Perhaps the central theme of Pudd'nhead Wilson is that classifications on the basis of race are completely arbitrary. Roxy, for example, is a beautiful woman, who to the unknowing observer, appears white. She is incredibly clever, and has a strong spirit. Further, she claims to be descended from the First Families of Virginia. Not only would these qualities typically guarantee a person success in Dawson's Landing, they would likely make the individual one of town's most prominent citizens. But, because a tiny fraction of Roxy's blood, 1/16 to be exact, is black, she is condemned to a life of slavery. By making Roxy one of strongest, most resourceful, and most likeable characters in the novel, Twain highlights the irrationality of relegating her to the lowest trenches of society.
The arbitrariness of racial classifications is most clearly evident in the switching of the infants. Like Roxy, her baby has been condemned to a harsh life of servitude due to the fraction of his blood that is black. In contrast, her master's son, Tom, is ensured a life of luxury by fortune of his birth. These vastly divergent destinies seem arbitrary and unfair, given that the children are so identical and that not even Percy Driscoll, father of one of the babies, can tell them apart but for their attire. The ease with which Roxy swaps the infants and radically alters their respective fates demonstrates just how artificially constructed these distinctions are.