Monday, May 12, 2014

What is so philosophical about measurement?

Let’s start by framing some analytical questions.

Scientific engagement with the world by making measurements tells us something about reality. Engagement by measurement involves a physical interaction with the world. Scientists use instruments to monitor, examine, and sometimes poke and prod the objects of measurement. Engagement by measurement also involves gathering information about the world. Through measurement we get outputs that tell us something about the objects of measurement. What does engagement by measurement tell us about reality? This can be broken down into two simpler questions. First, what sort of physical interaction occurs during measurement? That is, what is the relationship between measurement practice and the thing measured? Answering this question will depend on characterizing both the process of measurement and the target of measurement—sometimes referred to as ‘the phenomenon’ or ‘the real system’. Second, what sort of information does scientific measurement provide? This is a question about the reliability of scientific measurement practices and also about the kind of realism that these practices ground.

Why is measurement important for the philosopher as well as the scientist?

A theory of measurement useful for philosophers and scientists should account for interaction and information. Cartwright and Chang (2008) nicely summarize the interests of scientists and philosophers when it comes to asking questions about measurement. Cartwright and Chang write, “To the practitioner, the all-important question is whether measurements are carried out correctly” (2008, 367). In a scientific context, questions about correct measurement break down to questions about reliability and error within the measurement process. Some examples of practical questions during measurement might be: did we calibrate the instrument properly; were confounding variables controlled for; can we reproduce these results within an independent experiment? These are questions about how to measure reliably. According to Cartwright and Chang, the fundamental question about correct measurement is fleshed out and given significance by the philosopher in the following form, “does a measurement operation really measure what it purports to measure” (2008, 367)? We can break this question down into two parts. First, does the presumed target of measurement (quantity, quality, phenomenon, etc.) really exist? Second, are our measurement practices “latching onto” the target? When asking questions of the latter kind, like—did scientists really detect the motion of the aether? Do IQ tests really measure intelligence? Do neutrinos really travel faster than the speed of light?—we’re combining questions about the physical interaction of measurement with questions about reliability and error in information gathering. In order to answer them we must have a technical account of measurement. This account should satisfy the philosopher by illustrating what reliability and error are while also satisfying the scientist by demonstrating how to apply a reliable method of measurement.

So how have philosophers of science addressed such questions? Let’s take a brief look at the evolution of measurement theory.

Early accounts of measurement focus on the systematic assignment of quantitative values (e.g. numbers or vectors) to objects in the world (see Hemholtz 1887; Campbell 1920). Nagel (1932) characterizes this approach to measurement as “the correlation of numbers with entities which are not numbers” (7). These early accounts approach the assignment of numbers to objects by looking at the conditions that make number assignment possible. This begins a technical area of measurement theory that has as its focus the mathematical representability of the physical world—echoing Galileo’s metaphor that Nature speaks the language of mathematics. This technical area of measurement theory is later continued by Stevens 1946; Suppes 1969; Ellis 1960, 1966; Pfanzagl 1968—among others; and is referred to by philosophers of science as the ‘representation theory of measurement’.

Many problems arise for the representational theory of measurement--including: 1) How do we develop non-arbitrary methods for assigning abstract things (numbers) to concrete things (physical objects)? 2) Are numerical descriptions necessary and/or sufficient for making/describing measurements? 3) What is the relation between the measurement procedure and number assignment? These problems call into question the standards of the early representational theories of measurement, but do not imply that representation is the wrong approach to a theory of measurement, but rather that number assignment may be the wrong way to express representation in measurement.

After decades of technical assessment of physical-to-mathematical correspondence, van Fraassen (2009) re-envisions the role of representation in measurement theory to solve problems like the ones listed above.

He maintains the representational aspect of measurement theory while loosening the strict mathematical standards of correspondence rules. On van Fraassen’s view of measurement, the relation between measurement and the world is not rigidified by physical-to-mathematical correspondence rules. Sometimes representations are mathematical, and other times they are physical. According to van Fraassen (2009) we can represent empirical phenomena by means of “artifacts,” both “concrete/physical” and “abstract/mathematical” (1-2). The key aspects of representation through measurement are:
  1.  Measurement tells us what things look like (from a specified vantage point), rather than what they are like. 
  2. Measurement involves selective perspectival input. 
Van Fraassen uses the analogy of visual perspective to illustrate (1) and (2). Think of measurement as taking a vantage point on some phenomenon. For example, when we measure evolutionary processes, the scientist decides the perspective (e.g. the view from the gene, epigene, individual, population, niche, etc.). Each view will give us a limited view of the phenomenon. For instance, if you’re focused on the gene’s eye view, you may miss epigenetic feedback loops and phenotypic development. Think of this as partitioning a phenomenon into variables and parameters and then representing a limited set of each.

