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• In the Basic Evaluation Equation Q[a]  ≈  x q ref , for a given x, the expressions
“Q[a]” and “x q ref ” have different senses but could have the same individual
length as their referent.
The concept system about can then be depicted as in Fig. 6.7.
As discussed in Sect. 5.1, there is nothing arbitrary in the fact that an individual
quantity q is identified as the quantity Q[a] of an object a. Once again, this shows
that the Basic Evaluation Equation L[a] = 1.2345 m conveys the information that the
length L[a] of rod a and the value 1.2345 m of length are claimed to be instances of
the same individual length.
The previous construction, which has led us to reach a conclusion about what
values of quantities are, explicitly relies on the additivity of length. In the next two
sections we discuss how this conclusion generalizes to nonadditive cases. We discuss here values of nonadditive quantities, in particular those represented on interval scales, while reserving a discussion of the most general case of values of possibly
nonquantitative properties to Sect. 6.5.2.
referent—i.e., 1.2345 metres and 48.602 inches are the same length—but they have different
senses. For short, they are conceptually different but referentially the same.
Fig. 6.7 The concept system about and an example (just a specialization of Fig. 5.2)
6 Values, scales, and the existence of properties