I present a very general and simple argument — based on the no-signalling theorem — showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility of reproducing the macroscopic measurement results). Although I believe this form of the argument is new, I argue it is essentially a variant of Einstein’s reasoning in the context of the EPR paradox — which is thereby illuminated from a new angle. 1 Von Neumann’s insolubility argument In 1932, J. von Neumann provided one of the earliest and most famous discussions of the measurement process, in chapter VI of his Mathemati∗Department of Philosophy, University of Aberdeen, and Institut d’Histoire et de Philosophie des Sciences et des Techniques (CNRS, Paris 1, ENS). Address for correspondence: Department of Philosophy, University of Aberdeen, Old Brewery, High Street, Aberdeen AB24 3UB, Scotland, U.K. (e-mail: email@example.com).