interfere with the success of whalers, nor does it prevent recognition of a whale when seen, while to conceive it not as fish but as mammal serves the practical end equally well, and also furnishes a much more valuable principle for scientific identification and classification. Popular definitions select certain fairly obvious traits as keys to classification. Scientific definitions select conditions of causation, production, and generation as their characteristic material. The traits used by the popular definition do not help us to understand why an object has its common meanings and qualities; they simply state the fact that it does have them. Causal and genetic definitions fix upon the way an object is constructed as the key to its being a certain kind of object, and thereby explain why it has its class or common traits.
Contrast of causal and descriptive definitions
Science is the most perfect type of knowledge because it uses causal definitions
If, for example, a layman of considerable practical experience were asked what he meant or understood by metal, he would probably reply in terms of the qualities useful (i) in recognizing any given metal and (ii) in the arts. Smoothness, hardness, glossiness, and brilliancy, heavy weight for its size, would probably be included in his definition, because such traits enable us to identify specific things when we see and touch them; the serviceable properties of capacity for being hammered and pulled without breaking, of being softened by heat and hardened by cold, of retaining the shape and form given, of resistance to pressure and decay, would probably be included—whether or not such terms as malleable or fusible were used. Now a scientific conception, instead of using, even with additions, traits of this kind, determines meaning on a different basis. The present definition of metal is about like this: Metal means any chemical element that enters into combination with oxygen so as to form a base, i.e. a compound that combines with an acid to form a salt. This scientific definition is founded, not on directly perceived qualities nor on directly useful properties, but on the way in which certain things are causally related to other things; i.e. it denotes a relation. As chemical concepts become more and more those of relationships of interaction in constituting other substances, so physical concepts express more and more relations of operation: mathematical, as expressing functions of dependence and order of grouping; biological, relations of differentiation of descent, effected through adjustment of various environments; and so on through the sphere of the sciences. In short, our conceptions attain a maximum of definite individuality and of generality (or applicability) in the degree to which they show how things depend upon one another or influence one another, instead of expressing the qualities that objects possess statically. The ideal of a system of scientific conceptions is to attain continuity, freedom, and flexibility of transition in passing from any fact and meaning to any other; this demand is met in the degree in which we lay hold of the dynamic ties that hold things together in a continuously changing process—a principle that states insight into mode of production or growth.
Chapter Ten
Concrete and Abstract Thinking
False notions of concrete and abstract
The maxim enjoined upon teachers, "to proceed from the concrete to the abstract," is perhaps familiar rather than comprehended. Few who read and hear it gain a clear conception of the starting-point, the concrete; of the nature of the goal, the abstract; and of the exact nature of the path to be traversed in going from one to the other. At times the injunction is positively misunderstood, being taken to mean that education should advance from things to thought—as if any dealing with things in which thinking is not involved could possibly be educative. So understood, the maxim encourages mechanical routine or sensuous excitation at one end of the educational scale—the lower—and academic and unapplied learning at the upper end.
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
