Abstract
This chapter aims to expand on the ontological and epistemological analysis of properties introduced in the previous chapter, with a discussion of three fundamental issues for measurement science. Restarting from the distinction between general and individual properties, the first is about the nature of values of quantities and more generally of properties, thus allowing us to further discuss the epistemic role of Basic Evaluation Equations. The second issue relates to the classification of properties, or of property evaluations, in terms of scale types, and thus particularly to the characterization of quantities as specific kinds of properties, thus leading to the question of whether, and under what conditions, nonquantitative properties can be measured. On this basis, the third problem is explored: the conditions of existence of general properties and the role of measurement in the definition of general properties.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In the case of quantities, it might be that individual quantities are those entities sometimes called “magnitudes”. On the other hand, the concept <magnitude> is used in radically different ways: quantities are magnitudes but also have magnitudes, as in the current edition of the VIM, which defines <quantity> as follows: “property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference” (JCGM, 2012: 1.1). Given this confusion, and the fact that measurement results can be, and usually are, reported without reference to magnitudes, we avoid including <magnitude> in the ontology we are presenting here (for an analysis of the relations between <quantity> and <magnitude> see Mari & Giordani, 2012: pp. 761–763).
- 2.
A foundational ontology might endeavor to build a framework on properties eventually based on one entity, from which everything else can be derived (an example of this monism is trope theory; see Maurin, 2018) or reduced, as nominalism would do by assuming that both individual properties and general properties are just concepts, and only properties of objects exist outside our minds (see Sect. 5.3.1). However, this philosophical task has no direct consequences for measurement science.
- 3.
In fact, the analysis that follows may be easily generalized to the case of properties and values of properties, as we do later on in this chapter, where we also discuss the characterization of quantities as specific kinds of properties. We start by presenting the more specific case of values of quantities because the very concept of <value of a property> is not widely used, and some would consider it controversial. It should be noted that the boundary between quantitative and nonquantitative properties is not uniquely defined, and in particular there are controversies whether ordinal properties are quantitative or not. However, that additive properties are quantities is not an issue, and we start our discussion from them.
- 4.
One example of a term used to communicate a value is a numeral, which is a term for a number; for example, “4” and “IV” are both numerals that stand for the number 4. As was previously discussed, Campbell (1920) defined measurement as “the assignment of numerals to represent properties”, and Stevens (1959) defined measurement as “the assignment of numerals to objects or events according to rule”; such statements may have inadvertently contributed to the confusion between values and terms. It may be worth noting that even though both Campbell and Stevens are associated with representational theories of measurement, the wider literature on representationalism emphasizes the mapping of objects or properties to numbers, not numerals, as discussed further below.
- 5.
For example, André Weyl wrote that “measurement permits things … to be represented conceptually, by means of symbols” (1949: p. 144). While not false, this claim is by no means characteristic of measurement in particular, and therefore is not very informative.
- 6.
The fact that distinct objects can have the same quantity, e.g., the same length, and therefore are mapped to the same number, makes the quantity-related mapping non-injective, thus a homomorphism. What Louis Narens wrote (1985: p. 7) on this matter is interesting (note that he uses the term “scale” to refer to such mappings): “I often prefer to change the character of the representational theory a little and consider a scale to be an isomorphism between the empirical or qualitative situation and some mathematical situation. The primary reason for this is that isomorphisms preserve truth whereas homomorphisms do not.” According to the ontology we are proposing, a way for making the mapping injective, and therefore an isomorphism, is to assume that its domain is the set of individual properties, rather than of the properties of objects or of objects. Our ontology highlights that individual properties can be measured only in their being properties of objects, thus making the mapping that formalizes such an experimental process non-injective. (Admittedly, consistently with this thinking, Narens chose to title his book “Abstract Measurement Theory” (emphasis added); hence perhaps the prior question is whether the very concept of <abstract measurement> has anything to do with actual measurement as it is commonly understood.)
