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The ongoing dialog between empirical science and measurement theory
 Journal of Mathematical Psychology
, 1996
"... 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 placed on the ongoing interplay between the development of abstract theory and the attempts to apply it to empiric ..."
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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 placed on the ongoing interplay between the development of abstract theory and the attempts to apply it to empirically testable phenomena. The article has four major sections. The first concerns classical representational measurement, which was the successful attempt to formulate the major measurement methods of classical physics: extensive and additive conjoint structures, their distributive interlock in dimensional analysis, and intensive (averaging) structures. The second illustrates a nontrivial behavioral example using both extensive and conjoint measurement plus functional equations to arrive at rank and signdependent utility (also called cumulative prospect) representations for decision making under risk. The third section, contemporary representational measurement, somewhat overlaps the classical one but includes new findings and approaches: representations of nonadditive concatenation and conjoint structures; a general theory of scale types; results for general, finitely unique, homogeneous structures; structures that are homogeneous between singular points; generalized distributive triples; and a generalization of dimensional analysis to include any ratio scalable attribute; and the concept of meaningfulness. The final section concerns applications of the latter ideas to psychophysical scaling and merging functions.] 1996 Academic Press, Inc. 1.
MEASUREMENTTHEORETIC OBSERVATIONS ON FIELD’S INSTRUMENTALISM AND THE APPLICABILITY OF MATHEMATICS
"... In this paper I examine Field’s account of the applicability of mathematics from a measurementtheoretic perspective. Within this context, I object to Field’s instrumentalism, arguing that it depends on an incomplete analysis of applicability. I show in particular that, once the missing piece of anal ..."
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In this paper I examine Field’s account of the applicability of mathematics from a measurementtheoretic perspective. Within this context, I object to Field’s instrumentalism, arguing that it depends on an incomplete analysis of applicability. I show in particular that, once the missing piece of analysis is provided, the role played by numerical entities in basic empirical theories must be revised: such revision implies that instrumentalism should be rejected and mathematical entities be regarded not merely as useful tools but also as conceptual schemata by means of which we can articulate our understanding of experience.
doi:10.1006/jmps.2002.1429 The Irony of Measurement by Subjective Estimations
"... measurement that radically differed from the dominate theory of the time. The dominate theory held that all strong forms of scientific measurement— for example, those that yielded ratio scales—had to be based on an observable ordering and an observable commutative and associative operation. Stevens ..."
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measurement that radically differed from the dominate theory of the time. The dominate theory held that all strong forms of scientific measurement— for example, those that yielded ratio scales—had to be based on an observable ordering and an observable commutative and associative operation. Stevens proposed different criteria and introduced his method of magnitude estimation. Stevens as well as measurement theorists considered his method to be radically different from those based on commutative and associative operations. Although his method was controversial, it became a standard tool in the behavioral sciences. This article argues that Stevens ’ method, together with implicit assumptions he made about the scales of measurement it generated, is from a mathematical perspective the same as the measurement process based on commutative and associative operations. The article also provides a theory of qualitative numbers and shows an interesting relationship