1. The correspondence framework

The most popular measurement theory in philosophy is the representational theory of measurement (RTM). According to this view, a quantity is measurable just in case there exists an isomorphism between a construct and the number system. In what follows, I provide a brief history of the development of the RTM and discuss the kind of realism I take this theory to be committed to. I then turn to measurement and validity theories in psychology and consider whether operationalism prevents this kind of realism.

The initial motivation for what later became the RTM was not to use numbers to represent properties but to use properties to define numbers. When von Helmholtz wrote Zählen und Messen ([1887] Reference von Helmholtz and Bryan1930), his aim was to found arithmetic by axiomatizing counting. To him, therefore, the measurement target (discrete objects) is more fundamental than the numbers we use to represent it because, coming from a Kantian perspective, the measurement target is more empirically accessible than numbers.

Not all empirically accessible properties are representable by numbers, however. Helmholtz lists the usual suspects—length and weight—as examples of attributes that share enough structural similarities with numbers such that they can be “counted” (measured) in the same way as the quantity of discrete objects. Other attributes, such as pain and pleasure, cannot be represented in this way. Whether an attribute has enough structural features to be measurable is something we discover in the world. The fact that length and weight are representable by numbers by way of an isomorphism is true regardless of whether we have ever tried to measure them. The fact that pleasure and pain lack key structural features, which prevents them from being (fully) representable by numbers, is true even if the psychologists do not like it.

The subsequent debate between the physicists and the psychologists^{Footnote 2} on the measurability of sensations likewise did not turn on the properties of sensations, which were taken as given in the world, but on the definition of measurability. Stevens’s (Reference Stevens1946) insight is that numbers can carry partial information about an attribute without full-blown isomorphism. His theory of scales differentiates between the kinds of structural information that numbers can carry and that warrant some but not other inferences. It is true that the sensation of brightness does not admit a concatenation procedure and therefore does not obey the additivity axiom of numbers, but we can still measure it on an ordinal scale; we just have to be careful not to use addition in our subsequent statistical analysis.

Although Stevens (Reference Stevens1946) makes assertions like “measurement … is defined as the assignment of numerals to objects or events according to rules,” his operationalism is not as antirealist as that of others in his circle, such as Boring (Reference Boring1923) when he claims that “intelligence is simply what the tests of intelligence test” (Hardcastle Reference Hardcastle1995). Stevens, as well as his successors, such as Suppes and Zinnes (Reference Suppes and Zinnes1963), still operate on the assumption that the measurement target is given in the world, and the job of the measurement theorist is to discover its structural properties and represent them with accuracy.

Talking about success in measurement in terms of representational accuracy immediately brings up two philosophical issues. The first is metaphysical: What is the thing that is accurately (or inaccurately) represented? As explained previously, the RTM operates on the assumption that there is a well-defined, objectively existing attribute that we are trying to represent through measurement. In their RTM-inspired theory of measurement, Bradburn et al. (Reference Bradburn, Cartwright, Fuller and McClimans2017) argue that measurement can be seen as a three-step process. First, we define the target concept (characterization); next, we define a metric system that represents it (representation); finally, we formulate rules for applying the metric system (procedures). According to this view, concepts that cannot be characterized with enough clarity cannot be candidates for measurement.

The second issue with evaluating measurement in terms of accuracy is epistemological: How do we know if a representation is accurate? In the traditional RTM, representation is accomplished through isomorphism, which is proven between axiomatizations of the target concept and the metric system. Whether the representation is accurate, therefore, depends on whether the axiomatization is faithful, which in turn depends on how much we know about the behavior of the target concept. This is easy to determine in the case of mesoscale, observable attributes that can be easily manipulated, such as the lengths of rods. It is much less feasible when the target concept cannot be accessed through measurement-independent ways.

The difficulty of determining whether our metric system accurately corresponds with an unobservable target has been termed the problem of nomic measurement by Chang (Reference Chang2004). The worry is that if the only way to access a construct is through measurement, we have no epistemic foundation on which to calibrate that measurement. One common coping strategy is to invoke a kind of robustness reasoning across multiple forms of measurement—even if none of them is independently calibratable, if they all give the same output, perhaps that is evidence that they are all accurate. But this strategy runs into another problem, one of quantity individuation identified by Tal (Reference Tal2019). Tal argues that when multiple measurement procedures produce different outcomes, it is often underdetermined whether this is evidence for the inaccuracies of the procedures or that they actually measure different constructs.

