fundamentalsmeasurement continued of achievable in any measurement of a given measurand " , in the sense that using a measuring instrument with a better resolution would produce a value for a measurand that is not the length of the rod anymore, but, say, the distance between two extreme points on the opposite faces of the rod. Definitional uncertainty is then the uncertainty about our possibility to identify the property as it is defined and, as such, it depends on both the object and the way we have defined the property. Scales, Values of Properties, and Types of (Kinds of) Properties Relation (1) is about indistinguishability of comparable properties, and as such it is in principle applicable to any kind of property. For example, we could discover that individuals x and y are indistinguishable with respect to their blood group (i.e., " they have the same blood group " , as mentioned above), and then write: blood group of x = blood group of y (3) where the " = " sign is customarily adopted to indicate that the blood of the two individuals belongs to the same group (i.e., indistinguishability class), and that that group is labeled as A in the ABO System: blood group of x (and of y) = A in the ABO System (4) Both (3) and (4) require a classification criterion of blood groups, but the second one conveys a more sophisticated information, due to presence on its right-hand side of a reference to a value of a property (a value of blood group, in this case). As it is clear, values of properties operate as selectors in given classifications. In this example, we first learn how to compare blood groups, then we agree upon a comparison-based classification of blood groups, and finally we assign an information entity as unique identifier (A, B, AB, O) to each class. Thus, we create a scale, i.e., a mapping from classes of indistinguishable properties to identifiers (someone might object against using the term " scale " about structures that are only classificatory, and not at least ordered; let us say that we are using it by extension). The construction of a scale generates a value for each property of the considered kind, where in (4) the identifier A corresponds to the value (A in the ABO System) and so on. While A is simply an identifier of an equivalence class of blood groups, what is a value like (A in the ABO System) is a more delicate issue. Indeed, the common view that values are " symbols " to represent properties is not informative, as everything can be used to symbolize everything. What are values of properties then? To better discuss this issue, let us come back to more usual cases of physical quantities. Even still lacking a unit, or a scale, of length, we could discover that: 14 Hence, a new issue arises: what are units? Of course, an extensional, reductionist stance can be adopted also in this case, by taking for example the metre as an equivalence class of lengths (how such class is established, and therefore how the metre is defined, is not relevant here: it could be identified (the dates that follow refer to the Metre Convention [8]) as the length of an artifact (from 1889 to 1960); or as a multiple or submultiple of the length of a natural phenomenon (from 1960 to 2019); or by assuming a given numerical value for a length of a natural phenomenon when expressed in metres (since 2019)). But this simplicity generates quite complex interpretations: for example, is 1.2345 m really the multiple of a class of equivalence of lengths? We believe that the traditional, realist stance is well justified here: the metre is not an equivalence class of lengths but what the lengths in the class have in common, i.e., an abstract length, and of course the same applies to any other unit. Everything becomes simple and consistent in this way: if a unit like the metre is a length, a value like 1.2345 m is a multiple of a length and therefore a length in turn. Accordingly, relation (1) is an equation of two properties, one of them identified concretely as the property of an object and the other identified abstractly as an element of a classification, so that the information actually conveyed by such a relation is that the considered property of the object belongs to an indistinguishability class. In the example about the length of a rod, claiming that the IEEE Instrumentation & Measurement Magazine February 2023 A value of a property is a property identified abstractly as an element of a classification corresponding to a scale. length of a given steel rod = width of a given door (5) (of course, always within the limits of the identification of these properties, as discussed above), and then, when the scale generated by the unit metre is available, that: length of a given steel rod (and width of a given door) = 1.2345 m (6) Different from the value (A in the ABO System), that is only about a classification, the value 1.2345 m reveals the underlying structure of lengths, that may be additively composed ( " concatenated " as sometimes it is said) so that, if it is true that length of a given steel rod = width of a given door, then their composition is twice as long as each of them, and so on. This supports the usual interpretation of the value 1.2345 m as what is obtained by taking 1.2345 times the metre, whatever the metre is.

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