When Sir Arthur Eddington passed away in 1944, TIME magazine noted that we had lost “one of mankind’s most reassuring cosmic thinkers.” “Sir Arthur,” TIME said, had “discoursed on his cosmic subject with a wit and clarity rare among scientists.” One of Eddington’s favorite cosmic subjects was “Time’s Arrow”, a term he himself introduced to the literature in his 1927 book, The Nature of the Physical World. Eddington thought that there is something essential about time that physics is liable to neglect: the fact that it “goes on”, as he often puts it. Despite the best efforts of D C Williams, Adolf Grunbaum, J J C Smart, and many other philosophers to pour cold water on this idea, similar claims are still made today, in physics as well as in philosophy. All sides in these debates can profit, in my view, by going back to Eddington. Eddington appreciates some of the pitfalls of these claims with greater clarity than most of their contemporary proponents; and also issues a challenge to rival views that deserves to be better known.