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The study of logic itself—the principles, systems, and [assumptions] that underlie [logical reasoning]. Metalogic doesn't use logic to argue about the world; it uses logic to argue about logic. It asks: What makes a logical system consistent? Complete? Decidable? What are the limits of formal systems? (Gödel's incompleteness theorems are metalogical results.) How do different logical systems relate? Metalogic is logic turned reflexive, examining its own [foundations], its own tools, its own boundaries. It's the discipline that prevents logic from becoming dogmatic by forcing it to confront its own contingency.
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