14
Third, in our view, and despite our previous point, we see that there has been an
overemphasis on the relevance of the Euclidean tradition to measurement science.
In particular, this tradition refers to a concept that is only loosely related to the
abovementioned empirical and informational process of measurement: the mathematical concept, i.e., a numerical ratio of entities. Hence, our conclusion
is that the contention that measurement applies only to quantitative properties cannot be justified by kowtowing to the Euclidean tradition.
At this point in the book, we begin our own explorations beyond these basic positions, and address the question: Given these necessary conditions, what complementary conditions are sufficient to characterize measurement?
As a background to answering that question, we review, in Chap. 4, three broad
perspectives on measurement—realism, operationalism, and representationalism—
and discuss, in the context of each of them, the epistemic status of measurement and
the conditions of its proper use. We present the main findings of this discussion in a
simple two-by-two mapping,
10
and the whole discussion leads us to the conclusion
that an essential characterization of measurement is as an empirically structured
model of the process, rather than some set of mathematical constraints on the inputs
or the outputs of the process. This, coupled with an acknowledgment of the inevitable role of models in the measurement process, can be summarized as a modeldependent realism about measurement.
Next, in Chap. 5, we take up the very target of measurement, i.e., properties. We
analyze properties from both ontological and epistemological perspectives, and
identify a core issue in terms of the meaning of the Basic Evaluation Equation (BEE):
Property of an object value of a property
=
which displays the basic components of any measurement result, and which must
also be complemented with some information about uncertainty. From our modeldependent realist standpoint, we interpret the BEE relation as the (simple though
controversial) claim of an actual referential equality: the BEE conveys information
on the measurand because the measurand and the measured value remain conceptually distinct entities, though they identify the same individual property. Our position
that measurement is an empirical process forces us to conclude that properties cannot be conceptual entities, and hence we must investigate the very existence of
properties. An additional complexity of the subject of the existence of properties is
that is a cluster concept, including 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 RCA)
• (e.g., mass and RCA)
In our realist perspective, individual properties exist as universals, but the interpretation of the BEE as a referential equality is compatible with other positions, and
10 As in Fig. 4.6, whose axes highlight whether measurement has been characterized as being
dependent on empirical and/or mathematical constraints, respectively.
1 Introduction
Third, in our view, and despite our previous point, we see that there has been an
overemphasis on the relevance of the Euclidean tradition to measurement science.
In particular, this tradition refers to a concept that is only loosely related to the
abovementioned empirical and informational process of measurement: the mathematical concept
is that the contention that measurement applies only to quantitative properties cannot be justified by kowtowing to the Euclidean tradition.
At this point in the book, we begin our own explorations beyond these basic positions, and address the question: Given these necessary conditions, what complementary conditions are sufficient to characterize measurement?
As a background to answering that question, we review, in Chap. 4, three broad
perspectives on measurement—realism, operationalism, and representationalism—
and discuss, in the context of each of them, the epistemic status of measurement and
the conditions of its proper use. We present the main findings of this discussion in a
simple two-by-two mapping,
10
and the whole discussion leads us to the conclusion
that an essential characterization of measurement is as an empirically structured
model of the process, rather than some set of mathematical constraints on the inputs
or the outputs of the process. This, coupled with an acknowledgment of the inevitable role of models in the measurement process, can be summarized as a modeldependent realism about measurement.
Next, in Chap. 5, we take up the very target of measurement, i.e., properties. We
analyze properties from both ontological and epistemological perspectives, and
identify a core issue in terms of the meaning of the Basic Evaluation Equation (BEE):
Property of an object value of a property
=
which displays the basic components of any measurement result, and which must
also be complemented with some information about uncertainty. From our modeldependent realist standpoint, we interpret the BEE relation as the (simple though
controversial) claim of an actual referential equality: the BEE conveys information
on the measurand because the measurand and the measured value remain conceptually distinct entities, though they identify the same individual property. Our position
that measurement is an empirical process forces us to conclude that properties cannot be conceptual entities, and hence we must investigate the very existence of
properties. An additional complexity of the subject of the existence of properties is
that
•
•
•
•
In our realist perspective, individual properties exist as universals, but the interpretation of the BEE as a referential equality is compatible with other positions, and
10 As in Fig. 4.6, whose axes highlight whether measurement has been characterized as being
dependent on empirical and/or mathematical constraints, respectively.
1 Introduction