A hundred years of numbers. An historical introduction to measurement theory 1887-1990 - part II: Suppes and the mature theory. Representation and uniqueness [Book Review]

In Part I we saw that the works of Helmholtz, Holder, Campbell and Stevens contain the main ingredients for the analysis of the conditions which make measurement possible, but, so to speak, that what is lacking in the work of the first three is to be found in the work of the last, and vice versa. The first tradition focuses on the conditions that an empirical qualitative system must satisfy in order to be numerically representable, but pays no attention to the relation between possible different representations. The second tradition focuses on the study of scale types and the mathematical properties of the transformations that characterize the scales, but says nothing about the empirical facts these scales represent and the nature of such representation. Then, these two lines of research need to be appropriately integrated. In this Part II, we shall see how this integration is brought about in the foundational work of Suppes, the extensions and modifications which are generated around this work and the mature theory which results from all of this
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