The child does not think in such words (he has, as yet, no knowledge of words), but that is the nature of the process which his mind performs wordlessly. And that is the principle which his mind follows, when, having grasped the concept “length” by observing the three objects, he uses it to identify the attribute of length in a piece of string, a ribbon, a belt, a corridor or a street.
The same principle directs the process of forming concepts of entities—for instance, the concept “table.” The child’s mind isolates two or more tables from other objects, by focusing on their distinctive characteristic: their shape. He observes that their shapes vary, but have one characteristic in common: a flat, level surface and support(s). He forms the concept “table” by retaining that characteristic and omitting all particular measurements, not only the measurements of the shape, but of all the other characteristics of tables (many of which he is not aware of at the time).
Tables, for instance, are first differentiated from chairs, beds and other objects by means of the characteristic of shape, which is an attribute possessed by all the objects involved. Then, their particular kind of shape is set as the distinguishing characteristic of tables—i.e., a certain category of geometrical measurements of shape is specified. Then, within that category, the particular measurements of individual table-shapes are omitted.
Please note the fact that a given shape represents a certain category or set of geometrical measurements. Shape is an attribute; differences of shape—whether cubes, spheres, cones or any complex combinations—are a matter of differing measurements; any shape can be reduced to or expressed by a set of figures in terms of linear measurement. When, in the process of concept-formation, man observes that shape is a commensurable characteristic of certain objects, he does not have to measure all the shapes involved nor even to know how to measure them; he merely has to observe the element of similarity.
Concepts are not and cannot be formed in a vacuum; they are formed in a context; the process of conceptualization consists of observing the differences and similarities of the existents within the field of one’s awareness (and organizing them into concepts accordingly). From a child’s grasp of the simplest concept integrating a group of perceptually given concretes, to a scientist’s grasp of the most complex abstractions integrating long conceptual chains—all conceptualization is a contextual process; the context is the entire field of a mind’s awareness or knowledge at any level of its cognitive development.
Objectivity begins with the realization that man (including his every attribute and faculty, including his consciousness) is an entity of a specific nature who must act accordingly; that there is no escape from the law of identity, neither in the universe with which he deals nor in the working of his own consciousness, and if he is to acquire knowledge of the first, he must discover the proper method of using the second; that there is no room for the arbitrary in any activity of man, least of all in his method of cognition—and just as he has learned to be guided by objective criteria in making his physical tools, so he must be guided by objective criteria in forming his tools of cognition: his concepts.
Just as man’s physical existence was liberated when he grasped the principle that “nature, to be commanded, must be obeyed,” so his consciousness will be liberated when he grasps that nature, to be apprehended, must be obeyed—that the rules of cognition must be derived from the nature of existence and the nature, the identity, of his cognitive faculty.
Man’s sense organs function automatically; man’s brain integrates his sense data into percepts automatically; but the process of integrating percepts into concepts—the process of abstraction and of concept-formation—is not automatic.
See also: Abstractions and Concretes; Abstraction (process of); Concepts; Conceptual Common Denominator; Definitions; Genus and Species; Integration (Mental); Language; Measurement; Unit; Words.