Abstract
This chapter aims to present a brief conceptual history of philosophical thinking about measurement, concentrating in particular on the issues of objectivity and subjectivity, realism and nonrealism, and role of models in measurement, as well as a discussion of how these philosophical issues have shaped thinking and discourse about measurement in both the human and physical sciences. First, three perspectives on measurement and its epistemic status are discussed, grouped as (a) naïve realism, (b) operationalism, and (c) representationalism. Following this, we discuss how these perspectives have informed thinking about the concept of validity in the human sciences, and how they have influenced the way in which measurement is characterized in different contexts as being dependent on empirical and/or mathematical constraints. We then attempt to synthesize these perspectives and propose a version of model-dependent realism which maintains some of the elements of each of these perspectives and at the same time rejects their most radical aspects, by acknowledging the fundamental role of models in measurement but also emphasizing that models are always models of something: the empirical components of measurement are designed and operated so as to guarantee that, via such models, measurement results convey information on the intended property. The analysis also provides a simple explanation of two of the most critical stereotypes that still affect measurement science: the hypotheses that (1) measurement is quantification, which hides the relevance of the empirical component of the process, and (2) measurement is only a process of transmission and presentation of preexisting information, usually intended as the “true value” of the measurand, which instead neglects the role of models in the process.
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Notes
- 1.
As noted in Footnote 19 of Chap. 2, we use the term “evaluation” to refer to an attribution of a value to the property of an object.
- 2.
For an introduction to the philosophical understanding of measurement see also Tal (2020).
- 3.
Under a Pythagorean conception that “numbers are in the world”, another position would be that each property (or at least each quantitative property; see, e.g., Michell, 1999) of each object already is a value prior to measurement.
- 4.
If a property is specifically a quantity—which, again, is taken by this view (and consistently with the Aristotelian tradition) to be an empirical feature of the property itself, independently of the way in which it is modeled—the aforementioned reference for comparison would be a measurement unit, and the aforementioned process of discovery of values specializes as a discovery of ratios of quantities (see, e.g., Michell, 2004).
- 5.
The usual notation “measured property of an object = measured value of a property” (which we have introduced as the Basic Evaluation Equation in Sect. 2.2.4) might contribute to such a confusion. As an example, consider the relation c = 299,792,458 m/s: Does the symbol “c” stand for (a) the speed of light in vacuum or (b) its value? In the first case the relation conveys a claim about the physical world, which (were the metre defined independently of the speed of light in vacuum) is in principle true or false: the ratio of the speed of light in vacuum and the metre is 299,792,458. In the second case the relation is just a conventional alias: “c” is synonymous with “299,792,458 m/s”.
- 6.
Of course, the problem remains whether the number in the value of position is a real number with infinitely many significant digits, as a geometric model might imply. Were such a hypothesis to be maintained, and given that planets are not geometric points, the measurand should be changed to, e.g., the position of the center of mass of the planet. This would create the new problem that, for the center of mass of a body to be uniquely defined, what is part of the body itself needs to be uniquely established, a condition that is hardly fulfilled by planets. Hence the unavoidability of a non-null definitional uncertainty—as introduced in Sect. 3.2.4—soon emerges also in these cases.
- 7.
For a longer discussion of the history of operationalism, see, e.g., Chang (2019).
- 8.
Whether such informational entities need to be numbers, with or without measurement units, is where Stevens, and since him representational theories of measurement, departed from Campbell. While, as just mentioned, numbers are required “to enable the powerful weapon of mathematical analysis to be applied to the subject matter of science” according to Campbell, Stevens (1946) made the representability of properties by means of numbers sufficient, but not necessary, for measurability.
- 9.
Stevens’ theory is not without objections (for one synthesis of criticisms, see Velleman & Wilkinson, 1993). In part, such criticisms have reacted to Stevens’ choice of calling the invariant scale transformations “admissible” or “permissible”, the objection being, in essence, that research should not be driven by prescriptions and surely not inhibited by proscriptions. Our analysis of these criticisms is in Sect. 6.5.1.
- 10.
