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. Impossible worlds are controversial objects in philosophy, logic, and semantics. They have been around since the advent of possible world semantics for modal logic, as well as world based semantics for non-classical logics, but have yet to find the ubiquitous acceptance, that their possible counterparts have found in all walks of philosophy.

Argument from ways

Possible worlds

Possible worlds are often regarded with suspicion, which is why their proponents have struggled to find arguments in their favor. An often-cited argument is called the argument from ways. It defines possible worlds as "ways how things could have been" and relies for its premises and inferences on assumptions from natural language, for example:

(1) Hillary Clinton could have won the 2016 US election.

(2) So there are other ways how things could have been.

(3) Possible worlds are ways how things could have been.

(4) So there are other possible worlds.