265
5. Property comparison (2.2): An empirical process by which individual properties of the same kind, i.e., instances of the same general property, are compared.
The simplest case of comparison leads to property-related indistinguishability/
distinguishability, or similarity/dissimilarity. Measurement is a property evaluation based on direct or indirect property comparison [the VIM does not define
this concept].
6. Property evaluation, evaluation (2.2): A process aimed at attributing a value
to a property of an object, as reported in a Basic Evaluation Equation.
Measurement is a property evaluation [the VIM does not define this concept].
7. Property evaluation type (6.5): A criterion for classifying property evaluations, based on the algebraic invariance of values obtained through comparison.
The simplest, but not uniquely defined, classification is between quantitative
and nonquantitative evaluations. Types are (partially) ordered by the algebraic
constraints that characterize them. For example, ratio type is algebraically
stronger than interval type, because ratio type adds the constraint of a “natural
zero” to interval type [the VIM does not define this concept].
8. Property type (6.5): A criterion for classifying general properties, based on the
algebraically strongest known evaluation type for the property. For example, a
property is considered of quantitative type, i.e., a quantity for short, if at least
one quantitative evaluation is known for it [the VIM does not define this
concept].
9. Quantity, quantitative property (2.2): A property of sufficiently strong type.
There is not a clear-cut criterion for distinguishing quantitative and nonquantitative properties. For example, while ratio and interval properties are commonly
considered to be quantitative, the VIM considers ordinal properties to be quantitative, whereas they are sometimes considered to be nonquantitative [analogous to the VIM definition [1.9]].
10. System of quantities, nomic network (4.3): A set of general quantities together
with a set of relations connecting them. The International System of Quantities
(ISQ) is the most well-known example of a system of quantitative physical
properties. The term “nomological network” is also sometimes used for this [a
generalization of the VIM definition [1.3]].
11. Property of an object (2.1): An individual property identified as a property that
a given object carries, such as length of a given rigid body and reading comprehension ability of a given individual. Any property under measurement is a
property of an object. The set of all relevant properties of an object is supposed
to provide an adequate description of the object, sometimes called its “state”.
In formal contexts (e.g., formulas) we write properties of objects as P[a, c]
where P is the general property of which the considered individual property is
an instance, a is the considered object, and c is the context in reference to which
the object has been identified. In most cases the reference to the context can be
omitted and properties of objects are written as P[a]. Hence L[a] and length[a]
designate the length of rigid body a and RCA[a] and reading comprehension
ability[a] designate the reading comprehension ability of individual reader a
Appendix A: A basic concept system of measurement
5. Property comparison (2.2): An empirical process by which individual properties of the same kind, i.e., instances of the same general property, are compared.
The simplest case of comparison leads to property-related indistinguishability/
distinguishability, or similarity/dissimilarity. Measurement is a property evaluation based on direct or indirect property comparison [the VIM does not define
this concept].
6. Property evaluation, evaluation (2.2): A process aimed at attributing a value
to a property of an object, as reported in a Basic Evaluation Equation.
Measurement is a property evaluation [the VIM does not define this concept].
7. Property evaluation type (6.5): A criterion for classifying property evaluations, based on the algebraic invariance of values obtained through comparison.
The simplest, but not uniquely defined, classification is between quantitative
and nonquantitative evaluations. Types are (partially) ordered by the algebraic
constraints that characterize them. For example, ratio type is algebraically
stronger than interval type, because ratio type adds the constraint of a “natural
zero” to interval type [the VIM does not define this concept].
8. Property type (6.5): A criterion for classifying general properties, based on the
algebraically strongest known evaluation type for the property. For example, a
property is considered of quantitative type, i.e., a quantity for short, if at least
one quantitative evaluation is known for it [the VIM does not define this
concept].
9. Quantity, quantitative property (2.2): A property of sufficiently strong type.
There is not a clear-cut criterion for distinguishing quantitative and nonquantitative properties. For example, while ratio and interval properties are commonly
considered to be quantitative, the VIM considers ordinal properties to be quantitative, whereas they are sometimes considered to be nonquantitative [analogous to the VIM definition [1.9]].
10. System of quantities, nomic network (4.3): A set of general quantities together
with a set of relations connecting them. The International System of Quantities
(ISQ) is the most well-known example of a system of quantitative physical
properties. The term “nomological network” is also sometimes used for this [a
generalization of the VIM definition [1.3]].
11. Property of an object (2.1): An individual property identified as a property that
a given object carries, such as length of a given rigid body and reading comprehension ability of a given individual. Any property under measurement is a
property of an object. The set of all relevant properties of an object is supposed
to provide an adequate description of the object, sometimes called its “state”.
In formal contexts (e.g., formulas) we write properties of objects as P[a, c]
where P is the general property of which the considered individual property is
an instance, a is the considered object, and c is the context in reference to which
the object has been identified. In most cases the reference to the context can be
omitted and properties of objects are written as P[a]. Hence L[a] and length[a]
designate the length of rigid body a and RCA[a] and reading comprehension
ability[a] designate the reading comprehension ability of individual reader a
Appendix A: A basic concept system of measurement