For example, temperature, thought in antiquity to be an ordinal property, was upgraded (with the introduction of thermometers and thermometric scales) to a quantity. At first only interval-level measurement was possible; eventually the thermodynamic redefinition of temperature, which introduced a nonconventional zero point in the scale, made ratio-level measurement possible.
- 11.
Oftentimes validity is introduced alongside the concept of reliability, which usually refers to the extent to which measurement results are free from random sources of measurement error. Although some sources (e.g., Moss, 1994) describe reliability and validity as separate, complementary issues, most contemporary descriptions emphasize that reliability is a precondition for validity rather than a separate issue. As was discussed in Sect. 3.2.1, this usage of the terms “reliability” and “validity” then seems to map fairly closely onto what the VIM refers to as “precision” and “accuracy”, respectively (JCGM, 2012: 2.15 and 2.13).
- 12.
The influence of operationalism seems clear: while today one might still speak of a correlation coefficient as a tool for the evaluation of validity, speaking of such a correlation as definitional of validity blurs the distinction between what we know and how we know it. See also Borsboom and Mellenbergh (2004).
- 13.
Cronbach and Meehl’s conception of nomological networks drew from Carnap’s (1950) project to specify how theoretical terms are defined implicitly through the role they play in networks of lawful relations. However, as discussed briefly in Chap. 1, this project did not work for the simple reason that “there were (and are) no nomological networks involving concepts like general intelligence” (Borsboom et al., 2009: p. 136).
- 14.
Although many sources treat (or appear to treat) the term “construct” as synonymous with “property” (or at least “psychosocial property”), other sources also use it to refer to a concept or linguistic label that refers to a property (for a discussion, see, e.g., Slaney & Racine, 2013), and some sources even do both simultaneously: for example, the Standards for Educational and Psychological Testing (AERA, 2014), which are discussed further below, define a construct as “the concept or characteristic that a test is designed to measure” (p. 11). To avoid confusion, we use the terms “property” and “concept of property” rather than “construct”, except when specifically referring to language used by others. We also discuss in Sect. 4.5 properties that are in some sense constructed by human minds or human activities. Perhaps jarringly, in the terminology common in the human sciences (and construct validity theory in particular), the term “construct” might or might not imply that the property is thought of as having been constructed (see, e.g., Slaney, 2017).
- 15.
The term “influence properties” could be thought of as referring to sources of construct- (or property-) irrelevant variance.
- 16.
A legalistic conception of validity “operationalizes the concept in a way that makes it clear for test developers what the exact standard for validity is: they have to convince the jury. This bears all the marks of a licensing procedure. However, for scientific research, licensing procedures do not suffice. Truth cannot be […] equated to amounts of evidence” as noted by Borsboom (2012: p. 40).
- 17.
This definition of <validity> could be viewed as a re-statement of what in Sect. 3.2.1 was referred to as non-null instrument sensitivity.
- 18.
Consistently with this perspective, Wilson (2005) has advocated that instrument development efforts in the human sciences focus on the development of the definition of the property, and then the specification of theory regarding how this property is related to test outcomes. This perspective is explored further by Wilson (2013), and in Chap. 7 of this book.
- 19.
See for example the answer that is given to the question in Table 4.1: “Is measurement characterized by the structure of the process?”.
- 20.
For example, a traditional condition might be the invariance of ratios of properties.
- 21.
This is indeed the Euclidean position: x measures y if y is a multiple of x.
- 22.
As in definition 1 of Book 5 of the Elements, as previously quoted, the condition for a quantity (a “magnitude” in the traditional translation) “to measure” another quantity is that the first is a part of the second: “a magnitude is a part of a(nother) magnitude, the less of the greater, when it measures the greater” (Euclid, 2008). But for a property P which makes objects a, b, …, comparable through an order relation (or least as a partial order), it is clear that P[a] < P[b] does not generally mean that the property P of a is a part of the property of b. Indeed, it is additivity that guarantees this meaningfulness.
- 23.
This condition can be generalized by admitting that sometimes the zero of Q is not an intrinsic feature of Q, so that the numerical value x in the relation Q[a] = x qref is determined only when a zero property q0 is set for Q, as x = (Q[a] − q0)/(qref − q0) (for example, this was the case of temperature before the introduction of thermodynamic temperature and its measurement in kelvins, and is the case of position along a line, which, differently from length, can be measured only having chosen a reference/zero position). Since, in most cases, nonphysical properties do not have an intrinsic or obvious zero, this generalization—leading to what Stevens called an “interval scale” (1946)—proved to be very important for the development of measurability conditions for nonphysical properties.