Both Chang and Tal reject a kind of measurement foundationalism whereby the (objectively existing, stable) features of the measurement target serve as the foundation that informs the construction of the measuring instrument, which in turn dictates the interpretation of its results. The RTM subscribes to this kind of foundationalism. So, as I shall argue later on, do other existing measurement and validity theories. However, although I will end up rejecting this kind of foundationalism like Chang and Tal, I will not endorse coherentism like they do. Instead, I will propose a different kind of foundationalism that makes validity theory the foundation for measurement theory and avoids the aforementioned problems.

It is worth noting^{Footnote 3} that some (Baccelli Reference Baccelli2020; Vessonen Reference Vessonen2021) have argued that the RTM should not be understood as a theory of measurement but instead as a theory of measurability. It is, therefore, not a fair criticism to point out that the RTM fails to describe how measurement actually occurs in science. Adopting this (in my view, convincing) perspective on the RTM, the present article can be seen as challenging the RTM definition of measurability.

Two other popular measurement theories exist in addition to the RTM: classical test theory (CTT) and item response theory (IRT; also called latent variable theory). Traditionally, CTT has been associated with operationalism, which is relatively weak in its realist commitments when compared with the RTM and IRT. Nevertheless, the core idea of CTT is that a measurement result (“observed score”) is composed of two parts, the true score and a random error, where the true score is the measurement-independent reality we are trying to study. CTT has been criticized along lines similar to Tal’s, where critics complain that there is no interpretation of the true score that is both epistemically justified and scientifically useful.^{Footnote 4}

In a sense, IRT avoids the problem of quantity individuation by starting with the assumption that a collection of instruments measures the same small number of latent variables, which are causally responsible for the observed measurement results. Once this assumption is in place, IRT helps us determine the degree to which each test item measures each latent variable. It is the causal relationship between the latent variable and the test item that grounds measurement, and it is a fact in the world whether this relationship exists.

Insofar as measurement is seen as a descriptive project, this correspondence picture seems inevitable.^{Footnote 5} Indeed, all three theories of measurement just reviewed rely on the assumption that the measurement target has a measurement-independent existence, and to measure is to capture its properties through the establishment of a relationship, representational in the case of the RTM and causal in the case of IRT and CTT, between a target and the results. This naturally entails the concept of validity as the evidenced success of such an establishment.

Validity theory, as it currently stands, is composed of three aspects:^{Footnote 6} content-oriented validity, criterion-oriented validity, and construct validity. Very briefly, content-oriented validity consists of seeing if the wording of test questions sounds like reasonable descriptions of the desired attitudes. Criterion-oriented validity involves correlating results from the present test with other observables expected to correlate with the construct under measure, such as predicted behaviors. Finally, construct validity involves building an elaborate theory of the behavioral implications of a construct and testing it through extensive research.

The extent to which these validity theories rely on the realist assumption is not always clear. Stemming from education research, there is a significant practical aspect to the problems faced by validity theorists. Many are tempted to adopt a “thin” notion of validity, where a test is called valid if it correlates relatively strongly with some plausible criteria. This makes validity claims easier to come by, but test results become less scientifically useful. On the other hand, insisting on a “thick” notion of validity, where a test is only valid if it is capable of truthfully describing the external world, leads to an inconveniently few tests we want to use qualifying as practically validatable.

In fact, the tension between theoretical strengths and practical limitations has been a recurrent struggle within validity theory. When Cronbach and Meehl (Reference Cronbach and Meehl1955) proposed their influential theory of construct validation, many testers claimed to have been convinced—they understood that test validation was a process by which researchers gathered behavioral data in order to empirically confirm a “strong theory” about the objectively existing construct, which was the target of measurement. Heavily influenced by logical positivism, the idea was that a construct is a theoretical entity that connects to the world through a “nomological network,” which ultimately exhausts into a set of observational sentences. To validate a construct is to confirm (or refute) this strong theory by providing observational evidence for or against it. Because theory confirmation is a difficult and possibly never-ending process, so is validation.

