  In De Interpretatione 12–13, Aristotle (i) concludes that modal operators modify the whole predicate (or the copula, as he puts it), not just the predicate term of a sentence. (ii) He states the logical relations that hold between modal operators, such as that ‘it is not possible for A not to hold of B’ implies ‘it is necessary for A to hold of B’. (iii) He investigates what the contradictories of modalized sentences are, and decides that they are obtained by placing the negator in front of the modal operator. (iv) He equates the expressions ‘possible’ and ‘contingent’, but wavers between a one-sided interpretation (where necessity implies possibility) and a two-sided interpretation (where possibility implies non-necessity).