Differentia

“ Such definitions, however, are always liable to be overthrown by the discovery of new objects in nature.
Definitions of this kind are what logicians have had in view, when they laid down the rule, that the definition of a species should be per genus et differentiam. Differentia being seldom taken to mean the whole of the peculiarities constitutive of the species, but some one of those peculiarities only, a complete definition would be per genus et differentias, rather than differentiam. ”

“ 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. ”

“ Thus, warm-blooded, applied to man, stands under the class proprium; but 168 when applied to the animals which stand distinguished from the cold-blooded, as constituting a class, it becomes the differentia, and rational, with respect to this comprehensive class, is only an accidens.50
50 The author says, that no very distinct boundaries are marked by the three terms, Differentia, Proprium, and Accidens, nor do they effect a scientific division. ”

“ Accordingly, against one who holds the doctrine of Ideas, declaring the genus to be unum numero, the negative differentia will furnish grounds for attack; but not against any other respondent.290 For there are various cases in which the negative must be employed as a part of the differentia: e.g., in privative terms, blind is one whose nature it is to see but who does not see. ”

“ This community will be more fully appreciated on observing that progressive differentiation of structures is accompanied by progressive differentiation of functions.
The multiplying divisions, primary, secondary, and tertiary, which arise in a developing animal, do not assume their major and minor unlikenesses to no purpose. Along with diversities in their shapes and compositions there go diversities in the actions they perform: they grow into unlike organs having unlike duties. ”

“ At the same time, it is not possible for any of the things which are differentiated to be exactly like one another till they all once more become the same.
(6) Since, then, differentiation is multiform, living creatures are multiform and many, and they are like one another neither in appearance nor in intelligence, because of the multitude of differentiations. At the same time, they all live, and see, and hear by the same thing, and they all have their intelligence from the same source. ”

“ We are consequently reduced to a condition exactly parallel to that which we find, according to the theory of evolution, in biology.172 Variations are the result of a differentiation of some unit. It is the object, in the classification of biological data, to demonstrate, by means of a series of ascending forms, the evolution of the most highly differentiated from the least differentiated. ”

“ To me it seems a self-evident proposition that nothing whatsoever can differentiate one body of men from another, except the physical conditions in which they are set, - including, of course, under the term physical conditions the relations of place and time in which they stand with regard to other bodies of men. To suppose otherwise is to deny the primordial law of causation. To imagine that the mind can differentiate itself is to imagine that it can be differentiated without a cause. ”

“ And through this continuous differentiation and integration of changes or motions, which constitutes nervous function, there is gradually wrought that differentiation and integration of matter, which constitutes nervous structure.
§ 128. In social evolution, the collecting together of the like and the separation of the unlike, by incident forces, is primarily displayed in the same manner as we saw it to be among groups of inferior creatures. The human races tend to differentiate and integrate, as do races of other living forms. ”

“ The various organs are developed by the process of specialization during the course of the evolution of the organism. Organic life on earth divides into various species. And in the sphere of social life we have an example in the division of labor. — Whatever differentiation proceeds one-sidedly, dissolution quickly follows. A third characteristic of evolution must therefore be added, namely, that it consists of a determination which presupposes a definite harmony between integration and differentiation. ”

“ Indeed, if we may take the principle of evolution to be the differentiation of the homogeneous, we may go further and say that the whole theory of evolution, and not merely a particular historic science, such as the science of religion, {24} postulates differentiation and the principle of difference, and does not explain it,—evolution cannot start, the homogeneous cannot be other than homogeneous, until the principle of difference and the power of differentiation is assumed. ”

“ That those classed under differentia, are regarded as more expressly involved in the definition of the Species which they seem to cut out from the Genus. Thus, both rational, and risible, when applied to animal, cut out of it the class Man; but rational is called DIFFERENTIA, risible PROPRIUM, because rational, is strictly involved in the definition of man ”

“ Nothing can, of course, differentiate itself, nor can any two things differentiate each other, even when functionally allied. The actual coëfficient sought is the difference effected, in functional value, in one of two independent variables. ”

“ But whatever means Nature adopts, her aim is always the same—to specialise, to differentiate, to produce diversity from uniformity.
Differentiation not only raises the level of organisation; it usually also takes the direction of adaptation to particular habits of life, and this is perhaps the most fruitful cause of diversity. ”

“ Sometimes a term connotes all the attributes that another does, and more besides, which, as distinguishing it, are called differential. Thus 'man' connotes all that 'animal' does, and also (as differentiæ) the erect gait, articulate speech, and other attributes. In such a case as this, where there are well-marked classes, the term whose connotation is included in the others' is called a Genus of that Species. We have a Genus, triangle; and a Species, isosceles, marked off from all other triangles by the differential quality of having two equal sides: again—Genus, book; Species, quarto ”

