Formalizing Paradoxes in Grounded Arithmetic using Isabelle/HOL

Ananthajit Srikanth and Bryan Ford Isabelle Workshop 2026 June 24–25, 2026 Lisbon, Portugal Abstract: Standard logical foundations in theorem proving constrain the set of recursive functions that are directly expressible to avoid inconsistencies. However, this prevents us from expressing all Turing-complete computations via direct recursive definitions. We consider Grounded Arithmetic, a reasoning…