Abstract
This chapter aims to present the general context of a measurement system and basic concepts of measurement and related terms. The presentation develops according to a step-by-step, top-down strategy, which progressively characterizes measurement as (1) an empirical process, (2) designed on purpose, (3) whose input is a property of an object, and (4) that produces information in the form of values of that property. These are proposed as necessary but not sufficient conditions for a process to be identified as a measurement: as such the contents of this chapter should be uncontroversial to be read and accepted by most, if not all, researchers and practitioners.
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Notes
- 1.
The current member organizations of JCGM are the two intergovernmental organizations concerned with metrology: the Bureau International des Poids et Mesures (BIPM) and the Organisation Internationale de Métrologie Légale (OIML); the two principal international standardization organizations: the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC); three international unions: the International Union of Pure and Applied Chemistry (IUPAC), the International Union of Pure and Applied Physics (IUPAP), and the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC); and one international accreditation organization: the International Laboratory Accreditation Cooperation (ILAC) (JCGM, 2009).
- 2.
- 3.
The distinction between what is physical and what is not is complex, and touches the fundamental problem of reductionism (can chemistry be considered a part of physics? And what about biology? etc.), which is a key subject of philosophy of science, but which can safely remain in the background in a discourse on measurement science. We avoid a systematic use of the term “nonphysical” here (and not only for political correctness: characterizing something in negative terms does not necessarily convey a clear meaning), and use instead the adjectives “human science” and “psychosocial”, in a broad sense, as attributed to a science, a measurement, a property, etc., to emphasize that that entity is not effectively defined in purely physical terms. Of course, some nonphysical measurement may not be human (e.g., behavior of dogs), and some human measurement may be entirely physical (e.g., height), but we are not concerned with such cases here. A discussion on the compatibility of reductionism with the acknowledgment of the possibility of multiple layers of description is in Philip Warren Anderson’s (1972) paper More is Different, whose main thesis is twofold. On the one hand, “the reductionist hypothesis [is that] the workings of our minds and bodies, and of all the animate or inanimate matter […], are assumed to be controlled by the same set of fundamental laws”. On the other hand, “the reductionist hypothesis does not by any means imply a ‘constructionist’ one: the ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe” (p. 393). In other terms, a principled reductionism can be maintained together with the acknowledgment that effective descriptions of parts of the world are given in reference to non-reduced parts. Daniel Dennett has proposed a high-level interpretation of this subject in terms of physical vs. design vs. intentional stance (Dennett, 1987).
- 4.
The concept is so fundamental that, not surprisingly, together with “property” several other terms are used to designate it, with meanings more or less analogous, like “attribute”, “feature”, “characteristic”, “quality”, “observable”, and “parameter”. The differences in standpoints about properties are not only lexical: some approaches to measurement avoid discussion of properties, by dealing only with empirical objects, represented by means of informational entities (usually but not necessarily numbers) through procedures. Whether properties do exist in the world or are just conceptual tools we adopt to organize our knowledge of empirical objects is a core topic for a fundamental ontology (see, e.g., Orilia & Swoyer, 2020) and deeply affects any measurement-related concept system (for example, do we measure objects or properties of objects?). In this book we maintain the usual position that what is measured are properties of objects, like the mass of solid bodies and the reading comprehension ability of individuals, and therefore that properties of objects exist, and are therefore not concepts. This position is developed further and defended in Chap. 5. See also the summary in Table 2.1.
- 5.
Compare this to the more specific definition of <measurement> in the VIM: “process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity” (JCGM, 2012: 2.1). Our use of the indefinite article “a” rather than the definite article “the” (“a process …”, not “the process …”) emphasizes that in this chapter we introduce necessary but not sufficient conditions to characterize measurement.
- 6.
In this characterization the term “object” is used in a broad sense and refers to what the VIM calls a “phenomenon, body, or substance” (for example in JCGM, 2012: 1.1) but also to an individual, an organization, a process, etc. There is no claim that an object, in this sense, is a single, unitary entity, and instead it may be a system, or even a conglomerate, of parts. Furthermore, “object” is ambiguous, given that in semiotics an object is meant to be an object of the discourse and therefore properties are, in this sense, objects. Without any further specific ontological commitment, here we consider an object to be anything that bears properties; in Chaps. 5 and 6 we develop a more analytical consideration of properties.
