> I think there's nothing to say to the first two sentences but that I regard it as an argument that may be more or less convincing. I don't know exactly what it means for something to be an argument vs. a coincidence; it is a coincidence that, say, my name is what it is, but it is nonetheless correct for me to argue that that is my name.

Sure. But we're talking about whether to index arrays from 0 or 1. It is true that naming an array element after the quantity of its predecessors will tell you the number of predecessors the element has. But that's not an argument for why you should do it; there would need to be some kind of benefit to having that information. Without a benefit, it's just something that happens to be true.

That's the difference between an argument and a coincidence.