  The second aspect of the principle expresses “the Humean denial of necessary connections” (ibid., 87), that is, the idea that anything can fail to coexist with anything else. For  “if there could be a talking head contiguous to the rest of a  living human body, but there couldn't be a talking head separate from the rest of a human body, that too would be a failure of  plenitude” (ibid). To express this a bit more  rigorously, say that objects a1,  a2, ..., are independent of objects  b1, b2, ..., if no sum of any  parts of the former are parts or duplicates of any sum of any parts  of the latter and vice versa; then we have: 