- 7.
The term “value” is ambiguous. In particular, a phrase such as “to be of little value to somebody” shows that it can be used, as an uncountable, for <the quality of being useful or important>, as mentioned in the Oxford English Dictionary. In measurement science, and in this book, “value” has a meaning analogous to what in mathematics is <element of the range of a function> (so that, for example, 1 is the value of the function cos(x) when applied to the argument x = 0), thus devoid of any ethical or axiological components. However, an ambiguity remains: if X is a variable ranging over a set {xi}, each xi is said to be a value of X; hence by modeling a property, such as mass or shape, as a variable, each of its instances, such as a given mass and a given shape, would be considered to be a value of that variable. As we discuss in the following pages, and further in Chap. 6, in the tradition of measurement science the term “value of a property/quantity” is reserved for the instances of properties/quantities that are identified as elements of a classification, which in the case of quantities is induced by the appropriate composition of a quantity chosen as the unit.
- 8.
Even though these terminological choices are very preliminary, they are not void of content. In particular, while we maintain that properties of objects may be empirical entities, modeled as variables, sometimes properties and variables are not formally distinguished, “for economy of notation”, as in the case of the GUM (JCGM, 2008: 4.1.1, Note 1), or perhaps because the difference between empirical entities and their mathematical counterparts is neglected. A telling example is found in the following sentence: “By a variable we will mean an attribute, measurement or inquiry that may take on one of several possible outcomes, or values, from a specified domain” (Pearl, 2009: p. 8), which also includes the term “measurement” plausibly in the sense of <measurand>. While this sentence may make sense in Pearl’s terms, given our definitions above, it makes no sense.
- 9.
This is generally a two-way interaction, and hence the inputs of a measurement may be affected by their being measured. In reference to the traditional distinction between observation and experiment, not all experiments are measurements, and some measurements are only specific kinds of observations, whenever the measured property is unaffected by its being measured. A paradigmatic example is the case of the measurement of the spectral characteristics of the electromagnetic radiation emitted by stars: a star does not change its state because of this process. However, an intervention might be required on the object under measurement before the measurement and in preparation for it, an operation sometimes called “signal conditioning”, with the aim of making the property measurable as expected. For example, electrical resistance measurement typically assumes that a potential difference has been applied, thus in fact changing the state of the system. This justifies the idea that usually measurement is a kind of experiment. Other perspectives about measurement are possible. According to a slightly different construal (which still connects measurement and quantification, a relation about which we provide some critical comments in the following), “there are three modes of generating data: by observation, measurement, and experiment. Observation, whether direct or with the help of instruments and theories, is deliberate and controlled perception, and it is the basic mode of data generation. […] Measurement […] may be characterized as quantitative observation, or the observation of quantitative properties. Experiment [is] the observation (and possibly measurement) of changes under our partial control” (Bunge, 1983: p. 91).
- 10.
We do not define here the distinction between measurement and computation, though we aim instead to provide a pragmatic characterization. In the words of Percy Bridgman, “There are certain human activities which apparently have perfect sharpness. The realm of mathematics and of logic is such a realm, par excellence. Here we have yes-no sharpness. But this yes-no sharpness is found only in the realm of things we say, as distinguished from the realm of things we do. Nothing that happens in the laboratory corresponds to the statement that a given point is either on a given line or it is not” (1959: p. 226, emphasis added). According to Bridgman’s metaphor, measurement is something “we do”, and computation is something “we say”. This helps point up the paradigmatic contrast between the exactitude of computation and the uncertainty of the empirical activities of measurement.
- 11.
If the final output of the measurement process were the decision about the person’s health state rather than the temperature value, then this would be an example of a nonquantitative evaluation, whose values might be, e.g., healthy, rather sick, and seriously sick. We return to a discussion of the conditions under which such an evaluation might be considered a measurement in Sect. 6.5.
