The answer depends on if it is science or math. In the case of political science the "science" means the study of politics. Log in. Science Experiments. See Answer. Best Answer. How does measurements relate to experimental science. Study guides. Q: How do measurements relate to experimental science? Write your answer Related questions. How does measurements relate to experimental science? How do horse jockeys relate to math andor science they relate to math and science?
Why is experimental design a key factor in science inquiry? What is investigative science? Do experimental measurements give the true value of physical quantity?
How you Relate political science as to history? What does experimental observation mean? How does science relate to political science? Lavoisier helped make chemistry a science of what? What are the science processes involve? What is the difference between discovery science and experimental science? What is the Difference between experimental and non experimental?
Why is using ounces inappropriate in a science experiment? How does math science and technology relate? How does history relate to other branches of social science?
Relate physics to other branches of natural science? How does science storms relate to science? Why science is an art? What is experimental method? Who is known as father of experimental science? What encouraged experimental science? Simply put, a measurement scale is a many-to-one mapping—a homomorphism—from an empirical to a numerical relational structure, and measurement is the construction of scales.
Each type of scale is associated with a set of assumptions about the qualitative relations obtaining among objects represented on that type of scale. From these assumptions, or axioms, the authors of RTM derive the representational adequacy of each scale type, as well as the family of permissible transformations making that type of scale unique.
In this way RTM provides a conceptual link between the empirical basis of measurement and the typology of scales. On the issue of measurability, the Representational Theory takes a middle path between the liberal approach adopted by Stevens and the strict emphasis on concatenation operations espoused by Campbell.
Like Campbell, RTM accepts that rules of quantification must be grounded in known empirical structures and should not be chosen arbitrarily to fit the data. However, RTM rejects the idea that additive scales are adequate only when concatenation operations are available Luce and Suppes Instead, RTM argues for the existence of fundamental measurement operations that do not involve concatenation.
Here, measurements of two or more different types of attribute, such as the temperature and pressure of a gas, are obtained by observing their joint effect, such as the volume of the gas. Luce and Tukey showed that by establishing certain qualitative relations among volumes under variations of temperature and pressure, one can construct additive representations of temperature and pressure, without invoking any antecedent method of measuring volume.
This sort of procedure is generalizable to any suitably related triplet of attributes, such as the loudness, intensity and frequency of pure tones, or the preference for a reward, it size and the delay in receiving it Luce and Suppes Under this new conception of fundamentality, all the traditional physical attributes can be measured fundamentally, as well as many psychological attributes Krantz et al.
Above we saw that mathematical theories of measurement are primarily concerned with the mathematical properties of measurement scales and the conditions of their application. A related but distinct strand of scholarship concerns the meaning and use of quantity terms. A realist about one of these terms would argue that it refers to a set of properties or relations that exist independently of being measured.
An operationalist or conventionalist would argue that the way such quantity-terms apply to concrete particulars depends on nontrivial choices made by humans, and specifically on choices that have to do with the way the relevant quantity is measured. Note that under this broad construal, realism is compatible with operationalism and conventionalism.
That is, it is conceivable that choices of measurement method regulate the use of a quantity-term and that, given the correct choice, this term succeeds in referring to a mind-independent property or relation.
Nonetheless, many operationalists and conventionalists adopted stronger views, according to which there are no facts of the matter as to which of several and nontrivially different operations is correct for applying a given quantity-term. These stronger variants are inconsistent with realism about measurement. This section will be dedicated to operationalism and conventionalism, and the next to realism about measurement. The strongest expression of operationalism appears in the early work of Percy Bridgman , who argued that.
Length, for example, would be defined as the result of the operation of concatenating rigid rods. According to this extreme version of operationalism, different operations measure different quantities.
Nevertheless, Bridgman conceded that as long as the results of different operations agree within experimental error it is pragmatically justified to label the corresponding quantities with the same name Operationalism became influential in psychology, where it was well-received by behaviorists like Edwin Boring and B. Skinner As long as the assignment of numbers to objects is performed in accordance with concrete and consistent rules, Stevens maintained that such assignment has empirical meaning and does not need to satisfy any additional constraints.