So where does this leave us?

Van Fraassen’s expression of the representational theory of measurement is refreshing. We’re no longer bogged down with formalization. The philosophy of measurement can work collaboratively with the science of measurement to figure out useful perspectives to take on phenomena and to combine those perspectives under elegant theoretical models. But there’s one major problem. This view of measurement may be wrong. To see why, you’ll have to keep reading Dance of Reason.


Campbell, N. R. (1957). Foundations of Science, the Philosophy of Theory and
Experiment. New York: Dover.

Cartwright, N., Chang, H. (2008). Measurement. In Psillos, S. and Curd, M. (eds), The
Routledge Companion to Philosophy of Science (pp. 375-387). New York: Routledge.

Ellis, B. (1960) Some Fundamental Problems of Direct Measurement, Australasian
Journal of Philosophy, 38, 3747.

Ellis, B. (1966). Basic Concepts of Measurement. London: Cambridge University Press.

Helmholtz, H. V. (1887) Zählen und Messen erkenntnis-theoretisch betrachet, in

Helmholtz, Schriften zur Erkenntnistheorie, pp. 70-108. Engl trans,. Numbering and Measuring from an Epistemological Viewpoint, in Helmoltz, Epistemological Writings, 72-114.

Nagel, E. (1930) On the Logic of Measurement (Stanford University Press).

Pfanzagl, J. (1968) Theory of Measurement. New York: Wiley.

Stevens, S. S. (1946) ‘On the Theory of Scales of Measurement’, Science 103, 667-680.

Suppes, P. (1969) Studies in the Methodology and Foundations of Science. Dordrecht:

van Fraassen, B. C. (2009). Scientific representation: Paradoxes of perspective. Oxford: Oxford University Press.


  1. Vadim, thanks for introducing this interesting subject. I have to say that I am having a hard time getting my head around the dispute here. I wonder if you could apply it to a familiar example of measurement, such as measuring length or mass, or temperature rather than the complicated examples you give.

    It seems to me that when we devise ways of measuring things we often change very fundamentaly our understanding of the thing being measured. I think, for example, of Einstein's procedure for measuring whether two remote events are simultaneous. Or Shannon figuring out how to measure the quantity of information in a message.

    Einstein, of course, destroyed the idea of absolute time and distance. Shannon fundamentally changed our understanding of information from a purely qualitative notion to a quantitative one, and that also seems to me to be a defining property of novel measurement procedures. Developing techniques to measure motion,e..g, fundamentally converted our understanding of motion as a quality or property of an object to a relation of change of distance between objects, with rest simply being a change of 0.

    Another good example might be the way that procedures for measuring risk, utility, and degrees of belief are changing our understanding of those properties.

    Do you agree with that, and if so doesn't that suggest that the representationalist picture is a bit naive? I think philosophers might be particularly susceptible to this form of naivete, because we often seem to believe that when a powerful measurement procedure is developed that it has somehow missed the boat entirely by ignoring some property of the target that we believe is essential.

  2. R, thanks for the response. I'll start with your second point. I fully agree. I think the representationalist picture carries some assumptions that don't fit with scientific practice. For example: measurement is a passive activity (akin to taking perspective in painting). Measurement is an active process where a lot of manipulation is involved--especially when you're talking about measurement in biology. In bio, sometimes the organism is used both as an apparatus and also as the target of measurement. The simple view of putting an apparatus up to an object and recording the results doesn't do well with cases like that. The representationalist picture also focuses on the act of measurement rather than the process of measurement. But when you measure there are all sorts of important things happening in the measurement setup that require analysis. This is where your point is relevant. When we discover that a phenomenon is relational, this is because we have analyzed the conditions within our measurement setup during the process of measurement.

    To address your first point: There's no dispute here; rather, just a representation of representationalism. My aim was to set the state with some questions and talk about the main tradition in measurement theory. However, when we use representationalism in areas of physics and biology, the dispute arises. To see why, you'll have to keep reading DR.

  3. Vadim, very interesting post... Apologies for the delayed comment. I was wondering something similar to Randy, I think. But my concern is how the representational view of eyes surrender would address something like the observation (measurement) of a phenomenon like a proton moving through a vacuum or the observation of the existence of an entity here, now, like this Higgs-Boson, where the very observation of the phenomenon as measured is substantially theory-dependent. That is, for some meaaurements, there simply is nothing to measure absent a well developed theoretical model which anticipates the observation of x at t under c conditions. Of course, I could be missing something, but I wonder what the us relying metaphysical assumptions might be for a theory of measurement like this, that is, do we have to assume any kind of realism for measurement of this sort, and if so, what kind of realism? As you might surmise, my interest in the implications extend beyond the scientific to the ethical, but even if the extension doesn't hold there might be some interesting implications. Thoughts?