In considering generalisation, the law of continuity was applied chiefly to physical properties capable of mathematical treatment. But in the classificatory sciences, also, the same important principle is often beautifully exemplified. Many objects or events seem to be entirely exceptional and abnormal, and in regard to degree or magnitude they may be so termed; but it is often easy to show that they are connected by intermediate links with ordinary cases. In the organic kingdoms there is a common groundwork of similarity running through all classes, but particular actions and processes present themselves conspicuously in particular families and classes. Tenacity of life is most marked in the Rotifera, and some other kinds of microscopic organisms, which can be dried and boiled without loss of life. Reptiles are distinguished by torpidity, and the length of time they can live without food. Birds, on the contrary, exhibit ceaseless activity and high muscular power. The ant is as conspicuous for intelligence and size of brain among insects as the quadrumana and man among vertebrata. Among plants the Leguminosæ are distinguished by a tendency to sleep, folding their leaves at the approach of night. In the genus Mimosa, especially the Mimosa pudica, commonly called the sensitive plant, the same tendency is magnified into an extreme irritability, almost resembling voluntary motion. More or less of the same irritability probably belongs to vegetable forms of every kind, but it is of course to be investigated with special ease in such an extreme case. In the Gymnotus and Torpedo, we find that organic structures can act like galvanic batteries. Are we to suppose that such animals are entirely anomalous exceptions; or may we not justly expect to find less intense manifestations of electric action in all animals?
Some extraordinary differences between the modes of reproduction of animals have been shown to be far less than was at first sight apparent. The lower animals seem to differ entirely from the higher ones in the power of reproducing lost limbs. A kind of crab has the habit of casting portions of its claws when much frightened, but they soon grow again. There are multitudes of smaller animals which, like the Hydra, may be cut in two and yet live and develop into new complete individuals. No mammalian animal can reproduce a limb, and in appearance there is no analogy. But it was suggested by Blumenbach that the healing of a wound in the higher animals really represents in a lower degree the power of reproducing a limb. That this is true may be shown by adducing a multitude of intermediate cases, each adjoining pair of which are clearly analogous, so that we pass gradually from one extreme to the other. Darwin holds, moreover, that any such restoration of parts is closely connected with that perpetual replacement of the particles which causes every organised body to be after a time entirely new as regards its constituent substance. In short, we approach to a great generalisation under which all the phenomena of growth, restoration, and maintenance of organs are effects of one and the same power.[601] It is perhaps still more surprising to find that the complicated process of reproduction in the higher animals may be gradually traced down to a simpler and simpler form, which at last becomes undistinguishable from the budding out of one plant from the stem of another. By a great generalisation we may regard all the modes of reproduction of organic life as alike in their nature, and varying only in complexity of development.[602]
Limits of Classification.
Science can extend only so far as the power of accurate classification extends. If we cannot detect resemblances, and assign their exact character and amount, we cannot have that generalised knowledge which constitutes science; we cannot infer from case to case. Classification is the opposite process to discrimination. If we feel that two tastes differ, the tastes of two kinds of wine for instance, the mere fact of difference existing prevents inference. The detection of the difference saves us, indeed, from false inference, because so far as difference exists, inference is impossible. But classification consists in detecting resemblances of all degrees of generality, and ascertaining exactly how far such resemblances extend, while assigning precisely the points at which difference begins. It enables us, then, to generalise, and make inferences where it is possible, and it saves us at the same time from going too far. A full classification constitutes a complete record of all our knowledge of the objects or events classified, and the limits of exact knowledge are identical with the limits of classification.
It must by no means be supposed that every group of natural objects will be found capable of rigorous classification. There may be substances which vary by insensible degrees, consisting, for instance, in varying mixtures of simpler substances. Granite is a mixture of quartz, felspar, and mica, but there are hardly two specimens in which the proportions of these three constituents are alike, and it would be impossible to lay down definitions of distinct species of granite without finding an infinite variety of intermediate species. The only true classification of granites, then, would be founded on the proportions of the constituents present, and a chemical or microscopic analysis would be requisite, in order that we might assign a specimen to its true position in the series. Granites vary, again, by insensible degrees, as regards the magnitude of the crystals of felspar and mica. Precisely similar remarks might be made concerning the classification of other plutonic rocks, such as syenite, basalt, pumice-stone, lava.
