Conceptual Common Denominator

The Conceptual Common Denominator (CCD) is the characteristic, reducible to a unit of measurement, in terms of which two or more existents are differentiated from other existents that also possess it. Objectivism treats it as the ground of every act of concept formation: nothing can be distinguished from anything except against something the two have in common.

“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."”
   ~ Ayn Rand, "Concept-Formation", Introduction to Objectivist Epistemology

Why differentiation needs a shared dimension

A difference can only be registered along some dimension. To notice that two tables differ from a chair is already to be comparing them in respect of something — here, shape and the function shape serves. Shape is what all three possess, and it is the possession of it in common that lets the difference show up as a difference.

This is what the CCD names. It is not the concept's distinguishing characteristic; it is the wider characteristic within which the distinguishing one is a specified range:

• CCD: shape.
• Distinguishing characteristic of "table": a particular range of shapes — flat level surface with supports.
• Distinguishing characteristic of "chair": a different range within the same dimension.

The same structure holds elsewhere. Colours are differentiated within the CCD of hue; lengths within the CCD of linear extension; emotions within the CCD of their relation to one's values.

What it rules out

The CCD is the reason Objectivist concept formation is not a matter of noticing whatever resemblances one likes. Any two things resemble each other in some respect, so unconstrained similarity would license any grouping at all — the standing objection to nominalism.

Requiring a commensurable characteristic constrains this. A grouping is valid only if its members differ from the contrast cases within a dimension all of them share, and that is a question of fact rather than of convenience. A supposed concept assembled from things with no common measurable characteristic is an invalid concept, and one that bundles incompatible things under a single term is a package deal.

The CCD is also what makes the resulting differences ordered rather than merely noted. Within a shared dimension, differences are quantitative, which is what measurement omission then operates on. See Measurement.

Position in the hierarchy

Because every concept is formed against a CCD, and the CCD is itself a characteristic that had to be identified, concepts arrive in an order. Wider concepts are reached by integrating narrower ones, narrower by subdividing wider, and all of them reduce eventually to perceptual entities, which are the given. See Hierarchy and Existents.

Common misunderstandings

• That the CCD is the definition. It is the dimension the definition operates in. "Shape" is not what a table is; it is what tables and chairs both have, and within which they differ.
• That the CCD must be a single characteristic. Rand's definition allows more than one, and complex concepts often need several.
• That finding a common denominator makes a grouping valid. It is necessary, not sufficient. The differences within it must also be small relative to the differences from the contrast cases, which is what makes them quantitative rather than a change of kind.
• That the choice of CCD is arbitrary because different comparisons are possible. Different purposes select different dimensions, and each selection is either supported by the facts or not. That two valid classifications of the same things exist does not make either one a convention. See Context and Objectivity.

See also

• Concept formation · Concept · Unit · Measurement omission · Measurement
• Hierarchy · Fundamental · Rule of Fundamentality · Rand's Razor
• Invalid Concept · Package-Deal · Floating Abstraction
• Nominalism · Realism · Intrinsicism · Objectivity

Discussion

• Attribute vs quality
• A criticism of Objectivist epistemology

References

• Rand, Ayn. "Concept-Formation" and "Abstraction from Abstractions", Introduction to Objectivist Epistemology. The Objectivist, 1967.
• Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 3.