What do numbers measure?: A new approach to fundamental measurement

Abstract Unlike the standard representational theory of measurement, which takes the real numbers as a pregiven numerical domain, the approach presented in this paper is based on an abstract concept of a procedure of measurement, and ‘values of measurement’ are understood in terms of such procedures. The resulting ‘type approach’ makes use of elementary model-theoretic notions and emphasizes the constructibility of scales. It provides a natural starting point for a systematic discussion of issues that tend to be neglected in the standard framework (such as the relation between measurement and computation). At the same time it is perfectly compatible with the modern representational theory of measurement and helps elucidate a number of issues central to that theory (e.g. the role of Archimedean axioms).

[1]  Theodore M. Alper,et al.  A classification of all order-preserving homeomorphism groups of the reals that satisfy finite uniqueness , 1987 .

[2]  Louis Narens,et al.  Measurement without Archimedean Axioms , 1974, Philosophy of Science.

[3]  Eric W. Holman,et al.  Strong and weak extensive measurement , 1969 .

[4]  Hermann v. Helmholtƶ.  Zählen und Messen, erkenntnistheoretisch betrachtet , 1971, Philosophische Vorträge und Aufsätze.

[5]  J. Leeuw,et al.  Abstract Measurement Theory. , 1986 .

[6]  Heinz J. Skala,et al.  Non-Archimedean Utility Theory , 1975 .

[7]  Johann Pfanzagl,et al.  Theory of measurement , 1970 .

[8]  Patrick Suppes,et al.  Foundational aspects of theories of measurement , 1958, Journal of Symbolic Logic.

[9]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[10]  Thomas L. Heath,et al.  A History of Greek Mathematics , 1923, The Classical Review.

[11]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[12]  Peter P. Wakker,et al.  The algebraic versus the topological approach to additive representations , 1988 .

[13]  E. W. Adams,et al.  On the empirical status of axioms in theories of fundamental measurement , 1970 .

[14]  Kenneth L. Manders.  The Theory of all Substructures of a Structure: Characterisation and Decision Problems , 1979, J. Symb. Log..

[15]  Louis Narens,et al.  A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness , 1981 .

[16]  Brent Mundy,et al.  The metaphysics of quantity , 1987 .

[17]  Louis Narens,et al.  On the scales of measurement , 1981 .

[18]  H. Colonius.  On Weak Extensive Measurement , 1978, Philosophy of Science.