Abstract
The concept of measurement is fundamental to a whole range of different disciplines, including not only the natural and engineering sciences, but also laboratory medicine and certain branches of the social sciences. This being the case, the concept of measurement has a particular relevance to the development of top-level ontologies in the area of knowledge engineering. For this reason, the present paper is concerned with ontological aspects of measurement. We are searching for a list of concepts that are apt to characterize measurement methods in a general manner. To establish such means of characterization, we will primarily deal with the semantics of measurement values.
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Notes
Requiring the metrization to be a standard one is necessary, since it is possible to set up arbitrary extensive metrizations for any quantity. A metrization is a standard one if it recognized as such, either by explicit conventions as the SI system or the practice of measurement or both.
In extending the use of the expression “metrization” to empirical quantities, we are following Diez (1997).
This account presupposes the framework of pre-relativistic physics, where the concept of simultaneity does not depend on the system of reference chosen.
For theoretical background of the triple point of water and the technical means to reproduce it see Nicholas and White (2001, pp. 95–105).
Resistance thermometer are based on the dependency between the temperature of a wire and its electrical resistance. For a thorough treatment see Nicholas and White (2001, pp. 114–119).
For the latter see Riedi (1988).
At least in the case of Suppes (1963), this is somewhat surprising since it appeared in the Handbook of Mathematical Psychology.
In addition to having a different zero point, mercury and gas thermometers show a significant difference when intervals at very low temperatures are measured even though the intervals of the Celsius-scale and of the thermodynamic temperature scale are chosen to be equivalent. This equivalence holds only well within a limited range of these scales. Again it is necessary to know the underlying metrization. Since only then we are able to compute the transformation between both scales.
Definitions in mathematical logic are required to be conservative extensions of the language system, i.e., the adoption of a definition must not extend the valid consequence relations between sets of sentences and single sentences, where in these sentence only non-defined symbols are used. This requirement is, in general, not satisfied by rules or axioms introducing symbols for an empirical metrical concepts into a language system.
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Acknowledgements
This work was supported by a grant of the DAAD, the German Academic Exchange Service. I am also grateful to an unknown reviewer for helpful comments on an earlier draft.
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Andreas, H. Ontological Aspects of Measurement. Axiomathes 18, 379–394 (2008). https://doi.org/10.1007/s10516-008-9039-y
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DOI: https://doi.org/10.1007/s10516-008-9039-y