Although the construct-validity program gave validation a long-sought-after theoretical framework that is philosophically well grounded and scientifically intuitive, it also highlighted the core conflict between the theoretical demands and practical challenges of validation in full and unavoidable terms. Test developers realized that very few constructs had the kind of strong theories Cronbach and Meehl envisioned, and they often needed to make test-use decisions when the evidence was nowhere near theory-confirmation level. Only a couple of decades later, Cronbach (Reference Cronbach1980) complained that a typical validation report in the literature had become “an unordered array of correlations with miscellaneous other tests and demographic variables. Some of these facts bear on construct validity, but a coordinated argument is missing.”

We can see another example of the tension between realism-assuming validity theories (notably, the construct-validity theory) and practical demands of validation in the debate around whether the context of test use should affect the assessment of validity. Shepard (Reference Shepard1997) considers a case where pre-med students prioritize science classes over humanities as a way to increase Medical College Admission Test (MCAT) scores, thus making the MCAT no longer an adequate test for identifying students who are more likely to succeed in medical school. The act of using the test has changed the usefulness of its results. As Shepard points out, if we take the usefulness of a test’s results to be indicative of, but not identical to, its validity, then we must conclude that either (1) the validity of the MCAT changed in response to students’ choice of classes, or (2) our earlier assessment of the validity of the MCAT was mistaken. The problem with (1) is that according to construct validity and the general correspondence framework of measurement I have been sketching, the validity of a measurement consists of the quality of the relationship between the measurement result and the objectively existing construct, and it is unclear how this relationship should have changed in the MCAT example. Option (2) is even less desirable because almost all (external) validation procedures come down to claims of usefulness. If the MCAT was useful before students’ change of behavior, then there is little reason to retroactively deny the earlier claim of validity. Shepard uses this example to motivate a thin view of validity, where validity claims do not rely on the successful discovery of a specific way that the world is and thus can change as contexts change.

Ultimately, the choice between thick and thin views of validity is a matter of preference: Would we rather hand out lots of validity claims that don’t mean very much, or would we rather hold validity as the ultimate stamp of approval even if it means that large parts of science need to make do with unvalidated measurements? Historically, measurement theorists have mostly opted for thick views of validity that are difficult to obtain but carry substantive theoretical weight once established. From the perspective of the correspondence framework of measurement, a measurement is valid if the measurement results have accurately captured the objective properties of a construct that really exists in the world. A validity claim about a measurement procedure, therefore, warrants a corresponding realism claim about the target construct.

The present article can be seen as advocating for a serious entertainment of the thin option. The theoretical strength and practical limitations of the thick-construct-validity project have been extensively studied by the measurement community, but theorists are, understandably, resistant to the suggestion that we should weaken the epistemic power of our science to fit practical constraints. It is part of my goal in this article to show that taking the thin conception of validity does not need to be a theoretical concession; it may be philosophically and scientifically fruitful enough to be a genuine competitor to the standard conception. In the next section, I review some reasons for adopting the thin view of validity that go beyond its practical convenience.

2. Measuring the nonexistent

The kind of measurement cases I will focus on are ones that start with a relatively clearly defined practical context of a test without any accompanying substantive theory of a construct. For example, a company might use a simple customer satisfaction survey to determine whether changing its service in certain ways will lead to an increase in satisfaction, consumer loyalty, and ultimately, profit. In cases like this,^{Footnote 7} it is usually fairly straightforward to determine whether a test has succeeded in being useful—it is successful if the increase in profit coheres with what the test developers promise. It is much trickier to claim that this success is the result of accurately capturing the objectively existing degree of satisfaction each customer feels about a product. More importantly, it is unclear why the lack of such a theory of the construct of customer satisfaction should be an obstacle to calling some of these surveys good or “valid.” In other words, the reality of the construct is an unnecessary intermediary between the test context and claims of its validity.