- 24.
See Sect. 6.5.1 for an analysis of this condition and of the critiques it has received.
- 25.
- 26.
More generally, the fact that many physical properties are quantized would appear to lead to the paradoxical conclusion that they are not really quantities, and that they can be interpreted as quantities only in view of an approximate model that neglects the quantization. Hence, under the supposition that only quantities (in Hölder’s sense) are measurable, the peculiar conclusion would be that such physical properties are only approximately measurable. This has to do with the traditional distinction of quantities as either pluralities (or multitudes) or magnitudes, i.e., discretely or continuously divisible properties. According to Aristotle, “‘Quantum’ means that which is divisible into two or more constituent parts of which each is by nature a ‘one’ and a ‘this’. A quantum is a plurality if it is numerable, a magnitude if it is measurable. ‘Plurality’ means that which is divisible potentially into non-continuous parts, ‘magnitude’ that which is divisible into continuous parts” (Metaphysics, Book 5, Part 13; classics.mit.edu/Aristotle/metaphysics.5.v.html). The idea that measurability only refers to continuous quantities is désuet today.
- 27.
Examples of such pluralism are not limited only to the human sciences. A well-known case from the physical sciences is about mechanical phenomena, for which Newtonian and relativistic mechanics are studied and operationally used, even though for some aspects they are incompatible (e.g., the speed of light in vacuum is relative in the former and constant in the latter). The justification of this multiplicity is pragmatic: at nonrelativistic speeds the two theories basically provide the same results, and Newtonian mechanics is simpler than relativistic mechanics.
- 28.
As was briefly discussed in Sect. 4.3.2, one interpretation of the term “construct” as used in the human sciences is that it refers to a property that is in some sense constructed by us. As discussed by Earl Babbie (2013: p. 167), in reference to Kaplan’s (1964) seminal analysis: “concepts such as compassion and prejudice are … created from your conception of them, my conception of them, and the conceptions of all those who have ever used these terms. They cannot be observed directly or indirectly, because they don’t exist. We made them up” (p. 168). As is argued in this section, however, it is fallacious to infer from the observation that we “made up” a property that its referents do not exist.
- 29.
Sometimes the very existence of modeled phenomena actually does depend to at least some extent on models, which then become illocutionary (Austin, 1975). For example, whether a set of neurophysiological facts about an individual make it more difficult for that individual to focus attention over long periods of time compared to other individuals is arguably a model-independent fact about that individual, but whether the individual has attention-deficit hyperactivity disorder (ADHD) is a fact about how that individual has been labeled by other individuals, and is therefore at least partially dependent on a model of ADHD.
- 30.
Figure 4.7 is intended only as a rough visual representation of the role of models in producing measurement results, not as a representation of the whole measurement process, which (of course) involves actually performing measurements, which entails more than simply looking at reality through the lens of models. Also, the concepts used in the figure—<model of the general property>, etc.—will be explained further in later chapters.
- 31.
Using terminology from Searle (1992), ontological subjectivity is not necessarily a barrier to epistemic objectivity (see also Maul, 2013). Or, using terminology from Dennett (1987), we may choose to model and study psychosocial properties by adopting a “design stance” and (especially) an “intentional stance” rather than a “physical stance”.
References
American Educational Research Association (AERA) and Other Two Organizations. (2014). Standards for psychological and educational tests. Washington, DC: American Educational Research Association (AERA), American Psychological Association (APA), and National Council for Measurement in Education (NCME).
Austin, J. L. (1975). How to do things with words (Vol. 88). Oxford: Oxford University Press.
Babbie, E. (2013). The practice of social research (13th ed.). Wadsworth: Belmont.
Bell, S. (1999). A beginner’s guide to uncertainty of measurement. Measurement Good Practice Guide No. 11 (Issue 2). National Physical Laboratory. Retrieved from www.dit.ie/media/physics/documents/GPG11.pdf
Bentley, J. P. (2005). Principles of measurement systems. New York: Pearson.