- 12.
The definitions of <measurement>—“process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity” (JCGM, 2012: 2.1)—and <measurement procedure>—“detailed description of a measurement according to one or more measurement principles and to a given measurement method, based on a measurement model and including any calculation to obtain a measurement result” (JCGM, 2012: 2.6)—given by the VIM are very clear in maintaining this distinction.
- 13.
The notation P[a] is used here to recall the functional notation, where in fact P[a] stands for the property P of the object a and is not a mathematical function as such, but at the same time to emphasize that P can be formalized as a function.
- 14.
Note Campbell’s use of the term “quality” in place of “property”, which we avoid because <quality> explicitly contrasts with <quantity>: while stating that quantities are specific qualities is indeed odd, in the conceptual framework of the VIM—which we generally adopt here—quantities are specific properties. Furthermore, whether measurement is actually an assignment and its results are representations is an issue that we discuss in the following chapters.
- 15.
This is what a reference text (the so-called Red Book) of the International Union of Pure and Applied Physics (IUPAP) says about the distinction between general and individual properties in the specific case of physical quantities: “There are two somewhat different meanings of the term physical quantity. One refers to the abstract metrological concept (e.g., length, mass, temperature), the other to a specific example of that concept (an attribute of a specific object or system: diameter of a steel cylinder, mass of the proton, critical temperature of water). Sometimes it is important to distinguish between the two and, ideally, it might be useful to be able to do so in all instances” (IUPAP, 2010: 1.1). Note that the terms “general property” and “individual property” are not standard, and usually the same term “property”, and thus more specifically “quantity”, is used to designate both general and individual properties. Other corresponding pairs of terms are “properties in the general sense” and “particular properties”, as in the second edition of the VIM in reference to quantities (BIPM et al., 1993: 1.1), but also, e.g., “property” and “property manifestation” (Benoit & Foulloy, 2013; Pfanzagl, 1971), “attribute” and “level of attribute” (Michell, 2002), “quality” and “state of a quality” (Piotrowski, 1992), and—only applicable to quantities—“quantity” and “magnitude” (Hölder, 1901, as translated by Michell and Ernst, and then adopted, among others, by Kyburg, 1997). Given that in some definitions of the VIM the term “magnitude” appears (e.g., “quantity” is defined as “property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference”, JCGM, 2012: 1.1), a few more words may be useful to justify why we do not use the term “magnitude” here. We have three basic reasons to justify this position. First, the term “magnitude” is used today with different and incompatible meanings—by claiming for example that magnitudes are quantities or that quantities have magnitudes (and in this second case the reference could be either to general quantities (mass has a magnitude) or to individual quantities (the mass of this object has a magnitude))—so that adopting it would require a more or less arbitrary selection. And while the term “magnitude” is used to translate the Greek μεγεθος, a lexical reference to this tradition is now outdated, given the Aristotelian contraposition of “magnitude” and “plurality” (πληθος, also translated as “multitude”): “a quantum is a plurality if it is numerable, a magnitude if it is a measurable” (Aristotle’s Metaphysics, Book 5, Part 13). Second, the pair of terms “quantity” and “magnitude” seems to be so semantically superposed that in languages other than English they are not distinguished (so that, for example, the official French text of the VIM definition of “quantity” mentioned above is “grandeur”, “propriété d’un phénomène, d’un corps ou d’une substance, que l’on peut exprimer quantitativement sous forme d’un nombre et d’une référence”: the concept “magnitude” just disappeared …). The third reason is related to our interest in providing a general presentation of properties, of which quantities are a specific case. While the term “magnitude” could be intended as synonymous with “amount”, so that for example one could say that mass is a quantity because objects have mass in amounts, nonquantitative properties do not have magnitudes (as in the VIM3 definition of <nominal property>, JCGM, 2012: 1.30), with the consequence that one or more terms corresponding to what magnitudes are for quantities should be adopted for nonquantitative properties. Indeed, sometimes for ordinal properties the term “level” is used to this goal. In summary, we believe that the pair “general property” and “individual property” provides a lexically simple and semantically encompassing terminology.
