Remark 3: However, defining negation in terms of Boolean complement or non-overlap doesn’t work with all predicates. Consider the adjective cheap. Fix the context of speech so that what counts as cheap is specified and what counts as not cheap is also specified. The pieces of furniture a and b may each count as cheap, while together they (a∨b) count as not cheap. So non-overlap isn’t satisfied here: something not cheap overlaps with something cheap. Cheap is a vague predicate. But the same phenomenon is observed with an exact predicate like costs fifty euros: a and b may each cost fifty euros, while together they don’t, costing ninety euros, for instance. So non-overlap should not be required. In general, [not P] cannot be defined in terms of [P]. Instead, it seems that [P] and [not P] should be separately specified. (This is done in many approaches to vagueness.)