Eran Tal

Axiomatic measurement theories are commonly interpreted as claiming that, in order to quantify an empirical domain, the qualitative structure of data about that domain must be mapped to a numerical structure. Such mapping is supposed to be established independently, i.e., without presupposing that the domain can be quantified. This interpretation is based on two myths: that it is possible to independently infer the qualitative structure of objects from empirical data, and that the adequacy of numerical representations can only be justified by mapping such qualitative structures to numerical ones. I dispel the myths and show that axiomatic measurement theories provide an inadequate characterization of the kind of evidence required to detect quantities.

When discrepancies are discovered between the outcomes of different measurement procedures, two sorts of explanation are open to scientists. Either some of the outcomes are inaccurate or the procedures are not measuring the same quantity. I argue that, due to the possibility of systematic error, the choice between and is underdetermined in principle by any possible evidence. Consequently, foundationalist criteria of quantity individuation are either empty or circular. I propose a coherentist, model-based account of measurement that avoids the underdetermination problem, and use this account to explain how scientists individuate quantities in practice.

This article develops a model-based account of the standardization of physical measurement, taking the contemporary standardization of time as its central case-study. To standardize the measurement of a quantity, I argue, is to legislate the mode of application of a quantity-concept to a collection of exemplary artefacts. Legislation involves an iterative exchange between top-down adjustments to theoretical and statistical models regulating the application of a concept, and bottom-up adjustments to material artefacts in light of remaining gaps. The model-based account clarifies the cognitive role of ad hoc corrections, arbitrary rules and seemingly circular inferences involved in contemporary timekeeping, and explains the stability of networks of standards better than its conventionalist and constructivist counterparts.

This article develops a model-based account of the standardization of physical measurement, taking the contemporary standardization of time as its central case study. To standardize the measurement of a quantity, I argue, is to legislate the mode of application of a quantity concept to a collection of exemplary artefacts. Legislation involves an iterative exchange between top-down adjustments to theoretical and statistical models regulating the application of a concept, and bottom-up adjustments to material artefacts in light of remaining gaps. The model-based account clarifies the cognitive role of ad hoc corrections, arbitrary rules, and seemingly circular inferences involved in contemporary timekeeping, and explains the stability of networks of standards better than its conventionalist and constructivist counterparts. 1 Introduction2 Making Time Universal2.1 Stability and accuracy2.2 Multiple realizability2.3 The challenges of synchronicity2.4 Divergent standards2.5 The leap second3 The Two Faces of Stability3.1 An explanatory challenge3.2 Conventionalist explanations3.3 Constructivist explanations4 Models and Standardization4.1 A third alternative4.2 Stability reconceived4.3 Legislative freedom4.4 Discovering gaps4.5 Nature and society entangled4.6 Remark on scope5 Conclusions.

The philosophy of measurement studies the conceptual, ontological, epistemic, and technological conditions that make measurement possible and reliable. A new wave of philosophical scholarship has emerged in the last decade that emphasizes the material and historical dimensions of measurement and the relationships between measurement and theoretical modeling. This essay surveys these developments and contrasts them with earlier work on the semantics of quantity terms and the representational character of measurement. The conclusions highlight four characteristics of the emerging research program in philosophy of measurement: it is epistemological, coherentist, practice oriented, and model based

This work develops an epistemology of measurement, that is, an account of the conditions under which measurement and standardization methods produce knowledge as well as the nature, scope, and limits of this knowledge. I focus on three questions: (i) how is it possible to tell whether an instrument measures the quantity it is intended to? (ii) what do claims to measurement accuracy amount to, and how might such claims be justified? (iii) when is disagreement among instruments a sign of error, and when does it imply that instruments measure different quantities? Based on a series of case studies conducted in collaboration with the US National Institute of Standards and Technology (NIST), I argue for a model-based approach to the epistemology of physical measurement. To measure a physical quantity, I argue, is to estimate the value of a parameter in an idealized model of a physical process. Such estimation involves inference from the final state (‘indication’) of a process to the value range of a parameter (‘outcome’) in light of theoretical and statistical assumptions. Contrary to contemporary philosophical views, measurement outcomes cannot be obtained by mapping the structure of indications. Instead, measurement outcomes as well as claims to accuracy, error and quantity individuation can only be adjudicated relative to a choice of idealized modelling assumptions.

Contrary to the claim that measurement standards are absolutely accurate by definition, I argue that unit definitions do not completely fix the referents of unit terms. Instead, idealized models play a crucial semantic role in coordinating the theoretical definition of a unit with its multiple concrete realizations. The accuracy of realizations is evaluated by comparing them to each other in light of their respective models. The epistemic credentials of this method are examined and illustrated through an analysis of the contemporary standardization of time. I distinguish among five senses of ‘measurement accuracy’ and clarify how idealizations enable the assessment of accuracy in each sense.

This paper draws attention to an increasingly common method of using computer simulations to establish evidential standards in physics. By simulating an actual detection procedure on a computer, physicists produce patterns of data (‘signatures’) that are expected to be observed if a sought-after phenomenon is present. Claims to detect the phenomenon are evaluated by comparing such simulated signatures with actual data. Here I provide a justification for this practice by showing how computer simulations establish the reliability of detection procedures. I argue that this use of computer simulation undermines two fundamental tenets of the Bogen–Woodward account of evidential reasoning. Contrary to Bogen and Woodward’s view, computer-simulated signatures rely on ‘downward’ inferences from phenomena to data. Furthermore, these simulations establish the reliability of experimental setups without physically interacting with the apparatus. I illustrate my claims with a study of the recent detection of the superfluid-to-Mott-insulator phase transition in ultracold atomic gases