Nonetheless, Stevens probably did not embrace an anti-realist view about psychological attributes. Instead, there are good reasons to think that he understood operationalism as a methodological attitude that was valuable to the extent that it allowed psychologists to justify the conclusions they drew from experiments Feest For example, Stevens did not treat operational definitions as a priori but as amenable to improvement in light of empirical discoveries, implying that he took psychological attributes to exist independently of such definitions Stevens Operationalism met with initial enthusiasm by logical positivists, who viewed it as akin to verificationism.
Nonetheless, it was soon revealed that any attempt to base a theory of meaning on operationalist principles was riddled with problems. Among such problems were the automatic reliability operationalism conferred on measurement operations, the ambiguities surrounding the notion of operation, the overly restrictive operational criterion of meaningfulness, and the fact that many useful theoretical concepts lack clear operational definitions Chang Accordingly, most writers on the semantics of quantity-terms have avoided espousing an operational analysis.
A more widely advocated approach admitted a conventional element to the use of quantity-terms, while resisting attempts to reduce the meaning of quantity terms to measurement operations. Mach noted that different types of thermometric fluid expand at different and nonlinearly related rates when heated, raising the question: which fluid expands most uniformly with temperature?
According to Mach, there is no fact of the matter as to which fluid expands more uniformly, since the very notion of equality among temperature intervals has no determinate application prior to a conventional choice of standard thermometric fluid.
Conventionalism with respect to measurement reached its most sophisticated expression in logical positivism. These a priori , definition-like statements were intended to regulate the use of theoretical terms by connecting them with empirical procedures Reichenbach 14—19; Carnap Ch. In accordance with verificationism, statements that are unverifiable are neither true nor false. Instead, Reichenbach took this statement to expresses an arbitrary rule for regulating the use of the concept of equality of length, namely, for determining whether particular instances of length are equal Reichenbach At the same time, coordinative definitions were not seen as replacements, but rather as necessary additions, to the familiar sort of theoretical definitions of concepts in terms of other concepts Under the conventionalist viewpoint, then, the specification of measurement operations did not exhaust the meaning of concepts such as length or length-equality, thereby avoiding many of the problems associated with operationalism.
Realists about measurement maintain that measurement is best understood as the empirical estimation of an objective property or relation. A few clarificatory remarks are in order with respect to this characterization of measurement. Rather, measurable properties or relations are taken to be objective inasmuch as they are independent of the beliefs and conventions of the humans performing the measurement and of the methods used for measuring.
For example, a realist would argue that the ratio of the length of a given solid rod to the standard meter has an objective value regardless of whether and how it is measured. Third, according to realists, measurement is aimed at obtaining knowledge about properties and relations, rather than at assigning values directly to individual objects. This is significant because observable objects e.
Knowledge claims about such properties and relations must presuppose some background theory. By shifting the emphasis from objects to properties and relations, realists highlight the theory-laden character of measurements. Realism about measurement should not be confused with realism about entities e. Nor does realism about measurement necessarily entail realism about properties e.
Nonetheless, most philosophers who have defended realism about measurement have done so by arguing for some form of realism about properties Byerly and Lazara ; Swoyer ; Mundy ; Trout , These realists argue that at least some measurable properties exist independently of the beliefs and conventions of the humans who measure them, and that the existence and structure of these properties provides the best explanation for key features of measurement, including the usefulness of numbers in expressing measurement results and the reliability of measuring instruments.
The existence of an extensive property structure means that lengths share much of their structure with the positive real numbers, and this explains the usefulness of the positive reals in representing lengths. Moreover, if measurable properties are analyzed in dispositional terms, it becomes easy to explain why some measuring instruments are reliable.
A different argument for realism about measurement is due to Joel Michell , , who proposes a realist theory of number based on the Euclidean concept of ratio. According to Michell, numbers are ratios between quantities, and therefore exist in space and time. Specifically, real numbers are ratios between pairs of infinite standard sequences, e. Measurement is the discovery and estimation of such ratios.