The correspondence framework relies on this intermediary. Because the correspondence framework takes measurement to be a descriptive project, the success of measurement (as shown through validation) naturally implies the success of the description, which in turn implies the existence of the thing being described. Validity needs explanation. In a descriptive project, the best explanation for validity is the reality of the thing being described.

In what follows, I challenge the view of measurement as a merely descriptive project. Drawing on historical and anthropological studies of measurement, I show how measurement often changes our conceptualization of the world—and consequently, the world itself—in profound ways. I will then argue how this new view of measurement does not see validity as something needing to be explained by realism.

There are, roughly speaking, three kinds^{Footnote 8} of measurement–world interactions I will highlight. The first is when “merely” arbitrary choices about measurement procedures change which parts of the world are open to scientific study and in what ways. The second is when choices made during measurement build into the foundations of our theoretical understanding of the phenomena. The third is when the act of measurement literally causes the world to change in response.

Despite the widespread acknowledgment of the inevitability of arbitrary procedural choices during measurement, it is difficult to appreciate the extent of their influence on measurement results. For example, as Porter (Reference Porter1996) observes,

There is a sense in which it doesn’t matter which way we choose, as long as we take care to be consistent across time. But consistency assumes a certain level of retainment of auxiliary information that doesn’t always occur. If I’m trying to measure population growth, then including legal aliens but not military personnel seems harmless as long as this is done consistently across time and there isn’t a sudden surge in enlistment. But the judgment that this is done consistently can only be formed if there is some memory of how it was done in the past. Because these arbitrary choices are often dismissed as theoretically uninteresting, they are seldomly recorded. For example, the National Comorbidity Survey (NCS) “did not include supplemental samples of other institutional populations (e.g., prisons, hospitals, nursing homes) or of the homeless population” (Mickelson et al. Reference Mickelson, Kessler and Shaver1997) for cost reasons, but it also did not include a sketch of the kind of institution that would fall under this category.

The decision is arbitrary in the sense that choosing one way or another (often) does not have (immediate) consequences for the data-based theorizing at hand, but the innocence of these decisions also shields them from critical scrutiny. Although one could, in principle, contact the NCS surveyors to get a more detailed picture of all the judgment calls they’ve made in the survey, in practice, there is rarely an incentive for that. As data sets age, they become more entrenched and less challenged, which, paradoxically, makes it difficult to assess the true extent of their innocence.

Merry (Reference Merry2016) calls this phenomenon data inertia. Because gathering data is expensive, organizations prefer to either repurpose old data or, when they must generate new data, minimally adapt entrenched measurement procedures. Even when there is a genuine effort to develop new measurements, old instruments and data are often taken to be starting points at first and validation anchors afterward. In other words, entrenched ways of measurement, however arbitrary they may have been at their creation, often end up exerting disproportional influence over subsequent measurement efforts.

Merry argues that phenomena like data inertia and expertise inertia, where experts who were there at the beginning of the project exert disproportional influence over later development, make international collaborations on measurement less democratic than they advertise. Once the initial attempt is made, it defines the key parameters of subsequent development. Deviations need to be justified, whereas conformities do not. Challenges are expected to be posed with existing terms and concepts before they are taken seriously. In Merry’s words (2016):

To be clear, the worry is not that we have reasons to believe that some entrenched framework of measuring is flawed. The worry is that the cause for its entrenchment is not truth tracking and that once a framework is entrenched, it is difficult to assess its real merit. In other words, if some frameworks are in fact flawed, we would never know.

We may call data inertia an example of an epistemic consequence of practical constraints. Theoretically speaking, nothing prevents us from constructing completely new tests of the same phenomenon each time we need to measure it. Practically, however, doing so would be deemed a waste of time and resources. Moreover, because measurement results are usually only interpretable in reference to the measuring instrument, having multiple radically different instruments also harms the usability of results. All of these practical reasons discourage experimentation.

In fact, Porter (Reference Porter1996) argues that the fact that we tend to overestimate the strength of the measurement–nature correspondence necessary for measurement success is exactly why numerical measurement is so ubiquitously adopted in social settings. Quantification, argues Porter, is often valued for what it has to leave out as much as for what it is capable of capturing. The process of taking a diverse set of phenomena, imposing a kind of quantitative uniformity onto them, and making it look like the decision is objective and therefore fair is an act of political control that is very often consciously done by measurement agencies. More recently, John (Reference John, Newfield, Alexandrova and John2022) has similarly observed the use of spuriously precise numbers as a mechanism for behavioral manipulation.^{Footnote 9}

Not only is the manipulative use of numbers often successful, but measurement can also change how we relate to the world in ways that hide the fact that their descriptive success was not caused by their correspondence with nature. One way that this can happen is when the adoption of a measurement framework changes how we understand the world.

For example, Siegel (Reference Siegel1994) has documented the conceptual change during the late 19th century in understanding women’s household labor as a kind of work. The initial movement was motivated by a legal demand that wives should have a share of the domestic property. Because property rights were tied to labor contribution, the issue naturally fell on the question of whether a wife made a labor contribution to her family. That is, the question was essentially about how we should measure labor contributions: Should we count household chores or not?

It is not the kind of question that could be answered rightly or wrongly in the same way that a question about which rod is longer could be. But it is also not the kind of question that is completely arbitrary. Indeed, through years of difficult feminist work, the question has been given an answer that we now commonly think of as correct: full-time housewives do make labor contributions to the household. Providing this answer not only resolves the original measurement question, however; it also shapes our understanding of what labor is and what making a contribution to the household can look like.

However, not recognizing housewives’ labor was not a mistaken assessment of reality, like failing to properly count the number of people in a room is. Switching from the old way of measuring labor to the new way is not the same as replacing the inaccuracies of an old understanding with accurate details. To say that the present way of measuring labor is the right way because it corresponds with facts in the world is to overlook the conceptual revolution that was necessary to get us here. In Merry’s words, “those who create indicators aspire to measure the world but, in practice, create the world they are measuring” (Merry Reference Merry2016).

Finally, how we choose to measure the world can not only change how we understand the world; it can also cause the world to literally change. To give an example that is outside the stereotypical social sciences, Scott (Reference Scott1996) has observed how standardized measurement practices in forestry change people’s relationship with forests:

That is, the fruitfulness of the imposed measurement system has caused a change, whereby nature is intentionally and explicitly manipulated to conform to the measurement system. Although it is true that a valid measurement result provides an accurate (in the correspondence sense) representation of reality, this is not because the measuring instrument has succeeded in its descriptive goal. It is the exact opposite: the world has been bent to the prescriptive power of the measuring instrument. The correspondence framework, which treats valid measurement as an accurate description of the measurement-independent reality, obscures the creative dynamics often present between the world and our attempts at making sense of it.

To be clear, neither I nor these authors are suggesting that measurement creates concepts out of thin air and imposes them onto the world against its will. What I am arguing is that the structural features of successful measurement are often not chosen to best reflect nature but are selected for a variety of practical and political reasons. Once selected, it is difficult not to see the world through the carefully crafted lens that is the measurement system. As theorists, we should therefore be especially careful when making inferences about the structure of the world on the grounds of measurement results alone. In the next section, I provide a sketch of how I believe we should approach measurement theory instead.

3. A validity-first framework of measurement

If measurement procedures are not developed for their ability to accurately capture objective features in the world, then how can we judge measurement quality? In fact, once we abandon the correspondence framework, judging the quality of a measure is often easier than theorizing about why a measure achieves this quality.

As already mentioned in section 1, the construct-validity program of Cronbach and Meehl (Reference Cronbach and Meehl1955) enjoyed widespread celebration for its theoretical virtue. It is still the most acknowledged validity theory today, even by philosophers who have pointed to its deficiencies (e.g., Alexandrova and Haybron Reference Alexandrova and Haybron2016; Stone Reference Stone2019). Nevertheless, by 1980, Cronbach had already conceded to testers who were prevented from following the spirit of the program by practical difficulties.

In the fourth edition of Educational Measurement (Brennan Reference Brennan2006), a self-described “bible in its field” and recurrent publication sponsored by the American Council on Education and the National Council on Measurement in Education, Kane advocates understanding validity as a relationship between an interpretation of the test scores and a specific use context. In Kane’s words, “to validate a proposed interpretation or use of test scores is to evaluate the rationale for this interpretation or use. The evidence needed for validation necessarily depends on the claims being made” (Brennan Reference Brennan2006).