- 7.
This highlights another barrier to the elimination of values of quantities in favor of numbers: for all properties evaluated in scales of types algebraically weaker than ratio (see the related discussion in Sect. 6.5), the social acceptance of “natural units” is not sufficient. In particular, in the case of an interval scale a “natural zero” would also need to be universally adopted.
- 8.
This construction is assumed to be performed in one inertial frame of reference, so that problems due to relativistic effects do not arise.
- 9.
- 10.
The length n L[r] is customarily defined by induction: 1 L[r] := L[r], and n L[r] := (n − 1) L[r] ⊕ L[r]. Since we are operating with empirical quantities, not numbers, one might challenge the correctness of the equation L[r] ⊕ L[r] = 2 L[r], contesting, in particular, that the geometry of our world on the one hand and the features of our instruments on the other hand do not allow us to guarantee the perfect collinear concatenation of rods. The argument is that numerically L[a] ⊕ L[b] = (L[a]2 − 2cos(ϑ) L[a] L[b] + L[b]2)½, where ϑ is the angle between the rods a and b, so that substituting L[r] ⊕ L[r] with 2 L[r] is correct only if ϑ = π, i.e., in the case of collinearity. This is true, of course, but the same argument can be exploited to provide an empirical check of collinearity, via the condition that ⊕ is associative: it is indeed trivially proved that for (L[a] ⊕ L[b]) ⊕ L[c] = L[a] ⊕ (L[b] ⊕ L[c]) to hold ϑ must be π (or, interestingly, (1 + 2k)π/2, for k = 0, 1, …, where the Pythagorean theorem applies: in a peculiar world, “collinear concatenation” means concatenation at right angles …).
- 11.
This problem is arguably even more pernicious in the human sciences, wherein properties commonly vary not only by time but also by sociocultural-historical context, as also discussed in Sect. 4.4.
- 12.
The inverse approach is also possible: given a predefined reference length ℓref and a given factor k, a new reference length ℓref* could be defined as ℓref* := k ℓref. In this case, finding an object r* such that L[r*] = ℓref* (thus an empirical relation, not a definition) would correspond to realizing the definition of the new reference length.
- 13.
The fact that this is possible is a compelling reason to maintain the distinction between the quantities on the left- and right-hand sides of Basic Evaluation Equations. Unfortunately this is sometimes confused. Take the following example: “Suppose we had chosen as our standard [of mass] a cube of iron rather than platinum. Then, as the iron rusted, all other objects would become lighter in weight” (Kaplan, 1964: p. 186). This is wrong: the other objects do not become lighter; they only seem to be lighter when compared to the rusted cube, given that it is only the numerical representation of their mass that changes. A very-well-studied case of such changes is that of the kilogram, which before the 2019 revision of the SI was defined as the mass of a given artifact, the International Prototype of the Kilogram (IPK).
- 14.
- 15.
An example of this is the well-known case of the intelligence quotient (IQ), defined by taking the median raw score of the chosen sample as IQ 100 and one sample standard deviation as corresponding to 15 IQ points. It has been observed that since the early twentieth century raw scores on IQ tests have increased in most parts of the world, a situation called the Flynn effect (Flynn, 2009). Whether intelligence has also increased is, of course, another matter.
- 16.
On this matter Eran Tal (2019) introduces the distinction between types and tokens, and proposes thermal expansion coefficient of aluminum at 20 °C and thermal expansion coefficient of a particular piece of aluminum at a given temperature as examples of a type and a corresponding token, such that “quantity types may be instantiated by more than one object or event”. Since there can be an element other than aluminum that at a given temperature has the same thermal expansion coefficient of aluminum at 20 °C, quantity types are not the same as general properties, as we have introduced them. We do not consider that this distinction deserves to be adopted here: the vast majority of properties actually measured would be tokens with no type (e.g., what is the type of the length of a given rod? or of the reading comprehension ability of a given student?).
