195
a corollary, such an integrated set of necessary and sufficient conditions provides a
characterization of measurability: a property is measurable if and only if there exists
a property-related process fulfilling these conditions.
From this perspective, the analysis of the structure of a measurement process
plays a crucial role: in the metrological tradition, the general description of the
structure of such a process is provided by a so-called measurement method, defined
as a “generic description of a logical organization of operations used in a measurement” by the International Vocabulary of Metrology (VIM) (JCGM, 2012: 2.5). A
key related distinction is between direct and indirect (methods of) measurement,
first introduced in Sect. 2.3. To this we first devote our attention here, using the
model proposed by Giordani and Mari (2019) as a starting point, which we develop
to encompass the scenarios that arise across the sciences.
7.2 Direct and indirect measurement
Though it contradicts what is currently specified by the VIM, which defines to be an experimental process (JCGM, 2012: 2.1), and also against our
own presentation of this as a necessary condition (see Sect. 2.2.1), the idea that
measurement is not necessarily empirical is not new. In his seminal 1920 book,
Norman Campbell defined as “the process of assigning numbers to
represent qualities” (1920: p. 267). A linguistic detail is again revealing: Campbell
wrote “the process”, not “a process”, thus supposedly implying that any process of
assigning numbers to properties—with only a slight paraphrase—is a measurement.
This was conceived in the context of a foundationalist endeavor aimed at framing
measurement as a core enabler of science (1920: p. 267):
Physics could be distinguished from other sciences by the part played in it by measurement.
Other sciences measure some of the properties they investigate but it is generally recognized that when they make such measurements they are always depending, directly or indirectly, on the results of physics. All fundamental measurements belong to physics, which
might almost be described as the science of measurement.
Here the term “fundamental measurement” is used with a specific meaning, introduced by Campbell himself: being fundamental is what characterizes properties
whose instances are directly comparable with each other by equivalence and order,
and which are additive (Campbell used the term “physical addition”, p. 279, for
what has later been called “concatenation”, e.g., by Krantz, Luce, Suppes, and
Tversky, 1971: p. 2). The fundamentality is due to the fact that, for any three objects
a, b, and c having the property P, if P[a] ≈ P[b] and P[a] + P[b] ≈ P[c] then
P[c] = 2 P[a], or P[c]/P[a] = 2: with no other conditions—hence with no previously
defined units, measurement standards, metrological traceability chains, instrument
calibrations, etc.—numbers have been thus assigned to ratios of properties (and this
is also the basic logic of the construction of values of quantities which we presented
in Sect. 6.3). Moreover, were P[a] conventionally set as the unit and given a symbol,
7.2 Direct and indirect measurement
a corollary, such an integrated set of necessary and sufficient conditions provides a
characterization of measurability: a property is measurable if and only if there exists
a property-related process fulfilling these conditions.
From this perspective, the analysis of the structure of a measurement process
plays a crucial role: in the metrological tradition, the general description of the
structure of such a process is provided by a so-called measurement method, defined
as a “generic description of a logical organization of operations used in a measurement” by the International Vocabulary of Metrology (VIM) (JCGM, 2012: 2.5). A
key related distinction is between direct and indirect (methods of) measurement,
first introduced in Sect. 2.3. To this we first devote our attention here, using the
model proposed by Giordani and Mari (2019) as a starting point, which we develop
to encompass the scenarios that arise across the sciences.
7.2 Direct and indirect measurement
Though it contradicts what is currently specified by the VIM, which defines
own presentation of this as a necessary condition (see Sect. 2.2.1), the idea that
measurement is not necessarily empirical is not new. In his seminal 1920 book,
Norman Campbell defined
represent qualities” (1920: p. 267). A linguistic detail is again revealing: Campbell
wrote “the process”, not “a process”, thus supposedly implying that any process of
assigning numbers to properties—with only a slight paraphrase—is a measurement.
This was conceived in the context of a foundationalist endeavor aimed at framing
measurement as a core enabler of science (1920: p. 267):
Physics could be distinguished from other sciences by the part played in it by measurement.
Other sciences measure some of the properties they investigate but it is generally recognized that when they make such measurements they are always depending, directly or indirectly, on the results of physics. All fundamental measurements belong to physics, which
might almost be described as the science of measurement.
Here the term “fundamental measurement” is used with a specific meaning, introduced by Campbell himself: being fundamental is what characterizes properties
whose instances are directly comparable with each other by equivalence and order,
and which are additive (Campbell used the term “physical addition”, p. 279, for
what has later been called “concatenation”, e.g., by Krantz, Luce, Suppes, and
Tversky, 1971: p. 2). The fundamentality is due to the fact that, for any three objects
a, b, and c having the property P, if P[a] ≈ P[b] and P[a] + P[b] ≈ P[c] then
P[c] = 2 P[a], or P[c]/P[a] = 2: with no other conditions—hence with no previously
defined units, measurement standards, metrological traceability chains, instrument
calibrations, etc.—numbers have been thus assigned to ratios of properties (and this
is also the basic logic of the construction of values of quantities which we presented
in Sect. 6.3). Moreover, were P[a] conventionally set as the unit and given a symbol,
7.2 Direct and indirect measurement