Argument from ignorance is an informal fallacy where a claim is asserted as true or false solely because it lacks proof to the contrary. The fallacy occurs when one concludes a proposition is true because it hasn't been proven false, or vice versa. While generally considered fallacious, limited exceptions exist, such as in legal proceedings where the presumption of innocence applies.
A research paper proposes the Claim-Offence Theory, which argues that the burden of proof for a claim should scale with its cost to those it affects; the theory is tested on false accusations, public-health claims, and religious doctrines.
Thomas Hales discusses the importance of formal mathematical proofs verified by computer using theorem provers like Lean, which can exhaustively check proofs at the foundations of logic. Recent advances in autoformalization—using AI to automatically convert paper proofs into formal proofs—have made this process practical, with major milestones achieved in 2025–2026 including formalization of the prime number theorem and large portions of topology textbooks.