- 17.
This is one more case in which the distinction between sense and reference (see Sect. 5.3.2) is relevant. The assumption of validity of the principle of continuity can be written as metre1889 = metre1960, in which the fact that the metre was defined in different ways in 1889 and in 1960 makes the senses of the two expressions (“the metre as defined in 1889” and “the metre as defined in 1960”) different, while their referents are the same.
- 18.
A generalized version of this condition is usually part of an axiomatic system of quantities. For example, the seventh axiom of Patrick Suppes’ system (1951: p. 165) is, in our notation, if Q[ai] ≤ Q[ak] then there exists a number x such that Q[ak] = x Q[ai].
- 19.
- 20.
As explained in Footnote 12 of Chap. 5, we use the concept <multiple of a quantity> in a broad sense, admitting also non-integer multiples.
- 21.
As a consequence, we can provide a simple answer to a question such as whether, e.g., 1.2345 metres and 48.602 inches are the same value or not: “1.2345 m” and “48.602 in” have the same referent—i.e., 1.2345 metres and 48.602 inches are the same length—but they have different senses. For short, they are conceptually different but referentially the same.
- 22.
For the sake of simplicity, we assume that this construction is done in a context in which sufficiently clear ideas are available about what temperature is and therefore in particular how temperature and heat are related but different properties (note that sometimes temperature is considered to be the intensity of heat, and this justifies its nonadditivity). The actual historical development of these ideas was convoluted, and some sorts of “candidate measurements” were instrumental to the clarification (see Chang, 2004; Sherry, 2011).
- 23.
The condition that this construction applies to multiple bodies/thermometers avoids the problems of radical operationalism, which would define temperature as what is measured by a given instrument.
- 24.
Differences of volumes of the relevant bodies have been assumed to be somehow observable. However, instead of operating on empirical properties it might be more convenient to measure volumes and then to operate mathematically on the measured values. The change is immaterial here. Note furthermore that this role of volume as a transduced property that is a function of temperature played an important historical role, as the scientific principle at the basis of the construction of the first thermometers, but is by no means unique. An analogous presentation could be made, for example, with voltage in place of volume in reference to the thermoelectric effect.
- 25.
As we discuss in Chap. 7, each question of a test operates as a transducer, in this case transforming the RCA of a reader to a score.
- 26.
The definition (or content) of this item universe is often referred to as the “domain”.
- 27.
Equation (6.2) has no closed-form solution for θ and δ; hence we are not providing equations for them.
- 28.
This contrasts with any position which attributes a special ontic role to values. For example, Hasok Chang, as an illustration of “ontological principles … that are regarded as essential features of reality in the relevant epistemic community” and in defense of what he calls “the pursuit of ontological plausibility”, mentions the “Principle of single value (or, single-valuedness): a real physical property can have no more than one definite value in a given situation” (Chang, 2001: p. 11, also presented in Chang, 2004: p. 90).
- 29.
- 30.
This subject has been widely debated at least since the seminal analysis by von Helmholtz (1887), who opened his paper by claiming that “counting and measuring are the bases of the most fruitful, most certain, and most exact of all known scientific methods”. Such prestige and epistemic authority makes measurement a yearned-for target. From another perspective, “Measurement is such an elegant concept that even with [properties] apparently lacking multiples, if the [property] is capable of increase or decrease (like temperature is, for example), the temptation to think of it as quantitative is strong” (Michell, 2005: p. 289). See Chap. 7 for more on this.
- 31.
- 32.
