Background: Personalized clinical decision-making requires knowing when to follow precedent and when to deviate for an individual patient. Clinical artificial intelligence (AI) aspires to automate such reasoning, but as these systems become new precedents, a regress emerges: the AI must also recognize when to deviate from its own recommendations. We term this the AI Socratic Paradox (AISP), a metacognitive challenge that affects the entire AI development lifecycle. Objectives: To formalize the AISP as a diagnostic lens for identifying epistemic limitations in clinical AI; trace its manifestations across feature selection, model specification, and model validation; and review technical strategies that partially address these challenges. Methods: We organize our review around a Triad of complementary domains: uncertainty quantification (formalizing confidence), ambiguity awareness (handling multiple valid representations), and causal AI (linking models to underlying mechanisms). For each development phase, we map specific epistemic obstacles to Triad-informed approaches. Results: In feature selection, core challenges include feature ontology ambiguity and the identification problem. These can be mitigated with causal inference frameworks and latent variable methods. In model specification, problems like the signification problem and misaligned class ontologies motivate concept alignment techniques and ontology-constrained architectures. In model validation, issues of misaligned uncertainty semantics and domain shift vulnerability call for advances in calibrated uncertainty quantification, out-of-distribution detection, adaptive learning, and continual validation in hybrid workflows. Conclusions: The AI Socratic Paradox is a foundational barrier that technical advances can only asymptotically reduce. Addressing it requires embedding Triad-informed methods within non-linear, feedback-rich development frameworks while sustaining epistemic humility.