Why Conclusions Diverge from the Same Observations: Formalizing World-Model Non-Identifiability via an Inference

Abstract

When people share the same documents and observations yet reach different conclusions, the disagreement often shifts into a judgment that the other party is cognitively defective, irrational, or acting in bad faith. This paper argues that such divergence is better described as a form of non-identifiability inherent in inference and learning, rather than as a defect of the other party. We organize the phenomenon into two levels: (i) $\theta$-level non-identifiability, where conclusions diverge under the same world model $W$ because inference settings differ; and (ii) $W$-level non-identifiability, where repeated use of an inference setting $\theta$ biases data exposure and update rules, causing the learned world model $W$ itself to diverge. We introduce an inference profile $\theta = (R, E, S, D)$, consisting of Reference, Exploration, Stabilization, and Horizon, and show how outputs can split even for the same observation $o$ and the same $W$. We further explain why disagreements tend to project onto a small number of bases -- abstract versus concrete, externalizability, and order versus freedom -- as a consequence of general constraints on learning systems: computational, observational, and coordination constraints. Finally, we relate the framework to deep representation learning, including representation hierarchy, latent-state estimation, and regularization-exploration trade-offs, and illustrate the framework through a case study on AI regulation debates.