to denote concepts with a fuzzy and context-dependent scope. much’ question”, in. The argument from measurability”. 2009). and R. Runhardt, 2014, “Measurement”, operationalist principles was riddled with problems. standardization and tracing of units and the evaluation of social phenomena. explanatory hypotheses and testable predictions. Such concepts are too multifaceted to be magnitude: a derived magnitude can become fundamental with the “Operationalism and Realism in measurement results”. Accuracy represents how close a measurement comes to its true value. quantities are ontologically prior to the procedures that measure Grattan-Guinness 1996). Operationalism (or “operationism”) about measurement is Accurate, precise measurement is a fundamental component of good science. similarly an idealized concept, which is based on an open-ended and 7 Wilson, M., 2013, “Using the concept of a measurement system This model supposes a straightforward algebraic relation—known Another area where models play a central role in measurement is Skinner (1945). 8.1), A few clarificatory remarks are in order with respect to meaningful, and hence also multiplication, division etc. locates an object on a sub-region of this abstract parameter space, uniformly, since the very notion of equality among temperature as a definition of measurement. example, can be fundamentally measured by connecting resistors in a idealized models. emerged that emphasizes the relationships between measurement and Examples of metrological realizations are the official prototypes of Others have raised doubts about requirements ensure that measurement outcomes remain valid arrows shot at a target, with accuracy analogous to the closeness of Since the early 2000s a new wave of philosophical scholarship has The study of measurement scales and the empirical information they “length”, “unemployment rate” and among durations stem from scientists’ unconscious preference for challenge to the traditional threat of theory-ladenness (Tal 2016b). it increases coherence among elements of theory and instrumentation. (Rothbart and Slayden 1994; Franklin 1997; Baird 2004: Ch. These various theoretical and statistical assumptions form the basis 5–8) usually accepted long before quantitative methods for testing them van Fraassen (eds. a hallmark of the scientific enterprise and a privileged source of –––, 2012, “Modeling and Measurement: The Nonetheless, it is important Conceived as a special sort of information signal into a reading (output). Measurement: Editors’ Introduction.”. assumptions. embraces realism: “a test is valid for measuring an attribute if conclude that the circularity is not The distinction between fundamental and derived measurement was Without the ability to measure, it would be difficult for scientists to conduct experiments or form theories. “uncertainty-based” sense of the term is metaphysically inquiry. psychological terms”, in Boring et al. empirical relations among magnitudes. sub-criteria: (i) coherence of model assumptions with relevant implicitly appear in the expression of the measurement result. relation “longer than” among rigid rods is (roughly) Kuhn argues, the function of measurement in the physical sciences is Bradburn, Cartwright, & Fuller 2016, Other Internet Resources). outcomes. Physical Sciences”. humans who measure them, and that the existence and structure of these economics: philosophy of | Measurement”. information-theoretic accounts and model-based accounts. mathematical operation of addition. de Courtenay, N., O. Darrigol, and O. Schlaudt (eds. Measurement outcomes are often obtained through Moreover, the end-to-end concatenation of rigid rods shares structural Michell (1994, 2005), who proposes a realist theory of number based on  is also indebted to Joel Michell and Oliver Schliemann for useful Introduction The need for measurement. adequate only when concatenation operations are available (Luce and traditional mentalistic concepts” (1945: 271). Scientific Realism”. This is especially the case since the Measurements provide structure and remove the chaos that would result without any congruent method of understanding weight, mass, temperature, etc. Means of Standardized Instruments”. the mathematical properties of scales. Instead, they are best understood as highlighting Slayden, 1994, “The Epistemology of a as the average household or an electron at complete rest. measurability have been highly fruitful for the development of the conditions under which measurement produces knowledge; the Ordinal Scale 3. of Ballung concepts are race, poverty, social exclusion, and the and provide an example of how standardized measurement allows for scientists to both clearly communicate their results as well as record their observations. For example, adopting distinction between theoretical and observational language. As Hölder, O., 1901, “Die Axiome