Given this, the reader will not find here the proposal of a clear-cut criterion to distinguish between quantities and non-quantities. At least since Hölder’s (1901) paper, several axiomatizations of quantities have been proposed (e.g., Mundy, 1987; Suppes, 1951; Suppes & Zanotti, 1992), and choosing among them is not relevant here. On this matter a general issue is whether order is sufficient for a property to be considered a quantity. While the sources just cited all answer this question in the negative, more encompassing positions are possible, such as Ellis’, according to whom “a quantity is usually conceived to be a kind of property. It is thought to be a kind of property that admits of degrees, and which is therefore to be contrasted with those properties that have an all-or-none character” (1968: p. 24). By using the term “ordinal quantity”, the VIM adopted the same stance (JCGM, 2012: 1:26): ordinal properties are considered to be quantities. This multiplicity is one more reason not to fall in the trap of what Abraham Kaplan called the “mystique of quantity” (1964: p. 172).
- 33.
For example, Nicholas Chrisman mentions the following ten “levels [which] are by no means complete”, where for each level the “information required” is specified (1998: p. 236): (1) Nominal (definition of categories). (2) Graded membership (definition of categories plus degree of membership or distance from prototype). (3) Ordinal (definition of categories plus ordering). (4) Interval (definition of unit and zero). (5) Log interval (definition of exponent to define intervals). (6) Extensive ratio (definition of unit—additive rule applies). (7) Cyclic ratio (unit and length of cycle). (8) Derived ratio (units—formula of combination). (9) Counts (definition of objects counted). (10) Absolute (type: probability, proportion, etc.).
- 34.
We are not concerned here with whether the general property applies to single entities or to pairs, triples, etc. of them, and therefore whether—in the traditional terminology—it is a property or a relation (see Sect. 5.2.3).
- 35.
- 36.
This is why in the definition of <quantity> given by the VIM—“property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference” (JCGM, 2012: 1.1)—the last part “that can be expressed as a number and a reference” is not an actual specification, and could be removed.
- 37.
Of course, nationality-related orderings can be defined; for example, names of nations are ordered alphabetically and nations are ordered by the size of their population, but the former is a relation among linguistic terms and the latter is a relation among cardinalities of sets: neither of them involve the property of nationality, in the sense that one’s nationality is not a linguistic entity, nor is it a number.
- 38.
This is thus in sharp contrast with radically constructionist presentations, such as Kaplan’s view that “the order of a set of objects is something which we impose on them. We take them in a certain order; the order is not given by or found in the objects themselves” (1964: p. 180).
- 39.
This lack of a context—seen, for example, in that reporting that the shape of a given object is cube does not in itself provide any hint about what other shapes the object might have had—is a problem in particular for computing the quantity of information obtained by a value. According to Claude Shannon (1948), this is related to the probability of selecting that value, which in turn supposes knowledge of the underlying probability distribution. We further discuss this fundamental idea by Shannon in Sect. 8.1, in terms of quantity of (syntactic) information conveyed by measurement.
- 40.
This is clearly analogous to the way information is reported in ordinal cases, such as Mohs’ hardness, e.g., hardness(given sample) = 5 on the Mohs’ scale.
- 41.
As a consequence, the possible concern that only numbers (or numerals) count as values of properties is unjustified. This also shows that the values of nonquantitative properties are not merely “symbols” or “names”. The discussion in Sect. 6.2.1 about values of quantities applies more generally to values of properties.
- 42.
For example, Fred Roberts describes what he calls “the representation problem” as follows: “Given a particular numerical relational system Y, find conditions on an observed relational system X (necessary and) sufficient for the existence of a homomorphism from X into Y” (1979: p. 54).
- 43.
It seems paradoxical that representationalism—a weak position about the epistemic state of measurement, as also discussed in Chap. 4—assumes some strong ontic requirements on properties.
- 44.
This hypothesis of linearity can be empirically corroborated by ascertaining that different temperatures produce proportional changes in different thermometers, operating according to different transduction effects. Four conceptual (though not necessarily historical) stages may be envisioned to such a process:
-
1.
A property is known only via a single transduction effect: for example, temperature can be transduced to a single kind of thermometric fluid (e.g., alcohol). In this case, the hypothesis of linearity is only grounded on the meta-hypothesis of simplicity.
