Bridge laws in Nagel's model need not assert identity; they may express nomological coextension, which is sufficient for inter-theoretic reduction without full materialist commitment.

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Bridge laws(Philosophy of mind, type-identity theory): Strict biconditional laws of the form 'P1 ↔ M1' that correlate physical predicates with mental predicates, forming the basis of type-identity theories of mind.
Identity (philosophical)(as used in metaphysics and logic): When two things are actually the same thing, not just similar—like how Clark Kent and Superman are identical (the same person with two names).
Inter-theoretic reduction(the main concept being discussed): When one scientific theory is shown to be explainable by another, more fundamental theory—basically proving that the bigger theory was right all along by deriving it from smaller pieces.
Materialism (in philosophy)(in metaphysics and philosophy of mind): The view that everything in the universe is ultimately made of physical matter and its properties, with no non-physical things needed to explain reality.

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