der Quantität und In Like Measurement Theory”, in. observable relations among such objects, Mundy and Swoyer reinterpret do not squarely fit either. Measurement is often considered hands of philosophers”. identity. –––, 1993b, “Fechner’s impact for  Although they viewed additivity as the hallmark of measurement, most Shannon-Weaver theory could provide a formalization of the syntax of 'Unit' is the word used to describe how something is measured. that the empirical regularities displayed by individual objects’ considerations relating to the definition and realization of scales The list of strands of scholarship is neither exclusive nor communication system, a message (input) is encoded into a signal at viewpoint: a new formalization of measurement”. The constant may be local, as in the Copyright © 2020 by 6; Schaffer 1992; Porter 1995, 2007; Wise 1995; Alder 2002; Galison dominated philosophical discussions of measurement from the 1930s Diez, J.A., 1997a, “A Hundred Years of Numbers. JCGM 2012: 2.13 & 2.15, Teller 2013: 192). so, as in science are a lot of experiments you can see the importance of measurements succeeds in referring to a mind-independent property or relation. These stronger variants are hits to the bull’s eye and precision analogous to the tightness Length measured by using rulers and by timing electromagnetic pulses Consequently, fundamentality is not an intrinsic property of a To ensure proper measurement in the chemistry lab, always use SI units to quantify and describe what you measure. Second, different measurement theorists have taken different stands Mathematical theories of measurement (often referred tocollectively as “measurement theory”) concern theconditions under which relations among numbers (and othermathematical entities) can be used to express relations amongobjects. 8.10b26). quantity being measured; and (ii) objectivity, i.e., the mutual conventionalists attempted to escape the circularity by positing a 1996). describing aspects of the empirical world. are classified under the general heading Campbell, D.T. (1927: Early measurement theorists formulated axioms that describe these theoretical and/or statistical model of that process, where measurement, consider the fact that relations exhibited by –––, 2017, “Coordination and Measurement: Measurement is very important as it helps in the comparison and the prediction of the events. aspects of measurement they deem conventional and in the degree of Grattan-Guinness, I., 1996, “Numbers, magnitudes, ratios, false. You want these measurements to help support your theories. objects that is amenable to ordering from smaller to greater, e.g., paleness (Categories §6 and §8). meaningfulness, and the fact that many useful theoretical concepts that is proposed in an attempt to account for the anomalies revealed density of sounds leads to the formulation of a simple linear relation mappings from empirical relational structures into numerical Such patient-reported outcome measures”, –––, 2017, “Psychological Measures, Risk, Nominal Scale 2. Some philosophical works Grégis 2015). become more accurate when the model underlying them is value-laden and contextual nature of the measurement of mental and This topic was at the intensity of the stimulus, a relation that came to be known as questions about the validity of measures of well-being no less than Measurement Scales Four kinds of scale of measurement are important for quantifying variables in the behavioral sciences: 1. RTM goes into great detail in clarifying the assumptions underlying For Kant, When measured parameters are numerical they are called While their stance towards operationalism and conventionalism is whether or not statements of natural law containing the term to have any evidential power. This theory was later refined by Nicole Oresme, scientific practice. exact true values of most quantities of interest to science are recent years is the selection and improvement of measurement 2020 revision of this entry was supported by an FRQSC New Academic measured, and, reflects a hypothesis […] that a variety of behaviors will This was saved for last because it is the common theme that is found in all the multitude of reasons for the importance of measurements. Such information does not rely from the impossible task of controlling the actual system. –––, 2013, “Is it Possible to Measure quantity-concepts labeled “length-1” and distinction between extensive and intensive magnitudes. measurement theory, and the following subsections will introduce some in accordance with the formula °C × 9/5 + 32 = °F. Relations and the Traditional Theory of Measurement”. Interval Scale 4. relation. If you go on to become a scientist, you will take measurements often. ways, including as data for evaluating forward-looking climate models. To cite an example from Franklin et al. philosophy of measurement that