Remark 2: Indeed, the proposed treatment of negation can be adapted within the mixed approach. The basic idea is that if something x P and something y not P, then x and y do not overlap (have no part in common, have 0 as intersection). So, within the mixed view, one may define [not P] as the set comprising anything that does not overlap ∨[P], the sum of everything that P. This solves the problems above, without requiring homogeneity.