4 papers
Idealizing Useful Fictions in Omega Grounded Arithmetic
Bryan Ford
Grounded arithmetic is a family of formal systems for reasoning about computation in which a statement may be asserted only when a terminating computation backs it; the logics are…
Internalized Truth in Reflective Grounded Arithmetic
Bryan Ford
By Tarski's undefinability theorem, no consistent classical formal system that includes arithmetic can define its own truth predicate. Reflective Grounded Arithmetic (RGA) is a pow…
Computable Quantification in Reflective Grounded Arithmetic
Bryan Ford
Informal statements of Gödel's incompleteness theorems often run: "no consistent formal system with arithmetic can be complete" - omitting the fact that the theorems as proved assu…
Reasoning Around Paradox with Grounded Deduction
Bryan Ford
How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic…