A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness

@article{Narens1981AGT,
  title={A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness},
  author={Louis Narens},
  journal={Theory and Decision},
  year={1981},
  volume={13},
  pages={1-70}
}
  • L. Narens
  • Published 1 March 1981
  • Education
  • Theory and Decision
The role of mathematics in empirical science is puzzling, mysterious, and in my opinion has defied rational explanation. Why mathematics should be so enormously productive and effective in the handling of empirical phenomena is clearly an important foundational problem in science, but one for the most part that has been ignored. This is somewhat surprising given the rich theory and the abundance of results that have been developed in the philosophy and foupdations of mathematics. While there… 
Three Aspects of the Effectiveness of Mathematics in Science
TLDR
This paper dissects the normal use of mathematics in theoretical science into three aspects: idealizations of the scientific domain to continuum mathematics, empirical realizations of that mathematical structure, and the use in scientific arguments of mathematical constructions that have no empiricalrealizations.
Mathematical and Theoretical Systems Luce Mathematical Psychology and the Computer Revolution
As computers increasingly pervade science the question arises; Do psychologists have reason to study any more mathematics than is needed to program control of experiments, analyses of data, and
On the Theory of Meaningfulness of Ordinal Comparisons in Measurement: II a
The theory of measurement is a source of many interesting combinatorial problems. (See the recent surveys by Roberts [lS, 191.) In this paper, we discuss a particular problem that arises from the
Quantitative science and the definition of measurement in psychology
^ge d that establishing quantitative science involves two research tasks: the scientific one of showing that the relevant attribute is quantitative; and the instrumental on& of constructing
Further Comments on the “Nonrevolution” Arising From Axiomatic Measurement Theory
Cliff's (1992) commentary on the failure of axiomatic measurement theory (AMT) to generate as much impact on cognitive psychology and psychometrics as he had once anticipated invites further
Several unresolved conceptual problems of mathematical psychology
Abstract This article is a personal commentary on the following, to my mind, unresolved issues of mathematical psychology: (1) the failure of the field to have become a fully accepted part of most
The ongoing dialog between empirical science and measurement theory
Abstract This review article attempts to highlight from my personal perspective some of the major developments in the representational theory of measurement during the past 50 years. Emphasis is
Meaningfulness and Invariance
TLDR
Theories of meaningfulness are methods for investigating such matters, and invariance concepts are their primary tools.
Representational Measurement Theory
This chapter focuses on empirical structures, with an ordering attribute, leading to numerical or geometric representations. A historical sketch of physical, behavioral, and social science
Measurement Theory and the Research Psychologist
Among all the variants of theory in our discipline, measurement must rank as the oldest in tradition, the deepest in formal development, but, for the majority of psychologists, the lowest in
...
...

References

SHOWING 1-9 OF 9 REFERENCES
A theory of appropriate statistics
TLDR
It is argued that the use of inappropriate statistics leads to the formulation of statements which are either semantically meaning-less or empirically nonsignificant.
Dimensionally Invariant Numerical Laws Correspond to Meaningful Qualitative Relations
  • R. Luce
  • Mathematics
    Philosophy of Science
  • 1978
In formal theories of measurement meaningfulness is usually formulated in terms of numerical statements that are invariant under admissible transformations of the numerical representation. This is
On the Theory of Scales of Measurement.
TLDR
The current issues will remain at 32 pages until a more adequate supply of paper is assured, due to a shortage of paper for Bacto-Agar research.
The algebra of measurement
On the possible psychophysical laws.
  • R. Luce
  • Philosophy
    Psychological review
  • 1959