Steering, or maybe why Einstein did not go all the way to Bell's argument

It is shown that a main source of conflict between Einstein and the mainstream quantum physicists was his insistence that wave functions, like classical probability distributions, do not refer to individual particles and, in particular, do not describe individual systems completely. The EPR paper was written to argue for this position. By aiming at showing that wave functions are unsuitable as local hidden variables, the authors failed to see that a slight extension could have ruled out such local hidden variables in general. As background for this analysis of the EPR argument the notion of steering is described, and a version of the Bell argument is proved which emphasizes non-local signalling aspects. Finally, some background is given concerning a well-known paper by the present author, which is celebrating 25 years this year, and in which the first non-steering models were constructed. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'. (paper)