Conceptual Common Denominator

A commensurable characteristic (such as shape in the case of tables, or hue in the case of colors) is an essential element in the process of concept-formation. I shall designate it as the “Conceptual Common Denominator” and define it as “The characteristic(s) reducible to a unit of measurement, by means of which man differentiates two or more existents from other existents possessing it.”

The distinguishing characteristic(s) of a concept represents a specified category of measurements within the “Conceptual Common Denominator” involved.

Two fundamental attributes are involved in every state, aspect or function of man’s consciousness: content and action—the content of awareness, and the action of consciousness in regard to that content. These two attributes are the fundamental Conceptual Common Denominator of all concepts pertaining to consciousness.

When concepts are integrated into a wider one, the new concept includes all the characteristics of its constituent units; but their distinguishing characteristics are regarded as omitted measurements, and one of their common characteristics determines the distinguishing characteristic of the new concept: the one representing their “Conceptual Common Denominator” with the existents from which they are being differentiated.

When a concept is subdivided into narrower ones, its distinguishing characteristic is taken as their “Conceptual Common Denominator”—and is given a narrower range of specified measurements or is combined with an additional characteristic(s), to form the individual distinguishing characteristics of the new concepts.

The rules of correct definition are derived from the process of concept-formation. The units of a concept were differentiated—by means of a distinguishing characteristic(s)—from other existents possessing a commensurable characteristic, a Conceptual Common Denominator. A definition follows the same principle: it specifies the distinguishing characteristic(s) of the units, and indicates the category of existents from which they were differentiated.

The distinguishing characteristic(s) of the units becomes the differentia of the concept’s definition; the existents possessing a Conceptual Common Denominator become the genus.

Since axiomatic concepts are not formed by differentiating one group of existents from others, but represent an integration of all existents, they have no Conceptual Common Denominator with anything else. They have no contraries, no alternatives.

Copyright © 1986 by Harry Binswanger. Introduction copyright © 1986 by Leonard Peikoff. All rights reserved. For information address New American Library.


Excerpts from The Ominous Parallels, by Leonard Peikoff. Copyright © 1982 by Leonard Peikoff. Reprinted with permission of Stein and Day Publishers. Excerpts from The Romantic Manifesto, by Ayn Rand. Copyright © 1971, by The Objectivist. Reprinted with permission of Harper & Row, Publishers, Inc. Excerpts from Atlas Shrugged, copyright © 1957 by Ayn Rand, The Fountainhead, copyright © 1943 by Ayn Rand, and For the New Intellectual, copyright © 1961 by Ayn Rand. Reprinted by permission of the Estate of Ayn Rand. Excerpts from Philosophy: Who Needs It, by Ayn Rand. Copyright © 1982 by Leonard Peikoff, Executor, Estate of Ayn Rand. Reprinted by permission of the Estate of Ayn Rand. Excerpts from “The Philosophy of Objectivism” lecture series. Copyright © 1976 by Leonard Peikoff. Reprinted by permission. Excerpts from Alvin Toffler’s interview with Ayn Rand, which first appeared in Playboy magazine. Copyright © 1964. Reprinted by permission of Alvin Toffler. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Plume, a member of Penguin Group (USA), Inc.