Edited by Alessandro Giordani (Università Cattolica di Milano, Università Cattolica di Milano)
|Summary||Measurement is a fundamental empirical process aimed at acquiring and codifying information about an entity, the object or system under measurement. This process is commonly interpreted in functional terms as a production process, accomplished by means of a measurement system, whose input is the system under measurement and whose output is a piece of information, the property value, about a certain instance of a general property of that system, the measurand. As a consequence, the central problem concerning the definition of measurement turns into the one of characterizing the just mentioned process. When an empirical general property is specified, any system under measurement can be viewed as a member of a class of systems characterized by that property. When provided with a set of relations between its elements, this class is called an empirical relational system and measurement can be conceived of as a mapping assigning numbers to elements of this system in such a way that the relations between these elements are preserved by relations between numbers in a numerical relational system. This is the model underlying the so-called representational theory of measurement, considered nowadays the standard measurement theory. According to this model to measure is to construct a representation of an empirical system to a numerical system, under the hypothesis that relations in the empirical system are somehow observable. The model has many merits, but it is also subject to many problems. In particular, the crucial drawback is given by the difficulty of linking the proposed conception of measurement with the way in which measurement is accounted for from a metrological point of view, specifically the point of view underlying the International Vocabulary of Metrology. Hence, the debate concerning the characterization of measurement is still open, where the principal task consists in defining a general model aiming at (i) providing a sound interpretation of measurement as structured process; (ii) identifying the ontological conditions to be fulfilled for measurement to be possible; (iii) identifying the epistemic conditions to be fulfilled for measurement results to be able to justify empirical assertions.|
|Key works||The representational theory of measurement has its roots in the work of Scott and Suppes 1958 and has found its more extensive exposition in the three volumes of the Foundations of Measurement (1971, 1989, 1990), but see also Roberts 1985, for a more friendly presentation, and Narens 1985. The metrological standpoint is summarized in the International Vocabulary of Metrology (VIM). For a problematization of the representational theory see Domotor et al. 2008, where an analytical approach to measurement is developed, and Frigerio et al. 2010, where a synthesis between the representional approach and the metrological approach is proposed.|
|Introductions||See Suppes 2002 for a general introduction to the representational standpoint.|
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