Fabien Grégis

The guest editors would like to thank the University of Paris and the ENSA Paris-Val de Seine for having provided premises to successfully host the 2018 "Measurement at the Crossroads" conference in Paris.Our thanks extend to our funding sources: the conference was made possible thanks to the generous support of the Institut Humanités, Sciences et Sociétés, the SPHERE laboratory and the Laboratoire Matériaux et Phénomènes Quantiques of the University of Paris, the department of History and Philosophy of Science of the University of Paris, the Laboratoire National de métrologie et d'Essais, and the University of Geneva.We would like to thank the many people who contributed to the organization of...

Abstract : A measurement result is never absolutely accurate: it is affected by an unknown “measurement error” which characterizes the discrepancy between the obtained value and the “true value” of the quantity intended to be measured. As a consequence, to be acceptable a measurement result cannot take the form of a unique numerical value, but has to be accompanied by an indication of its “measurement uncertainty”, which enunciates a state of doubt. What, though, is the value of measurement uncertainty? What is its numerical value: how does one calculate it? What is its epistemic value: how one should interpret a measurement result? Firstly, we describe the statistical models that scientists make use of in contemporary metrology to perform an uncertainty analysis, and we show that the issue of the interpretation of probabilities is vigorously debated. This debate brings out epistemological issues about the nature and function of physical measurements, metrologists insisting in particular on the subjective aspect of measurement. Secondly, we examine the philosophical elaboration of metrologists in their technical works, where they criticize the use of the notion of “true value” of a physical quantity. We then challenge this elaboration and defend such a notion. The third part turns to a specific use of measurement uncertainty in order to address our thematic from the perspective of precision physics, considering the activity of the adjustments of physical constants. In the course of this activity, physicists have developed a dynamic conception of the accuracy of their measurement results, oriented towards a future progress of knowledge, and underlining the epistemic virtues of a never-ending process of identification and correction of measurement errors.

This article discusses the definitions of ‘‘measurement uncertainty” given in the three editions of the International Vocabulary of Metrology (VIM) and a fourth definition which was suggested for the next edition of this document. It is argued that none of the definitions is satisfying. First, a thorough definition of measurement uncertainty should supply an explanation about the meaning of the concept, which is missing from the VIM2&3. Secondly, when provided, the meanings are not accurate enough: the VIM1 version is flawed and the possible future definition appeals to an overly restrictive notion of ‘‘belief”. Alternative options are then proposed, based on the conclusions that (i) measurement uncertainty is a statement – an inference – made by the experimenter about the measurand; (ii) it is only based on what is accessible to one’s knowledge, and therefore rests on the hypothesis that no unknown systematic error affects the measurement.

The way metrologists conceive of measurement has undergone a major shift in the last two decades. This shift can in great part be traced to a change in the statistical methods used to deal with the expression of measurement results, and, more particularly, with the calculation of measurement uncertainties. Indeed, as we show, the incapacity of the frequentist approach to the calculus of uncertainty to deal with systematic errors has prompted the replacement of the customary frequentist methods by fully Bayesian procedures. The epistemological ramifications of the Bayesian approach merge with a deep empiricist mood tantamount to an “epistemic turn”: measurement results are analysed in terms of degrees of belief, and central concepts such as error and accuracy are called into question. We challenge the perspective entailed by this epistemic turn: we insist on the centrality of the concepts of error and accuracy by underlining the intentional character of measurement that is intimately linked to the process of correction of experimental data. We further circumvent the difficulties posed by the classical analysis of measurement by stressing the social rather than the epistemic dimension of measurement activities.

This article develops a historico-critical analysis of uncertainty and accuracy in measurement through a case-study of the adjustment of the fundamental physical constants, in order to investigate the sceptical “problem of unknowability” undermining realist accounts of measurement. Every scientific result must include a “measurement uncertainty”, but uncertainty cannot be be eval- uated against the unknown, and therefore cannot be taken as an assessment of “accuracy”, defined in the metrological vocabulary as the closeness to the truth. The way scientists use and interpret uncertainty in the adjustment activity illustrates how they try to overcome this predicament. I iden- tify two operative roles of measurement uncertainty, in the comparison and in the combination of measurement results. This duality implies a tension between selection and combination when aggregating results, leading to a crucial question: should the evaluation of uncertainties favour safety over precision? I present contrasting answers and identify a specific account of physicists who implicitly try to conciliate realism with the problem of unknowability. I argue that this invites us to reconsider accuracy from a dynamical standpoint, as the gradual achievement of scientific progress through error correction. Finally, I present two interpretations of measurement uncertainty, objective and epistemic, which I criticize and suggest improvements to.