A hundred years of numbers. An historical introduction to measurement theory 1887–1990: Part I: The formation period. Two lines of research: Axiomatics and real morphisms, scales and invariance

The aim of this paper is to reconstruct the historical evolution of the so-called Measurement Theory (MT). MT has two clearly different periods, the formation period and the mature theory, whose borderline coincides with the publication in 1951 of Suppes' foundational work, ‘A set of independent axioms for extensive quantities’. In this paper two previous research traditions on the foundations of measurement, developed during the formation period, come together in the appropriate way. These traditions correspond, on the one hand, to Helmholtz's, Campbell's and Hölder's studies on axiomatics and real morphisms and, on the other, to the work undertaken by Stevens and his school on scale types and transformations. These two lines of research are complementary in the sense that neither of them is enough taken alone, but together they contain all that is necessary to develop the theory, and it is in Suppes (1951) that these complementary approaches converge and all the elements of the theory are appropriately integrated for the first time. With Suppes' work, then, begins what may be called the ‘mature’ theory, which was to develop rapidly later on, especially during the 1960s. Our historical reconstruction is divided into two parts, each part devoted to one of the periods mentioned. Part I also contains a conceptual introduction which aims to establish the use of some notions, specifically those of measurement and metrization. Although the reconstruction is not exhaustive, it intends to be quite complete and up to date compared to what is available in measurement literature; in this sense the aim of this paper is mainly historical but, although secondarily, it also attempts to make some conceptual and metascientific clarifications on the subject of the theory.