, The attempt to divide 'student' according to play-status raises, however, a fundamental difficulty. For the F.D. 'play-status cannot be included, even as an indeterminate mark, in the definition of 'student.' A student cannot be defined as one who patronizes some form of play or takes some form of recreation. Problematic properties cannot, even at the call of the dividing-interest, be transfigured into differentiæ. There is certainly a difficulty here, but the logical remedy is simple and direct. The genus or dividendum may be altered so as to answer appropriately to the requirements of the case. We cannot accept 'play-status' as an F.D. of 'student,' but we can accept it as an F.D. of 'student who is interested in games.' It should not, however, be supposed that this procedure is a mere subterfuge or dodge. We are not infrequently asked to perform operations on inappropriate objects. We might be asked, for instance, to multiply 8 cows by 15 sheep, or to divide 15 sheep by 5 sheep. We might be asked to decide upon the specific spiritual quality of a ghost's body or a comet's tail. We may even be asked to convert an O proposition. Against all such questions as these we safeguard ourselves by pointing out that the requirement cannot be met, and that the nature of the object resents the subjective demand inconsiderately made upon it. A number can be divided by another number, but not a sheep by a sheep, nor so many cows by so many horses. A comet's tail cannot grow spiritual by the simple process of becoming sufficiently thin. Similarly a student cannot put on a games-interest in order to suit the caprices of a question in logical Division. A question in Logic may itself be illogical. When we are asked, then, to divide 'student' according to play-status, we answer that it is only the play-student that has a play-status, and that, from the point of view of play, the student who does not play must be cancelled, not, indeed, as a 'skulk,' a 'shirker,' or a 'book-worm'-for these pretty labels do not express feelings controlled by logical interests-but as an irrelevance-an irrelevance to the limited interests of the play-topic. We may adopt, then, as our division according to play-status, some such classification as the following : (iv.) 'Quadrilateral figure' into 'square, rectangle, parallelogram, or rhomboid.' We take 'quadrilateral figure' to mean 'plane rectilinear quadrilateral figure.' The classes overlap, with breach of Rule III. The correction needed here is therefore not that of co-division (the cross-division remedy), but that of subdivision. Species and sub-species are confused together, the division taking leaps along the predicamental line. We may correct the division thus : We now see very clearly that, in the original division, the classes are not mutually exclusive (Breach of Rule II.). The square is a rectangle, and the rectangle a parallelogram; and, further, the rhomboid is a parallelogram. Thus, what the given division tells us is, briefly, that the quadrilateral figure is a parallelogram. No account, therefore, is taken of the non-parallelogram-the trapezium and trapezoid. The division, then, is not exhaustive (Breach of Rule IV.). It may be worth while to consider this division more closely from the point of view of the fundamenta involved. Unless the first rule of Division is to be broken, the fundamentum must remain generically the same throughout. Now the division according to parallelism of sides and the subsequent division of the parallelogram-(1) according to angle-relations, (2) according to siderelations-introduce fundamenta which do not at once appear to be modifications of one and the same generic idea. But on closer scrutiny they are seen to be so. We may accept side-relation as the generic fundamentum, and characterize our three specific fundamenta as (1) side-parallelism, (2) side-inclination, (3) (relative) side-length. With regard to (2), we see that the angle-relation is itself a specification of the side-relation; it is that relation of one side to another which is measured by the inclination of each to the other. According as the two sides which contain the angle are more or less inclined to each other, the angle itself is greater or less. We conclude, then, that Rule I. is not in any way broken, but rather legitimately applied. (v.) Plane Triangle' into 'equilateral, obtuse-angled, or rightangled.' Identifying 'equilateral' with the commensurate term 'equiangular,' we notice that the division is not exhaustive. The acuteangled triangle which is not equiangular is not included (Breach of Rule IV.). There is no overlapping. But the division, as given, involves two fundamenta, which, though not generically, are still specifically different-namely, 'siderelation of relative magnitude' and 'angle-relation.' And it is a breach of Rule III. (though not necessarily of Rule I.) to utilize simultaneously at any given stage two fundamenta that are specifically different. Proper subdivision, then, might seem to be the natural remedy, and we might present the corrected division as follows: But the division, so framed, seems to require to be completed by the subdivision of the two remaining members of the first division, and the total result is unnecessarily complex. It would be simpler in this case to institute a co-division which, when completed, would run as follows: Triangle into equilateral, isosceles, scalene (F.D. relative side-length), and into acute-angled, right-angled, obtuseangled (F.D. side-inclination). (vi.) 'Yorkshire' into 'North, East, and West Ridings.' This is physical division. (vii.) 'Lemonade' into 'fluid, acid, sweet,' etc. This is an incomplete metaphysical division. (viii.) 'Accident' into 'misadventure or irrelevant predicable.' This is verbal division, the discrimination of the possible meanings of an ambiguous term. CHAPTER V. II. (v.) CLASSIFICATION.