Generoso Immediato

Generoso Immediato

In direct response to requests for a logico-mathematical test of the conjecture, we formally disprove a recently conjectured artificial intelligence trade-off between epistemic certainty and scope in its published universal hyperbolic product form, as introduced in Philosophy and Technology. Certainty is defined as the worst-case correctness probability over the input space, and scope as the sum of the Kolmogorov complexities of the input and output sets. Using standard facts from coding theory and algorithmic information theory, we show, first, that when the conjecture is instantiated with prefix (self-delimiting, prefix-free) Kolmogorov complexity, it leads to an internal inconsistency, and second, that when it is instantiated with plain Kolmogorov complexity, it is refuted by a constructive counterexample. These results establish a main theorem: contrary to the conjecture's claim, no universal "certainty-scope" hyperbola holds as a general bound under the published definitions. We further show that a subsequent "entropy-based" revision, replacing the Kolmogorov scope with Shannon joint entropy and redefining the epistemic certainty level accordingly, cannot restore universality either.

Generoso Immediato

The recently published "certainty-scope" conjecture offers a compelling insight into the inherent trade-off present within artificial intelligence (AI) systems. As general research, this investigation remains vital as a philosophical undertaking and a potential guide for directing AI investments, design, and deployment, especially in safety-critical and mission-critical domains where risk levels are substantially elevated. While maintaining intellectual coherence, its formalization ultimately consolidates this insight into a suspended epistemic truth, which resists operational implementation within practical systems. This paper argues that the conjecture's objective to furnish insights for engineering design and regulatory decision-making is limited by two fundamental factors: first, its dependence on incomputable constructs and its failure to capture the generality factors of AI, rendering it practically unimplementable and unverifiable; second, its foundational ontological assumption of AI systems as self-contained epistemic entities, distancing it from the complex and dynamic socio-technical environments where knowledge is co-constructed. We conclude that this dual breakdown - an epistemic closure deficit and an embeddedness bypass - hinders the conjecture's transition to a practical and actionable framework suitable for informing and guiding AI deployments. In response, we point towards a possible framing of the epistemic challenge, emphasizing the inherent epistemic burdens of AI within complex human-centric domains.