 Contradiction-Realizers: a still more specific definition has it that an impossible world is a world where sentences of the form \(A\) and \(\neg A\) hold, against the Law of Non-Contradiction (see e.g. Lycan 1994). Impossible worlds of the fourth kind will be impossible in the third sense, but not vice versa. Our intuitionistic world above will have the Law of Non-Contradiction hold unrestrictedly: it will be impossible in the third, but not in the fourth sense.