Spacetime singularities and incompleteness: epistemic and ontological remarks

TL;DR

This paper clarifies that spacetime singularities are about mathematical incompleteness rather than implying the existence of material entities, and compares this with G"odel's theorem to explore philosophical implications.

Contribution

It offers a novel interpretation of Penrose's singularity theorem as a statement of incompleteness and distinguishes physical assumptions from formal ones in general relativity.

Findings

Penrose's theorem is best understood as a theorem of incompleteness

Differentiation between physical and formal assumptions in GR

Philosophical insights on epistemic limits of physical theories

Abstract

I argue that spacetime singularities entail no ontological commitment to material entities. First, I show that Penrose's singularity theorem is best understood as a theorem of incompleteness, it demonstrates the failure of specific spacetime models within General Relativity (or any theory incorporating the Raychaudhuri equation) under certain general conditions. Although this has been done before, I adopt a novel approach based on differentiating between physical and purely formal assumptions in the axiomatic foundation of general relativity. Next, I compare Penrose's result with G\"odel's incompleteness theorem, highlighting key similarities and differences. Finally, I draw philosophical conclusions regarding the limits and prospects of our epistemic reconstructions of the physical world.