Do LLMs have core beliefs?

[Preprint] The rise of Large Language Models (LLMs) has sparked debate about whether these systems exhibit human-level cognition. In this debate, little attention has been paid to a structural component of human cognition: core beliefs, truths that provide a foundation around which we could build a stable worldview. These commitments resist virtually any attempt at debunking, as abandoning them would represent a fundamental shift in how we see reality. In this paper, we ask whether LLMs hold anything akin to core commitments. Using systematic probes across five domains (science, history, geography, biology, and mathematics), we find that most LLMs fail to maintain a stable representation of reality. Though some recent models, tested under the identical protocol, showed improved stability on some key commitments, they still failed under pressure. These results document an improvement in argumentative skills across model generations but indicate that all current models fall short of human-level cognition.