An interesting consequence of this empirical realism about numbers is that measurement is not a representational activity, but rather the activity of approximating mind-independent numbers Michell Realist accounts of measurement are largely formulated in opposition to strong versions of operationalism and conventionalism, which dominated philosophical discussions of measurement from the s until the s.
In addition to the drawbacks of operationalism already discussed in the previous section, realists point out that anti-realism about measurable quantities fails to make sense of scientific practice. By contrast, realists can easily make sense of the notions of accuracy and error in terms of the distance between real and measured values Byerly and Lazara 17—8; Swoyer ; Trout A closely related point is the fact that newer measurement procedures tend to improve on the accuracy of older ones.
If choices of measurement procedure were merely conventional it would be difficult to make sense of such progress. In addition, realism provides an intuitive explanation for why different measurement procedures often yield similar results, namely, because they are sensitive to the same facts Swoyer ; Trout Finally, realists note that the construction of measurement apparatus and the analysis of measurement results are guided by theoretical assumptions concerning causal relationships among quantities.
The ability of such causal assumptions to guide measurement suggests that quantities are ontologically prior to the procedures that measure them. While their stance towards operationalism and conventionalism is largely critical, realists are more charitable in their assessment of mathematical theories of measurement. Brent Mundy and Chris Swoyer both accept the axiomatic treatment of measurement scales, but object to the empiricist interpretation given to the axioms by prominent measurement theorists like Campbell and Ernest Nagel ; Cohen and Nagel Ch.
Rather than interpreting the axioms as pertaining to concrete objects or to observable relations among such objects, Mundy and Swoyer reinterpret the axioms as pertaining to universal magnitudes, e. Moreover, under their interpretation measurement theory becomes a genuine scientific theory, with explanatory hypotheses and testable predictions. Building on this work, Jo Wolff a has recently proposed a novel realist account of quantities that relies on the Representational Theory of Measurement.
Specifically, an attribute is quantitative if its structure has translations that form an Archimedean ordered group. It also means that being a quantity does not have anything special to do with numbers, as both numerical and non-numerical structures can be quantitative.
Information-theoretic accounts of measurement are based on an analogy between measuring systems and communication systems. The accuracy of the transmission depends on features of the communication system as well as on features of the environment, i. The accuracy of a measurement similarly depends on the instrument as well as on the level of noise in its environment. Conceived as a special sort of information transmission, measurement becomes analyzable in terms of the conceptual apparatus of information theory Hartley ; Shannon ; Shannon and Weaver Ludwik Finkelstein , and Luca Mari suggested the possibility of a synthesis between Shannon-Weaver information theory and measurement theory.
As they argue, both theories centrally appeal to the idea of mapping: information theory concerns the mapping between symbols in the input and output messages, while measurement theory concerns the mapping between objects and numbers.
If measurement is taken to be analogous to symbol-manipulation, then Shannon-Weaver theory could provide a formalization of the syntax of measurement while measurement theory could provide a formalization of its semantics.
Nonetheless, Mari also warns that the analogy between communication and measurement systems is limited. Information-theoretic accounts of measurement were originally developed by metrologists — experts in physical measurement and standardization — with little involvement from philosophers. Independently of developments in metrology, Bas van Fraassen — has recently proposed a conception of measurement in which information plays a key role.
He views measurement as composed of two levels: on the physical level, the measuring apparatus interacts with an object and produces a reading, e. Measurement locates an object on a sub-region of this abstract parameter space, thereby reducing the range of possible states and This reduction of possibilities amounts to the collection of information about the measured object. Since the early s a new wave of philosophical scholarship has emerged that emphasizes the relationships between measurement and theoretical and statistical modeling Morgan ; Boumans a, ; Mari b; Mari and Giordani ; Tal , ; Parker ; Miyake The central goal of measurement according to this view is to assign values to one or more parameters of interest in the model in a manner that satisfies certain epistemic desiderata, in particular coherence and consistency.
Model-based accounts have been developed by studying measurement practices in the sciences, and particularly in metrology. Metrologists typically work at standardization bureaus or at specialized laboratories that are responsible for the calibration of measurement equipment, the comparison of standards and the evaluation of measurement uncertainties, among other tasks.
It is only recently that philosophers have begun to engage with the rich conceptual issues underlying metrological practice, and particularly with the inferences involved in evaluating and improving the accuracy of measurement standards Chang ; Boumans a: Chap. A central motivation for the development of model-based accounts is the attempt to clarify the epistemological principles underlying aspects of measurement practice.
For example, metrologists employ a variety of methods for the calibration of measuring instruments, the standardization and tracing of units and the evaluation of uncertainties for a discussion of metrology, see the previous section. Traditional philosophical accounts such as mathematical theories of measurement do not elaborate on the assumptions, inference patterns, evidential grounds or success criteria associated with such methods. As Frigerio et al. By contrast, model-based accounts take scale construction to be merely one of several tasks involved in measurement, alongside the definition of measured parameters, instrument design and calibration, object sampling and preparation, error detection and uncertainty evaluation, among others —7.
Other, secondary interactions may also be relevant for the determination of a measurement outcome, such as the interaction between the measuring instrument and the reference standards used for its calibration, and the chain of comparisons that trace the reference standard back to primary measurement standards Mari Although measurands need not be quantities, a quantitative measurement scenario will be supposed in what follows. Two sorts of measurement outputs are distinguished by model-based accounts [JCGM 2.
As proponents of model-based accounts stress, inferences from instrument indications to measurement outcomes are nontrivial and depend on a host of theoretical and statistical assumptions about the object being measured, the instrument, the environment and the calibration process. Measurement outcomes are often obtained through statistical analysis of multiple indications, thereby involving assumptions about the shape of the distribution of indications and the randomness of environmental effects Bogen and Woodward — Measurement outcomes also incorporate corrections for systematic effects, and such corrections are based on theoretical assumptions concerning the workings of the instrument and its interactions with the object and environment.
Systematic corrections involve uncertainties of their own, for example in the determination of the values of constants, and these uncertainties are assessed through secondary experiments involving further theoretical and statistical assumptions. Moreover, the uncertainty associated with a measurement outcome depends on the methods employed for the calibration of the instrument.
Calibration involves additional assumptions about the instrument, the calibrating apparatus, the quantity being measured and the properties of measurement standards Rothbart and Slayden ; Franklin ; Baird Ch.
Finally, measurement involves background assumptions about the scale type and unit system being used, and these assumptions are often tied to broader theoretical and technological considerations relating to the definition and realization of scales and units. These various theoretical and statistical assumptions form the basis for the construction of one or more models of the measurement process.
Measurement is viewed as a set of procedures whose aim is to coherently assign values to model parameters based on instrument indications. Models are therefore seen as necessary preconditions for the possibility of inferring measurement outcomes from instrument indications, and as crucial for determining the content of measurement outcomes. As proponents of model-based accounts emphasize, the same indications produced by the same measurement process may be used to establish different measurement outcomes depending on how the measurement process is modeled, e.
As Luca Mari puts it,. Similarly, models are said to provide the necessary context for evaluating various aspects of the goodness of measurement outcomes, including accuracy, precision, error and uncertainty Boumans , a, , b; Mari b. Model-based accounts diverge from empiricist interpretations of measurement theory in that they do not require relations among measurement outcomes to be isomorphic or homomorphic to observable relations among the items being measured Mari Indeed, according to model-based accounts relations among measured objects need not be observable at all prior to their measurement Frigerio et al.
Instead, the key normative requirement of model-based accounts is that values be assigned to model parameters in a coherent manner.
The coherence criterion may be viewed as a conjunction of two sub-criteria: i coherence of model assumptions with relevant background theories or other substantive presuppositions about the quantity being measured; and ii objectivity, i. The first sub-criterion is meant to ensure that the intended quantity is being measured, while the second sub-criterion is meant to ensure that measurement outcomes can be reasonably attributed to the measured object rather than to some artifact of the measuring instrument, environment or model.
