248
and and the measured value remain conceptually distinct entities, though they identify the same individual property. Given the conditions that measurement is an
empirical process and that empirical processes cannot be performed on conceptual
or mathematical entities, this forced us to take on an analysis of the existence of
properties. The complexity of this subject is also due to the fact that is a
cluster concept, encompassing four sub-concepts: (e.g., the
mass of a given object and the reading comprehension ability of a given individual),
(e.g., 1.234 kg and 1.23 logits on a specific RCA scale),
(e.g., a given mass and a given reading comprehension ability), and (e.g., mass and reading comprehension ability). From
our model-dependent realist perspective individual properties exist as universals,
but other positions are also compatible with the interpretation of the Basic Evaluation
Equation as a referential equality, and thus possible disagreements over the actual
nature of the entities exemplified by one or more of the sub-concepts of
did not block continued progress in our exploration.
Three fundamental issues for measurement science were then discussed in Chap.
6. The first was about the nature of values of quantities and more generally values
of properties. A step-by-step construction was provided to show that values are
individual properties, identified as elements of a scale, rather than symbols for the
representation of properties. From this perspective, the difference between values of
quantitative and nonquantitative properties is a matter of the structure of the scale to
which they belong.
The second issue was then about the structure of scales and the related conditions
of invariance, which provided a criterion for classifying property evaluations and
then properties themselves in terms of scale types. This analysis found no unique
condition for separating quantitative and nonquantitative properties, and reinforced
the position that being quantitative and being measurable are distinct conditions.
The third issue concerned the conditions of the existence of general properties
and the possible role of measurement in the definition of general properties. Our
basic assumption was that an empirical process can interact only with an empirically existing entity, and that this applies both to the objects that bear the properties
and the properties of the objects. Thus, the distinction needs to be maintained
between empirical properties and mathematical variables that may be used as models of properties. The hypothesis of existence of an empirical property is corroborated by the observation of effects causally attributed to the property.
In Chap. 7 we finally proposed a general model of a measurement process, consistent with the ontological and epistemological commitments developed in the previous chapters. The distinction between empirical and informational processes was,
again, the starting point: measurement is neither a purely empirical nor a purely
informational process. We broadly distinguished between direct and indirect methods of measurement as a fundamental classification of measurement methods
related to the complementary roles of empirical and informational components,
where indirect measurements necessarily include at least one direct measurement.
As a consequence, a structural characterization of direct measurement is the actual
foundation of measurement science: this is what we proposed with the Hexagon
8 Conclusion
and and the measured value remain conceptually distinct entities, though they identify the same individual property. Given the conditions that measurement is an
empirical process and that empirical processes cannot be performed on conceptual
or mathematical entities, this forced us to take on an analysis of the existence of
properties. The complexity of this subject is also due to the fact that
cluster concept, encompassing four sub-concepts:
mass of a given object and the reading comprehension ability of a given individual),
our model-dependent realist perspective individual properties exist as universals,
but other positions are also compatible with the interpretation of the Basic Evaluation
Equation as a referential equality, and thus possible disagreements over the actual
nature of the entities exemplified by one or more of the sub-concepts of
did not block continued progress in our exploration.
Three fundamental issues for measurement science were then discussed in Chap.
6. The first was about the nature of values of quantities and more generally values
of properties. A step-by-step construction was provided to show that values are
individual properties, identified as elements of a scale, rather than symbols for the
representation of properties. From this perspective, the difference between values of
quantitative and nonquantitative properties is a matter of the structure of the scale to
which they belong.
The second issue was then about the structure of scales and the related conditions
of invariance, which provided a criterion for classifying property evaluations and
then properties themselves in terms of scale types. This analysis found no unique
condition for separating quantitative and nonquantitative properties, and reinforced
the position that being quantitative and being measurable are distinct conditions.
The third issue concerned the conditions of the existence of general properties
and the possible role of measurement in the definition of general properties. Our
basic assumption was that an empirical process can interact only with an empirically existing entity, and that this applies both to the objects that bear the properties
and the properties of the objects. Thus, the distinction needs to be maintained
between empirical properties and mathematical variables that may be used as models of properties. The hypothesis of existence of an empirical property is corroborated by the observation of effects causally attributed to the property.
In Chap. 7 we finally proposed a general model of a measurement process, consistent with the ontological and epistemological commitments developed in the previous chapters. The distinction between empirical and informational processes was,
again, the starting point: measurement is neither a purely empirical nor a purely
informational process. We broadly distinguished between direct and indirect methods of measurement as a fundamental classification of measurement methods
related to the complementary roles of empirical and informational components,
where indirect measurements necessarily include at least one direct measurement.
As a consequence, a structural characterization of direct measurement is the actual
foundation of measurement science: this is what we proposed with the Hexagon
8 Conclusion