-
2.
A property is known via multiple transduction effects related to the same transduction principle: for example, temperature can be transduced to different kinds of thermometric fluid (e.g., alcohol and mercury). In this case, if (for example) it were discovered that the temperature that produces the midpoint in volume between the volumes produced by two fixed points (e.g., the freezing and boiling points of water at sea level) is the same for different fluids, the hypothesis of linearity gains more plausibility. (As it happens, this is not exactly the case for mercury and alcohol.)
-
3.
A property is known via multiple transduction principles: for example, temperature can also be transduced to electric tension, via the thermoelectric effect. In this case, if (for example) it were discovered that the temperature that produces the midpoint in volume between the volumes produced by the two fixed points and the temperature that produces the midpoint in tension between the tensions produced by the same fixed points are the same for different bodies, the hypothesis of linearity gains more plausibility.
-
4.
A property becomes part of a nomic network (see Sect. 6.6.2); if, for example, a law is discovered that connects proportional differences of temperature of a given body to transferred heats, the hypothesis of linearity gains even more plausibility.
-
1.
- 45.
For an extensive presentation of conjoint measurement, see Michell (1990: ch. 4), where conjoint measurement is introduced as a “general way […] in which evidence corroborating the hypothesis [that a property is quantitative] may be obtained” (p. 67). In the light of the discussion in Sect. 3.4.2, a method of quantification is not necessarily a method of measurement: hence a more correct term for conjoint measurement would be “conjoint quantitative evaluation”.
- 46.
For example, the diameter of objects, whose evaluation is usually of ratio type, may be evaluated by means of a sequence of sieves of smaller and smaller opening, where each sieve is identified by an ordinal value and the evaluation sets the diameter of each object to be equal to the value of the last sieve crossed by the object. Such an evaluation is then only ordinal.
- 47.
The identification of the conditions that make such modeling possible is one of the primary contributions of the representational theories of measurement, the stated aim of which is “to construct numerical representations of qualitative structures” (Krantz et al., 1971: p. xviii). (Perhaps peculiarly, in the terminology of representationalism, the term “qualitative” is used to refer to the structure of properties even when they are quantities.)
- 48.
Again, as discussed in Sect. 4.5 (and at more length in a variety of sources such as Mislevy, 2018), there are many important differences in the ontological character of psychosocial properties compared to (classical) physical properties, including the facts that their existence depends on human consciousness (with all the ontological challenges this entails; see, e.g., Dennett, 1991; Kim, 1998; Searle, 1992), and perhaps also on social groups and the actions thereof (with all the ontological challenges this entails; see, e.g., Searle, 2010). However, the key point remains: none of these differences imply that psychosocial properties are not part of the empirical world, any less so than physical properties.
- 49.
To be clear, we do not aim to provide a sufficient set of criteria for the justification of a claim about the existence of any given property, as this will surely involve issues specific to that property.
- 50.
Our stance here is broadly consistent with Ian Hacking’s (1983) perspective on entity realism, which entails that a claim about the existence of an entity is justified if it can be used to create effects that can be investigated and understood independently of their cause. As Hacking famously put it, in reference to experiments involving the spraying of electrons and positrons onto a superconducting metal sphere: “if you can spray them, then they are real” (p. 24). To this we would add a friendly amendment: if you can spray them, something is real, though it remains an open question to what extent the actual causal forces at work are well described by our current best theories and terminology. This is easily illustrated by the historical example of phlogiston (as also discussed in Box 5.1): although contemporary theories deny the existence of the substance referred to as “phlogiston” by seventeenth- and eighteenth-century theorists, contemporary theories would not deny the existence of the causal forces responsible for the putative effects of phlogiston (e.g., flammability, oxidation, rusting), but instead offer more nuanced explanations for the identity and mechanisms of these causal forces.
- 51.