Taken together, these two requirements ensure that measurement outcomes remain valid independently of the specific assumptions involved in their production, and hence that the context-dependence of measurement outcomes does not threaten their general applicability. Besides their applicability to physical measurement, model-based analyses also shed light on measurement in economics. Like physical quantities, values of economic variables often cannot be observed directly and must be inferred from observations based on abstract and idealized models.
The nineteenth century economist William Jevons, for example, measured changes in the value of gold by postulating certain causal relationships between the value of gold, the supply of gold and the general level of prices Hoover and Dowell —; Morgan Taken together, these models allowed Jevons to infer the change in the value of gold from data concerning the historical prices of various goods. The ways in which models function in economic measurement have led some philosophers to view certain economic models as measuring instruments in their own right, analogously to rulers and balances Boumans , c, , a, , a, ; Morgan Marcel Boumans explains how macroeconomists are able to isolate a variable of interest from external influences by tuning parameters in a model of the macroeconomic system.
This technique frees economists from the impossible task of controlling the actual system. As Boumans argues, macroeconomic models function as measuring instruments insofar as they produce invariant relations between inputs indications and outputs outcomes , and insofar as this invariance can be tested by calibration against known and stable facts.
When such model-based procedures are combined with expert judgment, they can produce reliable measurements of economic phenomena even outside controlled laboratory settings Boumans Chap. Another area where models play a central role in measurement is psychology. The measurement of most psychological attributes, such as intelligence, anxiety and depression, does not rely on homomorphic mappings of the sort espoused by the Representational Theory of Measurement Wilson These models are constructed from substantive and statistical assumptions about the psychological attribute being measured and its relation to each measurement task.
For example, Item Response Theory, a popular approach to psychological measurement, employs a variety of models to evaluate the reliability and validity of questionnaires. One of the simplest models used to calibrate such questionnaires is the Rasch model Rasch New questionnaires are calibrated by testing the fit between their indications and the predictions of the Rasch model and assigning difficulty levels to each item accordingly.
The model is then used in conjunction with the questionnaire to infer levels of English language comprehension outcomes from raw questionnaire scores indications Wilson ; Mari and Wilson Psychologists are typically interested in the results of a measure not for its own sake, but for the sake of assessing some underlying and latent psychological attribute, e.
A good fit between item responses and a statistical model does not yet determine what the questionnaire is measuring. One way of validating a psychometric instrument is to test whether different procedures that are intended to measure the same latent attribute provide consistent results.
A construct is an abstract representation of the latent attribute intended to be measured, and. Constructs are denoted by variables in a model that predicts which correlations would be observed among the indications of different measures if they are indeed measures of the same attribute. In recent years, philosophers of science have become increasingly interested in psychometrics and the concept of validity. One debate concerns the ontological status of latent psychological attributes.
Elina Vessonen has defended a moderate form of operationalism about psychological attributes, and argued that moderate operationalism is compatible with a cautious type of realism Another recent discussion focuses on the justification for construct validation procedures.
According to Anna Alexandrova, construct validation is in principle a justified methodology, insofar as it establishes coherence with theoretical assumptions and background knowledge about the latent attribute.
This defeats the purpose of construct validation and turns it into a narrow, technical exercise Alexandrova and Haybron ; Alexandrova ; see also McClimans et al. A more fundamental criticism leveled against psychometrics is that it dogmatically presupposes that psychological attributes can be quantified. Michell , b argues that psychometricians have not made serious attempts to test whether the attributes they purport to measure have quantitative structure, and instead adopted an overly loose conception of measurement that disguises this neglect.
In response, Borsboom and Mellenbergh argue that Item Response Theory provides probabilistic tests of the quantifiability of attributes. Psychometricians who construct a statistical model initially hypothesize that an attribute is quantitative, and then subject the model to empirical tests.
When successful, such tests provide indirect confirmation of the initial hypothesis, e. Several scholars have pointed out similarities between the ways models are used to standardize measurable quantities in the natural and social sciences. Others have raised doubts about the feasibility and desirability of adopting the example of the natural sciences when standardizing constructs in the social sciences. Examples of Ballung concepts are race, poverty, social exclusion, and the quality of PhD programs.