Bickhard, M. H. (2001). The tragedy of operationalism. Theory and Psychology, 11(1), 35–44.
Boring, E. G. (1923). Intelligence as the tests test it. New Republic, 36, 35–37.
Borsboom, D. (2005). Measuring the mind: Conceptual issues in contemporary psychometrics. Cambridge: Cambridge University Press.
Borsboom, D. (2006). The attack of the psychometricians. Psychometrika, 71(3), 425–440.
Borsboom, D. (2009). Educational measurement, 4th edition: Book review. Structural Equation Modeling, 16, 702–711.
Borsboom, D. (2012). Whose consensus is it anyway? Scientific versus legalistic conceptions of validity. Measurement: Interdisciplinary Research and Perspectives, 10, 38–41.
Borsboom, D., & Mellenbergh, G. (2004). Why psychometrics is not pathological: A comment on Michell. Theory and Psychology, 14, 105–120.
Borsboom, D., Cramer, A. O. J., Kievit, R. A., Zand Scholten, A. & Franic, S. (2009). The end of construct validity. In R.W. Lissitz (Ed.), The concept of validity: Revisions, new directions and applications (pp. 135–170). Charlotte, NC: Information Age Publishing.
Boumans, M. (2007). Invariance and calibration. In M. Boumans (Ed.), Measurement in economics: A handbook (pp. 231–248). London: Academic Press.
Bridgman, P. W. (1927). The logic of modern physics. New York: Macmillan.
Campbell, D. T., & Fiske, D. W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. Psychological Bulletin, 56(2), 81.
Campbell, N. R. (1920). Physics: The elements. Cambridge: Cambridge University Press.
Carnap, R. (1950). Empiricism, semantics, and ontology. Revue internationale de philosophie, 4, 20–40.
Carnap, R. (1966). Philosophical foundations of physics (Vol. 966). New York: Basic Books.
Cartwright, N. (1983). How the laws of physics lie. Oxford: Oxford University Press.
Chang, H. (2019). Operationalism. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Stanford, CA: Stanford University. Retrieved from plato.stanford.edu/entries/operationalism
Cliff, N. (1992). Abstract measurement theory and the revolution that never happened. Psychological Science, 3, 186–190.
Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52(4), 281.
De Morgan, A. (1836). The connection of number and magnitude: At attempt to explain the fifth book of Euclid. London: Taylor and Walton.
Dennett, D. (1987). The intentional stance. Cambridge: MIT Press.
Dennett, D. (1991). Consciousness explained. Boston, MA: Little, Brown and Company.
DIN 1319:1995. Fundamentals of metrology, Part 1: Basic terminology (German standard). Deutsche Institut für Normung.
Dingle, H. (1950). A theory of measurement. The British Journal for the Philosophy of Science, 1(1), 5–26.
Doignon, J. P. (1993). Geometry is measurement but measurement theory is more than geometry. Journal of Mathematical Psychology, 37, 472–476.
Edgeworth, F. Y. (1885). Observations and statistics: An essay on the theory of errors of observation and the first principles of statistics. Transactions of the Cambridge Philosophical Society, 14, 138–169.
Ente Italiano di Normazione (UNI). (1984). UNI 4546:1984. Misure e misurazioni. Termini e definizioni fondamentali (Italian standard). Milano: UNI (in Italian).
Euclid’s Elements of geometry, the Greek text of J.L. Heiberg (1883-1885) edited, and provided with a modern English translation, by Richard Fitzpatrick (2008). Retrieved from farside.ph.utexas.edu/Books/Euclid/Euclid.html
Ferguson, A., Myers, C. S., Bartlett, R. J., Banister, H., Bartlett, F. C., Brown, W., et al. (1940). Final report of the committee appointed to consider and report upon the possibility of quantitative estimates of sensory events. Report of the British Association for the Advancement of Science, 2, 331–349.
Finkelstein, L. (1984). A review of the fundamental concepts of measurement. Measurement, 2, 25–34.
Finkelstein, L. (1994). Measurement: Fundamental principles. In L. Finkelstein & K. Grattan (Eds.), Concise encyclopedia of measurement and instrumentation (pp. 201–205). Oxford: Pergamon.
