183
property”, “ordinal property”, etc.—are meant as shorthands for something like
“property that at the current state of knowledge is known to be evaluable on a nominal scale at best”, and so on. Even the very distinction between quantitative and
nonquantitative properties has, then, this same quality: as the historical development of the measurement of temperature shows, a property that we can evaluate
only in a nonquantitative way today might tomorrow also become evaluable
quantitatively.
On this basis, we may finally devote some consideration to our most fundamental
problem here: the conditions of existence of general properties.
6.6 About the existence of general properties
A basic commitment at the core of our perspective on measurement is that it is both
an empirical and an informational process, aimed at producing information about
the world, and more specifically, about properties of objects. A direct consequence
of this view is that a property cannot be measured if it does not exist as part of the
empirical world; that is, the empirical existence of a property is a necessary, though
not sufficient, condition for its measurability (Mari, Maul, & Wilson, 2018). This
statement may seem so obvious as to approach banality, but it has some less obvious
features and consequences worthy of further exploration. In particular, one may ask:
How can we know that a property exists? Stated alternatively, under what conditions
is a claim about the existence of a property justified? And, more specifically, what
does a claim of existence of a general property assume?
This section is dedicated to an analysis of this question, beginning with some
conceptual house cleaning, related to the distinction between empirical properties
and mathematical variables.
6.6.1 Properties and variables
We have proposed that empirical properties are associated with modes of empirical
interaction of objects with their environments. To help sharpen up this statement, let
us consider the distinction between empirical properties and mathematical variables. An (existing) empirical property can, in principle, be modeled by a mathematical variable; indeed, this is one of the primary activities involved in a
measurement process, as described in more detail in the following chapter.
47
an ordinal value and the evaluation sets the diameter of each object to be equal to the value of the
last sieve crossed by the object. Such an evaluation is then only ordinal.
47 The identification of the conditions that make such modeling possible is one of the primary contributions of the representational theories of measurement, the stated aim of which is “to construct
numerical representations of qualitative structures” (Krantz et al., 1971: p. xviii). (Perhaps pecu6.6 About the existence of general properties
property”, “ordinal property”, etc.—are meant as shorthands for something like
“property that at the current state of knowledge is known to be evaluable on a nominal scale at best”, and so on. Even the very distinction between quantitative and
nonquantitative properties has, then, this same quality: as the historical development of the measurement of temperature shows, a property that we can evaluate
only in a nonquantitative way today might tomorrow also become evaluable
quantitatively.
On this basis, we may finally devote some consideration to our most fundamental
problem here: the conditions of existence of general properties.
6.6 About the existence of general properties
A basic commitment at the core of our perspective on measurement is that it is both
an empirical and an informational process, aimed at producing information about
the world, and more specifically, about properties of objects. A direct consequence
of this view is that a property cannot be measured if it does not exist as part of the
empirical world; that is, the empirical existence of a property is a necessary, though
not sufficient, condition for its measurability (Mari, Maul, & Wilson, 2018). This
statement may seem so obvious as to approach banality, but it has some less obvious
features and consequences worthy of further exploration. In particular, one may ask:
How can we know that a property exists? Stated alternatively, under what conditions
is a claim about the existence of a property justified? And, more specifically, what
does a claim of existence of a general property assume?
This section is dedicated to an analysis of this question, beginning with some
conceptual house cleaning, related to the distinction between empirical properties
and mathematical variables.
6.6.1 Properties and variables
We have proposed that empirical properties are associated with modes of empirical
interaction of objects with their environments. To help sharpen up this statement, let
us consider the distinction between empirical properties and mathematical variables. An (existing) empirical property can, in principle, be modeled by a mathematical variable; indeed, this is one of the primary activities involved in a
measurement process, as described in more detail in the following chapter.
47
an ordinal value and the evaluation sets the diameter of each object to be equal to the value of the
last sieve crossed by the object. Such an evaluation is then only ordinal.
47 The identification of the conditions that make such modeling possible is one of the primary contributions of the representational theories of measurement, the stated aim of which is “to construct
numerical representations of qualitative structures” (Krantz et al., 1971: p. xviii). (Perhaps pecu6.6 About the existence of general properties