Conceptual Common Denominator

The “conceptual common denominator” (CCD) is what allows for abstract differentiation to occur. In the words of Ayn Rand, the CCD is:

The characteristic(s) reducible to a unit of measurement, by means of which man differentiates two or more existents from other existents possessing it.¹

So, we can reduce the shape of a table down to a unit of measurement, namely feet, and radians, etc.—we define the shape of a specific table with reference to the concepts of length, and angle. We then differentiate this “table-ey” shape from other shapes, and thus we can form the concept “table”—we do not differentiate the shape of a table from objects that are red, because shape and colour are incommensurable. Peikoff elaborates:

[…] one can differentiate tables from chairs or beds, because all these groups possess a commensurable characteristic, shape. This CCD, in turn, determines what feature must be chosen as the distinguishing characteristic of the concept “table”: tables are distinguished by a specific kind of shape, which represents a specific category or set of geometric measurements within the characteristic of shape—as against beds, e.g., whose shapes are encompassed by a different set of measurements. (Once the appropriate category has been specified, one completes the process of forming “table” by omitting the measurements of the individual table shapes within that category.)²