Impossible world

<p>In <a href="/facts/Philosophical_logic/Ld8lnKDA">philosophical logic</a>, 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 <a href="/facts/Possible_world/6jr7P8jV">possible worlds</a>. 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 <a href="/facts/Contradiction/PQHH5a2J">contradictions</a>, statements of the form  
  
    
      
        p
        ∧
        ¬
        p
      
    
    {\displaystyle p\land \lnot p}
  
 are true at 
  
    
      
        i
      
    
    {\displaystyle i}
  
,  or that the normal laws of <a href="/facts/Logic/8JnpJLtt">logic</a>, <a href="/facts/Metaphysics/fSFt6SHe">metaphysics</a>, and <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, fail to
hold at 
  
    
      
        i
      
    
    {\displaystyle i}
  
, or both. Impossible worlds are controversial objects in <a href="/facts/Philosophy/zAH5PVD6">philosophy</a>, <a href="/facts/Logic/8JnpJLtt">logic</a>, and <a href="/facts/Semantics/1L4WwLAP">semantics</a>. They have been around since the advent of possible world semantics for <a href="/facts/Modal_logic/I7uXvYYT">modal logic</a>, 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.
</p>

Impossible world open-in-new

Impossible world