Alexandrova points out that ethical considerations bear on questions about the validity of measures of well-being no less than considerations of reproducibility. Such ethical considerations are context sensitive, and can only be applied piecemeal. In a similar vein, Leah McClimans argues that uniformity is not always an appropriate goal for designing questionnaires, as the open-endedness of questions is often both unavoidable and desirable for obtaining relevant information from subjects.
In such cases, small changes to the design of a questionnaire or the analysis of its results may result in significant harms or benefits to patients McClimans ; Stegenga , Chap. These insights highlight the value-laden and contextual nature of the measurement of mental and social phenomena. Rather than emphasizing the mathematical foundations, metaphysics or semantics of measurement, philosophical work in recent years tends to focus on the presuppositions and inferential patterns involved in concrete practices of measurement, and on the historical, social and material dimensions of measuring.
In the broadest sense, the epistemology of measurement is the study of the relationships between measurement and knowledge. Central topics that fall under the purview of the epistemology of measurement include the conditions under which measurement produces knowledge; the content, scope, justification and limits of such knowledge; the reasons why particular methodologies of measurement and standardization succeed or fail in supporting particular knowledge claims, and the relationships between measurement and other knowledge-producing activities such as observation, theorizing, experimentation, modelling and calculation.
In pursuing these objectives, philosophers are drawing on the work of historians and sociologists of science, who have been investigating measurement practices for a longer period Wise and Smith ; Latour Ch.
The following subsections survey some of the topics discussed in this burgeoning body of literature. A topic that has attracted considerable philosophical attention in recent years is the selection and improvement of measurement standards.
Generally speaking, to standardize a quantity concept is to prescribe a determinate way in which that concept is to be applied to concrete particulars. This duality in meaning reflects the dual nature of standardization, which involves both abstract and concrete aspects. In Section 4 it was noted that standardization involves choices among nontrivial alternatives, such as the choice among different thermometric fluids or among different ways of marking equal duration.
Appealing to theory to decide which standard is more accurate would be circular, since the theory cannot be determinately applied to particulars prior to a choice of measurement standard. A drawback of this solution is that it supposes that choices of measurement standard are arbitrary and static, whereas in actual practice measurement standards tend to be chosen based on empirical considerations and are eventually improved or replaced with standards that are deemed more accurate.
A new strand of writing on the problem of coordination has emerged in recent years, consisting most notably of the works of Hasok Chang , , ; Barwich and Chang and Bas van Fraassen Ch. These works take a historical and coherentist approach to the problem. Rather than attempting to avoid the problem of circularity completely, as their predecessors did, they set out to show that the circularity is not vicious. Chang argues that constructing a quantity-concept and standardizing its measurement are co-dependent and iterative tasks.
The pre-scientific concept of temperature, for example, was associated with crude and ambiguous methods of ordering objects from hot to cold. Thermoscopes, and eventually thermometers, helped modify the original concept and made it more precise. With each such iteration the quantity concept was re-coordinated to a more stable set of standards, which in turn allowed theoretical predictions to be tested more precisely, facilitating the subsequent development of theory and the construction of more stable standards, and so on.
From either vantage point, coordination succeeds because it increases coherence among elements of theory and instrumentation. It is only when one adopts a foundationalist view and attempts to find a starting point for coordination free of presupposition that this historical process erroneously appears to lack epistemic justification The new literature on coordination shifts the emphasis of the discussion from the definitions of quantity-terms to the realizations of those definitions.
JCGM 5. Examples of metrological realizations are the official prototypes of the kilogram and the cesium fountain clocks used to standardize the second.
Recent studies suggest that the methods used to design, maintain and compare realizations have a direct bearing on the practical application of concepts of quantity, unit and scale, no less than the definitions of those concepts Riordan ; Tal The relationship between the definition and realizations of a unit becomes especially complex when the definition is stated in theoretical terms.
