Spacetime Singularities and Incompleteness: Epistemic and Ontological Remarks

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 formulation of general relativity. Next, I compare Penrose’s result with Gödel’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.