Finkelstein, L. (2003). Widely, strongly and weakly defined measurement. Measurement, 34, 39–48.
Finkelstein, L. (2005). Problems of measurement in soft systems. Measurement, 38, 267–274.
Frank, P. G. (1956). The validation of scientific theories. Boston, MA: Beacon Press.
Frigerio, A., Giordani, A., & Mari, L. (2010). Outline of a general model of measurement. Synthese, 175, 123–149.
Galilei, G. (1632). The Assayer. In S. Drake (Ed.), Discoveries and Opinions of Galileo (1957), New York: Doubleday.
Galton, F. (1869). Hereditary genius: An inquiry into its laws and consequences. London: Macmillan.
Gescheider, G. A. (2013). Psychophysics: The fundamentals (3rd ed.). Hoboken, NJ: Taylor and Francis.
Giordani, A., & Mari, L. (2012). Property evaluation types. Measurement, 45, 437–452.
Green, C. D. (1992). Of immortal mythological beasts: Operationism in psychology. Theory and Psychology, 2(3), 291–320.
Green, C. D. (2001). Operationalism again: What did Bridgman say? Theory and Psychology, 11, 45–51.
Hacking, I. (1983). Representing and intervening: Introductory topics in the philosophy of natural science. Cambridge: Cambridge University Press.
Hacking, I. (1990). The taming of chance. Cambridge: Cambridge University Press.
Haig, B. D. (2014). Investigating the psychological world: Scientific method in the behavioral sciences. Cambridge: MIT Press.
Heath, T. L. (1897). The works of Archimedes. Cambridge: Cambridge University Press.
Hölder, O. (1901). Die Axiome der Quantität und die Lehre vom Mass, Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Mathematisch-Physische Klasse, 53, 1–46.
International Bureau of Weights and Measures (BIPM) and Other Six International Organizations. (1993). International vocabulary of basic and general terms in metrology (VIM) (2nd ed.). Geneva: ISO.
International Organization for Standardization (ISO) and Other Three International Organizations. (1984). International vocabulary of basic and general terms in metrology (VIM) (1st ed.). Geneva: International Bureau of Weights and Measures (BIPM), International Electrotechnical Commission (IEC), International Organization for Standardization (ISO), International Organization of Legal Metrology (OIML).
Joint Committee for Guides in Metrology (JCGM). (2012). JCGM 200:2012. International vocabulary of metrology—Basic and general concepts and associated terms (VIM) (3rd ed.). Sèvres: JCGM (2008 version with minor corrections). Retrieved from www.bipm.org/en/publications/guides/vim.html
Kane, M.T. (1992). An argument-based approach to validity. Psychological Bulletin, 112, 527–535.
Kaplan, A. (1964). The conduct of inquiry. San Francisco, CA: Chandler.
Kim, J. (1998). Mind in a physical world. Cambridge: MIT Press.
Koyré, A. (1948). Du monde de l’à peu près à l’univers de la précision, in: Etudes d’histoire de la pensée philosophique (pp.311–29). Gallimard: Paris, 1981. Originally in: Critique, 4, 28, 806–823.
Krantz, D. H., Luce, R. D., Suppes, P., & Tverski, A. (1971). Foundations of measurement - Additive and Polynomial Representations (Vol. I). New York: Academic Press.
Kula, W. (1986). Measures and men. Princeton, NJ: Princeton University Press.
Kyburg, H. E. (1984). Theory and measurement. Cambridge: Cambridge University Press.
Leahey, T. H. (1980). The myth of operationism. The Journal of Mind and Behavior, 1(2), 127–144.
Loevinger, J. (1957). Objective tests as instruments of psychological theory. Psychological Reports, 3, 635–694.
Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
Luce, R. D., Krantz, D. H., Suppes, P., & Tverski, A. (1990). Foundations of measurement - Representation, Axiomatization, and Invariance (Vol. III). New York: Academic Press.
Margenau, H. (1958). Philosophical problems concerning the meaning of measurement in physics. Philosophy of Science, 25, 23–33.
Mari, L. (1997). The role of determination and assignment in measurement. Measurement, 21, 79–90.
