84
quantity is selected as the unit, then the additive combination of that quantity with
itself has to be associated with the numerical value 2, and so on. This is indeed a
condition of morphic mapping which does not require any empirical action to be
performed on given measurands, and is in fact preliminary to any such empirical
action. In other words, scale construction is a critical precondition for the execution
of measurement (see Sect. 7.3) but it is surely not measurement as such: representational theories take as their starting point the availability of an observed set of relations among objects, and thus bracket out everything that must take place in order
for such relations to be observed in the first place (see, e.g., Borsboom, 2005; Mari,
2013; Michell, 1990). Indeed, RTMs as such have little or nothing to say about the
activities involved in data acquisition, including the definition of measured properties, design and operation of measuring instruments, empirical and statistical strategies for controlling the effects of influence properties, and management and
reporting of measurement uncertainty. In the words of Marcel Boumans, himself
referring to Michael Heidelberger, “The disadvantage of a general RTM is that it is
much too liberal […]: we could not make any difference between a theoretical
determination of the value of a theoretical quantity and the actual measurement”
(2007: p. 234). Instead, RTMs might be better interpreted as a purely formal and
idealized interpretation of measurement (sometimes even explicitly noted in
accounts of representational theories, e.g., “the theory of measurement is difficult
enough without bringing in the theory of making measurements”, Kyburg, 1984:
p. 7), but as such are unable to distinguish between measurement and morphic mapping in general (Mari, 2013; Mari et al., 2012). From this perspective one could
argue that the representational theories of measurement are simply misnamed: they
are at most a theory of scale construction, presupposing the availability of the right
sorts of empirical inputs to form the basis of the resulting scale. A better term for
them might be then representational theories of scaling.
Representationalism also has the consequence that evaluations based on orderings and even classifications count as measurements (related to what Stevens called
“ordinal” and “nominal” scales, respectively), and therefore introduced a multiplicity of algebraic structures in which the properties and their values can be embedded.
Specific to each scale type is the set of relations that are invariant under particular
scale transformations.
9
The acknowledgment that such structures are not inherent
features of properties, but instead depend on the state of knowledge about that property (Giordani & Mari, 2012),
10
can be interpreted as an attempt to give measurement
9 Stevens’ theory is not without objections (for one synthesis of criticisms, see Velleman &
Wilkinson, 1993). In part, such criticisms have reacted to Stevens’ choice of calling the invariant
scale transformations “admissible” or “permissible”, the objection being, in essence, that research
should not be driven by prescriptions and surely not inhibited by proscriptions. Our analysis of
these criticisms is in Sect. 6.5.1.
10 For example, temperature, thought in antiquity to be an ordinal property, was upgraded (with the
introduction of thermometers and thermometric scales) to a quantity. At first only interval-level
measurement was possible; eventually the thermodynamic redefinition of temperature, which
introduced a nonconventional zero point in the scale, made ratio-level measurement possible.
4 Philosophical perspectives on measurement
quantity is selected as the unit, then the additive combination of that quantity with
itself has to be associated with the numerical value 2, and so on. This is indeed a
condition of morphic mapping which does not require any empirical action to be
performed on given measurands, and is in fact preliminary to any such empirical
action. In other words, scale construction is a critical precondition for the execution
of measurement (see Sect. 7.3) but it is surely not measurement as such: representational theories take as their starting point the availability of an observed set of relations among objects, and thus bracket out everything that must take place in order
for such relations to be observed in the first place (see, e.g., Borsboom, 2005; Mari,
2013; Michell, 1990). Indeed, RTMs as such have little or nothing to say about the
activities involved in data acquisition, including the definition of measured properties, design and operation of measuring instruments, empirical and statistical strategies for controlling the effects of influence properties, and management and
reporting of measurement uncertainty. In the words of Marcel Boumans, himself
referring to Michael Heidelberger, “The disadvantage of a general RTM is that it is
much too liberal […]: we could not make any difference between a theoretical
determination of the value of a theoretical quantity and the actual measurement”
(2007: p. 234). Instead, RTMs might be better interpreted as a purely formal and
idealized interpretation of measurement (sometimes even explicitly noted in
accounts of representational theories, e.g., “the theory of measurement is difficult
enough without bringing in the theory of making measurements”, Kyburg, 1984:
p. 7), but as such are unable to distinguish between measurement and morphic mapping in general (Mari, 2013; Mari et al., 2012). From this perspective one could
argue that the representational theories of measurement are simply misnamed: they
are at most a theory of scale construction, presupposing the availability of the right
sorts of empirical inputs to form the basis of the resulting scale. A better term for
them might be then representational theories of scaling.
Representationalism also has the consequence that evaluations based on orderings and even classifications count as measurements (related to what Stevens called
“ordinal” and “nominal” scales, respectively), and therefore introduced a multiplicity of algebraic structures in which the properties and their values can be embedded.
Specific to each scale type is the set of relations that are invariant under particular
scale transformations.
9
The acknowledgment that such structures are not inherent
features of properties, but instead depend on the state of knowledge about that property (Giordani & Mari, 2012),
10
can be interpreted as an attempt to give measurement
9 Stevens’ theory is not without objections (for one synthesis of criticisms, see Velleman &
Wilkinson, 1993). In part, such criticisms have reacted to Stevens’ choice of calling the invariant
scale transformations “admissible” or “permissible”, the objection being, in essence, that research
should not be driven by prescriptions and surely not inhibited by proscriptions. Our analysis of
these criticisms is in Sect. 6.5.1.
10 For example, temperature, thought in antiquity to be an ordinal property, was upgraded (with the
introduction of thermometers and thermometric scales) to a quantity. At first only interval-level
measurement was possible; eventually the thermodynamic redefinition of temperature, which
introduced a nonconventional zero point in the scale, made ratio-level measurement possible.
4 Philosophical perspectives on measurement