Actually, all dealing with things, even the child's, is immersed in inferences; things are clothed by the suggestions they arouse, and are significant as challenges to interpretation or as evidences to substantiate a belief. Nothing could be more unnatural than instruction in things without thought; in sense-perceptions without judgments based upon them. And if the abstract to which we are to proceed denotes thought apart from things, the goal recommended is formal and empty, for effective thought always refers, more or less directly, to things.
Direct and indirect understanding again
Yet the maxim has a meaning which, understood and supplemented, states the line of development of logical capacity. What is this signification? Concrete denotes a meaning definitely marked off from other meanings so that it is readily apprehended by itself. When we hear the words, table, chair, stove, coat, we do not have to reflect in order to grasp what is meant. The terms convey meaning so directly that no effort at translating is needed. The meanings of some terms and things, however, are grasped only by first calling to mind more familiar things and then tracing out connections between them and what we do not understand. Roughly speaking, the former kind of meanings is concrete; the latter abstract.
What is familiar is mentally concrete
To one who is thoroughly at home in physics and chemistry, the notions of atom and molecule are fairly concrete. They are constantly used without involving any labor of thought in apprehending what they mean. But the layman and the beginner in science have first to remind themselves of things with which they already are well acquainted, and go through a process of slow translation; the terms atom and molecule losing, moreover, their hard-won meaning only too easily if familiar things, and the line of transition from them to the strange, drop out of mind. The same difference is illustrated by any technical terms: coefficient and exponent in algebra, triangle and square in their geometric as distinct from their popular meanings; capital and value as used in political economy, and so on.
Practical things are familiar
The difference as noted is purely relative to the intellectual progress of an individual; what is abstract at one period of growth is concrete at another; or even the contrary, as one finds that things supposed to be thoroughly familiar involve strange factors and unsolved problems. There is, nevertheless, a general line of cleavage which, deciding upon the whole what things fall within the limits of familiar acquaintance and what without, marks off the concrete and the abstract in a more permanent way. These limits are fixed mainly by the demands of practical life. Things such as sticks and stones, meat and potatoes, houses and trees, are such constant features of the environment of which we have to take account in order to live, that their important meanings are soon learnt, and indissolubly associated with objects. We are acquainted with a thing (or it is familiar to us) when we have so much to do with it that its strange and unexpected corners are rubbed off. The necessities of social intercourse convey to adults a like concreteness upon such terms as taxes, elections, wages, the law, and so on. Things the meaning of which I personally do not take in directly, appliances of cook, carpenter, or weaver, for example, are nevertheless unhesitatingly classed as concrete, since they are so directly connected with our common social life.
The theoretical, or strictly intellectual, is abstract
By contrast, the abstract is the theoretical, or that not intimately associated with practical concerns. The abstract thinker (the man of pure science as he is sometimes called) deliberately abstracts from application in life; that is, he leaves practical uses out of account. This, however, is a merely negative statement. What remains when connections with use and application are excluded? Evidently only what has to do with knowing considered as an end in itself. Many notions of science are abstract, not only because they cannot be understood without a long apprenticeship in the science (which is equally true of technical matters in the arts), but also because the whole content of their meaning has been framed for the sole purpose of facilitating further knowledge, inquiry, and speculation. When thinking is used as a means to some end, good, or value beyond itself, it is concrete; when it is employed simply as a means to more thinking, it is abstract. To a theorist an idea is adequate and self-contained just because it engages and rewards thought; to a medical practitioner, an engineer, an artist, a merchant, a politician, it is complete only when employed in the furthering of some interest in life—health, wealth, beauty, goodness, success, or what you will.
Contempt for theory
For the great majority of men under ordinary circumstances, the practical exigencies of life are almost, if not quite, coercive. Their main business is the proper conduct of their affairs. Whatever is of significance only as affording scope for thinking is pallid and remote—almost artificial. Hence the contempt felt by the practical and successful executive for the "mere theorist"; hence his conviction that certain things may be all very well in theory, but that they will not do in practice; in general, the depreciatory way in which he uses the terms abstract, theoretical, and intellectual—as distinct from intelligent.
But theory is highly practical
This attitude is justified, of course, under certain conditions. But depreciation of theory does not contain the whole truth, as common or practical sense recognizes. There is such a thing, even from the common-sense standpoint, as being "too practical," as being so intent upon the immediately practical as not to see beyond the end of one's nose or as to cut off the limb upon which one is sitting. The question is one of limits, of degrees and adjustments, rather than one of absolute separation. Truly practical men give their minds free play about a subject without asking too closely at every point for the advantage to be gained; exclusive preoccupation with matters of use and application so narrows the horizon as in the long run to defeat itself. It does not pay to tether one's thoughts to the post of use with too short a rope. Power in action requires some largeness and imaginativeness of vision. Men must at least have enough interest in thinking for the sake of thinking to escape the limits of routine and custom. Interest in knowledge for the sake of knowledge, in thinking for the sake of the free play of thought, is necessary then to the emancipation of practical life—to make it rich and progressive.
We may now recur to the pedagogic maxim of going from the concrete to the abstract.
Begin with the concrete means begin with practical manipulations
1. Since the concrete denotes thinking applied to activities for the sake of dealing effectively with the difficulties that present themselves practically, "beginning with the concrete" signifies that we should at the outset make much of doing; especially, make much in occupations that are not of a routine and mechanical kind and hence require intelligent selection and adaptation of means and materials. We do not "follow the order of nature" when we multiply mere sensations or accumulate physical objects. Instruction in number is not concrete merely because splints or beans or dots are employed, while whenever the use and bearing of number relations are clearly perceived, the number idea is concrete even if figures alone are used. Just what sort of symbol it is best to use at a given time—whether blocks, or lines, or figures—is entirely a matter of adjustment to the given case. If physical things used in teaching number or geography or anything else do not leave the mind illuminated with recognition of a meaning beyond themselves, the instruction that uses them is as abstract as that which doles out ready-made definitions and rules; for it distracts attention from ideas to mere physical excitations.
Confusion of the concrete with the sensibly isolated
The conception