All this fooferaw about the meaning of "uncirculated" brings to mind the story told about Honest Abe when he was a lawyer instead of a profile on a coin.
He is said to have asked "How many legs would a dog have if you called the tail a leg?"
His answer was "Four, because calling the tail a leg doesn't make it a leg." In other words, if a "rose is a rose is a rose", then a coin which has circulated is "circulated"; but a coin that
looks like it did before it left the mint is "mint state". So Lucy must be right.
On the other hand, as Humpty Dumpty told Alice, when someone uses a word it means what the user intends, so if "uncirculated" is defined as "showing no signs of wear", Doug must be right.
But then . . . (ain't this fun?)