The same reasoning applies to the case of educational tests, which would in general not be valued unless the competencies they purport to measure are demonstrably valuable in contexts beyond the immediate testing situation.
- 52.
For further arguments along these lines, see also Rozeboom (1984).
- 53.
The adjective “nomic” comes from the ancient Greek “nomos”, meaning <law>. When attributed to a conceptual network it refers to a set of entities (in this case general properties) interconnected via relations interpreted as laws. The paradigmatic example of this is the International System of Quantities (ISQ), a system of (general) quantities based on length, mass, duration, intensity of electric current, thermodynamic temperature, amount of substance, and luminous intensity (JCGM, 2012: 1.6), from which other physical quantities may be derived through physical laws.
- 54.
In this we agree with Carl Hempel: “We want to permit, and indeed count on, the possibility that [candidate properties] may enter into further general principles, which will connect them with additional variables and will thus provide new criteria of application for them” (1952: p. 29).
- 55.
Y and Z would be expected to covary as the effects of the common cause P. This is, in fact, the canonical example of how “correlation is not causation”: the observation that two properties Y and Z correlate may be explained by the presence of a third, “hidden” property P which is their common cause.
References
Babbie, E. (2013). The practice of social research (13th ed.). Belmont: Wadsworth.
Beebee, H., Hitchcock, C., & Menzies, P. (Eds.). (2009). The Oxford handbook of causation. Oxford: Oxford University Press.
Bentley, J. P. (2005). Principles of measurement systems (4th ed.). New York: Pearson.
Borsboom, D. (2006). The attack of the psychometricians. Psychometrika, 71(3), 425–440.
Borsboom, D., Mellenbergh, G. J., & Van Heerden, J. (2003). The theoretical status of latent variables. Psychological Review, 110, 203–219.
Briggs, D. C. (2019). Interpreting and visualizing the unit of measurement in the Rasch model. Measurement, 146, 961–971.
Campbell, N. R. (1920). Physics—The elements. Cambridge: Cambridge University Press.
Carnap, R. (1966). Philosophical foundations of physics. New York: Basic Books.
Chang, H. (2001). How to take realism beyond foot-stamping. Philosophy, 76(295), 5–30.
Chang, H. (2004). Inventing temperature. Measurement and scientific progress. Oxford: Oxford University Press.
Chrisman, N. R. (1998). Rethinking levels of measurement for cartography. Cartography and Geographic Information Systems, 25, 231–242.
De Boer, J. (1995). On the history of quantity calculus and the International System. Metrologia, 31, 405–429.
Dennett, D. (1991). Consciousness explained. Boston: Little, Brown and Company.
Dybkaer, R. (2013). Concept system on ‘quantity’: Formation and terminology. Accreditation and Quality Assurance, 18, 253–260.
Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5, 155–174.
Ellis, B. (1968). Basic concepts of measurement. Cambridge: Cambridge University Press.
Flynn, J. R. (2009). What is intelligence: Beyond the Flynn Effect. Cambridge: Cambridge University Press.
Freund, R. (2019). Rasch and rationality: Scale typologies as applied to item response theory. Unpublished doctoral dissertation, University of California, Berkeley.
Giordani, A., & Mari, L. (2012). Property evaluation types. Measurement, 45, 437–452.
Glaser, R. (1963). Instructional technology and the measurement of learning outcomes. American Psychologist, 18, 510–522.
Guttman, L. (1944). A basis for scaling qualitative data. American Sociological Review, 9, 139–150.
Hacking, I. (1983). Representing and intervening: Introductory topics in the philosophy of natural science. Cambridge: Cambridge University Press.
Heil, J. (2003). From an ontological point of view. Oxford: Clarendon Press.
Hempel, C. G. (1952). Fundamentals of concept formation in physical science. Chicago, IL: Chicago University Press.
Holder, 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. Transl. J. Michell, C. Ernst, The axioms of quantity and the theory of measurement, Journal of Mathematical Psychology, 40, 235–252, 1996.
