David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 70 (3):373 - 400 (1987)
The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong extensive measurement, in the sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom.
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Configure|
Similar books and articles
Jean-Claude Falmagne (1980). A Probabilistic Theory of Extensive Measurement. Philosophy of Science 47 (2):277-296.
A. A. J. Marley (1968). An Alternative "Fundamental" Axiomatization of Multiplicative Power Relations Among Three Variables. Philosophy of Science 35 (2):185-186.
Eric W. Holman (1974). Extensive Measurement Without an Order Relation. Philosophy of Science 41 (4):361-373.
Brent Mundy (1991). Embedding and Uniqueness in Relationist Theories. Philosophy of Science 58 (1):102-124.
Brigitte Falkenburg (1997). Incommensurability and Measurement. Theoria 12 (3):467-491.
R. Duncan Luce (1965). A "Fundamental" Axiomatization of Multiplicative Power Relations Among Three Variables. Philosophy of Science 32 (3/4):301-309.
Reinhard Niederée (1992). What Do Numbers Measure? A New Approach to Fundamental Measurement. Mathematical Social Sciences 24:237-276.
Hans Colonius (1978). On Weak Extensive Measurement. Philosophy of Science 45 (2):303-308.
Louis Narens (1974). Measurement Without Archimedean Axioms. Philosophy of Science 41 (4):374-393.
Brent Mundy (1988). Extensive Measurement and Ratio Functions. Synthese 75 (1):1 - 23.
Added to index2009-01-28
Total downloads8 ( #136,258 of 1,008,294 )
Recent downloads (6 months)1 ( #64,735 of 1,008,294 )
How can I increase my downloads?