TGS THEORY: A CANDIDATE UNIFIED FRAMEWORK FOR GODEL INCOMPLETENESS, TURING UNDECIDABILITY, AND SHANNON INFORMATION

Abstract

This work proposes a candidate unification of three fundamental limitation principles:G¨odel incompleteness, Turing undecidability, and Shannon information constraints. The centralobject of the theory is the resolutive deficit, defined textually as the difference between the informationaldemand required to decide a proposition and the informational capacity of a formalsystem. The guiding thesis is that undecidability, incompleteness, and informational insufficiencyare manifestations of a common structural phenomenon: positive resolutive deficit. The presentwork should be regarded as a formal research program rather than a completed theory.