Impossible Worlds Logic

Origin. Routley's non-classical worlds (1980) and Rescher–Brandom (1979); Priest's development (1997, 2005); Nolan's defence of impossible worlds (1997); Berto and Jago's Impossible Worlds (2019) is the standard treatment. Extension of possible worlds. Worlds where contradictions hold. Non-trivial impossible reasoning. Hyperintensional semantics.

Models. Some worlds violate logic. Contradictions true at impossible worlds. Counterpossible conditionals meaningful. Distinguish logically equivalent content. Beyond possible worlds.

Formalism.

World types: W = Wₚ ∪ Wᵢ Possible worlds: classically behaved. Impossible worlds: logic may fail. Both in semantics.

Impossible worlds features: At some w: A ∧ ¬A true. At some w: B, B → C true, but C false. Logic "local" not global. Anything goes (at impossible worlds).

Counterpossibles: "If 2+2 were 5, then 2+2+1 would be 6." Classical: vacuously true. Impossible worlds: non-trivially true/false. Meaningful counterfactual reasoning.

Hyperintensionality: A, B necessarily equivalent, yet: "Believes A" ≠ "Believes B" Impossible worlds distinguish them. Fine-grained content.

Ternary accessibility: Routley-Meyer semantics. Rabc: from a, via b, access c. Impossible worlds: b may be impossible. Models relevant implication.

Applications: Belief about impossibilities. Fiction with impossible content. Counterpossible reasoning. Fine-grained propositions.

Realist vs instrumentalist: Are impossible worlds real? Or just semantic tools? Meinongianism: they exist. Ersatzism: they're representations.

Symbols.

Symbol	Unicode	Meaning
Wᵢ	—	impossible worlds
Wₚ	—	possible worlds
□→	—	counterfactual
@ᵢ	—	at impossible world

Metatheory. Extended modal semantics. Hyperintensionality. Counterpossible reasoning. World ontology.

Applies to. Modal logic. Philosophy of mind. Fiction logic. Metaphysics.

Limitations. Ontological cost. Unrestricted = trivial. Logical constraints. Metaphysical debate.