Abstract

Building upon the works of Gödel, Zalta ; and Benzmüller and Paleo, this paper introduces a formal system and testable system for Metaphysical Cosmology, referring to the study of the nature of existence, non-existence, and their interplay. The aim is to integrate metaphysics into a testable scientific framework, beyond speculative reasoning. The system abides by three principles which serve as a foundation for implementing a scientific methodology in metaphysics: (i) axioms must be minimized, incorporating Cartesian-like skepticism ; (ii) theorems must be inferred through proof-theoretic derivations ; (iii) theorems must be tested experimentally through computation. The system borrows from type-theoretic concepts and introduces new logical notions as tools for Metaphysical Cosmology, such as a metric-space-based predicate system, and a revised version of the existential quantifier. These tools offer an exhaustive approach to metaphysical entities and provide mechanisms to address contradictions. Formulae and equations depicting the structure of the Metaphysical Cosmos are inferred from the system through proof-theoretic derivations. Theorems inferred from the system have been tested using the theorem-prover Z3, encoded in Python, which determines whether a formula is satisfiable. While testing a theorem, its negation is inputted in Z3, and if the output displays that its negation is satisfiable, then the theorem is falsified and rejected, otherwise it is accepted as valid. This method thus follows the falsifiability criteria, as per Karl Popper, reinforcing testable scientific methodology in metaphysics. The code used in computational experimentation is given in full in the appendix for reproducibility.