CHAPTER XXX.

CLASSIFICATION.

THE extensive subject of Classification has been deferred to a late part of this treatise, because it involves many questions of difficulty, and did not seem naturally to fall into any earlier place. But it must not be supposed that, in now formally taking up the subject, we are for the first time entertaining the notion of classification. All logical inference involves classification, which is indeed the necessary accompaniment of the action of judgment. It is impossible to detect a point of similarity between two or more objects without thereby joining them together in thought, and thus forming an incipient or potential class. Nor can we ever bestow a common name upon two or more objects without thereby equally implying the existence of a class. Every common name is the name of a class, and every name of a class is a common name. It is evident also that every general notion, or concept is but another way of speaking of a class. Usage alone leads us to use the word classification in some cases and not in others. We are said to form the general notion parallelogram when we regard an infinite number of possible foursided rectilinear figures as resembling each other in the common property of possessing parallel sides. We should be said to form a class, Trilobite, when we place alongside of each other in a museum a number of hand specimens resembling each other in certain defined qualities. But

the logical nature of the operation is, or should be, exactly the same in both cases. We form a class of figures called parallelograms, and we form a general notion of Trilo

bites.

Science, it has been said at the outset, is the detection of identity, and classification is the placing together, either in thought or in actual proximity of space, those notions or objects between which identity has been detected. Accordingly the value of classification is co-extensive with the value of science and general reasoning. Whenever we form a class we reduce multiplicity to unity, and detect, as Plato said, the one in the many. The result of such classification is to yield generalized knowledge, as distinguished from the direct and sensuous knowledge of particular facts. Of every class, so far as it is correctly formed, the great principle of substitution is true, and whatever we know of one object in a class we also know of the other objects, so far as identity has been detected between them. The facilitation and abbreviation of mental labour is at the bottom of all mental progress. The reasoning faculties of Newton were not different in qualitative character from those of a ploughman; the difference lay in the extent to which they were exerted, and the number of facts which could be treated. Every thinking being generalizes more or less, but it is the depth and extent of his generalizations which distinguish the philosopher. Now it is the exertion of the classifying and generalizing powers which thus enables the intellect of man to cope in some degree with the infinite number and variety of natural phenomena and objects. In the chapters upon Combinations and Permutations it was rendered quite evident, that from a few elementary differences immense numbers of various combinations can be produced. The process of classification enables us to resolve these combinations, and refer each one to its place according to

one or other of the elementary circumstances out of which it was produced. We restore nature, as it were, to the simple conditions out of which its endless variety was developed. As Professor Bowen has excellently saida, The first necessity which is imposed upon us by the constitution of the mind itself, is to break up the infinite wealth of Nature into groups and classes of things, with reference to their resemblances and affinities, and thus to enlarge the grasp of our mental faculties, even at the expense of sacrificing the minuteness of information which can be acquired only by studying objects in detail. The first efforts in the pursuit of knowledge, then, must be directed to the business of Classification. Perhaps it will be found in the sequel, that Classification is not only the beginning, but the culmination and the end, of human knowledge.'

Classification Involving Induction.

The purpose of classification must always be the detection of resemblances and laws of nature. However much the process may in some cases be disguised, classification is not really distinct from the process of perfect induction, whereby we endeavour to ascertain the connexions which exist between the several properties of the objects under treatment. There can be no use in placing an object in a class unless something more than the fact of being in that class is thereby implied. If we arbitrarily formed a class of metals and placed therein a selection from the list of known metals made by the ballot-we should have no reason to expect that the metals in question would resemble each other in any points except that they are

a 'A Treatise on Logic, or, the Laws of Pure Thought,' by Francis Bowen, Professor of Moral Philosophy in Harvard College, Cambridge, United States, 1866, p. 315.

metals, and have been selected by the ballot. But when chemists carefully selected from the list the five metals, Potassium, Sodium, Casium, Rubidium, and Lithium, and called them the Alkaline metals, a great deal was implied in this classification. On comparing the qualities of these substances, they are all found to combine very energetically with oxygen, to decompose water at all temperatures, and to form strongly basic oxides, which are very soluble in water, yielding powerfully caustic and alkaline hydrates from which water cannot be expelled by heat. Their carbonates are also soluble in water, and each metal forms only one chloride. It may also be expected as a general rule that each salt into which one of the five metals enters will correspond to salts into which the other metals enter, there being a general analogy between the properties and compounds of these metals.

Now in forming this class of alkaline metals, we have done more than merely select a convenient order of statement. We have arrived at a discovery of certain empirical laws of nature, the probability being very considerable that a metal which exhibits some of these properties will also possess the others. If we discovered another metal whose carbonate was soluble in water, and which energetically combined with water at all temperatures, producing a strongly basic oxide, we should infer that it would form only a single chloride, and that, generally speaking, it would enter into a series of compounds corresponding to the salts of the other alkaline metals. The formation of this class of alkaline metals, then, is no mere matter of convenience; it is an important and highly successful act of inductive discovery, enabling us to register many undoubted propositions as results of perfect induction, and to make an almost indefinite series of inferences depending upon the principles of imperfect induction.

Professor Huxley has defined the process of classification in the following terms b. By the classification of any series of objects, is meant the actual or ideal arrangement together of those which are like and the separation of those which are unlike; the purpose of this arrangement being to facilitate the operations of the mind in clearly conceiving and retaining in the memory the characters of the objects in question.'

This statement is doubtless correct, so far as it goes, but it does not include all that Professor Huxley himself implicitly treats under classification. He is fully aware that deep correlations, or in other terms deep uniformities or laws of nature, will be disclosed by any well chosen and profound system of classification. I should therefore propose to modify the above statement, as follows: By the classification of any series of objects, is meant the actual or ideal arrangement together of those which are like and the separation of those which are unlike, the purpose of this arrangement being, primarily, to disclose the correlations or laws of union of properties or circumstances, and, secondarily, to facilitate the operations of the mind in clearly conceiving and retaining in the memory the characters of the objects in question.'

Multiplicity of Modes of Classification.

In approaching the question how any given group of objects may best be classified, let it be remarked that there must generally be an unlimited number of modes of classifying any group of objects. Misled, as we shall see, by the problem of classification in the natural sciences, philosophers often seem to think that in each subject there must be one essentially natural classification which

b Lectures on the Elements of Comparative Anatomy,' 1864, p. 1.