29
This position—that measurement is necessarily of a property of an object—is
less obvious than it might seem. For example, while Norman Campbell was clear on
this matter in defining measurement as “the process of assigning numbers to represent qualities” (1920: p. 267),
14
the widely quoted rephrasing by Stanley Stevens—
“measurement, in the broadest sense, is defined as the assignment of numerals to
objects or events according to rules” (1946: p. 677)—may be interpreted as aimed
at avoiding any reference to properties in a conceptual framework about measurement. While we devote part of Chap. 5 to this subject, we maintain here that, properly, we do not measure objects, but properties of objects. Warren Torgerson stated
it clearly (1958: p. 14; the original text contains “system” where we have written
“object”):
While [the] distinction between [objects] and their properties is perhaps obvious, it is nevertheless an important distinction. It is of special importance here because of the fact that it
is always the properties that are measured and not the [objects] themselves. Measurement
is always measurement of a property and never measurement of a[n object].
Vice versa, some presentations claim that the input of a measurement is a value. For
example, John Bentley (2005: p. 3) writes that “the input to the measurement system is the true value of the variable”. If values of properties (and quantities) are
distinguished from properties (and quantities) of objects, as we consider necessary
to account for the basic conceptual structure of measurement (a point developed
further in Chap. 5), the conclusion is that this is a categorical mistake: the empirical
interaction on which a measurement is based cannot be with mathematical entities,
such as property values.
Traditionally measurement is presented as related to quantities, not more generically to properties. Given the importance of this subject, Chap. 6 discusses the relation between properties and quantities. We do not venture to propose a definition of
what a property is, because it is a complex and controversial pre-metrological topic
requiring a fundamental ontological framework (for an introduction see, e.g., Orilia
& Swoyer, 2020). While Chaps. 5 and 6 are devoted to better analyzing this subject,
it is sufficient to mention here that an empirical property of an object—and thus
more specifically an empirical quantity of an object—such as the length of a rod or
the reading comprehension ability of an individual is associated with a mode of
empirical interaction of the object with its environment. This association happens
under the conditions that:
• An object a empirically interacts with its environment in multiple modes, and
each of them is supposed to correspond to a property of the object, say, its length
L[a], its weight W[a], its reading comprehension ability R[a], ….
• Some objects, a 1 , a 2 , …, are comparable with respect to some of their properties,
and sometimes distinct objects are discovered to have empirically indistinguish14 Note Campbell’s use of the term “quality” in place of “property”, which we avoid because explicitly contrasts with : while stating that quantities are specific qualities is
indeed odd, in the conceptual framework of the VIM—which we generally adopt here—quantities
are specific properties. Furthermore, whether measurement is actually an assignment and its results
are representations is an issue that we discuss in the following chapters.
2.2 The abstract structure of measurement
This position—that measurement is necessarily of a property of an object—is
less obvious than it might seem. For example, while Norman Campbell was clear on
this matter in defining measurement as “the process of assigning numbers to represent qualities” (1920: p. 267),
14
the widely quoted rephrasing by Stanley Stevens—
“measurement, in the broadest sense, is defined as the assignment of numerals to
objects or events according to rules” (1946: p. 677)—may be interpreted as aimed
at avoiding any reference to properties in a conceptual framework about measurement. While we devote part of Chap. 5 to this subject, we maintain here that, properly, we do not measure objects, but properties of objects. Warren Torgerson stated
it clearly (1958: p. 14; the original text contains “system” where we have written
“object”):
While [the] distinction between [objects] and their properties is perhaps obvious, it is nevertheless an important distinction. It is of special importance here because of the fact that it
is always the properties that are measured and not the [objects] themselves. Measurement
is always measurement of a property and never measurement of a[n object].
Vice versa, some presentations claim that the input of a measurement is a value. For
example, John Bentley (2005: p. 3) writes that “the input to the measurement system is the true value of the variable”. If values of properties (and quantities) are
distinguished from properties (and quantities) of objects, as we consider necessary
to account for the basic conceptual structure of measurement (a point developed
further in Chap. 5), the conclusion is that this is a categorical mistake: the empirical
interaction on which a measurement is based cannot be with mathematical entities,
such as property values.
Traditionally measurement is presented as related to quantities, not more generically to properties. Given the importance of this subject, Chap. 6 discusses the relation between properties and quantities. We do not venture to propose a definition of
what a property is, because it is a complex and controversial pre-metrological topic
requiring a fundamental ontological framework (for an introduction see, e.g., Orilia
& Swoyer, 2020). While Chaps. 5 and 6 are devoted to better analyzing this subject,
it is sufficient to mention here that an empirical property of an object—and thus
more specifically an empirical quantity of an object—such as the length of a rod or
the reading comprehension ability of an individual is associated with a mode of
empirical interaction of the object with its environment. This association happens
under the conditions that:
• An object a empirically interacts with its environment in multiple modes, and
each of them is supposed to correspond to a property of the object, say, its length
L[a], its weight W[a], its reading comprehension ability R[a], ….
• Some objects, a 1 , a 2 , …, are comparable with respect to some of their properties,
and sometimes distinct objects are discovered to have empirically indistinguish14 Note Campbell’s use of the term “quality” in place of “property”, which we avoid because
indeed odd, in the conceptual framework of the VIM—which we generally adopt here—quantities
are specific properties. Furthermore, whether measurement is actually an assignment and its results
are representations is an issue that we discuss in the following chapters.
2.2 The abstract structure of measurement