23
Since these conditions are necessary, each of them restricts the set of candidate
processes to be identified as measurements—for example, the first condition implies
that anything that is not an empirical process cannot be a measurement. A more
specific characterization of measurement requires that these necessary conditions
be complemented with sufficient conditions, as introduced and discussed in Chap. 7.
Given the ambiguities mentioned above around the basic concepts of measurement, it may be useful to point out some of our background assumptions and terminological choices, as listed in Table 2.1.
Some consequences of these assumptions are listed in Table 2.2.
Table 2.1 Some background assumptions
Objects (e.g., physical bodies, phenomena, events, human beings, organizations, systems) have
properties.
For example, a solid body has a mass, a shape, …; a human being has an age, a reading
comprehension ability, …; a reading event has a duration, a comprehension outcome, ….
Some properties of objects are comparable.
For example, two human beings are comparable by their masses and by their reading
comprehension abilities, but the mass of an individual cannot be compared with the reading
comprehension ability of another individual.
Properties that are comparable are said to be of the same kind, being instances of the same
general property: comparable properties are individual properties, i.e., instances of the same
general property.
For example, two given masses are individual masses, instances of the same general property
mass.
Some properties have a quantitative structure,
a i.e., they are quantities.
For example, mass is a quantity, whereas shape is a property but not a quantity.
Properties that are not quantities may admit of ordering among the objects (e.g., a preference
among options) or at least a classification among the objects (e.g., a classification according to
the shape of bodies): these are called ordinal properties and nominal properties, respectively.
Properties of objects are empirical entities, modeled as variables taking property values.
For example, “this body is a cube” is a shorthand for “the shape of this body is cubical”,
stating that the body has a shape, hence a property of an object, which is cubical, hence a
shape, i.e., a value of shape.
If properties are quantities, their values, i.e., quantity values, are customarily (possibly
non-integer) multiples of the unit
b for the quantity.
For example 1.2345 kg is a value of mass, where the kilogram is the unit of mass.
Measurements are processes aimed at producing information on properties of objects in the
form of property values, and therefore in the form of quantity values if the property is a
quantity.
a
What characterizes a property as a quantity is a delicate subject: Chap. 6 is devoted to discussing
it as well as other topics.
b
The usual term—“measurement unit” or “unit of measurement”, as in the VIM (JCGM, 2012:
1.9)—misleadingly conveys the idea that values of quantities only come from measurement, a
plainly false position (one can guess that a given rod is longer than 0.1 m, with no measurements
implied in the production of this result). Hence we use instead the term “quantity unit”, or “unit of
quantity”, which is also easier to reconcile with linguistic customs, such as “unit of length”: length
is a quantity, not a measurement.
2.2 The abstract structure of measurement
Since these conditions are necessary, each of them restricts the set of candidate
processes to be identified as measurements—for example, the first condition implies
that anything that is not an empirical process cannot be a measurement. A more
specific characterization of measurement requires that these necessary conditions
be complemented with sufficient conditions, as introduced and discussed in Chap. 7.
Given the ambiguities mentioned above around the basic concepts of measurement, it may be useful to point out some of our background assumptions and terminological choices, as listed in Table 2.1.
Some consequences of these assumptions are listed in Table 2.2.
Table 2.1 Some background assumptions
Objects (e.g., physical bodies, phenomena, events, human beings, organizations, systems) have
properties.
For example, a solid body has a mass, a shape, …; a human being has an age, a reading
comprehension ability, …; a reading event has a duration, a comprehension outcome, ….
Some properties of objects are comparable.
For example, two human beings are comparable by their masses and by their reading
comprehension abilities, but the mass of an individual cannot be compared with the reading
comprehension ability of another individual.
Properties that are comparable are said to be of the same kind, being instances of the same
general property: comparable properties are individual properties, i.e., instances of the same
general property.
For example, two given masses are individual masses, instances of the same general property
mass.
Some properties have a quantitative structure,
a i.e., they are quantities.
For example, mass is a quantity, whereas shape is a property but not a quantity.
Properties that are not quantities may admit of ordering among the objects (e.g., a preference
among options) or at least a classification among the objects (e.g., a classification according to
the shape of bodies): these are called ordinal properties and nominal properties, respectively.
Properties of objects are empirical entities, modeled as variables taking property values.
For example, “this body is a cube” is a shorthand for “the shape of this body is cubical”,
stating that the body has a shape, hence a property of an object, which is cubical, hence a
shape, i.e., a value of shape.
If properties are quantities, their values, i.e., quantity values, are customarily (possibly
non-integer) multiples of the unit
b for the quantity.
For example 1.2345 kg is a value of mass, where the kilogram is the unit of mass.
Measurements are processes aimed at producing information on properties of objects in the
form of property values, and therefore in the form of quantity values if the property is a
quantity.
a
What characterizes a property as a quantity is a delicate subject: Chap. 6 is devoted to discussing
it as well as other topics.
b
The usual term—“measurement unit” or “unit of measurement”, as in the VIM (JCGM, 2012:
1.9)—misleadingly conveys the idea that values of quantities only come from measurement, a
plainly false position (one can guess that a given rod is longer than 0.1 m, with no measurements
implied in the production of this result). Hence we use instead the term “quantity unit”, or “unit of
quantity”, which is also easier to reconcile with linguistic customs, such as “unit of length”: length
is a quantity, not a measurement.
2.2 The abstract structure of measurement