Implications of Tarski's undefinability theorem on the Theory of Everything

¹ Canadian Quantum Research Center - 204-3002, 32 Ave Vernon, BC V1T 2L7, Canada
² Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan Kelowna, BC V1V 1V7, Canada
³ Department of Mathematical Sciences, Durham University, Lower Mountjoy - Stockton Road, Durham DH1 3LE, UK
⁴ Facultat de Física, Universitat de Barcelona (UB) - Martí i Franquès 1, E-08028, Barcelona, Spain

Received: 28 August 2024
Accepted: 27 September 2024

Abstract

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