Implications of Tarski's undefinability theorem on the theory of everything

The Theory of Everything (SToE) 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 SToE. However, we also argue that the Lucas-Penrose argument suggests that non-algorithmic understanding can transcend these formal limitations.