when a contrast situation is construed as an identificational construction, the propositional content is asserted against a background of an alternative proposition (or propositions) expressed or evoked in the discourse context. Example: in the exchange John bought apples. No, he bought PEACHES, the proposition that John bought peaches is asserted against the background of the alternative proposition that John bought apples. The shared part of the proposition and its alternative, that John bought something, is presupposed -- that is, John bought X is a presupposed open proposition. (Section 11.4.1)