113
Furthermore, we consider that phrases such as “the objects a and b are comparable
with respect to a given property” and “a given property of the object a and a given
property of the object b are comparable” refer to the same empirical situation.
6
Whenever this happens, we say that the given properties of a and b are of the same
kind (as in JCGM, 2012: 1.2), and thus we assume that a general property exists of
which the given properties of a and b, which we call individual properties, are
instances (see also an introduction of these concepts in Sect. 2.2). General and individual properties—such as mass and any given mass, respectively—are sometimes
called, particularly in the philosophical literature, “determinables” and “determinates”, respectively (see, e.g., Wilson, 2017). Hence length and reading comprehension ability are examples of general properties, and the length of a given rod and the
reading comprehension ability of a given individual are examples of individual
properties. The length of a given rod and the radius of a given disk are comparable,
being individual properties of the same kind, i.e., the general property length,
whereas the length and the mass of any two objects are not comparable, as they are
individual properties of different kinds.
Even given this modest perspective, several important issues remain open for
consideration, regarding in particular the distinction between the existence of a
property and the knowledge that we can have of it. This chapter is devoted to an
analysis of this subject, and to providing an interpretation of the (measurement)
relation
measurand measured value of a property
=
as introduced in Sect. 2.2.4, a specific case
7
of the Basic Evaluation Equation
property of an object value of a property
=
itself. Not surprisingly, these concepts are also sometimes used in a somewhat confusing way in
pivotal texts of measurement science, for example Foundations of Measurement (Krantz et al.,
1971: p. 1) which states in its opening sentence: “when measuring some attribute of a class of
objects or events, we associate numbers (or other familiar mathematical entities, such as vectors)
with the objects in such a way that the properties of the attribute are faithfully represented as
numerical properties”. The idea that an attribute has properties represented as properties is not
exactly obvious, to say the least.
6 In fact, the first phrase, while seemingly better reporting what empirically happens (“in the comparison we handle objects, right?”, as a colleague of ours told us), assumes a greater ontic burden,
given that the entity with respect to which objects are compared is a kind of property, whereas
kinds of properties do not explicitly appear in the second phrase. Furthermore, it is surely possible
that properties of the same object are compared, for example the height and the width of a rigid
body: in terms of comparison of objects this would require a cumbersome phrasing like “an object
is compared with itself with respect to a (kind of) property”.
7 Measurands are “quantities intended to be measured” (as defined in JCGM, 2012: 2.3): hence,
while measurands are properties of objects, a property of an object becomes a measurand for us
only when we are interested in obtaining a value for it via a measurement. Several aspects of our
analysis apply to the generic case, thus for example also to Basic Evaluation Equations which
describe specifications, instead of reporting results of measurements.
5.1 Introduction
Furthermore, we consider that phrases such as “the objects a and b are comparable
with respect to a given property” and “a given property of the object a and a given
property of the object b are comparable” refer to the same empirical situation.
6
Whenever this happens, we say that the given properties of a and b are of the same
kind (as in JCGM, 2012: 1.2), and thus we assume that a general property exists of
which the given properties of a and b, which we call individual properties, are
instances (see also an introduction of these concepts in Sect. 2.2). General and individual properties—such as mass and any given mass, respectively—are sometimes
called, particularly in the philosophical literature, “determinables” and “determinates”, respectively (see, e.g., Wilson, 2017). Hence length and reading comprehension ability are examples of general properties, and the length of a given rod and the
reading comprehension ability of a given individual are examples of individual
properties. The length of a given rod and the radius of a given disk are comparable,
being individual properties of the same kind, i.e., the general property length,
whereas the length and the mass of any two objects are not comparable, as they are
individual properties of different kinds.
Even given this modest perspective, several important issues remain open for
consideration, regarding in particular the distinction between the existence of a
property and the knowledge that we can have of it. This chapter is devoted to an
analysis of this subject, and to providing an interpretation of the (measurement)
relation
measurand measured value of a property
=
as introduced in Sect. 2.2.4, a specific case
7
of the Basic Evaluation Equation
property of an object value of a property
=
itself. Not surprisingly, these concepts are also sometimes used in a somewhat confusing way in
pivotal texts of measurement science, for example Foundations of Measurement (Krantz et al.,
1971: p. 1) which states in its opening sentence: “when measuring some attribute of a class of
objects or events, we associate numbers (or other familiar mathematical entities, such as vectors)
with the objects in such a way that the properties of the attribute are faithfully represented as
numerical properties”. The idea that an attribute has properties represented as properties is not
exactly obvious, to say the least.
6 In fact, the first phrase, while seemingly better reporting what empirically happens (“in the comparison we handle objects, right?”, as a colleague of ours told us), assumes a greater ontic burden,
given that the entity with respect to which objects are compared is a kind of property, whereas
kinds of properties do not explicitly appear in the second phrase. Furthermore, it is surely possible
that properties of the same object are compared, for example the height and the width of a rigid
body: in terms of comparison of objects this would require a cumbersome phrasing like “an object
is compared with itself with respect to a (kind of) property”.
7 Measurands are “quantities intended to be measured” (as defined in JCGM, 2012: 2.3): hence,
while measurands are properties of objects, a property of an object becomes a measurand for us
only when we are interested in obtaining a value for it via a measurement. Several aspects of our
analysis apply to the generic case, thus for example also to Basic Evaluation Equations which
describe specifications, instead of reporting results of measurements.
5.1 Introduction