We begin with the fact that everyone has parents. Let’s assume that parents with names always give names to their children. Adam and Eve had names. So we conclude that every person who ever lived had a name. For if not, let Person be the first person with no name. Person was not Adam or Eve, who had names. So Person had parents. Person’s parents had names, since Person is the first person without a name. But by assumption, the parents must have given Person a name. So it cannot be that Person had no name. Thus there cannot have been a first person without a name. So everyone had a name.