The Differing Challenges of Explicating a Standard of Measurement

Measurement is the process of identifying a quantitative relationship between aspects of entities. This is done implicitly in order to form concepts in the first place.^[1] However, to explicate such a measurement--i.e. "to express in numerical terms the implicit measurements involved in concept-formation"^[2]--requires further work, that may be easier in some instances than others.

On the one hand, it is relatively trivial to understand the relationship that 3 feet has to 1 foot--all that is required here is the process of counting--but on the other hand, in order for man to explicitly understand in numerical terms the units of colour requires highly advanced scientific knowledge. To do such a thing man must not just implicitly grasp that there are colours and to notice their differences, but to discover that those differences arise from different wavelengths of light ("colour" refers to chromaticity + luminance, where chromaticity is the hue and saturation of the object in question---ultimately this boils down to the measurement of wavelengths).

The same is true of the measurements of different shapes---it is easy to calculate the area of a square, harder to do so for a circle, and to do so for any shape requires the complex mathematics of calculus.

A form of measurement, in sum, makes concept-formation possible---and concepts in turn make numerical measurement possible. This interdependence reflects a fundamental fact about human cognition: the perspective essential to both processes--the quantitative reduction to a unit--is the same.^[3]