An ongoing project to formalise Gödel's incompleteness theorems using the theory of hereditarily finite sets in the Lean theorem prover. The work closely follows S. Swierczkowski's 'Finite Sets and ...

Exploring the possibilities of unfamiliar artefacts and perceptual technologies, the incompleteness theorem promises to distract and disorientate in the service of a feedback system of mirrors, lights ...

Philosophical change (Platonism): Mathematical truth transcends formal proof. We can recognize truth that our systems cannot prove. Reality contains truths beyond our deductive reach. This supports ...

Pick a formal system. Any formal system. Whatever your favourite formal system is, as long as it's capable of reasoning about elementary arithmetic. The First Spectral Gap Incompleteness Theorem of ...