Iterated public announcements are self-fulfilling in Merton's sociological sense: repeated declarations of ignorance collectively produce the very knowledge state they deny, confirming rather than refuting the announcement's social function.

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Iterated public announcements(as used in logic and social theory): When the same statement is repeated multiple times in front of a group of people, with each repetition making it more widely known and accepted.
Knowledge state(what permissibility results are measured against): A person's current collection of beliefs and information at a particular time—what they know and don't know right now.
Merton's sociological sense(as used in sociology): A concept developed by sociologist Robert K. Merton about how predictions or statements can actually cause the very outcome they describe, just by people believing and acting on them.
Robert K. Merton(as a historical reference): An influential 20th-century American sociologist who studied how society works and who introduced the famous idea of 'self-fulfilling prophecy' — the idea that what we believe can make itself come true.

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