 But this does not make good sense of many disputes between intuitionists, classical logicians, paraconsistentists, quantum logicians, etc. It is more fruitful to assume that each party generally understands the rival logics as intelligible, albeit necessarily false, theories. Even if classical logic actually is the one true logic, one can reason counterpossibly about what would be the case if a certain non-classical logic were the correct one (e.g., “if intuitionistic logic were correct, then the Law of Excluded Middle would fail” is true and “if intuitionistic logic were correct, then the Law of Explosion would fail” is false). One can take into account situations in which the Law of Excluded Middle fails and argue about what would and would not be the case in them. These situations are, by classical standards, just impossible worlds (of the third kind: Classical Logic Violators).