The nature of a ray of homogeneous light is strictly defined, either by its place in the spectrum or by the corresponding wave-length, but a ray of mixed light admits of no simple classification; any of the infinitely numerous rays of the continuous spectrum may be present or absent, or present in various intensities, so that we can only class and define a mixed colour by defining the intensity and wave-length of each ray of homogeneous light which is present in it. Complete spectroscopic analysis and the determination of the intensity of every part of the spectrum yielded by a mixed ray is requisite for its accurate classification. Nearly the same may be said of complex sounds. A simple sound undulation, if we could meet with such a sound, would admit of precise and exhaustive classification as regards pitch, the length of wave, or the number of waves reaching the ear per second being a sufficient criterion. But almost all ordinary sounds, even those of musical instruments, consist of complex aggregates of undulations of different pitches, and in order to classify the sound we should have to measure the intensities of each of the constituent sounds, a work which has been partially accomplished by Helmholtz, as regards the vowel sounds. The different tones of voice distinctive of different individuals must also be due to the intermixture of minute waves of various pitch, which are yet quite beyond the range of experimental investigation. We cannot, then, at present attempt to classify the different kinds or timbres of sound.
The difficulties of classification are still greater when a varying phenomenon cannot be shown to be a mixture of simpler phenomena. If we attempt to classify tastes, we may rudely group them according as they are sweet, bitter, saline, alkaline, acid, astringent or fiery; but it is evident that these groups are bounded by no sharp lines of definition. Tastes of mixed or intermediate character may exist almost ad infinitum, and what is still more troublesome, the tastes clearly united within one class may differ more or less from each other, without our being able to arrange them in subordinate genera and species. The same remarks may be made concerning the classification of odours, which may be roughly grouped according to the arrangement of Linnæus as, aromatic, fragrant, ambrosiac, alliaceous, fetid, virulent, nauseous. Within each of these vague classes, however, there would be infinite shades of variety, and each class would graduate into other classes. The odours which can be discriminated by an acute nose are infinite; every rock, stone, plant, or animal has some slight smell, and it is well known that dogs, or even blind men, can discriminate persons by a slight distinctive odour which usually passes unnoticed.
Similar remarks may be made concerning the feelings of the human mind, called emotions. We know what is anger, grief, fear, hatred, love; and many systems for classifying these feelings have been proposed. They may be roughly distinguished according as they are pleasurable or painful, prospective or retrospective, selfish or sympathetic, active or passive, and possibly in many other ways; but each mode of arrangement will be indefinite and unsatisfactory when followed into details. As a general rule, the emotional state of the mind at any moment will be neither pure anger nor pure fear, nor any one pure feeling, but an indefinite and complex aggregate of feelings. It may be that the state of mind is really a sum of several distinct modes of agitation, just as a mixed colour is the sum of the several rays of the spectrum. In this case there may be more hope of some method of analysis being successfully applied at a future time. But it may be found that states of mind really graduate into each other so that rigorous classification would be hopeless.
A little reflection will show that there are whole worlds of existences which in like manner are incapable of logical analysis and classification. One friend may be able to single out and identify another friend by his countenance among a million other countenances. Faces are capable of infinite discrimination, but who shall classify and define them, or say by what particular shades of feature he does judge? There are of course certain distinct types of face, but each type is connected with each other type by infinite intermediate specimens. We may classify melodies according to the major or minor key, the character of the time, and some other distinct points; but every melody has, independently of such circumstances, its own distinctive character and effect upon the mind. We can detect differences between the styles of literary, musical, or artistic compositions. We can even in some cases assign a picture to its painter, or a symphony to its composer, by a subtle feeling of resemblances or differences which may be felt, but cannot be described.
Finally, it is apparent that in human character there is unfathomable and inexhaustible diversity. Every mind is more or less like every other mind; there is always a basis of similarity, but there is a superstructure of feelings, impulses, and motives which is distinctive for each person. We can sometimes predict the general character of the feelings and actions which will be produced by a given external event in an individual well known to us; but we also know that we are often inexplicably at fault in our inferences. No one can safely generalise upon the subtle variations of temper and emotion which may arise even in a person of ordinary character. As human knowledge and civilisation progress, these characteristic differences tend to develop and multiply themselves, rather than decrease. Character grows more many-sided. Two well educated Englishmen are far better distinguished from each other than two common labourers, and these are better distinguished than two Australian aborigines. The complexities of existing phenomena probably develop themselves more rapidly than scientific method can overtake them. In spite of all the boasted powers of science, we cannot really apply scientific method to our own minds and characters, which are more important to us than all the stars and nebulæ.