156
• Second, having a reference quantity defined as the quantity of one object implies
that all traceability chains must start from that object, in the sense that all measuring instruments for that quantity must be directly or indirectly calibrated
against the reference object: this is operationally inconvenient and may require
careful handling in a political sense, given the power that the situation confers to
the owner of the object.
Alternative strategies to define stable and accessible reference quantities may be
envisaged to avoid or at least reduce these flaws. Such alternative strategies are
particularly required in the case where the quantities intended to be measured are
properties of human beings, which, if the steps described above were to be followed, would imply that, in principle, reference objects should be certain individual
humans, a situation that of course is not usually appropriate for several reasons.
14
Rather than selecting specific objects, a representative sample of objects—hence
persons, in some cases—could be then selected, their property of interest somehow
evaluated, and the reference quantity defined as a statistic (e.g., the mean or the
median) of the obtained values. This makes the reference quantity depend on the
selected sample, and therefore in principle it is not entirely stable if new samples are
taken or if characteristics of the sampled population change. (In psychometrics,
evaluations performed according to this strategy are called “norm-referenced”, to
emphasize the normative role of the sample that defines the reference quantity; see
Glaser, 1963.
15
)
Another possible strategy for dealing with these issues may be based on the consideration that according to the best available theories there is a class of objects,
R = {r i }, that when put in given conditions invariantly have the same quantity of
interest, which is then a constant.
16
Defining the reference quantity as a constant
only seem to be lighter when compared to the rusted cube, given that it is only the numerical representation of their mass that changes. A very-well-studied case of such changes is that of the
kilogram, which before the 2019 revision of the SI was defined as the mass of a given artifact, the
International Prototype of the Kilogram (IPK).
14 For discussions of strategies for defining reference quantities in human measurement using
resources from the Rasch measurement tradition, see, e.g., Maul, Mari, and Wilson (2019), Wilson
et al. (2019), and Briggs (2019).
15 An example of this is the well-known case of the intelligence quotient (IQ), defined by taking the
median raw score of the chosen sample as IQ 100 and one sample standard deviation as corresponding to 15 IQ points. It has been observed that since the early twentieth century raw scores on
IQ tests have increased in most parts of the world, a situation called the Flynn effect (Flynn, 2009).
Whether intelligence has also increased is, of course, another matter.
16 On this matter Eran Tal (2019) introduces the distinction between types and tokens, and proposes
thermal expansion coefficient of aluminum at 20 °C and thermal expansion coefficient of a particular piece of aluminum at a given temperature as examples of a type and a corresponding token,
such that “quantity types may be instantiated by more than one object or event”. Since there can be
an element other than aluminum that at a given temperature has the same thermal expansion coefficient of aluminum at 20 °C, quantity types are not the same as general properties, as we have
introduced them. We do not consider that this distinction deserves to be adopted here: the vast
majority of properties actually measured would be tokens with no type (e.g., what is the type of the
length of a given rod? or of the reading comprehension ability of a given student?).
6 Values, scales, and the existence of properties
• Second, having a reference quantity defined as the quantity of one object implies
that all traceability chains must start from that object, in the sense that all measuring instruments for that quantity must be directly or indirectly calibrated
against the reference object: this is operationally inconvenient and may require
careful handling in a political sense, given the power that the situation confers to
the owner of the object.
Alternative strategies to define stable and accessible reference quantities may be
envisaged to avoid or at least reduce these flaws. Such alternative strategies are
particularly required in the case where the quantities intended to be measured are
properties of human beings, which, if the steps described above were to be followed, would imply that, in principle, reference objects should be certain individual
humans, a situation that of course is not usually appropriate for several reasons.
14
Rather than selecting specific objects, a representative sample of objects—hence
persons, in some cases—could be then selected, their property of interest somehow
evaluated, and the reference quantity defined as a statistic (e.g., the mean or the
median) of the obtained values. This makes the reference quantity depend on the
selected sample, and therefore in principle it is not entirely stable if new samples are
taken or if characteristics of the sampled population change. (In psychometrics,
evaluations performed according to this strategy are called “norm-referenced”, to
emphasize the normative role of the sample that defines the reference quantity; see
Glaser, 1963.
15
)
Another possible strategy for dealing with these issues may be based on the consideration that according to the best available theories there is a class of objects,
R = {r i }, that when put in given conditions invariantly have the same quantity of
interest, which is then a constant.
16
Defining the reference quantity as a constant
only seem to be lighter when compared to the rusted cube, given that it is only the numerical representation of their mass that changes. A very-well-studied case of such changes is that of the
kilogram, which before the 2019 revision of the SI was defined as the mass of a given artifact, the
International Prototype of the Kilogram (IPK).
14 For discussions of strategies for defining reference quantities in human measurement using
resources from the Rasch measurement tradition, see, e.g., Maul, Mari, and Wilson (2019), Wilson
et al. (2019), and Briggs (2019).
15 An example of this is the well-known case of the intelligence quotient (IQ), defined by taking the
median raw score of the chosen sample as IQ 100 and one sample standard deviation as corresponding to 15 IQ points. It has been observed that since the early twentieth century raw scores on
IQ tests have increased in most parts of the world, a situation called the Flynn effect (Flynn, 2009).
Whether intelligence has also increased is, of course, another matter.
16 On this matter Eran Tal (2019) introduces the distinction between types and tokens, and proposes
thermal expansion coefficient of aluminum at 20 °C and thermal expansion coefficient of a particular piece of aluminum at a given temperature as examples of a type and a corresponding token,
such that “quantity types may be instantiated by more than one object or event”. Since there can be
an element other than aluminum that at a given temperature has the same thermal expansion coefficient of aluminum at 20 °C, quantity types are not the same as general properties, as we have
introduced them. We do not consider that this distinction deserves to be adopted here: the vast
majority of properties actually measured would be tokens with no type (e.g., what is the type of the
length of a given rod? or of the reading comprehension ability of a given student?).
6 Values, scales, and the existence of properties