146
6.2 Towards values of properties
A Basic Evaluation Equation, in its simplest version in which uncertainty is not
taken into account, is
property of an object value of a property
=
When Norman Campbell famously stated that “the object of measurement is to
enable the powerful weapon of mathematical analysis to be applied to the subject
matter of science” (1920: p. 267), it is plausible that he was indeed referring to this
kind of equation, and expressly to the specific case
quantity of an object value of a quantity
=
which, when expressed in the Q-notation (see Sect. 5.1), enables “the powerful
weapon of mathematical analysis” by explicitly including numbers in the equation, e.g.,
L a
[ ] = 1 2345
.
m
as multipliers of units. (Henceforth we write “L[a]” as a shorthand for “length[rod
a]”.) Analogous is the case of the modified notation
L
a
in metres [ ] = 1 2345
.
as in some formalizations, such as those adopted in representational theories of
measurement (see, e.g., Krantz, Luce, Suppes, & Tversky, 1971, and also Kyburg,
1984: p. 17). Through Basic Evaluation Equations, values of properties, and thus
values of quantities in particular, are indeed the mathematical counterparts of
empirical properties of objects. Values play the fundamental role of providing the
information that is the reason for which measurement is performed: before measurement the measurand is known only as a property of an object; after measurement we also know a value for it. (Once again, references to uncertainty are
important for a more complete presentation of measurement, but are not relevant
here.) Once the relation is accepted as dependable, the value can be mathematically
manipulated in place of experimentally operating on the property of the object. (As
a trivial example, if L[a] = 1.2345 m and L[b] = 2.3456 m then we can infer that
L[a] < L[b] directly from 1.2345 m < 2.3456 m.)
An analysis of the nature and the role of values of properties is then a core component for the development of a measurement-related ontology and epistemology of
properties. Let us start by considering the specific case of quantities and their
6 Values, scales, and the existence of properties
6.2 Towards values of properties
A Basic Evaluation Equation, in its simplest version in which uncertainty is not
taken into account, is
property of an object value of a property
=
When Norman Campbell famously stated that “the object of measurement is to
enable the powerful weapon of mathematical analysis to be applied to the subject
matter of science” (1920: p. 267), it is plausible that he was indeed referring to this
kind of equation, and expressly to the specific case
quantity of an object value of a quantity
=
which, when expressed in the Q-notation (see Sect. 5.1), enables “the powerful
weapon of mathematical analysis” by explicitly including numbers in the equation, e.g.,
L a
[ ] = 1 2345
.
m
as multipliers of units. (Henceforth we write “L[a]” as a shorthand for “length[rod
a]”.) Analogous is the case of the modified notation
L
a
in metres [ ] = 1 2345
.
as in some formalizations, such as those adopted in representational theories of
measurement (see, e.g., Krantz, Luce, Suppes, & Tversky, 1971, and also Kyburg,
1984: p. 17). Through Basic Evaluation Equations, values of properties, and thus
values of quantities in particular, are indeed the mathematical counterparts of
empirical properties of objects. Values play the fundamental role of providing the
information that is the reason for which measurement is performed: before measurement the measurand is known only as a property of an object; after measurement we also know a value for it. (Once again, references to uncertainty are
important for a more complete presentation of measurement, but are not relevant
here.) Once the relation is accepted as dependable, the value can be mathematically
manipulated in place of experimentally operating on the property of the object. (As
a trivial example, if L[a] = 1.2345 m and L[b] = 2.3456 m then we can infer that
L[a] < L[b] directly from 1.2345 m < 2.3456 m.)
An analysis of the nature and the role of values of properties is then a core component for the development of a measurement-related ontology and epistemology of
properties. Let us start by considering the specific case of quantities and their
6 Values, scales, and the existence of properties