119
5.1.2 A pragmatic introduction to the problem
Basic Evaluation Equations are at the core of any measurement, and therefore an
understanding of them is a requirement for a well-grounded measurement science.
However, “equality gives rise to challenging questions which are not altogether easy
to answer” (Frege, 1892: p. 25): Quoting again Price (2001: p. 294), in a Basic
Evaluation Equation does the equality sign mean “is expressed, modeled, or represented by”? or something else?
In what follows, we introduce the problem only in terms of ordinal comparisons.
This does not affect the generality of the presentation, and hopefully makes it clearer
by referring to a less controversial relation than equality, thus avoiding the “challenging questions”—including the ones connected with the possible role of uncertainty—that equality brings with itself.
Let us consider the case of mass.
1. In measurement we deal with entities such as masses of given objects, e.g.,
mass[rod a], and values of mass, e.g., 1.23 kg. For the sake of argument, let us
call the former “O-entities” (i.e., related to objects) and the latter “V-entities”
(i.e., related to values), by noting that different terms may (but do not necessarily) correspond to different kinds of entities, and the conclusion that we might
well reach is that properties of objects, i.e., O-entities, and values of properties,
i.e., V-entities, are different ways of referring to the same kind of entity.
2. O-entities and V-entities are such that we can compare
• O-entities among themselves (the mass of rod a is less than the mass of rod b)
• V-entities among themselves (1.23 kg is less than 2.34 kg)
• O-entities and V-entities (the mass of rod a is less than 1.23 kg)
3. In particular, the chain of inequalities
mass rod a
mass rod b
>
@
>
@
1 23
234
.
.
kg
kg
is understandable and does not pose problems of interpretation, also about the
transitivity of the relation (e.g., from mass[rod a] < 1.23 kg and 1.23 kg < 2.34 kg
the conclusion is unproblematically obtained that mass[rod a] < 2.34 kg).
3.2.2 and 4.2.1). While sometimes considered to be a useless metaphysical residual, in some contexts the reference to true values is maintained and emphasized. As an example, the current version
of the NIST Quality Manual for Measurement Services (the National Institute of Standards and
Technology, NIST, is the US National Metrology Institute) defines as (emphasis
added) “an experimental or computational process that, by comparison with a standard, produces
an estimate of the true value of a property of a material or virtual object or collection of objects, or
of a process, event, or series of events, together with an evaluation of the uncertainty associated
with that estimate, and intended for use in support of decision-making” (11th version, 2019, www.
nist.gov/system/files/documents/2019/04/09/nist_qm-i-v11_controlled_and_signed.pdf, including
the note that “the NIST Measurement Services Council approved [this] definition of measurement
to include value assignments of properties using qualitative techniques”) (Possolo, 2015: p. 12).
5.1 Introduction
5.1.2 A pragmatic introduction to the problem
Basic Evaluation Equations are at the core of any measurement, and therefore an
understanding of them is a requirement for a well-grounded measurement science.
However, “equality gives rise to challenging questions which are not altogether easy
to answer” (Frege, 1892: p. 25): Quoting again Price (2001: p. 294), in a Basic
Evaluation Equation does the equality sign mean “is expressed, modeled, or represented by”? or something else?
In what follows, we introduce the problem only in terms of ordinal comparisons.
This does not affect the generality of the presentation, and hopefully makes it clearer
by referring to a less controversial relation than equality, thus avoiding the “challenging questions”—including the ones connected with the possible role of uncertainty—that equality brings with itself.
Let us consider the case of mass.
1. In measurement we deal with entities such as masses of given objects, e.g.,
mass[rod a], and values of mass, e.g., 1.23 kg. For the sake of argument, let us
call the former “O-entities” (i.e., related to objects) and the latter “V-entities”
(i.e., related to values), by noting that different terms may (but do not necessarily) correspond to different kinds of entities, and the conclusion that we might
well reach is that properties of objects, i.e., O-entities, and values of properties,
i.e., V-entities, are different ways of referring to the same kind of entity.
2. O-entities and V-entities are such that we can compare
• O-entities among themselves (the mass of rod a is less than the mass of rod b)
• V-entities among themselves (1.23 kg is less than 2.34 kg)
• O-entities and V-entities (the mass of rod a is less than 1.23 kg)
3. In particular, the chain of inequalities
mass rod a
mass rod b
>
@
>
@
1 23
234
.
.
kg
kg
is understandable and does not pose problems of interpretation, also about the
transitivity of the relation (e.g., from mass[rod a] < 1.23 kg and 1.23 kg < 2.34 kg
the conclusion is unproblematically obtained that mass[rod a] < 2.34 kg).
3.2.2 and 4.2.1). While sometimes considered to be a useless metaphysical residual, in some contexts the reference to true values is maintained and emphasized. As an example, the current version
of the NIST Quality Manual for Measurement Services (the National Institute of Standards and
Technology, NIST, is the US National Metrology Institute) defines
added) “an experimental or computational process that, by comparison with a standard, produces
an estimate of the true value of a property of a material or virtual object or collection of objects, or
of a process, event, or series of events, together with an evaluation of the uncertainty associated
with that estimate, and intended for use in support of decision-making” (11th version, 2019, www.
nist.gov/system/files/documents/2019/04/09/nist_qm-i-v11_controlled_and_signed.pdf, including
the note that “the NIST Measurement Services Council approved [this] definition of measurement
to include value assignments of properties using qualitative techniques”) (Possolo, 2015: p. 12).
5.1 Introduction