equation is true implies that the length identified as the length of the rod and the length identified as 1.2345 times the length that is the metre are the same length. Basically, this applies also to blood groups, with only some differences, due to the fact that the classification of blood groups is not generated by a unit. In relation (4) above, claiming that the equation is true implies that the blood group identified as the blood group of a given individual and the blood group identified as the value (A in the ABO System) are the same blood group. With this broad, encompassing interpretation, relation (1) can be called the Basic Evaluation Equation [9], and on this ground the framework of property (or scale) types is developed. Indeed, relations other than indistinguishability or operations can be often applied to properties of a given kind. For example, some properties can be ordered, like temperatures, whereas there is not a general criterion to order others, like blood groups and shapes, and only an indistinguishability relation holds for them. As another example, for some kinds of properties, two or more objects can be combined in such a way that the relation between their properties and the property of the resulting object fulfills the conditions of the addition between numbers, as happens for example for lengths and masses in non-relativistic conditions. Thus, in the set of kinds of properties different types can be distinguished based on which relations or operations apply to the properties of that kind ( " kind " and " type " , that in everyday language are often taken as synonyms, have then specifically distinct meanings here). Claiming that a given kind of properties is of a given type means that the properties of that kind are comparable according to the relations and can be combined according to the operations that are characteristic of that type. For example, stating that the type of mass is ordinal and additive means that masses can be ordered and combined additively. Stevens [10] set the framework for the types of (kinds of) properties (that in fact he operationally characterized as types of scales), by identifying four types. The first two, that he called " nominal " and " ordinal " , assume that the properties of the considered kind are only comparable with each other, as either indistinguishable or distinguishable in the nominal type (as for blood groups and shapes), or also ordered in the ordinal type (as for hardness of minerals in the case of Mohs scale). The other two types, that Stevens called " interval " and " ratio " , assume that on the concerned properties some empirical operations are also possible, and this makes them richer in the information they convey but also more complex in their characterization. A basic issue comes from the traditional distinction between intensive and extensive properties, as exemplified by positions in space (let us say, a one-dimensional space for the sake of simplicity) and lengths. Positions can be operated by difference, and the difference of two positions is their distance and therefore a length, but cannot be operated by sum in February 2023 the sense that there is not an operation between pairs of positions with the features of an arithmetic addition. Lengths can instead be operated by both sum and difference. Exactly the same applies to positions in time, sometimes called " calendar times " , and durations: durations can be added and subtracted, whereas positions in time can only be subtracted ( " today plus yesterday " is meaningless), and the result is their distance in time, i.e., a duration. On this matter Stevens focused on the condition that interval scales / properties, like positions in space and in time, do not have an intrinsic zero: a zero can be set (what in physics is done by defining a spatiotemporal frame of reference) but remains conventional. Vice versa, we consider the existence of a zero property as an integral part of what we know of ratio properties (or ratio scales according to Stevens), like length and duration. However, things are more complex than the possible association intensive = interval and extensive = ratio could suggest, as the historical development of temperature scales shows. Plausibly thought of as only ordinal in a far past, thermometric scales, like Celsius and Fahrenheit, upgraded temperature to an interval property, and in fact such scales do not identify an intrinsic zero, as witnessed by the fact that the temperatures mapped to the identifier 0 in Celsius and Fahrenheit scales are not the same, at the same time recognizing the intensive nature of temperature, such that the temperature of a body obtained by putting two bodies in thermal contact is not the sum of their temperatures but a weighted mean of them. The development of thermodynamic scales, like Kelvin, led to recognition of an intrinsic ( " absolute " ) zero temperature, thus upgrading temperature to a ratio property, while maintaining its intensive nature. This shows that the correct association is extensive = additive, instead of extensive = ratio [11]. The four types originally proposed by Stevens are by no means the only ones. Stevens himself later introduced a fifth type, called " absolute " , related to properties that are countable and therefore are considered to have both an intrinsic zero and an intrinsic unit, but examples of other types can be found, like in the case of angle amplitude, that is " circularly additive " , i.e., additive modulo 2π. Furthermore, note that the type-related structure of a kind of properties is observed under specified empirical conditions. For example, electrical resistances of resistors combine additively if combined in series but not in parallel (in a hypothetical world in which only parallel combination of electrical resistances were possible or known, electrical resistance would be supposed to be an intensive ratio property, analogous to temperature). Hence, stating that a given kind is of a given type is a shorthand for something like: given the currently best available knowledge, at least one procedure is known to operate on the properties of that kind according to the type-related structure [12]. IEEE Instrumentation & Measurement Magazine 15

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