Several of the base units of the International System SI — including the meter, kilogram, ampere, kelvin and mole — are no longer defined by reference to any specific kind of physical system, but by fixing the numerical value of a fundamental physical constant. The kilogram, for example, was redefined in as the unit of mass such that the numerical value of the Planck constant is exactly 6. Realizing the kilogram under this definition is a highly theory-laden task.
The study of the practical realization of such units has shed new light on the evolving relationships between measurement and theory Tal ; de Courtenay et al ; Wolff b. As already discussed above Sections 7 and 8. On the historical side, the development of theory and measurement proceeds through iterative and mutual refinements. On the conceptual side, the specification of measurement procedures shapes the empirical content of theoretical concepts, while theory provides a systematic interpretation for the indications of measuring instruments.
This interdependence of measurement and theory may seem like a threat to the evidential role that measurement is supposed to play in the scientific enterprise. After all, measurement outcomes are thought to be able to test theoretical hypotheses, and this seems to require some degree of independence of measurement from theory.
This threat is especially clear when the theoretical hypothesis being tested is already presupposed as part of the model of the measuring instrument. To cite an example from Franklin et al. There would seem to be, at first glance, a vicious circularity if one were to use a mercury thermometer to measure the temperature of objects as part of an experiment to test whether or not objects expand as their temperature increases.
Nonetheless, Franklin et al. The mercury thermometer could be calibrated against another thermometer whose principle of operation does not presuppose the law of thermal expansion, such as a constant-volume gas thermometer, thereby establishing the reliability of the mercury thermometer on independent grounds.
To put the point more generally, in the context of local hypothesis-testing the threat of circularity can usually be avoided by appealing to other kinds of instruments and other parts of theory. A different sort of worry about the evidential function of measurement arises on the global scale, when the testing of entire theories is concerned.
As Thomas Kuhn argues, scientific theories are usually accepted long before quantitative methods for testing them become available. The reliability of newly introduced measurement methods is typically tested against the predictions of the theory rather than the other way around. Hence, Kuhn argues, the function of measurement in the physical sciences is not to test the theory but to apply it with increasing scope and precision, and eventually to allow persistent anomalies to surface that would precipitate the next crisis and scientific revolution.
Note that Kuhn is not claiming that measurement has no evidential role to play in science. The theory-ladenness of measurement was correctly perceived as a threat to the possibility of a clear demarcation between the two languages.
Contemporary discussions, by contrast, no longer present theory-ladenness as an epistemological threat but take for granted that some level of theory-ladenness is a prerequisite for measurements to have any evidential power. Without some minimal substantive assumptions about the quantity being measured, such as its amenability to manipulation and its relations to other quantities, it would be impossible to interpret the indications of measuring instruments and hence impossible to ascertain the evidential relevance of those indications.
This point was already made by Pierre Duhem —6; see also Carrier 9— Moreover, contemporary authors emphasize that theoretical assumptions play crucial roles in correcting for measurement errors and evaluating measurement uncertainties. Indeed, physical measurement procedures become more accurate when the model underlying them is de-idealized, a process which involves increasing the theoretical richness of the model Tal This problem is especially clear when one attempts to account for the increasing use of computational methods for performing tasks that were traditionally accomplished by measuring instruments.
As Margaret Morrison and Wendy Parker argue, there are cases where reliable quantitative information is gathered about a target system with the aid of a computer simulation, but in a manner that satisfies some of the central desiderata for measurement such as being empirically grounded and backward-looking see also Lusk Such information does not rely on signals transmitted from the particular object of interest to the instrument, but on the use of theoretical and statistical models to process empirical data about related objects.
For example, data assimilation methods are customarily used to estimate past atmospheric temperatures in regions where thermometer readings are not available. These estimations are then used in various ways, including as data for evaluating forward-looking climate models.
Two key aspects of the reliability of measurement outcomes are accuracy and precision. Consider a series of repeated weight measurements performed on a particular object with an equal-arms balance. JCGM 2. Though intuitive, the error-based way of carving the distinction raises an epistemological difficulty. It is commonly thought that the exact true values of most quantities of interest to science are unknowable, at least when those quantities are measured on continuous scales.
