Fundamental Trade-Off Between Certainty and Scope in Symbolic and Generative AI (arxiv.org)

Researchers have proposed a conjecture that formalizes a fundamental trade-off in AI: systems that can offer deductive, provable correctness (the classical symbolic/logic-based paradigm) must operate in narrowly pre-structured domains, while systems that map high‑dimensional inputs to rich, open-ended outputs (modern generative models) necessarily sacrifice the possibility of zero-error guarantees and carry an irreducible risk of mistakes. The paper casts this intuition as an information-theoretic inequality, situating it between formal verification, epistemology, and the empirical behavior of large-scale models, and argues the trade-off is both testable and mathematically expressible. This framing matters because it turns an implicit engineering tension into a principled constraint that would reshape evaluation metrics, verification expectations, and governance: if the conjectured inequality holds, it explains why fully general, trustworthy AI with provable no-error guarantees is infeasible and motivates hybrid architectures and calibrated epistemic-risk management. The analysis links to underdetermination, moral responsibility for model failures, and practical guidance for system designers (e.g., when to prefer constrained symbolic modules vs. flexible generative components). Proving or refuting the conjecture would materially influence standards for trustworthy AI, regulatory frameworks, and the technical trade-offs teams accept when balancing scope against certainty.