The Theory of Fundamental Measurement

Formalization of Measurement

In this chapter, we introduce the theory of fundamental measurement and the theory of derived measurement, and study the uniqueness of fundamental and derived measures. Fundamental measurement deals with the measurement process that takes place at an early stage of scientific development, when some fundamental measures are first defined. Derived measurement takes place later, when new measures are defined in terms of others previously developed. In this section, we shall' begin with fundamental measurement. Derived measurement will be treated in Section 2.5. Our approach to measurement follows those of Scott and Suppes [1958], Suppes and Zinnes [1963], Pfanzagl [1968], and Krantz et al. [1971].

Russell [1938, p. 176] defines measurement as follows: “Measurement of magnitudes is, in its most general sense, any method by which a unique and reciprocal correspondence is established between all or some of the magnitudes of a kind and all or some of the numbers, integral, rational, or real as the case may be.” Campbell [1938, p. 126] says that measurement is “the assignment of numerals to represent properties of material systems other than number, in virtue of the laws governing these properties.” To Stevens [1951, p. 22], “measurement is the assignment of numerals to objects or events according to rules.” Torgerson [1958, p. 14] says that “measurement of a property … involves the assignment of numbers to systems to represent that property.”