“ I trust that some one with the right intellectual equipment will endeavor to follow this guide; and I am sanguine enough to think that a comprehensive study of the geometrical phenomena of differentiation will suggest to a penetrative mind that critical experiment which may one day reveal the meaning of spontaneous division, the mystery through which lies the road, perhaps the most hopeful, to a knowledge of the nature of life. ”

“ Every differentiation of structure being a result of some difference in the relations of the parts to the agencies acting on them, it follows that the more multiplied and more unlike the agencies, the more varied must be the differentiations wrought. Hence the change from a state of homogeneity to a state of heterogeneity, will be marked in proportion as the environing actions to which the organism is supposes it is only are complex. ”

“ But “change of consciousness” is too loose an expression to take the place of the unwieldy phrase differentiation of a Gradual Differentiation of Presentation-Continuum. presentation-continuum, to which we have been driven. For not only does the term “consciousness” confuse what exactness requires us to keep distinct, an activity and its object, but also the term “change” fails to express the characteristics which distinguish new presentations from other changes. Differentiation implies that the simple becomes complex or the complex more complex ”

“ We have seen in the fourth chapter that the degree of differentiation and specialisation of the parts in organic beings, when arrived at maturity, is the best standard, as yet suggested, of their degree of perfection or highness. ”

“ And as the use of the differential method is to find the lengths of ordinates not given, standing upon points of the absciss that are given, by means of the equation, so the use of attempts to make general conclusions by induction and analogy, from particular effects or phænomena, in different given circumstances, by applying the general law conclusion to these circumstances. ”

“ The differing results of a high differentiation of centralized organisms arise in accordance with the changing combinations of elementary parts and nerve activities. These results are not, however, to be regarded as the mere effects of matter, but as phenomena of the same, in fact, as the consummation and crown of the whole evolution of nature. Even in the sense-organs we see the differentiation of matter advance beyond the sphere of sense-perception. ”

“ Seeing indeed that some differentiation must have existed primordially it is as easy to imagine that the original body was composed of a series grading from the condition of the anterior segment to that of the posterior, as any other arrangement. ”

“ These and other like instances do not however militate against the hypothesis. They merely show that the tendency is sometimes antagonized by other tendencies. Bearing in mind which qualification, we may say, that as [73] differentiation of parts is connected with difference of function, so there appears to be a connexion between integration of parts and sameness of function.
Closely related to the general truth that the evolution of all organisms is carried on by combined differentiations and integrations, is another general truth, which physiologists appear not to have recognized. ”

“ It is manifest, too, that whereas the differentiation of functions proceeds, not necessarily by division into two, but often by division into several, and usually in such ways as not to leave any two functions that are just complementary to one another, the restorations of equilibrium cannot be so simple as above supposed. ”

“ Without enumerating the minor differentiations which these three great classes afterwards undergo, we will merely note that throughout, they follow the same general law with the differentiations of an individual organism. In a society, as in a rudimentary animal, we have seen that the most general and broadly contrasted divisions are the first to make their appearance ”

“ Such portions of a group, however, as remain sheltered from conditions unsuited to their present line of development, retain their ancient forms. This change of structure by which organisms or portions of organic bodies are modified so as to perform more complicated functions, or those better suited to their environment, is denominated differentiation; hence the degree of differentiation attained by a structure determines the stage of development which it has reached. ”

“ Throughout the evolutionist theory, as in its biological branch, the theory of descent—the great law of specialization or differentiation—teaches us that a multiplicity of phenomena is developed from original unity, heterogeneity from original similarity, and the composite organism from original simplicity. The conditions of existence are dissimilar for each individual from the beginning of its existence ”

“ Natural development always proceeds from the simple to the complex—not inversely; progress consists in differentiation, i.e., in the evolution of originally similar parts into special organs of different structure and independent functions, and not in the retrogression of differentiated beings of rich specialization to a protoplasm without physiognomy. ”

“ This differentiation of functions implies a corresponding differentiation of organs, but it is functional differentiation which always takes the lead. "Where division of labour has not been introduced into the organism there must exist a great simplicity of structure. But just as uniformity in the functions of the different parts of the body implies a uniformity in their mode of constitution, so diversity in function must be accompanied by particularities in structure ”

“ And so we find that while Evolution is a transformation of the homogeneous into the heterogeneous, and of the indefinite into the definite, it is also a transformation of the incoherent into the coherent. Along with the differentiation shown in increasing contrasts of parts with each other, there goes on an integration, by which the parts are rendered distinct units, as well as closely united components of one whole. ”

“ If the number of different parts in an aggregate must determine the number of differentiations produced in the energies passing through it—if the distinctness of these parts from one another, must involve distinctness in their reactions, and therefore distinctness between the divisions of the differentiated energy; there cannot but be a complete parallelism between the development of structure and the development of function. If structure advances from the simple and general to the complex and special, function must do the same. ”

“ Differentiation, the direct process, is always capable of performance by fixed rules, but as these rules produce considerable variety of results, the inverse process of integration presents immense difficulties, and in an infinite majority of cases surpasses the present resources of mathematicians. ”