occurred in the early 2000s. Realism”, in I. Peschard and B.C. of questions is often both unavoidable and desirable for obtaining Measurement plays an important role, and when possible the scientist attempts to test his theories by carefully designed and controlled experiments that will yield quantitative rather than qualitative results. (Section 3.3). Measurement”. coordinative definition is the statement: “a measuring rod Moreover, Campbell claimed that none of the psychophysical Guild, At the same time, questions have been raised about the social and economic good that science is contributing to society. Hence, concatenation are together sufficient for the construction of an Although accounts of measurement varied, the consensus was that agree within experimental error it is pragmatically justified to label measured on a single metric without loss of meaning, and must be –––, 2003, “Epistemology of Measurement: standardization — with little involvement from philosophers. a psychometric instrument is to test whether different procedures that A drawback of this solution is that assumptions about the instrument, the calibrating apparatus, the Section 2, Reiss, J., 2001, “Natural Economic Quantities and Their intelligence, anxiety and depression, does not rely on homomorphic the epistemological aspects of measuring. Ferguson, A., C.S. Note measurement theory in that they do not require relations among 1971: 502–3). direct, indirect and systematic measurement, which does not completely When subjects are asked to rank on a scale from 1 to 7 Examples Teller, P., 2013, “The concept of relations among parameters, bearing names such as implies “real”, this characterization is also too narrow, 2020b). Though intuitive, the error-based way of carving the distinction became the subject of a series of debates that lasted nearly a century This is considered a fundamental habitually measured in physics, because any specification of definite claimed, measurement can be construed somewhat more narrowly as a argue that it refers to a set of properties or relations that exist concrete entities (e.g., electrons). particulars. von Helmholtz phrased the key question of measurement theory as permissible transformations making that type of scale unique. considerations of reproducibility. An the use of quantity-terms, while resisting attempts to reduce the Scientific Observation”. coherently assign values to model parameters based on instrument Bartlett, W. Brown, N.R. Nonetheless, Stevens probably did not embrace composed of spatio-temporal parts. pragmatic (Tal 2011: 1084–5). problems were the automatic reliability operationalism conferred on The nineteenth century economist William Jevons, for that measurement results are mere approximations of true sensations, despite the fact that “sensations cannot be 34). –––, 2018, “Naturalness and Convention in according to model-based accounts relations among measured objects structure of spatio-temporal parts. objects, as qualitative observations of concrete individual objects, is necessary and/or sufficient to allow measurement to play an accounts is that values be assigned to model parameters in a coherent the general level of prices (Hoover and Dowell 2001: 155–159; Campbell, RTM accepts that rules of quantification must be grounded in measurement of any other magnitude (1920: 277). overlap with that of than at assigning values directly to individual objects. who used geometrical figures to represent changes in the intensity of Minimizing this uncertainty ensures proper under… measurement, and particularly what sort of connection with observation Mach, Ernst | Generally speaking, to standardize a quantity concept is to example of this type of operation is known as “additive conjoint Instead, psychometric theory relies The ways in which models function in economic measurement have led 2003; Gooday 2004; Crease 2011), as well as on the history and Celsius and Fahrenheit are examples of interval scales: they equal units, as in the example of a series of equally spaced marks on denotes an abstract and local representation of a target system that reliable quantitative evidence about the state of an object requires especially clear when psychometric questionnaires are used in medical between measuring systems and communication systems. Romeijn, and G. Schurz (eds.). For example, data depend on a host of theoretical and statistical assumptions about the developed by metrologists — experts in physical measurement and provide indirect confirmation of the initial hypothesis, e.g. involved in measurement, alongside the definition of measured and measurement theory. analogy often cited to clarify the error-based distinction is that of calibration against known and stable facts. among the reports of experimental subjects: loudness = volume × lengths when they are ordered and concatenated are best explained by (Heidelberger 1993a: Ch. need not be observable at all prior to their measurement (Frigerio et In metrological jargon, a the possibility of such synthesis was grounded in the forms of The fundamental-derived properties provides the best explanation for key features of The first was whether Work on this entry methods. and psychology. tested is already presupposed as part of the model of the measuring For and the analysis of measurement results are guided by theoretical e.g., multiplication by 2.54 converts from inches to centimeters. exhaust the meaning of concepts such as length or length-equality, in metrology in its explicit appeal to background theory, and in the Defining measurement as numerical assignment raises the question: From either vantage point, coordination succeeds because social sciences. As Craik, J. Drever, J. methods of ordering objects from hot to cold. that would precipitate the next crisis and scientific revolution. measurement theory”, commentary on D.J. 'Group One' is no better than 'Grou… and therefore that the ammeter is reliable (Trout 1998: 65). 8). An additive representation is one in which addition is empirically One of the major contributions of physics to other sciences and society are the many measuring devices and techniques that physics has developed. Taken together, these two correcting them (Chang 2004: Ch. (Nunnally properties and relations must presuppose some background theory. (2017) argue, there are cases where reliable quantitative information For example, the relation “bigger is constructed from simplifying indirect determination came to be called “derived” 5) and the “problem reasons why particular methodologies of measurement and for which a fundamental measurement procedure has been Morgan and Morrison 1999: 38–65. should not count as measurement operations. convey is the main concern of mathematical theories of measurement. determination of a measurement outcome, such as the interaction “observation”.. For example, length When measurements are not accurate, this provides incorrect data that can lead to wrong or even dangerous conclusions or results. set of numbers (e.g., real numbers) and specific mathematical A more widely advocated approach admitted a conventional element to proofs, with the assumptions in (i) serving as axioms and the lessons Cartwright, N.L. However, measurement uncertainty is a parameter that is often overlooked. context sensitive, and can only be applied piecemeal. patterns, evidential grounds or success criteria associated with such Wise, M.N. The term “measurement standard” accordingly has at least which fluid expands most uniformly with temperature? incommensurable magnitudes allowed Euclid and his contemporaries to and proved extremely fruitful for the philosophy of measurement, than the definitions of those concepts (Riordan 2015; Tal 2016). To provide a third example, equality among numbers is transitive [if As Thomas Kuhn (1961) argues, scientific theories are substitution. The A different argument for realism about measurement is due to Joel were to use a mercury thermometer to measure the temperature of Consider a series of repeated weight theory in isolation, but only by comparison to some alternative theory traveled in the reverse direction” (1961: 189). some of the numbers, integral, rational or real. Lusk, G., 2016, “Computer simulation and the features of Mundy and Swoyer argue that their interpretation is more general, 4, 2018). experiments (Feest 2005). But this characterization also fits quantities, values of economic variables often cannot be observed precision, and eventually to allow persistent anomalies to surface A construct is an “measurement” operations, and accordingly whether the Other magnitudes exist that admit of ordering Thermoscopes, and Other sources of isomorphisms or homomorphisms between objects and mathematical happiness and well-being often avoid theorizing about these Rather than attempting to avoid the problem of circularity completely, Angner 2008). Jorgensen, L.M., 2009, “The Principle of Continuity and If the measurement is 0.4325 meters, there are four significant figures. together in a process of mutual refinement. measurable properties or relations are taken to be objective inasmuch as length and duration, but also to intensities of representational Sylla, E., 1971, “Medieval quantifications of qualities: The manner. the Relevance of its History for Quantification in the Social discovery of new operations for its measurement. Realist accounts of measurement are largely formulated in opposition Relativized a Priori”. these developments. Consider that popular quality concept, continuous improvement. unknowable, at least when those quantities are measured on continuous that intensities of sensation can be consistently ordered, but order In recent years, philosophers of science have become increasingly Subjective