118
• a weak ontology, which assumes that values are assigned as a means of
representation.
The common ground of these positions is the acknowledgment that (i) in performing measurement, the starting point is the identification of a property of an object to
be measured, i.e., the measurand, and the discovery (according to a strong ontology)
or the selection (according to a weak ontology) of a set of possible values of that
property, and (ii) the outcome of the process is that one value in the set (or a subset
of them, as in JCGM, 2012: 2.1, if measurement uncertainty is taken into account)
is attributed to the measurand. The issue is about how to interpret such an attribution: Is the value established because it exists in the object before and independently
of any experimental activity, or is it (just) chosen to suitably report the acquired
information on the object? Is then measurement akin to discovery or invention?
Even more fundamentally, this issue is grounded upon the issue of the very existence of properties: Do entities such as length and reading comprehension ability
exist in the world, or are they just constructs by which we organize our knowledge?
Positions like the one underlying the representational theories of measurement
(see Sect. 4.2.3) emphasize the representational aspect of measurement, plainly stating that the task of measurement is “to construct numerical representations of qualitative structures” (Krantz, Luce, Suppes, & Tversky, 1971: p. xviii), and from their
beginnings have acknowledged that “the major source of difficulty in providing an
adequate theory of measurement is to construct relations which have an exact and
reasonable numerical interpretation” (Scott & Suppes, 1958: p. 113). Such weaker
ontologies are less demanding, and this may make their practical consequences
applicable also to those who accept a stricter position: a value may be chosen to
represent a property of an object exactly because that property has that value.
10
If
instead it is maintained that properties of objects do not inherently have values, the
representation may be chosen according to different criteria, and is required to be at
least consistent: if properties of objects are observed to be ordered then their
assigned values should be ordered in turn, but any ordered set would be suitable,
and so on. However, a stronger ontology invites interpretation of advancements in
measurement-related knowledge and practices as an evolutionary process: at the
beginning the available information could be so “meager and unsatisfactory” (quoting Lord Kelvin; see the related discussion by Kuhn, 1961) that the evaluation
results are more or less everything that is known of the considered property, and
therefore consistency in the representation is the only condition that can be sought.
Such an approach could be later abandoned with the acquisition of more and better
information, leading to corroboration of the hypothesis of the very existence of the
property, up to the extreme position that the measurand has a knowledge-independent true value, to be estimated through measurement.
11
10 Interestingly, the form of the Basic Evaluation Equation, in which the property of the object and
the value of the property are related by an “=” sign, suggests the interpretation that the property is
the value: we discuss this delicate point in Sect. 6.4.
11 The history of the concept of true value is complex, and definitely still not settled (see also Sects.
5 What is measured?
• a weak ontology, which assumes that values are assigned as a means of
representation.
The common ground of these positions is the acknowledgment that (i) in performing measurement, the starting point is the identification of a property of an object to
be measured, i.e., the measurand, and the discovery (according to a strong ontology)
or the selection (according to a weak ontology) of a set of possible values of that
property, and (ii) the outcome of the process is that one value in the set (or a subset
of them, as in JCGM, 2012: 2.1, if measurement uncertainty is taken into account)
is attributed to the measurand. The issue is about how to interpret such an attribution: Is the value established because it exists in the object before and independently
of any experimental activity, or is it (just) chosen to suitably report the acquired
information on the object? Is then measurement akin to discovery or invention?
Even more fundamentally, this issue is grounded upon the issue of the very existence of properties: Do entities such as length and reading comprehension ability
exist in the world, or are they just constructs by which we organize our knowledge?
Positions like the one underlying the representational theories of measurement
(see Sect. 4.2.3) emphasize the representational aspect of measurement, plainly stating that the task of measurement is “to construct numerical representations of qualitative structures” (Krantz, Luce, Suppes, & Tversky, 1971: p. xviii), and from their
beginnings have acknowledged that “the major source of difficulty in providing an
adequate theory of measurement is to construct relations which have an exact and
reasonable numerical interpretation” (Scott & Suppes, 1958: p. 113). Such weaker
ontologies are less demanding, and this may make their practical consequences
applicable also to those who accept a stricter position: a value may be chosen to
represent a property of an object exactly because that property has that value.
10
If
instead it is maintained that properties of objects do not inherently have values, the
representation may be chosen according to different criteria, and is required to be at
least consistent: if properties of objects are observed to be ordered then their
assigned values should be ordered in turn, but any ordered set would be suitable,
and so on. However, a stronger ontology invites interpretation of advancements in
measurement-related knowledge and practices as an evolutionary process: at the
beginning the available information could be so “meager and unsatisfactory” (quoting Lord Kelvin; see the related discussion by Kuhn, 1961) that the evaluation
results are more or less everything that is known of the considered property, and
therefore consistency in the representation is the only condition that can be sought.
Such an approach could be later abandoned with the acquisition of more and better
information, leading to corroboration of the hypothesis of the very existence of the
property, up to the extreme position that the measurand has a knowledge-independent true value, to be estimated through measurement.
11
10 Interestingly, the form of the Basic Evaluation Equation, in which the property of the object and
the value of the property are related by an “=” sign, suggests the interpretation that the property is
the value: we discuss this delicate point in Sect. 6.4.
11 The history of the concept of true value is complex, and definitely still not settled (see also Sects.
5 What is measured?