Let’s Take the Metaphysical Bull by the Horns
Bas C. van Fraassen
Teller’s critique, which focuses on the identification of quantities, goes well beyond the problems that bedeviled the twentieth century “representational” theory of measurement. Equally, it stops nowhere short of the obvious “open question” response to the “analytic” theory of measurement: “Just what are those quantities that are postulated to be real?”
At the same time, lest the entire discussion should seem to fall squarely in a context of traditional metaphysics, Teller adds a disclaimer. Quantities, as well as relations and properties generally, are universals, but Teller moves his challenge outside the venerable problem of universals: “My claim is that the term, ‘the temperature of the water in this glass,’ does not have a referent. My reason is not in any way metaphysical” (chapter 11).
Teller adds that he is not taking sides on the metaphysical question of whether quantities in general, or the specific quantities dealt with in physics that he takes as examples, are or are not real. He writes, “I am not claiming that there are no quantities with exact values in nature,” but he adds in a note “Nor would I claim that there are such things ‘in nature,’ whatever that might mean.” The reality of quantities—or to put it in formal mode, the question of what (if anything) such quantity terms as “velocity” or “mass” have as referent—is not going to be assimilated to the problem of universals. Though philosophical, this question will be broached in issues actually faced in scientific practice as well as in the lay understanding of scientific modeling.
Empiricism and pragmatism meet here in a desire for the irrelevance of metaphysics. But it seems to me that we cannot very well wave away all questions about the reality of quantities when the focal question is about the referent of quantity terms or property terms. Such questions seem to arise very close to home. Is there, was there ever, such a quantity as Galileo’s force of the vacuum? Or, nearer to home yet, when I explain Einstein’s relativity revolution in class, it seems natural for me to say things like this:
Some quantities that classical physics takes as fundamental, such as length, duration, and mass, lost their status. There really is no such thing as, for instance, the duration of a rocket’s flight, as classically conceived. The real quantity is the space-time interval between departure and arrival. As it happens, a space-time interval between events during its flight (while unaccelerated) is measured by the rocket’s own clock. But the classical quantity of time, equally measured by all clocks anywhere—there really is no such quantity at all.
“There is,” Quine taught us, is the vernacular for “exists” and equally for the vernacular “is real.” Thus, in my talk to the class, certain classically conceived quantities are said not to be real, unlike the quantity whose values are the magnitudes of space–time intervals. But what is this being real?
Philosophers aplenty have answers ready-to-wear. Teller and I agree in wanting most of those answers to be irrelevant. For example, some following David Lewis, more or less, would tell us that a real universal’s extension is a natural class. Boundaries between natural classes are the lines along which nature is carved at the joints. The distinction between natural and unnatural classes saves metaphysical realism. The contemporary realist may consistently and piously point to “our best science” as discovering exactly which postulated or imagined quantities are real universals, with the claim that it is in our best science that reality will be carved at the joints.
Would any of this give us a clue as to what is meant by the assertion that Einstein’s fundamental quantities rightly replace those of classical physics? However superficial or quick my in-class introduction to relativity may be, it is certain that a proper follow-up will expand on measurement, and not on Socrates’s butcher’s metaphor.
For what did Einstein point out about the classically conceived length, time, and mass? With the assumption, central to his view, that the speed of light is a universal constant, disruptive consequences followed for classical measurement operations for those quantities. Choose standard rods and clocks, and measure spatial or temporal extension at a distance: the relative motion of the measurement setups results in discordant measurement outcomes. Without concordance in different proper measurement results for the same quantity, there is no such quantity. Or, to avoid red flags waving before metaphysicians’ eyes, say it this way: the classical theory fails to meet the requirement of empirical grounding.
Teller, following Tal, gives appropriate place to the requirement of concordance in the special garb of robustness, explained so as to take approximation into account: “The robustness condition is essential to the success of so proceeding. The condition functions as a prescription to check—with great thoroughness—that the various ways in which we assign values to quantities as described in our theories all fit together well enough not to engender difficulties” (chapter 11). To align our two ways of pointing to this requirement of concordance, read “ways in which we assign values” as “operations theoretically classified as measurements.” The point made by Tal and Teller has its place in a larger historical context. I use the term “empirical grounding” (see, e.g., van Fraassen 2012, 2014). With this term I refer to the central requirement on the empirical sciences that Hermann Weyl spelled out in his classic Philosophy of Mathematics and Natural Science:
1. Concordance. The definite value which a quantity occurring in the theory assumes in a certain individual case will be determined from the empirical data on the basis of the theoretically posited connections. Every such determination has to yield the same result . . . Not infrequently a (relatively) direct observation of the quantity in question . . . is compared with a computation on the basis of other observations . . .
2. It must in principle always be possible to determine on the basis of observational data the definite value which a quantity occurring in the theory will have in a given individual case. (1927/1963, 121–22)
Teller would certainly have emphasized to Weyl that the “in principle” signals an extreme degree of idealization, and that to determine a value of some quantity through measurement can only be a matter of determining some bounds on the value within significant margins of error. Weyl would readily have agreed. Let us take that as said, and return to it later. If we accept Weyl’s dicta as specifying what is required for empirical adequacy, and take empirical adequacy as replacement for truth as the criterion to assess scientific success, then the metaphysical question about the reality of quantity terms falls away. For the only reference needed for a theoretical quantity term is a well-defined element of the algebra of quantities in each model of the theory. Assessment of the theory will not pertain to relations between such a quantity term and what there is in nature, but to the relations between the theory’s models and measurement results. There is no metaphysical residue.