This view has been called the argument-based conception of validity. It was adopted by the 2014 edition of the Standards for Educational and Psychological Testing, a joint publication by the American Educational Research Association, the American Psychological Association, and the National Council on Measurement in Education, according to which:

In other words, the Standards advocates viewing validity not as a property of the test—that it accurately describes the world—but as the success of test results when applied to a specific context. Because tests are almost always developed for a specific practical goal, there usually exist some concrete criteria by which funding agencies can judge if their goal has been achieved. For example, an academic entrance exam serves its purpose if students who do well on this exam tend to do well academically after admission.

I have been calling this the “thin” conception of validity. Unlike the thick-construct-validity program, the thin conception makes the validity label easy to apply while also taking away its theoretical substance. We are no longer justified in inferring anything straightforward about the world or about the test from a claim of validity alone because claims of validity are always relativized to specific interpretations and use contexts.

For those who see measurement as a scientific process by which we understand the world, the thin conception of validity looks like throwing the baby out with the bathwater. For example, Borsboom and Markus (Reference Borsboom and Markus2013) worry that, insofar as measurement is supposed to generate knowledge (as justified true belief) about the world, giving up on the truth condition means losing our grasp on reality.

However, if we step away from the battlefield for a moment, we can see that the point of contention does not run as deep as the heat of battle might suggest. The thick camp has never denied the value of validation tailored to specific use contexts, just as the thin camp has never refused a truth claim when it’s on offer. Some (Hood Reference Hood2009; Cizek Reference Cizek2012) have suggested ways of accommodating both conceptions, where validity in terms of capturing true constructs sits at the core of validity theory and goal-specific validations help bridge theory with use contexts. Some theories of causation routinely invoke contextual information (e.g., Woodward Reference Woodward, Price and Corry2007), and Larroulet Philippi (Reference Larroulet Philippi2021) goes as far as arguing that it is impossible to have a context-independent causal account of validity at all. In other words, there is nothing intrinsically inconsistent for a theory to both provide causal information and do so in a context-sensitive way. The ideal measurement should be both true and useful.

The dispute, instead, is about a much more surface-level problem that, at the same time, has a much greater potential to cause harm. Shepard (Reference Shepard2016) points to an important stake in this fight that provides a positive reason for giving up validity’s implication for truth:

She goes on to cite several legal cases that rely on an understanding of validity as goal specific, such as the 1971 Griggs v. Duke Power Co. case, where the US Supreme Court ruled against the use of intelligence tests to select employees for higher-level jobs because, as Justice Burger explained, tests were supposed to evaluate people only in their capacity as employees, not people in any holistic sense. Shepard argues that because tests are routinely evaluated in the thin, argument-based sense, it is epistemically irresponsible to sneak truth in retrospectively.

Recall that the IBE argument from validity to realism relies on the assumption that measurement is a descriptive project that aims at capturing some target that objectively exists in the world. To call a measurement valid is to claim that one has succeeded in this task, which implies the existence of this target that is supposed to have been successfully captured. As I have argued in section 2, the view that measurement is a descriptive project about some objectively existing part of the world does not fit many measurement situations. Consequently, to say that success in measurement implies a particular way the world has to be is both epistemically irresponsible and, as Shepard points out, politically dangerous.

Nevertheless, I don’t think we should see this as a simple defeat in our theorizing about measurement. The correspondence framework fails to provide a fruitful account of how measurement works not only because measurement often fails to correspond but also because measurement often succeeds in doing a lot more than corresponding. What we need is to develop theories of measurement that properly respect its creative powers. In what follows, I turn to my positive thesis. I argue that, far from a mere concession in the face of practical challenges, the thin conception of validity can serve as the basis of a new, and hopefully more scientifically fruitful, kind of measurement theory.

