecedents, shall express the whole essence of a species. (In saying a single differentia by itself I mean such an isolated¹⁸ differentia as Cleft-footed; in saying a single differentia with antecedent I mean, to give an instance, Manycleft-footed preceded by Cleft-footed. The very continuity of a series of successive differentiae in a division is intended to show that it is their combination that expresses the character of the resulting unit, or ultimate group. But one is misled by the usages of language into imagining that it is merely the final term of the series, Manycleft-footed for instance, that constitutes the whole differentia, and that the antecedent terms, Footed, Cleft-footed, are superfluous¹⁹. Now it is evident that such a series cannot consist of many terms. For if one divides and subdivides²⁰, one soon reaches the final differential term, but for all that will not have got to the ultimate division, that is, to the species.) No single differentia, I repeat, either by itself or with its antecedents, can possibly express the essence of a species. Suppose, for example, Man to be the animal to be defined; the single differentia will be Cleft-footed, either by itself or with its antecedents, Footed and Two-footed. Now if man was nothing more than a Cleft-footed animal, this single differentia would duly represent his essence. But seeing that this is not the case, more differentiae than this one will necessarily be required to define him; and these cannot come under one division; for each single branch of a dichotomy ends in a single differentia, and cannot possibly include several differentiae belonging to one and the same animal.

It is impossible then to reach any of the ultimate animal forms by dichotomous division.

1 inevitably   

adv.不可避免地；必然发生地

参考例句：

• In the way you go on,you are inevitably coming apart.照你们这样下去，毫无疑问是会散伙的。
• Technological changes will inevitably lead to unemployment.技术变革必然会导致失业。

2 negation   

n.否定；否认

参考例句：

• No reasonable negation can be offered.没有合理的反对意见可以提出。
• The author boxed the compass of negation in his article.该作者在文章中依次探讨了各种反面的意见。

3 generic   

adj.一般的，普通的，共有的

参考例句：

• I usually buy generic clothes instead of name brands.我通常买普通的衣服，不买名牌。
• The generic woman appears to have an extraordinary faculty for swallowing the individual.一般妇女在婚后似乎有特别突出的抑制个性的能力。

4 hoofs   

n.（兽的）蹄，马蹄( hoof的名词复数 )v.（兽的）蹄，马蹄( hoof的第三人称单数 )

参考例句：

• The stamp of the horse's hoofs on the wooden floor was loud. 马蹄踏在木头地板上的声音很响。 来自辞典例句
• The noise of hoofs called him back to the other window. 马蹄声把他又唤回那扇窗子口。 来自辞典例句

5 nay   

adv.不；n.反对票，投反对票者

参考例句：

• He was grateful for and proud of his son's remarkable,nay,unique performance.他为儿子出色的，不，应该是独一无二的表演心怀感激和骄傲。
• Long essays,nay,whole books have been written on this.许多长篇大论的文章，不，应该说是整部整部的书都是关于这件事的。

6 contradictories   

n.矛盾的，抵触的( contradictory的名词复数 )

参考例句：

7 differentiated   

区分，区别，辨别( differentiate的过去式和过去分词 )； 区别对待； 表明…间的差别，构成…间差别的特征

参考例句：

• The development of mouse kidney tubules requires two kinds of differentiated cells. 小鼠肾小管的发育需要有两种分化的细胞。
• In this enlargement, barley, alfalfa, and sugar beets can be differentiated. 在这张放大的照片上，大麦，苜蓿和甜菜都能被区分开。

8 apparently   

adv.显然地；表面上，似乎

参考例句：

• An apparently blind alley leads suddenly into an open space.山穷水尽，豁然开朗。
• He was apparently much surprised at the news.他对那个消息显然感到十分惊异。

9 differentiation   

n.区别，区分

参考例句：

• There can be no differentiation without contrast. 有比较才有差别。
• The operation that is the inverse of differentiation is called integration. 与微分相反的运算叫做积分。

10 virtue   

n.德行，美德；贞操；优点；功效，效力

参考例句：

• He was considered to be a paragon of virtue.他被认为是品德尽善尽美的典范。
• You need to decorate your mind with virtue.你应该用德行美化心灵。

11 requisite   

adj.需要的，必不可少的；n.必需品

参考例句：

• He hasn't got the requisite qualifications for the job.他不具备这工作所需的资格。
• Food and air are requisite for life.食物和空气是生命的必需品。

12 bifurcate   

adj.二叉的，双峰的

参考例句：

• Drainage was to the north and individual channels bifurcate in that direction.整个水系向北排水,各个河道朝该方向分叉。
• Communicative and semantive translation bifurcate at a later stage of analytical or cognitive translation.交际翻译和语义翻译在认知翻译的后阶段分道扬镳。

13 purely   

adv.纯粹地，完全地

参考例句：

• I helped him purely and simply out of friendship.我帮他纯粹是出于友情。
• This disproves the theory that children are purely imitative.这证明认为儿童只会单纯地模仿的理论是站不住脚的。

14 bent   

n.爱好，癖好；adj.弯的；决心的，一心的

参考例句：

• He was fully bent upon the project.他一心扑在这项计划上。
• We bent over backward to help them.我们尽了最大努力帮助他们。

15 appellations   

n.名称，称号( appellation的名词复数 )

参考例句：

• The list of odd appellations goes on, and anything goes-just name it. 像这种奇怪的名字还有许多，但一切还在继续-----学一句流行词，想取就取吧。 来自互联网
• In the present Chinese characters teaching, the radicals' appellations cause much confusion. 目前的识字教学中，部首的名称较混乱。 来自互联网

16 unity   

n.团结，联合，统一；和睦，协调

参考例句：

• When we speak of unity,we do not mean unprincipled peace.所谓团结，并非一团和气。
• We must strengthen our unity in the face of powerful enemies.大敌当前，我们必须加强团结。

17 agglomeration   

n.结聚，一堆

参考例句：

• The Guangxi's sugar industry has the characters of industrial agglomeration.广西糖业在发展过程中体现出了产业集聚特征。
• This agglomeration of funds resolves a number of problems.这种集资的办法解决了以下几个问题。

18 isolated   

adj.与世隔绝的

参考例句：

• His bad behaviour was just an isolated incident. 他的不良行为只是个别事件。
• Patients with the disease should be isolated. 这种病的患者应予以隔离。

19 superfluous   

adj.过多的，过剩的，多余的

参考例句：

• She fined away superfluous matter in the design. 她删去了这图案中多余的东西。
• That request seemed superfluous when I wrote it.我这样写的时候觉得这个请求似乎是多此一举。

20 subdivides   

再分，细分( subdivide的第三人称单数 )

参考例句：

• This latter subdivides into the split off Exciting Object and Rejecting Object. 后来，又再次分隔成分裂性的兴奋性客体和拒绝性客体。
• Medical Pedal Switch has two models, such as single and duplex, and subdivides into 3 specs. 医用脚踏开关系列有单联和双联两种型号3个规格。