Implications of Tarski's Undefinability Theorem on the Theory of Everything

Abstract

The Theory of Everything ($S_{\text{ToE}}$) seeks to unify all fundamental forces of nature, including quantum gravity, into a single theoretical framework. This theory would be defined internally using a set of axioms, and this paper proposes a set of axioms for any such theory. Furthermore, for such a theory, all scientific truth would be defined internally as consequences derivable from the rules of such a theory. This paper then examines the implications of Tarski's undefinability theorem on scientific truths derived from such axioms. We demonstrate that Tarski's theorem imposes limitations on any such formal system $S_{\text{ToE}}$. However, we also argue that the Lucas-Penrose argument suggests that non-algorithmic understanding can transcend these formal limitations.

arXiv commentAccepted for publication in EPL

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Cited by in corpus (4)

• Information Theoretical Approach to Detecting Quantum Gravitational Corrections
• Can quantum gravity be both consistent and complete?
• Geometry-Information Duality: Quantum Entanglement Contributions to Gravitational Dynamics
• Probing quantum criticality near the BTZ black hole horizon: Insights from coupled fermion-antifermion pairs