15
hence our continued progress in our exploration is not thwarted by possible disagreements over the actual nature of the entities exemplified by one or more of the
sub-concepts of.
In Chap. 6 we discuss three fundamental issues for measurement science. The
first issue concerns the nature of values of properties, though we start by discussing
the values of quantities. We provide a step-by-step construction to show that values
are not symbols for the representation of properties, but that values are individual
properties, identified as elements of a scale. Taking this perspective, we can see that
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 is then
about the structure of scales and the related conditions of invariance, so that scale
types provide a classification for property evaluations and then properties themselves. Our analysis finds no unique condition for separating quantitative and nonquantitative properties, and this finding reinforces the distinction between being
quantitative and being measurable. The third issue in this chapter concerns general
properties. Our basic assumption here is 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, a distinction needs to be maintained between empirical properties and mathematical variables that may be used as
mathematical models of properties. Regarding the conditions of the existence of
general properties and the possible role of measurement in the definition of general
properties, the hypothesis of existence of an empirical property can be corroborated
by the observation of effects causally attributed to the property.
In Chap. 7 we reach the high point of our story where we propose a general
model of the measurement process, one consistent with the ontological and epistemological commitments developed in the chapters before. Again, we start with the
distinction between empirical and informational processes, and recall that measurement is neither a purely empirical nor a purely informational process. We broadly
distinguish between direct and indirect methods of measurement as a fundamental
classification of measurement methods related to the complementary roles of these
empirical and informational components: indirect measurements necessarily include
at least one direct measurement. In consequence, we give a structural characterization of direct measurement as the actual foundation of measurement science. This
structural characterization we call the Hexagon Framework, and we exemplify it for
both physical and psychosocial properties. We also use the Framework to highlight
the importance of evaluating the quality of the information produced by a measurement, but now frame this in terms of the high-level, complementary requirements of
object relatedness (“objectivity”) and subject independence (“intersubjectivity”).
Finally, the Framework provides a sufficient condition for measurability: a property
is measurable if it is the input of at least one process that has been successfully
structured according to the Framework.
Thus, in the conclusion of our story in Chap. 8, we revisit the arguments and
discussions of the earlier chapters. We come back to address our initial question:
Following the necessary conditions we discuss in Chaps. 2 and 3, and the conclusions we reach in the subsequent chapters, what sufficient conditions, complementary to the necessary conditions, do we propose for characterizing measurement
across the sciences?
1.3 The path we will travel in this book
hence our continued progress in our exploration is not thwarted by possible disagreements over the actual nature of the entities exemplified by one or more of the
sub-concepts of
In Chap. 6 we discuss three fundamental issues for measurement science. The
first issue concerns the nature of values of properties, though we start by discussing
the values of quantities. We provide a step-by-step construction to show that values
are not symbols for the representation of properties, but that values are individual
properties, identified as elements of a scale. Taking this perspective, we can see that
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 is then
about the structure of scales and the related conditions of invariance, so that scale
types provide a classification for property evaluations and then properties themselves. Our analysis finds no unique condition for separating quantitative and nonquantitative properties, and this finding reinforces the distinction between being
quantitative and being measurable. The third issue in this chapter concerns general
properties. Our basic assumption here is 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, a distinction needs to be maintained between empirical properties and mathematical variables that may be used as
mathematical models of properties. Regarding the conditions of the existence of
general properties and the possible role of measurement in the definition of general
properties, the hypothesis of existence of an empirical property can be corroborated
by the observation of effects causally attributed to the property.
In Chap. 7 we reach the high point of our story where we propose a general
model of the measurement process, one consistent with the ontological and epistemological commitments developed in the chapters before. Again, we start with the
distinction between empirical and informational processes, and recall that measurement is neither a purely empirical nor a purely informational process. We broadly
distinguish between direct and indirect methods of measurement as a fundamental
classification of measurement methods related to the complementary roles of these
empirical and informational components: indirect measurements necessarily include
at least one direct measurement. In consequence, we give a structural characterization of direct measurement as the actual foundation of measurement science. This
structural characterization we call the Hexagon Framework, and we exemplify it for
both physical and psychosocial properties. We also use the Framework to highlight
the importance of evaluating the quality of the information produced by a measurement, but now frame this in terms of the high-level, complementary requirements of
object relatedness (“objectivity”) and subject independence (“intersubjectivity”).
Finally, the Framework provides a sufficient condition for measurability: a property
is measurable if it is the input of at least one process that has been successfully
structured according to the Framework.
Thus, in the conclusion of our story in Chap. 8, we revisit the arguments and
discussions of the earlier chapters. We come back to address our initial question:
Following the necessary conditions we discuss in Chaps. 2 and 3, and the conclusions we reach in the subsequent chapters, what sufficient conditions, complementary to the necessary conditions, do we propose for characterizing measurement
across the sciences?
1.3 The path we will travel in this book