196
say, u, the previous equality would become P[c] = 2 u, which is an example of a
Basic Evaluation Equation and the simplest case of a measurement result, under the
condition that measurement uncertainty need not be reported explicitly. If this is all
that is required for (fundamental) measurement, then only the adjective “physical”
in the term “physical addition” ties measurement to the empirical world: indeed,
exactly the same structural conditions may apply to properties of mathematical
objects, through purely computational processes.
In fact, given his interest in establishing measurement as a foundation for science, Campbell included an almost incidental second condition: “in order that a
property should be measured as a fundamental magnitude, involving the measurement of no other property, it is necessary that a physical process of addition should
be found for it” (p. 267). Together with additivity, he considered “involving the
measurement of no other property” as the basis for the distinction between fundamental and derived properties, and then fundamental and derived measurement.
This distinction was later refined and became a sort of default reference, in particular in the version presented by Brian Ellis (1968), where measurements—and more
properly measurement methods—are classified as either fundamental (for which
Ellis also used the term “direct”) or indirect, so that every measurement method that
is not fundamental (direct) is considered indirect.
As the scope of measurement broadened, and (especially) psychophysicists and
psychologists argued against the necessity of physical addition operations for measurement, Campbell’s second condition—that no other properties are involved in
the process—became the characterizing feature of those methods which were then
called “direct methods” of measurement, as exemplified by the first edition of the
VIM, which defines as a “method of measurement
in which the value of a measurand is obtained directly, rather than by measurement
of other quantities functionally related to the measurand” and
obtained by measurement of other quantities functionally related to the measurand”
(ISO et al., 1984: 2.13 and 2.14). Similar definitions can be found elsewhere in the
literature, for example (Lira, 2002: p. 39):
Many times the information about the measurand is acquired from the readings of a single
measuring instrument. We will refer to such a quantity as subject to a direct measurement.
However, the metrological meaning of the word ‘measurement’ is more ample: it also refers
to quantities whose values are indirectly estimated on the basis of the values of other quantities, which in turn may or may not have been directly measured.
Or (Gertsbakh, 2003: p. viii):
There are two principal types of measurements: direct and indirect. For example, measuring
the voltage by a digital voltmeter can be viewed as a direct measurement: the scale reading
of the instrument gives the desired result. On the other hand, when we want to measure the
specific weight of some material, there is no such device whose reading would give the
desired result. Instead, we have to measure the weight W and the volume V, and express the
specific weight p as their ratio: p = W/V. This is an example of an indirect measurement.
7 Modeling measurement and its quality
say, u, the previous equality would become P[c] = 2 u, which is an example of a
Basic Evaluation Equation and the simplest case of a measurement result, under the
condition that measurement uncertainty need not be reported explicitly. If this is all
that is required for (fundamental) measurement, then only the adjective “physical”
in the term “physical addition” ties measurement to the empirical world: indeed,
exactly the same structural conditions may apply to properties of mathematical
objects, through purely computational processes.
In fact, given his interest in establishing measurement as a foundation for science, Campbell included an almost incidental second condition: “in order that a
property should be measured as a fundamental magnitude, involving the measurement of no other property, it is necessary that a physical process of addition should
be found for it” (p. 267). Together with additivity, he considered “involving the
measurement of no other property” as the basis for the distinction between fundamental and derived properties, and then fundamental and derived measurement.
This distinction was later refined and became a sort of default reference, in particular in the version presented by Brian Ellis (1968), where measurements—and more
properly measurement methods—are classified as either fundamental (for which
Ellis also used the term “direct”) or indirect, so that every measurement method that
is not fundamental (direct) is considered indirect.
As the scope of measurement broadened, and (especially) psychophysicists and
psychologists argued against the necessity of physical addition operations for measurement, Campbell’s second condition—that no other properties are involved in
the process—became the characterizing feature of those methods which were then
called “direct methods” of measurement, as exemplified by the first edition of the
VIM, which defines
in which the value of a measurand is obtained directly, rather than by measurement
of other quantities functionally related to the measurand” and
obtained by measurement of other quantities functionally related to the measurand”
(ISO et al., 1984: 2.13 and 2.14). Similar definitions can be found elsewhere in the
literature, for example (Lira, 2002: p. 39):
Many times the information about the measurand is acquired from the readings of a single
measuring instrument. We will refer to such a quantity as subject to a direct measurement.
However, the metrological meaning of the word ‘measurement’ is more ample: it also refers
to quantities whose values are indirectly estimated on the basis of the values of other quantities, which in turn may or may not have been directly measured.
Or (Gertsbakh, 2003: p. viii):
There are two principal types of measurements: direct and indirect. For example, measuring
the voltage by a digital voltmeter can be viewed as a direct measurement: the scale reading
of the instrument gives the desired result. On the other hand, when we want to measure the
specific weight of some material, there is no such device whose reading would give the
desired result. Instead, we have to measure the weight W and the volume V, and express the
specific weight p as their ratio: p = W/V. This is an example of an indirect measurement.
7 Modeling measurement and its quality