The NUSAP Categories: Numeral, Unit and Spread

Abstract

We now consider the NUSAP categories in the order of their appearance. The most quantitative, and also the one which most basically defines the expression as a whole, is numeral. A notation for numeral will express an “arithmetic”: a set of elements and the relations among them, which correspond to analogous operations in the empirical system under consideration. The simplest example, of course, is the set of integers and its various extensions (such as fractions and negative numbers, and quantities like $\sqrt 2$ and π). We have seen that even in these ordinary number systems, the appropriate set of arithmetical relations may be artefactual or non-standard.