If they send it back an infinite number of times, then an infinite number of widgets arrive. But why would they do that? That sounds like an awful lot of work, and I don’t think my grant has funding for an infinite number of time-travels. What if they only send it back once?
But back to the thread, another one: In the Duel of Wits in The Princess Bride, Vizzini’s “logic” of “Clearly I cannot choose the glass in front of you” is meaningless. He’s not trying to reason out where the poison is. Rather, as he presents his “logic”, he’s watching Wesley’s reactions, and indeed, his reactions are different when Vizzini is concluding it’s in one cup or the other. From there, Vizzini just has to figure out whether Wesley is bluffing or not (or more precisely, whether he’s bluffing an even or odd number of times), and he’s very good at that.
Of course, Wesley is a very tough nut to crack, and he can tell that, too, so he does the cup-swap just to be sure.