- 16.
For such a key concept the VIM unfortunately has only an entry about measurands as individual properties (e.g., the measurand is the length of rod a), but does not provide a term for the general property intended to be measured (e.g., length): we use “general measurand” in this case.
- 17.
Values of properties could be, for example, cube, in a given set of shapes (a value of the nominal property shape), or second preferred, in a given sequence of preferences (a value of the ordinal property preference).
- 18.
As customary, we write this relation as an equality, =, instead of as an equivalence, ≅, or as a similarity, ≈. The nature of this relation is discussed in Chap. 5. More completely, a measurement result must also include information of some sort on the measurement uncertainty (JCGM, 2012: 2.26), a condition that in a following section we show to be a critical characteristic of measurement. Note that, together with “measured value”, the GUM also uses the term “estimated value” (JCGM, 2008: 2.2.4), with a more explicit statistical-probabilistic connotation.
- 19.
The term “evaluation” inherits the ambiguity of “value”, as mentioned in Footnote 7. We are using it here in the technical, non-axiological sense of attribution of a value to the property of an object.
- 20.
The notation qref for a generic unit is consistent with both the recommendations of the SI Brochure (“Unit symbols are printed in upright type regardless of the type used in the surrounding text. They are printed in lower-case letters unless they are derived from a proper name, in which case the first letter is a capital letter.” (BIPM, 2019: 5.2)) and our convention of designating individual properties with lowercase roman characters (about the nature of units as individual quantities see Mari, Ehrlich, & Pendrill, 2018).
- 21.
Nordin, Dybkaer, Forsum, Fuentes-Arderiu, and Pontet (2018) adopt the term “examination”, which we consider less clearly referring to the production of values of properties.
- 22.
What defines a quantitative property is in turn a controversial issue. For example, while a strict interpretation assumes that properties must be additively composed to be quantities, sometimes (e.g., by Ellis, 1968: p. 25) only their linear ordering is required. Physical quantities, as length, duration, energy, etc., are examples of such quantitative properties.
- 23.
Here and in what follows we assume the distinction between entities of the empirical world and entities of the information world. While we do not dare to propose a general definition of what empirical and informational are and how they are related, a simple example may be helpful to convey the basic message, about a word and an utterance emitted by a speaker: the utterance is a physical phenomenon, and as such characterized by empirical properties such as its duration, frequency spectrum, and total energy; a word is instead a piece of information, characterized by its length (in number of characters), number (singular or plural), gender (masculine or feminine), and so on. Of course attributing a gender to a sound or a bandwidth to a word is nonsense.
- 24.
- 25.
The VIM has different definitions for measuring instrument, a “device used for making measurements, alone or in conjunction with one or more supplementary devices” (JCGM, 2012: 3.1), and measuring system, a “set of one or more measuring instruments and often other devices, including any reagent and supply, assembled and adapted to give information used to generate measured quantity values within specified intervals for quantities of specified kinds” (JCGM, 2012: 3.2). The difference is subtle: Is a balance a measuring instrument? Its graduated scale? One of its pans? A screw in it? In order to maintain a distinction with measurement system—as introduced in Sect. 2.2.2—we will use one term, “measuring instrument”, for both. Hence a measurement system is an overall entity that includes both empirical and informational components, while a measuring instrument is an empirical component of a measurement system.
- 26.
More precisely, the function which models the transduction maps properties under measurement to indications. In performing this third stage it is then assumed that (1) through the instrument calibration the function is known and can be computed in terms of values of the involved properties, and (2) the function is invertible, so that values of the property under measurement can be obtained from values of the indication.
- 27.
- 28.
The general idea that the measurement process is constituted of an empirical component and an information component is not new, of course. On this matter of particular interest are the presentations by Roman Morawski, who introduces the two components as conversion and reconstruction (2013), and by Giovanni Battista Rossi and Francesco Crenna, who call them observation and restitution (2018).
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Mari, L., Wilson, M., Maul, A. (2021). Fundamental concepts in measurement. In: Measurement across the Sciences. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-65558-7_2
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