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Definition and division
As definition sets forth intension, so division (or the reverse process, classification) expounds extension. Intension and extension, definition and division, are clearly correlative; in language previously used, intension is meaning as a principle of identifying particulars; extension is the group of particulars identified and distinguished. Meaning, as extension, would be wholly in the air or unreal, did it not point to some object or group of objects; while objects would be as isolated and independent intellectually as they seem to be spatially, were they not bound into groups or classes on the basis of characteristic meanings which they constantly suggest and exemplify. Taken together, definition and division put us in possession of individualized or definite meanings and indicate to what group of objects meanings refer. They typify the fixation and the organization of meanings. In the degree in which the meanings of any set of experiences are so cleared up as to serve as principles for grouping those experiences in relation to one another, that set of particulars becomes a science; i.e. definition and classification are the marks of a science, as distinct from both unrelated heaps of miscellaneous information and from the habits that introduce coherence into our experience without our being aware of their operation.
Definitions are of three types, denotative, expository, scientific. Of these, the first and third are logically important, while the expository type is socially and pedagogically important as an intervening step.
We define by picking out
I. Denotative. A blind man can never have an adequate understanding of the meaning of color and red; a seeing person can acquire the knowledge only by having certain things designated in such a way as to fix attention upon some of their qualities. This method of delimiting a meaning by calling out a certain attitude toward objects may be called denotative or indicative. It is required for all sense qualities—sounds, tastes, colors—and equally for all emotional and moral qualities. The meanings of honesty, sympathy, hatred, fear, must be grasped by having them presented in an individual's first-hand experience. The reaction of educational reformers against linguistic and bookish training has always taken the form of demanding recourse to personal experience. However advanced the person is in knowledge and in scientific training, understanding of a new subject, or a new aspect of an old subject, must always be through these acts of experiencing directly the existence or quality in question.
and also by combining what is already more definite,
2. Expository. Given a certain store of meanings which have been directly or denotatively marked out, language becomes a resource by which imaginative combinations and variations may be built up. A color may be defined to one who has not experienced it as lying between green and blue; a tiger may be defined (i.e. the idea of it made more definite) by selecting some qualities from known members of the cat tribe and combining them with qualities of size and weight derived from other objects. Illustrations are of the nature of expository definitions; so are the accounts of meanings given in a dictionary. By taking better-known meanings and associating them,—the attained store of meanings of the community in which one resides is put at one's disposal. But in themselves these definitions are secondhand and conventional; there is danger that instead of inciting one to effort after personal experiences that will exemplify and verify them, they will be accepted on authority as substitutes.
and by discovering method of production
3. Scientific. Even popular definitions serve as rules for identifying and classifying individuals, but the purpose of such identifications and classifications is mainly practical and social, not intellectual. To conceive the whale as a fish does not 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