Holland, P. (1990). On the sampling theory foundations of item response theory models. Psychometrika, 55, 577–601.
International Bureau of Weights and Measures (BIPM). (2019). The International System of Units (SI) (9th ed.). Sèvres: BIPM. Retrieved from www.bipm.org/en/si/si_brochure
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). (2008). JCGM 100:2008, Evaluation of measurement data—Guide to the expression of uncertainty in measurement (GUM). Sèvres: JCGM. Retrieved from www.bipm.org/en/publications/guides/gum.html
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
Kaplan, A. (1964). The conduct of inquiry. San Francisco, CA: Chandler.
Kelly, E. J. (1916). The Kansas silent reading tests. Journal of Educational Psychology, 7, 63–80.
Kim, J. (1998). Mind in a physical world. Cambridge: MIT Press.
Kintsch, W. (2004). The construction-integration model of text comprehension and its implications for instruction. In R. Ruddell & N. Unrau (Eds.), Theoretical models and processes of reading (5th ed.). Newark, DE: International Reading Association.
Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of measurement (Vol. 1). New York: Academic Press.
Kuhn, T. S. (1969). The structure of scientific revolutions. Chicago, IL: University of Chicago Press.
Kyburg Jr., H. E. (1984). Theory and measurement. Cambridge: Cambridge University Press.
Lord, F. M. (1953). On the statistical treatment of football numbers. American Psychologist, 8, 750–751.
Luce, R. D., & Tukey, J. W. (1964). Simultaneous conjoint measurement: A new type of fundamental measurement. Journal of Mathematical Psychology, 1, 1–27.
Maraun, M. D. (1996). Meaning and mythology in the factor analysis model. Multivariate Behavioral Research, 31(4), 603–616.
Mari, L., & Giordani, A. (2012). Quantity and quantity value. Metrologia, 49, 756–764.
Mari, L., Maul, A., Torres Irribarra, D., & Wilson, M. (2017). Quantities, quantification, and the necessary and sufficient conditions for measurement. Measurement, 100, 115–121.
Mari, L., Maul, A., & Wilson, M. (2018). On the existence of general properties as a problem of measurement science. Journal of Physics: Conference Series, 1065, 072021.
Mari, L., & Sartori, S. (2007). A relational theory of measurement: Traceability as a solution to the non-transitivity of measurement results. Measurement, 40, 233–242.
Markus, K. A., & Borsboom, D. (2013). Frontiers of test validity theory: Measurement, causation, and meaning. New York: Routledge.
Maul, A. (2017). Rethinking traditional methods of survey validation. Measurement: Interdisciplinary Research and Perspectives, 15, 51–69.
Maul, A., Mari, L., & Wilson, M. (2019). Intersubjectivity of measurement across the sciences. Measurement, 131, 764–770.
Maurin, A. S. (2018). Tropes. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Stanford, CA: Stanford University. Retrieved from plato.stanford.edu/entries/tropes
McGrane, J., & Maul, A. (2020). The human sciences, models and metrological mythology. Measurement, 152. https://doi.org/10.1016/j.measurement.2019.107346
Michell, J. (1990). An introduction to the logic of psychological measurement. Hillsdale, NJ: Erlbaum.
Michell, J. (1999). Measurement in psychology—Critical history of a methodological concept. Cambridge: Cambridge University Press.
Michell, J. (2000). Normal science, pathological science and psychometrics. Theory & Psychology, 10(5), 639–667.
Michell, J. (2004). Item response models, pathological science and the shape of error: Reply to Borsboom and Mellenbergh. Theory & Psychology, 14(1), 121.
Michell, J. (2005). The logic of measurement: A realist overview. Measurement, 38, 285–294.
Mislevy, R. J. (2018). Sociocognitive foundations of educational measurement. New York: Routledge.