But can Teller’s critique perhaps be turned against this empiricist account? For while such an empiricist account removes the question of the reality of, for instance, the temperature of the water in this glass (or equivalently, the existence of a referent in nature of the term “the temperature of the water in this glass”), it hinges on the feasibility of humanly realizable measurement operations properly pertaining to theoretical models—I mean, to such models as may be offered, within the domain of a given theory (for, e.g., temperature in a glass of water, or the shape of that glass, or its mass).
There is, without question, the problem of achieving some degree of precision. Teller quotes VIM: “‘Even the most refined measurement cannot reduce the interval [that can reasonably be attributed to the measurand] to a single value because of the finite amount of detail in the definition of a measurand.’” Quite so. But concordance in measurement outcomes is something we can ask for at any level of precision. Suppose that two different methods are used to measure the mass flow rate of a gas. Whether the outcomes of the two procedures are concordant does not depend on how precise they are; it requires consistency, which can be as appropriate and clearly defined for intervals or fuzzy sets as for numbers.
Automobiles today offer a simple, practical example. To regulate the fuel for internal combustion requires, in today’s electronically governed engine, data about the mass flow-rate of the air intake. One sort of mass flow sensor is thermal (“hot wire”); there are various mechanical sorts as well, such as the vane flow meter and the Karman vortex meter. Teller is right: the sensor signals cannot reasonably be thought to discriminate between one real number and nearby real numbers, or between any small real number interval and equally sized overlapping ones. But there is no difficulty in assessing whether the signals, obtained in these various ways, are consistent with each other. Notice, though, the question of principle in the background, behind the automobile design: What is the connection between the thermal sensing operation, which measures differences in temperature, and the mechanical one, which relies, for instance, on the rotation of a small vane? The connection is one in a model of the fluid or gas, whose equations relate the various theoretical quantities to one another.
What Teller denies in his critique is neither that quantity terms are precisely and definitely connected, in a theory, to specific elements of models, nor that such models are used by, for example, the automobile industry to represent certain everyday phenomena of practical concern, nor that measurement procedures are realized in physical form following a design dictated by this modeling. What Teller denies is the metaphysical “traditional realist” story that glosses this practice:
The current proposal is not to scrap the concept of traditional accuracy realism in favor of some substantially different concept. Rather, I am urging a change in how we think about the concept. We apply the familiar concept but no longer in a traditional realist spirit. Instead we appreciate its status as an idealization. (chapter 11)
But can we really just stop with a comfortable acquiescence in the traditional metaphysics by ruling it a practically useful fiction or idealization? I am left dissatisfied if left without an alternative account that takes the problems seriously, even if I will be equally dismissive of the traditional answers. What can satisfy alone is an alternative account that answers the questions about identification and reference directly, without buying into realist metaphysics but as directly as the realist.
What the empiricist account adds is a rationale for declaring the metaphysical gloss to be irrelevant, and to show, without entering upon questions of “reference in nature,” the form that assessment of success in science takes, properly understood, so as to bypass metaphysical questions.
In summary then, I cannot rest with Teller’s practical and pragmatic acquiescence in the use of scientific language without a way to make sense of truth and reference for that language. The alternative to Teller’s reconciliation of our use of theoretical quantity terms with his far-reaching critique is an account that provides direct answers to questions of reference and truth. It is the account that treats the language of science as semi-interpreted. Quantity terms do have referents: they refer to specific elements of theoretical models. To say that these terms are theory-laden, or that their reference is context-dependent, means just this: they refer to elements of models, and their connection with concrete natural phenomena is indirect.
The “cash value” of that connection lies entirely in the relation of those models to their targets, when offered as candidates for representation of those phenomena. That relation to the phenomena in turn is spelled out entirely in the theoretical classification of certain operations as determining values or ranges of value for those quantities. It is the theory itself, or the theory in the context of a larger background in science, that alone can tell us what the relevant measurements are. That those operations are measurements at all is something we see only through theory-colored glasses. After that, judgments of robustness or concordance are themselves true or false, and are checked by comparison of observable outcomes. In this way, scientific theories are understood as genuinely empirical and about the natural world, without their quantity terms understood as referring to something in nature, without metaphysical residue.
1. See Weyl’s section 79, “Measurement.” In the same section of this book, first published in 1927, Weyl also emphasizes his awareness of the theory-dependence of measurement: “any such quantitative determination . . . is possible only on the basis of theories” (142).
2. In a more general form this point is of long standing in the semantic approach to science, as well as in, for example, Ronald Giere’s related “model-based view.” Thus, Giere said, “On a representational conception of models, language connects not directly with the world, but rather with a model, whose characteristics may be precisely defined. The connection with the world is then by way of similarity between a model and designated parts of the world” (1999, 56).
Giere, Ronald N. 1999. “Using Models to Represent Reality.” In Model-Based Reasoning in Scientific Discovery, edited by L. Magnani, N. J. Nersessian, and P. Thagard, 41–57. New York: Kluwer/Plenum.
van Fraassen, Bas C. 2012. “Modeling and Measurement: The Criterion of Empirical Grounding.” Philosophy of Science 79: 773–84.
van Fraassen, Bas C. 2014.“The Criterion of Empirical Grounding in the Sciences.” In Bas van Fraassen’s Approach to Representation and Models in Science, edited by W. J. Gonzalez, 79–100. Dordrecht, the Netherlands: Springer Verlag.
Weyl, Hermann. (1927) 1963. Philosophy of Mathematics and Natural Science. Translated by Olaf Helmer. New York: Atheneum. First published in German in 1927.