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A system that takes logical systems themselves as its objects of study, but does so from a fixed, immutable perspective. It is a "closed theory about logic." For example, a specific, dogmatic philosophy of mathematics that definitively states what mathematics is (e.g., "Mathematics is nothing but the manipulation of symbols according to formal rules") and refuses to consider alternative philosophies (e.g., intuitionism, realism) is a meta-logical closed system.
Meta-Logical Closed Systems Example: Strict Logical Positivism, with its verifiability principle of meaning, acted as a Meta-Logical Closed System. It declared that any statement not empirically verifiable or analytically true was literally meaningless. This meta-framework itself was not open to empirical verification, making it a self-sealing, closed system for judging all other forms of discourse and logic.
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