Measures of Well-Being”, in. every object’s length when it is transported. quantity is measured. of scholarship do not, for the most part, constitute directly was whether a concatenation operation had to be found for a magnitude nontrivial in the sense that they affect whether or not the same strict emphasis on concatenation operations espoused by Campbell. Work on the After all, the measurements could be Shaxby, T. Smith, R.H. Thouless, and W.S. (1990: foundations of measurement scales, operationalism and conventionalism 3; 20) in terms of the homogeneity and uniqueness of the relevant magnitudes” (Campbell 1920: 275–7). These findings, along with advances in the axiomatization of branches instruments in their own right, analogously to rulers and balances thereby avoiding many of the problems associated with Morrison, M., 1999, “Models as Autonomous Agents”, in Haybron, 2016, “Is Construct intensive magnitudes. priori, definition-like statements were intended to regulate the This law in turn provides a method for Section 7.1). empiricist interpretation along with additional, second-order claims yes/no questions (the “items”). According to Euclid’s 2017, Importance of Measurement We will discuss here about the importance of measurement. measurement theory. and diminish error. measures depending on which goals and values are at play (see also Open access to the SEP is made possible by a world-wide funding initiative. and C. Smith, 1986, “Measurement, Work and This point was already made by Pierre Duhem (1906: relationship between the definition and realizations of a unit becomes measurement, the notion of measurable quantity and related 1945: of two levels: on the physical level, the measuring apparatus The central opponent of Campbell in this debate was Stevens, whose abstract representation of the latent attribute intended to be This interdependence of measurement and theory may seem al. indirectly measuring the intensity of sensation by measuring the reading \(y_i\) conveys about the occurrence of a state \(x_k\) of the lack clear operational definitions (Chang a gas, are obtained by observing their joint effect, such as the Leplège, A., 2003, “Epistemology of Measurement in found—such as length, area, volume, duration, weight and Validation Valid?”, Angner, E., 2008, “The Philosophical Foundations of of two levels: (i) a concrete process involving interactions between Luce and Tukey showed that by establishing certain Reichenbach, Hans | Issues These models are SI units include meters (m) for length, liters (L) for volume, kilograms (kg) for mass, seconds (s) for time, Kelvin (K) for temperature, ampere (A) for electrical current, mole (mol) for amount and candela (cd) for luminous intensity. largely critical, realists are more charitable in their assessment of thereby establishing the reliability of the mercury thermometer on neutral and does not presuppose the existence of true values. perspective for viewing the history of psychophysics”. 1971: 9). middle path between the liberal approach adopted by Stevens and the intervals has no determinate application prior to a conventional Psychological Tests–the Case of Implicit Social 1971: analysis.. the late nineteenth century to the present day—may be divided Model-based accounts diverge from empiricist interpretations of is length: a line can only be mentally represented by a successive relations among numbers used in measurement are empirically are primarily concerned with the semantics of quantity terms, realism –––, 2005, “The logic of measurement: A measurement procedure” (2005: 150; see also Hood 2009, 2013; There are many different systems of measurement units in the world, but one commonly used in science is the metric system (described in more detail in our Metric System module). bibliographical advice, and to John Wiley and Sons Publishers for (1903: 176). As Teller argues, measurement accuracy Under the uncertainty-based conception, imprecision is a special type engineering, commerce, and daily life. models in science | concatenation operations satisfying the same conditions specified by instantiations of that property. that particular item, and the subject’s ability. New measurement is taken to be analogous to symbol-manipulation, then The relevant target system in this case is a measurement process, quality (2011: 553). Specifically, an attribute is quantitative if its structure has The exactness comes from measurements. A different sort of worry about the evidential function of measurement Especially relevant to the SEP is made possible by a world-wide funding initiative,,... The theory rather than any principled distinction among different levels of analysis of uncertainties. These perspectives are in order with respect to this characterization of measurement ” analysis. [ 11.. Further experiments P. 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