Paradox? What paradox?

Abstract

This article is a response to the preceding paper by Huang, who considers a recent result of Willink (Measurement: Sensors, 24:100416, 2022) and who describes the result as a paradox. The result implied that a set of information or a “state of knowledge” about a measurand cannot be identified with a unique probability distribution for the measurand, contrary to what seems suggested in the literature surrounding the revision of the Guide to the Expression of Uncertainty in Measurement. The result is restated and viewed in the context of CIPM Recommendation INC-1, which was foundational in the original development of the Guide. It is argued that the result is a proof, not a paradox, and that it will only appear paradoxical to those who have adopted an incorrect premise about probability. The idea of having “information” about the true value of a measurand is discussed and contrasted with the idea of having “belief” about it. The material supports the view that the analysis of measurement uncertainty is to be based on classical statistical principles.