If this assumption is granted, the accuracy with which such quantities are measured cannot be known with exactitude, but only estimated by comparing inaccurate measurements to each other. And yet it is unclear why convergence among inaccurate measurements should be taken as an indication of truth.
After all, the measurements could be plagued by a common bias that prevents their individual inaccuracies from cancelling each other out when averaged. In the absence of cognitive access to true values, how is the evaluation of measurement accuracy possible? At least five different senses have been identified: metaphysical, epistemic, operational, comparative and pragmatic Tal —5. Instead, the accuracy of a measurement outcome is taken to be the closeness of agreement among values reasonably attributed to a quantity given available empirical data and background knowledge cf.
Thus construed, measurement accuracy can be evaluated by establishing robustness among the consequences of models representing different measurement processes Basso ; Tal b; Bokulich ; Staley Under the uncertainty-based conception, imprecision is a special type of inaccuracy. The imprecision of these measurements is the component of inaccuracy arising from uncontrolled variations to the indications of the balance over repeated trials.
Other sources of inaccuracy besides imprecision include imperfect corrections to systematic errors, inaccurately known physical constants, and vague measurand definitions, among others see Section 7. Paul Teller raises a different objection to the error-based conception of measurement accuracy. Teller argues that this assumption is false insofar as it concerns the quantities habitually measured in physics, because any specification of definite values or value ranges for such quantities involves idealization and hence cannot refer to anything in reality.
Removing these idealizations completely would require adding infinite amount of detail to each specification. As Teller argues, measurement accuracy should itself be understood as a useful idealization, namely as a concept that allows scientists to assess coherence and consistency among measurement outcomes as if the linguistic expression of these outcomes latched onto anything in the world.
The author is also indebted to Joel Michell and Oliver Schliemann for useful bibliographical advice, and to John Wiley and Sons Publishers for permission to reproduce excerpt from Tal Overview 2. Quantity and Magnitude: A Brief History 3. Operationalism and Conventionalism 5.
Realist Accounts of Measurement 6. Information-Theoretic Accounts of Measurement 7. Model-Based Accounts of Measurement 7. The Epistemology of Measurement 8. Overview Modern philosophical discussions about measurement—spanning from the late nineteenth century to the present day—may be divided into several strands of scholarship.
The following is a very rough overview of these perspectives: Mathematical theories of measurement view measurement as the mapping of qualitative empirical relations to relations among numbers or other mathematical entities. Information-theoretic accounts view measurement as the gathering and interpretation of information about a system. Quantity and Magnitude: A Brief History Although the philosophy of measurement formed as a distinct area of inquiry only during the second half of the nineteenth century, fundamental concepts of measurement such as magnitude and quantity have been discussed since antiquity.
Bertrand Russell similarly stated that measurement is any method by which a unique and reciprocal correspondence is established between all or some of the magnitudes of a kind and all or some of the numbers, integral, rational or real.
Operationalism and Conventionalism Above we saw that mathematical theories of measurement are primarily concerned with the mathematical properties of measurement scales and the conditions of their application. The strongest expression of operationalism appears in the early work of Percy Bridgman , who argued that we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations.
Realist Accounts of Measurement Realists about measurement maintain that measurement is best understood as the empirical estimation of an objective property or relation. Information-Theoretic Accounts of Measurement Information-theoretic accounts of measurement are based on an analogy between measuring systems and communication systems. Model-Based Accounts of Measurement Since the early s a new wave of philosophical scholarship has emerged that emphasizes the relationships between measurement and theoretical and statistical modeling Morgan ; Boumans a, ; Mari b; Mari and Giordani ; Tal , ; Parker ; Miyake Indications may be represented by numbers, but such numbers describe states of the instrument and should not be confused with measurement outcomes, which concern states of the object being measured.
As Luca Mari puts it, any measurement result reports information that is meaningful only in the context of a metrological model, such a model being required to include a specification for all the entities that explicitly or implicitly appear in the expression of the measurement result.
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