The twins, Marion and Shiva, are often discussed as being two parts of one whole. Dualism, in their case, will relate to the notion that Marion and Shiva are two parts of a single whole. Monism will relate to the idea that the two brothers are in fact one, not separate parts of a whole, but an indivisible identity.
An argument for a dualism or dualistic relationship between the brothers can be seen from the birth of the twins. The two are cojoined, coming from a single egg, but their situations at birth are different. Shiva nearly dies and Marion is healthy. We see in this example that the brothers are two different sides of the same entity.
As the brothers grow up their similarities fade, experiencing events which emphasize the differences that emerge in their personalities. These differences are not final however.
... long after he and his brother grow apart, Shiva still understands that he is ultimately tied to Marion and thus makes the decision to sacrifice his life to save Marion’s.
An argument for monism as the basis for the relationship between the twins can be most strongly made with evidence from the end of the novel, where Marion copes with Shiva's death by reverting to an understanding that he and his brother are one person.