A Conjecture on a Fundamental Trade-Off between Certainty and Scope in Symbolic and Generative AI

TL;DR

This paper proposes a formal conjecture that highlights a fundamental trade-off in AI systems between achieving provable correctness and handling broad, high-dimensional data, impacting future AI design and evaluation.

Contribution

It introduces a formal information-theoretic conjecture that explicitly states the trade-off between certainty and scope in AI, linking it to philosophical and practical considerations.

Findings

Formalizes the certainty-scope trade-off in AI systems.

Contextualizes the trade-off within epistemology and AI governance.

Highlights implications for trustworthy AI development.

Abstract

This article introduces a conjecture that formalises a fundamental trade-off between provable correctness and broad data-mapping capacity in Artificial Intelligence (AI) systems. When an AI system is engineered for deductively watertight guarantees (demonstrable certainty about the error-free nature of its outputs) -- as in classical symbolic AI -- its operational domain must be narrowly circumscribed and pre-structured. Conversely, a system that can input high-dimensional data to produce rich information outputs -- as in contemporary generative models -- necessarily relinquishes the possibility of zero-error performance, incurring an irreducible risk of errors or misclassification. By making this previously implicit trade-off explicit and open to rigorous verification, the conjecture significantly reframes both engineering ambitions and philosophical expectations for AI. After reviewing the historical motivations for this tension, the article states the conjecture in information-theoretic form and contextualises it within broader debates in epistemology, formal verification, and the philosophy of technology. It then offers an analysis of its implications and consequences, drawing on notions of underdetermination, prudent epistemic risk, and moral responsibility. The discussion clarifies how, if correct, the conjecture would help reshape evaluation standards, governance frameworks, and hybrid system design. The conclusion underscores the importance of eventually proving or refuting the inequality for the future of trustworthy AI.