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.

“Concepts of Consciousness”
Introduction to Objectivist Epistemology, 30

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.

“Concepts of Consciousness”
Introduction to Objectivist Epistemology, 41

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.

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