 While the standard conditional logics based on this idea have been quite successful in the treatment of counterfactuals, the approach entails that any counterfactual whose antecedent is impossible is vacuously true. For if there are no possible worlds at which \(A\) is true, then trivially, all closest \(A\)-worlds (worlds where \(A\) is true) are \(B\)-worlds. This is unsatisfying in many respects, for we often need to reason nontrivially about theories that (perhaps unbeknownst to us) cannot possibly be correct; and we often need to reason from antecedents that may turn out to be not only false, but necessarily so. (Compare the example conditionals (1.1) and (1.2) in  section 1  for an example.)