An Incompleteness Result Regarding Within-System Modeling
15 Pages Posted: 23 Nov 2021 Last revised: 11 Feb 2022
Date Written: November 20, 2021
Abstract
Models typically represent phemonena within-system, but there are times we want to represent the system itself. System-modeling depends on the perspective of the modeler, as demonstrated in Wolpert [1, 2]. Using meta-mathematical techniques, we prove a more general result for within-system modeling by demonstrating a novel set of impossibility results, namely, that a system cannot be completely modeled from within the system. Notably, our proof does not require specifying the functional form of inference, and seems to put additional constraints on inference devices. We discuss implications of our result for the social sciences, biological sciences, and physics.
Keywords: metamathematics, incompleteness, Gödel, inference, epistemics
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