# Instrumentation & Measurement Magazine 26-1 - 13

```property of the object. For example, a given steel rod can be hard
to move because it has a certain mass and can be hard to fold
because it has a certain stiffness. That mass and that stiffness
are properties of that object (please note that we do not take
these as definitions but only as identification criteria: roughly,
an object is thought of as something that has properties, and
a property as something that characterizes how an object interacts
with its environment). Further, different objects may
interact in a similar or the same way with their environment
and therefore can be compared with respect to some of their
properties. For example, the length of a steel rod and the width
of a door are comparable, whereas the mass of a steel rod and
the width of a door are not. It is such a comparability, and the
related possibility to discover that some objects behave in the
same or similar way and some others do not, that make the observation
of properties an informative activity.
Given this preliminary understanding, a metrological
framework can be grounded on two basic assumptions:
◗ there are objects with properties;
◗ for any pair of properties of objects, either such properties
are empirically comparable with each other or not, and
comparability is an equivalence relation.
The property of an object
corresponds to a way an object
in the empirical world interacts
or is made to interact with its
environment, according to our
knowledge and investigation goals.
Through comparability, the set of the properties of objects is
then partitioned into classes of equivalence, so that the length
of a steel rod and the width of a door belong to the same class,
while the mass of a steel rod and the width of a door belong to
different classes. Properties belonging to the same class, i.e.,
comparable with each other, are commonly said to be of the
same kind, where a name is usually associated to the class itself,
like " mass " or " temperature " . According to an extensional, and
in fact somewhat reductionist, stance, mass is then the set of all
masses, temperature the set of all temperatures, and so on.
Each kind of property can be analyzed in its structure,
as induced by the comparison relation. The simplest type of
structure is such that any two properties of the same kind are
either indistinguishable or not, where such a relation is also
assumed to be an equivalence. Accordingly, any class of comparability,
i.e., any kind of properties, is in turn partitioned
into a set of equivalence classes of indistinguishability, where
the situation of different objects having empirically indistinguishable
properties is commonly described as " having the
February 2023
same property " (e.g., the same length, or mass, etc). After the
preliminary recognition that a given object has a given property,
the recognition of the indistinguishability class to which
the property of an object belongs is the basic information that
can be obtained on that property: the rod not only has a length,
but it has a given length.
However, while the membership of a property to a comparability
class is intrinsic, in the sense that there is no ambiguity
whether a property is a length, or a mass, etc., the membership
of a property to an indistinguishability class depends on the
way the objects are compared with respect to their properties.
For example, the length of a steel rod and the width of a door
could be indistinguishable in a rough observation but become
distinguishable at an enhanced resolution.
Furthermore, relation (1) assumes that the property referred
to on its left-hand side is well identified, so that the length
of a given steel rod is a uniquely characterized property of a
well-identified object, but in practice this may be a non-trivial
condition to guarantee. For example, we are used to talking
about the length and the temperature of a steel rod, but if such
properties are to be identified with a sufficiently high resolution,
we should acknowledge that the faces of the rod are not
exactly plane and parallel, and the rod is not perfectly thermally
homogeneous. A possible conclusion is that there is nothing in
the world like the length and the temperature of that rod, also
because at the atomic scale the rod itself ceases to be identifiable
as an object. While being aware that a perfect, unique identification
of empirical properties is usually not feasible (possible
counterexamples are properties that are fundamental constants
according to our best theories, like the speed of light in vacuum
and the charge of the electron), it is a fact that both in daily practice
and in scientific activity we keep on dealing with entities
like the length and the temperature of macroscopic objects. The
good, pragmatic justification of this is that it proves to be effective:
even though we know that a given rod does not really have
one length and one temperature, sometimes this simplification
does not prevent us from making appropriate predictions and
decisions about the rod, for example as related to how it would
behave if immersed in a cooler fluid, etc. Of course, as is for any
model, such a simplification comes at the price that some details
are neglected: since there is an obvious trade-off between
simplification and effectiveness, it is important to acknowledge
that the simplified model remains effective until the information
conveyed by relation (1) does not become more specific
than what the description of the property admits. For example,
what we know of the structure of the rod could lead us to
consider that the rod can be effectively modeled as having one
length, and therefore relation (1) is meaningful, until length is
evaluated with a resolution of the tenth of millimeter.
According to the VIM, this is about definitional uncertainty,
" resulting from the finite amount of detail in the definition
of a measurand " : " the practical minimum [...] uncertainty
IEEE Instrumentation & Measurement Magazine
13
```

# Instrumentation & Measurement Magazine 26-1

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