True value, error, and measurement uncertainty: two views

Measurement uncertainty, as established in the Guide to the Expression of Uncertainty in Measurement (GUM), is a central concept in metrology. The GUM is known for its detailed discussions on the concepts of true value and error and their relation to measurement uncertainty. However, the GUM statements on true value and error have been a source of conceptual controversies, sometimes leading to inconsistent or unclear descriptions on true value, error, and uncertainty. Here, we discuss that such controversies arise from an unclear distinction between two views of measurement with fundamentally different premises. In one of the views, called the realist view, measurement is regarded as an activity of estimating or determining the true value, in which case measurement uncertainty represents the dispersion of reasonable estimates of true values. In the other view, called the instrumentalist view, measurement is regarded as an activity of assigning values to a measurand, in which case measurement uncertainty represents the dispersion of values that could reasonably be assigned to a measurand. By examining the philosophy of measurement in each view, we show that a clear understanding of the two views is critical for understanding the GUM.