This paper develops a structural account of intelligence and rationality centered on correctability. Human beings, theories, institutions, and artificial systems require enough internal coherence to preserve continuity and function. Yet coherence can become epistemically dangerous when the organizing form protects itself against evidence, consequence, or other perspectives that should revise it. The paper distinguishes discrepancy, contact, correction claim, warrant, response, and binding. Warrant concerns whether a proposed correction is evidentially supported, procedurally contestable, and proportional to the available reasons. This makes it possible to distinguish calibrated revision from defensive closure, reasoned resistance, compliance, suspended judgment, and performative revision. Correction-capacity is defined as the ability for response to track warrant over time and for justified revision to alter later confidence, behavior, repair, or evidential practice. A further claim concerns fixed worth and person-belief differentiation: self-relevant correction may become more survivable when a person is not treated as identical with the belief, role, achievement, or self-representation being challenged. The framework is then extended to relationships, institutions, and AI while preserving differences in mechanism. For artificial systems, the paper separates fluent self-correction, persistent memory, corrective continuity, social presence, and phenomenal consciousness. It does not claim that corrigibility establishes sentience. The broader thesis is that intelligence is better understood not as the preservation of coherence, but as the capacity to reorganize under warranted correction while remaining open to further revision.