ceeds apace when one sees the marvels of curious problems solved, unlikely properties discovered, among numbers and geometrical figures. A certain ease in holding in the memory the abstract symbols, after a moderate application, is enough to prepare us for a positive relish in the pursuit. Such is the case with generalities in all departments. If we can hold on till they bear their fruits in the explanation of things that we have already begun to take notice of, the pursuit is sustained by a genuine and proper scientific interest, whose real groundwork, however deeply hidden, is the stimulus of agreement among differing particulars, and the lightening of the intellectual labor in comprehending the world. These are the feelings that have to be awakened in the minds of pupils when groaning under the burden of abstractions.
The opposition of the concrete and the abstract, while but another way of expressing the opposition of the particular and the general, brings into greater prominence the highly composite or combined character of individuality. The individual thing is usually a compound of many qualities, each of which has to be abstracted in turn, in rising to general notions; any individual ball has, in addition to its round form, the properties called weight, hardness, color, and so on. Now, this composite nature, by charming several senses at once, gives a greater interest to individuals, and urges us to resist that process of decomposition, and separate attention, to which are given the designations "abstraction" and "analysis." It is for individuals in all their multiplicity of influence that we contract likings or affections; and, according as the charm of sense, and especially the color-sense, is strong in us, we are averse to the classing or generalizing operation. A fire is an object of strong individual interest: to rise from this to the general notion of the oxidation of carbon under all varieties of mode, including cases with no intrinsic charm, is to quit with reluctance an agreeable contemplation. The emotions now described—the pleasure of identity, and the lightening of labor—are of avail to counterwork this reluctance.
The second of the two motives that we have coupled together—the easing of intellectual labor—may be viewed in another light. When objects are viewed as operating agents in the economy of the world, as causes or instruments of change, they work by their qualities or powers in separation, and not by their entire individuality or concreteness. An iron bar, or a poker, is an individual concrete thing; but, when we come to use it, we put in action its various qualities separately. We may employ it as a weight, in which case its other properties are of no account; we use it as a lever, and bring into play simply its length and its tenacity. We can put it in motion as a moving power, wherein its inertia is alone taken into account, with perhaps its form. In all these instances, the magnetical and the chemical and the medicinal properties of iron are unthought of. Now, this consideration opens up an important aid to the abstracting process, the analytic separation of properties, as opposed to the mind's fondness for clinging to concrete individuality.