by Ayn Rand
From Introduction to Objectivist Epistemology
Introduction to Objectivist Epistemology
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“Concept-Formation,” which is chapter 2 of Introduction to Objectivist Epistemology, was first published in the July 1966 issue of The Objectivist, then in a booklet containing the entire work (1967), then in a mass market paperback (1979) and most recently in an expanded second edition (1990).

A concept is a mental integration of two or more units which are isolated according to a specific characteristic(s) and united by a specific definition.

The units involved may be any aspect of reality: entities, attributes, actions, qualities, relationships, etc.; they may be perceptual concretes or other, earlier-formed concepts. The act of isolation involved is a process of abstraction: i.e., a selective mental focus that takes out or separates a certain aspect of reality from all others (e.g., isolates a certain attribute from the entities possessing it, or a certain action from the entities performing it, etc.). The uniting involved is not a mere sum, but an integration, i.e., a blending of the units into a single, new mental entity which is used thereafter as a single unit of thought (but which can be broken into its component units whenever required).

In order to be used as a single unit, the enormous sum integrated by a concept has to be given the form of a single, specific, perceptual concrete, which will differentiate it from all other concretes and from all other concepts. This is the function performed by language. Language is a code of visual-auditory symbols that serves the psycho-epistemological function of converting concepts into the mental equivalent of concretes. Language is the exclusive domain and tool of concepts. Every word we use (with the exception of proper names) is a symbol that denotes a concept, i.e., that stands for an unlimited number of concretes of a certain kind.

(Proper names are used in order to identify and include particular entities in a conceptual method of cognition. Observe that even proper names, in advanced civilizations, follow the definitional principles of genus and differentia: e.g., John Smith, with “Smith” serving as genus and “John” as differentia — or New York, U.S.A.)

Words transform concepts into (mental) entities; definitions provide them with identity. (Words without definitions are not language but inarticulate sounds.) We shall discuss definitions later and at length.

The above is a general description of the nature of concepts as products of a certain mental process. But the question of epistemologyEpistemology is a science devoted to the discovery of the proper methods of acquiring and validating knowledge...
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is: what precisely is the nature of that process? To what precisely do concepts refer in reality?

Let us now examine the process of forming the simplest concept.

Let us now examine the process of forming the simplest concept, the concept of a single attribute (chronologically, this is not the first concept that a child would grasp; but it is the simplest one epistemologically) — for instance, the concept “length.” If a child considers a match, a pencil and a stick, he observes that length is the attribute they have in common, but their specific lengths differ. The difference is one of measurement. In order to form the concept “length,” the child’s mind retains the attribute and omits its particular measurements. Or, more precisely, if the process were identified in words, it would consist of the following: “Length must exist in some quantity, but may exist in any quantity. I shall identify as ‘length’ that attribute of any existentThe building-block of man’s knowledge is the concept of an “existent”—of something that exists, be it a thing, an attribute or an action...
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possessing it which can be quantitatively related to a unit of length, without specifying the quantity.”

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).

An adult definition of “table” would be: “A man-made object consisting of a flat, level surface and support(s), intended to support other, smaller objects.” Observe what is specified and what is omitted in this definition: the distinctive characteristic of the shape is specified and retained; the particular geometrical measurementsMeasurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves as a unit...
Cognition and Measurement, 7-8View Full Lexicon Entry
of the shape (whether the surface is square, round, oblong or triangular, etc., the number and shape of supports, etc.) are omitted; the measurements of size or weight are omitted; the fact that it is a material object is specified, but the material of which it is made is omitted, thus omitting the measurements that differentiate one material from another; etc. Observe, however, that the utilitarian requirements of the table set certain limits on the omitted measurements, in the form of “no larger than and no smaller than” required by its purpose. This rules out a ten-foot tall or a two-inch tall table (though the latter may be sub-classified as a toy or a miniature table) and it rules out unsuitable materials, such as non-solids.

Bear firmly in mind that the term “measurements omitted” does not mean, in this context, that measurements are regarded as non-existent; it means that measurements exist, but are not specified. That measurements must exist is an essential part of the process. The principle is: the relevant measurements must exist in some quantity, but may exist in any quantity.

A child is not and does not have to be aware of all these complexities when he forms the concept “table.” He forms it by differentiating tables from all other objects in the context of his knowledge. As his knowledge grows, the definitions of his concepts grow in complexity. (We shall discuss this when we discuss definitions.) But the principle and pattern of concept-formation remain the same.

The first words a child learns are words denoting visual objects, and he retains his first concepts visually. Observe that the visual form he gives them is reduced to those essentials which distinguish the particular kind of entities from all others — for instance, the universal type of a child’s drawing of man in the form of an oval for the torso, a circle for the head, four sticks for extremities, etc. Such drawings are a visual record of the process of abstraction and concept-formation in a mind’s transition from the perceptual level to the full vocabulary of the conceptual level.

There is evidence to suppose that written language originated in the form of drawings — as the pictographic writing of the Oriental peoples seems to indicate. With the growth of man’s knowledge and of his power of abstraction, a pictorial representation of concepts could no longer be adequate to his conceptual range, and was replaced by a fully symbolic code.

A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.

A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.

The element of similarity is crucially involved in the formation of every concept; similarity, in this context, is the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree.

Observe the multiple role of measurements in the process of concept-formation, in both of its two essential parts: differentiation and integration. Concepts cannot be formed at random. All concepts are formed by first differentiating two or more existents from other existents. All conceptual differentiations are made in terms of commensurable characteristics (i.e., characteristics possessing a common unit of measurement). No concept could be formed, for instance, by attempting to distinguish long objects from green objects. Incommensurable characteristics cannot be integrated into one unit.

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Ayn Rand
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