In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics, on the possibility of quantitative psychology, and on the meaning of temperature measurement. Late nineteenth-century scrutinisers of the foundations of mathematics made little of Helmholtz’s essay. Yet it inspired two mathematicians with an eye on physics, and a few philosopher-physicists. The aim of the present paper is to situate Helmholtz’s contribution (...) in this complex array of nineteenth-century philosophies of number, quantity, and measurement.Author Keywords: Helmholtz; Measurement; Arithmetic; P. Du Bois-Reymond; H. and R. Grassmann; J. von Kries. (shrink)

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. (shrink)