227
empirical and informational interpretations of measurement. As a consequence, the
central concept of measurement science is arguably no longer the “true value” that
exists independently of measurement and that would be obtained by an error-free
empirical process. While measurement is still sometimes characterized as a process
aimed at estimating the true value of a property (a prominent example is given by
Possolo, 2015: p. 12), the very idea of a measured property having an inherent true
value requires clarification as soon as the unavoidable role of models in measurement is accepted. (For example: Does the true value of a property change if the
model of the property or the model of the measurement change? Is therefore a truein-a-model value?)
Hence, in what follows we do not deny in principle the hypothesis that properties
have a true value, but neither do we rely on it: instead, we attempt to provide an
encompassing standpoint which should be understandable and acceptable independently of this hypothesis. Like the rest of this chapter, and like most of this book,
what follows may be read as starting from the VIM definition of as
a process of reasonable attribution of values to properties of objects (JCGM, 2012:
2.1) and aimed at establishing sufficiently well-defined criteria of such reasonableness. An appropriate characterization of measurement uncertainty plays a key role
in the service of this goal. What follows may be interpreted as a reconsideration of
the basic components of measurement uncertainty, as introduced in Sect. 3.2.4, in
light of the model presented above. But, first of all, we need to reconsider the
Hexagon Framework and expand it in order to take into account the possibility of
feedback with a measuring instrument.
7.4.1 Measurement that involves feedback
We have assumed so far that the interaction between the object under measurement
and the measuring instrument, as realized in the transduction stage (see Sect. 7.3.2),
is unidirectional: the interaction changes the state of the instrument as related to the
transduced property X m , where indeed Θ[a] → X m . In a more general case, however,
the interaction produces a change also in the state of the object under measurement.
In particular, when the object under measurement is a human being (or collection
thereof), as is usually the case in the human sciences, the objects under measurement may be aware of their being objects under measurement. In this circumstance,
not only might interaction uncertainty become a critical component of the uncertainty budget, but also the structure of the process itself becomes more complex due
to the presence of one or more feedback loops.
Three structural cases may be identified, as follows:
First case (no feedback): These are measurements in which the interaction with the
measuring instrument does not induce a change in the measurand (an obvious
example is the measurement of the spectral density of the radiation emitted by a
star: of course, the state of the star is not affected by the operation of the spec7.4 Measurement quality according to the model
empirical and informational interpretations of measurement. As a consequence, the
central concept of measurement science is arguably no longer the “true value” that
exists independently of measurement and that would be obtained by an error-free
empirical process. While measurement is still sometimes characterized as a process
aimed at estimating the true value of a property (a prominent example is given by
Possolo, 2015: p. 12), the very idea of a measured property having an inherent true
value requires clarification as soon as the unavoidable role of models in measurement is accepted. (For example: Does the true value of a property change if the
model of the property or the model of the measurement change? Is therefore a truein-a-model value?)
Hence, in what follows we do not deny in principle the hypothesis that properties
have a true value, but neither do we rely on it: instead, we attempt to provide an
encompassing standpoint which should be understandable and acceptable independently of this hypothesis. Like the rest of this chapter, and like most of this book,
what follows may be read as starting from the VIM definition of
a process of reasonable attribution of values to properties of objects (JCGM, 2012:
2.1) and aimed at establishing sufficiently well-defined criteria of such reasonableness. An appropriate characterization of measurement uncertainty plays a key role
in the service of this goal. What follows may be interpreted as a reconsideration of
the basic components of measurement uncertainty, as introduced in Sect. 3.2.4, in
light of the model presented above. But, first of all, we need to reconsider the
Hexagon Framework and expand it in order to take into account the possibility of
feedback with a measuring instrument.
7.4.1 Measurement that involves feedback
We have assumed so far that the interaction between the object under measurement
and the measuring instrument, as realized in the transduction stage (see Sect. 7.3.2),
is unidirectional: the interaction changes the state of the instrument as related to the
transduced property X m , where indeed Θ[a] → X m . In a more general case, however,
the interaction produces a change also in the state of the object under measurement.
In particular, when the object under measurement is a human being (or collection
thereof), as is usually the case in the human sciences, the objects under measurement may be aware of their being objects under measurement. In this circumstance,
not only might interaction uncertainty become a critical component of the uncertainty budget, but also the structure of the process itself becomes more complex due
to the presence of one or more feedback loops.
Three structural cases may be identified, as follows:
First case (no feedback): These are measurements in which the interaction with the
measuring instrument does not induce a change in the measurand (an obvious
example is the measurement of the spectral density of the radiation emitted by a
star: of course, the state of the star is not affected by the operation of the spec7.4 Measurement quality according to the model