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

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