Mari, L. (2003). Epistemology of measurement. Measurement, 34, 17–30.
Mari, L. (2013). A quest for the definition of measurement. Measurement, 46, 2889–2895.
Mari, L., Carbone, P., & Petri, D. (2012). Measurement fundamentals: A pragmatic view. IEEE Transactions in Instrumentation and Measurement, 61, 2107–2115.
Mari, L., Maul, A., Torres Irribarra, D., & Wilson, M. (2017). Quantities, quantification and the necessary and sufficient conditions for measurement. Measurement, 100, 115–121.
Markus, K. A., & Borsboom, D. (2013). Frontiers of test validity theory: Measurement, causation, and meaning. New York: Routledge.
Maul, A. (2013). The ontology of psychological attributes. Theory & Psychology, 23, 752–769.
Maul, A. (2014). Justification is not truth, and testing is not measurement: Understanding the purpose and value of the standards. Educational Measurement: Issues and Practice, 33, 39–41.
Maul, A. (2018). Validity. In B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 1771–1775). Thousand Oaks, CA: SAGE Publications.
Maul, A., Torres Irribarra, D., & Wilson, M. (2016). On the philosophical foundations of psychological measurement. Measurement, 79, 311–320.
McGrane, J. (2015). Stevens’ forgotten crossroads: The divergent measurement traditions in the physical and psychological sciences from the mid-twentieth century. Frontiers in Psychology, 6, 431.
McGrane, J., & Maul, A. (2020). The human sciences, models and metrological mythology. Measurement, 152. https://doi.org/10.1016/j.measurement.2019.107346
Messick, S. (1989). Validity. In R. L. Linn (Ed.), Educational measurement (3rd ed., pp. 13–103). New York: American Council on Education/Macmillan.
Michell, J. (1990). An introduction to the logic of psychological measurement. New York: Psychology Press.
Michell, J. (1997). Quantitative science and the definition of measurement in psychology. British Journal of Psychology, 88, 355–383.
Michell, J. (1999). Measurement in psychology: A critical history of a methodological concept. Cambridge: Cambridge University Press.
Michell, J. (2004). Item response models, pathological science and the shape of error: Reply to Borsboom and Mellenbergh. Theory & Psychology, 14, 121.
Michell, J. (2005). The logic of measurement: A realist overview. Measurement, 38(4), 285–294.
Michell, J. (2009). Invalidity in validity. In R.W. Lissitz (Ed.), The concept of validity: Revisions, new directions and applications (pp. 135–170). Charlotte, NC: Information Age Publishing.
Mislevy, R. J. (2018). Sociocognitive foundations of educational measurement. New York: Routledge.
Molenaar, P. C. M., & Von Eye, A. (1994). On the arbitrary nature of latent variables. In A. von Eye & C. C. Clegg (Eds.), Latent variables analysis. Thousand Oaks, CA: Sage.
Moss, P. A. (1994). Can there be validity without reliability? Educational Researcher, 23(2), 5–12.
Narens, L. (1985). Abstract measurement theory. Cambridge, MA: MIT Press.
Narens, L. (2002). Theories of meaningfulness. Mahwah, NJ: Lawrence Erlbaum.
Narens, L., & Luce, R. (1986). Measurement: The theory of numerical assignments. Psychological Bulletin, 99(2), 166–180.
Neurath, O., Hahn, H., & Carnap, R. (1973). The scientific conception of the world: The Vienna circle. Empiricism and sociology. Boston, MA: Reidel.
Newton, P. E. (2012). Clarifying the consensus definition of validity. Measurement: Interdisciplinary Research & Perspectives, 10(1–2), 1–29.
Newton, P., & Shaw, S. (2014). Validity in educational and psychological assessment. London, UK: Sage.
Nisbett, R. E., Aronson, J., Blair, C., Dickens, W., Flynn, J., Halpern, D. F., et al. (2012). Intelligence: New findings and theoretical developments. American Psychologist, 67, 130–159.
Putnam, H. (1985). Realism and reason (Philosophical papers) (Vol. 3). Cambridge: Cambridge University Press.
Putnam, H. (1990). Realism with a human face. Cambridge, MA: Harvard University Press.
