During the course of some work on the Parmenides, I found I was coming to a conclusion about the First Part of the dialogue which was at variance with what I supposed to be the traditional and commonly accepted view. It therefore seemed advisable to ascertain precisely what this traditional view was, and what were the arguments in favour of it; and the contents of this paper represent some part of an attempt to do this. As it happens, they also tend to make the writer appear as one playing the part of a Zeno to his own Parmenides, showing that even stranger results follow from the hypotheses of those from whom he differs than from his own.