Although the construct-validity program is most frequently associated with the realist ontology I have been resisting, let us take a moment to remember its logical positivist roots. In Cronbach and Meehl’s original conception, the construct is a node in a nomological network of other constructs, all of which eventually trace to some verificationist, empiricist interface with the world. In other words, the meaning of a construct is exhausted by its observational consequences. Whether we should make an ontological commitment to a construct depends on whether positing the construct is scientifically useful, given our observations in the world and the theory’s predictive and explanatory powers. The goal is not to find constructs that correspond with entities in the world; that would be doing metaphysics, after all.

Because the meaning of a construct is given by its theory, this view has the standard problem that plagues any project with a verificationist sense of meaning—validation of tests is always internal to the theory. “A consumer of the test who rejects the author’s theory cannot accept the author’s validation,” explains Cronbach and Meehl (Reference Cronbach and Meehl1955). Nevertheless, we may salvage one essential attitude of this program: that the ontology of a construct must be built on how useful it is in a broader scientific system.

Instead of taking the existence of the construct as the precondition for measurement and validity, I propose a reversal of the inferential order. According to the argument-based theory of validity, a test is valid if it is useful in the right contexts. Because tests are almost always developed with specific uses in mind, there should be little ambiguity in determining the validity of a test.

In many testing situations, it is enough to know that a test is valid for its purpose. Sometimes, however, we may want to develop theories for the purpose of adapting test scores across context or offering unified explanations of multiple valid tests. These measurement theories can be developed by reflecting upon the tests’ design principles. They may posit constructs, causes, or any other theoretical entities often employed to explain and unify phenomena. Their qualities are then judged by how they cohere with phenomena in the usual way, with “phenomena” in this case being valid (useful) results. If a theory is sufficiently scientifically powerful, the reality of its posits can be discussed in the same way we assess the reality of other nonobservables.

Put in a different way, the correspondence framework of measurement is a foundationalist framework with the target of measurement at the foundation. The reality of the target grounds its measurability conditions, which give rise to a measurement theory. The measurement theory posits a particular kind of relationship between numbers and the measured reality, which defines a validity theory. In contrast to this picture, my proposed validity-first framework puts validity judgments at the foundation. Validity judgments, understood in the thin, argument-based way, are practically easy to obtain but epistemically insubstantial. A measurement theory—multiple measurement theories—can be built on top of validity claims through the unification and theorization of valid tests. Finally, if some of these measurement theories are sufficiently scientifically powerful, we may use them to justify existential claims about the unobserved constructs that play explanatory roles in these theories.

This new, “validity-first” framework of measurement has several advantages over the correspondence framework. First, in the validity-first framework, the theoretical commitment increases with the evidential burden. Instead of starting with an assumption that the world is a particular way, we start by answering a small, well-defined question (Does this test do what its developers want it to do?), the answer to which provides a small piece of the puzzle (that this test is valid in this particular context). To make contentious claims, such as that a construct exists in the world and admits a total order, we would need not only a lot of empirical evidence about valid tests but also a lot of theorizing. In other words, it is easier to be certain of the usefulness of a test than it is to be certain about the objective existence of a construct.

Second, the validity-first framework does not depend on any particular view of reality. In the correspondence framework of measurement, measurement is made possible by the assumption that the world bears some kind of relationship with the measurement results, which depends on the world being a certain way that allows for this kind of relationship. For example, in the RTM, a construct is representable by numbers if it can be axiomatized in a certain way. In IRT, a construct is measured by a test if it is causally responsible for the test results. By contrast, the validity-first framework is agnostic about whether a valid test is a measurement at all until we construct a theory about why it would be fruitful to consider these test results as measurement. The theory will then have to be evaluated before it is accepted. If we have a specific commitment about the nature of truth or the structure of the world, it will be reflected in the theories we propose.

Finally, the validity-first framework is more descriptively apt for real measurement situations. As discussed in section 2, measurement interacts with the world in complex ways. An accurate description of the world is often not the main driving force behind the development, implementation, and assessment of a test. Sometimes, trying to measure the world in a certain way can profoundly alter the world in the process. The scientific reality requires us to have a more flexible view of what is achieved when a piece of measurement is deemed successful. The validity-first framework offers that flexibility by giving us space to theorize about how a piece of measurement is successful.