Putnam, H. (1994). Words and life. Cambridge, MA: Harvard University Press.
Putnam, H. (2000). The threefold cord: Mind, body and world. New York City: Columbia University Press.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Chicago, IL: University of Chicago Press.
Regtien, P. P. L. (2004). Measurement science for engineers. London: Elsevier.
Rossi, G. B. (2006). An attempt to interpret some problems in measurement science on the basis of Kuhn’s theory of paradigms. Measurement, 39, 512–521.
Rossi, G.B. (2007). Measurability. Measurement, 40, 545–562.
Rossi, G. B. (2014). Measurement and probability: A probabilistic theory of measurement with applications. Dordrecht: Springer.
Rossi, G. B., & Crenna, F. (2013). On ratio scales. Measurement, 46(8), 2913–2920.
Russell, B. (1903). The principles of mathematics. Cambridge: Cambridge University Press.
Searle, J. (1992). The rediscovery of the mind. Cambridge: MIT Press.
Shannon, C. E., & Weaver, W. (1949). The mathematical theory of communication. Urbana, IL: University of Illinois Press.
Shepard, L. A. (1993). Evaluating test validity. In L. Darling-Hammond (Ed.), Review of research in education (Vol. 19). Washington, DC: AERA.
Skinner, B. F. (1945). The operational analysis of psychological terms. Psychological Review, 52, 270.
Skinner, B. F. (1971). Beyond freedom and dignity. New York: Knopf.
Slaney, K. (2017). Validating psychological constructs: Historical, philosophical, and practical dimensions. Cham: Springer.
Slaney, K. L., & Racine, T. P. (2013). What’s in a name? Psychology’s ever evasive construct. New Ideas in Psychology, 13, 4–12.
Speitel, K. (1992). Measurement assurance. In G. Salvendy (Ed.), Handbook of industrial engineering (pp. 2235–2251). New York: Wiley.
Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677–680.
Stevens, S. S. (1959). Measurement, psychophysics, and utility, in: C. West Churchman, P. Ratoosh (eds.), Measurement, definitions and theories, Wiley, New York, pp.18–63.
Stevens, S. S. (1975). Psychophysics: Introduction to its perceptual, neural, and social prospects. New York: Wiley.
Stigler, S. M. (1986). The history of statistics: The measurement of uncertainty before 1900. Cambridge, MA: Harvard University Press.
Stigler, S. M. (1992). A historical view of statistical concepts in psychology and educational research. American Journal of Education, 101, 60–70.
Stigler, S. M. (1999). Statistics on the table: The history of statistical concepts and methods. Cambridge, MA: Harvard University Press.
Suppes, P. (2002). Representation and invariance of scientific structures. Stanford, CA: CSLI Publications.
Suppes, P., & Zinnes, J. L. (1963). Basic measurement theory. In Handbook of mathematical psychology (Vol. 1, pp. 1–76). New York: Wiley.
Suppes, P., Krantz, D.H., Luce, R.D., & Tverski, A. (1989). Foundations of measurement - Geometrical, Threshold, and Probabilistic Representations (Vol. II). New York: Academic Press.
Tal, E. (2020). Measurement in science. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Stanford, CA: Stanford University. Retrieved from plato.stanford.edu/entries/measurement-science
Teller, P. (2013). The concept of measurement-precision. Synthese, 190, 189–202.
Velleman, P. F., & Wilkinson, L. (1993). Nominal, ordinal, interval, and ratio typologies are misleading. The American Statistician, 47(1), 65–72.
Weyl, H. (1949/2009). Philosophy of mathematics and natural science. Princeton, NJ: Princeton University Press.
Wilson, M. (2005). Constructing measures: An item response modeling approach. Mahwah, NJ: Lawrence Erlbaum Associates.
Wilson, M. (2013). Using the concept of a measurement system to characterize measurement models used in psychometrics. Measurement, 46(9), 3766–3774.
Wilson, M. (2018). Making measurement important for education: The crucial role of classroom assessment. Educational Measurement: Issues and Practice, 37(1), 5–20.
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Mari, L., Wilson, M., Maul, A. (2021). Philosophical perspectives on 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_4
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DOI: https://doi.org/10.1007/978-3-030-65558-7_4
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