* THE first main object of Classification is to keep control over facts by marshalling them in order; and the general principle which guides * As already indicated in the last chapter (vide p. 42), the term 'Classification' is more comprehensive than the term 'Real Division'; for, in the first place, it includes not only the downward movement from summum genus to infimæ species to which we are restricted in Real Division, but also the upward movement from the lowest species to the highest genus. In the treatment of Classification here every such endeavour is that of bringing together those things which are most alike and separating those things which are most unlike. Thus, to take the case of animals, we have here an immense and bewildering variety of individual beings. A sufficient knowledge of Anatomy enables us to detect within this maze of life certain relatively permanent types of structure by the aid of which we form zoological species. When these are compared together, some will be seen to have characters in common by which they resemble one another and differ from all other species. These we group together into what is here technically called a genus. From genera we pass by similar steps to families, orders, classes, and finally to sub-kingdoms. The words ' class,' ' genus,' 'species' have here acquired meanings quite different from those involved in stating that the definition of a class or species is given by stating genus and differentia. In this latter statement all the terms are general and relative. From the point of view of the predicables, the word 'class' is used generally for any group of objects resembling each other in certain characteristics.* Thus, a sub-kingdom, or an order, or a class proper, or a genus, or a species is a class in this sense of the word. So, again, if we take any two successive groups in the scheme of classification, the first will stand to the second as genus to species in the predicable sense of these terms. 'Class' is the genus of which 'Order' is the species. But in these classifications the words 'class,' 'genus,' species' have fixed specialized meanings. A 'class' between a sub-kingdom and an order, a 'genus' between a family and a species, a 'species' between a genus and a variety. TYPES OF CLASSIFICATION. comes Classifications are of two kinds: they may be either real or formal. When we state that classifications are governed by the paramount consideration of order, our primary meaning is that classifications arise in response to a dominating subjective purpose, the need for order. But there are two main ways in which this subjective purpose realizes itself: it may either develop in whole-hearted conformity to the nature of the material studied, or it may show a divided adherence, conforming partly to the requirements of the material, but partly also to one or other of the specialized demands for order which the subject makes in the interests of his own practical life and culture. In the former case the classification may be called real; in the latter, formal. In each case the dominating factor is the subjective interest in order, and here, as well as there, the interest may be 'disinterested.' But in the one case this interest is fixed on the discovery of the material's own order imposed upon it by the laws of its own nature; in the other-whether through choice or necessity-it is bent on arranging the material in a selective spirit by the help of such of its characters as happen to be relevant to the classifier's specific requirements. given we have used the term almost exclusively in that sense in which it cannot be mistaken for Real Division-i.e., we have considered the up-building of a classification rather than its explication from the most general concepts downwards. But even where the direction of Classification coincides with that of Real Division, the two processes remain distinct. For Classification includes processes of Definition as well as of Division; whereas Division and Definition, as we have defined them, are mutually exclusive. The extension-import of a class is here assumed, as the more convenient for our purpose (vide p. 146). All the classification-schemes of the Natural Sciences are real in the sense above defined. There are two main types of Real Classification, respectively known as natural and diagnostic. But they do not stand on the same level, for the diagnostic type of Classification has its sole raison d'être in the service of the natural. As the distinction between these two types of Real Classification is particularly important, we proceed to consider it at some length. Natural Classification. In classifying according to Nature, scientists have been guided by the following important clue, which may be regarded as the guiding-thread of true Natural Classification-to wit, that it is characteristic of the ways of Nature that, when she makes a difference in any single fundamental particular-e.g., possession or lack of a spinal cord-she correlates with this difference a large number of other differences. In the case of the Genetic Sciences, which view their object-matter from the standpoint of its development, this characteristic admits of a ready explanation. Given two species, one with and the other without the rudiment of a spinal cord, it is obvious, from the point of view of Evolution, that they will develop in very different ways, and acquire very different properties. Such classes as are formed of things which agree among themselves and differ from others in a multitude of characters were called by J. S. Mill 'natural kinds.' A classification is natural only in so far as it keeps to natural kinds throughout. A natural classification, then, may be defined as one in which, roughly speaking, the divisions are so constituted that the objects included in any one of them resemble each other and differ from all others in many significant respects. In Natural Classification the more important characters-i.e., those which are accompanied by the larger number of correlated differences are selected for determining the higher groups, and thus the kinds classified will, on the whole, be arranged, from the primary divisions downwards, according to the principle of 'sub |