Impossible world
In philosophical logic, the concept of an impossible world (sometimes called a non-normal world) is used to model certain phenomena that cannot be adequately handled using ordinary possible worlds. An impossible world, i {\displaystyle i} , is the same sort of thing as a possible world w {\displaystyle w} (whatever that may be), except that it is in some sense "impossible." Depending on the context, this may mean that some contradictions, statements of the form p ∧ ¬ p {\displaystyle p\land \lnot p} are true at i {\displaystyle i} , or that the normal laws of logic, metaphysics, and mathematics, fail to hold at i {\displaystyle i} , or both.