Mundy, B. (1987). The metaphysics of quantity. Philosophical Studies, 51, 29–54.
Narens, L. (1985). Abstract measurement theory. Cambridge: MIT Press.
Narens, L. (2002). Theories of meaningfulness. London: Lawrence Erlbaum Associates.
Popper, K. (1959). The logic of scientific discovery. Abingdon-on-Thames: Routledge.
Rasch, G. (1960/1980). Probabilistic models for some intelligence and attainment tests. Chicago, IL: University of Chicago Press.
Rasch, G. (1961). On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 4, 321-33. Berkeley, CA: University of California Press.
Roberts, F. S. (1979). Measurement theory with applications to decision-making, utility and the social sciences. Reading, MA: Addison-Wesley.
Rossi, G. B. (2006). A probabilistic theory of measurement. Measurement, 39, 34–50.
Rossi, G. B. (2007). Measurability. Measurement, 40, 545–562.
Rozeboom, W. W. (1984). Dispositions do explain: Picking up the pieces after hurricane Walter. In J. R. Royce & L. P. Mos (Eds.), Annals of theoretical psychology (Vol. 1, pp. 205–224). New York: Plenum.
Russell, B. (1903). The principles of mathematics. London: Bradford & Dickens.
Searle, J. (1992). The rediscovery of the mind. Cambridge: MIT Press.
Searle, J. (2010). Making the social world: The structure of human civilization. Oxford: Oxford University Press.
Shannon, C. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423. and 623–656.
Sherry, D. (2011). Thermoscopes, thermometers, and the foundations of measurement. Studies in History and Philosophy of Science Part A, 42, 509–524.
Siegel, S. (1956). Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill.
Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 667–680.
Stevens, S. S. (1959). Measurement, psychophysics, and utility. In C. West Churchman & P. Ratoosh (Eds.), Measurement, definitions and theories (pp.18–63). Wiley, New York.
Suppes, P. (1951). A set of independent axioms for extensive quantities. Portugaliæ Mathematica, 10(4), 163–172.
Suppes, P., & Zanotti, M. (1992). Qualitative axioms for random-variable representation of extensive quantities. In C. W. Savage & P. Ehrlich (Eds.), Philosophical and foundational issues in measurement theory (pp. 39–52). Hillsdale, NJ: Lawrence Erlbaum.
Tal, E. (2019). Individuating quantities. Philosophical Studies, 176(4), 853–878.
Thurstone, L. L. (1928). Attitudes can be measured. American Journal of Sociology, 33, 529–544.
Velleman, P. F., & Wilkinson, L. (1993). Nominal, ordinal, interval, and ratio typologies are misleading. The American Statistician, 47, 65–72.
von Helmholtz, H. (1887). Zählen und Messen Erkenntnis–theoretisch betrachtet, Philosophische Aufsätze Eduard Zeller gewidmet. Leipzig: Fuess. Translated as: Numbering and measuring from an epistemological viewpoint. In From Kant to Hilbert: A sourcebook in the foundations of mathematics: Vol. 2. Ewald, W. (Ed.). Oxford: Clarendon Press, 1996, pp. 727–752.
Weyl, H. (1949). Philosophy of mathematics and natural science. Princeton, NJ: Princeton University Press.
Wilson, M., Mari, L., & Maul, A. (2019). The status of the concept of reference object in measurement in the human sciences compared to the physical sciences. Proc. Joint International IMEKO TC1+ TC7+ TC13+TC18 Symposium, St Petersburg, Russian Federation, 2–5 July 2019, IOP Journal of Physics: Conference Series, 1379, 012025. Retrieved from iopscience.iop.org/article/10.1088/1742-6596/1379/1/012025/pdf
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Mari, L., Wilson, M., Maul, A. (2021). Values, scales, and the existence of properties. In: Measurement across the Sciences. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-65558-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-65558-7_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-65557-0
Online ISBN: 978-3-030-65558-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)